Aerodynamics and flight dynamics
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This document is a translation of a Russian text on the aerodynamics and flight dynamics of turbojet aircraft. It covers topics such as compressible flow, subsonic and supersonic air flow, shock waves, aerodynamic characteristics of wings and aircraft like lift and drag coefficients, effects of Mach number, high-speed flight characteristics, takeoff and climb performance, and horizontal flight forces. The translation was produced by NASA and is being provided for public use.
![98. Methods of Improving Takeoff C h a r a c t e r i s t i c s
As we analyzed above, t h e l e n g t h .of t h e t a k e o f f r u n depends on t h e
s e p a r a t i o n speed and a c c e l e r a t i o n d u r i n g t h e t a k e o f f run. I n t u r n , t h e
s e p a r a t i o n speed depends on t h e s p e c i f i c loading p e r 1 m2 o f wing a r e a and
C while t h e a c c e l e r a t i o n depends on t h e excess t h r u s t a v a i l a b l e .
Y sep’
A decrease i n s p e c i f i c loading on t h e wing i s t h e most e f f e c t i v e method
o f decreasing V and Ltor. However, t h i s always i n v o l v e s a d e c r e a s e i n
seP
t h e u s e f u l weight c a r r i e d , s i n c e with t h e s u r f a c e area of t h e wing c o n s t a n t ,
a decrease i n t a k e o f f weight can b e achieved only by d e c r e a s i n g t h e u s e f u l
load. A decrease i n t h e weight c a r r i e d i n a passenger a i r c r a f t means a
d e c r e a s e i n o p e r a t i o n a l economy. Therefore, t h i s means o f decreasing t h e
t a k e o f f run length i s used t o a l i m i t e d e x t e n t , p a r t i c u l a r l y s i n c e t h e
tendency t o u s e t h e maximum p o s s i b l e f l i g h t range r e q u i r e s an i n c r e a s e i n
s p e c i f i c loading on t h e wing.
The most a c c e p t a b l e method of d e c r e a s i n g t h e t a k e o f f run length i s an
i n c r e a s e i n t h e l i f t i n g f o r c e of t h e wing u s i n g t h e wing mechanisms.
A s w e know, t h e main means of mechanization o f t h e wing c o n s i s t s of t h e
f l a p s . A l l modern j e t passenger a i r c r a f t have extendable ( s l i d i n g ) s l i t
t y p e wing f l a p s 1 . The ef?�ectiveness o f t h e f l a p s (magnitude o f i n c r e a s e i n
A c ) i n c r e a s e s as t h e s l i d e (outward movement) of t h e f l a p s and angle o f
Y
f l a p d e f l e c t i o n a r e i n c r e a s e d . With low angles o f f l a p d e f l e c t i o n , t h e
l i f t i n g f o r c e i s p r i m a r i l y i n c r e a s e d without any e s s e n t i a l i n c r e a s e i n drag,
and t h e aerodynamic q u a l i t y i s decreased o n l y i n s i g n i f i c a n t l y . These angles
can be used f o r t a k e o f f d u r i n g high temperature c o n d i t i o n s , when t h e length
o f t h e t a k e o f f run can b e r e t a i n e d w i t h i n t h e r e q u i r e d l i m i t s i n s p i t e of
t h e decrease i n q u a l i t y . The lower drag during t h e t a k e o f f run allows a
considerable a c c e l e r a t i o n t o b e achieved.
Usually, attempts a r e made t o produce t h e maximum a i r c r a f t aerodynamic
q u a l i t y with t h e f l a p s d e f l e c t e d t o t h e t a k e o f f p o s i t i o n , s i n c e t h e q u a l i t y
determines t h e t h r u s t consumed and t h e excess t h r u s t which a c c e l e r a t e s t h e
a i r c r a f t during t h e t a k e o f f run. For a i r c r a f t with t a k e o f f weights of
55-80 and aerodynamic q u a l i t y o f 12-14, a t h r u s t o f consumption of 5000
6000 kg i s r e q u i r e d , and with a t o t a l a v a i l a b l e t h r u s t o f 13,000-28,000 kg,
t h e excess t h r u s t provides r a p i d (25-30 sec) a c c e l e r a t i o n of t h e a i r c r a f t t o /=
t h e s e p a r a t i o n speed; t h e t a k e o f f run l e n g t h i s 1000-1200 m .
Long experience of passenger a i r c r a f t o p e r a t i o n h a s proven t h e u s e f u l
ness of t h e method o f d e c r e a s i n g t a k e o f f run l e n g t h by i n c r e a s i n g t h e
a v a i l a b l e power ( g r e a t e r excess t h r u s t ) . The Boeing 727 a i r c r a f t c a r r i e s a
. .
I S M Yege r-, Proyektirovaniye Passazhirskikh Reaktivnikh SumoZetov
[Design of Passenger J e t A i r c r a f t ] , Mashinostroyeniye P r e s s , 1964.
100](https://image.slidesharecdn.com/aerodynamicsandflightdynamics-121121065124-phpapp01/85/Aerodynamics-and-flight-dynamics-109-320.jpg)
![Turbofan engines expand t h e p o s s i b i l i t y f o r u s i n g BLAC i n passenger j e t
a i r c r a f t , s i n c e t h e removal of c o n s i d e r a b l e masses of a i r from t h e o u t e r
channel does not d i s r u p t t h e o p e r a t i o n o f t h e engine.
The placement of a s l a t on t h e f r o n t edge of t h e wing and i n j e c t i o n o f
t h e boundary l a y e r a t t h e f l a p s and a i l e r o n s can produce a c o n s i d e r a b l e
decrease i n landing and t a k e o f f speeds and allow t h e l e n g t h of runways t o be
decreased by 30-40%. The placement of a s l a t on t h e wing o f a j e t a i r c r a f t ,
i n a d d i t i o n t o decreasing t a k e o f f and landing speeds, a l s o improves i t s
maneuverability a t high speeds, s i n c e i t d e l a y s t h e p o i n t o f flow s e p a r a t i o n
t o higher angles o f a t t a c k . P r a c t i c e has shown t h a t s l a t s can be used up t o
M = 0.9.
A laminar flow c o n t r o l system i s i n t h e s t a g e of development. I t has
been experimentally e s t a b l i s h e d t h a t t h e t r a n s i t i o n o f laminar flow t o
t u r b u l e n t flow can be prevented by sucking t h e slow, t u r b u l i z a t i o n - i n c l i n e d
boundary l a y e r away from t h e wing s u r f a c e through a l a r g e number of t h i n
s l o t s c u t i n t h e wing covering. This i s c a l l e d laminar flow c o n t r o l .
I n v e s t i g a t i o n s performed i n t h e USA' have shown t h a t t h i s method can.
i n c r e a s e t h e p r o f i l e d r a g c o e f f i c i e n t of a swept wing t o a v a l u e n e a r t h e
drag c o e f f i c i e n t of a p l a t e with laminar flow, i . e . , decrease i t by approx
imately s i x t i m e s .
Laminar flow c o n t r o l by sucking away t h e boundary l a y e r , n a t u r a l l y ,
i n c r e a s e s t h e load-carrying c a p a c i t y of t h e wing. However, t h e usage o f l f c
t o i n c r e a s e c alone i s not expedient, s i n c e t h i s problem can be more
Y
simply solved by i n j e c t i o n i n t o t h e boundary l a y e r . The production of high
aerodynamic q u a l i t y ( i n c r e a s e d by a f a c t o r of 1 . 5 times) b o t h during t a k e o f f
and during f l i g h t , allows t h e t a k e o f f and o t h e r c h a r a c t e r i s t i c s of t h e
a i r c r a f t t o be improved. C a l c u l a t i o n s have shown t h a t f o r an a i r c r a f t l i k e
t h e Lockheed C-141 with a t a k e o f f weight of about 120 t and a c r u i s i n g speed
o f 850 km/hr, laminar flow c o n t r o l can i n c r e a s e t h e f l i g h t range by 30-33%.
With t h i s f l i g h t range, t h e t a k e o f f weight of t h e a i r c r a f t can be decreased
by 18-20% by decreasing t h e f u e l r e s e r v e s c a r r i e d .
In conclusion f o r t h i s c h a p t e r , we n o t e t h a t an improvement of t a k e o f f
( a s well as landing) c h a r a c t e r i s t i c s of passenger j e t a i r c r a f t - - decreased
t a k e o f f run l e n g t h and s e p a r a t i o n speed -- makes i t p o s s i b l e t o expand t h e
network of a i r f i e l d s and connect a r e a and a d m i n i s t r a t i v e c e n t e r s . I t i s
always e a s i e r t o f i n d a r e a s f o r small a i r f i e l d s t h a n f o r l a r g e a i r f i e l d s . /111
-
B e t t e r t a k e o f f and landing c h a r a c t e r i s t i c s of a i r c r a f t w i l l a l s o provide a
lower "minimum weather" (see Chapter I X , S8).
A t t h e p r e s e n t time, c o n s i d e r a b l e a t t e n t i o n i s being turned t o t h e
c r e a t i o n of s p e c i a l passenger j e t a i r c r a f t with s h o r t t a k e o f f and landing
characteristics.
~ _ -_
S. M. Yeger , Proyektirovaniye Passazhirskikh Reaktivnykh ShoZetov
[Design of Passenger J e t A i r c r a f t ] , Mashinostroyeniye P r e s s , 1964.
104](https://image.slidesharecdn.com/aerodynamicsandflightdynamics-121121065124-phpapp01/85/Aerodynamics-and-flight-dynamics-113-320.jpg)
![If t h e wheel r o t a t e s without s l i p p i n g , t h e flywheel i n t h e automatic d e v i c e
r o t a t e s i n synchronism with t h e l a n d i n g wheel. I f t h e wheel begins t o s l i d e ,
t h e flywheel i n t r o d u c e s an a c c e l e r a t i o n and, working through a s p e c i a l d e v i c e ,
i n t e r r u p t s t h e supply o f p r e s s u r e t o t h e b r a k e , as a r e s u l t of which t h e
b r a k i n g f o r c e on t h e wheel i s decreased. A f t e r t h e r o t a t i n g speed of t h e
wheel i s i n c r e a s e d once more and synchronism i s e s t a b l i s h e d between r o t a t i o n
o f wheel and flywheel, t h e p r e s s u r e t o t h e brakes i s j n c r e a s e d t o t h e r e q u i r e d
l e v e l and t h e wheel i s once more braked. I n o p e r a t i o n , t h i s c y c l e i s u s u a l l y
r e p e a t e d q u i t e r a p i d l y and a c t u a l l y t h e p r e s s u r e i n t h e brakes never d e c r e a s e s
completely. Thus, t h i s d e v i c e p r o v i d e s optimal b r a k i n g , pumping a t t h e
boundary of s l i d i n g 1 . When t h i s d e v i c e i s t u r n e d on, t h e p i l o t immediately
provides f u l l p r e s s u r e i n t h e b r a k e s ( d e p r e s s e s b r a k e p e d a l s completely).
Smoothly d e p r e s s i n g t h e b r a k e s , a s i s recommended f o r nonautomatic
b r a k i n g , i n t h i s c a s e o n l y i n c r e a s e s t h e l e n g t h o f t h e l a n d i n g run, s i n c e t h e
maximum b r a k i n g regime will n o t be used.
The usage of automatic brakes has allowed t h e l e n g t h o f t h e l a n d i n g run /164
t o be decreased by an a d d i t i o n a l 20-25%.. The s e r v i c e l i f e o f t h e pneumatic
system h a s a l s o been i n c r e a s e d . The mean a c c e l e r a t i o n of automatic b r a k i n g i s
1 . 7 - 1 . 8 m/sec2 ( d i s k b r a k e s ) . In a i r c r a f t with s p o i l e r s opened a t t h e moment
of touchdown, t h e e f f e c t i v e n e s s of t h e brakes i s even g r e a t e r and
= 2.25-2.5 m/sec2. For example, i n an a i r c r a f t with s p o i l e r s
Jxmlr
( j m = 2.25 m/sec2) with a l a n d i n g speed o f 216 km/hr (60 m/sec), Llr = 800 m.
For t h e TU-104 a i r c r a f t (no s p o i l e r s ) with V = 240 km/hr (66.7 m/sec) w i t h
142
an average b r a k i n g a c c e l e r a t i o n of 1 . 3 m/sec2 (drum brake) t h e l a n d i n g run
l e n g t h i s 1700 m. For t h e TU-104 w i t h d i s k brakes (with an average a c c e l e r
a t i o n o f 1.55 m/sec2) t h e l a n d i n g run l e n g t h i s 1430 m .
Even g r e a t e r b r a k i n g a c c e l e r a t i o n (drag) can b e produced by r e l e a s i n g a
b r a k i n g p a r a c h u t e . For example, i f t h e p a r a c h u t e i s open a t 225-215 km/hr,
t h e drag i s i n c r e a s e d by 4600-4900 kg (TU-124 a i r c r a f t ) .
Figure 106a shows a diagram of t h e usage o f a braking p a r a c h u t e . A f t e r
touchdown, a b u t t o n i s p r e s s e d dropping t h e p a r a c h u t e from i t s c o n t a i n e r
through h a t c h 1. A f t e r t h i s , t h e p i l o t chute p u l l s t h e braking chute o u t ,
c r e a t i n g r e s i s t a n c e t o t h e movement of t h e a i r c r a f t . The p a r a c h u t e i s
connected t o t h e a i r c r a f t by c a b l e 3 through c a t c h 2 . A t t h e end of t h e r u n ,
t h e braking p a r a c h u t e s a r e disconnected. Braking p a r a c h u t e s 4 a r e
s t r i p t y p e , and t h e s t r e n g t h o f t h e l i n e s and canopy i s s u f f i c i e n t f o r run /165
-
speeds of 260-230 km/hr. In a s t r i p type parachute, the a i r p a r t i a l l y passes
through t h e canopy and t h e r e f o r e f o r t h i s t y p e o f chute Acx = 0.25-0.55 ( f o r
an o r d i n a r y p a r a c h u t e A c = 1 . 2 - 1 . 3 ) . For example, one f o r e i g n b r a k i n g
X
p a r a c h u t e with a canopy diameter of 9 . 7 6 m and A c = 0.55 c r e a t e s a b r a k i n g
X
A. V. C h e s t n o v , Letnaya Ekspzuatatsiya S h o Z e t a [ F l y i n g Operation of Air
c r a f t ] , Voyenizdat. P r e s s , 1962.
159
J](https://image.slidesharecdn.com/aerodynamicsandflightdynamics-121121065124-phpapp01/85/Aerodynamics-and-flight-dynamics-170-320.jpg)
![arrow) w i l l b e t h e same as a t s t a n d a r d c o n d i t i o n s , s i n c e w i t h a change i n a i r
d e n s i t y t h e v e l o c i t y i n d i c a t o r d e c r e a s e s t h e i n d i c a t e d speed due t o methodic
e r r o r . The f i n e n e e d l e o f t h e i n d i c a t o r shows t h e t r u e speed i n t h i s c a s e .
The i n f l u e n c e o f head winds and t a i l winds on t h e l e n g t h of t h e landing
r u n i s t h e same a s t h i s i n f l u e n c e on t h e l e n g t h of t h e t a k e o f f r u n .
The b r a k i n g e f f e c t i s always g r e a t e s t with t h e maximal speeds of
u t i l i z a t i o n of s p o i l e r s and p a r a c h u t e . Therefore, a d e l a y i n u s i n g t h e
s p o i l e r s of 1.5-2 s e c i n c r e a s e s t h e run l e n g t h by 100-150 m, w h i l e e j e c t i o n of
t h e p a r a c h u t e a t 180-140 km/hr decreases i t s b r a k i n g e f f e c t by 35-50%. The
wheel b r a k e s should be a p p l i e d immediately a f t e r t h e s p o i l e r s are extended,
i . e . , a t 250-220 km/hr.
56. S p e c i f i c Features of Landing R u n s on Dry, Ice o r Snow Covered Runways
A t t h e p r e s e n t t i m e we s t i l l do not have s u f f i c i e n t d a t a on methods of
determining t h e e f f e c t o f b r a k i n g on wet o r snow covered runways.
I n s p i t e of t h e v a r i e t y of means of b r a k i n g , t h e p r i n c i p a l means remains
t h e d i s k wheel b r a k e s . I t has been e s t a b l i s h e d t h a t when l a n d i n g on a d r y
c o n c r e t e runway, about 70% of t h e energy o f movement of t h e a i r c r a f t i s
absorbed by t h e b r a k e s , and 30% by aerodynamic d r a g of t h e a i r c r a f t (usage of
f l a p s and a i r b r a k e s ) . When landing on a wet runway, o n l y about 50% of t h e
k i n e t i c energy i s absorbed by t h e b r a k e s , o r i f t h e t i r e s a r e worn -- even
l e s s . The wheel b r a k e s have an important r o l e t o p l a y d u r i n g a landing run i f
f l i g h t i s t e r m i n a t e d a t speeds less t h a n t h e s e p a r a t i o n speed by 15-20%, i n
which t h e s p o i l e r s and landing p a r a c h u t e are less e f f e c t i v e . The p r e s s u r e i n
t h e t i r e s has a g r e a t i n f l u e n c e on t h e e f f e c t i v e n e s s of b r a k i n g : t h e l e s s t h e
p r e s s u r e , t h e g r e a t e r t h e c o n t a c t a r e a and t h e more r e l i z b l y t h e brakes
operate .
A t t h e p r e s e n t time, t h e runway l e n g t h r e q u i r e d f o r a i r c r a f t o p e r a t i o n i s
determined e i t h e r on t h e b a s i s of t h e c o n d i t i o n of t h e p r o v i s i o n of s a f e t y of
i n t e r r u p t e d o r extended t a k e o f f ( s e e Figure 7 1 ) , o r from t h e c o n d i t i o n s of t h e /169
c o n d i t i o n s of t h e landing c h a r a c t e r i s t i c s of t h e a i r c r a f t ( s e e Figure 1 0 3 ) .
These c h a r a c t e r i s t i c s a r e g e n e r a l l y c a l c u l a t e d f o r a d r y runway s u r f a c e .
However, a t most a i r p o r t s due t o c l i m a t i c c o n d i t i o n s o v e r one t h i r d of t h e
y e a r o r perhaps even. more t h e runway s u r f a c e s are m o i s t , snow covered o r
f r o z e n . S t a t i s t i c s show t h a t on t h e world s c a l e , one l a n d i n g of twelve i s
performed on a wet runway’.
’[Technical Information Department, S tAa tier T rcai n snpt ofrit c ResearchONTIs tGOSNIIf GAr
I
_____I_
.__
Zarubezhnyy Aviatransport , (Foreign
---
S e i
--
) No. 7,
In itute o
C i v i l A v i a t i o n ] , 1965.
164](https://image.slidesharecdn.com/aerodynamicsandflightdynamics-121121065124-phpapp01/85/Aerodynamics-and-flight-dynamics-175-320.jpg)
![c o e f f i c i e n t o r c o e f f i c i e n t of f r i c t i o n , equal t o t h e r a t i o o f t h e t a n g e n t i a l
b r a k i n g f o r c e t o t h e normal l o a d i n g on t h e wheel.
.q D i r e c t i o n of
movement
320
[I Wheelf f e c t i v e
ine
brakes
I
n
f
-0
a,
a,
C r i t i c a l speed f o r
a i r c r a f t i n question
/
Whee 1 brakes
effective
6M G i ven
a
m 0 1
I 1
2
I
3
1
4
Mdl
5 6 7 2
3
pressure i n t i r e s , k d c m
D
5 -
-
Figure 108. Formation of Hydrodynamic L i f t i n g Force A s
Wheels Roll Along W t Runway ( a ) and Aquaplaning S p e e d
e
A s a Function of P r e s s u r e and T i r e s ( b ) : 1-2, Hydro
dynamic l i f t and d r a g
O a c l e a n , d r y s u r f a c e , t h e coupling c o e f f i c i e n t o f t h e t i r e s i s q u i t e
n
high and, i f t h e r u b b e r does n o t melt o r burn due t o t h e h i g h temperature a t
t h e p o i n t o f c o n t a c t with t h e runway s u r f a c e , t h i s c o e f f i c i e n t may v a r y
between 0 . 7 and 0.8 depending on t h e t r e a d p r o f i l e (dry c o n c r e t e ) . As t h e
speed of t h e a i r c r a f t i s i n c r e a s e d , t h e c o e f f i c i e n t d e c r e a s e s by 2-3 t i m e s .
T h e r e f o r e , t h e mean v a l u e of coupling c o e f f i c i e n t f o r a d r y c o n c r e t e
runway i s 0.15-0.25; f o r a moist runway t h i s f i g u r e i s 0.1-0.21 and f o r a w e t /171
runway, about 0 . 2 l 1 . For an a s p h a l t runway (according t o t h e d a t a of t h e
S t a t e Planning I n s t i t u t e and t h e S c i e n t i f i c Research I n s t i t u t e f o r C i v i l
Aviation) 2 , t h e coupling c o e f f i c i e n t f o r a l l of t h e pavement c o n d i t i o n s
analyzed above is somewhat h i g h e r : from 0.33 t o 0.23; f o r snow covered cement
and a s p h a l t pavements i t i s 0.3-0.25. Therefore t h e c a l c u l a t e d l a n d i n g run
l e n g t h o f an a i r c r a f t on t h e s e pavements i s 15-20% l e s s .
When landing on an i c e covered runway, t h e e f f e c t i v e n e s s o f t h e b r a k e s i s
s h a r p l y decreased, by an average of 25-30% i n comparison w i t h a l a n d i n g on a
d r y , c o n c r e t e runway. Due t o t h i s , i t i s g e n e r a l l y recommended t h a t a b r a k i n g
p a r a c h u t e be used, t h a t one o r two engines be s h u t down, e t c . I t i s known
t h a t r a p i d dropping o f t h e f r o n t wheel o n t o t h e runway a f t e r touchdown c r e a t e s
t h e b e s t c o n d i t i o n s f o r b r a k i n g . However, as a r u l e , t h i s method i s most
s u i t a b l e f o r a d r y runway pavement, s i n c e on w e t pavement, f r o z e n o r
~~ ~ ~ ~-
~.. ~ ..
.. . . .~
~ - .- .. ~. ._ _ - .--__._ - .. .
. . - , .
Chestnov, A. V . , Letnaya EkspZuatatsiya S m o Z e t a [Flying Operation of t h e
A i r c r a f t ] , Voyenizdat. P r e s s , 1962.
GPI and NIIGA.
166](https://image.slidesharecdn.com/aerodynamicsandflightdynamics-121121065124-phpapp01/85/Aerodynamics-and-flight-dynamics-177-320.jpg)
![immediately a f t e r l a n d i n g i n o r d e r t o avoid zooming and t o m a i n t a i n t h e
d i r e c t i o n from t h e l a n d i n g run u s i n g t h e c o n t r o l wheel. The c o n t r o l s t i c k
should b e pushed forward t o t h e s t o p i n o r d e r t o b r i n g t h e nose wheel down t o
t h e pavement.
When l a n d i n g w i t h a s i d e wind, t h e l e n g t h o f t h e landing run i s i n c r e a s e d -
/173
by 10-15%. The maximum p e r m i s s i b l e v a l u e o f s i d e wind component (90" t o
runway a x i s ) i s 12-15 m/sec. I n case o f a l a r g e r o t a t i o n a l moment, t h e down
wind engine may b e switched o f f , t h e b r a k i n g p a r a c h u t e can b e r e l e a s e d , t h r u s t
r e v e r s a l and b r a k i n g can b e used..
58. T h e "Minimum" Weather f o r Landings and Takeoffs
The t a k e o f f - l a n d i n g c h a r a c t e r i s t i c s of an a i r c r a f t determine t h e
l i m i t i n g m e t e o r o l o g i c a l c o n d i t i o n s ("minimum weather") f o r which o p e r a t i o n of
t h e a i r c r a f t ( t a k e o f f and landing) can be p e r m i t t e d .
The c o n d i t i o n s i n c l u d e : a) minimum c e i l i n g ; b) minimum v i s i b i l i t y a t
runway l e v e l ; c) minimum l a t e r a l component o f wind speed Wz.
The minimum c e i l i n g determines t h e f l y i n g a l t i t u d e t o which t h e a i r c r a f t
should come down o u t o f t h e clouds and c l e a r v i s i b i l i t y of r e f e r e n c e p o i n t s on
t h e ground o r runway l i g h t s should be e s t a b l i s h e d . A t t h i s a l t i t u d e , t h e crew
can guide t h e a i r c r a f t down on t h e landing l i n e v i s u a l l y . For t u r b o j e t
a i r c r a f t landing a t a i r f i e l d s equipped w i t h IL S, w i t h a g l i d e p a t h angle o f
2" 40 min, t h e minimum cloud cover c e i l i n g i s 60-100 m.
The minimum v i s i b i l i t y i s considered t h e range a t which t h e crew o f an
a i r c r a f t begins t o s e e r e f e r e n c e p o i n t s on t h e ground and t h e beginning of t h e
runway during t h e daytime, o r landing l i g h t s and t h e i l l u m i n a t e d runway
s u r f a c e a t n i g h t . This range should be s u f f i c i e n t t o make it p o s s i b l e t o
c o r r e c t i n a c c u r a c i e s i n a i r c r a f t course and s e p a r a t i o n from runway a x i s . The
accuracy of guidance o f t h e a i r c r a f t r e l a t i v e t o t h e c e n t e r l i n e o f t h e
runway depends on t h e accuracy of o u t p u t of c o u r s e d a t a by on-board and ground
b a s e apparatus and t h e p r e c i s i o n of p i l o t i n g according t o t h e i n d i c a t o r on
board t h e a i r c r a f t . Experiments performed by GOSNII G A 1 have e s t a b l i s h e d t h a t
f o r passenger j e t a i r c r a f t t h e mean v a l u e of t o t a l d e v i a t i o n from t h e runway
a x i s i s 560 m. Coming down out of t h e clouds with t h i s amount of e r r o r , t h e
p i l o t must c o r r e c t t h e e r r o r with two s e q u e n t i a l t u r n s (Figure 1 1 1 ) . During
t h i s t i m e , t h e a i r c r a f t continues t o descend on t h e g l i d e p a t h , g e n e r a l l y
between 2" 40 min and 4" ( t h e h i g h e r v a l u e f o r a i r f i e l d s w i t h d i f f i c u l t
approaches). The time r e q u i r e d t o c o r r e c t l a t e r a l d e f l e c t i o n i s i n f l u e n c e d
c o n s i d e r a b l y by t h e i n e r t i a of t h e a i r c r a f t , i t s d e l a y (4-5 s e c ) t o movements
.
S M. Yeger Proyektirovaniye Passazhirskikh Rgaktivnykh Smnozetov [Design
of J e t Passenger A i r c r a f t ] Mashinostroyeniye P r e s s , 1964.
168](https://image.slidesharecdn.com/aerodynamicsandflightdynamics-121121065124-phpapp01/85/Aerodynamics-and-flight-dynamics-179-320.jpg)
![If Y i s expressed through t h e overload n = Y/G, t h e n
This formula shows t h e r e l a t i o n s h i p between overloading, which must be used t o
perform t h e h o r i z o n t a l t u r n and t h e banking a n g l e y (Figure 1 1 4 ) . As we can
y-
see from t h e graph, i n o r d e r t o perform a h o r i z o n t a l t u r n a t y = 6 0 " , we must
create n = 2.
Y
I n passenger a i r c r a f t , t h e bank angle i s
u s u a l l y s e t a t 2 0 - 3 0 ° , which a f f o r d s t h e
necessary maneuverab i 1i t y .
40
I
During an approach t o landing under i n s t r u
w 1 I
ment f l i g h t r u l e s , t h e bank cannot exceed 15'.
I .I
'f 2 3 4 5 -67 With most modern a i r c r a f t , h o r i z o n t a l t u r n s
a r e performed u s i n g t h e a i l e r o n s a l o n e , almost
Figure 114. Over- without u s i n g t h e r u d d e r , with t h e a i r c r a f t
load A s a F u n c t i o n " i t s e l f " s e l e c t i n g an a n g u l a r t u r n i n g r a t e s o
of Banking Angle t h a t t h e r e w i l l be no s l i p p a g e . This has become
p o s s i b l e due t o t h e high degree o f d i r e c t i o n a l
s t a b i l i t y , which g r e a t l y f a c i l i t a t e s maintenance
of s o - c a l l e d "coordination," i . e . , a combination o f o p e r a t i o n s o f t h e a i l e r o n s
and rudder f o r which t h e v e l o c i t y v e c t o r remains i n t h e p l a n e of symmetry of
t h e a i r c r a f t and no s l i p p i n g occurs1.
52. Cornering Parameters
Cornering parameters i n c l u d e t h e r a d i u s o f t h e h o r i z o n t a l t u r n , time of
t h e t u r n , angular v e l o c i t y of t h e t u r n , e t c .
The following formulas are known f o r t h e r a d i u s and time o f a h o r i z o n t a l
turn :
m a r S t a b i 1 i t y of t h e A i r c r a f t ," Letchiku
o Prakticheskoy Aerod?k"ke [ P r a c t i c a l Aerodynamics f o r t h e P i l o t ] ,
Voyenizdat. P r e s s , 1961.
174](https://image.slidesharecdn.com/aerodynamicsandflightdynamics-121121065124-phpapp01/85/Aerodynamics-and-flight-dynamics-185-320.jpg)
![When t h e angle o f a t t a c k i s changed, a d d i t i o n a l l i f t i n g f o r c e a r i s e s on
t h e wing, and ends on t h e h o r i z o n t a l t a i l s u r f a c e s , a p p l i e d t o t h e aero
dynamic c e n t e r s of t h e wing and h o r i z o n t a l t a i l s u r f a c e s (Figure 1 2 1 d ) . The
r e s u l t a n t of p a r a l l e l f o r c e s AYw and AYht i s a p p l i e d a t d i s t a n c e s i n v e r s e l y
p r o p o r t i o n a l t o t h e v a l u e s o f t h e s e f o r c e s . The p o i n t o f a p p l i c a t i o n o f t h i s
r e s u l t a n t i s c a l l e d t h e aerodynamic c e n t e r of t h e a i r c r a f t . W must n o t e h e r e
e
t h a t f o r a i r c r a f t o f known t y p e s , b o t h t h e h o r i z o n t a l t a i l s u r f a c e l i f t i n g
f o r c e and i t s increment AYht are d i r e c t e d downward, no matter what t h e angle
o f a t t a c k of t h e wing.
As w e can s e e from t h e
f i g u r e , t h e moment of
supplementary f o r c e s r e l a t i v e
t o t h e a i r c r a f t aerodynamic
c e n t e r i s zero; consequently,
t h e l o n g i t u d i n a l moment o f t h e
aircraft relative t o this
40 c e n t e r does n o t change when t h e
angle o f a t t a c k i s changed.
1
' F.t max r e a r 1 I'Stabi 1 i t y Reserve
T h e r e f o r e , t h e p o s i t i o n of t h e
a i r c r a f t aerodynamic c e n t e r
does n o t change when t h e angle
30
42 43 44
I , ,4 8 M
95
I ,7
4 46
of a t t a c k i s changed.
The aerodynamic c e n t e r of
Figure 122. Neutral Centering o f Air the a i r c r a f t is shifted t o the
c r a f t w i t h Respect t o Overloads As a r e a r under t h e i n f l u e n c e o f
Function of M Number (example): aerodynamic f o r c e increments
a , Maximal indicated speed 1 imita arising i n the stabilizer,
t i o n ; b , Minimum permissible f u s e l a g e and engine c e l l s . For
indicated s p e e d l i m i t a t i o n example, i f f o r t h e wing
without t h e h o r i z o n t a l t a i l
s u r f a c e ) X = 2 0 - 2 2 % mac, f o r
F
the aircraft xF = 46-50% mac.
If t h e loads on t h e a i r c r a f t a r e so d i s t r i b u t e d t h a t t h e c e n t e r of
g r a v i t y o f t h e a i r c r a f t corresponds with i t s aerodynamic c e n t e r , t h e a i r c r a f t
becomes n e u t r a l i n t h e l o n g i t u d i n a l r e s p e c t . I n t h i s c a s e , t h e c e n t e r i n g i s
c a l l e d n e u t r a l . Since i n t h i s c a s e t h e l o n g i t u d i n a l moment of t h e a i r c r a f t
w i l l n o t change as a f u n c t i o n of angle of a t t a c k , we must conclude t h a t
n e u t r a l c e n t e r i n g i s t h e aerodynamic c e n t e r of t h e e n t i r e a i r c r a f t 1 . N e u t r a l
a i r c r a f t c e n t e r i n g s are c a l c u l a t e d f o r v a r i o u s a l t i t u d e s and f l i g h t speeds
(Figure 122).
r-l-.V. Ostoslavskry, Aerodinamika SamoZeta [Aerodynamics o f t h e A i r c r a f t ] ,
Oborongiz. P r e s s , 1957.
187
I](https://image.slidesharecdn.com/aerodynamicsandflightdynamics-121121065124-phpapp01/85/Aerodynamics-and-flight-dynamics-198-320.jpg)
![.
8 max
gel mac considering deformation t h e balancing
/,////////, I , I , . . , ' / I/ / / L .,I'.I11111 / / / / / / / I / / / . I L deflection, further /205
1
i n c r e a s e i n t h e angle
min of a t t a c k does n o t
- -t4=@75 7
h
occur and t h e a i r c r a f t
_ _ _ M=a,S 2 :,/k g 1 i s balanced a t angle of
-4 : I
a t t a c k ct and w i l l
1
________---- --- r e t a i n t h i s angle2.
The behavior of an
a i r c r a f t i n t h i s curved
f l i g h t with n > 1 w i l l
Y
b e c h a r a c t e r i z e d by a
tendency t o i n c r e a s e
t h e p i t c h angle without
i n c r e a s i n g t h e angle of
attack.
In order t o return
Figure 133. Required Elevator Deflection As the aircraft t o its
a Function of c i n i t i a l f l i g h t regime,
Y t h e p i l o t s t i l l has t h e
e l e v a t o r r e s e r v e A6
s e p a r a t i n g t h e balancing e l e v a t o r d e f i e c t i o n from t h e maximal d e f l e c t i o n ,
corresponding t o complete d e f l e c t i o n downward ( t o t h e s t o p ) . T'ne f u r t h e r t h e
p i l o t moves t h e e1evato.r downward from t h i s balancing p o s i t i o n , t h e g r e a t e r
t h e angular v e l o c i t y with which t h e a i r c r a f t w i l l begin t o decrease t h e angle
of a t t a c k , i . e . , t h e more r a p i d l y t h e overload w i l l b e decreased t o u n i t y .
A p o s i t i o n should not a r i s e i n which t h e r e q u i r e d downward e l e v a t o r
d e f l e c t i o n t o r e s t o r e balancing is g r e a t e r than t h a t a v a i l a b l e , i n c l u d i n g
c o n s i d e r a t i o n of deformation of f o r c e t r a n s m i t t i n g hardware. Otherwise, it
w i l l be impossible t o balance t h e a i r c r a f t , and t h e p i l o t w i l l not be a b l e t o
r e t u r n i t t o t h e i n i t i a l f l i g h t regime.
Figure 133 shows t h a t with more forward c e n t e r i n g ( 2 5 % mac) t h e e l e v a t o r
r e s e r v e i s g r e a t e r , and t h e c o n t r o l l a b i l i t y i s b e t t e r . This r e s u l t s from t h e
f a c t t h a t with forward c e n t e r i n g i n t h e i n i t i a l balancing regime t h e e l e v a t o r
c o n t r o l s t i c k must b e h e l d c l o s e r t o t h e p i l o t than with rearward c e n t e r i n g
and, consequently, t h e e l e v a t o r r e s e r v e t o maximum d e f l e c t i o n i s i n c r e a s e d .
I t has been noted i n t h e p r o c e s s of f l i g h t t e s t s t h a t a f t e r an a i r c r a f t
i s put i n a high overload p o s i t i o n , s o a r i n g r e q u i r e s t h a t a p o s i t i v e p i t c h
moment be c r e a t e d by applying a f o r c e of 80-100 kg t o t h e s t i c k . This f o r c e ,
which e q u a l i z e s t h e aerodynamic load a c t i n g on t h e d e f l e c t e d e l e v a t o r , deforms
t h e f o r c e t r a n s m i t t i n g elements, s h o r t e n i n g them. A s a r e s u l t , f u l l forward
d e f l e c t i o n of t h e s t i c k d i d not r e s u l t i n f u l l d e f l e c t i o n o f t h e e l e v a t o r .
With maximum d e f l e c t i o n s o f t h e e l e v a t o r (29-31O) t h e a c t u a l angle of p o s i t i o n
M. V . Rozenblat, PiZoter o Peregrazke [To t h e P i l o t Concerning Overloading],
k r o f l o t Redizdat P r e s s , 1964.
201](https://image.slidesharecdn.com/aerodynamicsandflightdynamics-121121065124-phpapp01/85/Aerodynamics-and-flight-dynamics-212-320.jpg)
![112. Vertical G u s t s . P e r m i s s i b l e M Number i n Cruising F l i g h t
During f l i g h t through atmospheric t u r b u l e n c e , i n t e n s i v e and f r e q u e n t
v e r t i c a l g u s t s o f a i r r e s u l t i n l a r g e l o n g i t u d i n a l and l a t e r a l o s c i l l a t i o n s of
t h e a i r c r a f t . The a c c e l e r a t i o n s a r i s i n g i n t h i s case l e a d t o t h e appearance
o f i n e r t i a l f o r c e s c h a r a c t e r i z e d by overloads on t h e a i r c r a f t . A v e r t i c a l /207
g u s t i s a v e r t i c a l a i r movement r e s u l t i n g i n an i n c r e a s e i n overload i n n o t
over 2 sec.
The h o r i z o n t a l components of wind g u s t s have no e s s e n t i a l s i g n i f i c a n c e
f o r t h e movement o f t h e a i r c r a f t . For example, h o r i z o n t a l wind g u s t s up t o
6-15 m/sec cause s l i g h t v e l o c i t y p u l s a t i o n s i n modern a i r c r a f t f l y i n g between
200 and 250 m/sec, and c r e a t e s l i g h t o v e r l o a d s , whereas v e r t i c a l wind g u s t s a t
t h e s e speeds cause 10-15 times more overloading 3 .
Longitudinal overloading ( o r more a c c u r a t e l y an increment i n overloading)
a c t i n g i n t h e h o r i z o n t a l p l a n e can be determined according t o t h e following
formula :
An,=-, AV
gAf
where AV i s t h e change i n v e l o c i t y r e s u l t i n g from an oncoming g u s t ;
A t i s t h e time of a c t i o n of t h e g u s t .
Thus, i f a h o r i z o n t a l wind g u s t causes a v e l o c i t y v a r i a t i o n of 11 m/sec i n
two seconds, t h e increment t o t h e l o n g i t u d i n a l o v e r l o a d w i l l be
An X = 11/2-9.81 = 0.56; with a t i m e of a c t i o n o f t h r e e seconds, AnX = 0.37.
The s i g n of t h e o v e r l o a d w i l l depend on whether t h e g u s t i s a headwind o r
t a i l w i n d . I n t h e case of a headwind g u s t , t h e s i g n w i l l b e p l u s ( t h e crew and
passengers w i l l b e p r e s s e d a g a i n s t t h e backs of t h e i r s e a t s ) , and with a
t a i l w i n d g u s t t h e s i g n w i l l be minus ( t h e crew and passengers w i l l be p u l l e d
away from t h e backs of t h e i r s e a t s ) .
What must t h e v e l o c i t y of a v e r t i c a l g u s t be i n o r d e r f o r t h e a i r c r a f t t o
b e brought t o c o r t o t h e mode of i n v o l u n t a r y i n c r e a s e i n overload
Y SUP
("captureIf)? As we can s e e from Figure 135, a t M = 0 . 8 when a g u s t of W
i sup'
an a i r c r a f t with an i n i t i a l v a l u e of c w i l l reach c while t h e e f f e c t s
Y f
h Y SUP'
of a g u s t a t Wi capt w i l l cause it t o r e a c h c I n t h i s case, t h e
y capt'
b a l a n c i n g p o s i t i o n of t h e e l e v a t o r w i l l b e i n s u f f i c i e n t t o r e t u r n t h e a i r c r a f t
t o i t s i n i t i a l parameters.
I n o r d e r t o estimate t h e e f f e c t s of a v e r t i c a l a i r stream on t h e wings of /208
an a i r c r a f t , we must u s e t h e s o - c a l l e d v e l o c i t y o f t h e e f f e c t i v e g u s t . The
i n d i c a t o r e f f e c t i v e g u s t Wief d i f f e r s from t h e r e a l i n d i c a t o r g u s t (measured
under c o n c r e t e c o n d i t i o n s ) , s i n c e t h e r e are no s h a r p l y d i f f e r e n t i a t e d v e r t i c a l
jKu 1 ik M . M . , Obosnovmiye rekomendatsky o P i Z o t i r o v m i y u Sam0 Zetov p&
Poleta& v Zonakh Atmospernoy Turbulentnos% [Basis f o r Recommendat ions,
f o r P t l g t j n g Aircrzjft on F1 i i h t s i ~ nZones of Atmospheric Turbulence]
G Q s N I ( GA P r e s s , 1963.
203
I](https://image.slidesharecdn.com/aerodynamicsandflightdynamics-121121065124-phpapp01/85/Aerodynamics-and-flight-dynamics-214-320.jpg)
![515. Automatic A n g l e o f Attack and Overload Device
The automatic a n g l e o f a t t a c k and overload d e v i c e (AUAP) i s used t o warn
t h e p i l o t t h a t t h e a i r c r a f t i s f l y i n g a t l a r g e a n g l e s of a t t a c k as t h e minimum
v e l o c i t y i s approached and d u r i n g f l i g h t s i n bumpy a i r .
During f l i g h t s u s i n g t h i s d e v i c e , t h e i n s t a n t a n e o u s angle o f a t t a c k a t
which t h e a i r c r a f t i s f l y i n g and t h e v e r t i c a l overload are determined. Also,
a t each moment i n time t h e v a l u e of t h e c r i t i c a l a n g l e o f a t t a c k i s determined /*
a s a f u n c t i o n of t h e M number of f l i g h t .
The d e v i c e c o n s i s t s of a number o f a g g r e g a t e s . The main u n i t s a r e :
1) t h e angle o f a t t a c k measuring d e v i c e , which measures t h e l o c a l angles of
a t t a c k i n c o n j u n c t i o n with t h e wind vane on t h e f u s e l a g e ; 2) t h e c r i t i c a l
angle measuring d e v i c e which o u t p u t s t h e r e q u i r e d v o l t a g e a s a f u n c t i o n o f t h e
M number of t h e f l i g h t ; 3) t h e overload t r a n s d u c e r , i n s t a l l e d i n t h e a r e a of
t h e c e n t e r o f g r a v i t y of t h e a i r c r a f t ; 4) an i n d i c a t o r d e v i c e on t h e i n s t r u
ment p a n e l i n f r o n t o f t h e p i l o t . Using t h i s d e v i c e , t h e p i l o t can observe
t h e c u r r e n t angles of a t t a c k a t which he i s f l y i n g , t h e c r i t i c a l a n g l e of
a t t a c k (more p r e c i s e l y , t h e angle of a t t a c k a t which t h e automatic d e v i c e
o p e r a t e s under t h e given c o n d i t i o n s ) and t h e v e r t i c a l overload.
When t h e a i r c r a f t e n t e r s a c r i t i c a l regime ( t h e o p e r a t i n g regime, which
i s somewhat less t h a n t h e p e r m i s s i b l e ) t h e lower s e c t o r o f t h e movable
c r i t i c a l angle o f a t t a c k s e c t o r on t h i s instrument corresponds with t h e arrow
i n d i c a t i n g t h e i n s t a n t a n e o u s angle of a t t a c k ( F i g u r e 1 4 0 ) . A t t h i s moment, a 1217
lamp with t h e i n s c r i p t i o n "ac: l i g h t s up i n f r o n t o f t h e c o p i l o t . Also, i f
t h e a i r c r a f t undergoes overlo-ads g r e a t e r t h a n t h o s e p e r m i s s i b l e t h e arrow
i n d i c a t i n g i n s t a n t a n e o u s overload approaches t h e s e c t o r of dangerous overloads
and t h e ].amp with t h e i n s c r i p t i o n 'In '' l i g h t s up.
Y SUP
When e i t h e r of t h e s e lamps l i g h t s up, t h e " a t t e n t i o n " lamp on t h e d i s p l a y
begins t o f l a s h .
Adjustment of t h i s d e v i c e i s performed i n d i v i d u a l l y f o r o p e r a t i o n i n
f l i g h t with a l l f l a p s and g e a r up and f o r f l i g h t with f l a p s down f o r t a k e o f f
and f o r l a n d i n g . For example, i n t h e o r d i n a r y f l y i n g mode ( f l a p s u p ) , t h e aCr
warning l i g h t s up when a n g l e s o f a t t a c k of 1 . 4 - 2 " less t h a n t h e p e r m i s s i b l e
angles a r e reached. These parameters a r e shown f o r one a i r c r a f t equipped with
t h e AUAP d e v i c e i n Table 13.
W can see from Figure 140 t h a t t h e a n g l e o f a t t a c k r e s e r v e up t o t h e
e
moment o f o p e r a t i o n i s 1.8-3.2" (M = 0.7-0.82). For example, f o r M = 0 . 8 , t h e
r e s e r v e from c1 = 3" t o c1 = 5 . 2 " i s 2 . 2 " , and t h e r e s e r v e t o c i s 4".
hf OP Y SUP
I n o r d e r t o achieve c = 0 . 7 i n f l i g h t a t M = 0.8, we must c r e a t e an
Y SUP
overload n = 0 . 7 / 0 . 2 7 5 = 2 . 5 2 . However, a t cx = 5.2" (c = 0.53), i . e . , a t
Y OP Y
overload n = 0.53/0.275 = 1.93, t h e "n '' l i g h t comes on. The p i l o t ' s
Y Y SUP
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![I'
(12-16 m/sec) i n 3-5 min. The same t h i n g occurs d u r i n g t h e d e s c e n t . The
g r e a t e s t p o s s i b i l i t y o f i c i n g o c c u r s d u r i n g c i r c l i n g f l i g h t i n t h e a r e a of an
a i r f i e l d , a t which time t h e a i r c r a f t f l i e s a t 350-380 km/hr, spending
10-12 min i n t h e approach t o landing.
When f l y i n g a t very high speeds, t h e s u r f a c e o f t h e a i r c r a f t i s heated; /242
which p r e v e n t s i c i n g t o some e x t e n t . The s u r f a c e of t h e wing i s p a r t i c u l a r l y
h e a t e d , s i n c e h e a t is l i b e r a t e d due t o i n t e r n a l f r i c t i o n i n t h e boundary l a y e r
and t h e temperature of t h e l e a d i n g edge o f t h e wing i s i n c r e a s e d . There i s a
p o i n t along t h e p r o f i l e of t h e wing where t h e flow i s completely d e c e l e r a t e d ,
which i s accompanied by an i n c r e a s e i n temperature AT o f t h e a i r i n r e l a t i o n
t o t h e temperature of t h e surrounding a i r . This temperature i n c r e a s e depends
on t h e f l i g h t speed and can be c a l c u l a t e d u s i n g t h e formula
V2
AT=--
2000 '
where speed V i s t a k e n i n m/sec.
The v a l u e s of temperature i n c r e a s e f o r v a r i o u s f l i g h t speeds a r e shown i n
Table 14.
T A B L E 14
However, during i c i n g of an a i r c r a f t t h e a c t u a l i n c r e a s e i s 30-50% l e s s .
This r e s u l t s from t h e f a c t t h a t t h e water d r o p l e t s which d e p o s i t on t h e
s u r f a c e of t h e a i r c r a f t w i l l be p a r t i a l l y o'r completely evaporated and
t h e r e f o r e w i l l d e c r e a s e t h e temperature of t h e s u r f a c e . A l s o , h e a t exchange
occurs i n t h e boundary s u r f a c e , a l s o reducing t h e temperature.
52. Types and Forms o f Ice Deposition. I n t e n s i t y of Icing
The forms of a i r c r a f t i c i n g a r e v a r i o u s and depend p r i m a r i l y on t h e
e x t e n t of s u p e r c o o l i n g o f t h e d r o p l e t s i n t h e clouds. The following t y p e s o f
ice are differentiatedl :
I20. K. Trunov, ObZedeneniye SamoZetov i Sredstva B o r ' b y s N i m i [ I c i n g o f
A i r c r a f t and Methods o f I t s C o n t r o l ] , Mashinostroyeniye P r e s s , 1965.
237](https://image.slidesharecdn.com/aerodynamicsandflightdynamics-121121065124-phpapp01/85/Aerodynamics-and-flight-dynamics-248-320.jpg)
Aerodynamics and flight dynamics
- 1. N A S A T E C H N I C A L - N A S A T T F-542 - T R A N S L A T I O N c?, 1 LOAN COPY: RETURN TO AFWL [WLOL-2) KtRTtANO AFB, N MU( AERODYNAMICS A N D FLIGHT DYNAMICS OF TURBOJET AIRCRAFT Tramport Press, Moscozc; 1967 N A T I O N A L A E R O N A U T I C S A N D SPACE A D M I N I S T R A T I O N W A S H I N G T O N , D. C. SEPTEMBER 1969
- 2. TECH LIBRARY KAFB, NM IllllllllslllllllllllllI AERODYNAMICS AND FLIGHT DYNAMICS OF TURBOJET AIRCRAFT By T. I. Ligum Translation of "Aerodinamika i Dinamika Poleta Turboreaktivnykh Samoletov" Transport Press, Moscow, 1967 NATIONAL AERONAUTICS AND SPACE ADMlN ISTRATION For sale by the Clearinghouse for Federal Scientific and Technical Information Springfield, Virginia 22151- CFSTl price $3.00
- 4. Table o f Contents Introduction . vi Chapter 1 . The P h y s i c a l Basis o f High-speed Aerodynamics . 1 5 1 . V a r i a t i o n s i n t h e Parameters o f A i r w i t h A l t i t u d e . The Standard Atmosphere . 1 52. C o m p r e s s i b i l i t y o f A i r . 5 53. The Propagation o f Small Disturbences i n A i r Sound and Sound Waves . 5 54. The Speed o f Sound as a C r i t e r i o n f o r t h e C o m p r e s s i b i l i t y o f Gases . 7 55. The Mach Number and i t s Value i n F l i g h t Problems . 8 56. F l i g h t Speed. C o r r e c t i o n s t o Instrument Readings N e c e s s i t a t e d . by C o m p r e s s i b i l i t y 9 §7. The Character o f t h e Propagation o f Minor P e r t u r b a t i o n s . i n F l i g h t a t Various A l t i t u d e s 11 58. Trans- o r Supersonic Flow. o f A i r Around Bodies . 14 59. Sonic "boom". 15 510. Features o f t h e Formation o f Compression Shock During Flow Around Various Shapes o f Bodies. 18 911. C r i t i c a l Mach Number. The E f f e c t o f C o m p r e s s i b i l i t y on t h e Motion o f A i r F l y i n g Around a Wing . 20 912. The Dependence o f t h e Speed o f t h e Gas Flow on t h e Shape o f t h e Channel. The Lava1 Nozzle . 22 §13. Laminar and T u r b u l e n t Flow o f A i r . 22 514. Pressure D i s t r i b u t i o n a t Sub- and S u p e r c r i t i c a l Mach Numbers 24 Chapter I I . Aerodynamic C h a r a c t e r i s t i c s o f t h e Wing and A i r c r a f t . . The E f f e c t o f A i r C o m p r e s s i b i l i t y 27 5 1 . The Dependence o f t h e C o e f f i c i e n t c on t h e Angle o f A t t a c k . 27 Y 92. The E f f e c t o f t h e Mach Number on t h e Behavior o f t h e Dependence c = f(a) Y . 30 93. The P e r m i s s i b l e C o e f f i c i e n t c p e r and i t s Dependence on t h e Mach Number . Y 31 54. Dependence o f t h e C o e f f i c i e n t c on t h e Mach Number f o r F l i g h t Y a t a Constant Angle o f A t t a c k . 32 55. The A f f e c t o f t h e Mach Number o f t h e C o e f f i c i e n t cx . 33 56. Wing Wave Drag . 36 57. I n t e r f e r e n c e . 38 58. The A i r c r a f t P o l a r . The E f f e c t o f t h e Landing Gear and Wing Mechanization on t h e P o l a r . 59. The A f f e c t o f t h e Mach Number on t h e A i r c r a f t P o l a r . Chapter I l l . Some Features o f Wing C o n s t r u c t i o n . 43 §I. Means o f I n c r e a s i n g t h e C r i t i c a l Mach Number . 43 iii
- 5. 52. Features o f Flow Around Swept Wings . . 49 53, Wing C o n s t r u c t i o n i n T u r b o j e t Passenger A i r ' c r a f t . * 53 54. Drag Propagation Between Separate P a r t s o f A i r c r a f t . 59 Chapter I V . C h a r a c t e r i s t i c s o f t h e Power System . . 61 51. T w o - C i r c u i t and Turbofan Engines . . 61 52. Basic C h a r a c t e r i s t i c s o f T u r b o j e t Engines . . 66 53. T h r o t t l e C h a r a c t e r i s t i c s . 67 §4. High-speed C h a r a c t e r i s t i c s . . 69 §5. H i g h - A l t i t u d e C h a r a c t e r i s t i c s . . 71 56. The E f f e c t o f A i r Temperature on T u r b o j e t Engine T h r u s t . . 72 S7. T h r u s t Horsepower . . 73 98. P o s i t i o n i n g t h e Engines on t h e A i r c r a f t . . 74 Chapter V . Takeoff. . 81 51. Taxiing . . 81 92. Stages o f T a k o f f . . 81 53. Forces A c t i n g on t h e A i r c r a f t D u r i n g t h e T a k e o f f Run and Takeoff 84 54. Length o f Takeoff Run. L i f t - o f f Speed. . 87 55. Methods o f Takeoff. . 88 56. F a i l u r e o f Engine During T a k e o f f . . 90 §7. I n f l u e n c e o f Various F a c t o r s on T a k o f f Run Length . . 98 58. Methods o f Improving Takeoff C h a r a c t e r i s t i c s . . 100 Chapter V I . Climbing . . 105 51. Forces A c t i n g on A i r c r a f t . . 105 §2. D e t e r m i n a t i o n o f Yost S u i t a b l e C l i m b i n g Speed . . 107 53. V e l o c i t y Regime o f Climb . . 110 94. Noise Reduction Methods. . 111 S5. Climbing w i t h One Motor Not Operating . . 115 Chapter VI I . H o r i z o n t a l F1 i g h t . . 116 51. Diagram o f Forces A c t i n g on A i r c r a f t . . 116 52. Required T h r u s t f o r H o r i z o n t a l F l i g h t . . 117 53. Two H o r i z o n t a l F l i g h t Regimes . . 120 54. I n f l u e n c e o f E x t e r n a l A i r Temperature on Required T h r u s t . . 121 55. Most Favorable H o r i z o n t a l F1 i g h t Regimes. I n f l u e n c e o f A1 t i tude and Speed . . 123 $6. D e f i n i t i o n o f Required Q u a n t i t y o f Fuel . . 129 57. F1 i g h t a t the " C e i l ings" . 131 58. P e r m i s s i b l e F l y i n g A l t i t u d e s . I n f l u e n c e o f A i r c r a f t Weight . 133 59. ' Engine F a i l u r e During H o r i z o n t a l F1 i g h t . . 134 510. Minimum P e r m i s s i b l e H o r i z o n t a l F l i g h t Speed. . 136 Chapter VIII. Descent . 138 5 1 . General Statements. Forces A c t i n g on A i r c r a f t During Descent . . 138 52. Most Favorable Descent Regimes . * 139 53. P r o v i s i o n o f Normal C o n d i t i o n s i n Cabin During High A l t i t u d e F l y i n g . . 140
- 6. 54. Emergency Descent . . 144 Chapter I X . T h e Landing . . 150 51. Diagrams of Landing Approach . . 150 52. Flight After Entry into Glide Path. Selection of Gliding Speed . . 151 53. Stages in the Landing . . 154 54. Length of Post-landing Run and Methods of Shortening it . . 158 55. Length of Landing Run As a Function of Various Operational Factors . . 163 56. Specific Features of Landing Runs o n Dry, Ice o r Snow Covered Runways . . 164 57. Landing with Side Wind . 167 58. T h e "Minimum" Weather for Landings and Takeoffs . 168 59. Moving into a Second Circle . 171' Chapter X. Cornering . . 173 5 1 . Diagram of Forces Operating During Cornering . . 173 52. Cornering Parameters . . 174 Chapter X I . Stability and Controlability of Aircraft . 177 5 1 . General Concepts o n Aircraft Equilibrium . . 177 52. Static and Dynamic Stability . . 178 53. Controllability of an Ai rcraft . . 11 8 54. Centering of the A rcraft and Mean Aerodynamic Chord . 184 55. Aerodynamic Center of Wing and Aircraft. Neutral Center i ng . 185 56. Longitudinal Equil brium . . 188 57. Static Longitudina Overload Stabi 1 i ty . . 190 58. Diagrams o f Moments . . 194 59. Static Longitudinal Velocity Stability . . 195 510. Longitudinal Control labi 1 i ty . . 197 5 1 1 . Construction of Balancing Curve for Deflection of Elevator . . 199 512. Vertical Gusts. Permissible M Number in Cruising F1 ight , . 203 513. Permissible Overloads During a Vertical Maneuver . 205 514. Behavior of Aircraft a t Large Angles of Attack . . 206 515. Automatic Angle of Attack and Overload Device . . 212 516. Lateral Stability . . 213 517. Transverse Static Stabi 1 i ty . 214 518. Directional Static Stabi 1 ity . . 216 519. Lateral Dynamic Stabi 1 i ty . . 2i6 520. Yaw Damper . . 218 521. Transverse Control 1 ab i 1 i ty . . 223 522. Directional Controllability. Reverse Reaction for Banking . . 225 923. Involuntary Banking ('lValezhka'l) . 229 V
- 7. 124. I n f l u e n c e o f C o m p r e s s i b i l i t y o f A i r on C o n t r o l Surface E f f e c t i v e n e s s . . 230 525. Methods o f Decreasing Forces on A i r c r a f t C o n t r o l Levers . . 231 526. Balancing o f t h e A i r c r a f t During T a k e o f f and Landing . 233 Chapter X I I. I n f l u e n c e o f I c i n g on F l y i n g C h a r a c t e r f s t i c s . 236 §l. General Statements . . 236 52. Types and Forms o f I c e Deposi t i o n . In t e n s i t y o f Icing . . 237 S3. I n f l u e n c e o f I c i n g on S t a b i l i t y and C o n t r o l l a b i l i t y o f A i r c r a f t i n P r e - l a n d i n g Guide Regime . . 239 vi
- 8. I NTRODUCTI ON Jet-powered passenger a i r c r a f t have been adopted and introduced i n t o g e n e r a l use i n c i v i l a v i a t i o n . - / 3* The f i r s t t u r b o j e t passenger a i r c r a f t b u i l t i n t h e S o v i e t Union w a s t h e Tu-104, and t h e first f o r e i g n t u r b o j e t s were t h e De Havilland Comet, t h e Sud Aviation Caravelle, t h e Boeing-707, t h e Douglas DC-8, t h e Convair 880 and o t h e r s . These a i r c r a f t have been given t h e name f i r s t - g e n e r a t i o n t u r b o j e t aircraft. In b u i l d i n g t h e first t u r b o j e t passenger a i r c r a f t , t h e designers attempted t o achieve long f l i g h t range and t o p e r f e c t t h e high-speed p r o p e r t i e s of t h e a i r c r a f t , thereby compensating f o r t h e heavy f u e l consumption r e q u i r e d by t h e j e t engines. The d e s i r e t o c r e a t e new a i r c r a f t capable o f competing w i t h t h e o l d passenger a i r c r a f t which were equipped with highly economic p i s t o n engines l e d t o a maximum i n c r e a s e i n t h e l i f t i n g c a p a c i t y , and f l i g h t d i s t a n c e and speed. The r e a l i z a t i o n of t h e s e q u a l i t i e s became p o s s i b l e only because of t h e appearance of j e t engines. Experience i n using a i r c r a f t has shown t h a t t u r b o j e t passenger a i r c r a f t may be economic n o t only i n terms of long-range f l i g h t , b u t f o r medium- and even s h o r t - r a n g e f l i g h t as w e l l . As a r e s u l t , second-generation t u r b o j e t passenger a i r c r a f t have appeared: i n t h e S o v i e t Union t h e r e a r e t h e Tu-124, t h e Tu-134 and t h e Yak-40, w h i l e abroad t h e r e are- t h e D e Havilland-121 "Tridentf1, t h e Bak-1-11, t h e Boeing-727, t h e DC-9'and o t h e r s . These air c r a f t a r e s u b s t a n t i a l l y s m a l l e r i n dimensions and intended f o r u s e on s h o r t - range n e t s . The high power and low u n i t load on t h e wing permit f l i g h t s from a i r f i e l d s having r e l a t i v e l y s h o r t take-off and landing runways. Turbojet engines surpass p i s t o n engines i n r e l i a b i l i t y . With t h e i r s h o r t time i n s e r i e s production and u s e , s e r v i c e p e r i o d s o f 2,000 - 3,000 hours between maintenance checks have been e s t a b l i s h e d . This i s an important f a c t i n i n c r e a s i n g t h e economy of using t u r b o j e t a i r c r a f t , because t h e c o s t of t h e s e engines s u b s t a n t i a l l y exceeds t h a t of p i s t o n engines. In t h e Five Year Plan f o r t h e development of t h e Russian economy from 1966 t o 1970, t h e f u r t h e r development of c i v i l a v i a t i o n is a n t i c i p a t e d and t h e volume o f a i r /4 t r a v e l should i n c r e a s e by a f a c t o r o f 1.8. N w passenger a i r c r a f t a r e going e i n t o service i n the a i r l i n e s . Turbojet passenger a i r c r a f t have f l i g h t c h a r a c t e r i s t i c s which d i f f e r from t h o s e of a i r c r a f t with p i s t o n and turboprop engines i n s e v e r a l r e s p e c t s . These f l i g h t f e a t u r e s r e s u l t from t h e unique high-speed and h i g h - a l t i t u d e c h a r a c t e r i s t i c s of t h e engines, as w e l l as t h e f l i g h t c o n d i t i o n s a t t h e s e high speeds and a l t i t u d e s . - .. * Numbers i n t h e margin i n d i c a t e pagination i n t h e f o r e i g n t e x t . vii
- 9. With t h e appearance o f j e t a v i a t i o n , t h e r e has been a r e s u l t a n t i n c r e a s e i n t h e importance of h i g h - v e l o c i t y aerodynamics, i . e . , t h e motion o f bodies i n air viewed i n terms of t h e e f f e c t of i t s c o m p r e s s i b i l i t y , i . e . , t h e p r o p e r t i e s t o change d e n s i t y with a change i n p r e s s u r e . . 'The f i r s t t o i n d i c a t e the n e c e s s i t y of e s t i m a t i n g t h e e f f e c t of air c o m p r e s s i b i l i t y w a s t h e Russian s c i e n t i s t S.A. Chaplygin, i n h i s work "On G a s Flows" published i n 1902. I t was he who developed a method f o r t h e t h e o r e t i c a l s o l u t i o n of problems of t h e motion of gas with allowance made f o r i t s c o m p r e s s i b i l i t y . The S o v i e t s c i e n t i s t s Academicians S.A. Khristianovich, M.V. Keldysh, A.A. Dorodnitsyn, Professors V.S. Pyshnov, F . I . Frankl' , I . V . Ostoslavskiy, B.T. Goroshchenko, Ya.M. S e r e b r i y s k i y , A.P. Mel'nikov and o t h e r s , through t h e i r s t u d i e s i n t h e f i e l d of h i g h - v e l o c i t y aerodynamics , c o n t r i b u t e d much which w a s of g r e a t value i n t h e design of high-speed a i r c r a f t . The S o v i e t turbo j e t passenger a i r c r a f t c r e a t e d by a e r o n a u t i c a l engineers A.N. Tupolev, S.V. I l u s h i n and A.S. Yakovlev, take t h e i r p l a c e s i n t h e ranks o f t h e f i r s t - c l a s s aircraft. The s u c c e s s f u l use of new a v i a t i o n technology by*f l i g h t and engineering personnel i s unthinkable without a deep understanding of t h e laws of aero dynamics . A i r c r a f t aerodynamics, when thought of i n terms of t h e f l i g h t crew, i s u s u a l l y c a l l e d p r a c t i c a l aerodynamics. The number of problems involved i n aerodynamics i s q u i t e s u b s t a n t i a l . These i n c l u d e s t u d y i n g t h e laws of t h e motion of a i r and t h e i n t e r a c t i o n of a i r flows with bodies moving i n them, t h e i n t e r a c t i o n of shock waves with various p a r t s o f t h e a i r c r a f t , a i r c r a f t f l i g h t dynamics as a f f e c t e d by t h e f o r c e s a p p l i e d t o t h e a i r c r a f t (including aerodynamic f o r c e s ) , and a i r c r a f t s t a b i l i t y and handiness. I t i s t h e o b j e c t of t h i s book t o examine t h e s e q u e s t i o n s i n terms of turbo j e t pas s enger a i r c r a f t . viii
- 10. NASA TT F-542 CHAPTER 1 THE PHYSICAL BASIS OF HIGH-SPEED AERODYNAMICS ABSTRACT. T h i s book p r e s e n t s t h e physical bases of h i g h - s p e e d aerodynamics, and t h e influence of a i r c o m p r e s s i b i l i t y on t h e aerodynamic c h a r a c t e r i s t i c s of w i n g s and a i r c r a f t . Primary a t t e n t i o n is turned t o passenger j e t s . T h e following a r e a s a r e covered: takeoff c h a r a c t e r i s t i c s of j e t s and methods o f Improving them; b e s t c l i m b i n g modes; h o r i z o n t a l f l l g h t ; t h e d e s c e n t ; t h e landing approach; t u r n s and c o r n e r s ; c o n t r o l l a b i l i t y and s t a b i l i t y ; icing and i t s influence on f l y i n g c h a r a c t e r i s t i c s ; and t h e c h a r a c t e r i s t i c s o f modern j e t e n g i nes . 5 1 . Variations i n the Parameters of Air w i t h A l t i t u d e . T h e Standard Atmosphere The f l i g h t of a i r c r a f t , l i k e t h a t o f o t h e r f l i g h t v e h i c l e s , i s a f f e c t e d by t h e condition of t h e atmosphere -- t h e s h e l l of a i r surrounding t h e e a r t h . - /5 Therefore, i t i s q u i t e v i t a l t o know the processes occurring i n t h e abnos phere. Only the atmosphere's lower boundary, t h e e a r t h ' s s u r f a c e i t s e l f , i s c l e a r l y d e l i n e a t e d . The upper atmosphere i s more d i f f i c u l t t o e s t a b l i s h because t h e d e n s i t y o f air decreases c o n s t a n t l y with a l t i t u d e and even a t an a l t i t u d e o f .lo0 km i t measures approximately one m i l l i o n t h t h a t on t h e e a r t h ' s s u r f a c e . Normally, t h e upper l i m i t of t h e atmosphere i s considered t h e a l t i t u d e a t which t h e air d e n s i t y approaches t h a t of the gases f i l l i n g i n t e r p l a n e t a r y space. Data from d i r e c t and i n d i r e c t observations show t h a t t h e atmosphere has a layered s t r u c t u r e . In 1951 t h e I n t e r n a t i o n a l Geodesic and Geophysical Union adopted t h e d i v i s i o n of t h e atmosphere i n t o f i v e b a s i c spheres o r l a y e r s : t h e troposphere, t h e s t r a t o s p h e r e , t h e mesosphere, t h e thermosphere and t h e exosphere. The Troposphere is t h e lcwest l a y e r of t h e atmosphere, which i n t h e middle l a t i t u d e s extends t o an a l t i t u d e o f 10-12 km, i n t h e t r o p i c s -- t o an a l t i t u d e o f 16-18 km, and i n t h e p o l a r regions -- t o an a l t i t u d e o f 8-10 k . This m l a y e r i s o f tremendous p r a c t i c a l i n t e r e s t i n a v i a t i o n , because a l l t h e most important phenomena encountered by t h e p i l o t occur b a s i c a l l y i n t h e tropo sphere. I t i s h e r e t h a t t h e formation of clouds and f o g s , t h e f a l l o f p r e c i p i t a t i o n , and t h e development of storms occur.
- 11. The most s i g n i f i c a n t f e a t u r e of t h e troposphere i s t h e decrease i n temperature with a r i s e i n a l t i t u d e (averaging 6.5" p e r km of a l t i t u d e ) . The troposphere i s t h e area of thermal turbulence r e s u l t i n g from t h e unequal h e a t i n g o f l a y e r s o f air a t t h e e a r t h ' s s u r f a c e and a t v a r i o u s a l t i t u d e s , as w e l l as t h e dynamic turbulence r e s u l t i n g from t h e f r i c t i o n o f t h e air w i t h t h e e a r t h ' s s u r f a c e and i t s i n t e n s e v e r t i c a l displacement a t t h e boundaries - /5 between cold and warm a i r masses of atmospheric f r o n t s . The troposphere ends i n t h e l a y e r of t h e tropopause. The t h i c k n e s s of t h e tropopause f l u c t u a t e s from a f e w hundred meters t o s e v e r a l kilometers. I t i s u s u a l l y a continuous l a y e r which surrounds t h e e a r t h ' s sphere i t s e l f , while i t s a l t i t u d e and temperature are f u n c t i o n s of t h e geographic l a t i t u d e , t h e time o f y e a r and t h e atmospheric processes developing. Over t h e e q u a t o r and i t s neighboring a r e a s , t h e tropopause i s l o c a t e d a t an average a l t i t u d e o f 16-18 km ( I n d i a ) , while i n t h e middle l a t i t u d e s i t i s l o c a t e d a t an a l t i t u d e of 10-12 km, and i n t h e p o l a r regions i t has an a l t i t u d e of 8-10 km, while over t h e p o l e i t may drop t o 5-6 km. J e t a i r c r a f t n o m a l l y f l y c l o s e t o t h e l i m i t of t h e tropopause, a c h a r a c t e r i s t i c f e a t u r e of which i s t h e e x i s t e n c e o f c y c l i c bumps beneath t h e tropopause i t s e l f . The s t r a t o s p h e r e i s l o c a t e d above t h e tropopause and extends t o approxi mately an a l t i t u d e of 35-40 km. Constant temperature with a l t i t u d e is c h a r a c t e r i s t i c of i t s lower l a y e r s . The i n s i g n i f i c a n t content of water vapor i n the s t r a t o s p h e r e r e s u l t s i n t h e lack of clouds from which p r e c i p i t a t i o n would f a l l . According t o d a t a from p i l o t s who have flown a t a l t i t u d e s o f 12-16 km, i n t h e lower s t r a t o s p h e r e i t i s most f r e q u e n t l y c l o u d l e s s . The a i r i s s t a b l e and v e r t i c a l motion i s s l i g h t . This a i d s i n smooth f l i g h t . There i s seldom bumpiness, and only then c l o s e t o t h e tropopause. The mesosphere runs from t h e upper boundary o f t h e s t r a t o s p h e r e t o an a l t i t u d e of 80 km. The thermosphere i s l o c a t e d above t h e mesosphere and extends t o an a l t i t u d e of 800 km. The exosphere i s t h e o u t e r l a y e r of the atmosphere, o r t h e d i s s i p a t i v e l a y e r , and i s l o c a t e d above t h e thermosphere. Gases h e r e a r e so r a r e f i e d and a t the high temperatures observed t h e r e have such high v e l o c i t i e s t h a t t h e i r p a r t i c l e s (helium and hydrogen) break away from t h e e a r t h ' s a t t r a c t i v e f o r c e and move i n t o i n t e r p l a n e t a r y space. Thus we have a b r i e f d e s c r i p t i o n of a s t r u c t u r e of t h e atmosphere. Atmospheric conditions a r e c h a r a c t e r i z e d by t h e various meteorological elements -- atmosphere p r e s s u r e , temperature, humidity, cloud cover, p r e c i p i t a t i o n , wind, e t c . The atmosphere may be c h a r a c t e r i z e d as a v a r i a b l e medium. As a r e s u l t of unequal h e a t i n g of the a i r masses a t t h e equator and p o l e s , flows a r e formed which r e s u l t i n t h e passage o f cold a i r toward t h e equator and warmer air toward t h e p o l e s . The e f f e c t of t h e e a r t h ' s r o t a t i o n i n t h e northern hemisphere causes t h e a i r flow t o d e v i a t e t o the r i g h t and move from 2
- 12. t h e south t o t h e southwest, while approaching 30° N i t moves t o t h e west. Therefore, f l i g h t s from west t o e a s t over t h e t e r r i t o r y of t h e USSR a r e - /7 accompanied by t a i l winds, while east-to-west f l i g h t s encounter head winds. The s h i f t from w e s t e r l y winds t o e a s t e r l y occurs a t a l t i t u d e s around 20 km. Whereas p i s t o n a i r c r a f t f l y only i n t h e lower troposphere, j e t a i r c r a f t , i n c o n t r a s t , f l y i n t h e upper and - - t o a c e r t a i n e x t e n t -- i n t h e lower s t r a t o sphere. The f u r t h e r development of high-speed a v i a t i o n w i l l i n t h e n e a r f u t u r e permit us t o f l y a t s u p e r s o n i c speeds corresponding t o Mach = 2.5-3. A t this p o i n t , f l i g h t s w i l l be i n t h e s t r a t o s p h e r e . Before t h e p e r f e c t i o n i n g of j e t a i r c r a f t , i t w a s assumed t h a t a t high a l t i t u d e s t h e f l i g h t s would encounter f a v o r a b l e weather c o n d i t i o n s . However, i t w a s found t h a t a t a l t i t u d e s of 10,000 - 12,000 m cloud cover and bumpiness were sometimes encountered. To t h e s e well-known phenomena, t h e r e were added t h e j e t streams c h a r a c t e r i s t i c of a l t i t u d e s of 9-12 km. The j e t streams are t h e broad expanses o f zones of very s t r o n g winds observed i n t h e upper l a y e r s of t h e troposphere, u s u a l l y a t a l t i t u d e s of 9000 - 12,000 m. Post-war s t u d i e s showed t h a t t h e minimum v e l o c i t y of t h e j e t stream (along i t s a x i s ) e q u a l l e d approximately 100 km/hr, while t h e maximum w a s 750 km/hr (over t h e P a c i f i c Ocean). Over t h e USSR, t h e wind speed i n t h e j e t stream reaches 100 - 200 and sometimes even 350 km/hr, while over t h e North A t l a n t i c and Northern Europe it reaches 300 - 400, 500 over t h e USA, and 650 km/hr over Japan. The j e t stream i s comparable t o a g i g a n t i c h i g h l y o b l a t e channel with a h e i g h t averaging 2-4 km and a width of 500 - 1000 km. These flows run b a s i c a l l y west-east, b u t i n c e r t a i n s e c t i o n s they may vary significantly . F l i g h t speed may be i n c r e a s e d by t h e s e l e c t i v e u s e of j e t stream t a i l winds, while f l i g h t a g a i n s t t h e head wind should be one o r two km above o r below t h e a x i s of t h i s stream. A s a r u l e , t h e j e t streams a r e t o be found i n t h e region where the tropopause i s s i t u a t e d . In studying a i r c r a f t f l i g h t and determining t h e f o r c e s a c t i n g on a i r c r a f t , we may consider t h e a i r as a continuous medium. A t s e a l e v e l , t h e a i r c o n s i s t s of a mixture of n i t r o g e n (78.08% of t h e volume of dry a i r ) , oxygen (20.95%) and i n s i g n i f i c a n t q u a n t i t i e s of o t h e r gases (argon, carbon dioxide, hydrogen, neon, helium, e t c . ) . The a i r a l s o contains water vapors. In t h e troposphere and s t r a t o s p h e r e t h e temperature, p r e s s u r e and d e n s i t y of the a i r vary w i t h i n r a t h e r broad 1 i . m i t s as a f u n c t i o n o f the geo g r a p h i c l a t i t u d e of t h e l o c a l e , t h e time of y e a r , t h e time of day and t h e weather. In o r d e r t o achieve a common concept o f t h e c h a r a c t e r i s t i c s of t h e atmosphere (pressure, temperature and d e n s i t y ) , t h e s t a n d a r d atmosphere w a s 3 I
- 13. a r r i v e d a t -- t h e a r b i t r a r y d i s t r i b u t i o n , i n t h e atmosphere, of p r e s s u r e , - /8 d e n s i t y and temperature f o r d r y , clean a i r ( c o n t a i n i n g n e i t h e r moisture n o r d u s t ) of a c o n s t a n t composition a p p l i c a b l e f o r engineering. -- p r i m a r i l y a v i a t i o n -- c a l c u l a t i o n s with r e s p e c t t o t h e i r comparability ( f o r example, i n c a l c u l a t i n g t h e l i f t and drag and f o r graduating v a r i o u s aerial n a v i g a t i o n instruments such as altimeters and o t h e r s ) . I n t h e s t a n d a r d atmosphere, t h e a l t i t u d e i s computed from s e a l e v e l . Normal conditions a t sea l e v e l are: atmospheric p r e s s u r e p = 760 mm Hg, a i r 0 2 4 d e n s i t y p = 0.125 k G sec /m , temperature t - 15OC ( o r To = 288OK) and 0 - s p e c i f i c weight of t h e a i r y = 1.225 kG/m 0 3 . Variations i n a i r p r e s s u r e and d e n s i t y with a l t i t u d e , which proceed i n accordance with a s p e c i f i c l a w , are c a l c u l a t e d p e r each a l t i t u d e according t o s p e c i a l formulas. The air temperature i n t h e s t a n d a r d atmosphere up t o an a l t i t u d e of 11,000 m drops uniformly by 6.5OC p e r 1000 m. Above 11,000 m , t h e temperature i s considered c o n s t a n t and equal t o -56.5OC. In f a c t , how ever, a t t h i s a l t i t u d e it may reach -8OOC. Results of c a l c u l a t i o n s a r e given i n t h e t a b l e . Below w e p r e s e n t an a b b r e v i a t e d t a b l e of t h e s t a n d a r d atmosphere. TABLE 1. STANDARD ATMOSPHERE (SA) - A l t i - f Tempera- Mass lelativ Speed I tude , t u r e density lens i t y Ao. 7 of I ,m (tH) > O C a ) - 7 km/hr j kG/m3 m 4 II 1000 21.5 854,6 - 1,3476 1,1374 1,096 1242 0 15 760 : 1O332,3 1,225 0,1250 1,oo 1225 1 000 8,5 674 j 9164,Z. 1.11 0,1134 0,9074 1211 2000 2,o 596 8105,4 1,006 0,1027 0,8215 1197 3000, I -4.5 526 7148,O 0,909 0,0927 0,742 1183 4000 I -1 1 462 6284,2 0,819 0,0636 0,6685 0,754 324.7 1168 5 000 -17.5 405 i 5507,O 0,7362 0,0751 0,6007 0,70 . 320,7 1154 6 000 -24,O 354 i 4809,5 0,659 0,0673 0,5383 0,648 316,6 1139 7000 -30,5 308 4185.3 0,589 0,0601 0,4810 0,599 312,4 ~ 1125 8000 I -37,O 267 3628,4 0,525 0,0536 0,4285 0,553 30S,2 1110 go00 i -43,5 230 3133.1 0,466 0,0476 0,3805 1094 10000 -50,5 188 2694,O 0,412 0,0421 0,337 1078 11000 i -56,5 i 169,6 2306.1 0,363 0,0371 0,297 1063 12000 13000 * 1 -56,5 -56,5 ! 144,6 123.7 1969,5 1682,O 0,310 0,265 0,0317 0,0270 0,253 0,216 1063 1063 14000 ! -56.5 105;6 1436,5 0,226 0,0231 0,185 1063 15000 -56,5 90,l 1226,9 0,193 0,0197 0,155 1063 1 000 6 -56.5 77,l 1047,8 0,165 0,0166 0,135 1063 17 000 -56.5 65,8 894,8 0,141 0,0144 0,115 1063 18 000 -56,5 56,2 764,2 0,120 0,123 OI09S4 1063 19 ooa -56,5 48 ,O 652,7 0,103 0,0105 0,084 1063 20 000 -56,5 40,9 557,4 0,088 0,009 0,0717 1063 Tr. Note: Commas i n d i c a t e decimal p o i n t s . 4
- 14. 5 2. Cmpressibi 1 i t y of A i r Compressibility i s t h e p r o p e r t y of gases (and f l u i d s ) t o change t h e i r i n i t i a l volume (and, consequently, d e n s i t y ) under t h e e f f e c t of p r e s s u r e o r a change i n temperature. I n s o l v i n g t e c h n i c a l problems, c o m p r e s s i b i l i t y i s taken i n t o account i n those cases when changes i n volume (density) are considerable by comparison t o t h e i n i t i a l volume ( d e n s i t y ) . If t h e volume of water w i t h an i n c r e a s e i n p r e s s u r e of 1 a t . with c o n s t a n t temperature changes an average of only 1/21,000 o f i t s i n i t i a l v a l u e , i . e . , only 1/210 of a p e r c e n t , a i r , which has a high c o m p r e s s i b i l i t y , r e q u i r e s a change i n p r e s s u r e of only one one hundredth t h a t of atmosphere (0.01 a t . ) t o change i t s volume by 1% under normal atmospheric c o n d i t i o n s . Therefore, a l l gases are considerably more compressible than dropping liquid. For example, i f t h e p r e s s u r e i n a given m a s s of gas i n c r e a s e s i n such a way t h a t i t s temperature does n o t vary during t h i s change, t h e volume of t h e gas decreases. When t h e i n i t i a l p r e s s u r e i s doubled, t h e volume decreases by 50%. .The change i n volume f o r gas i s e q u a l l y high during heating. Differences i n c o m p r e s s i b i l i t y of l i q u i d s and gases a r e explained by t h e i r molecular s t r u c t u r e . In l i q u i d s , t h e i n t e r - m o l e c u l a r d i s t a n c e i s small, i . e . , t h e molecules a r e r a t h e r dense, which determines t h e small c a p a b i l i t y l i q u i d s have of compressing. B comparison with l i q u i d s , gases have an y extremely low d e n s i t y . For example, t h e d e n s i t y of water i s 816 times t h a t of a i r . The low d e n s i t y of a i r and o t h e r gases i s explained by t h e f a c t t h a t i n gases t h e i n t e r - m o l e c u l a r d i s t a n c e s u b s t a n t i a l l y exceeds t h e dimensions of t h e molecules themselves. Therefore, when t h e r e i s an i n c r e a s e i n t h e pressure, t h e volume of t h e gas decreases due t o t h e decreasing d i s t a n c e between molecules. Thus a r i s e s the e l a s t i c i t y which gas possesses. I n a v i a t i o n problems, t h e need t o account f o r a i r c o m p r e s s i b i l i t y r e s u l t s from t h e f a c t t h a t a t high f l i g h t speeds i n a i r , s u b s t a n t i a l d i f f e r e n c e s i n p r e s s u r e a r i s e which are t h e cause of s u b s t a n t i a l changes i n i t s d e n s i t y . To e v a l u a t e t h e e f f e c t of c o m p r e s s i b i l i t y , l e t us examine t h e speed of sound . § 3. T h e Propagation o f Small Disturbances i n Air. Sound and Sound Waves. The p r o p e r t y of c o m p r e s s i b i l i t y i s i n t i m a t e l y r e l a t e d t o t h e phenomenon of t h e propagation of sound i n gases. The speed of t h e propagation of sound p l a y s a v i t a l r o l e i n high-speed aerodynamics. The e f f e c t of c o m p r e s s i b i l i t y on t h e aerodynamic c h a r a c t e r i s t i c s of a i r c r a f t i s a f u n c t i o n of t h e degree t o which t h e f l i g h t speed of t h e a i r c r a f t approaches t h e speed of sound. When air flows a t speeds g r e a t e r t h a n t h e speed o f sound, q u a l i t a t i v e changes occur / 10 i n t h e c h a r a c t e r of t h e flow. The s e n s a t i o n which w e p e r c e i v e as sound i s t h e r e s u l t of t h e e f f e c t , on 5
- 15. our a u d i t o r y apparatus, of t h e o s c i l l a t o r y motion of a i r caused, f o r example, by t h e motion of some body i n it. The displacement of each p a r t i c l e o f a i r during i t s v i b r a t i o n i s i n s i g n i f i c a n t l y small. The p a r t i c l e s v i b r a t e around t h e i r e q u i l i b r i u m c o n f i g u r a t i o n , which corresponds t o t h e i r i n i t i a l s t a t e . However, t h e l a b o r a t o r y p r o c e s s i s propagated a v e r y long d i s t a n c e . The human ear p e r c e i v e s as sound t h o s e d i s t u r b a n c e s which a r e t r a n s m i t t e d with a frequency from 20 t o 20,000 v i b r a t i o n s p e r second. Those w i t h a frequency of less than 20 p e r second are c a l l e d i n f r a s o u n d , and t h o s e above 20,000 p e r second a r e c a l l e d ultrasound. B small d i s t u r b a n c e s w e mean s l i g h t changes i n t h e p r e s s u r e and d e n s i t y y o f t h e medium (gas o r l i q u i d ) . Disturbances being propagated i n t h e medium, such as a i r , a r e c a l l e d waves (due t o t h e s i m i l a r i t y o f t h i s phenomenon t o waves on t h e s u r f a c e of w a t e r ) . The speed of t h e propagation o f t h e d i s t u r b a n c e s i n space ( t h e wave v e l o c i t y ) i s q u i t e s u b s t a n t i a l . The speed of propagation of a sound wave, i . e . , small changes i n d e n s i t y and p r e s s u r e , i s c a l l e d t h e speed o f sound. It i s a f u n c t i o n of t h e medium i n which t h e sound is being propagated and of i t s temperature. I n high-speed aerodynamics, sound i s considered as waves of p e r t u r b a t i o n s c r e a t e d i n t h e a i r by a f l y i n g a i r c r a f t . The speed of sound i n gases i s a function of temperature. The h i g h e r t h e gas temperature, t h e l e s s compressed i t i s . Heated gas has a high e l a s t i c i t y and t h e r e f o r e i s more d i f f i c u l t t o compress. Cold a i r i s e a s i l y compressed. For example, a t a gas temperature T = 0 ( o r t = -273OC), t h e speed of sound equals zero because under t h e s e conditions t h e gas p a r t i c l e s a r e immobile and e x e r c i s e only s l i g h t d i s t u r b a n c e s , with t h e r e s u l t t h a t they can c r e a t e no sound . The dependence o f t h e speed o f sound i n a i r on temperature may be determined according t o t h e following approximate formula: a = 20 JTm/sec. Within t h e l i m i t s of troposphere, t h e a i r temperature decreases with a l t i t u d e . Consequently, i n t h e troposphere t h e speed o f sound a l s o decreases with a l t i t u d e . On t h e e a r t h ' s s u r f a c e under s t a n d a r d c o n d i t i o n s (p = 760 mm Hg, t = 15 s e c ) , a = 340 m/sec. With an i n c r e a s e i n a l t i t u d e f o r every 250 m , /11 t h e speed of sound decreases by 1 m/sec. A t a l t i t u d e s above 11,000 m, t h e temperature i s (according t o t h e s t a n d a r d atmosphere) considered constant and equal t o -56.5OC. Consequently, the speed of sound a t t h e s e a l t i t u d e s should a l s o be considered constant and equal t o a = 20 4273 - 56.5 = 296 m/sec (Fig. 1 ) . 6
- 16. I § 4. T h e S p e e d of Sound as a C r i t e r i o n f o r the Compress i b i 1 i t y of Gases I n gas dynamics, f o r t h e speed of sound t h e r e is t h e well-known formula: m/sec, AP where A is t h e change i n p r e s s u r e , Ap i s t h e p change i n gas d e n s i t y which it causes. The more compressed t h e gas i s , t h e slower t h e speed of sound, s o t h a t one and t h e same change i n d e n s i t y ec. may b e obtained through a s l i g h t change i n p r e s s u r e . And, i n c o n t r a s t , t h e l e s s t h e com p r e s s i b i l i t y of t h e medium and t h e g r e a t e r i t s Figure 1 . The Change i n tt--. Speed of Sound w i t h e l a s t i c i t y , t h e g r e a t e r t h e speed o f sound i n A1 t i t u d e . t h e same medium. In t h i s c a s e , a s l i g h t change i n d e n s i t y may be achieved only through a g r e a t change i n p r e s s u r e . The speed of sound i s taken i n t o c o n s i d e r a t i o n i n any case i n which t h e r e i s an e v a l b a t i o n o f t h e e f f e c t of c o m p r e s s i b i l i t y i n any aerodynamic phenomena, because t h e value of t h e speed of sound c h a r a c t e r i z e s t h e c o m p r e s s i b i l i t y of t h e medium. I f t h e medium is e l a s t i c (compressible), compressions and expansions w i l l vary s u b s t a n t i a l l y from l a y e r t o l a y e r with t h e speed of sound. I f t h e medium is a b s o l u t e l y incompressible, i . e . , f o r any i n c r e a s e i n p r e s s u r e t h e volume o r d e n s i t y remains unchanged, then as can b e seen from t h e formula given above, t h e speed of sound w i l l be q u i t e high. In such a medium, any d i s t u r b a n c e s a r e propa gated any d i s t a n c e i n s t a n t a n e o u s l y . A s was shown above, t h e value of t h e speed of sound v a r i e s i n d i f f e r e n t gases and, i n a d d i t i o n , it i s a f u n c t i o n of temperature. With an i n c r e a s e i n a l t i t u d e , temperature and t h e speed of sound decrease. Therefore, t h e e f f e c t of c o m p r e s s i b i l i t y on t h e f l i g h t of a i r c r a f t a t high a l t i t u d e s should appear even g r e a t e r . Let us introduce s e v e r a l values f o r the speed o f sound a t t = 0 ° C : f o r n i t r o g e n i t is 3 3 7 . 3 , f o r hydrogen it i s 1300, and f o r water i t i s 1450 m/sec. For s o l i d b o d i e s , which a r e l e s s compressible than g a s e s , t h e speed of sound i s s t i l l g r e a t e r . Thus, i n wood t h e speed o f sound i s 2800 m/sec, while i n s t e e l i t i s 5000 and i n g l a s s i t i s 5600. A a i r c r a f t i n f l i g h t , r e p e l l i n g a i r on a l l s i d e s , p a r t i a l l y compresses n i t as w e l l . A t low f l i g h t speeds, t h e a i r i n f r o n t of t h e a i r c r a f t succeeds i n being d i s p l a c e d and adapts i t s e l f t o t h e flow around t h e a i r c r a f t so t h a t compression i s i n s i g n i f i c a n t i n t h i s case. A t h i g h e r f l i g h t speeds, however, t h e a i r compression begins t o p l a y a more important r o l e . In t h i s case, t h e r e f o r e , f o r a s c a l e of f l i g h t speed w e must use a c h a r a c t e r i s t i c speed which may / 2 1 s e r v e a s a c r i t e r i o n f o r t h e c o m p r e s s i b i l i t y of t h e medium. Such a speed is t h e speed of sound, inasmuch as i t i s a f u n c t i o n o f t h e temperature and 7
- 17. p r o p e r t i e s o f t h e gas. § 5. T h e Mach Number and i t s Value i n F l i g h t Problems The r a t i o of t h e f l i g h t ( o r flow) speed t o t h e speed of sound i s c a l l e d t h e Mach number: Let us assume t h a t t h e t r u e f l i g h t speed ( s e e § 6 of t h i s Chapter) o f an a i r c r a f t at an a l t i t u d e o f 10,000 m i s 920 km/hr (255 m/sec). Then t h e Mach 255 - number M = - - 0.85, where a = 300 m/sec. I n o t h e r words, t h e f l i g h t speed 300 i s 85% of t h e speed of sound a t t h i s given a l t i t u d e . Thus, i n comparing t h e speed of t h e motion of t h e body i n t h e a i r with t h e speed of sound under t h e same c o n d i t i o n s , w e may determine t h e e f f e c t of a i r c o m p r e s s i b i l i t y on t h e c h a r a c t e r of t h e flow around t h e body. The Mach number i s t h e index of t h e air c o m p r e s s i b i l i t y . The g r e a t e r t h e Mach number, t h e g r e a t e r t h e a i r c o m p r e s s i b i l i t y should be during f l i g h t . To monitor t h e Mach number i n f l i g h t , an instrument -- the Mach i n d i c a t o r (Machmeter) -- i s u s u a l l y s e t up on t h e p i l o t ' s instrument panel. In high- speed f l i g h t , e s p e c i a l l y when maneuvers a r e b e i n g performed which r e s u l t i n a l o s s of a l t i t u d e , t h e reading on t h i s instrument must be followed, and t h e p i l o t must not exceed t h e Mach number which t h e i n s t r u c t i o n s permit f o r t h e given a i r c r a f t . I f f l i g h t speed remains c o n s t a n t as a l t i t u d e i n c r e a s e s , t h e Mach number w i l l i n c r e a s e due t o t h e decrease i n t h e speed of sound. F a i l u r e t o monitor t h e Mach number i n j e t a i r c r a f t would r e s u l t i n grave t r o u b l e because knowing t h e i n d i c a t e d speed ( s e e § 6 of t h i s Chapter) and even t h e t r u e speed does n o t g i v e t h e p i l o t a f u l l understanding of t h e f l i g h t Mach number a t any s p e c i f i c a l t i t u d e . For example, i f t h e a i r c r a f t i s f l y i n g a t an i n d i c a t e d speed of 500 km/hr a t an a l t i t u d e of 12,000 m, t h e t r u e speed w i l l be around 930 km/hr while t h e speed of sound i s 1063 km/hr, s o t h a t under t h e s e given f l i g h t conditions t h e Mach number = 0.875. I f , however, t h e a i r c r a f t i s f l y i n g with an i n d i c a t e d speed of 500 km/hr a t an a l t i t u d e of 1000 m, the t r u e speed i s only 525 km/hr, while t h e Mach number = 0.43. I n t u r b o j e t a i r c r a f t , a change i n t h e Mach number may be represented i n t h e following way. A f t e r t a k e o f f and r e t r a c t i o n of t h e landing gear and wing f l a p s , t h e a i r c r a f t p i c k s up speed u n t i l i t achieves an i n d i c a t e d speed of 500 - 600 km/hr and starts climbing. S t a r t i n g a t an a l t i t u d e of around 1000 m, t h e Machmeter shows a Mach number of M = 0.5 - 0.55. As t h e a i r c r a f t climbs, the t r u e speed w i l l i n c r e a s e , t h e speed of sound w i l l decrease, and /13 - t h e Mach number i n c r e a s e . When t h e a i r c r a f t reaches an a l t i t u d e of 8-9 km, t h e Mach number reaches a v a l u e of 0.63 - 0.66 (depending on t h e a c t u a l temperature a t t h a t a l t i t u d e ) . A t a l t i t u d e s of 10-12 km, during a c c e l e r a t i o n t h e Mach number i n c r e a s e s t o 0.80 - 0.85. A t high a l t i t u d e s t h e Mach number 8
- 18. w i l l b e g r e a t e r when t h e same t r u e speeds are maintained. Turbojet a i r c r a f t , l i k e many o t h e r high-speed a i r c r a f t , have a l i m i t t o t h e i r Mach number because of conditions o f s t a b i l i t y and handiness (more w i l l b e s a i d concerning t h e s e l e c t i o n of t h e Mach number i n Chapters 7 and 11). Therefore ( e s p e c i a l l y a t high a l t i t u d e s ) , i t i s i n s u f f i c i e n t t o monitor f l i g h t simply with r e s p e c t t o speed; t h e Mach i n d i c a t o r m u s t a l s o be observed. 5 6 . F1 i g h t Speed. Corrections t o Instrument Readings Necessitated by Compressibility Aircraft speed i n d i c a t o r s measure d i r e c t l y n o t only t h e speeds, b u t t h e 2 v e l o c i t y head q = pV /2. The a c t u a l f l i g h t speed i s n o t t h e same a s t h i s speed, which i s i n d i c a t e d by t h e instrument, because t h e a i r - p r e s s u r e s e n s o r i n d i c a t e s the e f f e c t of p e r t u r b a t i o n s c r e a t e d by t h e aircraft and t h e a i r compressibility. In a d d i t i o n , t h e v a l u e of the a c t u a l f l i g h t speed depends on i n s t r u m e n t a l c o r r e c t i o n s . Therefore, t o e l i m i n a t e t h e above-mentioned e r r o r s i n t h e instrument r e a d i n g s , t h e following c o r r e c t i o n s a r e introduced: aerodynamic, which accounts f o r t h e d i f f e r e n c e i n the l o c a l p r e s s u r e s ( a t t h e p o i n t where t h e a i r - p r e s s u r e s e n s o r i s located) from p r e s s u r e s i n t h e undisturbed i n c i d e n t flow, c o r r e c t i o n s f o r c o m p r e s s i b i l i t y , and instrument c o r r e c t i o n s * . The speed which would be shown on an i d e a l ( i . e . , e r r o r - f r e e ) speed i n d i c a t o r i s c a l l e d t h e i n d i c a t e d speed V The speed which i s read from t h e i' instrument (read from t h e wide n e e d l e ) , does not as a r u l e equal t h e i n d i c a t e d speed. Therefore, a s p e c i a l name has been c r e a t e d f o r i t -- instrument speed 'inst' The t r u e a i r speed i s t h e speed of t h e a i r c r a f t ' s motion r e l a t i v e t o t h e a i r (and i s read from t h e t h i n arrow on t h e i n s t r u m e n t ) . The KUS11200 combined speed i n d i c a t o r , which j e t a i r c r a f t f l y i n g a t Mach speeds up t o 0 . 9 a r e equipped w i t h , shows t h e instrument speed and t h e t r u e a i r speed. During l o w - a l t i t u d e f l i g h t (where t h e a i r d e n s i t y i s c l o s e t o t h a t of t h e e a r t h ' s s u r f a c e , equal t o 0.125 kG - sec2/m4), t h e instrument and t r u e a i r speeds agree and both arrows on t h e instrument move t o g e t h e r , being superimposed. With an i n c r e a s e i n a l t i t u d e , t h e t r u e a i r speed s u r p a s s e s the instrument speed and t h e arrows diverge, forming a "fork." /14 Knowing t h e true a i r speed and wind speed, i t i s p o s s i b l e t o determine t h e ground speed, i . e . , t h e speed of t h e a i r c r a f t ' s displacement r e l a t i v e t o t h e e a r t h . In f l y i n g and aerodynamic computations, both t h e i n d i c a t e d and instrument speeds are used. And what i s t h e d i f f e r e n c e between them? To switch from instrument speed t o i n d i c a t e d speed, we must introduce an aero dynamic c o r r e c t i o n and a c o r r e c t i o n f o r a i r c o m p r e s s i b i l i t y : * M.G.Kotik, e t a l . , F l i g h t T e s t i n g o f A i r c r a f t , Mashinostroyeniye, 1965 (Available i n N S t r a n s l a t i o n ) . AA 9
- 19. 'ins t = vi + 6Va + 6Vcomp = vi + 6Va, g where Vi = i n d i c a t e d speed, 6V = aerodynamic c o r r e c t i o n , a = correction f o r compressibility, and "comp Vi = i n d i c a t e d ground speed. g For high-speed a i r c r a f t , an e s s e n t i a l c o r r e c t i o n i s t h e c o r r e c t i o n f o r a i r c o m p r e s s i b i l i t y , whose value may range from 10 t o 100 lan/hr. The e f f e c t of a i r c o m p r e s s i b i l i t y i n c r e a s e s the speed i n d i c a t o r reading, s o t h a t 6Vcomp i s always negative (Fig. 2 ) . 400 600 800 l0 o0 1200 1.~70 Vi , km/hr & i Figure 2. Nomogram f o r Determining t h e Correction f o r Air Compressibility The aerodynamic c o r r e c t i o n may reach values from 5 t o 25 km/hr and may b e - /15 e i t h e r p o s i t i v e o r negative. Whereas t h e c o r r e c t i o n f o r c o m p r e s s i b i l i t y i s i d e n t i c a l f o r a l l a i r c r a f t , the aerodynamic c o r r e c t i o n i s b a s i c a l l y a f u n c t i o n of t h e type of a i r c r a f t o r , more s p e c i f i c a l l y , t h e p o s i t i o n and f e a t u r e s of 10
- 20. P t h e engine. Therefore, each a i r c r a f t h a s i t s own graph o f aerodynamic corrections. The i n d i c a t e d speed w i t h t h e c o r r e c t i o n f o r c o m p r e s s i b i l i t y i s c a l l e d t h e i n d i c a t e d ground speed: V. = Vi + 6 V A t sea l e v e l , i r r e s p e c t i v e o f a i r 1 comp * g temperature, vi = vi. According t o t h e nomogram i n Figure 3 , w e may f i n d t h e . E f l i g h t Mach number b e i n g given t h e v a l u e of Vi , and t h e n determine t h e t r u e g f l i g h t speed: V = aM. For example, we m u s t determine t h e true speed and t f l i g h t Mach number f o r t h e a i r c r a f t i f a t an a l t i t u d e o f 10,000 m y Vinst - = 500 km/hr. = -10 km/hr, we f i n d : Taking t h e aerodynamic c o r r e c t i o n 6 V a Vi = 490 km/hr. For t h i s speed, according t o t h e nomogram (Figure 2 ) , w e g o b t a i n GVcomp = -23 km/hr. Then l e t us determine t h e i n d i c a t e d speed Vi = 'ins t - 10 - 2 3 = 500 -33 = 467 km/hr. The t r u e f l i g h t speed may b e found from t h e following e x p r e s s i o n : V. - 467 V = - - -= 810 km/hr, 1 0.58 t & where f o r H = 10,000 m, A = 0.337, a d = 0.58 ( s e e t h e t a b l e f o r t h e T / 16 - s t a n d a r d atmosphere). Or, f o r speed V = 490 km/hr, according t o t h e nomo i g gram (Fig,. 3 ) , w e o b t a i n a Mach number of 0.75. Knowing t h e speed of sound a t H = 10,000 m and t h e f l i g h t Mach number, i t is easy to. determine t h e t r u e speed: Vt = a = 300 M - 0.75 - 3.6 = 810 km/hr. The accepted v a l u e 6Va = -10 km/hr i s c h a r a c t e r i s t i c of modern high- speed a i r c r a f t w i t h i n t h e range o f t h e i r i n d i c a t e d speeds o f 220 - 600 km/hr. Later we w i l l determine t h e c.orrection f o r a i r c o m p r e s s i b i l i t y i n each c o n c r e t e case according t o t h e nomogram i n Figure 2 , while we w i l l assume t h a t t h e aerodynamic c o r r e c t i o n i s 6 V = -10 km/hr. a 5 7. T h e Character o f t h e Propagation o f Minor P e r t u r b a t i o n s i n F l i g h t a t Various A1 ti t u d e s I n an example of a i r c r a f t f l i g h t , l e t us examine t h e manner i n which s l i g h t f l u c t u a t i o n s i n d e n s i t y and p r e s s u r e , i . e . , minor p e r t u r b a t i o n s , w i l l b e propagated i n t h e a i r flow. 'The a i r c r a f t , being t h e s o u r c e of t h e per t u r b a t i o n s , has an e f f e c t on t h e a i r p a r t i c l e s l o c a t e d i n f r o n t of i t and p e r t u r b a t i o n s a r e s e n t forward from one p a r t i c l e t o t h e n e x t a t t h e speed of sound. L e t us f i r s t t a k e an a i r c r a f t f l y i n g a t below t h e speed o f sound (Fig. 4a). 11
- 21. P Figure 3. Nomogram f o r Determining t h e Mach Number -- -/ I I '.-- _ . ' Figure 4. Propagation C h a r a c t e r i s t i c s f o r Sound Waves 12
- 22. When t h e a i r c r a f t passes through p o i n t A t h e p e r t u r b a t i o n s c r e a t e d by it a t t h a t given moment, propagating along a sphere a t t h e speed of sound, over t a k e the aircraft. A f t e r a s h o r t t i m e , t h e Mach wave reaches p o i n t B y while during t h i s t i m e t h e a i r c r a f t has succeeded only i n progressing t o p o i n t C; t h u s , i t s f l i g h t speed is below t h e speed o f sound. Passing through p o i n t D, it again c r e a t e s p e r t u r b a t i o n s which w i l l be propagated with t h e speed of sound and i n a s h o r t while reach p o i n t E . The a i r c r a f t , however, during t h i s time w i l l n o t have reached p o i n t E b u t w i l l be located between p o i n t s C and E. Thus, t h e a i r c r a f t remains c o n s t a n t l y w i t h i n t h e s p h e r e c r e a t e d by i t s sound wave. I f , however, t h e a i r c r a f t f l i e s a t t h e speed of sound (Fig. 4b) , then p o i n t B i s reached simultaneously by both t h e a i r c r a f t and t h e sound waves, i . e . , t h e p e r t u r b a t i o n s c r e a t e d by it a t p o i n t s A, C and D. Thus, i n f r o n t of t h e a i r c r a f t t h e r e a r e always Mach waves which, becoming superimposed upon each o t h e r , f o n a dense s e c t i o n o f a i r c a l l e d t h e compression shock o r shock wave. If t h e a i r c r a f t f l i e s above t h e speed o f sound, it moves ahead of t h e s p h e r i c a l waves i t has c r e a t e d (Fig. 4c). The a i r c r a f t w i l l reach p o i n t C a t t h e moment when t h e p e r t u r b a t i o n i t c r e a t e d a t p o i n t A has reached only p o i n t B y while t h e p e r t u r b a t i o n c r e a t e d a t p o i n t D has reached p o i n t E . Thus, behind an a i r c r a f t f l y i n g a t s u p e r s o n i c speed a Mach cone i s formed which c o n s i s t s of an i n f i n i t e number of Mach waves propagated along t h e sphere a t t h e speed of sound. However, t h e air mass w i t h i n t h e Mach cone i s d i s p l a c e d / 17 r e l a t i v e t o t h e e a r t h a t t h e a i r c r a f t ' s speed. The g r e a t e r t h e a i r c r a f t ' s speed, t h e s h a r p e r t h e angle a t t h e t i p of the Mach cone. This angle i s determined according t o t h e formula (Fig. 4c): 1 sin 4 = -' M If t h e Mach number i s 1, then $ = go", while t h e f u l l angle is 180" (normal shock); f o r M = 2 , s i n 9 = 0 . 5 and t h e angle $ = 30" ( f u l l angle 6 0 ° ) . Compression shocks a r e both normal and oblique. A normal compression shock i s one whose s u r f a c e i s p e r p e n d i c u l a r t o the d i r e c t i o n o f t h e i n c i d e n t flow, i . e . , which forms an angle B = 90" w i t h i t (Fig. Sa). Oblique shocks a r e those whose s u r f a c e forms an a c u t e angle of f3 < 90" w i t h t h e d i r e c t i o n of t h e i n c i d e n t flow (Fig. 5b). The g r e a t e s t speed l o s s e s and i n c r e a s e s i n p r e s s u r e a r e observed when t h e flow passes through a normal compression shock. The braking of t h e flow on t h i s shock i s s o s u b s t a n t i a l t h a t behind the shock the flow v e l o c i t y must /8 1 be below t h e speed of sound (by a s much as i t was above t h e speed of sound i n f r o n t of t h e shock). I n an oblique shock t h e l o s s e s are l e s s than with a normal shock, s p e c i f i c a l l y , p r o p o r t i o n a t e l y l i t t l e t h e more t h e shock w a s i n c l i n e d i n t h e d i r e c t i o n o f t h e flow, i . e . , t h e l e s s t h e angle B . The i n t e n s i t y of an oblique shock i s a l s o s u b s t a n t i a l l y l e s s than a normal shock. If t h e angle B 13
- 23. i s c l o s e t o 9Qo, then behind t h e oblique shock t h e speed of t h e flow i s subsonic, while somewhat g r e a t e r than t h a t which would be obtained i f t h e shock were normal. Streams p a s s i n g through an oblique shock change t h e d i r e c t i o n o f t h e i r motion, d e v i a t i n g . from t h e i r i n i t i a l d i r e c t i o n . During flow around a wing o r f u s e l a g e with a speed exceeding t h e speed o f sound, an oblique shock developes i n f r o n t of t h e wing o r f u s e l a g e . oblique compress i g n A i r c r a f t intended f o r t r a n s - and super s o n i c speeds must have i aerodynamic shapes which perturbation f do n o t g e n e r a t e normal y- boundary compression shocks. The forward edge of t h e wing on s u p e r s o n i c a i r c r a f t Figure 5. Formation of Normal ( a ) and O b l i q u e must b e k n i f e - l i k e , and ( b ) Compress i on Shocks. t h e wing i t s e l f must be quite thin. 5 8. Trans- o r Supersonic Flow o f Air Around Bodies In t h e case of low-velocity flow around b o d i e s , t h e flow is deformed a t a s u b s t a n t i a l d i s t a n c e from t h e body and a i r p a r t i c l e s , i n breaking away, flow - /19 smoothly around i t (Fig. 6a) . When t h i s o c c u r s , t h e p r e s s u r e c l o s e t o t h e body v a r i e s i n s i g n i f i c a n t l y , which permits us t o consider a i r d e n s i t y as constant. As a MC 1 r e s u l t of t h e d i f f e r e n c e i n p r e s s u r e s under and over t h e wing, l e f t i s c r e a t e d . I n t h e case of s o n i c o r s u p e r s o n i c flow I Mach around a body, l o c a l a i r p r e s s u r e and d e n s i t y v a r i a t i o n s a r i s e which, propagating a t t h e speed of sound, form a s o n i c o r s u p e r s o n i c shock wave i n f r o n t of t h e body. This occurs because t h e speed of t h e a i r p a r t i c l e s c l o s e t o t h e body suddenly v a r i e s i n both amount and d i r e c t i o n . When t h i s occurs, t h e flow i n a s e n s e "encounters" an Figure 6 . Subsonic ( a ) and o b s t a c l e which, depending on t h e s i t u a t i o n , Supersonic ( b ) Flow Around may be t h e body i t s e l f o r an " a i r cushion" i n a Wing P r o f i l e . f r o n t of i t and form a compression shock 14
- 24. (shock wave). A t t h i s compression shock t h e r e i s an uneven change i n t h e b a s i c parameters c h a r a c t e r i z i n g t h e conditions of t h e a i r , i . e . , speed V, p r e s s u r e p , d e n s i t y p and temperature T. Shock waves may b e formed e i t h e r i n f r o n t of t h e p r o f i l e o r c l o s e t o i t s t r a i l i n g p o r t i o n . P r e c i s e c a l c u l a t i o n s and measurements have shown t h a t t h e thickness of t h e shock waves - o r compression shocks i s n e g l i g i b l y small and has an o r d e r of length o f t h e free path of the molecules, i . e . , 10-4 - 10-5 mm (0.0001 - 0.00001 mm). § 9. Sonic I'booml' Supersonic f l i g h t i s accompanied by t h e c h a r a c t e r i s t i c s o n i c %boom. This phenomenon i s t h e r e s u l t of t h e formation o f a system of compression shocks and expansion waves i n f r o n t of t h e nose o f a f u s e l a g e , t h e cabin, o r where t h e wing and t a i l assembly j o i n t h e f u s e l a g e . * The most powerful shock waves a r e formed by t h e a i r c r a f t ' s nose and wing, which during f l i g h t are t h e f i r s t t o encounter t h e a i r p a r t i c l e s , and t h e t a i l assembly. These shock waves are l a b e l e d bow and t a i l shock waves , r e s p e c t i v e l y (Fig. 7a). I n t e r i mediate shock waves e i t h e r c a t c h up with t h e bow shock and merge with i t o r /20 f a l l behind and merge w i t h t h e t a i l shock. Behind t h e bow shock, t h e a i r p r e s s u r e i n c r e a s e s unevenly, becoming g r e a t e r than atmospheric p r e s s u r e , and then decreases smoothly and becomes even l e s s than atmospheric, a f t e r which i t again i n c r e a s e s unevenly u n t i l i t i s p r a c t i c a l l y atmospheric again a t t h e t a i l wave. The sudden p r e s s u r e drop i s t r a n s m i t t e d t o t h e a i r around i t i n a d i r e c t i o n perpendicular t o t h e wave s u r f a c e . Persons on t h e ground f e e l t h i s drop as a s t r o n g Ifboom." Sometimes a second Yboom" i s heard -- t h i s i s the r e s u l t of t h e s u c c e s s i v e e f f e c t s o f b o t h t h e bow and t a i l shock waves. Figure 7. A i r Pressure Changes during a "boom" i n t h e Vertical Plane b e l o w t h e A i r c r a f t ( a ) , and t h e I n t e r c e p t i o n of t h e Conic Shock Wave w i t h t h e E a r t h ' s Surface ( b ) . . . * A. D. Mironov, Supersonic "Floc" i n Aircraft. Voyenizdat, 1964. 15
- 25. Repeated observations have e s t a b l i s h e d t h a t t h e two s u c c e s s i v e s o n i c booms are d i s t i n c t l y heard only when t h e r e i s more than 1/8th o f a second between them. The longer t h e a i r c r a f t , t h e longer t h e time i n t e r v a l between t h e occurrence of t h e bow wave and t h e t a i l wave. Therefore, two "booms" are d i s t i n c t l y heard i n t h e c a s e o f an a i r c r a f t with a long f u s e l a g e . And, i n c o n t r a s t , an only vaguely s e p a r a t e d "boom" i n d i c a t e s t h a t t h e a i r c r a f t has small dimensions o r i s f l y i n g a t a r e l a t i v e l y low a l t i t u d e . If t h e a i r c r a f t f l i e s a t a constant s u p e r s o n i c speed, t h e " b 0 0 m " i s heard simultaneously a t d i f f e r e n t p o i n t s on t h e e a r t h ' s s u r f a c e . If t h e s e p o i n t s were t o be j o i n e d by a l i n e , we would o b t a i n a hyperbola forming as a r e s u l t of t h e i n t e r c e p t i o n of t h e conic shock wave with t h e p l a n e o f t h e e a r t h ' s s u r f a c e (Fig. 7 b ) . One hyperbola corresponds t o t h e bow wave, and t h e o t h e r -- t o t h e t a i l wave. The l i n e s of simultaneous a u d i b i l i t y of t h e "boom" a r e d i s p l a c e d along t h e e a r t h ' s s u r f a c e , following behind t h e a i r c r a f t and forming unusual t r a i l s . A t t h e same time, d i r e c t l y below t h e a i r craft. t h e r e i s a s u b s t a n t i a l l y louder Itboom," which a t t e n u a t e s as a f u n c t i o n /21 of d i s t a n c e and under c e r t a i n circumstances it i s completely i n a u d i b l e . The ground observer who h e a r s t h e 'tboom" from an a i r c r a f t f l y i n g , l e t us s a y , a t an a l t i t u d e of 15 km with a speed twice t h a t o f sound w i l l not observe t h e a i r c r a f t above him; a t an a l t i t u d e of 15 km, i t takes sound approximately 50 s e c t o reach t h e ground a t an average speed o f 320 m/sec, while during t h i s time t h e aircraft w i l l have covered approximately 30 km. To g e t an i d e a of t h e e f f e c t of a p r e s s u r e d r o on b u i l d i n g s t r u c t u r e s , l e t us p o i n t out t h a t t h e overpressure A = 10 kG/m3 c r e a t e s a s h o r t - l i f t p load o f 20 kG on a door with an area of 2 m 2 , f o r example. A f i g h t e r with a f u s e l a g e length of 15 m a t Mach 1 . 5 and H = 6000 m c r e a t e s A = 11 kG/m2. p A heavy, delta-winged s u p e r s o n i c a i r c r a f t weighing 70 t o n s w i l l , f l y i n g a t an a l t i t u d e of 20 km and a t Mach 2 c r e a t e A = 5 kG/m2, and a t low a l t i t u d e s p (5-8 km) a drop may reach 12-18 kG/m2. I t i s a known f a c t t h a t i n t h e i r design, b u i l d i n g s are planned f o r t h e s o - c a l l e d wind load, which corresponds t o t h e f o r c e of t h e p r e s s u r e o f a i r moving a t a speed of 40 m/sec, i . e . , g r e a t e r than 140 km/hr. This type wind w i l l c r e a t e an overpressure o f 100 kg on 1 m2 of wall s u r f a c e . The p r e s s u r e i n t h e "boomT' a t p e r m i s s i b l e f l i g h t a l t i t u d e s i s 1/5th o r 1 / 6 t h t h a t of t h e design allowance f o r wind load. The c h a r a c t e r i s t i c s of t h e e f f e c t of p r e s s u r e drops i n shock waves during "booms" are given i n Table 2. For example, on a w a l l with an a r e a o f 1 2 m2 during an overpressure o f 50-150 kG/m2, t h e r e i s a s h o r t - l i v e d load o f 600 1800 kG. Under t h e e f f e c t of such a load, wooden s t r u c t u r e s may c o l l a p s e . Therefore, a i r c r a f t are forbidden t o a c c e l e r a t e t o s u p e r s o n i c v e l o c i t i e s below 9-10 km o v e r populated areas. In t h e opinion of f o r e i g n s p e c i a l i s t s , a s o n i c "boom" with an i n t e n s i t y of 5 kG/m2 i s t h e most which can b e t o l e r a t e d harmlessly . Therefore, f u t u r e s u p e r s o n i c j e t a i r c r a f t with heavy f l i g h t weights (140 - 170 tons) w i l l have t o f l y a t a l t i t u d e s of 18-24 km i n o r d e r t o minimize t h e e f f e c t of p r e s s u r e drops. In t h i s case, they w i l l have t o climb t o a l t i t u d e s of 9-10 km a t subsonic l i g h t regimes (Mach number = 0.9 - / 22 0.92), while beyond t h a t at up t o scheduled f l i g h t a l t i t u d e a t Mach M = 1.0 16
- 26. 1.2, and only at t h i s a l t i t u d e w i l l they be a b l e t o a c c e l e r a t e t o supersonic c r u i s i n g speed. TABLE 2 P res su re Drop, kG/m2 Relative Loudness and Resultant Destruction 0.5 - 1.5 Distant b l a s t 1.5 - 5 Close b l a s t o r thunder 5 - 15 Very c l o s e , loud t h u n d e r (window g l a s s r a t t l e s and s h a t t e r s ) 15 - 50 Large window panes s h a t t e r 50 - 150 L i g h t structures collapse The sound of t h e s o n i c boom i s a f u n c t i o n o f t h e f l i g h t a l t i t u d e , Mach number, a i r c r a f t ' s angle of a t t a c k , f l i g h t t r a j e c t o r y , atmospheric p r e s s u r e a t sea l e v e l and a t t h e f l i g h t a l t i t u d e , and wind d i r e c t i o n with r e s p e c t t o a l t i t u d e . For example, t h e ttboom't from an a i r c r a f t f l y i n g a t an a l t i t u d e of 15 km and a t Mach 2 (V = 2120 km/hr) i s heard t o a d i s t a n c e of 40 k from t h e m a i r c r a f t ' s p a t h , while a t an a l t i t u d e of 11 km i t i s heard only t o a d i s t a n c e of 33 km. During f l i g h t a t an a l t i t u d e of 1.5 km a t Mach 1.25, t h e "boom" i s heard only w i t h i n a b e l t 8 km wide. A t a i l wind may d i s p l a c e t h e shock wave, r e s u l t i n g i n d i s p l a c e o f t h e a u d i b i l i t y zone. The climbing and descent speeds and t h e angle of i n c l i n a t i o n 0 o f t h e t r a j e c t o r y have s i g n i f i c a n t effects on t h e s i z e of t h e a u d i b i l i t y zone and t h e loudness of t h e "boom." F o r example, i n gaining a l t i t u d e a t an angle of 0 = 15' a t H = 5 km, t h e t'boom't i s heard on t h e ground a t M > 1 . 2 . In descending from an a l t i t u d e o f 10-11 km a t an angle 0 = - l o " , t h e "boom" reaches t h e .ground only a t M = 1.03. In conclusion, l e t us dwell on t h e e f f e c t of t h e shock wave c r e a t e d by a s u p e r s o n i c a i r c r a f t on a passenger a i r c r a f t i n f l i g h t . A s has already been s a i d , t h e p r e s s u r e drop during a compression shock i s 5-18 kG/m2. If f o r t h e mean value we s e l e c t 10 kG/mZ, i t amounts t o l e s s than 0.1% of t h e a i r p r e s s u r e a t ground l e v e l (p = 10,332 kG/m2 = 1 a t . ) . The v e l o c i t y head f o r a j e t passenger a i r c r a f t f l y i n g st a speed o f 850 km/hr and a t an a l t i t u d e of 10 km i s approximately 1200kG/m2, i . e . , more than 100 times t h e p r e s s u r e drop i n t h e "boom." Consequently, such a drop has e s s e n t i a l l y no e f f e c t on an a i r c r a f t i n f l i g h t . However, t h e r e may be a c e r t a i n e f f e c t on t h e a i r c r a f t ' s behavior as c r e a t e d by t h e accompanying j e t from t h e a i r c r a f t f l y i n g by; t h i s e f f e c t i s comparable t o t h a t of a s l i g h t g u s t ( a s i n g l e g u s t o f "bumpy a i r " ) , d i r e c t e d along t h e propagating l i n e of t h e shock wave. As a r e s u l t , t h e a i r c r a f t w i l l experience s l i g h t bumpiness. 17
- 27. § 10. Features of t h e Formation of Compression Shock during F l m Around Various Shapes o f Bodies Let us now look a t t h e f e a t u r e s of t h e formation of compression shocks f i r s t with t h e example of flow around t h e a i r i n l e t o f a j e t engine during s u p e r s o n i c f l i g h t , and t h e n l e t us consider flow around t h e p r o f i l e . The e x i s t e n c e of a normal shock at t h e i n t a k e t o t h e d i f f u s e r leads t o s u b s t a n t i a l l o s s e s of t o t a l p r e s s u r e ( k i n e t i c energy) o f t h e air e n t e r i n g t h e compressor and t h e combustion chamber. During d e c e l e r a t i o n i n t h e d i f f u s e r , t h e s u p e r s o n i c flow i s transformed as i t passes through t h e normal compression shock. When t h i s occurs, one p a r t of t h e k i n e t i c energy of t h e a i r is used f o r i t s compression, while t h e - /23 o t h e r i s transformed i n t o h e a t ( l o s t energy). However, during f l i g h t of t h e Mach number M < 1 . 5 , l o s s e s a t t h e shock a r e small. A s a r u l e , t h e r e f o r e , f o r such f l i g h t speeds i n t a k e devices a r e used on subsonic a i r c r a f t . A t f l i g h t g r e a t e r t h a n 1 . 5 Mach, however, l o s s e s a t t h e normal shock become g r e a t e r . To e l i m i n a t e t h i s , t h e process o f a i r d e c e l e r a t i o n i n t h e i n t a k e device i s achieved through t h e c r e a t i o n of systems o f o b l i q u e shocks which terminate i n a weak normal shock. Because o v e r a l l energy l o s s e s i n a system of o b l i q u e shocks are l e s s than i n one normal shock, t h e p r e s s u r e a t t h e end of t h e d e c e l e r a t i o n w i l l r e t a i n a high v a l u e . Thus, t h e normal shock is divided i n t o a s e r i e s o f oblique shocks. S t r u c t u r a l l y , t h i s i s achieved through s e t t i n g up i n the d i f f u s e r a s p e c i a l s p i k e i n t h e shape of s e v e r a l cones whose t i p s a r e d i r e c t e d according t o f l i g h t (Fig. 8 a ) . When f l i g h t speed i s decreased, t h e angles o f i n c l i n a t i o n of t h e oblique shocks i n c r e a s e ( t h e angle B tends toward 9 0 ' ; see Figure 5 ) . A s speed i s i n c r e a s e d , t h e r e v e r s e occurs, and t h e s e angles decrease. This h i n d e r s t h e operation of t h e i n p u t device inasmuch as t h e f r o n t f o r a l l t h e shocks w i l l n o t pass through t h e i n p u t edge of t h e cone (Fig. 8b). Therefore, sometimes t h e s p i k e i s a d j u s t a b l e , s o t h a t i n t h e event of changes i n speed, i t s p o s i t i o n can b e v a r i e d a x i a l l y , thereby h e l p i n g t h e shock t o pass through t h e leading edge of the a i r i n t a k e a t a l l f l i g h t speeds. O t h e wing p r o f i l e , t h e formation of compression shocks OCCUTS even n s u b s t a n t i a l l y below t h e speed of sound. As soon as t h e flow speed o f t h e convergent stream exceeds t h e speed of sound somewhere on t h e p r o f i l e , Mach waves appear which, i n accumulating, form a shock. I t must be noted t h a t t h i s shock wave i s formed first on t h e upper p r o f i l e s u r f a c e c l o s e t o some p o i n t corresponding t o t h e maximum of t h e l o c a l speed and t h e minimum p r e s s u r e on t h e p r o f i l e . As soon as t h e speed of t h e flow s u r p a s s e s t h e speed /24 of sound, a shock wave forms on t h e lower p r o f i l e s u r f a c e as w e l l (Fig. 9 ) . 1. A t p o i n t C t h e p o i n t of l e a s t p r e s s u r e on t h e p r o f i l e , t h e speed o f t h e motion of t h e a i r has a t t a i n e d t h e l o c a l speed of sound (Fig. 9 a ) . The Mach waves move from t h e source of t h e p e r t u r b a t i o n toward p o i n t C and, running i n t o each o t h e r , form a weak normal compression shock. 18
- 28. F i g u r e 8. Formation of Compression Shocks a t t h e Intake t o t h e Diffuser of a Turbojet E n g i n e a t Supersonic F l i g h t Speeds: a - l i n e drawing o f i n p u t device w i t h cone: O A , BA -- oblique compression shocks, AK -- normal compression shock; b - operational c o n f i g u r a t i o n of supersonic d i f f u s e r d u r i n g f l i g h t speed below i t s design speed. Figure 9. The Formation of Compression Shocks a t Various Streamline Flows. 2. As t h e speed of sound i n c r e a s e s somewhat ( a t V2 > Vl), t h e speed of t h e flow around t h e p r o f i l e i n c r e a s e s (Fig. 9b). Behind p o i n t C y t h e speed of t h e flow becomes g r e a t e r than t h e speed of sound. A s e c t i o n appears where t h e flow moves a t s u p e r s o n i c v e l o c i t y , r e s u l t i n g i n t h e formation of an oblique shock. 19
- 29. 3. A t a speed o f V3 (V3 < a ) , regions o f s o n i c and s u p e r s o n i c flow a l s o form on t h e bottom of t h e p r o f i l e , r e s u l t i n g i n t h e formation o f compression shocks (Fig. 9 c ) . 4. A t a speed o f V4 c l o s e t o t h e speed of sound, t h e compression shocks are d i s p l a c e d toward t h e t r a i l i n g edge, thereby i n c r e a s i n g t h e s e c t i o n o f t h e p r o f i l e which encounters s u p e r s o n i c flow p a s t i t (Fig. 9d). 5. When v e l o c i t y V5 becomes somewhat g r e a t e r t h a n t h e speed o f sound, a bow wave forms i n f r o n t of t h e p r o f i l e and a t a i l wave forms behind i t (Fig. 9e). During flow around a b l u n t e d body, t h e compression shock forms a t a / 25 s l i g h t d i s t a n c e from i t s forward s e c t i o n and assumes a c u r v i l i n e a r form (Fig. l o a ) . A t i t s forward edge, t h e shock i s normal -- h e r e i t i s perpen d i c u l a r t o t h e i n c i d e n t flow. Depending on t h e d i s t a n c e from t h e body, t h e angles of i n c l i n a t i o n o f t h e shock decrease. During s u p e r s o n i c flow around a knife-edged body such as a wedge with a l a r g e open angle (Fig. l o b ) , t h e shock i s formed a l s o a t a s l i g h t d i s t a n c e from t h e bow p o i n t and a l s o has a c u r v i l i n e a r form. If t h e open angle o f t h e wedge i s small enough, t h e compression shock " s e a t s i t s e l f " on t h e s h a r p edges (Fig. 1Oc). Figure 10. T h e Formation of Compression Shocks a t I d e n t i c a l Flow V e l o c i t i e s : a - i n f r o n t of a b l u n t e d body, b and c - i n f r o n t of knife-edged bodies. § 1 1 . C r i t i c a l Mach Number. The E f f e c t of Compressibility on t h e Motion o f Air F l y i n g Around a Wing The c o m p r e s s i b i l i t y of t h e a i r begins t o m a n i f e s t i t s e l f g r a d u a l l y as speed i s increased. Up t o a Mach number o f 0.4, t h e e f f e c t of c o m p r e s s i b i l i t y on t h e aerodynamic c h a r a c t e r i s t i c s of t h e wing i s only s l i g h t and may i n practPce b e ignored. With a f u r t h e r i n c r e a s e i n speed, t h i s e f f e c t becomes more and more n o t i c e a b l e and can no longer b e ignored. S t a r t i n g a t f l i g h t speeds of 600 - 700 km/hr and above, drag i n c r e a s e s s h a r p l y because o f c o m p r e s s i b i l i t y . This occurs due t o t h e f a c t t h a t l o c a l speeds of t h e motion of t h e a i r o v e r t h e wing and a t p o i n t s where t h e wing a t t a c h e s t o t h e f u s e l a g e s u b s t a n t i a l l y surpass t h e f l i g h t speed. In flowing around t h e convex s u r f a c e of the wing, f o r example, t h e air streams are compressed and t h e i r 20
- 30. c r o s s - s e c t i o n decreases. However, because t h e span across t h e stream m u s t remain c o n s t a n t , t h e speed i n i t i s increased. A t any s u f f i c i e n t l y high f l i g h t speed, t h e l o c a l air speed a t any p o i n t on t h e wing o r o t h e r p o i n t on t h e s t r u c t u r e comes t o equal t h e l o c a l speed of sound (Fig. 11). Lava1 nozzle / Profile local=a Figure 1 1 . T h e Formation o f t h e Local Speed of Sound i n Flow around a P r o f i l e . The f l i g h t speed a t which t h e l o c a l speed of sound w i l l appear anywhere on t h e wing i s c a l l e d t h e c r i t i c a l f l i g h t speed Vcr, while i t s corresponding Mach number i s c a l l e d t h e c r i t i c a l Mach number Mcr. Higher values f o r t h e / 26 l o c a l speeds a r e observed on t h e upper a i r f o i l p r o f i l e . A s t h e speed of t h e i n c i d e n t flow o r t h e f l i g h t speed i n c r e a s e s , t h e l o c a l speed reaches the speed of sound f a s t e s t a t t h i s p o i n t . Let us examine t h e a i r stream surrounding t h e p r o f i l e (Fig. 11). Let us s e l e c t two c h a r a c t e r i s t i c c r o s s - s e c t i o n s of t h i s stream: t h e l a r g e one I and t h e small one 11. The l o c a l a i r speeds i n s e c t i o n I1 w i l l be g r e a t e r than t h e l o c a l speeds i n s e c t i o n I as a r e s u l t of d i f f e r e n c e s between t h e areas of t h e s e s e c t i o n s . If we i n c r e a s e t h e speed of t h e i n c i d e n t unperturbed flow, t h e l o c a l speeds i n c r e a s e i n both s e c t i o n s , b u t i n s e c t i o n I1 it i s g r e a t e r than i n s e c t i o n I . This is explained by t h e f a c t t h a t as a r e s u l t of t h e i n c r e a s e i n speed t h e r e i s a drop i n d e n s i t y which i s more i n t e n s e t h e f a s t e r the speed of t h e stream. To r e t a i n t h e s t e a d i n e s s of t h e mass flow weight r a t e o f a i r along the stream, t h e speed i n s e c t i o n I1 must i n c r e a s e addition a l l y i n o r d e r t o compensate f o r t h e g r e a t d e n s i t y drop i n t h i s s e c t i o n . A t t h e t h r e s h o l d , t h e l o c a l speed of t h e flow of a i r i n s e c t i o n I1 may come t o equal t h e l o c a l speed of sound. From t h i s i t follows t h a t during f l i g h t with speed Vcr, t h e l o c a l speed o f sound i s achieved a t t h e narrowest p o i n t o f t h e stream. I t has been e s t a b l i s h e d t h e o r e t i c a l l y t h a t a t t h i s i n s t a n t t h e c r i t i c a l p r e s s u r e drop forms between s e c t i o n I and I1 which i s equal t o pII : pI = 0.528. I t i s w e l l known t h a t i f t h e speed of sound i s achieved a t t h e narrowest p a r t of t h e stream, t h e speed i n c r e a s e s and becomes s u p e r s o n i c i f t h e stream continues broadening. Therefore, a f u l l y s u p e r s o n i c zone o f flow i s formed down w i t h p o r t i o n of t h e p r o f i l e s u r f a c e during f l i g h t with M > Mcr. 21
- 31. The g r e a t e r t h e f l i g h t speed, t h e g r e a t e r t h e zone of s u p e r s o n i c speed w i l l be. However, f a r behind t h e p r o f i l e t h e speed must b e t h e same a s t h e f l i g h t speed. Therefore, a t some poHnt on t h e p r o f i l e t h e r e must develop d e c e l e r a t i o n of t h e a i r from s u p e r s o n i c t o subsonic speed. Such d e c e l e r a t i o n , as experience has shown, occurs only with t h e formation of a compression shock. § 12. T h e Dependence o f t h e S p e e d o f t h e Gas Flow on t h e Shape o f t h e / 27 Channel. T h e Laval Nozzle A means f o r o b t a i n i n g s u p e r s o n i c speeds i n t h e motion o f t h e gas w a s . developed by t h e engineer Laval (Switzerland) during h i s work i n t h e 1880's on improving a steam t u r b i n e he had invented. Laval o b t a i n e d a s u p e r s o n i c flow of vapor as i t flowed from a s p e c i a l n o z z l e . This nozzle, subsequently c a l l e d t h e Laval Nozzle (Fig. l l ) , i s a t u b e which i s f i r s t compressed and then expanded. The narrowest s e c t i o n of t h e tube i s c a l l e d t h e c r i t i c a l s e c t i o n . If a vapor o r gas i s run through such a nozzle a t a s l i g h t p r e s s u r e drop i n which t h e speed o f t h e flow i n t h e c r i t i c a l s e c t i o n becomes subsonic, i n t h e expanded p o r t i o n o f t h e n o z z l e t h e speed w i l l drop; i n t h i s c a s e t h e Laval Nozzle o p e r a t e s as a t y p i c a l Venturi tube. However, i f t h e d i f f e r e n c e i n p r e s s u r e s a t t h e i n p u t t o t h e n o z z l e and a t i t s o u t p u t a r e s u f f i c i e n t l y g r e a t , i n t h e c r i t i c a l s e c t i o n t h e speed of t h e flow becomes equal t o t h e l o c a l speed of sound. In t h i s c a s e , beyond t h e c r i t i c a l s e c t i o n , i . e . , i n t h e broadened p o r t i o n of t h e n o z z l e , t h e speed o f t h e flow does n o t decrease b u t , on t h e c o n t r a r y , i n c r e a s e s . Thus, it was observed t h a t i n sub- and s u p e r s o n i c flows, t h e dependence of t h e speed of t h e flow of gases on t h e shape of t h e channel i s d i r e c t l y o p p o s i t e . Subsonic flow accelerates i n t h e compression channel and d e c e l e r a t e s i n t h e expansion p o r t i o n . In c o n t r a s t , however, s u p e r s o n i c flow l o s e s i t s speed i n t h e compression s e c t i o n , while i t i n c r e a s e s i t i n t h e expansion section Therefore, i n Figure 1 we s e e t h e appearance o f s u p e r s o n i c speed a f t e r 1 t h e stream has passed through t h e narrow s e c t i o n ( p o i n t K ) . However, s u p e r s o n i c speed does n o t i n c r e a s e along t h e e n t i r e length o f t h e nozzle; a t some p o i n t i t must d e c e l e s a t e t o subsonic speed. And h e r e i n l i e s t h e cause f o r t h e formation of t h e compression shock. § 13. Laminar and Turbulent Flow o f Air Under t h e e f f e c t of i n t e r n a l f r i c t i o n due t o t h e v i s c o s i t y of a i r and t h e roughness of t h e s u r f a c e of t h e body around which t h e flow moves, t h e speed of air a t t h i s s u r f a c e becomes equal t o zero. Depending on t h e d i s t a n c e from t h e s u r f a c e , t h e speed o f t h e flow i n c r e a s e s and reaches t h e speed of f r e e flow. The l a y e r of a i r i n which t h e r e i s a change i n speed from zero t o the speed of f r e e flow i s c a l l e d t h e boundary l a y e r . I t i s w e l l known t h a t t h e flow of a i r i n t h e boundary l a y e r may be laminar ( s t r a t i f i e d ) when t h e gas flows without being mixed i n t h e neighboring 22
- 32. l a y e r s and t u r b u l e n t when t h e r e i s random mixing of gas p a r t i c l e s throughout t h e volume o f t h e flow. The boundary l a y e r a l s o e n t a i l s phenomena such as - /28 b u r b l i n g (flow s e p a r a t i o n ) , t h e formation of s u r f a c e f r i c t i o n drag, aero dynamic h e a t i n g , e t c . The i n t e r a c t i o n of t h e boundary l a y e r and t h e compression shocks r e s u l t s i n t h e following. If t h e flow i n t h e boundary l a y e r i s laminar (Fig. 1 2 ) , an oblique compression shock developes d i r e c t l y on t h e a i r f o i l p r o f i l e . Behind t h e shock t h e r e i s s e p a r a t i o n and turbulence of t h e boundary l a y e r ; i n t h e t u r b u l e n t region a normal shock developes. I n g e n e r a l , t h e o b l i q u e and normal shocks are combined. When t h e r e is an oblique shock, t h e i n t e n s i t y of t h e normal shock w i l l be s u b s t a n t i a l l y l e s s because t h e flow approaches i t , having already a t t e n u a t e d i t s speed somewhat i n t h e oblique shock, with t h e r e s u l t t h a t t h e drag d e c r e a s e s , Therefore, 1,aminarized a i r f o i l s , i . e . , a i r f o i l s with very smooth s u r f a c e s , a r e Figure 12. Compression s u i t a b l e i n t h a t they o f f e r t h e l e a s t s u r f a c e Shocks on the Profi le: 1 - f r i c t i o n drag and wave drag a t s u p e r c r i t i c a l Supersoni c Zones ; 2 - Com- f l i g h t Mach numbers. pression Shocks; 3 - S u b - son i c Zones. A f t e r t h e normal compression shock t h e r e begins t h e s o - c a l l e d wave flow s e p a r a t i o n , which i s accompa.nied by a decrease i n t h e l o c a l a i r speed. This i n t u r n r e s u l t s i n a s h a r p drop i n t h e a i r f o i l l i f t . During t u r b u l e n t flow around an a i r f o i l t h e r e i s no oblique shock and only one normal shock. The appearance of l o c a l shocks on t h e a i r f o i l i n s t i t u t e s t h e s o - c a l l e d shock s t a l l . P a r t of t h e k i n e t i c energy i n t h e shock i s transformed i n t o h e a t which i s then i r r e v e r s i b l y propagated. A t high f l i g h t speeds, t h e c h a r a c t e r i s t i c s of t h e compression shock a r e a f u n c t i o n of t h e n a t u r e of t h e boundary l a y e r . Experience has shown t h a t flow i n a boundary l a y e r i s u s u a l l y laminar over a c e r t a i n p o r t i o n and then switches t o t u r b u l e n t . The p o s i t i o n of t h e t r a n s f e r p o i n t s o f laminar boundary flow t o turbu l e n t depend on t h e shape of t h e p r o f i l e , j.ts t h i c k n e s s , roughness, e t c . The s u r f a c e of a body i n laminar flow experiences l e s s f r i c t i o n and less aero dynamic h e a t i n g a t high speeds than does one i n a t u r b u l e n t l a y e r . The s t a t e of t h e boundary l a y e r i s r e f l e c t e d n o t only i n t h e wing drag, b u t i n i t s l i f t i n g c a p a c i t y as w e l l . I n t h e boundary l a y e r a flow s e p a r a t i o n arises which determines t h e c r i t i c a l angle of a t t a c k and i t s corresponding maximum l i f t ratio. 23
- 33. § 14. Pressure Distri-bution a t Sub- and S u p e r c r i t i c a l Mach Numbers /29 P r e s s u r e d i s t r i b u t i o n along a wing p r o f i l e under flow conditions i s shown i n Figure 13. The arrows r e p r e s e n t t h e values o f t h e d i f f e r e n c e s between t h e l o c a l and atmospheric p r e s s u r e s at each p a i n t on t h e p r o f i l e . b ) y c The p o s i t i v e overpressure (atmospheric p r e s s u r e l e s s -1 I- than l o c a l ) i s i n d i c a t e d by arrows p o i n t i n g toward t h e contour, whereas n e g a t i v e p r e s s u r e o r r a r e f a c t i o n (atmos p h e r i c p r e s s u r e g r e a t e r than l o c a l ) is shown by arrows p o i n t t i O P ed away from t h e contour. Figure 13. Diagram of t h e Pressure To determine and compute D i s t r i b u t i o n s along the A i r f o i 1 Pro- t h e f o r c e of t h e evacuation on f i l e : a - v e c t o r a l ; b - expressed by those points of the p r o f i l e a t t h e pressure c o e f f i c i e n t ( 1 - upper which p r e s s u r e measurements w i n g s u r f a c e , 2 - lower s u r f a c e ) . were taken, t h e p r o f i l e chord f o r a l i n e p a r a l l e l t o the chord i s p r o j e c t e d , then t h e measured v a l u e s f o r t h e p r e s s u r e a r e p l o t t e d a t a s e l e c t e d s c a l e from p o i n t s s p e c i f i e d along t h e p e r p e n d i c u l a r t o t h e chord: p o s i t i v e overpressure i s u s u a l l y p l o t t e d below and evacuation i s p l o t t e d above. The p o i n t s thus obtained then merge i n a smooth curve. In diagrams used i n aerodynamics, normally t h e p r e s s u r e c o e f f i c i e n t s (Fig. 13b), which r e p r e s e n t t h e r a t i o of t h e o v e r p r e s s u r e a t any given p o i n t on t h e p r o f i l e t o t h e v e l o c i t y head o f t h e t u r b u l e n t flow are p l o t t e d a t p o i n t s on t h e p r o f i l e r a t h e r than t h e o v e r p r e s s u r e , as f o l l o w s : Pover - P l o c a l - P a t . p=- 9 v2 where pl0 - i s t h e a b s o l u t e p r e s s u r e a t a given p o i n t ; cal Pat. - i s t h e s t a t i c p r e s s u r e i n t h e unperturbed flow, i . e . , t h e atmospheric p r e s s u r e a t f l i g h t a l t i t u d e s ; 9 - i s t h e v e l o c i t y head i n t h e unperturbed flow, determined by t h e f l i g h t speed and a l t i t u d e . From t h e above it follows t h a t t h e p r e s s u r e c o e f f i c i e n t characterizes /30 - t h e degree of d i f f e r e n t i a t i o n ( i n u n i t s of t h e v e l o c i t y head) o f t h e l o c a l p r e s s u r e a t any p o i n t on t h e upper and lower p r o f i l e s u r f a c e s from t h e s t a t i c p r e s s u r e i n t h e unperturbed flow. The c o e f f i c i e n t w i l l be negative i f t h e l o c a l p r e s s u r e on t h e g r o f i l e i s below atmospheric p r e s s u r e . Consequently, a n e g a t i v e v a l u e f o r p corresponds t o t h e presence on t h e p r o f i l e of r a r e f a c t i o n , where a p o s i t i v e value i n d i c a t e s an i n c r e a s e d p r e s s u r e . 24
- 34. ..- . , , . .. . . .. . . . . . -. . . ~ ~ I ~~ ~ A t small Mach numbers, t h e diagram f o r t h e p r e s s u r e d i s t r i b u t i o n f o r each angle of a t t a c k has i t s own constant form because t h e a i r c o m p r e s s i b i l i t y has no e f f e c t on t h e n a t u r e of the d i s t r i b u t i o n o f t h e p r e s s u r e c o e f f i c i e n t s on t h e upper and lower s u r f a c e s . A t high Mach numbers (0.6 and g r e a t e r ) , t h e r e i s an i n c r e a s e i n t h e r a r e f a c t i o n i n which g r e a t e r r a r e f a c t i o n arises t o a g r e a t e r degree. This i n c r e a s e i n t h e r a r e f a c t i o n i s explained by t h e e f f e c t of c o m p r e s s i b i l i t y -- d e n s i t y decreases as speed i n c r e a s e s . Consequently , t o maintain t h e constancy of t h e speed flow r a t e around t h e p r o f i l e , it must i n c r e a s e f u r t h e r , which i n t u r n causes a f u r t h e r i n c r e a s e i n t h e r a r e f a c t i o n . A t p o r t i o n s of t h e p r o f i l e where t h e flow around it has i t s g r e a t e s t speed, i . e . , where r a r e f a c t i o n i s g r e a t e s t , t h e a f f e c t o f c o m p r e s s i b i l i t y w i l l a l s o be greater. To f u r t h e r i n c r e a s e t h e speed o f t h e i n c i d e n t flow (above Mcr), the rare f a c t i o n on t h e leading edge of t h e a i r f o i l p r o f i l e decreases while i t i n c r e a s e s s h a r p l y a t t h e t r a i l i n g edge, s o t h a t h e r e t h e flow becomes s u p e r s o n i c and there is additional rarefaction. The r e s u l t a n t zone of s u p e r s o n i c speed culminates i n a compression shock behind which t h e l o c a l speeds become subsonic. Such a c h a r a c t e r i s t i c i n t h e change o f t h e l o c a l speeds f o r flow around an a i r f o i l p r o f i l e q u a l i t a t i v e l y changes t h e s i t u a t i o n with r e s p e c t t o p r e s s u r e r a r e f a c t i o n along t h e p r o f i l e as compared t o s u b c r i t i c a l flow. From Figure 14 it i s c l e a r t h a t a t t h a t p o i n t on the p r o f i l e where t h e compression shock formed t h e r e A d d i t i o n a l ra're f ac t i on i s a sharp and i r r e g u l a r p r e s s u r e i n c r e a s e ( i . e . , de c r e a s e of r a r e f a c t i o n ) . A t Mach numbers g r e a t e r than c r i t i c a l , the increase i n p r e s s u r e i n t h e leading p o r t i o n of t h e p r o f i l e and an i n c r e a s e i n r a r e f a c t i o n i n t h e trai l i n g p o r t i o n leads t o a s u b s t a n t i a l i n c r e a s e i n t h e drag co e f f i c i e n t . Shocks a r e normally manifested on t h e upper t h e n lower s u r f a c e i n modern pro- f i l e s a t p o s i t i v e angles of Figure 14. Pressure D i s t r i b u t i o n Along attack. t h e P r o f i l e f o r Mach Numbers Below (broken l i n e ) and Above ( s o l i d l i n e ) Let us look a t t h e p i c t u r e t h e C r i t i c a l Mach Number M c r . of p r e s s u r e d i s t r i b u t i o n along t h e chord of a symmetrical p r o f i l e a t a given angle of a t t a c k f o r various Mach numbers (Fig. 1 5 ) . I f a t small Mach numbers t h e values of t h e p r e s s u r e c o e f f i c i e n t p a r e small, then with an i n c r e a s e i n t h e speed of t h e i n c i d e n t flow t h e r a r e f a c t i o n on t h e upper p r o f i l e contour i n c r e a s e s and t h e curve of t h e p r e s s u r e d i s t r i b u t i o n i s d i s p l a c e d upward. When l o c a l s u p e r s o n i c zones and compression shocks are 25
- 35. formed on t h e p r o f i l e , i . e . , f o r Mach numbers g r e a t e r than c r i t i c a l , t h e r e is a zone of flow with V > a. "his zone i s enclosed by t h e normal com p r e s s i o n shock. me formation o f t h e shock causes a decrease i n t h e rare f a c t i o n on t h e upper p r o f i l e . When t h e r e i s a f u r t h e r i n c r e a s e i n t h e Mach number, t h e r e g i o n of s u p e r s o n i c speeds broaden and t h e shock g r a d u a l l y i s d i s p l a c e d t o t h e rear. Decreasing t h e r a r e f a c t i o n becomes much more s i g n i f i c a n t . The subsequent i n c r e a s e i n t h e Mach number r e s u l t s i n t h e shock being formed on t h e lower s u r f a c e as w e l l , where t h e r a r e f a c t i o n becomes g r e a t e r . With even h i g h e r values f o r t h e Mach number, both shocks reach t h e t r a i l i n g edge and t h e e n t i r e p r o f i l e i s surrounded by a s u p e r s o n i c flow. wave j Figure 15. Representative P i c t u r e of the Pressure D i s t r i b u t i o n o n a Symmetrical P r o f i l e ( s o l i d l i n e -- upper s u r f a c e , broken l i n e -- lower s u r f a c e ) . Examination of t h e p i c t u r e of p r e s s u r e d i s t r i b u t i o n gives proof of t h e f a c t t h a t an i n c r e a s e i n t h e Mach number s u b s t a n t i a l l y changes both t h e c h a r a c t e r i s t i c s of t h e curves of p r e s s u r e d i s t r i b u t i o n and t h e moment c h a r a c t e r i s t i c s of t h e wing. 26
- 36. I CHAPTER I I AERODYNAMI C CHARACTER1 STI CS OF THE W l NG AND AI RCRAFT. THE EFFECT OF A I R C O M P R E S S I B I L I T Y . 5 1. T h e Dependence of t h e C o e f f i c i e n t c on t h e A n g l e o f Attack Y The dependence o f t h e l i f t c o e f f i c i e n t c on t h e a n g l e o f a t t a c k a i s Y an important aerodynamic c h a r a c t e r i s t i c of t h e wing and t h e a i r c r a f t . The shape of t h e wing ( f o r a s p e c i f i c number of p r o f i l e s ) i n planform has a s i g n i f i c a n t e f f e c t on t h e c h a r a c t e r of t h e change of t h e c o e f f i c i e n t c f o r Y t h e a i r f o i l a t h i g h angles of a t t a c k a f t e r t h e l o c a l flow s t a r t s t o b r e a k away. Turbojet passenger a i r c r a f t have swept wings, and i t i s t h e s e which we s h a l l d i s c u s s . Figure 16 shows a graph f o r t h e change of t h e c o e f f i c i e n t c as a Y f u n c t i o n of t h e angle a of t h e a i r f o i l w i t h t h e sweep angle x = 35". According t o t h i s graph we may e v a l u a t e t h e l i f t i n g a b i l i t y of t h e a i r f o i l and determine t h e angles of a t t a c k a t which f l i g h t occurs. Depending on t h e f l i g h t speed and a l t i t u d e f o r v a r i o u s f l i g h t w e i g h t s , t h e r e q u i r e d v a l u e s of c are determined f o r h o r i z o n t a l f l i g h t . Y The performace of an a i r c r a f t a t h i g h angles of a t t a c k , t h e causes f o r flow s e p a r a t i o n ( b u r b l e ) and o t h e r c h a r a c t e r i s t i c s a r e a l s o determined and e x p l a i n e d by t h e dependence o f c on a. Y A t h i g h angles of a t t a c k b u r b l i n g begins which d i s t o r t s t h e p i c t u r e of t h e flow and i n t r o d u c e s a c e r t a i n decrease in t h e mean v a l u e o f t h e expansion above t h e a i r f o i l , t h e increa.se i n c slows down, and beyond a Y /33 c e r t a i n angle of a t t a c k c a l l e d t h e c r i t i c a l angle of a t t a c k , t h e r e i s no longer an i n c r e a s e , b u t r a t h e r a d e c r e a s e i n c . Y A t h i g h Mach numbers ( f l i g h t c r u i s i n g s p e e d s ) , a n a l y s i s of t h e dependents c = f (a) must b e c a r r i e d o u t w i t h allowance made f o r t h e a f f e c t of compress Y i b i l i t y , which changes t h i s c h a r a c t e r i s t i c t o a c e r t a i n degree. I n swept a i r f o i l s , v a r i a t i o n s i n t h e c o e f f i c i e n t c w i t h r e s p e c t t o t h e Y angle of a t t a c k have t h e i r own c h a r a c t e r i s t i c s . As can b e s e e n from Figure 16, a t angles o f a t t a c k from -1" t o 10 - 1'2" ( f o r small Mach numbers), there is a linear characteristic of increase i n c . Y However, a t angles o f a t t a c k g r e a t e r t h a n 10 - 12" t h e p r o p o r t i o n a l i t y i s e l i m i n a t e d between t h e increase i n t h e angle of a t t a c k and t h e i n c r e a s e i n c i n addition, Y'
- 37. t h e i n c r e a s e i n c slows down. This i s Y due t o t h e o n s e t o f b u r b l i n g . A t angles o f a t t a c k from 17 t o 20", t h e l i f t c o e f f i c i e n t reaches i t s maximum of c The change i n t h e dependents y ma' of c = f (a) a t t h i s p o r t i o n is a Y f u n c t i o n of t h e shape o f t h e leading edge o f t h e a i r f o i l . The wings i n passenger a i r c r a f t have a b l u n t e d leading edge, s o t h a t t h e change i n c Y i n t h e zone c i s smooth. Y m a Swept wings (as compared t o normal wings) have lower values f o r t h e c o e f f i c i e n t c due t o t h e flow around Y t h e wing a t a v e l o c i t y Vef, which by c r e a t i n g l i f t becomes a component of t h e speed V ( s e e Figure 3 3 ) . When POS t h e speed o f the flow around t h e wing does not correspond t o t h e f l i g h t speed, t h e r e a r i s e s a l a t e r a l displacement of t h e a i r p a r t i c l e s i n t h e boundary l a y e r which, f o r t h e c e n t r a l s e c t i o n s of t h e wing, i s e q u i v a l e n t t o t h e e f f e c t which i s obtained when t h e boundary l a y e r i s Figure 16. Graphs f o r t h e blown away o r drawn off ( s e e Chapter V, C o e f f i c i e n t c f o r a Swept § 8). The s e p a r a t i o n of a i r p a r t i c l e s Y from t h e upper s u r f a c e i s p r o t r a c t e d A i r f o i l a t Small Mach Numbers ( 1 - w i n g w i t h t o very s u b s t a n t i a l angles of a t t a c k , geometric t w i s t o f 3 " , 2 and b e f o r e they are reached t h e r e i s a w i thout geomet r i c steady increase i n t h e c o e f f i c i e n t c Y t w i s t j a n d the C o e f f i c i e n t f o r t h e c e n t r a l p o r t i o n of the wing. c f o r the A i r c r a f t as a X Because of t h e g r e a t i n c l i n a t i o n of Function of the Angle of t h e curve c = f ( a ) t o the h o r i z o n t a l Attack. Y a x i s i n swept wings (as compared t o normal wings), t h e i n c r e a s e i n c as Y the angle of a t t a c k i s i n c r e a s e d by l o i t i s l e s s than t h a t f o r a normal wing, i . e . , l e s s than the g r a d i e n t of t h e i n c r e a s e f o r t h e l i f t c o e f f i c i e n t . This a l s o determines t h e lower l i f t i n g a b i l i t y of swept wings as compared t o normal s t r a i g h t wings. For swept wings, w i t h i n t h e range of angles o f a t t a c k -1.0" - (10-12)" 28
- 38. ( l i n e a r flow of t h e r e l a t i o n c = f (a) on each degree of i n c r e a s e a) t h e Y c o e f f i c i e n t c i n c r e a s e s by approximately 0.09 - 0.11. Y The angle of a t t a c k a t which t h e decreased growth of c i s encountered Y and t h e c h a r a c t e r i s t i c v i b r a t i o n s i n a i r c r a f t a r e observed i s c a l l e d t h e p e r m i s s i b l e angle of a t t a c k aper, while t h e l i f t c o e f f i c i e n t corresponding t o it i s c (Figure 1 7 ) . The v i b r a t i o n i n t h e a i r c r a f t begins a f t e r t h e Y Per b u r b l i n g begins at t h e wing t i p s and the vortex flow s t r i k e s t h e t a i l assembly. On t h e curve (Figure 17) r e f l e c t i n g t h e t o t a l change i n c f o r Y t h e wing as a f u n c t i o n of a, t h e angle /34 of a t t a c k corresponding t o t h e onset of v i b r a t i o n i s determined through t h e s t a r t of l o c a l flow s e p a r a t i o n a t t h e wing t i p ( i n t h e f i g u r e , t h i s c o r r e s ponds t o t h e p o i n t where Curve 2 begins . I I I I t o d e v i a t e from t h e s t r a i g h t l i n e ) . When C Y m a i s reached by t h e wing t i p s , i n s p i t e of t h e subsequent s h a r p decrease i n c a t these t i p s , c f o r t h e e n t i r e Y Y I wing begins t o i n c r e a s e as t h e angle of I a t t a c k does, although slower than a t t h e beginning of s e p a r a t i o n . The i n c r e a s e i n c takes p l a c e due t o t h e Y s e p a r a t i o n - f r e e flow a t t h e c e n t r a l p o r t i o n of t h e wing which occurs a t high angles of a t t a c k . For high Mach numbers , t h e c r i t i c a l angle of a t t a c k Figure 17. The C o e f f i c i e n t c may reach 3 0 - 3 5 ' . Y f o r Various P a r t s o f a Swept Wing as a Function o f the The a i r c r a f t s moving i n t o the v i b r a t i o n zone i n d i c a t e s t h a t low Angle o f Attack: 1 - c e n t r a l speeds have been a t t a i n e d , and i n t h i s portion; 2 - w i n g t i p ; 3 - w i n g a s a whole. case t h e v i b r a t i o n i s a warning f o r t h e pilot. In t h e zone of high angles o f a t t a c k , t h e r e i s a smooth change i n c Y' especially close to its maximum. As a r e s u l t of t h i s , i n t h e s h i f t t o s u p e r c r i t i c a l angles of a t t a c k , swept wings have l e s s o f a tendency toward a u t o r o t a t i o n than do s t r a i g h t wings. I n g e n e r a l , t h e swept wings on t r a n s p o r t a i r c r a f t have l e s s of a tendency toward s p i n . 29
- 39. Because of geometric t w i s t , t h e running value of t h e c o e f f i c i e n t c f o r Y t h e c h a r a c t e r i s t i c angles of attack during t a k e o f f , climb, h o r i z o n t a l f l i g h t , e t c . , decreases. As can b e seen from Figure 16, f o r t h e same angle of attack al, t h e wing's l i f t without geometric twist i s b e t t e r , and c > c This i s Y2 Yl' why f l i g h t i n aircraft with wings having geometric twist i s performed a t g r e a t e r angles o f a t t a c k t h a n with wings without t h i s t w i s t . § 2. T h e E f f e c t of t h e Mach Number on t h e Behavior of the Dependence c = f(c1) Y A i r c o m p r e s s i b i l i t y a f g e c t s t h e dependence o f t h e c o e f f i c i e n t c on t h e Y a n g l e o f a t t a c k . Because of c o m p r e s s i b i l i t y , an i n c r e a s e i n t h e f l i g h t Mach number of more than 0 . 4 - 0.5 i s accompanied by a q u a l i t a t i v e change i n t h e c h a r a c t e r of flow around t h e wing, because t h e speed o f t h e flow on t h e wing i n c r e a s e s , as a r e s u l t o f which f o r one and t h e same angle of a t t a c k t h e - /3 6 c o e f f i c i e n t c increases , i . e . , t h e r e i s an improvement i n t h e l i f t i n g Y c a p a b i l i t y of t h e wing. This i s c l e a r from Figure 18 ( i n which, f o r example purposes, t h e angle c1 = 4.5" has been s e l e c t e d ) . The angle of a t t a c k a t which v i b r a t i o n begins decreases with an i n c r e a s e i n t h e Mach number, because t h e v i b r a t i o n and t h e flow s e p a r a t i o n begins sooner t h a n a t low Mach numbers. Therefore, t h e value c a l s o decreases y vib with an i n c r e a s e i n t h e Mach number. For example, a t M = 0.65, t h e c o e f f i c i e n t C = 0.99, while a t M = 0.85 i t w i l l y vib equal 0.52 (Figure 19). In a d d i t i o n , C a l s o decreases s h a r p l y . If from Y M = 0.65 t h e c o e f f i c i e n t cy v i b d i f f e r s s l i g h t l y from c then a t M = 0.85 y m a ' t h e value c w i l l be s u b s t a n t i a l l y y vib less than c F l i g h t accompanied by y max' v i b r a t i o n u s u a l l y precedes t h e onset of i n s t a b i l i t y i n t h e a i r c r a f t with r e s p e c t t o overload, while a t c e r t a i n values g r e a t e r than c t h e v i b r a t i o n s can l e a d Y' IJil iI !5 t o s t a l l i n g a t c e r t a i n Mach numbers. ~~ d l !I !I 1 cf Therefore t h e v a l u e c a t which v i b r a t i o n 0 $54222i&79[ Y per begins i s v i t a l f o r f l i g h t purposes. Figure 18. The Affect of t h e I f f o r M = 0 . 4 - 0 . 5 t h e angle of Mach Number on the Dependence a t t a c k f o r t h e o n s e t of v i b r a t i o n (see c = f ( a ) : - - - wind- t u n n e l Y Figure 19) equals 12-13', then f o r M = tests; - f 1 i g h t tests. = 0 . 8 - 0.9 i t decreases t o 5-7', and C a l s o d e c r e a s e s . This i s e s p e c i a l l y y vib dangerous a t high Mach numbers because a t t h e same time as t h e onset of v i b r a t i o n s , s t a l l i n g may s e t i n . 30
- 40. I Figure 19. T h e Dependence of a v i b and c on t h e y vib Mach Number. In t h e event t h a t t h e s h i f t t o h i g h e r c i s n o t accompanied by t h e Y c h a r a c t e r i s t i c v i b r a t i o n (of i n d i v i d u a l s e c t i o n s of t h e wing) , t o forewarn t h e p i l o t t h a t t h i s s h i f t has occurred, s p e c i a l tubulence s e n s o r s a r e a t t a c h e d t o t h e wings. They t r a p t h e l o c a l flow s e p a r a t i o n s on t h e wing and t r a n s m i t t h e v i b r a t i o n t o t h e c o n t r o l wheel. This, f o r example, i s what was done on t h e B r i t i s h t u r b o j e t Comet, on which t h e sensors a r e s e t symmetrically on t h e leading edge of t h e c e n t e r s e c t i o n of t h e wing (Figure 20). O t h e n p i l o t ' s instrument panel t h e r e i s a s p e c i a l instrument which s i g n a l s t h e p i l o t ahead of time (before c has been reached) t h a t t h e y vib a i r c r a f t i s s h i f t i n g toward t h i s regime (see Chapter X I , § 15). § 3. The Permissible C o e f f i c i e n t c and Y Per i t s Dependence on the Mach Number F l i g h t s a f e t y i s achieved i n t u r b o j e t a i r c r a f t a t high a l t i t u d e s and Mach numbers through r e s t r i c t i n g the i n c r e a s e i n t h e l i f t c o e f f i c i e n t by t h e determined p e r m i s s i b l e values of c This i s necessary t o - /37 Figure 20. Positioning o f Y per' maintain l o n g i t u d i n a l s t a b i l i t y i n t h e a i r Sensors on the Wing of the c r a f t . Horizontal f l i g h t must be performed Comet A i r c r a f t . a t an a l t i t u d e and speed i n which t h e value C does not exceed c f o r a normal y hor Y Per i z e d v e r t i c a l wind s e p a r a t i o n . The v a l u e c i s s e l e c t e d such t h a t i t i s Y per always somewhat l e s s than c o r matches i t (Figure 18). From Figure 2 1 y vib i t can be seen t h a t , f o r example, f o r a Mach number of 0.65 t h e c o e f f i c i e n t C = 0.86, f o r M = 0.80 i t equals 0.635, etc. The less t h e degree of Y Per 31
- 41. sweep of t h e a i r f o i l , t h e g r e a t e r t h e value C Careful s e l e c t i o n of t h e p r o f i l e s Y per' permits improving t h e c o n d i t i o n s f o r flow around t h e wing and y i e l d s h i g h e r values of C Y Per' Such s e l e c t i o n of p r o f i l e s i s e s p e c i a l l y c h a r a c t e r i s t i c of second-generation turbo- j e t aircraft. of v i b r a t i o n -1 L - 1 . I 2 4 '' 43 o,b 0,s 0,s 07 . o.a H With high values f o r t h e Mach number, the coefficient c decreases t o almost Y Per h a l f i t s v a l u e , and a t M = 0.85 it reaches Figure 21. The C o e f f i c i e n t as low as 0.54. I n t h e zone of small Mach C as a Function of t h e numbers (up t o 0 . 4 6 ) , a v a l u e of c - - Y Per Mach Number (angle of sweep Y Per = 1 . 1 2 - 1 . 2 is used, which permits d e t e r x = 35"): -.-.-.- first mination of t h e lowest p e r m i s s i b l e speed generation a i r c r a f t ; _----- second-gene rat i on a i r c r a f t . f o r an a i r c r a f t with smooth wings (wing flaps retracted). Further, i n examining h o r i z o n t a l f l i g h t and t h e s t a b i l i t y and handiness of t h e a i r c r a f t , we s h a l l r e t u r n t o c and, i n a d d i t i o n , we s h a l l consider Y Per c1 Per and i t s r e p r e s e n t a t i v e Val es . § 4. Dependence of the C o e f f i c ent c on t h e Mach Number f o r F l i g h t a t a Y Cons tan t Ang le of A t tack In examining t h e e f f e c t of a i r c o m p r e s s i b i l i t y on t h e l i f t i n g p r o p e r t i e s of t h e a i r f o i l i n § 2 , we noted t h a t f o r a constant ( f l i g h t value) angle of a t t a c k , each Mach number i s matched by a s p e c i f i c v a l u e of c . Y A s can b e seen from Figure 22 ( t h e curve f o r a = 4 . 5 " ) , the c o e f f i c i e n t c i n c r e a s e s c o n s t a n t l y up t o a value of M = 0.83, and then decreases. The Y reason f o r such a change i n c i s due t o t h e e f f e c t of a i r c o m p r e s s i b i l i t y Y on t h e p r e s s u r e d i s t r i b u t i o n along t h e p r o f i l e ( s e e Figure 9 ) . Even with a Mach number of 0 . 4 i n t h e v e i n flowing over t h e p r o f i l e , increase i n v e l o c i t y i s accompanied by a marked decrease i n a i r d e n s i t y , which leads t o / 38 an a d d i t i o n a l i n c r e a s e i n t h e expansion above t h e upper s u r f a c e ( § 10 of Chapter I ) . O the lower s u r f a c e , t h e a f f e c t of a i r c o m p r e s s i b i l i t y �or n t h e s e Mach numbers has a l e s s e r e f f e c t , s o t h a t i n i t i a l l y t h e r e i s an increase i n the c o e f f i c i e n t c During t h e formation of a compression Y' shock, t h e l i f t i n g c a p a b i l i t y of t h e a i r f o i l d e c r e a s e s . Shock-induction s e p a r a t i o n leads t o a decrease i n expansion on t h e upper p o r t i o n of t h e a i r f o i l p r o f i l e , and c decreases. A t a given Mach number, when t h e r e i s a Y shock on the lower s u r f a c e as w e l l , i t begins moving back, a t f i r s t slowly 32
- 42. and then r a t h e r rapi-dly. As a r e s u l t , on t h e lower s u r f a c e t h e expansion zone w i l l i n c r e a s e as t h e r e s u l t of which t h e l i f t and, consequently, c as w e l l w i l l Y 0: - 2 O s t a r t t o decrease. Later, as a given Mach number, t h e shock on 3 I t h e upper s u r f a c e w i l l a l s o s t a r t 03 1 . 1 I I I I t o move back f a s t e r and f a s t e r , 0.4 0.3 48 47 48 49 fl which w i l l e n t a i l an i n c r e a s e i n t h e expansion zone and t h e c o e f f i c i e n t c - ~ . The values of Figure 22. T h e E f f e c t of Air Compressi- Y t h e Mach number a t which we b i l i t y on t h e C o e f f i c i e n t c a t a Y observe t h e i n i t i a l i n c r e a s e i n Constant A n g l e of Attack: 1,2 - s w e p t c-- and i t s subsequent drop and w i n g w i t h geometric t w i s t ; 3 - non- Y renewed i n c r e a s e (ffspoon'') swept w i n g . depend on t h e angle o f a t t a c k fo; t h e p r o f i l e and t h e a i r f o i l as a whole. A s can be seen from Figure 22, f o r s m a l l e r angles of a t t a c k (2-3O), t h e flow c i s smoother with r e s p e c t t o t h e Mach number and t h e Y 'lspoonlt i s only s l i g h t l y expressed. This f e a t u r e of the change i n c with r e s p e c t t o t h e Mach number - - t h e Y 'lspoonll - - explains t h e " i n v e r s e r e a c t i o n " of an a i r c r a f t ( i n banking) t o d e c l i n a t i o n i n the c o n t r o l wheel (Chapter X I , § 22). § 5. The Affect of t h e Mach Number on the C o e f f i c i e n t cx Let us analyze t h e formula f o r drag where S i s the wing a r e a . I f the angle of a t t a c k ct i s maintained c o n s t a n t , a t small Mach numbers drag w i l l vary p r o p o r t i o n a t e l y t o the square of t h e speed, w h i l e t h e drag / 39 c o e f f i c i e n t c a t t h e s e Mach numbers w i l l be p r a c t i c a l l y independent of speed X and w i l l vary only with r e s p e c t t o the angle o f a t t a c k . As we can s e e from Figure 16, f o r ct = 6-8O t h e c o e f f i c i e n t c = 0.038 - 0.05 ( a t small a l t i t u d e s X and speeds). However, t h e dependence of cx on only t h e angle of a t t a c k i s observed a t speeds a t which t h e e f f e c t of a i r c o m p r e s s i b i l i t y may b e ignored. With an i n c r e a s e i n f l i g h t speed, however, when c o m p r e s s i b i l i t y does s t a r t t o have an e f f e c t , t h e c o e f f i c i e n t cx i n c r e a s e s , and more s u b s t a n t i a l l y t h e f a s t e r t h e shock s t a l l on t h e p r o f i l e developes. The r e l a t i o n s h i p between t h e 33
- 43. development of t h e shock s t a l l and t h e i n c r e a s e i n t h e c o e f f i c i e n t cx may b e considered from Figure 23. Under Mach = 0.7, t h e c o e f f i c i e n t c is p r a c t i c a l l y X changeless. After t h e i f l i g h t (flow) Mach number exceeds i t s c r i t i c a l I v a l u e , l o c a l compression shocks b e g i n forming on t h e wing, wave drag appears, and a s h a r p i n c r e a s e i n t h e curve c X 1I b e g i n s . This makes i t c l e a r t h a t the g r e a t e r t h e a i r f o i l angle of attack (or the g r e a t e r t h e f l i g h t c ) , t h e lower Y the c r i t i c a l value f o r t h e Mach number. With an i n c r e a s e i n t h e Mach Figure 23. Dependence of t h e C o e f f i c i e n t cX number, t h e compression on t h e Mach Number f o r a S w e p t Wing. shocks a r e d i s p l a c e d toward t h e t r a i l i n g edge and become more powerful. A t Mach = 1.1 - 1.15, a normal shock appears i n f r o n t and shocks appu ar on p both t h e top and bottom of the t r a i l i n g p o r t i o n of t h e p r o f i l e . I t must b e noted t h a t an understanding of t h e c r i t i c a l Mach number, as r e l a t e d t o t h e appearance of t h e l o c a l speed of sound a t any p o i n t on a swept wing, has less of a p r a c t i c a l value than i t does f o r a s t r a i g h t wing. In g e n e r a l , the appearance of the l o c a l speed of sound on s t r a i g h t and swept wings does not immediately have a s i g n i f i c a n t e f f e c t on t h e aerodynamic p r o p e r t i e s , and w i l l not be n o t i c e d by t h e p i l o t . The c r i t i c a l Mach number f o r a swept wing and t h e a i r c r a f t as a whole /40 i s u s u a l l y r e l a t e d t o changes i n the t o t a l aerodynamic c h a r a c t e r i s t i c s and t h i s i s understood t o mean t h a t f l i g h t Mach number a t which t h e p i l o t becomes aware of t h e e f f e c t of a i r c o m p r e s s i b i l i t y on the handling q u a l i t i e s of h i s a i r c r a f t , i . e . , changes i n t h e s t a b i l i t y and handiness. The c r i t i c a l Mach number as determined from t h e s e conditions i s M = 0.82 - 0.88. A t such a Mach cr number, a i r c r a f t i n s t a b i l i t y i n terms of speed developes ( t h e “spoonrt on t h e balance curve) and t h e r e v e r s e r e a c t i o n ( i n terms of banking) t o d e c l i n a t i o n of t h e rudder a l s o appears. In f l i g h t p r a c t i c e , concepts a r e used such as t h e s o - c a l l e d l i m i t i n g Mach number, which the p i l o t m u s t know a b s o l u t e l y . I t is u s u a l l y equal t o 0.86 0.9. This Mach number can reasonably s a f e l y be s u b s t i t u t e d f o r t h e c r i t i c a l Mach numbers d i s c u s s e d e a r l i e r . I t should be p o i n t e d out t h a t i n aerodynamic c a l c u l a t i o n s , the c r i t i c a l 34
- 44. Mach number i s sometimes taken t o b e a f l i g h t Mach number whose i n c r e a s e by 0.01 l e a d s t o a 1%increase i n t h e a i r c r a f t ' s c o e f f i c i e n t cx. .According t o t h e l a t e s t formulas, t h e Mach number M = 0.78 - 0.80 f o r c r u i s i n g v a l u e s cr c = 0.25 Y - 0.30. For c Y = 0.35 - 0 . 5 a t c e i l i n g a l t i t u d e s , depending on t h e t a k e o f f weight t h e v a l u e Mcr d e c r e a s e s 0.70 - 0.74. As w a s s t a t e d above, when t h e Mach number i s i n c r e a s e d above Mcr, a large s u p e r s o n i c zone of flow appears on t h e p r o f i l e , t h e compression shock i s moved back and expansion i n t h e t a i l p o r t i o n of t h e p r o f i l e i s i n c r e a s e d and i n i t i a t e s an i n c r e a s e i n t h e c o e f f i c i e n t c F o r non-swept wings, f o r example, X' t h i s phenomenon occurs a t Mach numbers 0 . 0 4 = 0 . 1 below Mcr. For a f u r t h e r i n c r e a s e i n t h e Mach number above t h e c r i t i c a l v a l u e , t h e c o e f f i c i e n t c i n c r e a s e s as a r e s u l t of t h e i n c r e a s e i n t h e l o c a l speeds on X t h e lower p r o f i l e s u r f a c e , where a compression shock i s a l s o formed. A more i n t e n s e i n c r e a s e i n c i n non-swept wings occurs i n t h e range o f Mach numbers X from M to M = 1; with a s h i f t beyond M = 1, however, t h e c o e f f i c i e n t c cr x u s u a l l y decreases. For swept wings, t h e ma-ximun v a l u e of c corresponds t o X t h e Mach number M = 1.1 - 1.15. I t i s known t h a t wing drag i s compcunded from t h e p r o f i l e drag t h e induced drag Qi; t h e formation of compression shocks on t h e wing2! :lis t h e wave drag t o these. With r e s p e c t t o t h i s , t h e i n v e r t e d form o f %he formu1.a f o r t h e drag c o e f f i c i e n t w i l l b e t h e f o l l o w i n g : c = c + c + cxw' x xp xi where c, i s t h e c o e f f i c i e n t of p r o f i l e drag f o r zero lift, and i s cornpiled xp from .the drag of t h e a i r F r i c t i o n on t h e wing s u r f a c e and t h e drag caused by .the d i f f e r e n c e between a i r p r e s s u r e s on t h e leading and t r a i l i n g p o r t i o n s of %he wing. The p r o f i l e drag f o r t h e wing /41 a t small Mach numbers can b e s t b e e s t a b l i s h e d from f r i c t i o n whose v a l u e i s only s l i g h t l y dependent on t h e angle of a t t a c k * ; a t high angles of a t t a c k t h e s e p a r a t i o n drag i s added t o t h e f r i c t i o n drag and t h e c o e f f i c i e n t i n c r e a s e s s h a r p l y : c = c -- c ! xp x fric x pres' c i s t h e c o e f f i c i e n t of induced drag, which i s a f u n c t i o n of t h e xi wing l i f t ; i t i s d i r e c t l y p r o p o r t i o n a l t o t h e s q u a r e of t h e l i f t c o e f f i c i e n t and i n v e r s e l y proportional. t o t h e wing a s p e c t r a t i o : 1 CL l2 c xi = 2 (here X = ~TX -- S wing a s p e c t r a t i o , 1 - span, and S - Wing a r e a ) ; .__ * A. P . Mel'nikov. High-speed Aerodynamics (Aerodinamika b o l t s h i k h s k o r o s t e y ) , Voyeni z d a t , 1961. 35
- 45. c i s t h e wave drag c o e f f i c i e n t . xw Induced and wave drag a r e by n a t u r e p r e s s u r e drags. When wave drag developes, t h e c o e f f i c i e n t cx i n c r e a s e s 3-6 times f o r s t r a i g h t wings and 40 70% f o r swept wings as compared t o i t s v a l u e s f o r slow speeds. Thus, t h e o n s e t of compression shocks leads t o an i n t e n s e i n c r e a s e i n t h e c o e f f i c i e n t cx because wave drag is added t o t h e normal p r o f i l e drag and induced drag. § 6. Wing Wave Drag I t w a s e s t a b l i s h e d e a r l i e r t h a t an i n c r e a s e i n t h e f l i g h t speed above c r i t i c a l leads t o t h e appearance of a new, a d d i t i o n a l form of drag c a l l e d p r o f i l e wave drag. To explain t h e n a t u r e of t h i s drag, l e t us once more examine the p i c t u r e of t h e p r e s s u r e d i s t r i b u t i o n along the upper wing s u r f a c e f o r subsonic flow a t sub- and s u p e r c r i t i c a l f l i g h t speeds (Figure 14 and 24). A s can be s e e n , i n Figure 24 one s e c t i o n of t h e expansion v e c t o r s s o r t of "draw" t h e pro- - /42 f i l e forward, while t h e - '+cr - - Y VZ v cr o t h e r draws i t back. To e v a l u a t e what would happen -L --4 -d - x=- t o t h e wing under t h e a f f e c t o f t h e s e "pulling" f o r c e s , a l l expansion v e c t o r s must be pro- F i g u r e 24. Examples o f Wave Drag. i ected i n the d i r e c t i o n of f l i g h t . When t h i s i s done we s e e t h a t a t sub- c r i t i c a l speeds t h e f o r c e s "pulling" forward a r e n e g l i g i b l y l e s s than those "pulling" back (Figure 24a). With an i n c r e a s e t o s u p e r c r i t i c a l speeds, t h e p r e s s u r e d i s t r i b u t i o n p i c t u r e changes (Figure 24b), as a r e s u l t of which t h e f o r c e s "pulling" the p r o f i l e forward decrease (expansion becomes l e s s a t t h e bow of t h e p r o f i l e ) while t h e f o r c e s "pulling" back i n c r e a s e (because expansion on the t r a i l i n g s l o p e of t h e p r o f i l e i n c r e a s e s by an a b s o l u t e v a l u e ) . From t h e f i g u r e i t i s c l e a r t h a t t h e d i f f e r e n c e i n t h e p r o j e c t i o n s of t h e v e c t o r s of the "pulling" f o r c e s d i r e c t e d t o t h e r e a r i n c r e a s e s , causing an i n c r e a s e i n drag. However, because t h e e x t e n t of t h e s u p e r s o n i c zones over and under t h e wing i n c r e a s e s as f l i g h t speed i n c r e a s e s , t h e r e i s an even g r e a t e r displacement of t h e l a r g e s t expansion toward t h e rear and t h e t r a i l i n g edge. The f o r c e s "pulling" t h e p r o f i l e forward i n c r e a s e a t t h e same time t h e p r e s s u r e on the leading edge of t h e p r o f i l e i n c r e a s e s . To sum up, t h e wing drag continues t o i n c r e a s e . Thus, t h e wave drag i s by n a t u r e a p r e s s u r e drag because i t i s dependent on t h e i n c r e a s e i n t h e p r e s s u r e d i f f e r e n c e i n f r o n t of t h e wing and behind i t . Therefore, i n aerodynamics wave drag has come t o mean t h e a d d i t i o n a l drag 36
- 46. 111 I - caused by an i n c r e a s e i n the p r e s s u r e d i f f e r e n c e s i n f r o n t of t h e wing and behind i t when t h e r e a r e supersonic zones of flow and compression shocks on t h e airf o i 1 p r o f i l e " . This drag i s c a l l e d t h e wave drag because t h e process of t h e development of s u p e r s o n i c zones of flow is accompanied by t h e development of shock waves o r compression shocks. From t h e e n e r g e t i c viewpoint, wave r e s i s t a n c e i s t h e r e s u l t of t h e d e c e l e r a t i o n of a i r flows on t h e compression shocks. When t h i s occurs, t h e k i n e t i c energy of t h e flow i s i r r e v e r s i b l y consumed i n h e a t i n g t h e a i r i n t h e shock . As can b e seen from Figure 25b, i n t h e range o f c r u i s i n g f l i g h t Mach numbers, the v a l u e of t h e wave drag c = 0.004 - 0.012 o r f o r t h e mean value xw c = 0.025, i t w i l l equal 25 - 50% ( f o r a i r c r a f t ) . X A t s u p e r s o n i c f l i g h t speeds (Mach z 1 - 1 . 2 , Figure 25a), a i r d e c e l e r a t i o n on t h e bow a d t a i l compression shocks decreases because t h e angles of i n c l i n a t i o n of t h e s e shocks decrease, which means t h a t t h e wave drag i t s e l f decreases. A t s u p e r c r i t i c a l Mach numbers, a i r c r a f t drag i n c r e a s e s i n t e n s e l y because i t i s a f u n c t i o n of both cx and V 2 . From t h e same f i g u r e we s e e t h a t a t a constant angle of a t t a c k , t h e drag f o r c e below M = 0.5 i n c r e a s e s as a parabola,& while beyond t h i s Mach number t h i s l u l l does n o t hold, and t h e curve d e v i a t e s from t h e square p a r a b o l a , which i s the r e s u l t of t h e e f f e c t of c o m p r e s s i b i l i t y and the development of compression shock. Figure 25. Dependence of t h e C o e f f i c i e n t cx on the Mach Number ( a ) a n d the E f f e c t of t h e Relative P r o f i l e Thick ness on Ac f o r the Wing ( b ) . xw * A. P . Mel'nikov. High-speed Aerodymamics (Aerodinamika b o l ' s h i k h skorostey) , Voyenizdat, 1961. 37 I
- 47. 9 7. Interference The i n c r e a s e i n . a i r c r a f t f l i g h t speeds has l e d t o an i n c r e a s e i n t h e importance o f i n t e r f e r e n c e , i. e . , t h e combined e f f e c t of v a r i o u s p a r t s of t h e a i r c r a f t such as t h e wing and t h e f u s e l a g e . Usually i n t e r f e r e n c e leads t o an s u b s t a n t i a l i n c r e a s e i n drag, e s p e c i a l l y i n t h e zone of t r a n s o n i c f l i g h t speeds. I t has been experimentally e s t a b l i s h e d t h a t " p o s i t i v e " i n t e r f e r e n c e can be achieved. This i s t h e i n t e r f e r e n c e which a i d s in. decreasing t h e a d d i t i o n a l drag r e s u l t i n g from t h e p o i n t s where t h e v a r i o u s a i r c r a f t components are joined. Turbojet passenger a i r c r a f t are b a s i c a l l y low-wing a i r c r a f t . When t h e wing and f u s e l a g e are j o i n e d i n t h i s way, t h e u s e of f a i r i n g s h e l p s t o smooth t h e j u n c t i o n p o i n t of the wing and f u s e l a g e t o a c e r t a i n degree. P o s i t i o n i n g the engines i n t h e b a s e of t h e wing ( s e e Chapter I V , § 8) as w a s done on t h e Tu-1.04, Tu-124 and Comet a i r c r a f t c r e a t e s an e j e c t o r e f f e c t -- an " a c t i v e f a i r i n g " -- a t t h e j u n c t i o n p o i n t f o r o p e r a t i n g engines. * Another way of decreasing t h e drag i s using t h e " r u l e of area," which i s a l s o a p p l i c a b l e f o r subsonic a i r c r a f t . With r e s p e c t t o t h i s r u l e , drag i n f l i g h t v e h i c l e s proves t o be minimal when t h e law of v a r i a t i o n s i n c r o s s - s e c t i o n s with r e s p e c t t o l e n g t h c o r r e s ponds t o the l a w of v a r i a t i o n s i n c r o s s - s e c t i o n s with r e s p e c t t o t h e l e n g t h G� a body of r e v o l u t i o n of l e a s t drag. I t i s w e l l known t h a t drag from t h e combination of t h e wing and f u s e l a g e (and o t h e r p a r t s of t h e f l i g h t v e h i c l e ) will be t h e same as e q u i v a l e n t drag, i . e . , drag having t h e same l a w f o r v a r i a t i o n s i n c r o s s - s e c t i o n with r e s p e c t t o length of a body of r e v o l u t i o n . Therefore vinimal drag may be achieved through decreasing t h e c r o s s - s e c t i o n of t h e f u s e l a g e ('ssqueezingtt), a t t h e p o i n t where i t j o i n s t h e wing, by a value equal t o t h e area of t h e corresponding wing c r o s s - s e c t i o n s (Figure 26) O r i g i n a l body, "r f cr Figure 26. Examples of t h e Use of t h e "Area Law": a - "fuselage - w i n g " combination without a1 lowance f o r t h e area law; b and c - the same combination w i t h allowance f o r t h e "area law." i-- * S.M. Yeger. Designing Passenger J e t A i r c r a f t (Proyektirovaniye p a s s a z h i r skikh reaktivnyk'n samoletov) . Mashinostroyeniye, 1964. 38
- 48. The "area l a w " i s a l s o a p p l i c a b l e t o t h e j u n c t i o n of engine n a c e l l e s , e x t e r n a l l y suspended f u e l t a n k s and o t h e r a i r c r a f t components. Thus, f o r example, on t h e Tu-104 and Tu-124 a i r c r a f t having wings with a r e l a t i v e l y high wing a s p e c t r a t i o , t h e wing and f u s e l a g e i n t e r f e r e n c e i s somewhat decreased by t h e s u b s t a n t i a l d i s t a n c e of the wing t i p s from t h e f u s e l a g e ; as a r e s u l t , i n s t e a d of thickening t h e f u s e l a g e behind t h e wing, drop-shaped n a c e l l e s a r e i n s t a l l e d on t h e wing. This y i e l d s a smoother change i n t h e volume of t h e a i r c r a f t along i t s length without modifying t h e f u s e l a g e . On t h e Convair 990, t h e r e are f o u r n a c e l l e s which a r e used t o c a r r y f u e l . A s a r e s u l t t h i s a i r c r a f t has achieved a maximum c r u i s i n g Mach number of 0.91. I t is f e l t t h a t allowance f o r t h e "area law!' i n designing a i r c r a f t can improve t h e i r f l i g h t q u a l i t i e s by 20-25%. I n some c a s e s , however, observance of t h i s law has proven u n s u i t a b l e due t o complications and d i f f i c u l t i e s i n designing t h e f u s e l a g e which have r e s u l t e d i n t h e need f o r curvature of i t s power p l a n t s . 5 8. T h e A i r c r a f t Polar. The E f f e c t of t h e Landing Gear and W i n g Mechanization on t h e Polar The p o l a r of an a i r c r a f t s e r v e s i n e v a l u a t i n g the a i r c r a f t ' s aerodynamics. I t o f f e r s a g r a p h i c r e p r e s e n t a t i o n of t h e values of the c o e f f i c i e n t s c and Y & a t various angles of a t t a c k , as w e l l as i n d i c a t i n g t h e i r v a r i a t i o n s when X t h e s e angles change. Figure 27'shows t h e p o l a r s of one a i r c r a f t obtained as t h e r e s u l t o f wind / 45 t u n n e l t e s t i n g and r e f i n e d with r e s p e c t t o d a t a from f l i g h t t e s t i n g . Let us determine t h e c h a r a c t e r i s t i c angles of attack and t h e i r corresponding aero dynamic parameters. The p o i n t of i n t e r s e c t i o n of t h e p o l a r a with t h e axis of t h e a b s c i s s a i s determined by t h e z e r o - l i f t angle of a t t a c k a0 = 1' and i t s corresponding c o e f f i c i e n t c = 0.018 ( f o r a r e l a t i v e a i r f o i l p r o f i l e xo thickness of c= 10 - 1 2 % ) ; f o r c= 1 2 - 15% t h e c o e f f i c i e n t cxo= 0.021 0.023. The small value f o r cxo i s obtained through t h e c r e a t i o n of a well s t r e a m l i n e d shape f o r t h e a i r c r a f t with a small c e n t e r s e c t i o n f o r t h e f u s e l a g e and engine n a c e l l e s . The aerodynamic t e s t s as t o t h e degree of refinement i n t h e a i r c r a f t i s i t s e f f i c i e n c y . Modern a i r c r a f t have a maximum e f f i c i e n c y of K = 15 - 18 a t t h e optimum angle of a t t a c k of 5-7" and Mach numbers of M < 0 . 5 . A air n c r a f t ' s l i f t drag r a t i o i n c r e a s e with an i n c r e a s e i n t h e angle of a t t a c k from /46 cio t o t h e optimal c1 because a t t h i s p o i n t c i n c r e a s e s f a s t e r than cx. opt' Y S t a r t i n g with an angle of 5-7", t h e c o e f f i c i e n t cx i n c r e a s e s more r a p i d l y (due to t h e i n c r e a s e i n t h e induced drag) and t h e r e f o r e t h e performance drops. Later i t w i l l b e shown t h a t ci i s t h e d i v i s i o n p o i n t between two f l i g h t opt 39
- 49. regimes: t h e f i r s t and t h e second. For t h e p o l a r a ( s e e Figure 27), a = 7 at c = O opt Y 0.55, w h i l e K = 17.2. When t h e landing g e a r i s lowered, t h e p o l a r moves t o t h e r i g h t ( p o l a r b i n Figure 27) because t h e c o e f f i c i e n t c increases t o the value X After t h e landing g e a r lg' i s r e t r a c t e d , t h e w e l l doors a r e normally c l o s e d s o t h a t AC = 0.015 - 0.020 and t h e x 1g l i f t i n g a b i l i t y of t h e wing does not change. As a r e s u l t t h e s e t t i n g f o r t h e angle of a t t a c k f o r p o l a r b remains t h e same as f o r p o l a r a. The maximum performance f o r an a i r c r a f t with landing g e a r extended decreases i n our case t o 12, while a increases t o 8.5O. opt Figure 27. A i r c r a f t P o l a r s : a - landing When t h e landing g e a r and g e a r and w i n g f l a p s withdrawn; b - landing wing f l a p s are extended ( i n g e a r down; c - landing g e a r and w i n g f l a p s 1anding c o n f i g u r a t i o n ) t h e extended i n landing c o n f i g u r a t i o n . p o l a r moves t o t h e r i g h t and upward ( p o l a r c i n Figure 27), and t h e c o e f f i c i e n t ci n c r e a s e s throughout t h e range o f angles of a t t a c k , t h e Y z e r o - l i f t angle of a t t a c k becomes n e g a t i v e (a = - 6 O ) , and t h e maximum p e r 0 formance of the a i r c r a f t decreases as a r e s u l t of t h e f a c t t h a t t h e c o e f f i c i e n t c i n c r e a s e s t o a g r e a t e r degree than t h e c o e f f i c i e n t c X . Y When t h e wing f l a p s are i n t h e t a k e o f f c o n f i g u r a t i o n , t h e maximum p e r formance (landing g e a r down) decreases t o 10-12 (Figure 65). I n g l i d i n g toward t h e landing with landing g e a r and wing f l a p s down i n t h e landing c o n f i g u r a t i o n , t h e performance decreases t o 7-8. Extending t h e a i r brake moves t h e graph of t h e p o l a r t o t h e r i g h t , as t h e r e s u l t of which t h e performance decreases s u b s t a n t i a l l y , p a r t i c u l a r l y i n g l i d i n g a t angles o f attack of 2-3', a t which t h e landing run i s made. Displacing t h e hinged f l a p s p o i l e r s causes a s h a r p e r drop i n t h e a i r c r a f t performance (see Figure 107). 40
- 50. J § 9. T h e E f f e c t of t h e Mach Number on t h e A i r c r a f t P o l a r For each f l i g h t Mach number w e may c o n s t r u c t a p o l a r by determining f o r t h i s value c and c with an allowance made f o r t h e e f f e c t o f c o m p r e s s i b i l i t y X Y and thereby o b t a i n t h e p o l a r n e t (Figure 2 8 a ) . E a r l i e r it w a s e s t a b l i s h e d t h a t a t s u b c r i t i c a l f l i g h t speeds t h e wing c o e f f i c i e n t cx i s almost i n v a r i a b l e , while t h e l i f t c o e f f i c i e n t c i n c r e a s e s s t a r t i n g a t M = 0.5 - 0.6. Therefore, Y with an i n c r e a s e i n t h e Mach number t o M t h e p o l a r i s p u l l e d forward cr’ because of t h e i n c r e a s e i n cy and i n t h e region of high angles of a t t a c k i s simultaneously s h i f t e d t o t h e r i g h t due t o t h e i n c r e a s e i n cx as a r e s u l t of an i n c r e a s e i n t h e induced drag. This i s c l e a r l y shown i n p o l a r s f o r Mach numbers 0.8 and 0.84 (wing with c= 12 - 15%). As i s w e l l known, aerodynamic performance / 47 A t s u p e r - c r i t i c a l f l i g h t speeds a t which t h e wave drag i n c r e a s e s s u b s t a n t i a l l y , f o r a s p e c i f i c Makh number t h e Dolar moves t o t h e r i g h t and i n c r e a s e s t h e s h i f t t o t h a t s i d e ( i n Figure 2ia, t h i s corresponds i o Mach number of M = 0.84) as a r e s u l t o f a decrease in c I f , however, t h e Y‘ K Mach number i s s o g r e a t t h a t t h e r e i s wave drag !J a t almost every angle of a t t a c k , t h i s Mach number ! - 6 /’ / ( f o r any c ) has an Y i n c r e a s e d value o f cx and - i$ t h e p o l a r proves t o be iz only s h i f t e d t o t h e r i g h t ( i n Figure 28a, t h e p o l a r 70 - f o r t h e Mach number 0.9). This b e a r s witness t o t h e decrease i n t h e maximum performance of t h e a i r c r a f t , as can be seen i n Figure 28. A i r c r a f t Polars and Dependence t h e f i g u r e , i n which a r e o f Aerodynamics Performance K on Mach given t h e tangents t o t h e numbers . p o l a r s and t h e angles f o r performance O 2 > O1. I n arranging t h e p o l a r n e t , we may c o n s t r u c t a graph f o r t h e dependence o f performance on c f o r v a r i o u s Mach numbers (Figure 28b). Usually maximum Y performance i s o b t a i n e d f o r v a l u e s of c which a r e 20-30% g r e a t e r than t h e Y 41
- 51. v a l u e f o r c i n h o r i z o n t a l f l i g h t . If a t M < 0.5 t h e m a x i m u m performance Y K = 15-17, then a t M = 0.8 it w i l l equal approximately 12-14.5. As can b e seen from Figure 29, f o r Mach numbers M = 0 . 8 - 0.84, Kmax = 12-14 and only a t high Mach numbers does i t decrease t o 11-12. High aerodynamic performance i n an a i r c r a f t has a f a v o r a b l e e f f e c t on t h e volume o f f u e l consumed p e r kilometer. ---_ The a f f e c t o f wing sweep i s t h a t with/48 an i n c r e a s e i n t h e angle of sweep, t h e ’ aerodynamic performance decreases a t low f l i g h t speeds and i n c r e a s e s a t high 47 48 n f l i g h t speeds. The parameters f o r second-generation a i r c r a f t wings a t c r u i s i n g Mach numbers of M = 0.8 - 0.85 Figure 29. Maximum Aerodynamic have been s e l e c t e d such t h a t K = 13-14 Performance as a Function of i s achieved (Figure 29). Mach Number: ----- f i r s t - generation a i r c r a f t ; ~ I t i s w e l l known t h a t f o r each Mach various second-generation ai r- number, a high-speed a i r c r a f t has i t s craft. own r e l a t i o n between t h e c o e f f i c i e n t cx and c Y . If f o r v a r i o u s Mach numbers we i n t r o d u c e i n t o the p o l a r network values of c f o r h o r i z o n t a l f l i g h t ( f o r Y s p e c i f i c weight and a l t i t u d e ) and then j o i n t h e s e p o i n t s , we o b t a i n t h e p o l a r f o r h o r i z o n t a l f l i g h t regimes ( t h e dot- and dash l i n e i n Figure 28a), which e s t a b l i s h e s a r e l a t i o n s h i p between c x’ cy’ t h e Mach number and t h e h o r i z o n t a l f l i g h t a l t i t u d e . I t i s c l e a r from t h e p i c t u r e t h a t t h i s p o l a r i n t e r s e c t s a l l t h e working p o l a r s f o r Mach numbers from 0.5 t o 0.84. The h i g h e r t h e Mach number, t h e lower t h e c a t which t h i s i n t e r s e c t i o n occurs. In o t h e r words, Y t h e h i g h e r t h e f l i g h t Mach number, t h e lower t h e v a l u e of c r e q u i r e d f o r horizontal f l i g h t . Y 42
- 52. CHAPTER I l l SOME FEATURES OF W I N G C O N S T R U C T I O N §I. Means of Increasing t h e C r i t i c a l Mach Number The i n c r e a s e i n drag a s t h e Mach number Mcr i s r a i s e d i s an unusual b a r r i e r which makes i t d i f f i c u l t t o achieve high f l i g h t speeds. Therefore, t e s t s have been run on aerodynamic shapes of a i r c r a f t a t which t h e shock s t a l l would begin a t t h e h i g h e s t p o s s i b l e f l i g h t Mach number and would be maintained a s long as p o s s i b l e smoothly, i . e . , s o t h a t means of i n c r e a s i n g t h e c r i t i c a l Mach number f o r t h e p r o f i l e could be achieved. The c r i t i c a l Mach number f o r t h e p r o f i l e may be detemhined according t o t h e following empirical formula: M =1-0.71/c-3.2cc,’ - -15 , CT where c is t h e r e l a t i v e t h i c k n e s s of t h e p r o f i l e ; c i s t h e l i f t c o e f f i c i e n t f o r t h e angle o f a t t a c k under c o n s i d e r a t i o n . Y Let us b e a r i n mind t h a t t h e c h a r a c t e r i s t i c parameters f o r t h e a i r f o i l p r o f i l e a r e (Figure 30): r e l a t i v e thickness a - t h e r a t i o of t h e maximum p r o f i l e t h i c k n e s s cmax t o t h e chord b ; t h e p o s i t i o n of t h e maximum p r o f i l e t h i c k n e s s zc% t h e - relative distance of t h e maximum p r o f i l e t h i c k n e s s x from t h e nose t o t h e chord b; C t h e r e l a t i v e p r o f i l e c u r v a t u r e % - t h e r a t i o of maximum buckle f t o t h e chord b ; t h e d i s t a n c e from t h e p r o f i l e nose t o t h e p-i n t o f maximum p r o f i l e curv o ature x expressed i n u n i t s of t h e chord b , - x f % . j’ Let us examine t h e e f f e c t of each of t h e s e parameters on t h e M number. cr The e f f e c t of c. The p r o f i l e t h i c k n e s s has a d i s t i n c t e f f e c t on t h e v a l u e o f t h e d r a g . The g r e a t e r i t i s , t h e g r e a t e r t h e degree t o which t h e a i r stream surrounding t h e p r o f i l e i s compressed, and consequently t h e sooner t h e shock s t a l l w i l l occur a t lower Mach numbers. In c o n t r a s t , decreasing t h e p r o f i l e t h i c k n e s s d i s p l a c e s t h e moment when t h e shock s t a l l occurs t o a h i g h e r Mach number. Figure 31 g i v e s a c l e a r example of t h e degree t o which t h e t h i n n e s s of t h e p r o f i l e r e s u l t s i n a g r e a t e r c r i t i c a l Mach number M cr’ 43
- 53. 4' Figure 30. Geometric Parameters and Shapes of an Air f o i 1 Profi le: a - p r o f i le w i t h p o s i t i v e c u r v a t u r e ; b- symmetrical prof i le; c - "inverted" prof i le w i t h nega t.ive c u r v a t u r e (Douglas DC-8). A i r c r a f t wings c a r r y f u e l , with t h e r e s u l t t h a t t h e r e l a t i v e p r o f i l e thickness i s 10 t o 15%. This i s necessary t o o b t a i n s u f f i c i e n t volume and maintain wing strength. As an example, l e t us determine t h e /50 - -- c r i t i c a l Mach number f o r p r o f i l e s with r e l a t i v e t h i c k n e s s e s of 10 and 15% i f = 0.3. Calculations show t h a t f o r 3 c = lo%, Mcr = 1 - 0 . 7 4' c - 3.2Fc 1.5 - Y = 1 - 0 . 7 m - 3.2.0.1 - 0 . 3 = 0.722, ~ ~ ~ Figure 31. T h e E f f e c t of Air- while f o r c= 15% M = 1 - 0 . 7 m cr f o i 1 P r o f i l e Thickness on t h e C o e f f i c i e n t c f o r Various Mach - 3.2'0.15 : 0.3l.' = 0.651. As w e can numbers. X see from t h i s example, t h e lower t h e r e l a t i v e p r o f i l e thickness, t h e g r e a t e r t h e c r i t i c a l Mach number. When t h e r e i s a change i n t h e angle of a t t a c k , and consequently t h e v a l u e c ( f o r example, l e t us t a k e Y c Y = 0 . 4 and c = l o % ) , we o b t a i n a d i f f e r e n t v a l u e f o r t h e c r i t i c a l Mach number M:Mcr = 1 - 0 . 7 m - 3.2 ' 0.10 - 0.4 1.5 - = 0.691. Thus, an i n c r e a s e i n t h e Mach number ( c ) has l e d t o a decrease i n Y from 0.722 t o 0.691. This i s explained by the f a c t t h a t as t h e angle o f a t t a c k i n c r e a s e s , t h e upper a i r stream i s compressed s t r o n g e r by t h e p r o f i l e . The straight-away s e c t i o n s i n t h e stream decrease more i n t e n s e l y , as a r e s u l t t h e v e l o c i t y i n c r e a s e s more s h a r p l y , and t h e speed of sound i s a t t a i n e d a t a lower Mach f l i g h t number. This i s why an i n c r e a s e i n t h e f l i g h t a l t i t u d e (an i n c r e a s e i n c ) decreases t h e c r i t i c a l Mach number. Y Second-generation a i r c r a f t have a i r f o i l p r o f i l e s from c = 10-12%, which makes i t p o s s i b l e t o i n c r e a s e t h e c r u i s i n g Mach f l i g h t number t o 0.8 - 0.85 44
- 54. without a s u b s t a n t i a l i n c r e a s e i n drag. Usually t h e optimum c r u i s i n g f l i g h t speed corresponds t o Mcr o r less. The e f f e c t of a p o s i t i v e maximum thickness and t h e r e l a t i v e p r o f i l e curvature. I t has been experimentally e s t a b l i s h e d t h a t with i d e n t i c a l wing t h i c k n e s s e s , t h e p r o f i l e which has a h i g h e r c r i t i c a l Mach number Mcr is -e th one i n which t h e maximum t h i c k n e s s i s c l o s e r t o t h e c e n t e r , . i . e . , f o r x = 35-50%. This i s explained by t h e f a c t t h a t with such a v a l u e f o r Fc, C t h e r e i s a smoother p r o f i l e contour, and consequently a smoother change i n p r e s s u r e and v e l o c i t y along i t (Figure 32). A decrease i n t h e p r o f i l e curvature has a favorable e f f e c t on t h e aerodynamic c h a r a c t e r i s t i c s a t high f l i g h t speeds. A symmetrical p r o f i l e (Figure 30,b), i n which T = 0 , o t h e r conditions being t h e same, as a h i g h e r c r i t i c a l Mach number. However, i n such p r o f i l e s t h e v a l u e s f o r c Y max a r e small (by comparison with asymmetric p r o f i l e s ) , s o t h a t t h e i r u s e on t r a n s p o r t a i r c r a f t i s Figure 32. E f f e c t of t h e Position of t h e d i f f i c u l t . Recent y e a r s have shown Maximum A i rfoi 1 P r o f i l e Thickness on t h e a broader u s e of t h e s o - c a l l e d C r i t i c a l Mach Number M c r : a - p r o f i l e "inverted" p r o f i l e , i e. , a . without r a r e f a c t i o n peak; b - p r o f i l e p r o f i l e having n e g a t i v e c u r v a t u r e w i t h r a r e f a c t i o n peak. (Figure 3 0 , c ) . These p r o f i l e s , u s u a l l y used i n t h e b a s i c s e c t i o n of t h e a i r f o i l , s a t i s f a c t o r i l y s o l v e t h e problem of t h e h i g h l y complex i n t e r f e r e n c e between t h e wing and t h e f u s e l a g e , c r e a t i n g smooth flow. The p h y s i c a l n a t u r e of t h e e f f e c t of r e l a t i v e c u r v a t u r e on t h e v a l u e M i s the same as the e f f e c t of t h e t h i c k n e s s . cr Decreasing t h e maximum p r o f i l e t h i c k n e s s , s h i f t i n g i t t o t h e middle of /51 t h e chord, and decreasing the p r o f i l e curvature a l l i n c r e a s e t h e v a l u e of t h e c r i t i c a l Mach number by a t o t a l of 0.02 - 0.06. The e f f e c t of wing sweep. The optimum e f f e c t i n i n c r e a s i n g t h e c r i t i c a l Mach number i s achieved through t h e use of swept wings. As wing sweep i n c r e a s e s t o 3S0, t h e c r i t i c a l Mach number i n c r e a s e s by 0.07 - 0 . 0 8 as compared with t h e c r i t i c a l Mach number f o r a s t r a i g h t wing o r profile. Let us s e e how t h i s i s achieved. The l i f t of t h e wing and t h e t a i l assembly is determined by t h e v a l u e of t h e aerodynamic f o r c e of the p r e s s u r e s a r i s i n g as a r e s u l t of changes i n t h e l o c a l flow v e l o c i t i e s induced by t h e e x t e r n a l contours of t h e p r o f i l e across t h e e n t i r e wingspan o r t a i l span. 45
- 55. L e t us expand t h e f l i g h t speed V over two components: one, perpen- POS d i c u l a r t o t h e leading edge* of t h e wing -- Vef, and t h e o t h e r d i r e c t e d along the leading edge o f t h e wing -- VI (Figure 33,a). The component Vef (effective speed) determines t h e v a l u e of t h e l o c a l speeds and expansions along t h e pro f i l e , and consequently t h e value of t h e l i f t as w e l l . The component V1 i s n o t involved i n t h e c r e a t i o n of t h e aerodynamic p r e s s u r e f o r c e s . I t does have an e f f e c t on t h e boundary l a y e r and, consequently, on t h e flow s e p a r a t i o n . I n conjunction w i t h t h e fact t h a t Vef i s always lower t h a n Vpos, t h e l o c a l speed of sound w i l l be achieved l a t e r and, consequently, t h e c r i t i c a l Mach number w i l l be g r e a t e r . The shock s t a l l on t h e p r o f i l e w i l l s e t i n a t a h i g h e r f l i g h t speed. This means t h a t t h e c r i t i c a l Mach number i n swept wings w i l l always b e g r e a t e r t h a n i n s t r a i g h t wings o r t h e p r o f i l e . The c r i t i c a l Mach number f o r a swept wing, w i t h allowance made f o r t h e e f f e c t of flow c h a r a c t e r i s t i c s on t h e p r e s s u r e d i s t r i b u t i o n along t h e span, - /52 may be determined from t h e formula: 2 M crX = *cr.prof 1 + cos x J where x i s t h e angle of sweep f o r t h e wing. F o r wings having a sweep of 35' (cos 35' = 0.821, t h e formula assumes t h e following form: M c r X - 3 ~= '*' 0 Mcr.prof . For example, f o r a r e l a t i v e p r o f i l e t h i c k n e s s of lo%, we o b t a i n a Mach number McrX.350 = 0.795. W must b e a r i n e mind t h a t t h e e m p i r i c a l formula f o r determining t h e c r i t i c a l Mach number o f f e r s an e r r o r of 1 5 2 0 % . Along i t s span, t h e a i r c r a f t wing has changing values r e l a t i v e t o t h e t h i c k n e s s . Therefore, t h e c r i t i c a l Mach number a l s o has v a r i o u s v a l u e s . The e f f e c t of wing sweep, by i n c r e a s i n g t h e c r i t i c a l Mach number, i s decreased a t t h e p o i n t where t h e c e n t r a l s e c t i o n of t h e wing j o i n s t h e f u s e l a g e . Here t h e wing i s s u b j e c t e d n o t t o oblique a i r f l o w ( r e s u l t i n g from decomposition of t h e i n c i d e n t flow i n t o two components), b u t t o s t r a i g h t a i r flow. The c r i t i c a l Mach number i s i n c r e a s e d through i n c r e a s i n g t h e sweep of t h e c e n t r a l p o r t i o n of t h e wing along t h e leading edge. Thus, i f t h e angle x = 30-3S0, i n t h e c e n t r a l s e c t i o n of t h e wing i t reaches 40-45', i . e . , t h e wing i s given a "crescent" shape i n planform. The Tu-104 and Tu-124 a i r - / 53 craft have a s l i g h t l y expressed "crescent" shape. .- . . . -. . .. - .... .... * S t r i c t l y speaking, Vef is perpendicular t o t h e aerodynamic c e n t e r l i n e MN, and t h e component V1 i s d i r e c t e d along t h i s l i n e , because t h e wing i s looked upon as t a p e r i n g . Our allowance has been made f o r s i m p l i c i t y i n exp 1anati on. 46
- 56. shock k c) 1 V m Figure 33. Development of F l i g h t Speed on Swept Wing and P o s s i b l e P o s i t i o n s of the Leading Wing d g e Relative t o t h e Mach Cone: 1 - subsonic leading edge -- w i n g located w i t h i n cone (subsonic f l o w ) ; I I - s o n i c leading edge (flow a t t h e speed o f sound); I I I - supersonic leading edge ( s u p e r s o n i c f l o w ) . The c r i t i c a l Mach number f o r t h e wing i n passenger a i r c r a f t i s below u n i t y . For c l a r i t y i n r e p r e s e n t a t i o n , we w i l l show t h a t f o r a wing with t h i n p r o f i l e s (F = 4-6%) , a t an angle x = 55-60" t h e c r i t i c a l Mach number, determined according t o t h e formula a l r e a d y p r e s e n t e d , may be g r e a t e r than u n i t y . However, f o r an i s o l a t e d p r o f i l e , as has already been noted, t h i s i s imp os s i b l e . The shock s t a l l i n a swept wing occurs l a t e r , and n o t simultaneously throughout t h e wingspan, and l e s s i n t e n s e l y than on a s t r a i g h t wing; i n a d d i t i o n , i t does n o t l e a d t o a s h a r p change i n the t o t a l aerodynamic c h a r a c t e r i s t i c s of t h e a i r c r a f t . A t various p o i n t s on t h e wing, t h e shock s t a l l developes i n d i f f e r e n t ways. Recent s t u d i e s have shown t h a t i n t h e c e n t e r of t h e wing t h e shock s t a l l begins l a t e r than a t t h e t i p s , but because of t h i s i n c r e a s e s more i n t e n s e l y . As a r e s u l t , t h e n e g a t i v e e f f e c t of t h e c e n t r a l p o r t i o n of t h e wing i s f e l t n o t s o much i n t h e s e n s e of a decrease i n t h e c r i t i c a l Mach numbe.r as a more r a p i d i n c r e a s e i n t h e wave drag than a t t h e wing t i p s , although i t starts t o i n c r e a s e sooner on t h e t i p s . There i s s u b s t a n t i a l l y l e s s wave drag i n a swept wing than i n a s t r a i g h t one, which may be c l a r i f i e d t h u s l y . 47
- 57. L e t us assume t h a t l o c a l compression shocks a r i s i n g i n p r o f i l e s from which t h e wing i s shaped s t a r t a t t h e l i n e MN (Figure 33,b). I n each p r o f i l e , t h e l o c a l shock w i l l b e normal, whil'e f o r t h e whole,wing t h e t o t a l shock, a l s o l o c a t e d along t h e l i n e MN, w i l l b e o b l i q u e (with r e s p e c t t o t h e i n c i d e n t flow). As has already been s t a t e d , t h e shock s t a l l developes more weakly when t h e r e i s an oblique shock. The shock f r o n t i s l o c a t e d along t h e l e a d i n g edge of a swept wing a t t h e i n s t a n t when Vef becomes equal t o t h e l o c a l speed of sound. On a wing with a sweep angle x = 3S0, t h i s occurs a t a f l i g h t Mach number e q u a l t o 1.22. Let us show t h i s . As can b e seen from Figure 33,a, t h e speed Vef = V cos 35O. L e t us POS equate it t o t h e speed of sound: a = V POS cos 3S0, i . e . , a = 0.821 V pos ' then - V M = E = a V 0.821 - - 1.22. Thus, a wing with x = 35O may be used a l s o f o r POS s l i g h t s a t low s u p e r s o n i c speeds. As can b e seen from Figure 33,c, a Mach cone forms a t t h e t i p of t h e angle forming t h e leading wing edge when a swept wing encounters s u p e r s o n i c flow. This Mach cone assumes t h e form of an o b l i q u e compression shock. If t h e leading wing edges l i e w i t h i n t h e Mach cone, they a r e c a l l e d subsonic. With r e s p e c t t o t h e degree t o which t h e s u r f a c e o f t h e Mach cone approaches t h e leading edge, t h e wave drag r a t i o i n c r e a s e s and reaches it h i g h e s t value / 54 a t t h e i n s t a n t when t h e l e a d i n g edges meet t h e cone s u r f a c e . When t h e r e i s a f u r t h e r i n c r e a s e i n t h e speed, t h e leading edges o f t h e wing go beyond t h e boundary of t h e Mach cone, a f t e r which t h e s u r f a c e s of t h e Mach cone move away from t h e edges. In t h i s case, t h e leading edges a r e c a l l e d supersonic. Passenger a i r c r a f t designed i n r e c e n t y e a r s have an optimum angle x = 20-35' and a mean r e l a t i v e thickness of 10-12%. The u s e of a g r e a t e r sweep angle ( p a r t i c u l a r l y one equal t o 45O) i s i n a d v i s a b l e i n terms o f a weight-drag r a t i o f o r t h e wing because of t h e onset o f torque and, a d d i t i o n a l l y , because of poorer t a k e o f f and landing conditions caused by a lower value f o r Use of a wing with a 35' sweep r e s u l t s i n a 10-25% drop i n wave drag f o r f l i g h t s a t M = 0.80 - 0.85, which s u b s t a n t i a l l y decreases t h e o v e r a l l drag. A t t h e same time it becomes p o s s i b l e t o maintain t h e l i f t - d r a g r a t i o f o r t h e a i r c r a f t w i t h i n l i m i t s of 13-15. The effect o f t h e sweep angle on t h e c o e f f i c i e n t c i s given i n Figure 34. X I n a d d i t i o n t o t h e parameters a l r e a d y d i s c u s s e d , t h e wing a s p e c t r a t i o X a l s o has a determining e f f e c t on t h e c r i t i c a l Mach number. A s u b s t a n t i a l i n c r e a s e i n t h e c r i t i c a l Mach number r e s u l t s f o r A = 1 - 1.5. In wings with small aspect r a t i o s ( A = 1 . 5 - 2 . 5 ) , t h e c r i t i c a l Mach number i s g r e a t e r than i n wings with high aspect r a t i o s ( A = 5-8). This i s explained b a s i c a l l y by t h e s o - c a l l e d end e f f e c t . 48
- 58. f ' ~-without flow / Figure 34. T h e E f f e c t of t h e Figure 35. T h e E f f e c t of Airflow Past Sweep A n g l e on t h e Dependence t h e W'ing T i p s on Pressure D i s t r i b u t i o n cx = f(M). over t h e Upper Surface. During f l i g h t , p r e s s u r e below t h e wing i s g r e a t e r t h a n above it. There f o r e , t h e r e i s an overflow of a i r a t t h e wingtip from t h e region of g r e a t e r p r e s s u r e toward t h a t of l e s s e r p r e s s u r e , i . e . , a c e r t a i n p r e s s u r e balance takes p l a c e , thanks t o which t h e m a x i m u m r a r e f a c t i o n over t h e wing decreases (Figure 3 5 ) . The i n f l u e n c e of t h e end e f f e c t i s s u b s t a n t i a l only c l o s e t o the /55 wingtip. If t h e wing aspect r a t i o is decreased, t h e r e l a t i v e length of t h e s e s e c t i o n s i n c r e a s e s and t h e end e f f e c t i s spread over a l a r g e s e c t i o n of t h e wing. F o r passenger a i r c r a f t a t an angle x = 3 S 0 , t h e optimum X = 6-8; t h e r e f o r e t h e c r i t i c a l Mach number i n t h i s case undergoes no change. § 2. Features of Flow Around S w e p t Wings I n t h e preceding s e c t i o n , which examined t h e development of t h e speed we s i m p l i f i e d t h e p i c t u r e of t h e flow around a swept wing. Actually, ",os however, t h i s p i c t u r e assumes a complex s p a t i a l scheme. Let us spend some time d i s c u s s i n g t h e v a r i o u s b a s i c moments. To t h i s end, l e t us examine a i r streams flowing around t h e middle and end p o r t i o n s of t h e wing (Figure 36). As a r e s u l t of t h e s p a t i a l c h a r a c t e r of t h e flow of t h e stream as we approach t h e c e n t e r s e c t i o n of t h e wing, i t becomes wider. A s a r e s u l t of t h e c o n s t a n t a i r consumption along t h e stream, t h i s leads t o a decrease i n speed i n t h e c e n t e r s e c t i o n of t h e p r o f i l e , and consequently t o a decrease i n t h e r a r e f a c t i o n over t h e r i s i n g p a r t of t h e p r o f i l e i n t h e middle of t h e wing. O t h e descending p a r t t h e r e i s a c o n s t r i c t i o n of t h e stream and a consequent n r i s e i n speed and i n c r e a s e i n r a r e f a c t i o n . Thus, i n t h e middle s e c t i o n of t h e wing t h e r a r e f a c t i o n s d e c r e a s e on t h e r i s i n g s e c t i o n of t h e p r o f i l e , while they i n c r e a s e on t h e descending s e c t i o n . A t t h e t i p s of swept wings, t h e p i c t u r e i s reversed. Here t h e streams approaching t h e wing a r e f i r s t c o n s t r i c t e d , which leads t o an i n c r e a s e i n v e l o c i t 5 e s on t h e r i s i n g p r o f i l e s e c t i o n . As a r e s u l t , r a r e f a c t i o n s on t h e 49
- 59. -- leading p r o f i l e s e c t i o n s i n c r e a s e . As t h e p r o f i l e descends, t h e stream s t a r t s broadening, which leads t o a decrease i n v e l o c i t i e s and r a r e f a c t i o n . P r chords Figure 3 6 . Representative Character Figure 37. Representative P i c t u r e of f o r t h e F l o w o f Air Streams i n the Pressure D i s t r i b u t i o n a t Various Middle and a t t h e Ends o f a S w e p t Wing. Sections along t h e Win.g: 1 - a t t h e t i p s ; 2 - i n t h e middle of t h e semi- span; 3 - i n the c e n t r a l s e c t i o n . Figure 37 shows t h a t at: the c e n t e r s e c t i o n s of t h e wing, t h e maximum /56 r a r e f a c t i o n i s d i s p l a c e d t o the rear, whereas a t t h e t i p s e c t i o n s , i n c o n t r a s t , t h e g r e a t e s t r a r e f a c t i o n i s found a t t h e leading p a r t of t h e pro f i l e . In a d d i t i o n , t h e v a l u e of t h e r a r e f a c t i o n peak i s h i g h e r a t t h e t i p s than i n t h e c e n t e r and base s e c t i o n s . Therefore, t h e t i p s e c t i o n s o f t h e wing a r e more loaded (have g r e a t e r l i f t ) than due t h e b a s e s e c t i o n s . The observed f e a t u r e o f p r e s s u r e d i s t r i b u t i o n along t h e chord of t h e wing Leads a l s o t o another d i s t r i b u t i o n of load along t h e span ( i n c o n t r a s t t o s t r a i g h t wings). Figure 38 shows t h e load d i s t r i b u t i o n along t h e span of swept and IC,ljec s t r a i g h t wings, as w e l l as changes i n t h e maximum values of the coefficient c y s e c max sec f o r v a r i o u s wing s e c t i o n s * . I - . -. The d i f f e r e n c e i n t h e j f l a t wing I c h a r a c t e r i s t i c f o r t h e change.I in c i n s t r a i g h t and y s e c max swept wings i s explained i n t h e following manner. The Figure 38. Diagram of Load D i s t r i b u t i o n overflow of air p a s t t h e wing Along t h e Span of a Swept and a S t r a i g h t t i p from t h e lower t o t h e Wing: -..-geometric t w i s t ; -.- aero- upper s u r f a c e i n a s t r a i g h t dynamic t w i s t ; -f l a t w i n g . wing has an e f f e c t only on a * Pashkovskiy, I . M . C h a r a c t e r i s t i c s of S t a b i l i t y and C o n t r o l l a b i l i t y i n High- Speed A i r c r a f t (Osobennosti us t o y c h i v o s t i i upravlyayemos ti skoros tnogo samoleta) . Voyenizdat. 1961 50
- 60. small s e c t i o n , as a r e s u l t of which t h e value c i s i d e n t i c a l almost y s e c max everywhere on t h e span and only toward t h e wing t i p s does it s t a r t t o decrease. I n swept wings, however, t h e decrease i n c from t h e base t o t h e t i p y sec max i s r e l a t e d n o t only t o t h e overflow of a i r p a s t t h e t i p b u t a l s o with t h e nonsimultaneous i n c r e a s e i n t h e flow s e p a r a t i o n along t h e span. This s e p a r a t i o n i s h i g h l y dependent on t h e a i r overflow i n t h e boundary l a y e r due t o t h e component V1 ( s e e Figure 3 3 , a ) . Therefore, t h e end s e c t i o n s of the swept wing undergo s e p a r a t i o n b e f o r e a l l t h e o t h e r s , i . e . , they a r e t h e f i r s t t o /57 a t t a i n t h e values c y s e c max' As can b e seen from t h e f i g u r e , t h e end s e c t i o n s of the swept wing achieve c f a s t e r than do t h e s e c t i o n s of t h e c e n t e r and b a s e y s e c max p o r t i o n s of t h e wing. In s t r a i g h t wings, on t h e o t h e r hand, cy max i s reached e a r l i e r i n t h e c e n t e r s e c t i o n of t h e wing. Therefore, with an i n c r e a s e i n t h e angle of attack t h e flow s e p a r a t i o n reaches t h e end s e c t i o n s of t h e swept wing and t h e c e n t e r s e c t i o n s of t h e s t r a i g h t wing sooner. In a d d i t i o n , t h e o v e r a l l end flow s e p a r a t i o n on t h e swept wing f a c i l i t a t e s t h e speed V which causes t h e boundary l a y e r t o move 1' Coward t h e wing t i p and causes i t t o thicken. The boundary l a y e r seems t o be i n a sense sucked from t h e c e n t e r s e c t i o n and b u i l t up a t t h e ends of the wing. The "swelling" o f t h e boundary l a y e r and the premature s e p a r a t i o n a t the wing t i p s is one of the b a s i c drawbacks o f swept wings. The end flow s e p a r a t i o n leads t o t h e development of t h e p i t c h i n g moment, which a f f e c t s t h e l o n g i t u d i n a l s t a b i l i t y of t h e a i r c r a f t a d v e r s e l y , e s p e c i a l l y a t slow f l i g h t speeds. Flow s e p a r a t i o n i n t h e a i l e r o n zone leads t o a drop i n t h e l a t e r i a l handiness. Along with end flow s e p a r a t i o n , a t low f l i g h t speeds ( g r e a t e r than t h e angle of a t t a c k ) , such a s e p a r a t i o n i s p o s s i b l e a l s o a t high speeds a t low angles o f a t t a c k , which i s explained by t h e i n t e r a c t i o n of compression shocks with t h e boundary l a y e r during f l i g h t a t high a l t i t u d e s . A s i n well known, a t high a l t i t u d e s f l i g h t i s performed a t high angles o f a t t a c k ( t o o b t a i n t h e necessary v a l u e f o r c ) . With an i n c r e a s e i n t h e angle of a t t a c k , t h e Y hf v a l u e f o r t h e c r i t i c a l Mach number decreases. When t h e angle c1 i n c r e a s e s due t o v e r t i c a l g u s t s , compression shocks may form e a r l i e r (because t h e c r i t i c a l Mach number i s low), which a i d s i n t h e development of flow s e p a r a t i o n . In a l l t h e s e cases , during s e p a r a t i o n t h e r e i s t h e c h a r a c t e r i s t i c v i b r a t i o n , and i n some cases t h e r e i s even p i t c h i n g down. R e d i s t r i b u t i o n of load along the span of a swept ( i n c o n t r a s t t o a s t r a i g h t ) wing always leads t o a displacement o f t h e e q u i v a l e n t aerodynamic f o r c e of t h e wing backward o r forward along t h e chord, and t h e r e f o r e i s accompanied by a change i n i t s l o n g i t u d i n a l moment. As can be seen from Figure 39, when t h e wing i s swept, each s e c t i o n i s 51 I
- 61. d i s p l a c e d r e l a t i v e t o each o t h e r i n such a way t h a t i n t o t o t h e p o i n t s of a p p l i c a t i o n o f t h e i n c r e a s i n g aerodynamic f o r c e s f o r t h e s e s e c t i o n s form a /58 l i n e which i s i n c l i n e d along t h e p e r p e n d i c u l a r t o t h e a x i s o f t h e wing ( t h e a x i s oz) by angle x. The d i s t a n c e from t h e a x i s oz t o t h e p o i n t s of a p p l i c a t i o n of t h e aerodynamic f o r c e s f o r t h e s e s e c t i o n s d i f f e r according t o span. I n s t r a i g h t wings, on t h e c o n t r a r y , t h e p o i n t s of a p p l i c a t i o n of t h e i n c r e a s i n g aerodynamic f o r c e s f o r t h e s e c t i o n s l i e p r a c t i c a l l y on a s t r a i g h t l i n e p a r a l l e l t o t h e a x i s , i.e. , they a r e e q u i d i s t a n t from t h e l a t e r i a l a x i s of t h e wing i n a l l s e c t i o n s a c r o s s t h e span. This f e a t u r e f o r t h e load d i s t r i b u t i o n along t h e span i n swept wings changes s u b s t a n t i a l l y e i t h e r with F i g u r e 39. Example of t h e a change i n t h e angle of attack o r a change i n E f f e c t of Load D i s t r i b u t i o n t h e Mach number. Along t h e Span on t h e Longitudinal Moment of a From Figure 40 we s e e t h a t an i n c r e a s e S w e p t Wing. i n IY, leads t o a g r e a t e r load on t h e c e n t r a l s e c t i o n o f t h e swept wing and a l i g h t e n i n g o f i t s end s e c t i o n s . In t h i s c a s e , t h e p r e s s u r e c e n t e r f o r t h e wing s h i f t s forward along t h e chord, which c r e a t e s a tendency taward p i t c h i n g . The onset of p i t c h i n g corresponds t o t h e moment of t h e onset of s e p a r a t i o n , which s t a r t s a t t h a t s e c t i o n of t h e wing where t h e a i l e r o n a r e located. I f t h e r e i s a change i n t h e Mach number and a remains c o n s t a n t , t h e r e i s a l s o a r e d i s t r i b u t i o n of load along t h e span. This i s accompanied by an unequal development of shock s t a l l on t h e wing i n t h e process o f reaching and s u r p a s s i n g c r i t i c a l speed. As we can s e e from Figure 40, an i n c r e a s e i n t h e f l i g h t speed up t o c r i t i c a l leads f i r s t t o a c e r t a i n loading o f t h e end s e c t i o n s o f t h e swept wing. Then, w i t h t h e development o f t h e shock s t a l l a t a Mach number somewhat g r e a t e r than MCr, t h e end s e c t i o n s s t a r t l o s i n g t h e i r load. The i n i t i a l i n c r e a s e i n t h e loading o f t h e end s e c t i o n leads t o t h e development of a s l i g h t diving moment , i . e . , t o a change i n t h e longi t u d i n a l s t a b i l i t y * . Subsequent changes i n t h e load d i s t r i b u t i o n a r e brought about through t h e propagation of t h e shock s t a l l along t h e upper wing s u r f a c e t o t h e base and middle s e c t i o n s of t h e c a n t i l e v e r s , as w e l l as t h e development of t h e s t a l l on t h e lower wing s u r f a c e . A l l t h i s leads t o a c e r t a i n d i s placement o f t h e wing p r e s s u r e c e n t e r (P.c.) forward along t h e chord and t h e appearance of a p i t c h i n g moment a t Mach numbers g r e a t e r than c r i t i c a l , b u t less than u n i t y ( s o n i c s p e e d s ) . D i s t i n c t changes i n t h e load d i s t r i b u t i o n along t h e span of a swept wing may a l s o l e a d t o i t s f l e x i b l e deformation (buckling and t w i s t i n g ) . In t h e event of deformation, t h e l o c a l angles of a t t a c k a t various p o i n t s along - * Pashkovskiy, I . M . C h a r a c t e r i s t i c s o f S t a b i l i t y and C o n t r o l l a b i l i t y i n High- Speed A i r c r a f t (Osobennosti us t o y c h i v o s t i i upravlyayemosti skorostnogo samoleta). Voyenizdat. 1961 52 I
- 62. t h e wing change d i s s i m i l a r l y , because t h e degree of t h e s e changes i s a f u n c t i o n of t h e aerodynamic f o r c e s a c t i n g on t h e wing. These l a t t e r , i n t u r n , are f u n c t i o n s of t h e angle of a t t a c k , f l i g h t speed and Mach number. iv /View along w i n g Figure 40. Change i n t h e Load Figure 41. Decrease i n A n g l e of Attack D i s t r i b u t i o n Along t h e Span o f f o r Bend i n a Swept Wing: a - non a S w e p t Wing as a Function of deformed f l e x u r a l a x i s ; b - f l e x u r a l the A n g l e o f Attack and t h e a x i s o f cranked w i n g . Mach Number. I n t h e event of buckling o f a swept wing (Figure 41) r e l a t i v e t o t h e 0-0 a x i s , t h e p o i n t s 1 ani 3 , lying c l o s e t o t h i s a x i s , w i l l have l e s s of a v e r t i c a l displacement than p o i n t s 2 and 4. A s a r e s u l t of t h i s , t h e chords 1 - 2 and 3-4 a r e turned r e l a t i v e t o t h e f l e x u r a l axis by a c e r t a i n a n g l e , and / 59 t h e e n t i r e wing t u r n s t o t h e s i d e o f t h e decrease i n t h e angle of a t t a c k . Thus, f o r a wing with normal sweep, i n t h e event of t w i s t i n g induced by aerodynamic loads d i r e c t e d upward from below, t h e r e is always a decrease i n t h e angle o f a t t a c k of t h e wing s e c t i o n the c l o s e r t h i s given s e c t i o n i s t o the end of t h e wing. This a l s o aggravates p i t c h i n g , i n t h a t t h e end s e c t i o n s have s m a l l e r angles of a t t a c k and, consequently, lower values f o r cy s e c ' This f a c t , along with t h e forward displacement of the p r e s s u r e c e n t e r as t h e angle of a t t a c k and speed i n c r e a s e , may a l s o l e a d t o a i r c r a f t i n s t a b i l i t i e s w i t h i n a s p e c i f i c range of Mach numbers. 5 3. Wing Construction i n Turbojet Passenger A i r c r a f t I n designing a i r c r a f t f o r c r u i s i n g Mach numbers of 0 . 8 - 0.85, s t r i c t a t t e n t i o n m u s t be given t o t h e s e l e c t i o n of wing parameters. W are a l r e a d y e familiar with c e r t a i n parameters, and now w e s h a l l continue our examination. I t has been e s t a b l i s h e d t h a t f o r subsonic passenger a i r c r a f t , t h e optimum 53
- 63. parameters a r e an angle of x = 35' and a wing a s p e c t r a t i o of A = 6 - 8 . With such values f o r A , f l i g h t d i s t a n c e i s s u b s t a n t i a l l y i n c r e a s e d . Narrowing t h e wing i n planform IT = bbas i s decided through t h e s e l e c t i o n / 60 end of conditions y i e l d i n g b e s t s t a b i l i t y c h a r a c t e r i s t i c s and c h a r a c t e r i s t i c s o f l o n g i t u d i n a l s t a b i l i t y , s o as t o e l i m i n a t e s e p a r a t i o n flows a t t h e wing t i p s . For a 3' sweep, t h e optimal s e l e c t i o n i s T = 3 . 5 - 4.5*. 5 I The remaining wing parameters are s e l e c t e d from c a l c u l a t i o n of t h e optimal l i f t p r o p e r t i e s f o r t h e wing. I t has been e s t a b l i s h e d t h a t t h e dependence of t h e c o e f f i c i e n t c (as Y w e l l as t h e c o e f f i c i e n t f o r t h e l o n g i t u d i n a l moment m Z , Figure 140) on t h e angle a proceeds l i n e a r l y t o avib, a t which p o i n t t h e r e are l o c a l flow s e p a r a t i o n s on t h e wing and t h i s r e l a t i o n i s no longer v a l i d . This leads t o t h e f a c t t h a t a t high angles of a t t a c k t h e r e i s a decrease i n l o n g i t u d i n a l s t a b i l i t y ( i n Figure 140, t h i s corresponds t o t h e s o - c a l l e d !'balance p o i n t " ) . The d i s r u p t i o n i n l o n g i t u d i n a l s t a b i l i t y i s q u i t e r e p r e s e n t a t i v e of swept wings. I t i s troublesome n o t only i n t h a t i t a f f e c t s t h e l o n g i t u d i n a l s t a b i l i t y of t h e aircraft a d v e r s e l y , b u t i n a d d i t i o n t h e flow s e p a r a t i o n from the wing t i p s decreases t h e e f f e c t i v e n e s s of t h e a i l e r o n s and asymmetric s e p a r a t i o n may r e s u l t i n p i t c h i n g down. Therefore, i n e s t a b l i s h i n g t h e aerodynamic arrangement of t h e swept wings i n passenger a i r c r a f t , maximum c r u i s i n g f l i g h t speeds and minimum landing speeds a r e achieved through holding t h e development of t h e flow s e p a r a t i o n t o t h e h i g h e s t p o s s i b l e angles of a t t a c k and t h e h i g h e s t Mach numbers. The following means a r e used t o achieve t h i s . 1. The aerodynamic t w i s t of t h e wing -- t h e s e l e c t i o n of t h e wing design from v a r i o u s p r o f i l e t y p e s , t h e p r o f i l e s o f f e r i n g t h e lowest l i f t being a t t h e base of t h e wing, while those with t h e g r e a t e s t l i f t a r e a t t h e t i p s . This r e s u l t s from t h e change c h a r a c t e r i s t i c f o r c with r e s p e c t t o t h e y s e c max wing dimensions (Figure 38). The s e l e c t i o n of p r o f i l e s with g r e a t e r l i f t f o r t h e wing t i p s (with T = 2 . 5 - 3% and g r e a t e r ) w i t h t h e r e v e r s e p o s i t i o n i n g of maximum thickness ( y = 35 - 50%) permits a c e r t a i n i n c r e a s e i n c C y s e c max a t t h e wing t i p s and, at t h e same time, i n c r e a s i n g t h e angle of a t t a c k and thereby achieving c y sec m a ' Symmetrical p r o f i l e s (sometimes with s l i g h t curvature) o r p r o f i l e s with n e g a t i v e c u r v a t u r e - - "inverted" p r o f i l e s -- a r e p o s i t i o n e d a t t h e base of t h e wing The DC-8, Convair 880, t h e Boeing-707 and t h e VC-10 have "inverted" . * Yeger, S.M. Design of Passenger J e t A i r c r a f t (Proyektirovaniye p a s s a z h i r skikh reaktivnykh samelotov) . Mashinostroyeniye. 1964. 54
- 64. p r o f i l e s i n t h e c e n t e r s e c t i o n s o f t h e wing. This has n o t hindered t h e o v e r a l l lift of t h e wing and has made i t p o s s i b l e t o use p r o f i l e s with 7 = 12-15% without a s i g n i f i c a n t i n c r e a s e i n cx a t high f l i g h t Mach numbers. 2. Geometrical t w i s t i s t h e gradual s p i r a l e f f e c t ( p o s i t i o n i n g a t a / 61 s m a l l e r angle) of t h e wing t i p s and middle wing s e c t i o n s r e l a t i v e t o t h e b a s e a t an angle of 2-5O ( f o r example, i f t h e angle i s + 3 O a t t h e wing base, while it i s -1" a t t h e wing t i p , t h e t w i s t angle equals -4'). This changes t h e l i f t d i s t r i b u t i o n along t h e span toward t h e s i d e of g r e a t e r load f o r t h e wing b a s e and unloading f o r t h e wing t i p s . During f l i g h t , t h i s type wing may achieve h i g h e r angles of a t t a c k ( c a l c u l a t e d with r e s p e c t t o t h e chord of t h e b a s e p r o f i l e ) b e f o r e t h e wing t i p s reach s e p a r a t i o n . Figure 16 shows t h a t t h e geometrical t w i s t has an affect on t h e extension of t h e r e l a t i o n c = f ( a ) , moving i t t o t h e r i g h t . Y Having e s t a b l i s h e d t h e geometric t w i s t , w m u s t t a k e i n t o account t h e e bending and warping of t h e wing, as shown i n Figure 41, s o as t o not o b t a i n negative l i f t a t the t i p s . I t w a s noted e a r l i e r t h a t with geometric t w i s t , t h e r e q u i r e d c is Y 1g achieved a t a s l i g h t l y h i g h e r f l i g h t angle of a t t a c k . 3 . P o s i t i o n i n g aerodynamic b a f f l e s 16-20 cm high (an average of 2-4% of t h e l o c a l wing chord, Figure 42) on t h e upper wing s u r f a c e . The b a f f l e s s e p a r a t e t h e wing i n t o p o r t i o n s and h i n d e r t h e overflow of a i r i n t h e boundary l a y e r along t h e wing span, r e s u l t i n g i n a decrease i n t h e thickness of t h e boundary l a y e r i n the t i p s e c t i o n s . This leads t o an i n c r e a s e i n the l o c a l values f o r c i n t h e end s e c t i o n s (by comparison t o a wing without y s e c mqx b a f f l e s ) , and consequently aids i n holding o f f t h e onset o f flow s e p a r a t i o n i n t h e s e s e c t i o n s u n t i l t h e high angles of a t t a c k . Figure 42, Arrangement o f Aerodynamic Baffles on Upper Wing Surface: 1 - l i n e of 1 / 4 chord; 2 - p o i n t of onset of flow s e p a r a t i o n and burbling; 3 - a i l e r o n ; 4 - b a f f l e ; 5 - a i r stream (enlarged s c a l e ) ; 6 , - v o r t i c e s s e p a r a t i n g from w i n g w i t h b a f f l e s ; 7 - p o s s i b l e b a f f l e shape. In t h e wing s e c t i o n c l o s e s t t o t h e f u s e l a g e (between t h e b a f f l e s and t h e 55
- 65. -- f u s e l a g e ) t h e r e i s a t h i c k e n i n g of theqboundary l a y e r and a d e c r e a s e i n C Lateral flows arise w i t h i n t h e l i m i t s of only one s e c t i o n , y sec m a ' v o r t i c e s form a t t h e b a f f l e s , and t h e boundary l a y e r flows o f f w i t h t h e s e . - / 62 Thus, because of t h e l a t e r a l overflow of air i n t h e boundary l a y e r when t h e wing i s equipped with b a f f l e s , t h e i n i t i a l flow s e p a r a t i o n on t h e wing s e c t i o n between t h e b a f f l e s and t h e f u s e l a g e i s maintained and s e p a r a t i o n from t h e o u t e r s e c t i o n o f t h e b a f f l e s and t h e wing t i p s i s f o r e s t a l l e d . Because the tendency toward s e p a r a t i o n of t h e boundary l a y e r weakens, t h e r e i s an improvement i n t h e l i f t d i s t r i b u t i o n along t h e wing span. The s e p a r a t i o n zone i s d i s p l a c e d toward the middle s e c t i o n s and, i n some i n d i v i d u a l cases, even toward t h e base of t h e wing. Aerodynamic b a f f l e s have been i n s t a l l e d on t h e wings of t h e Tu-104, Tu-124, Tu-134 and C a r a v e l l e aircraft . A similar e f f e c t is c r e a t e d by t h e pylons which support t h e engines on such a i r c r a f t as t h e Boeing-707, t h e Douglas DC-8 and t h e Convair 880 ( s e e Figure 65). However, pylons behave b a s i c a l l y l i k e b a f f l e s on t h e lower wing s u r f a c e , where t h e r e i s s u b s t a n t i a l l y l e s s cross c u r r e n t i n t h e boundary l a y e r . Only t h a t p o r t i o n o f t h e pylon which captures t h e upper wing s u r f a c e a t i t s nose has an e f f e c t on t h e wing. The 11-62 has swept wings with s o - c a l l e d "notches" i n t h e leading edge (Figure 4 3 ) . The "notch" forms a constant vortex cord on t h e wing s u r f a c e which acts i n t h e same manner as an aerodynamic b a f f l e , i n c r e a s i n g t h e b u i l d up o f t h e boundary l a y e r behind i t s e l f with t h e r e s u l t t h a t i t does not overflow t o t h e wing t i p . There are o f course o t h e r means f o r t i g h t e n i n g s e p a r a t i o n s from t h e wing a t low speeds, and they w i l l be discussed i n Chapter V, § 8. The Boeing-707, t h e DC-8 and o t h e r a i r c r a f t t i g h t e n t h e flow through t h e use of vortex g e n e r a t o r s . Their b a s i c purpose is t h e c r e a t i o n of a system of - /63 v o r t i c e s f o r a c t i v a t i n g the boundary l a y e r (Figure 44). F i g u r e 43. Positioning o f "Notches" on t h e Leading Edge o f a Swept Wing. 56
- 66. I d i r e c t i o n of vortex rotation Figure 44. P o s i t i o n i n g o f F l o w Vortex Generators on t h e Wing o f t h e Boeing-707 (h = 10-12 cm, 01 = I S " , 1 = 15-30 cm, D = 40-60 cm). The p r i n c i p l e behind t h e a c t i o n of v o r t e x generators i s based on t h e f a c t t h a t a system o f v o r t i c e s having a p a r a l l e l i n f l u e n c e on t h e boundary l a y e r flowing around t h e wing s u r f a c e a t t h e upper l i m i t causes an i n c r e a s e d mixing of t h e boundary l a y e r with t h e o u t e r flow. A i r p a r t i c l e s c a r r i e d from t h e o u t e r flow by the v o r t e x d i s p l a c e t h e p a r t i c l e s i n t h e boundary l a y e r and, through mixing with them, a r e entrapped i n t h e o u t e r l a y e r . There is i n t e n s i f i c a t i o n o f t h e boundary l a y e r which r e s t r i c t s i t s breaking away from t h e compression shock. I n those i n s t a n c e s where break away n e v e r t h e l e s s occurs, t h e vortex system e x c i t e d by t h e v o r t e x g e n e r a t o r s c r e a t e s i n intermixing e f f e c t i n t h e s e p a r a t e d flow as w e l l , as a r e s u l t of which t h e flow s e p a r a t i o n region i s l o c a l i z e d and t h e boundaxy l a y e r again "adheres" t o t h e wing surface*. S e t t i n g up v o r t e x g e n e r a t o r s has succeeded i n f o r e s t a l l i n g t h e development of flow s e p a r a t i o n a t high angles of a t t a c k and f l i g h t speeds (an i n c r e a s e i n t h e c r i t i c a l Mach number t o 0 . 0 2 - 0.07). Aileron e f f e c t i v e n e s s i n c r e a s e d because t h e vortex g e n e r a t o r s i n h i b i t s e p a r a t i o n of t h e boundary l a y e r along t h e r u p t u r e l i n e of t h e upper wing s u r f a c e when t h e a i l e r o n i s down. Vortex g e n e r a t o r s s e t i n t h e b a s e s e c t i o n of t h e wing (Boeing-707) decrease l i f t a t high angles of a t t a c k through flow s e p a r a t i o n . In a d d i t i o n , on t h e Comet-4c t h e r e are t h e s o - c a l l e d s e n s o r s ( s p e c i a l p l a t e s , Figure 20) which break up t h e flow a t t h e base s e c t i o n of t h e wing a t high angles o f attack and by s o doing decrease t h e p i t c h i n g moment. I n summary, t h e measures described (including t h o s e l a i d o u t i n Chapter / 64 V, § 8) make it p o s s i b l e t o design a i r c r a f t wings with t h e shape shown i n Figure 45. I t must be noted t h a t i f along t h e 1 / 4 chord l i n e t h e angle x = 3S0, then along t h e leading edge t h e sweep may b e somewhat g r e a t e r ( i n t h e . _- ~ * Yeger, Design of Passenger Jet Aircraft (Proyektirovaniye p a s s a c h i r S.M. skikh reaktivnykh samelotov) . Mashinostroyeniye. 1964. 57
- 67. lll I I f i g u r e t h i s corresponds t o an angle o f x = 41* i n t h e b a s e s e c t i o n o f t h e wing and x = 38' i n t h e o u t e r wing s e c t i o n ) . Figure 45. Schematic Diagram of A i r c r a f t Wing: 1 - inside s p o i l e r ; 2 - i n s i d e f l a p ; 3 - outside spoiler; 4 o u t s i d e f l a p ; 5 - i n s i d e ai l e r o n ; - 6 outside a i l e r o n ; 7 - f l e t t n e r trim tabs; 8 - intermediate r i b s ; 9 - landing g e a r pod; 10 - secondary c o n t r o l s u r f a c e s ; 1 1 - t i p r i b s ; 1 2 - s p a r a x e s ; 13 - w i n g s t u m p j o i n t ; 1 4 - w i n g joint,axis. Tables 3-5 p r e s e n t t h e values o f parameters ( i n percentage) f o r t h e following v a r i a t i o n s i n wing aerodynamic arrangement : a) f o r a wing without geometric t w i s t ( c r u i s i n g Mach number Mcruise - L = 0.75 - 0.78, $vib = + l o ) : TABLE 3 - - .~ .- . . - . . . ... Section C X C I A t wing stump j o i n t 15* 35 1.0 20 A t wing j o i n t axis 13 35 3.3 A t tip rib 12 37 2.5 50 25 * R e l a t i v e t h i c k n e s s along flow. 58
- 68. b) f o r a wing with geometric twist (engines i n t a i l s e c t i o n of f u s e l a g e , /65 c r u i s i n g Mach number M c r u i se = 0.8 - 0.82, and 4 vib = +lo, vib = -1'30'): otip TABLE 4 -- - .-. . .- . . S e c t i on . -- . . - - C X 1 - - - -f - - - - . .. . -- - -C Xf . [ . - . - . - - -.. .. - A t wing stump j o i n t A t wing j o i n t axis A t tip rib 9.75* 13 11.0 :: 35 ;:: 2.2 30 35 35 * R e l a t i v e thickness along flow. c r u i s i n g Mach number Mcruise = 0.82 - 0.85, +, c) f o r wing with geometric t w i s t (engines i n t a i l s e c t i o n of f u s e l a g e , ase vib = + 3 0 J 'inter. r i b - = o", = -1"): 'tip vib TABLE 5 Secti o n A t wing stump j o i n t 12 56 -0.7 30 Intermediate 40 A t tip rib § 4. Drag Propagation Between S e p a r a t e P a r t s o f A i r c r a f t T o t a l a i r c r a f t drag i s known t o be t h e composite of drag i n t h e i n d i v i d u a l s e c t i o n s . F o r various f l i g h t speeds (Mach numbers) diverging drag propagations r e s u l t between t h e s e p a r t s mainly due t o t h e onset of wave drag a t t h e r e s p e c t i v e Mach numbers. I n subsonic a i r c r a f t , around h a l f o f t h e t o t a l drag i s c r e a t e d by t h e wing. Table 6 shows r e p r e s e n t a t i v e v a l u e s Acx f o r t h e b a s i c a i r c r a f t components with t h e engines s e t i n t h e t a i l s e c t i o n of t h e f u s e l a g e ( t h e d a t a p e r t a i n t o h o r i z o n t a l f l i g h t a t a Mach number of M = 0.8, a t which c f o r t h e e n t i r e a i r c r a f t equals 0.0305, while c = 0 . 4 ) . X Y I t should be noted t h a t t h e p o r t i o n of wave drag f o r M = 0 . 8 a t c = 0 . 4 Y (corresponding roughly t o t h e high angle of attack c1 5.5') i s approximately 20% (Actail = 0.006). Having t h e landing g e a r down (Acx = 0.015 - 0.020) a t low f l i g h t speeds c r e a t e s approximately h a l f of t h e e n t i r e a i r c r a f t drag. 59 I
- 69. TABLE 6 Averaged In % of for A i r craf t compon ent total remaining aircraft aircraft (%I Wing 0.015 49.5 45-50 Elevator u n i t 0.001.7 5.57 5- 6 Rudder-fin u n i t 0.001 3.28 3- 4 Fus e 1age 0.008 26.2 25-30 Landing g e a r pods 0.00116 3.8 3- 5 Side engine pods 0.0027 8.83 8- 10 Center engine i n t a k e 0.001 3.28 Entire aircraft c =O. 0305 100 100 X 60
- 70. CHAPTER I V CHARACTER1 STI CS OF THE POWER SYSTEM J e t engines and, i n p a r t i c u l a r , t u r b o j e t engines g e n e r a t e high i n - f l i g h t / 66 t h r u s t and, consequently, high t h r u s t horsepower (30,000 - 60,000 hp) necessary f o r p r o p e l l i n g a i r c r a f t weighing 40 - 160 tons a t a speed o f 850 900 km/hr. P i s t o n and turboprop engines u s e up a l l o r almost a l l t h e energy from t h e f u e l i n r o t a t i n g t h e p r o p e l l e r . I t i s t h e p r o p e l l e r which, driven i n i t s r o t a t i o n by t h e engine, c r e a t e s t h e t h r u s t . Therefore t h e p r o p e l l e r i s c a l l e d t h e prime mover of t h e a i r c r a f t . The power system f o r p i s t o n and turboprop engines comprises b o t h t h e engine and t h e prime mover, which c r e a t e t h e t h r u s t . In t h e o p e r a t i o n of a j e t engine, however, t h e t h r u s t i s achieved in d i r e c t l y as t h e i n t e r a c t i o n of a l l the f o r c e s a c t i n g on t h e s u r f a c e of t h e engine components. The j e t engine o r g a n i c a l l y combines w i t h i n i t s e l f t h e engine i n the normal .concept of t h e word and t h e prime mover. During t e s t - s t a n d o p e r a t i o n of modern t u r b o j e t engines , t h e p r e s s u r e a t t h e compressor exhaust equals 5-10 atm o r more. The gas temperature a t t h e combustion chamber exhaust i s 1 , O O - 1,200" abs. The power generated by t h e gas t u r b i n e i s 60,000 - 90,000 hp f o r engines with a t h r u s t from 5,000 t o 10,000 kG. As i t e x i s t s from t h e t u r b i n e , t h e g a s s t i l l has a high amount of h e a t energy, i t s p r e s s u r e i s g r e a t e r than atmospheric, and i t s temperature equals 800 - 1,000" abs. Through t h e process of expansion, t h e thermal energy of t h e gas a t the- exhaust nozzle is transformed i n t o k i n e t i c energy, and as a r e s u l t of the high speed of t h e g a s exhaust, t h e exhaust t h r u s t i s generated. 5 1. Two-Ci rcui t a n d Turbofan Engines 1 67 Attempts by a e r o n a u t i c a l engineers t o i n c r e a s e engine t h r u s t and decrease f u e l consumption l e d t o t h e c r e a t i o n of t h e t w o - c i r c u i t and turbofan engines (Figure 46). Fuel consumption i n p a r t i c u l a r decreased by 1 5 2 0 %by comparison with consumption i n normal t u r b o j e t engines. The t w o - c i r c u i t (turbofan) engine i s a gas t u r b i n e engine i n which t h e excess t u r b i n e horsepower, i n c o n t r a s t t o t h e turboprop engine, i s t r a n s m i t t e d t o a compressor o r f a n enclosed i n t h e c i r c u l a r cowling. The t w o - c i r c u i t t u r b o j e t engine may assume one of s e v e r a l s t r u c t u r a l designs (Figure 46a and b ) which are c h a r a c t e r i z e d by t h e e x i s t e n c e of an 61
- 71. a d d i t i o n a l a i r c i r c u i t through which, a f t e r compression, p a r t o f t h e a i r which has been sucked i n i s fed t o t h e combustion chamber and t u r b i n e bypass d i r e c t l y t o t h e o u t l e t , thereby i n c r e a s i n g t h e m a s s and decreasing t h e speed o f t h e j e t s tream. Two-contour engines i n which t h e volume of a i r passing through t h e supplementary c i r c u i t i s r e l a t i v e l y g r e a t while t h e degree of compression of t h i s air i s small a r e u s u a l l y c a l l e d turbofan engines. A t p r e s e n t t h e r e are i n use t w o - c i r c u i t engines of t h i s type and turbofan engines, which are derived/68 through t h e i n s t a l l a t i o n of a f a n i n a d d i t i o n t o t h e normal t u r b o j e t engine (Figure 46c and d ) . The expediency of c r e a t i n g turbofan engines based on s e r i e s t u r b o j e t engines f o r c i v i l i a n a i r c r a f t i s j u s t i f i e d through t h e i r g r e a t economy and high r e l i a b i l i t y during use. Figure 46. Various Types of Two-Circuit and Turbofan Engines: a - normal scheme (Rolls Royce "Conway" engine) ; b - t w o - c i r c u i t engine w i t h a i r displacement from o u t e r contour w i t h gases from t h e inner contour (Rolls Royce JT8D "Spey"); c - turbofan scheme w i t h forward fan (Pratt-Whi tney JT3D) ; d - turbofan with r e a r fan (General E l e c t r i c CJ-805-23). When a t u r b o j e t engine i s being designed s t r i c t l y along t h e t w o - c i r c u i t p l a n , optimal parameters a r e obtained i f t h e design and the parameters of t h e turbofan engine a r e t o a g r e a t degree determined and l i m i t e d by t h e parameters of t h e i n i t i a l t u r b o j e t engine. Figure 47 shows a s i m p l i f i e d schematic of a t w o - c i r c u i t engine. Atmos p h e r i c a i r e n t e r s t h e a i r scoop through t h e two l a y e r s of blades which form t h e fan B. From t h i s f a n , which i s i n e f f e c t a low-pressure compressor, t h e a i r moves on i n two s e p a r a t e p a t h s . One p a r t of the a i r moves along t h e o u t e r body of t h e b a s i c engine contour through t h e second contour C , while the o t h e r p a r t moves through t h e high-pressure compressor D. From t h e r e i t moves through the combustion chamber E , i n t o which f u e l i s i n j e c t e d through f e e d l i n e F and, 62
- 72. f i n a l l y , a f t e r expanding, passes through t h e high-pressure t u r b i n e K and low- p r e s s u r e t u r b i n e H. Then t h e high-temperature gas e x i t s through t h e exhaust nozzle, which surrounds t h e o u t e r r i n g nozzle with a cold c u r r e n t of a i r . Figure 47. Simplified Schematic Diagram o f t h e Operation of a Two-Circuit J e t Engine. The a i r which has been speeded up through t h e fan of a turbofan engine i s exhausted with a slower speed than i n t h e normal t u r b o j e t engine o r t h e normal t w o - c i r c u i t engine. The slower t h e speed o f t h e flow behind t h e engine, t h e lower t h e energy l o s s e s w i l l be and t h e g r e a t e r t h e engine's e f f i c i e n c y . From j e t - e n g i n e theory we know t h a t t h e o v e r a l l e f f i c i e n c y ( o v e r a l l Q f a c t o r ) f o r t h e power system of any a i r c r a f t i s determined as t h e product of the two b a s i c f i g u r e s : t h a t of t h e i n t e r n a l ( e f f e c t i v e ) and exhaust ( f l i g h t ) factors. The e f f e c t i v e Q-factor i n c r e a s e s with an i n c r e a s e i n t h e a i r p r e s s u r e i n ~ the engine and with an i n c r e a s e i n t h e gas temperature. This leads t o a s u b s t a n t i a l decrease i n t h e s p e c i f i c f u e l consumption. Because only p a r t of the a i r passes through t h e t u r b i n e i n a two-system turbo j e t engine, the t u r b i n e blades may be s h o r t e r than i n a t u r b o j e t engine with t h e same o v e r a l l f u e l consumption. F o r i d e n t i c a l b l a d e s a f e t y f a c t o r s , t h i s i n /69 t u r n permits a 100 - 150° temperature i n c r e a s e i n t h e g a s i n f r o n t of t h e t u r b i n e , which gives a decided advantage over t h e t u r b o j e t engine i n terms of f u e l economy. This i s one of t h e reasons t h a t t h e t w o - c i r c u i t and turbofan engines have lower s p e c i f i c f u e l consumptions. For p r o p u l s i v e f l i g h t e f f i c i e n c y , from t h e theory of j e t engines we a r e familiar with t h e following formula: 2 ?f=- w ' 'fv' where W i s t h e speed of t h e j e t s t r e a m ; and V i s t h e f l i g h t speed. 63
- 73. When t h e d i f f e r e n c e between t h e speed of t h e j e t s t r e a m and t h e f l i g h t speed i s decreased, i . e . , when t h e r e i s l e s s of an unused p o r t i o n of t h e k i n e t i c energy, t h e p r o p u l s i v e e f f i c i e n c y i n c r e a s e s and reaches i t s maximum v a l u e (11 - 1) a t a f l i g h t speed equal t o t h e speed o f t h e exhaust j e t s t r e a m . f - When t h i s i s t r u e , t h e unused p o r t i o n of t h e k i n e t i c energy i s zero. A c l e a r example i s t h e turboprop engine, i n which t h e speed a t which t h e a i r i s t h r u s t back by t h e b l a d e i s c l o s e t o t h e f l i g h t speed. However, i n turboprop a i r c r a f t t h e f l i g h t e f f i c i e n c y drops as t h e f l i g h t speed i n c r e a s e s due t o a drop i n t h e blade e f f i c i e n c y , and reaches low values a t high s u b s o n i c speeds. In t w o - c i r c u i t and turbofan engines, t h e r e i s an i n c r e a s e i n t h e a r e a o f high e f f i c i e n c y , which t h e turboprop engine has a t low f l i g h t speeds, up t o high subsonic speeds a t which t h e f l i g h t e f f i c i e n c y i s s t i l l t o o low. To achieve t h i s , i n t w o - c i r c u i t and turbofan engines t h e r e i s a second c i r c u i t from which g r e a t masses of a i r flow a t speeds c l o s e t o t h e f l i g h t speed, which a i d s i n achieving a high f l i g h t e f f i c i e n c y as w e l l as a low s p e c i f i c f u e l consumption. The s p e c i f i c f u e l consumption f o r a t w o - c i r c u i t j e t engine and a t u r b o f a n engine i s 0.52 = 0.65 kG fuel/kG t h r u s t - hr for H = 0 and V = 0 and 0.75 - 0.85 kG fuel/kG t h r u s t - h r f o r H = 10-11 km a t V = 750 880 km/hr. I n designing t w o - c i r c u i t engines, t h e s e l e c t i o n of t h e two c h i e f v a r i a b l e s i s v i t a l : t h e forward o r r e a r p o s i t i o n i n g of t h e f a n and t h e r a t i o o f t h e mass flow of cold a i r p a s s i n g through c i r c u i t C t o t h e mass flow of h o t a i r passing through c i r c u i t D, t h e s o - c a l l e d t w o - c i r c u i t l e v e l m = G C/G D’ whose v a l u e may be from 0.23 t o 3.5. The t w o - c i r c u i t l e v e l i s a v i t a l engine parameter and determines i t s e f f i c i e n c y , weight and t h r u s t c h a r a c t e r i s t i c s . The g r e a t e r t h e l e v e l m , t h e / 70 lower the s p e c i f i c f u e l consumption; however, t h i s e n t a i l s an i n c r e a s e i n t h e engine dimensions and weight. A t p r e s e n t the optimum degree i s m = 0.6 - 0.7 f o r c i v i l i a n a i r c r a f t a t a f l i g h t Mach number of 0 . 8 - 0 . 9 . F i r s t - g e n e r a t i o n (Boeing-707-420, and Douglas DC-8) and second-generation (Vickers VC-10 and o t h e r s ) t r a n s p o r t a i r c r a f t a r e equipped with t h e Rolls Royce Conway t w o - c i r c u i t engine i n which m = 0.7 - 0.8. The engine t h r u s t f o r t h e Conway-509 i s 10,200 kG, while t h e s p e c i f i c f u e l consumption a t top conditions i s 0.725 kG/kG - hr. Even g r e a t e r economy may be obtained through mixing flows o f high p r e s s u r e ( a f t e r t h e t u r b i n e ) and low p r e s s u r e ( a f t e r t h e f a n ) ( i n t h e JT8D engine) o r a f t e r t h e f i r s t compressor s t a g e ( t h e Spey engine) i n t h e exhaust nozzle. When t h i s i s done, a r e l a t i v e l y low speed of flow i s achieved and t h e r e i s a correspondingly high e f f i c i e n c y . The combination of high thermo dynamic and t h r u s t e f f y c i e n c i e s has a l s o made it p o s s i b l e t o c r e a t e engines with low s p e c i f i c f u e l consumptions. As an example, Table 7 p r e s e n t s some d a t a on t h e JT8D and Spey engines. 64
- 74. TABLE 7 - Flight conditions -_ 1 Engine type 1 Thrust kG Specific I o ? Y kGj&e%r I 1 c n L ffm. v*km/hr Takeoff I JT8D flspeyf I I 6350 5150 0,585 0,611 I_ X 1 0 0 Maxi" (climbin?) I JTSD "Speyfl I I '% 7iI' I I 0 Cruising I l ~ ~ 1 ~ ~ 2140 1680 y l I l 0,838 0.77 1 7500 7600 I 730 870 T r . Note: Commas i n d i c a t e decimal p o i n t s There are t h r e e JT8D engines on t h e Boeing-727 and two on t h e DC-9, and t h e r e a r e two Spey engines on t h e Bak-1-11-200 and t h r e e on t h e Trident a i r c r a f t . S o v i e t t w o - c i r c u i t engines were f i r s t i n s t a l l e d on t h e Tu-124. Replacing normal t u r b o j e t engines with t w o - c i r c u i t engines o f f e r s an i n c r e a s e i n payload and a decrease i n t h e s p e c i f i c f u e l consumption and t h e noise level. As has already been s t a t e d , t u r b o f a n engines have t h e fans placed e i t h e r forward or behind. When t h e f a n i s placed behind, as w a s done by General E l e c t r i c (Figure 46d), t h e design o f t h e forward p a r t of the engine d i f f e r s i n no way from a normal t u r b o j e t engine: t h e compressor, t h e combustion chamber and t h e g a s t u r b i n e a r e i d e n t i c a l . However, with t u r b o f a n engines, a f t e r t h e gases have passed through t h e main t u r b i n e they run i n t o one more, t h e s o - c a l l e d fan t u r b i n e , which i s mechanically t i e d i n t o t h e main t u r b i n e . /71 The b l a d e t i p s i n t h e f a n t u r b i n e f u n c t i o n as they would i n a normal f a n and, i n t h e annular gap between t h e n o z z l e and t h e a d d i t i o n a l t u r b i n e , they t h r u s t back a s t r o n g flow of a i r running p a r a l l e l t o t h e b a s i c g a s j e t . The American Convair 990A has f o u r CJ-805-23B turbofan engines ( b u i l t by General E l e c t r i c ) with t h e r e a r f a n , each g e n e r a t i n g a t h r u s t of 7,300 kG. The same engines a r e used on t h e French Caravelle-XA i n replacement f o r t h e o b s o l e t e Avon t u r b o j e t engines. The P r a t t and Whitney JT3D engine, with m = 1.5, has t h e f a n p o s i t i o n e d forward. This t y p e of engine i s used on t h e Boeing-720B and DC-8. Table 8 o f f e r s some d a t a on t h e JT3D engine. Thus, u s e of t w o - c i r c u i t and f a n engines makes i t p o s s i b l e t o c r e a t e a i r c r a f t with optimal f l i g h t c h a r a c t e r i s t i c s f o r various purposes. The i n c r e a s e d t h r u s t makes i t p o s s i b l e t o decrease t h e t a k e o f f d i s t a n c e f o r any s p e c i f i c a i r c r a f t weight o r , i n maintaining t h e t a k e o f f d i s t a n c e , i t becomes p o s s i b l e t o i n c r e a s e t h e payload o r t h e f u e l r e s e r v e . 65
- 75. TABLE 8 Takeoff . . . . .. 8160 0,538 0 0 Aaximum (climbing). Cruising * -- . - '1 7400 1700 0,515 0,79 0 9100 0 865 ' 1 Tr. Note: Commas i n d i c a t e decimal p o i n t s . 9 2. Basic C h a r a c t e r i s t i c s o f Turbojet E n g i n e s In examining t h e f l i g h t conditions f o r t u r b o j e t passenger a i r c r a f t we must know t h e following b a s i c engine c h a r a c t e r i s t i c s : t h r u s t , s p e c i f i c t h r u s t , s p e c i f i c f u e l consumption, s p e c i f i c weight and maximum-power a l t i t u d e . Thrust i n t u r b o j e t engines is determined i n accordance with t h e following formula : p = - G s e c (W - V) kG, g where i s t h e per-second r a t e of a i r f l o w through t h e engine, Gsec (kG/sec) ; g = 9.81 m/sec2 is t h e a c c e l e r a t i o n ; W i s the speed of t h e r a t e of gas flow from t h e exhaust nozzle (m/sec) ; V i s t h e a i r c r a f t f l i g h t speed (m/sec) . Turbojet engines designed i n the last two decades have Gsec = 18 - 260 /72 kG/sec, which corresponds t o a t h r u s t of from 800 - 900 t o 10,000 - 13,000 kG, W = 550 - 600 m/sec ( s t a n d - s t i l l o p e r a t i o n ) , while i n f l i g h t i t reaches high values. Two-circuit engines have a discharge v e l o c i t y of 520 - 550 m/sec, whereas t u r b o f a n engines have only 350 - 370 m/sec. S p e c i f i c t h r u s t -- t h i s is t h e t h r u s t obtained from 1 kG of a i r passing through t h e engine per-second: - W - V --- kG ' s pe f g kG/sec * S p e c i f i c t h r u s t c h a r a c t e r i z e s t h e economy of an engine. I n modern turbo j e t engines , = 40 - 70 kG/kG/sec. S p e c i f i c t h r u s t depends s t r o n g l y on 'spef t h e compressor k f f i c i e n c y and t u r b i n e e f f i c i e n c y , as w e l l as t h e degree t o 66
- 76. which t h e air has been pre-heated. I t determines t h e r e l a t i v e dimensions and weight of t h e engine: t h e g r e a t e r t h e s p e c i f i c t h r u s t , t h e lower t h e engine dimensions and weight f o r a given t h r u s t . S p e c i f i c f u e l consumption -- t h i s i s t h e r e l a t i v e hourly f u e l consumed i n generating engine t h r u s t : c = -GG * P P k t fuel/kG - thrust - hr, where G t i s t h e hourly f u e l consumption (kG f u e l / h r ) . The s p e c i f i c consumption i n d i c a t e how many k of f u e l have been expended G i n c r e a t i n g 1 kG of t h r u s t i n an hour, and a l s o , c h a r a c t e r i z e s t h e engine e f f i c i e n c y . The lower t h e c t h e more e f f i c i e n t t h e engine and t h e g r e a t e r P' t h e a i r c r a f t f l i g h t range and duration. S p e c i f i c weight of the engine i s t h e r a t i o of the dry weight of t h e engine t o its thrust: In modern t u r b o j e t engines, = 0.19 - 0.35 kG/kG t h r u s t . For example, gtj f o r the 5-58 engine, t h e v a l u e of t h e s p e c i f i c weight i s g = 0.25 kG/kG tj t h r u s t . This means t h a t f o r a t h r u s t o f 13,600 kG, the engine weight i s G = 3,400 kG. A s can b e seen from t h e s e f i g u r e s , t u r b o j e t engines do n o t tj overload t h e a i r c r a f t by v i r t u e of t h e i r weight. Whereas t h e weight of t h e power system f o r a piston-engine a i r c r a f t may sometimes amount t o 2 2 - 25% of t h e takeoff weight, f o r t u r b o j e t a i r c r a f t t h i s value equals only 10 - 1 2 % . § 3. Throttle Characteristics Depending on how i t i s used and on i t s r a t e d s e r v i c e l i f e , each engine has s e v e r a l b a s i c modes of o p e r a t i o n which d i f f e r by t h e number of rpm's, t h e /73 temperature regimes, e t c . Usually t h e following o p e r a t i o n conditions a r e d i s t i n g u i s h e d : t a k e o f f , nominal, c r u i s i n g , and i d l i n g . P r a c t i c e i n a i r c r a f t and engine u s e has r e s u l t e d i n t h e need f o r an a d d i t i o n a l condition which, f o r t h e Tu-104 f o r example,has come t o be c a l l e d t h e "extreme" condition. As can be seen from t h e very name i t s e l f , t h i s i s used i n only c e r t a i n c a s e s , s p e c i f i c a l l y i n t h e event of f a i l u r e of one of the engines. In t h i s event, because of t h e engine f o r c i n g with r e s p e c t t o t h e temperature of t h e supply of a d d i t i o n a l f u e l and t h e i n c r e a s e d r e v o l u t i o n s , t h e t h r u s t i n c r e a s e s by 8 t o 10%by comparison t o t a k e o f f . However, t h i s emergency condition p u t s an overload on t h e engine which i n t u r n means t h a t t h e engine must be overhauled f a s t e r than normally. 67
- 77. The t a k e o f f c o n d i t i o n corresponds t o t h e maximum p e r m i s s i b l e number of rpm's and t h e m a x i m u m t h r u s t . Under t h i s c o n d i t i o n , t h e engine components are s u b j e c t e d t o t h e g r e a t e s t mechanical and thermal s t r e s s e s , as a r e s u l t o f which t h e i r p e r i o d of continuous u s e i s l i m i t e d and normally does n o t exceed 5 - 10 minutes. Takeoff c o n d i t i o n s are a p p l i e d t o decrease t h e t a k e o f f run through i n c r e a s i n g t h e h o r i z o n t a l f l i g h t speed, decreasing t h e a i r c r a f t a c c e l e r a t i o n t i m e and a c c e l e r a t i n g t h e breaking clouds i n g a i n i n g a l t i t u d e . The normal r a t i n g corresponds t o somewhat decreased (by 3-8%) r o t a t i o n with r e s p e c t t o t h e takeoff r a t i n g . The t h r u s t i s approximately 90% of t h e t a k e o f f t h r u s t . The o p e r a t i o n time a t a normal r a t i n g i s s u b s t a n t i a l l y longer: i t i s used i n gaining a l t i t u d e and f o r n e a r - c e i l i n g f l i g h t . During such o p e r a t i o n t h e engine components are s u b j e c t e d t o s u b s t a n t i a l l y l i g h t e r loads. Cruising performance d i f f e r s from t h e two preceding conditions through decreased rpm's (by 10-15%) and t h r u s t (by 25-50%) as opposed t o maximum. The i d l i n g p e r i o d corresponds t o t h e lowest number o f rpm's a t which t h e engine can o p e r a t e s t a b l y . Under t h e s e c o n d i t i o n s , t h e r e i s l i t t l e t h r u s t and t h e r e f o r e i t i s used i n landing runs, dropping from high a l t i t u d e s , e t c . The amount o f t h r u s t i s 300-600 kG a t low f l i g h t a l t i t u d e s and 150-300 kG a t a l t i t u d e s of 8,000 - 10,000 m. The c h a r a c t e r of t h e change i n engine t h r u s t with r e s p e c t t o rpm's i s shown i n Figure 48, from which we can s e e t h a t an i n c r e a s e i n t h e number of rpm's causes an i n c r e a s e i n t h r u s t . A t low rpm's, t h e amount o f a i r p a s s i n g through t h e engine i s a l s o low and as a consequence, t h e f u e l consumption, too, i s low. The amount o f gases formed i s small and develop a n e g l i g i b l e exhaust v e l o c i t y , so t h a t t h e t h r u s t g e n e r a t e d by t h e engines with t h i s v a l u e o f rpm's i s low, u s u a l l y 300 - 600 kG. A i n c r e a s e i n t h e n 1 - -- - - -- - - Pt-0 r p m ' s leads t o a s h a r p i n c r e a s e f&q i n t h e a i r exhaust, t h e f u e l d e l i v e r y i n c r e a s e s , t h e temperature o f gases i n f r o n t of t h e t u r b i n e i n c r e a s e s and, as a r e s u l t -- t h r u s t i n c r e a s e s . The h i g h e s t t h r u s t may be obtained a t t h e maximum p e r m i s s i b l e rpm's , i . e . , during t a k e o f f o r emergency con ditions. n , rpm(%) Figure 48. Engine T h r u s t , S p e c i f i c Thrust Figure 48 a l s o shows t h e /74 and S p e c i f i c Fuel Consumption a s Functions of t h e s p e c i f i c f u e l of t h e rpm's. n = n consumption on t h e number of rpm's. t-o take o f f ' The change i n cp i s a f u n c t i o n o f 68
- 78. I t h e degree of compression o f t h e air i n t h e combusion chamber. The more h i g h l y compressed the a i r i s , t h e more f u l l y t h e h e a t is used during t h e process of f u e l consumption and t h e lower t h e s p e c i f i c f u e l consumption w i l l be. P r e compression of t h e air depends b a s i c a l l y on t h e compressor (engine rpm's) and on t h e f l i g h t speed. Therefore, when t h e rpm's a r e i n c r e a s e d , t h e s p e c i f i c f u e l consumption decreases. During normal and t a k e o f f c o n d i t i o n s , t h e s p e c i f i c consumption i s c l o s e t o minimum. Engine u s e during c r u i s i n g rpm conditions y i e l d optimum economy. 5 4. High-speed Characteristics The high-speed c h a r a c t e r i st i c s of t u r b o j e t engines a r e t h e dependence of t h e engine t h r u s t , s p e c i f i c t h r u s t and s p e c i f i c f u e l consumption on f l i g h t speed a t a given a l t i t u d e f o r a s e l e c t e d r u l e of c o n t r o l . Let us examine t h e high-speed c h a r a c t e r i s t i c s f o r c o n s t a n t rpm, gas temperature i n f r o n t of t h e t u r b i n e and f l i g h t a l t i t u d e (Figures 49 and 50). Normally t h e c h a r a c t e r i s t i c s are examined f o r a nominal number o f rpm's. bs e c From t h e formula P = - (W - V) we can s e e t h a t t h e exhaust t h r u s t w i l l /75 g be g r e a t e r , t h e g r e a t e r t h e amount of a i r which passes through t h e engine p e r second and t h e g r e a t e r t h e d i f f e r e n c e between t h e g a s exhaust speed and t h e f l i g h t speed. I n i n c r e a s i n g t h e f l i g h t speed from 0 t o 700 - 800 W h r , t h r u s t de creas e s somewhat , becaus e i n c r e a s e s more s lowly Gsec than t h e d i f f e r e n c e W -V drops. With an a d d i t i o n a l i n c r e a s e i n speed, on t h e o t h e r hand, t h e i n c r e a s e i n a i r exhaust begins t o surpass t h e decrease i n t h e d i f f e r e n c e s between t h e speeds W and V. This is explained by t h e c h a r a c t e r of t h e change i n t h r u s t with r e s p e c t t o speed. When t h e f l i g h t speed i s i n c r e a s e d from 0 t o 700 - 800 km/hr, t h r u s t decreases by no 0,Z 0.3 04 . 0,5 OP Q7 0,8 0.0 fl more than 10-15%. This per m i t s us t o consider t h e avai l a b l e t h r u s t generated by Figure 49. E n g i n e Thrust as a Function of a subsonic t u r b o j e t engine t o Mach Number ( f l i g h t speed) f o r Various b e p r a c t i c a l l y independent of A1 t i t u d e s (standard c o n d i t i o n s , t h e broken f l i g h t speed. 1 i n e representing a temperature 10" above standard) . T-0 = Take-off.
- 79. W - The s p e c i f i c t h r u s t (Pspef - - ) drops as t h e speed i n c r e a s e s , because g t h e d i f f e r e n c e between speeds (W -V) decreases (Figure 50a). The s p e c i f i c f u e l consumption i n c r e a s e s with h i n c r e a s e i n f l i g h t speed (Figure 50b). When t h e r e i s a change i n t h e f l i g h t speed from zero t o 750 850 km/hr, t h e s p e c i f i c f u e l consumption i n c r e a s e s by 15-30%. Thus, i f f o r V = 0 t h e consumption i s cp = 0.89 kG/kG -h r , then a t a speed of 850 km/hr i t w i l l i n c r e a s e t o 1.15 ( f o r t h e RD-3M engine). For t h e JTSD turbofan engine, f o r V = 0 , t h e consumption i s c = 0.61, whereas f o r a speed o f 880 km/hr i t /76 - i s 0.781 kG/kG - h r (at ~ F I a l t i f u d e of 11 km). 1st , Figure 5 0 . Change i n S p e c i f i c Fuel Consumption ( b ) and S p e c i f i c Thrust ( a ) w i t h Respect t o F1 i g h t Speed. P,kG" kG on the ground, which i s increased t o 7,200 kG through t h r u s t augmentation by afterburning. I n f l i g h t 5000 a t a l t i t u d e , t h e drop i n 0 0 7 I t h r u s t i s compensated by I I 3000 ~. v e l o c i t y head. During 70
- 80. § 5. High-Altitude Characteristics The dependence of t h r u s t , s p e c i f i c t h r u s t and s p e c i f i c f u e l consumption on f l i g h t a l t i t u d e f o r a c o n s t a n t number of engine rpm's and c o n s t a n t f l i g h t / 77 speed i s c a l l e d t h e h i g h - a l t i t u d e c h a r a c t e r i s t i c s . The t h r u s t o f a t u r b o j e t engine decreases s h a r p l y with an i n c r e a s e i n f l i g h t a l t i t u d e because t h r u s t i s d i r e c t l y p r o p o r t i o n a l t o t h e weight r a t e of a i r f l o w , while t h e r a t e decreases with a l t i t u d e due t o a drop i n a i r d e n s i t y . The decrease i n t h r u s t with a l t i t u d e occurs i n s p i t e of t h e f a c t t h a t t h e s p e c i f i c t h r u s t , i . e . , t h e t h r u s t c r e a t e d by each kilogram of a i r passing through t h e engine, i n c r e a s e s by approximately h a l f again as much as compared t o t h e ground l e v e l . U t o an a l t i t u d e of 11,000 meters, because of precompression i n t h e p compressor, t h e weight r a t e of a i r f l o w decreases more slowly than t h e air d e n s i t y , whereas above 11,000 meters, where t h e temperature remains c o n s t a n t , i t drops more r a p i d l y . The change i n engine t h r u s t with a l t i t u d e may b e c a l c u l a t e d with r e s e c t t o the following formula: f o r a l t i t u d e s up t o 11,000 meters: P = P * f o r a l t i t u d e s g r e a t e r than 11,000 meters: PH = 1.44 A g a 7 ; H O A * Po (here PH i s t h e t h r u s t a t a l t i t u d e ; P is t h e ground engine t h r u s t ) ; 0 PH A = -is t h e r a t i o of d e n s i t i e s ( A < 1 ) . If we t a k e P 0 as loo%, then a t an a l t i t u d e of 10,000 meters the t h r u s t i s approximately 45-50% of t h e ground t h r u s t , while a t an a l t i t u d e of 20,000 meters i t i s only 10%. This comments on t h e lack of maximum-power a l t i t u d e i n t u r b o j e t engines. However, modified t u r b o j e t engines developing a ground t h r u s t of 10,000 - 13,000 kG have high f l i g h t speeds a t a l t i t u d e s of 10,000 12,000 meters. Figure 52 shows t h e v a r i a t i o n i n engine t h r u s t i n terms o f a l t i t u d e f o r various rpm's. I t should b e noted t h a t above t h e maximum-power a l t i t u d e boundary t h e power of p i s t o n engines drops more r a p i d l y than does t h e t h r u s t of j e t engines. Up t o an a l t i t u d e of 11,000 meters t h e s p e c i f i c f u e l consumption c P decreases, a f t e r which i t holds c o n s t a n t (Figure 53). The b a s i c p r i n c i p l e i n /78 t h e drop i n c (and t h e i n c r e a s e i n s p e c i f i c t h r u s t ) l i e s i n t h e f a c t t h a t P with a drop i n t h e temperature of t h e surrounding a i r t h e degree of com p r e s s i o n i n the compressor and t h e degree of precompression a r e i n c r e a s e d . The hourly f u e l consumption, which i s equal t o t h e product o f c P , P decreases with an i n c r e a s e i n f l i g h t a l t i t u d e by approximately t h e same i n t e n s i t y as does t h e a i r consumption and t h r u s t . The hourly f u e l consumption a t an a l t i t u d e of 11,000 meters i s l e s s t h a n one h a l f t h e ground consumption f o r t h e same engine rpm conditions. 71
- 81. I I I 5 io H,iKm Figure 52. Variation i n E n g i n e Figure 53. Dependence o f S p e c i f i c Thrust i n Terms o f F l i g h t A l t i t u d e Fuel Consumption on F l i g h t A l t i t u d e . (Mach = 0 . 7 5 ) . Thus, t h e s e engines a r e more e f f e c t i v e i n operation a t high a l t i t u d e s . 5 6. The Effect o f Air Temperature on Turbojet Engine Thrust Air temperature, l i k e a l t i t u d e ( p r e s s u r e ) , has a s i g n i f i c a n t e f f e c t on t h r u s t and s p e c i f i c f u e l consumption. During t e s t - s t a n d t r i a l runs of the engine t h e measured t h r u s t i s reduced t o standard conditions, i . e . , t h e s o - c a l l e d reduced t h r u s t i s d e t e r mined f o r p = 760 mm H and t = 15°C. Depending on t h e c o n t r o l system, the g e f f e c t of temperature changes on t h r u s t i s manifested i n d i f f e r e n t ways. Thus, f o r example, f o r t u r b o j e t engine with o p e r a t i o n a l rpm's of 4,000 - 5,000, a one-percent temperature i n c r e a s e decreases t h r u s t by approximately 2%. For two-circuit and turbofan engines with 6,700 - 11,000 rpm, a one-percent temperature change v a r i e s t h e t h r u s t by 1 - 1.5%. For example, t h e t h r u s t i n a t u r b o j e t engine equals 7,000 kG f o r t = 15OC and p = 760 mm Hg. A temperature i n c r e a s e of up t o t = 25°C has occurred. Let us determine t h e v a r i a t i o n i n engine t h r u s t . To do s o , l e t us express t h e temperature change i n a percentage r a t i o : T = t " C + 273" = 15" + 273" = 288O; T = 25" + 273" = 1 2 = 298"; 298 : 288 = 1.03, i . e . , the temperature increased by 3 % . Consequently, t h r u s t decreased by 6 % , amounting t o 420 kG. Thus, f o r t = 25"C, the engine w i l l generate around 6,600 kG of t h r u s t . If the temperature i n c r e a s e s t o 35"C, the t h r u s t decreases by 13.6%, i . e . , the engine w i l l generate only about 6,000 kG of t h r u s t . When the a i r temperature i n c r e a s e s , t h r u s t i n c r e a s e s , This comes about because of t h e c o n t r o l system on the fuel-supply arrangement i n t u r b o j e t engines, which i n c r e a s e s the f u e l supply when temperature drops. An i n c r e a s e i n t h r u s t u s u a l l y occurs when t h e temperature decreases t o + 3 - -15"C, 72
- 82. II depending on t h e engine c o n d i t i o n s and t h e c o n t r o l o f t h e f u e l pump and regul a t or. L e t us determine t h e i n c r e a s e i n t h r u s t f o r a temperature of -15OC i f f o r t = 15OC t h r u s t P = 7,000 kG: T 1 - 288OC, T2 = 258°C and 288 : 258 = 1.115, - i . e . , t h e temperature i n c r e a s e s by 11.5%, consequently, t h e t h r u s t i n c r e a s e s / 79 1 by 2 3 % , amounting t o 1,600 kG (Figure 54). To maintain t h e s e engine P,M- 8600 kG t h r u s t v a l u e s a t high a l t i t u d e s , water i n j e c t i o n i n t o t h e compressor 8000 t rbojet i s used. Figure 55 shows t h e change i n 7000 t h r u s t i n a JT3D turbofan engine with and without water i n j e c t i o n . A s can b e seen from t h e figure, 6000 --- "ZEY'L -- --- - water i n j e c t i o n a i d s i n maintaining t h e c a l c u l a t e d takeoff t h r u s t up I I t o and i n t a k e temperature of +3SoC. While t h i s h o l d s , t h e high-tempera ture flight characteristics for t h e a i r c r a f t change n e g l i g i b l y . I n Figure 54. E f f e c t o f External Air t h e case of t h e "Spey" engine, water Temperature on Thrust of Turbojet injection aids i n f o r e s t a l l i n g a Engines . drop i n i t s t h r u s t a t temperatures g r e a t e r than 2OoC. 5' 7. Thrust Horsepower / 80 - Thrust horsepower i s t h e a v a i l a b l e engine power: where V i s t h e f l i g h t speed i n m/sec. Figure 5 5 . Test-Stand Thrust i n t h e JT3D Turbofan E n g i n e and t h e I'Spey'' - type Two- Let us determine t h e t h r u s t C i r c u i t Turbojet E n g i n e as a Function o f horsepower f o r t h e engines of the A m b i e n t A i r Temperature. an a i r c r a f t f l y i n g a t an a l t i tude o f 10,000 meters and a speed of 900 km/hr, if t h e a v a i l a b l e engine t h r u s t is 6,000 kG: However, a t f l i g h t w i t h t h e maximum speed o f 1,000 km/hr a t an a l t i t u d e of 6,000 m and with an a v a i l a b l e t h r u s t o f 9,000 kG, t h e t h r u s t horsepower i s 73
- 83. The t h r u s t horsepower i n c r e a s e s d i r e c t l y p r o p o r t i o n a t e l y t o t h e speed. When r a c i n g t h e engines on t h e ground without t h e a i r c r a f t ' s moving, N = 0, because t h e r e i s no work being done, i . e . , PV = 0. A change i n t h e a v a i l a b l e horsepower with r e s p e c t t o a l t i t u d e (rpm's being constant) i s shown i n Figure 56. In contrast t o piston aircraft, i n which t h e a v a i l a b l e horsepower decreases with an i n c r e a s e i n speed above maximum 32000 - due t o a drop i n t h e p r o p e l l e r e f f i c i e n c y , i n j e t a i r c r a f t i t i n c r e a s e s with an i n c r e a s e i n f l i g h t speed. Therefore, r a p i d f l i g h t speeds may b e obtained only i n a i r c r a f t with t u r b o j e t engines o r o t h e r types of j e t engines. Like t h r u s t , t h e a v a i l a b l e horse power is a f u n c t i o n of t h e engine rpm's: - . t h e g r e a t e r t h e number of engine rpm's ( f o r a s p e c i f i c a l t i t u d e and f l i g h t speed), t h e higher the available horse- Figure 5 6 . Thrust Horsepower as power. a Function o f Mach Number f o r Various F l i g h t A l t i t u d e s ( c o n s t a n t rpm's). § 8. P o s i t i o n i n g the Engines on t h e A i rcraft / 81 The absence of p r o p e l l e r s , t h e r e l a t i v e l y low weight f o r high s t r e s s , and t h e i r s i m p l i c i t y with r e s p e c t t o design and s e r v i c i n g make i t p o s s i b l e t o i n s t a l l t u r b o j e t and turbofan engines i n such a way t h a t t h e i r optimal opera t i o n a l conditions and those of t h e a i r c r a f t a r e achieved. A t p r e s e n t , f i r s t - and second-generation t u r b o j e t passenger a i r c r a f t have t h e i r engines mounted on t h e wing, on pylons below t h e wing, o r i n t h e t a i l s e c t i o n of the f u s e l a g e . Engine I n s t a l l a t i o n i n wings. When t h e engines are i n s t a l l e d i n t h e wing (between t h e upper and lower p l a n k i n g s ) , t h e t o t a l drag i s reduced. I n p r a c t i c e , however, the engine i s f a s t e n e d t o t h e f u s e l a g e ( i n double-engine a i r c r a f t ) , while t h e a i r duct extends along t h e chord i n t h e wing. This leads t o a decrease i n t h r u s t as a r e s u l t of a p r e s s u r e l o s s i n t h e d u c t , b u t i n c o n t r a s t an advantage i s t h e almost " c l e a r " wing (without secondary s t r u c t u r e s ) which r e s u l t s . Engines arranged i n t h i s manner ( c l o s e t o t h e a i r c r a f t a x i s ) , if one of them f a i l s t h i s c r e a t e s only a s l i g h t t u r n i n g moment. Of t h e disadvantages which r e s u l t from t h i s arrangement, l e t us p o i n t o u t t h e f a c t t h a t i t becomes impossible t o make u s e o f t h e t h r u s t r e v e r s a l 74
- 84. due t o t h e h e a t e f f e c t s of t h e gas j e t on t h e f u s e l a g e ( f o r a double-engine a i r c r a f t ) and t h e p a r t i a l use of t h r u s t r e v e r s a l ( f o r a four-engine arrangement) (see Chapter I X ) . The stream of exhaust gases c r e a t e s s u b s t a n t i a l n o i s e i n t h e t a i l s e c t i o n of t h e f u s e l a g e and causes discomfort t o t h e passengers s e a t e d i n t h e r e a r . On t h e Tu-104 and t h e Tu-124 (Figure 57) , t h e engines a r e l o c a t e d i n t h e base of t h e wing, so t h a t t h e g r e a t e r p a r t o f the engine pod is hidden behind t h e wing. In t h e De Havilland Comet, however, t h e engines a r e f u l l y hidden i n the wing (Figure 58). The e n g i n e ' s small s i z e makes it p o s s i b l e t o design i t s pods with q u i t e small maximum c r o s s - s e c t i o n s . Figure 57. The Tu-124. Figure 58. T h e Comet Engines l o c a t e d a t the base of t h e wing c r e a t e p o s i t i v e i n t e r f e r e n c e a t t h e most complex aerodynamic p o i n t - - t h e j o i n t between t h e low-hung wing and t h e f u s e l a g e . The e f f e c t of t h e j e t s t r e a m causes the formation of an " a c t i v e / 82 f a i r i n g " h e r e , i . e . , an i n c r e a s e i n t h e "regeneration" o f t h e surrounding flow. This leads t o a decrease i n drag f o r t h e a i r c r a f t as a whole*. However, t h i s engine arrangement r e q u i r e s an i n c r e a s e i n t h e r e l a t i v e thickness of the a i r f o i l p r o f i l e , which causes a decrease i n t h e a i r c r a f t ' s __ __ . --- - . . * Yeger, S .M. Design of Passenger J e t A i r c r a f t (Proyektirovaniye p a s s a c h i r s k i k h reaktivnykh samelotov) . Mashinostroyeniye. 1964. 75
- 85. high-speed c h a r a c t e r i s t i c s . The angle a t which t h e engines a r e i n s t a l l e d r e l a t i v e t o t h e l o n g i t u d i n a l axis i s 3-So i n t h i s arrangement. This i n c l i n a t i o n i s necessary t o guarantee t h a t t h e engine exhaust flow does not h i t t h e elevator unit. In planform, t h e engines are turned outward by an angle of 2-4', i n o r d e r t h a t t h e exhaust gas j e t have less of an e f f e c t on t h e f u s e l a g e . P o s i t i o n i n g t h e engines on pylons beneath t h e wings. This is done on t h e American J e t s t h e Boeing-707 and 720, t h e Douglas DC-8 (Figure 5 9 ) , and t h e Convair 880 and 990. Even t h e newly c r e a t e d Boeing-737 shows a r e t u r n t o t h e pylon arrangement. In t h i s s e t u p , t h e p o s i t i o n i n g of t h e engines i n c r e a s e s a i r c r a f t drag s l i g h t l y , p a r t i c u l a r l y due t o negative i n t e r f e r e n c e from t h e wing and pylons. However, t h e s h o r t length of t h e e n g i n e ' s i n t a k e duct when t h e a i r admission i s we1 1 designed minimi zes t h r u s t l o s s e s and thereby improve t h e a i r c r a f t ' s t a k e o f f performance. Suspending t h e engine from a t h i n swept wing Figure 59. A i r c r a f t w i t h Pylon Suspension substantially lightens the of E n g i n e s . wing and decreases i t s s t r u c t u r a l weight. How ever, such a suspension r e q u i r e s i n c r e a s e d reinforcement of t h e engine and i t s pylon (due t o g r e a t e r i n e r t i a l loads during a i r c r a f t maneuvering) and as a r e s u l t t h e wing weight i s n e g l i g i b l y decreased. A i r c r a f t with pylon s u s pension of engines should be used only on concrete runways which have s u b s t a n t i a l l y c l e a n e r s u r f a c e s , because t h e engines a r e only 40-70 c above m / 83 - t h e ground. If f o r e i g n m a t t e r i s drawn i n t o t h e i n t a k e d u c t , t h e engine compressor may f a i l . Although p o s i t i o n i n g t h e engines t o t h e s i d e of t h e f u s e l a g e makes i t p o s s i b l e t o e f f e c t i v e l y u s e t h r u s t r e v e r s a l from a l l f o u r engines, the f a i l u r e of t h e o u t s i d e engine c r e a t e s a s u b s t a n t i a l t u r n i n g moment, which g r e a t l y impedes handling t h e a i r c r a f t . This moment, a c t i n g i n t h e h o r i z o n t a l p l a n e , causes an i n t e n s e r o l l i n g motion around t h e l o n g i t u d i n a l a x i s , which (with allowance made f o r t h e a i r c r a f t ' s s u b s t a n t i a l moment o f i n e r t i a r e l a t i v e t o t h e l o n g i t u d i n a l a x i s ) leads t o an emergency s i t u a t i o n . The b a s i c advantage of pylon engine suspension i s t h e decreased n o i s e w i t h i n t h e passengers' compartment. P o s i t i o n i n g of engines i n the f u s e l a g e t a i l s e c t i o n . This arrangement was f i r s t used i n the French Caravelle passenger a i r c r a f t (Figure 60). The following a i r c r a f t have a l s o been designed along t h e s e l i n e s : t h e 11-62, t h e 76
- 86. - .. ..... .. I I , , Tu-134, t h e DC-9, t h e BAC-1 11, t h e Boeing-727, t h e De Havilland D H . 1 2 1 T r i d e n t and t h e Vickers VC-10 (Figure 6 1 ) . Such an engine arrangement y i e l d s t h e I f c l e a r wing" and o f f e r s maximum mechanization of t h e wing. J e t passenger a i r l i n e s w i t h such engine arrange ments have s e v e r a l ad vantages. The b a s i c advantage i s t h e i r i n c r e a s e d ,aerodynamic c h a r a c t e r i s t i c s and i n creased comfort w i t h i n t h e passenger cabin (decreased n o i s e l e v e l ) . The absence of engine pods on t h e wing Figure 60. T h e C a r a v e l l e . r e s u l t s i n n e. a t i v e i n t e r - g , f e r e n c e being a f a c t o r only a t the j u n c t u r e of the wing and f u s e l a g e . I n a d d i t i o n , conditions a r e c r e a t e d f o r designing a wing with an i n c r e a s e d c r i t i c a l Mach number and a more e f f e c t i v e mechanical h i g h - l i f t device on t h e wing. The lack of secondary s t r u c t u r e s on t h e wing improves t h e wing's l i f t , which i n t u r n permits a drop i n t h e wing a r e a . a c _ e . Figure 61. T h e Vickers VC-10 ( a ) and t h e D Havilland DH.121 (b). e 77
- 87. Conditions are a l s o c r e a t e d f o r t h e o p e r a t i o n of t h e engine a i r scoops a t /84 high angles of a t t a c k as a r e s u l t of downwash, which i n a sense " c o r r e c t s " t h e - flow toward t h e s i d e engine. During g u s t s , t h e e n t r a n c e angle of t h e a i r f l o w i n t o t h e a i r scopp decreases almost t o h a l f t h e a i r f o i l angle o f a t t a c k , i . e . , /85 when t h e a i r f o i l angle of attack changes by 4 O , f o r example, t h e d i r e c t i o n of - the a i r f l o w around t h e a i r scoop varies by approximately. 2 O . The a i r w i l l e n t e r the engine a t less of an angle, which s u b s t a n t i a l l y decreases t h e p r e s s u r e l o s s a t t h e i n t a k e . When t h e engine is i n s t a l l e d i n t h e wing o r suspended from a pylon, however, t h e e n t r a n c e angle corresponds t o t h e angle o f attack at which t h e a i r c r a f t i s f l y i n g . Here t h e a i r c i r c u l a t i o n around t h e wing i n c r e a s e s t h e flow i n t a k e angle. A s is well known, t h i s causes a d d i t i o n a l losses. * One of t h e s t r u c t u r a l c h a r a c t e r i s t i c s of t h i s arrangement i s t h e T-shaped t a i l assembly with i t s a d j u s t a b l e s t a b i l i z e r . The e l e v a t o r assembly, l o c a t e d on t h e upper s e c t i o n of t h e v e r t i c a l f i n , is f r e e from t h e d e s t r u c t i v e e f f e c t of sound-waves c r e a t e d by t h e sound f i e l d s of t h e engine exhaust (Figure 62). This, t o o , has a s p e c i f i c e f f e c t i n decreasing v i b r a t i o n . datum l i n e Figure 62. Diagram of the E f f e c t of Eng.ine Exhaust J e t s on the S t a b i l i z e r and V e r t i c a l F i n . The aerodynamic advantage of t h e T-shaped t a i l assembly i s t h a t t h e flow bpyond the wing and i t s r e s u l t a n t s e p a r a t i o n s have l i t t l e e f f e c t on i t during horizontal f l i g h t . The engine pods form h o r i z o n t a l s u r f a c e s which i n c r e a s e t h e a i r c r a f t ' s l o n g i t u d i n a l s t a b i l i t y , i n view of which t h e a i r c r a f t ' s l o n g i t u d i n a l s t a b i l i t y c h a r a c t e r i s t i c progress l i n e a r l y up t o high angles of a t t a c k . A t the p o i n t of i n t e r s e c t i o n of t h e h o r i z o n t a l t a i l s u r f a c e s and t h e e l e v a t o r f o r t h e T-shaped arrangement a t high f l i g h t speeds, t h e i n c r e a s e i n drag drops as compared t o t h e normal arrangement. This i s an example of so- c a l l e d p o s i t i v e i n t e r f e r e n c e , and t h e e f f e c t i v e n e s s of t h e v e r t i c a l t a i l surface increases. The engine pods have a h o r i z o n t a l pylon. The angle a t which t h e pod i s s e t r e l a t i v e t o t h e a x i s of t h e f u s e l a g e v a r i e s from zero t o + 2 O , while i n t h e h o r i z o n t a l p l a n e t h e pods may b e turned o u t from t h e f u s e l a g e by an angle of 2-4" (Figure 62). .- - .- -- - .--.- -- - . * Yeger, S .M. Design of Passenger J e t A i r c r a f t (Proyektirovaniye p a s s a c h i r . skikh reaktivnykh samelotov) Mashinos t r o y e n i y e . 1964. 78
- 88. When t h e pod a x i s i s h i g h e r than t h e s t r u c t u r a l a x i s of t h e f u s e l a g e and consequently h i g h e r than t h e a i r c r a f t ' s c e n t e r of g r a v i t y , a n e g a t i v e p i t c h i n g moment i s c r e a t e d from t h e engine t h r u s t . Moving t h e engines t o t h e t a i l s e c t i o n of t h e f u s e l a g e c r e a t e s t h e / 86 following o p e r a t i o n a l advantages. As can be seen from Figure 6 3 , only a s l i g h ' t p o r t i o n of t h e a i r f l o w t h r u s t back by t h e nose wheels i s covered by t h e engine. The j e t s from t h e main wheels a r e covered by t h e wing b o t h during t a k e o f f and landing. This decreases t h e p o s s i b i l i t y t h a t f o r e i g n m a t t e r w i l l e n t e r t h e engines o f f the runway. Ground maintenance of t h e engine is made s i m p l e r through t h e e a s e w i t h which t h e pods can b e reached. Figure 6 3 . Diagram o f the E f f e c t o f Airstream Thrown Back from t h e Landi ng Gear Wheels : a - engines mounted i n wing; b - engines i n tail s e c t i o n o f f u s e l a g e ; c - engines on pylons. When t h e engines a r e suspended from pylons, as was s t a t e d above, t h e r e i s no need f o r long a i r scoops. However, when t h e engines a r e mounted i n t h e wing, as w a s done i n t h e Tu-104 and Tu-124 and t h e Comet, t h e length of t h e a i r i n t a k e i s 4-5 m e t e r s , as a r e s u l t of which l o s s e s i n a i r p r e s s u r e a t the i n t a k e decrease engine t h r u s t by 3 - 6 % . Moving t h e engines t o t h e t a i l , however, decreases l o s s e s a t t h e i n t a k e and t h e t h r u s t drop i s only 1 - 2 % , which improves t h e a i r c r a f t ' s t a k e o f f performance. In conclusion i t should be noted t h a t i n s p i t e of t h e numerous advantages derived from i n s t a l l i n g t h e engines i n t h e t a i l s e c t i o n o f t h e f u s e l a g e , t h i s arrangement a l s o has i t s drawbacks. Thus, f o r example, t h e engine performance decreases a t high angles of s i d e s l i p . The diving moment from engine t h r u s t i n c r e a s e s both t h e speed of r a i s i n g t h e landing g e a r nose wheels s t r u t during t h e takeoff run and t h e c o n d i t i o n s f o r t h e c o n t r o l wheel. The need a r i s e s f o r an a d j u s t a b l e s t a b i l i z e r . There i s an i n c r e a s e i n t h e weight of t h e rudder u n i t , which supports t h e e l e v a t o r u n i t . The s t r u c t u r e o f t h e a i r c r a f t 79
- 89. becomes h e a v i e r as a r e s u l t of t h e reinforcement f o r t h e c o n s t r u c t i o n o f t h e f u s e l a g e t a i l s e c t i o n due t o t h e a d d i t i o n a l m a s s and i n e r t i a l loads from t h e engines as w e l l as t h e need t o i n c r e a s e reinforcement f o r t h e engines t o /87 prevent i t s breakaway during emergency landing. During charging and f u e l i n g - up, t h e a i r c r a f t c e n t e r of g r a v i t y i s s h i f t e d s u b s t a n t i a l l y f a r t h e r forward, which makes t a k e o f f h a r d e r , and during f l i g h t r e q u i r e s p r e c i s e f u n c t i o n i n g of t h e automatic equipment which c o n t r o l s t h e f u e l output. Grouping t h e engines t o g e t h e r i n t h e t a i l s e c t i o n of t h e f u s e l a g e f a c i l i t a t e s using them f o r c o n t r o l l i n g t h e boundary l a y e r ( s e e Chapter I V ) and, f i n a l l y , with t h e power p l a n t arranged i n t h i s manner, t h e d i s t a n c e from the engines t o t h e ground i s determined only by t h e a i r c r a f t ' s landing c o n f i g u r a t i o n and the h e i g h t o f the landing gear. This makes i t p o s s i b l e t o decrease t h e landing g e a r h e i g h t and r e t a i n t h e p e r m i s s i b l e d i s t a n c e from t h e ground t o t h e edges of t h e a i r scoops. 80
- 90. CHAPTER V TAKE0 FF § 1. Taxiing A i r c r a f t with engines i n t h e t a i l s e c t i o n o f t h e f u s e l a g e o r i n t h e wing (along t h e s i d e s of t h e f u s e l a g e ) have s a t i s f a c t o r y t a x i i n g p r o p e r t i e s . The small t h r u s t arm has no adverse e f f e c t s on t h e a i r c r a f t ' s maneuvering pro p e r t i e s . In f a c t , a l l modern j e t a i r c r a f t have a p e d a l - c o n t r o l l e d leading strut, which makes i t easy t o perform t u r n s and maintain d i r e c t i o n during take o f f runs and landing runs. The angle of r o t a t i o n of the leading strut i s 35-45", w h i l e during take o f f runs and landing runs (with f l a p s down) i t i s decreased t o 5-6". The t a x i i n g speed along the ground, during t u r n s and c l o s e t o o b s t a c l e s reaches no more than 10 km/hr, while i n c l e a r and s t r a i g h t runway s e c t i o n s , i t is no more than 50 km/hr. Landing gears with nose wheels o f f e r good runway s t a b i l i t y during t a x i i n g on runways and taxiways. Turns a r e manipulated through t h e use of the leading s t r u t s , a s w e l l as the c r e a t i o n of asymmetrical t h r u s t and p a r t i a l braking, of t h e r i g h t o r l e f t landing gear t r o l l e y wheel. Turning an a i r c r a f t 180" r e q u i r e s a runway 50-60 meters wide, depending on t h e width o f t h e landing g e a r wheels. T u r b o j e t a i r c r a f t can a l s o t a x i over wet grass cover and over unsmoothed snow cover a t an a i r f i e l d . The f o u r t o s i x wheels on each main strut of t h e landing g e a r causes an even d i s t r i b u t i o n of load over t h e a i r f i e l d s u r f a c e , and reduced p r e s s u r e i n t h e pneumatic wheels (up t o 4.5 - 6 kG/cm2) i n c r e a s e s a b i l i t y t o t r a v e l over d i r t a i r f i e l d s . Modern a i r c r a f t using concrete landing s t r i p s maintain a t i r e p r e s s u r e of 6.5 - 9 . 5 kG/cm2. One drawback i n the use o f a i r c r a f t on d i r t a i r f i e l d s i s t h e damage t o the s u r f a c e caused by t h e wheels during t a x i i n g , t a k e o f f and landing, t h e - /88 formation of r u t s , and the g r e a t amount. of d u s t thrown up from t h e exhaust of the j e t engines, which reduces v i s i b i l i t y on t h e landing s t r i p f o r p i l o t s of a i r c r a f t approaching f o r a landing. 5 2. Stages of Takeoff Takeoff i s t h e a i r c r a f t ' s motion from t h e moment of s t a r t i n g u n t i l i t reaches an a l t i t u d e of 10.7 meters* and has a t t a i n e d a s a f e f l i g h t speed. . . * This i s t h e p r e s e n t l y accepted a l t i t u d e f o r complete t a k e o f f according t o t h e ICAO and norms f o r f l i g h t worthiness f o r c i v i l a i r c r a f t i n t h e USSR. 81
- 91. The d i s t a n c e covered by t h e a i r c r a f t from t h e moment o f s t a r t i n g u n t i l t h e a l t i t u d e of 10.7 meters has been reached i s c a l l e d t h e t a k e o f f d i s t a n c e . Aircraft t a k e o f f (Figure 64) c o n s i s t s of two s t a g e s : a) t a x i i n g u n t i l t h e speed o f l i f t - o f f and l i f t - o f f i t s e l f , b) a c c e l e r a t i o n from t h e l i f t - o f f speed t o a safe speed, w i t h simultaneous climbing. Figure 64. Diagram of A i r c r a f t Takeoff and t h e Calculated Takeoff T r a j e c t o r y According t o t h e I C A O : 1 - beginning o f run; 2 - takeoff run; 3 - a c c e l e r a t i o n and climbing; 4 - p o i n t of a i r c r a f t l i f t - o f f ; 5 - takeoff d i s t a n c e ; 6 - climbing t r a j e c t o r y f o r 100% e n g i n e t h r u s t ; 7 - l e n g t h of calculated takeoff t ra j ec t o r y ; 8 - permissible inclina t i o n s i n t r a j e c t o r y f o r extended takeoff d u e t o e n g i n e f a i l u r e ; 9 - a c t u a l t r a j e c t o r y of extended t a k e o f f . Immediately a f t e r l i f t - o f f , t h e a i r c r a f t ' s high t h r u s t - w e i g h t r a t i o permits i t t o g a i n a l t i t u d e and a c c e l e r a t e up t o i t s r a t e of climb along an inclined trajectory. In t h i s case, t h e gain i n a l t i t u d e i s c u r v i l i n e a r , because i t s angle of i n c l i n a t i o n c o n s t a n t l y i n c r e a s e s . The holding a f t e r l i f t - o f f , which i s used i n t h e a c c e l e r a t i o n o f p i s t o n a i r c r a f t p r i o r t o beginning g a i n i n g a l t i t u d e , i s n o t a p p l i e d i n t u r b o j e t aircraft. The take-off run up t o l i f t - o f f speed. A s a r u l e , t a k e o f f is performed w i t h f l a p d e f l e c t i o n , from t h e b r a k e s when t h e t a k e o f f regime f o r t h e engines /89 - i s used. To t h i s end, t h e engines are f i r s t p u t i n t o t a k e o f f rpm's and t h e n t h e brakes are slowly r e l e a s e d . Figure 65 shows a graph of t h e c o e f f i c i e n t c as a f u n c t i o n of t h e angle of a t t a c k and t h e a i r c r a f t p o l a r f o r t a k e o f f & s i t i o n of t h e wing f l a p s and s l a t s . An a i r c r a f t having t r i p l e - s l o t t e d f l a p s (high v a l u e f o r c ) was used as an example. y 1-0 82
- 92. A t t h e beginning of t h e take- /90 o f f r u n , d i r e c t i o n i s maintained by t h e brakes and d i r e c t i n g t h e nose wheel, and a t a speed of 150-170 km/hr, when t h e rudder becomes e f f e c t i v e , i t i s maintained through t h e a p p r o p r i a t e i n c l i n a t i o n of t h e rudder t o t h e s i d e as r e q u i r e d . When t h e p r o p e r t a k e o f f a n g l e of a t t a c k (9-10") i s maintained, l i f t - o f f of t h e a i r c r a f t from t h e ground occurs without a d d i t i o n a l movement of t h e c o n t r o l wheel when l i f t - o f f speed i s a t t a i n e d . With a l i f t - o f f a n g l e o f a t t a c k of 9-10", the t a i l section of the fuselage must be s u f f i c i e n t l y f a r o f f t h e runway and a s p e c i f i c s u b - c r i t i c a l angle of a t t a c k must b e maintained. If the p i l o t unintentionally i n c r e a s e s t h e angle of a t t a c k t o 11-12", c o n t a c t of t h e t a i l p o r t i o n of t h e f u s e l a g e with t h e c o n c r e t e must be avoided. An improperly chosen angle of a t t a c k during l i f t - o f f may e i t h e r extend t h e l e n g t h of t h e t a k e o f f r u n , o r , on t h e c o n t r a r y , l e a d t o premature l i f t - o f f a t a low speed. Thus, i f t h e p i l o t achieves l i f t - Figure 65. T h e D e p e n d e n c e of c on c1 Y o f f a t a lower angle of a t t a c k and t h e P o l a r s of an A i r c r a f t having ( f o r example, w i t h M = 6" i n s t e a d T r i p l e - S l o t t e d W i n g Flaps and S l a t s : o f 9-10">, i . e . , below c a - p o l a r f o r a i r c r a f t w i t h landing y 1-0' which corresponds t o a high speed, g e a r down and w i n g f l a p s d e f l e c t e d a t t h e length of t h e t a k e o f f run 2 5 " ; b - t h e same ai r c r a f t w i t h increases. In calculating t h e allowance made f o r t h e e f f e c t of a i r c r a f t 1 - i f t - o f f during t a k e o f f , s c r e e n i n g by t h e e a r t h during t h e t h e v a l u e s normally accepted a r e takeoff run ( K = 1.6 : 0.134 = 1 2 ) . Note: T-0 = Take Off c1 = 8-11" and cy l-o = 1 . 3 - 1 . 7 (depending on t h e design and arrangement o f t h e f l a p s ) . For t h e example shown i n Figure 65, w e have c1 = 1-0 = 11" and c = 1.6. y 1-0 A c c e l e r a t i o n from t h e l i f t - o f f speed t o a safe speed w i t h simultaneous climbing. P i l o t i n g an a i r c r a f t during t h i s s t a g e of f l i g h t i n v o l v e s t h e following. A f t e r l i f t - o f f , maintaining t h e t a k e o f f a n g l e , t h e a i r c r a f t smoothly s h i f t s i n t o g a i n i n g a l t i t u d e w i t h a subsequent d e c r e a s e i n t h e angle 83
- 93. of a t t a c k . The main wheels a r e braked, t h e time f o r complete braking averaging 0.2 - 0 . 3 s e c . To decrease drag a g a i n s t t h e a i r c r a f t during climbing ( a f t e r l i f t - o f f ) , t h e landing g e a r must be r e t r a c t e d without delay. The a i r c r a f t ' s h y d r a u l i c system r e t r a c t s t h e landing g e a r , with opening and c l o s i n g o f t h e main landing g e a r doors, i n 5-15 s e c . The landing g e a r i s r e t r a c t e d a t a speed of 20-30 km/hr above t h e l i f t - o f f speed, and a t a h e i g h t n o t below 5-7 meters. During t h e process of r e t r a c t i o n , t h e a i r c r a f t ' s speed i n c r e a s e s . After t h e landing g e a r i s r e t r a c t e d , t h e f l a p s are i n t u r n r e t r a c t e d a t a h e i g h t not l e s s t h a n 50-80 meters, and t h e a i r c r a f t a c c e l e r a t e s t o a speed f o r g a i n i n g a l t i t u d e . The p i l o t must f l y t h e a i r c r a f t during t h i s i n t e r v a l i n such a way t h a t b e f o r e t h e f l a p s a r e r e t r a c t e d , t h e speed does not exceed t h e p e r m i s s i b l e with r e s p e c t t o s t a b i l i t y c o n d i t i o n s . The time r e q u i r e d f o r r e t r a c t i n g f l a p s d e f l e c t e d a t a t a k e o f f angle i s 8-12 s e c . As t h e f l a p s a r e r e t r a c t e d , a p i t c h i n g moment i s c r e a t e d , s o t h a t p r e s s i n g f o r c e s a r e c r e a t e d on t h e c o n t r o l 'wheel which a r e e a s i l y r e l i e v e d by t h e e l e v a t o r t r i m t a b s . This i s a case i n which t h e e l e c t r i c a l c o n t r o l of t h e e l e v a t o r t r i m t a b s i s convenient t o use. A f t e r t h e f l a p s a r e r e t r a c t e d , t h e engine rpm's decrease t o normal and t h e r e i s a f u r t h e r a c c e l e r a t i o n up t o t h e climbing c r u i s i n g speed o r t o t h e f l i g h t speed along a r e c t a n g u l a r r o o t . § 3. Forces Acting on t h e A i r c r a f t During t h e Takeoff Run and Takeoff /91 Let us examine t h e f o r c e s a c t i n g on t h e a i r c r a f t during t h e takeoff run (Figure 66). The t o t a l f o r c e of t h e engine t h r u s t a c t s i n t h e d i r e c t i o n of t h e a i r c r a f t motion. The o v e r a l l f o r c e of wheel f r i c t i o n a g a i n s t t h e ground F = F + F and t h e a i r c r a f t drag Q a c t a g a i n s t t h e a i r c r a f t ' s motion, 1 2 braking i t . The d i f f e r e n c e i n the f o r c e s P -Q - F = R is called the acc a c c e l e r a t i o n f o r c e . The following f o r c e s a c t p e r p e n d i c u l a r t o t h e t r a j e c t o r y of motion: l i f t f o r c e Y , f o r c e N of t h e r e a c t i o n o f t h e ground on t h e landing g e a r wheels, and t h e f o r c e of weight G. The f o r c e Racc communicates t o t h e aircraft the acceleration where m i s t h e a i r c r a f t mass. The g r e a t e r t h e a c c e l e r a t i o n f o r c e and t h e lower t h e a i r c r a f t weight, the h i g h e r t h e a c c e l e r a t i o n w i l l be. If i n s t e a d o f Racc we s u b s t i t u t e i t s v a l u e i n t o t h e formula, we o b t a i n j,=9.81 ( -$-+). As t h e landing g e a r wheels r o l l along t h e ground, f r i c t i o n f o r c e s a r i s e whose v a l u e i s a f u n c t i o n of t h e condition of t h e runway (type o f s u r f a c e ) and 84
- 94. .. - - ., . .. ....-... .-,.., ...,, ,.. , , I , I I ,111 111.11 1 11 .1 1 11.11 I I1 I t h e degree o f deformation i n t h e t i r e s . The amount of t h e f o r c e of f r i c t i o n i s determined as t h e product of t h e loads on t h e wheels on t h e f r i c t i o n coefficient f. a) moment o f f r i c t i o n f o r c e +--l F i g u r e 6 6 . Diagram of Forces Acting on t h e A i r c r a f t During Takeoff Run ( a ) and A f t e r L i f t - o f f During C 1 i m b i ng ( b ) . During t h e t a k e o f f run, t h e a i r c r a f t wing begins c r e a t i n g a l i f t i n g f o r c e which r a p i d l y i n c r e a s e s and removes t h e l o a d from t h e landing g e a r wheels. The v a l u e of t h e f r i c t i o n f o r c e f o r each moment may b e determined according t o t h e following formula: F = f (G - Y ) . The f r i c t i o n c o e f f i c i e n t ( o r c o e f f i c i e n t of adhesion) f o r dry c o n c r e t e i s f = 0.03 - 0 . 0 4 , and f o r w e t c o n c r e t e i t is 0.05; f o r dry ground cover and f o r a c l e a r e d snow cover i t i s 0.07; f o r a w e t g r a s s s u r f a c e it i s 0.10. The v a l u e P/G i s t h e a i r c r a f t t h r u s t - w e i g h t r a t i o during t a k e o f f . The g r e a t e r t h e t h n i s t - w e i g h t r a t i o , t h e g r e a t e r t h e t a k e o f f run a c c e l e r a t i o n and /91 t h e s h o r t e r t h e l e n g t h of t h e t a k e o f f run. I n c r e a s i n g t h e t h r u s t - w e i g h t r a t i o i s an e f f e c t i v e means of improving t a k e o f f c h a r a c t e r i s t i c s . For example, when t h e Conway 550 d o u b l e - c i r c u i t engines w i t h t h e i r 7,500 k G t h r u s t were i n s t a l l e d on t h e Boeing-707, t h e t h r u s t - w e i g h t r a t i o i n c r e a s e d from 0.2 t o 0.26. A g r e a t e r t h r u s t - w e i g h t r a t i o i s enjoyed by a i r c r a f t w i t h two engines (0.28 0.33 kG t h r u s t / k g w e i g h t ) , and t h e l e a s t is t h a t of a i r c r a f t with f o u r engines (0.22 - 0.26 kG t h r u s t / k g w e i g h t ) . A s can b e s e e n from t h e formula above, t h e maximum a c c e l e r a t i o n i s during t h e f i r s t s t a g e of t h e t a k e o f f run ( t h e a i r c r a f t drag f o r c e i s low). With an i n c r e a s e i n speed t h e t h r u s t of j e t engines d e c r e a s e s , although during t h e t a k e o f f run i t may b e considered c o n s t a n t . B comparison w i t h y p i s t o n e n g i n e s , t h e t h r u s t of j e t engines d u r i n g t a k e o f f decreases l e s s s i g n i f i c a n t l y and a t t h e end of t h e t a k e o f f run amounts t o 87 - 92% of t h e s t a t i c thrust P . The drag f o r c e during t h e t a k e o f f run i n c r e a s e s from 0 t o Ql-0 ( a i r c r a f t grag a t t h e i n s t a n t of l i f t - o f f ) . A t l i f t - o f f , Y = G , s o t h a t t h e f r i c t i o n f o r c e w i l l equal zero. Thus, a t t h e end of t h e t a k e o f f p o r t i o n , when t h e a i r c r a f t s e p a r a t e s from t h e ground, t h e a c c e l e r a t i o n f o r c e ( r e s e r v e t h r u s t ) equals t h e d i f f e r e n c e between t h e t o t a l engine t h r u s t and t h e a i r c r a f t drag: Racc = P -Q. 85
- 95. A i r c r a f t drag a t t h e i n s t a n t of l i f t - o f f (1-0) may be determined according t o formula: where c X i s t h e drag c o e f f i c i e n t f o r an a i r c r a f t w i t h landing g e a r down and f l a p s extended i n takeoff p o s i t i o n a t an angle of a t t a c k a t t h e i n s t a n t of l i f t - o f f . For example, f o r an a i r c r a f t with a t a k e o f f weight of 76 tons and a wing area of S = 180 m2, t h e t h r u s t during t a k e o f f c o n f i g u r a t i o n f o r a l i f t - o f f speed of 300 km/hr (83.3 m/sec) i s approximately 17,000 kG. If we assume that at lift-off c = 0.07 - 0.075, then x 1-0 Q1-o= C.po PS V -83 0.071 *0.125*180 3 2 -5500 I - kG, 2 Then t h e a c c e l e r a t i o n f o r c e R = 17,000 -5,500 = 11,500 kG. The mean acc a c c e l e r a t i o n a t t h i s i n s t a n t w i l l be The lower t h e v a l u e c (due t o t h e p r o p e r s e l e c t i o n of t h e f l a p and x 1-0 s l a t systems), t h e lower Ql-o w i l l b e and t h e g r e a t e r t h e a c c e l e r a t i o n f o r c e w i l l be f o r the same assumed engi?e t h r u s t . For example, f o r an a i r c r a f t with a low takeoff weight (two e n g i n e s ) , during t h e t a k e o f f run below t h e l i f t - o f f speed Racc = 9,000 -5,800 kG, while t h e mean a c c e l e r a t i o n j x = 2.5 - 2 . 0 m/sec2J93 - I n such an a i r c r a f t , t h e t a k e o f f time decreases. During the climbing p o r t i o n of f l i g h t , under t h e e f f e c t of t h e f o r c e (Figure 66) t h e r e w i l l be a f u r t h e r i n c r e a s e i n f l i g h t speed. For t h i s Race case we may w r i t e the following equation of motion Race = P - Q - G sin 0 = mj, where G s i n 0 i s t h e a i r c r a f t component weight a c t i n g along t h e l i n e of flight; m i s t h e a i r c r a f t mass. Decreasing t h e t o t a l engine t h r u s t with an i n c r e a s e i n f l i g h t speed does n o t decrease the v a l u e of t h e a c c e l e r a t i o n f o r c e , because as a r e s u l t o f a decrease i n t h e angle of a t t a c k , t h e induced drag f o r t h e a i r c r a f t d e c r e a s e s . This allows an i n c r e a s e i n t h e speed during t h e t a k e o f f run p o r t i o n (achieving t h e r e q u i r e d climbing speed o r f l i g h t speed along a r e c t a n g u l a r r o o t ) . 86
- 96. The l e n g t h of t h e climbing p o r t i o n with a c c e l e r a t i o n i s a f u n c t i o n of t h e s p e c i f i c load, thrust-weight r a t i o , and o t h e r parameters. The component G s i n 0 i n i t i a l l y has a low v a l u e , because t h e angle of i n c l i n a t i o n of the t r a j e c t o r y during climbing i s small (0 = 6 - l o o ; s i n 0 = = 0.105 - 0.175). § 4. Length of Takeoff Run. Lift-off Speed The length of t h e a i r c r a f t takeoff run i s a f u n c t i o n of t h e l i f t - o f f speed and a c c e l e r a t i o n : L = v21-o ace 2 j x ave ' where jx ave i s the average a c c e l e r a t i o n value. The l i f t - o f f speed i s determined according t o formula: /-G S ~ km/hr , cYl-O. G where - i s t h e u n i t load p e r 1 m2 of wing area. S The g r e a t e s t u n i t load i s i n four-engined a i r c r a f t ( t h e Super Vickers VC-10, 570 kG/m2; DC-8-3C, 560 kG/m2) and somewhat lower i n two-engined a i r c r a f t (BAC-111-200, 370 k G / m 2 , t h e Caravelle-XB, 350 kG/m2) ; f o r t h r e e engined a i r c r a f t ( t h e Boeing-727 and t h e De Havilland Trident-1E) i t i s 450 kG/m2. For an average c = 1.6 ( t r i p l e - s l o t f l a p s and s l a t s ) , t h e l i f t - o f f y 1-0 speed f o r G/S = 450 - 500 kG/m2 i s 220 - 240 km/hr. For an average a c c e l e r a t i o n of j x = 2 m/sec2, t h e length of t h e t a k e o f f - r u n i s 1 , 1 0 0 - 1,300 m . A s has already been noted, t h e swept wing has a lower v a l u e f o r t h e /94 coefficient c then does t h e s t r a i g h t wing. This r e s u l t s i n a lower v a l u e Y Inax for c A l l i n a l l , t h i s leads t o a s u b s t a n t i a l i n c r e a s e i n Vlm0, and y 1-0' consequently i n the length of t h e t a k e o f f run. Therefore, t h e f l a p s and s l a t s a r e used t o i n c r e a s e cy m a ' Deflecting them t o t h e i r maximum angle a t take o f f may, of course, s u b s t a n t i a l l y decrease t h e l i f t - o f f speed, b u t i n t h i s event t h e r e i s a l s o an i n c r e a s e i n drag, a decrease i n a c c e l e r a t i o n and, lastly, an i n c r e a s e i n t h e length of t h e t a k e o f f run. This r e q u i r e s s e l e c t i o n of t h e optimum angle of i n c l i n a t i o n f o r t h e f l a p s , a t which c i n c r e a s e s and, Y 87
- 97. consequently, s o does c while t h e a i r c r a f t drag i n c r e a s e s n e g l i g i b l y . y 1-0' Designers are s t r i v i n g t o achieve b o t h t h e g r e a t e s t v a l u e f o r cy 1-0 and high aerodynamic performance i n a i r c r a f t . If during t a k e o f f t h e a i r c r a f t has a f i n e n e s s r a t i o of 14-15, t h i s makes i t p o s s i b l e t o s o l v e many problems such as, f o r example, achieving t h e c o n t i n u a t i o n o f t a k e o f f i n t h e event o f t h e f a i l u r e of an engine, decreasing n o i s e i n t h e area through a s h a r p e r climbing t r a j e c t o r y , t h e s e l e c t i o n of engines with optimal t h r u s t values f o r a given a i r c r a f t , e t c . C a l c u l a t i o n s and f l i g h t t e s t s have shown t h a t t h e optimum angle of d e f l e c t i o n f o r f l a p s during t a k e o f f i s 10-25". This angle y i e l d s t h e optimum r a t i o between c and cx, which leads t o a marked decrease i n y 1-0 t h e length of t h e t a k e o f f run. W must once more t a k e n o t e t h a t cy l-o i s e s e l e c t e d from t h e c o n d i t i o n of a s u f f i c i e n t r e s e r v e with r e s p e c t t o t h e angle of attack p r i o r t o l i f t - o f f ( c ) , s o as t o e l i m i n a t e s i d e s l i p . According Y m a t o norms of a i r w o r t h i n e s s , t h e a i r c r a f t l i f t - o f f speed must b e no l e s s than 20% g r e a t e r than t h e brakeaway speed ( s e e how i t is determined i n Chapter X I , 5 14). § 5. Methods of Takeoff E a r l i e r w e e s t a b l i s h e d t h a t a c c e l e r a t i o n during t h e t a k e o f f run and consequently t h e length of the t a k e o f f run a r e f u n c t i o n s of t h e d i f f e r e n c e i n t h e a v a i l a b l e t h r u s t and t h e o v e r a l l a i r c r a f t drag. The engine t h r u s t during the t a k e o f f run up t o t h e l i f t - o f f speed of 220-240 km/hr v a r i e s i n s i g n i f i c a n t l y (by 6-8%). The o v e r a l l a i r c r a f t drag during t h i s p o r t i o n o f t a k e o f f i s t h e s m of t h e aerodynamic drag (which i n c r e a s e s as t h e angle of a t t a c k u i n c r e a s e s ) and t h e f r i c t i o n f o r c e of t h e wheels (on t h e runway s u r f a c e ) , which .decreases as a r e s u l t of a l e s s e n i n g of t h e load on t h e wheels then i n c r e a s e i n wing l i f t . Therefore, t h e p i l o t must s e l e c t an angle a ( d i f f e r e n t f o r each a i r c r a f t ) a t which t h e t o t a l drag w i l l be minimal and, consequently, t h e t a k e o f f run w i l l be s h o r t e s t . Due t o t h e lack of a i r f l o w o f t h e s l i p s t r e a m from the p r o p e l l e r s , t h e e f f e c t i v e n e s s of t h e p i t c h c o n t r o l a t t h e beginning o f t h e takeoff run i s below t h a t of a prop-driven a i r c r a f t . The r e q u i r e d l o n g i t u d i n a l moment f o r l i f t - o f f o f the nose wheel i s c r e a t e d by t h e e l e v a t o r only a t a r a t h e r high speed, c l o s e t o t h e take-off speed. A s a r e s u l t of t h i s , t h e g r e a t e r p a r t of the take-off run f o r a t u r b o j e t a i r c r a f t i s achieved i n stand- - /95 ing configuration. The angle of attack during t h e t a k e o f f run i s a f u n c t i o n of t h e angle I$ of t h e wing s e t t i n g ; i f , f o r example, t h e s e t t i n g angle I$ = l o , then c1 = 1" a l s o . However, t h e wings of modern a i r c r a f t have geometric t w i s t (Chapter 11, § l ) , which c r e a t e s an angle c1 which v a r i e s along t h i s span. I n the graph shown i n Figure 65, t h e v a l u e c corresponds t o t h e average f o r y t-0 a t a k e o f f run of c1 = 1 - 3". B t h e l o n g i t u d i n a l p o s i t i o n of t h e a i r c r a f t ( t h e angle of t h e a i r c r a f t ' s y l o n g i t u d i n a l a x i s ) , i . e . , t h e angle of a t t a c k , t h e p i l o t may c o n t r o l i n achieving a speed a t which the e f f e c t i v e n e s s of t h e e l e v a t o r i s s u f f i c i e n t t o i n i t i a t e l i f t i n g t h e a i r c r a f t ' s nose ( f r o n t landing g e a r s t r u t ) . Often 88
- 98. I - I - .I --- t h i s speed i s s e l e c t e d from t h e condition of achieving rudder e f f i c i e n c y i n o r d e r t o prevent t h e a i r c r a f t from turning on t h e main landing g e a r struts with nose r a i s e d i n t h e event of engine f a i l u r e during t h e t a k e o f f run. I n t h i s event, t h e rudder should p a r r y t h e t u r n i n g moment from t h e asymmetric t h r u s t o f the o p e r a t i n g engines. Usually, a f t e r l i f t - o f f of t h e f r o n t s t r u t , t h e a i r c r a f t tends t o p r o g r e s s i v e l y i n c r e a s e t h e p i t c h angle under t h e e f f e c t of t h e i n c r e a s i n g wing l i f t . Therefore, i n i t i a l l y t h e c o n t r o l wheel i s brought back toward o n e s e l f , and then commensurably moved away, i n an attempt t o maintain t h e a i r c r a f t a t an angle of a t t a c k of 3 - 4 O . The length of t h e takeoff run i s a f u n c t i o n b a s i c a l l y of t h e a c c u r a t e s e t t i n g of t h e angle of a t t a c k . During t h e t a k e o f f run, minor d e v i a t i o n s from t h e optimum a, a t which drag i s minimal, do n o t l e a d t o a s u b s t a n t i a l i n c r e a s e i n t h e length of takeoff run. There are two ways of p u t t i n g t h e a i r c r a f t i n t o t h e t a k e o f f angle of a t t a c k . The f i r s t c o n s i s t s of t h e nose strut's l i f t i n g o f f a t t h e i n s t a n t when e l e v a t o r e f f i c i e n c y i s achieved. The a i r c r a f t achieves an angle o f at%ack of 3-4" and t h e r e s t of t h e run t a k e s p l a c e on t h e main landing g e a r s . Smoothly operating t h e e l e v a t o r , t h e p i l o t maintains t h e angle of a t t a c k during t h e t a k e o f f run and a t t h e i n s t a n t of l i f t - o f f he c r e a t e s t h e takeoff angle of a t t a c k . In the second way, which has only r e c e n t l y gained acceptance, t h e e n t i r e takeoff run i s performed i n t h e s t a n d i n g c o n f i g u r a t i o n , and when a speed c l o s e t o t h e l i f t - o f f speed (Vl-o - 15 - 20 km/hr) i s achieved, t h e c o n t r o l wheel i s smoothly b u t vigorously p u l l e d toward oneself ( i n 4-5 s e c ) , by which motion t h e p i l o t l i f t s t h e f r o n t strut o f f and, without maintaining t h e a i r c r a f t i n a two-point c o n f i g u r a t i o n , p u t s i t i n t o t h e t a k e o f f angle of a t t a c k . Separation occurs p r a c t i c a l l y from t h r e e p o i n t s without any p e r c e p t i b l e over load during t h e process of r o t a t i n g the a i r c r a f t r e l a t i v e t o t h e l a t e r a l a x i s and i n c r e a s i n g t h e p i t c h i n g angle. In t h i s way t h e p i l o t maintains complete c o n t r o l of t h e t a k e o f f r u n , t h e speed and t h e o p e r a t i o n of the engines. Usually during t h e t a k e o f f run, t h e n a v i g a t o r s t a t e s t h e a i r c r a f t speed over the intercom a t each 10 km/hr, s t a r t i n g a t a speed of 150 km/hr, while t h e p i l o t d i r e c t s a l l h i s a t t e n t i o n s t r a i g h t ahead. A c o n t r o l l a b l e leading s t r u t s i m p l i f i e s maintaining the d i r e c t i o n during t h e f i r s t s t a g e of / 96 the takeoff run, b e f o r e t h e rudder becomes responsive, which almost e l i m i n a t e s t h e use of the brakes i n t h e main landing g e a r t r o l l e y . In t h e second method of p i l o t i n g , the t a k e o f f d i s t a n c e remains p r a c t i c a l l y t h e same as i n the f i r s t , but t h e takeoff run i s somewhat s h o r t e r due t o t h e h i g h e r speed. Also, t a k e o f f with. a s i d e wind i s f a c i l i t a t e d , s i n c e t h e c o n t r o l l a b l e nose wheel i n combination with t h e rudder makes it p o s s i b l e t o hold a f i x e d d i r e c t i o n up t o t h e moment of s e p a r a t i o n without i n c r e a s i n g t h e t a k e o f f run length ( i n a i r c r a f t with u n c o n t r o l l e d nose wheel, t h e run length i s u s u a l l y i n c r e a s e d due t o t h e asymmetrical braking of main landing gear t r u c k s ) . A f t e r t h e a i r c r a f t breaks away, t h e s i d e wind causes it t o t u r n a g a i n s t t h e wind; f o r example, with a wind speed of 18-20 m/sec, t h e r o t a t i o n angle i s 18-20". 89
- 99. F l y i n g i n v e s t i g a t i o n s have shown t h a t t h e r e q u i r e d r o t a t i o n of t h e f r o n t wheel does n o t exceed 4-5" with a s i d e wind up t o 20 m/sec. This allows t h e maximum p e r m i s s i b l e s i d e wind d u r i n g t a k e o f f t o b e i n c r e a s e d , f o r example,a wind a t 90" t o t h e runway can be up t o 15-18 m/sec, and a l s o s i m p l i f i e s t h e t a k e o f f maneuver. Up t o t h e p r e s e n t time, no s i n g l e o p i n i o n h a s developed among p i l o t s as t o t h e way i n which t h e c o n t r o l system o f t h e f r o n t g e a r should be c o n s t r u c t e d . The predominant opinion i s t h a t t h e r o t a t i o n o f t h e wheels should b e c o n t r o l l e d by t h e rudder p e d a l s ( a s on t h e TU-124 a i r c r a f t ) , f r e e i n g t h e p i l o t ' s hands f o r o p e r a t i o n of t h e e l e v a t o r c o n t r o l l e v e r , motor t h r o t t l e s , e t c . However, i t i s known t h a t when t h e t a k e o f f speed reaches 150-200 km/hr and t h e rudder begins t o be e f f e c t i v e , i t i s more expedient t o u s e t h e rudder alone t o m a i n t a i n t h e t a k e o f f d i r e c t i o n , d i s c o n n e c t i n g t h e f r o n t l a n d i n g g e a r , which i s n o t always t e c h n i c a l l y p o s s i b l e i f t h e g e a r i s c o n t r o l l e d by t h e p e d a l s . Therefore, t h e wear r a t e of t h e rubber t i r e s on t h e f r o n t landing g e a r may be i n c r e a s e d . A second p l a n i s t h a t o f independent c o n t r o l o f r o t a t i o n of t h e f r o n t l a n d i n g g e a r , n o t connected t o t h e o p e r a t i o n o f t h e r u d d e r (TU-104 a i r c r a f t ) . Let us analyze t h e technique of performing a t a k e o f f u s i n g t h e second method ( s e p a r a t i o n from t h r e e p o i n t s ) . I t i s recommended t h a t t h e e l e v a t o r trimmer l e v e r be s e t a t 0 . 5 - 0 . 8 d i v i s i o n s forward i n advance, i n o r d e r t o i n c r e a s e t h e load on t h e s t i c k from t h e e l e v a t o r a t t h e moment o f s e p a r a t i o n . Thus, t h e s e a c t i o n s a r e i n o p p o s i t i o n t o t h e e s t a b l i s h e d t r a d i t i o n , according t o which t h e trimmer c o n t r o l i s moved 0.5-1 d i v i s i o n s back i n o r d e r t o d e c r e a s e l o a d s a t t h e moment o f l i f t i n g o f t h e f r o n t g e a r and s e p a r a t i o n o f t h e a i r c r a f t . Before beginning t h e t a k e o f f r u n , t h e s t i c k i s pushed forward approximately t o t h e n e u t r a l p o s i t i o n . Holding t h e a i r c r a f t with t h e b r a k e s , t h e engines are s e t a t t a k e o f f regime. A f t e r making s u r e t h a t t h e o p e r a t i n g regime of t h e engines corresponds t o t h e norm, t h e b r a k e s a r e r e l e a s e d and t h e t a k e o f f run i s begun, d u r i n g which t h e r e q u i r e d d i r e c t i o n i s maintained by c o n t r o l l i n g t h e f r o n t landing g e a r . The e f f e c t i v e n e s s o f c o n t r o l of t h e f r o n t l a n d i n g g e a r i s h i g h e r , t h e more s t r o n g l y t h e wheels a r e f o r c e d down t o t h e runway. When s u f f i c i e n t e f f e c t /% i v e n e s s o f t h e r u d d e r has been achieved t o m a i n t a i n t h e t a k e o f f c o u r s e , g e n e r a l l y 60-70% of t h e maximum speed, c o n t r o l of t h e f r o n t wheels can be disconnected ( i f t h i s i s p o s s i b l e i n t h e a i r c r a f t ) . When t h e t a k e o f f i s b e i n g performed with a s i d e wind, i n o r d e r t o p r e v e n t wind banking a t t h e moment o f s e p a r a t i o n , t h e a i l e r o n c o n t r o l must be t u r n e d " a g a i n s t t h e wind" by 30-80" with a wind speed of 8-18 m/sec b e f o r e s e p a r a t i o n . A f t e r s e p a r a t i o n , t h e r a t e of i n c r e a s e i n t h e p i t c h a n g l e must be s l i g h t l y decreased and t h e s t i c k smoothly moved t o t h e n e u t r a l p o s i t i o n . 86. F a i l u r e o f E n g i n e D u r i n g Takeoff Main t a k e o f f c h a r a c t e r i s t i c s of a i r c r a f t with one engine i n o p e r a t i v e . A s we know, one of t h e main requirements p l a c e d on passenger a i r c r a f t i s t h e p o s s i b i l i t y of c o n t i n u i n g t a k e o f f and climb i n c a s e o f engine f a i l u r e . A 90
- 100. knowledge o f t h e t a k e o f f c h a r a c t e r i s t i c s of an a i r c r a f t and t i m e l y usage o f t h e p i l o t i n g recommendations i n c a s e o f engine f a i l u r e w i l l guarantee a . s u c c e s s f u l c o n t i n u a t i o n o f t h e f 1i g h t The t a k e o f f c h a r a c t e r i s t i c s o f an a i r c r a f t with one i n o p e r a t i v e engine i n c l u d e t h e following: a ) t h e l e n g t h of t h e t a k e o f f run from t h e s t a r t i n g p o i n t t o t h e moment of engine f a i l u r e ; b) t h e l e n g t h of t h e t a k e o f f run from t h e moment o f engine f a i l u r e t o t h e moment o f s e p a r a t i o n ; c ) t h e i n c l i n a t i o n of t h e t r a j e c t o r y during t h e climbing s e c t o r with a c c e l e r a t i o n ; d) t h e i n c l i n a t i o n of t h e t r a j e c t o r y during t h e climbing s e c t o r with landing g e a r up; e ) t h e c r i t i c a l engine f a i l u r e speed ( t h e speed o f i n t e r r u p t i o n of t a k e o f f ) Vcr; f ) t h e s a f e t a k e o f f speed Vsto. I f we know t h e l e n g t h of t h e t a k e o f f run o f t h e a i r c r a f t from t h e s t a r t p o s i t i o n t o t h e moment o f engine f a i l u r e and t h e l e n g t h of t h e run from t h e moment of f a i l u r e t o complete a i r c r a f t h a l t , which make up t h e d i s t a n c e f o r i n t e r r u p t i o n of t a k e o f f , we can determine which a i r f i e l d s a r e s a f e f o r o p e r a t i o n of a given a i r c r a f t , which t y p e of approaches t o t h e runway should b e used, how t h e a i r c r a f t should b e p i l o t e d with an inoper a t i v e engine, e t c . I n o r d e r t o a s s u r e s a f e t y during c o n t i n u a t i o n of t h e t a k e o f f and climb with one motor i n o p e r a t i v e , i t i s necessary t h a t t h e angle of i n c l i n a t i o n of t h e t a k e o f f t r a j e c t o r y and climb t o a l t i t u d e measured during t e s t s be g r e a t e r than t h e minimum p e r m i s s i b l e angle (Figure 6 4 ) . A s we can s e e from t h e f i g u r e , a f t e r t h e landing gear are r a i s e d t h e i n c l i n a t i o n of t h e t r a j e c t o r y should be no less than 2 . 5 % , corresponding t o an angle 0 = 1' 30 min ( s i n 0 = V /V = 0 . 0 2 5 and 0 = 1' 30 min) . The end of t h e Y o p e r a t i o n of r a i s i n g t h e landing g e a r should correspond approximately t o t h e moment of passage of t h e t a k e o f f d i s t a n c e (H = 10.7 m p l u s 300 m . ) I n case of an engine f a i l u r e during t a k e o f f , t h e a v a i l a b l e t h r u s t d e c r e a s e s , t h e f l y i n g q u a l i t y of t h e a i r c r a f t becomes w o r s e and p i l o t i n g becomes more d i f f i c u l t due t o t h e asymmetrical n a t u r e of t h e t h r u s t and t h e /98 low f l i g h t speeds, decrease i n c o n t r o l l a b i l i t y and decrease i n r a t e of climb. The decrease i n a v a i l a b l e t h r u s t l e a d s t o an i n c r e a s e i n t h e dependence of t h e f l y i n g c h a r a c t e r i s t i c s of t h e a i r c r a f t on temperature and a i r p r e s s u r e . Therefore, t h e v e r t i c a l speed of t h e a i r c r a f t with one engine i n o p e r a t i v e , c h a r a c t e r i z i n g . t h e p o s s i b i l i t y of continuing t h e t a k e o f f and climb under design c o n d i t i o n s (p = 730 mm Hg and t = +3OoC) a r e s l i g h t l y l e s s than under s t a n d a r d c o n d i t i o n s (p = 760 mm H and t = +15'C). g The following speeds a r e c h a r a c t e r i s t i c f o r continued and i n t e r r u p t e d t a k e o f f s : a ) t h e c r i t i c a l speed o f engine f a i l u r e , V i s t h e speed c o r r e cr J sponding t o t h e " c r i t i c a l p o i n t " during t h e t a k e o f f r u n , a t which f a i l u r e of one of t h e engines i s p o s s i b l e . I n c a s e of f a i l u r e of one engine a t t h i s p o i n t , t h e p i l o t can e i t h e r end t h e t a k e o f f run w i t h i n t h e d i s t a n c e 91
- 101. a v a i l a b l e , s e p a r a t e and c o n t i n u e h i s f l i g h t , o r end h i s t a k e o f f run and s t o p w i t h i n t h e i n t e r r u p t e d t a k e o f f d i s t a n c e ; b ) t h e s a f e t a k e o f f speed i s t h e speed a t which t h e a i r c r a f t begins"to climb a f t e r s e p a r a t i o n and VstoJ a c c e l e r a t i o n with one engine i n o p e r a t i v e . According t o t h e norms of t h e ICAO, t h i s should be 15-20% (depending on t h e number o f engines on t h e a i r c r a f t ) g r e a t e r t h a n t h e s e p a r a t i o n speed f o r t h e t a k e o f f c o n f i g u r a t i o n of t h e a i r c r a f t : V s t o - (1.15-1.2) Vs > ( s e e Chapter X I , 514). 1 If t h e speed o f s e p a r a t i o n i s l e s s t h a n t h e s a f e speed o f t h e a i r c r a f t , t h e a i r c r a f t i s h e l d a f t e r s e p a r a t i o n with a c c e l e r a t i o n t o V s t o ' t h e n t h e climb : o a l t i t u d e i s begun. The main c h a r a c t e r i s t i c i n d i c a t i n g t o t h e p i l o t t h a t an engine has f a i l e d i s t h e appearance of a tendency of t h e a i r c r a f t t o t u r n and bank toward t h e engine which has f a i l e d . Also, f a i l u r e o f an engine can b e determined from t h e d r o p i n o i l p r e s s u r e and f u e l p r e s s u r e , d e c r e a s e i n engine r o t a t i n g speed i n d i c a t e d by t h e tachometer, e t c . I n o r d e r t o make i t p o s s i b l e f o r t h e p i l o t t o d e c i d e t o c o n t i n u e t h e t a k e o f f o r i n t e r r u p t t h e t a k e o f f , t h e p i l o t should know t h e c r i t i c a l speed f o r engine f a i l u r e and f o r i n t e r r u p t i o n of t h e t a k e o f f . During t h e p r o c e s s of a i r c r a f t t e s t i n g , i n t e r r u p t e d and continued t a k e o f f s a r e u s u a l l y performed w i t h one engine switched o f f d u r i n g v a r i o u s s t a g e s o f t h e t a k e o f f . When t h i s i s done, t h e l e n g t h of t h e t a k e o f f run t o s e p a r a t i o n o f t h e a i r c r a f t and t h e l e n g t h of t h e t r a j e c t o r y t o a l t i t u d e 1 0 . 7 m a r e measured i f t h e t a k e o f f i s continued, a s well a s t h e l e n g t h of t h e run t o h a l t i f it i s i n t e r r u p t e d . When an i n t e r r u p t e d t a k e o f f i s performed, f i r s t t h e engine i s turned o f f , t h e n a f t e r 3 s e c ( r e a c t i o n of p i l o t t o f a i l u r e ) t h e o p e r a t i n g engines a r e reduced t o t h e i d l e , t h e s p o i l e r s a r e extended and t h e b r a k i n g p a r a c h u t e i s r e l e a s e d and i n t e n s i v e b r a k i n g i s begun. The t r a n s i t i o n t o t h e i d l e i s made due t o t h e n e c e s s i t y of maintaining p r e s s u r e i n t h e h y d r a u l i c system c o n t r o l l i n g t h e s p o i l e r s and landing g e a r . When a continued t a k e o f f i s performed, t h e p i l o t , a f t e r t h e engine i s /E turned o f f , c o n t i n u e s h i s a c c e l e r a t i o n t o t h e s e p a r a t i o n speed and a c c e l e r a t i o n t o t h e s a f e f l y i n g speed. The d a t a produced by t h e s e t e s t s a r e used t o c o n s t r u c t graphs o f t h e dependence of t a k e o f f r u n , d i s t a n c e of continued f l i g h t t o H = 10.7 m and d i s t a n c e of i n t e r r u p t e d t a k e o f f on speed (Figure 6 7 ) . The c r i t i c a l speed f o r engine f a i l u r e ( p o i n t B) corresponds t o p o i n t A of t h e i n t e r s e c t i o n of t h e curves f o r i n t e r r u p t e d and continued t a k e o f f s . Here a l s o t h e s o - c a l l e d runway b a l a n c e l i n e i n t h e d i r e c t i o n of t h e t a k e o f f c o u r s e ( p o i n t C) i s determined, which i n c a s e of an engine f a i l u r e d u r i n g t a k e o f f provides f o r c o n t i n u a t i o n of t h e t a k e o f f o r s t o p p i n g 92
- 102. I111 of t h e a i r c r a f t (by braking) w i t h i n t h e l e n g t h o f t h e runway a f t e r t h e /- loo takeoff i s interrupted. I L I Figure 67. Diagram f o r Determination o f Balance Runway L e n g t h and C r i t i c a l S p e e d o f E n g i n e Failure I f t h e t a k e o f f i s continued, a c c e l e r a t i o n o f t h e a i r c r a f t t o t h e s a f e t a k e o f f speed should b e performed a t an a l t i t u d e of 5-7 m (above t h e runway), a t which p o i n t t h e l a n d i n g g e a r should begin t o b e r a i s e d . A t 1 0 . 7 m , t h e landing g e a r should be almost a l l t h e way up [ t a k e o f f d i s t a n c e ) . The complete r a i s i n g of t h e landing g e a r shou'ld be completed a f t e r t h e . t a k e o f f d i s t a n c e p l u s 300 m ( r e s e r v e ) have been covered. I n c a s e o f i n t e r r u p t i o n of t h e t a k e o f f , t h e run should b e completed on t h e runway. 93
- 103. The c r i t i c a l speed f o r engine f a i l u r e is t h e maximum speed, upon r e a c h i n g which t h e p i l o t can i n t e r r u p t t h e t a k e o f f o r c o n t i n u e i t with equal s a f e t y . If t h e t a k e o f f i s continued a t VM < 'cr (F.igure 68), t h e continued t a k e o f f d i s t a n c e LM t o a l t i t u d e 1 0 . 7 m i s g r e a t e r t h a n t h e balanced runway l e n g t h ; t h i s i s p a r t i c u l a r l y dangerous i f t h i s l e n g t h i n c l u d e s t h e 400-m t e r m i n a l s a f e t y s t r i p . This i s a paved c o n c r e t e s t r i p ( i n case t h e a i r c r a f t r o l l s beyond t h e a c t u a l runway d u r i n g an i n t e r r u p t e d t a k e o f f ) . 240 260 280 300 320 340 34 35 36 37 E.. �on zKM/hr r.0: Figure 68. V e r t i c a l S p e e d of Figure 69. V e r t i c a l S p e e d A i r c r a f t During C 1 imb w i t h O n e A s a Funct ion of Takeoff I n o p e r a t i v e Engine A s a Func Weight of Passenger Air t i o n of F l i g h t S p e e d ( A i r c r a f t c r a f t ( A i r c r a f t w i t h Two w i t h Two E n g i n e s , G t o = 35 t , E n g i n e s , S p e c i f i c Loading 360 kg/m2, O n e E n g i n e Landing Gear Up, H = 900 m) lnoperat i v e , A v a i l a b l e Power 0.14 kg t h r u s t / k g W i gh t ) e I n c a s e o f an i n t e r r u p t e d t a k e o f f a t t h e s e p a r a t i o n speed V s e p ' 'cr, t h e braking d i s t a n c e w i l l a l s o be i n c r e a s e d ( p o i n t P ) and t h e a i r c r a f t w i l l r o l l beyond t h e end o f t h e a i r f i e l d . The b e s t c a s e i s e q u a l i t y of c r i t i c a l speed and s e p a r a t i o n speed, s i n c e t h i s f a c i l i t a t e s p i l o t i n g o f t h e a i r c r a f t c o n s i d e r a b l y and makes i t p o s s i b l e t o i n t e r r u p t t h e t a k e o f f s a f e l y r i g h t up t o t h e moment of s e p a r a t i o n o f t h e aircraft. Let u s now analyze t h e s e l e c t i o n o f a safe speed f o r c o n t i n u i n g o f t h e t a k e o f f (Figure 6 8 ) . Usually a t speeds of 280-320 km/hr, t h e maximum v e r t i c a l speed i s achieved with t h e f l a p s i n t h e t a k e o f f p o s i t i o n . However, a c c e l e r a t i o n o f t h e a i r c r a f t from V = 220-260 km/hr t o a speed seP o f 280-320 km/hr r e q u i r e s a g r e a t d e a l o f time and l e n g t h e n s t h e t a k e o f f d i s t a n c e . Therefore, i n o r d e r t o avoid i n c r e a s i n g t h e t a k e o f f run l e n g t h u n n e c e s s a r i l y , l e a v i n g it w i t h i n l i m i t s o f 600-800 m , t h e s a f e t a k e o f f speed i s s e l e c t e d a s 10-15 km/hr g r e a t e r than t h e s e p a r a t i o n speed, i f t h i s w i l l provide a climb t r a j e c t o r y angle of no l e s s t h a n 2.5% f o r an a i r c r a f t with l a n d i n g g e a r up. With an average a c c e l e r a t i o n o f 1 m/sec2, 3-4 s e c a r e 94
- 104. r e q u i r e d t o i n c r e a s e t h e speed o f t h e a i r c r a f t by 10-15 km/hr (2.8 4 . 2 m/sec). During t h i s t i m e , t h e a i r c r a f t can climb 5-7 m . The c r i t i c a l /lo1 speed of engine f a i l u r e f o r an a i r c r a f t with a given weight under given c o n c r e t e atmospheric c o n d i t i o n s f o r t h e balanced runway length h a s a unique value. However, i t i s known t h a t t h e engine t h r u s t depends s t r o n g l y on temperature of t h e surrounding a i r and atmospheric p r e s s u r e , and, f o r example, decreases below t h e s t a n d a r d t h r u s t with i n c r e a s i n g temperature, s o t h a t t h e excess a v a i l a b l e t h r u s t d e c r e a s e s . T h i s means t h a t t h e t a k e o f f run l e n g t h and t a k e o f f d i s t a n c e i n c r e a s e , t h e v e r t i c a l speed d e c r e a s e s (Figure 69), t h e angle of i n c l i n a t i o n o f t h e a i r c r a f t t r a j e c t o r y with a continued t a k e o f f w i t h one engine i n o p e r a t i v e d e c r e a s e s . I n o r d e r t o go beyond t h e l i m i t a t i o n with r e s p e c t t o t r a j e c t o r y i n c l i n a t i o n , t h e angle o f i n c l i n a t i o n of t h e f l a p s must be decreased,' o r i f t h i s i s i n s u f f i c i e n t , t h e t a k e o f f weight must b e decreased. The o p e r a t i n g i n s t r u c t i o n s of every a i r c r a f t include graphs and nomograms which can be used t o determine t h e t a k e o f f c h a r a c t e r i s t i c s i n case o f engine f a i l u r e during t h e t a k e o f f run. For t h i s purpose, f i r s t of a l l on t h e b a s i s of t h e f a c t t h a t t h e t r a j e c t o r y i n c l i n a t i o n of a continued t a k e o f f should b e no l e s s t h a n 2 . 5 % , t h e p e r m i s s i b l e t a k e o f f weight i s determined f o r each s e l e c t e d f l a p angle and a c t u a l a i r temperature (Figure 7 0 ) . . Then, u s i n g t h e nomogram (Figure 71) f o r t h e same atmospheric c o n d i t i o n s and t h e weight which h a s been determined, t h e balanced runway length i s found (point K ) . Then, u s i n g t h e nonogram (of Figure 72), t h e c r i t i c a l engine f a i l u r e speed ( t a k e o f f i n t e r r u p t i o n ) i s found, a s w e l l a s t h e s a f e speed f o r continued t a k e o f f . Figure 72 shows a nomogram f o r determination o f t h e c r i t i c a l speed. The same form of nomogram as on Figure 72 i s c o n s t r u c t e d i n o r d e r t o determine t h e s a f e speed f o r continued t a k e o f f , t a k e o f f run l e n g t h , s e p a r a t i o n speed, e t c . The nomograms on Figures 70-72 correspond t o t h e norms of t h e ICAO. The arrows on t h e nomograms show t h e p a t h f o r determining d e s i r e d q u a n t i ties. P i l o t i n g of an a i r c r a f t with one engine i n o p e r a t i v e a f t e r s e p a r a t i o n . S e p a r a t i o n of an a i r c r a f t with one engine i n o p e r a t i v e occurs a t t h e same speeds as with a l l engines o p e r a t i n g . The e f f e c t i v e n e s s of t h e a i l e r o n s i s decreased. Therefore, t h e p i l o t should a c c e l e r a t e t h e a i r c r a f t t o a s a f e speed, exceeding t h e s e p a r a t i o n speed by 10-15 km/hr. This speed i s a l s o / l o2 c a l l e d t h e b e s t t a k e o f f speed, s i n c e i t provides s u f f i c i e n t t r a n s v e r s e c o n t r o l l a b i l i t y and allows a climb t o b e performed a t V :V = 2 . 5 % . Y A c c e l e r a t i o n a f t e r s e p a r a t i o n should b e performed n e a r t h e ground, s i n c e t h e aerodynamic i n f l u e n c e of t h e s u r f a c e i s f a v o r a b l e and t h e i n d u c t i v e drag of t h e a i r c r a f t i s decreased. A t V + 10-15 km/hr with SeP f l a p s d e f l e c t e d by 10-25", c1 = 7-9" and t h e aerodynamic q u a l i t y i s 12-13; t h e i n d u c t i v e d r a g ( c = 1.15-1.3) i s approximately equal t o one-half of t h e Y 95
- 105. e n t i r e d r a g o f t h e a i r c r a f t . With q u a l i t y v a l u e s o f 12-13, t h e t h r u s t consumption of t h e a i r c r a f t i s always c o n s i d e r a b l y less t h a n t h e a v a i l a b l e t h r u s t and t h e a i r c r a f t can be e i t h e r a c c e l e r a t e d o r t r a n s f e r r e d i n t o a climb. W can see from Figure 65 t h a t e f o r an a n g l e ci = l l " , t h e aero- SeP dynamic q u a l i t y of t h e a i r c r a f t K = 9 , while c o n s i d e r i n g t h e i n f l u ence of t h e e a r t h it i s i n c r e a s e d t o 1 2 . A t 10-15 m , t h e i n f l u e n c e o f t h e e a r t h d e c r e a s e s s h a r p l y , and b y t h i s time t h e a i r c r a f t i s a l r e a d y f l y i n g a t t h e s a f e speed ( i n our example t h i s corresponds t o c1 = 8" and K = 9 ) . The a i r b o r n e s e c t o r of a i r c r a f t a c c e l e r a t i o n d u r i n g which it climbs t o 5-7 m, i s 600-800 m , and t h e v e r t i c a l speed V = 1.5- Y 2.5 m/sec (depending on atmospheric c o n d i t i o n s ) . Upon a c h i e v i n g t h e f i e l d temp., O C safe a l t i t u d e a f t e r acceleration, t h e l a n d i n g g e a r must be r a i s e d , i n order t o decrease t h e drag. Figure 70. Nomogram f o r 6-8 s e c a f t e r t h e landing Determination o f P e r m i s s i b l e g e a r b e g i n t o come up, t h e d r a g of Takeoff W e i g h t from Cond i t ion t h e a i r c r a f t i s decreased s i g n i f of Product ion of T r a j e c t o r y i c a n t l y and t h e excess t h r u s t can I n c l i n a t i o n of 2.5% i n Con s u p p o r t a climb with h i g h e r v e r t i c a l t i n u e d Takeoff speed, i n c r e a s i n g t h e s a f e t y o f continuation of the f l i g h t . Therefore, i f t h e landing g e a r a r e r a i s e d q u i c k l y , t h i s should be done d u r i n g t h e a c c e l e r a t i o n s e c t o r , although t h e f l y i n g a l t i t u d e will s t i l l b e q u i t e low. Raising t h e landing g e a r /lo3 i n c r e a s e s t h e v e r t i c a l speed by 0.5-1.0 m/sec, i . e . , t h e climb w i l l occur a t V = 2-2.7 m/sec (depending on t h e a i r c r a f t w e i g h t ) . Y Climbing up t o 100 m a l t i t u d e should b e continued a t c o n s t a n t speed. A t t h i s a l t i t u d e , t h e a i r c r a f t can b e a c c e l e r a t e d t o t h e p e r m i s s i b l e f l i g h t speed with mechanical d e v i c e s r e t r a c t e d , and t h e f l a p s can b e r a i s e d . I n o r d e r t o avoid a l o s s i n a l t i t u d e , it i s recommended t h a t t h e f l a p s b e r a i s e d i n two t o t h r e e p a r t i a l movements. A f t e r t h e f l a p s a r e r a i s e d , t h e engines should b e s e t i n t h e nominal regime. The d i r e c t i o n of f l i g h t can be maintained with one engine i n o p e r a t i v e by d e f l e c t i o n of t h e p e d a l s and c r e a t i o n of a 2-3-degree bank toward t h e engine s t i l l o p e r a t i n g . 96
- 106. E Figure 71. Nomogram f o r Determination of Balanced Runway Length Fiel'd TemD.9 OC Takeoff w t . , T Flgure 7 2 . Nomogram f o r Determination o f C r i t i c a l E n g i n e Failure Speed F l i g h t t r a j e c t o r y with one engine i n o p e r a t i v e . A s we noted above, t h e /lo4 angle of i n c l i n a t i o n of t h e t r a j e c t o r y during t h e f l i g h t s e c t o r a f t e r t h e landing gear a r e r a i s e d should be no l e s s t h a n 1' 30 min, i . e . , 2 . 5 % . However, depending on t h e c o n c r e t e c o n d i t i o n s i n which t h e a i r c r a f t i s being o p e r a t e d , t h i s t r a j e c t o r y i n c l i n a t i o n may vary. Under s t a n d a r d c o n d i t i o n s , t h e a i r c r a f t h a s g r e a t v e r t i c a l speed, s o t h a t it i s not d i f f i c u l t t o p r o v i d e t h e necessary t r a j e c t o r y a n g l e . The problem i s somewhat more d i f f i c u l t under design c o n d i t i o n s , and p a r t i c u l a r l y a t high a i r temperatures, a t which t h e v e r t i c a l speed d u r i n g t a k e o f f with one engine i n o p e r a t i v e i s s h a r p l y decreased. Usually, t h e f i r s t marker beacon i s l o c a t e d 900-1000 m from t h e runway, and has a tower 10-12 m h i g h . I f t h e takeoff i s continued, t h e a i r c r a f t
- 107. w i l l f l y over thTs p o i n t w i t h l a n d i n g g e a r almost up a t 90-25 m. E r r o r s i n p i l o t i n g t e c h n i q u e s and i n s t r u m e n t a l e r r o r s , as w e l l a s f a i l u r e t o f o l l o w t h e f l y i n g i n s t r u c t i o n s may r e s u l t i n reduced a l t i t u d e of f l i g h t over t h i s beacon. I t i s t h e r e f o r e r e q u i r e d t h a t t h e approach t o t h e runway b e open i n o r d e r t o avoid c o l l i s i o n of a i r c r a f t w i t h o b s t a c l e s i n c a s e o f a continued takeoff . S7. Influence of Various Factors on Takeoff Run L e n g t h During t h e p r o c e s s o f f l y i n g o p e r a t i o n s , t h e l e n g t h o f t h e t a k e o f f r u n may d i f f e r from t h e v a l u e s c a l c u l a t e d f o r s t a n d a r d c o n d i t i o n s under t h e i n f l u e n c e of changes i n engine t h r u s t , a i r c r a f t weight, temperature, d e n s i t y and p r e s s u r e of t h e a i r , p o s i t i o n of t h e f l a p s , speed and d i r e c t i o n of t h e wind. Engine t h r u s t h a s a c l e a r l y expressed dependence on engine r o t a t i o n speed. For example, i f t h e r o t a t i n g speed i s decreased from t h e t a k e o f f t o t h e nominal speed, t h e t h r u s t i s decreased by 5-7% ( s e e F i g u r e 5 2 ) . T h e r e f o r e , a d e c r e a s e i n r o t a t i n g speed may i n c r e a s e t h e t a k e o f f r u n l e n g t h c o n s i d e r a b l y . During t a k e o f f a t t h e nominal regime, t h e t a k e o f f run l e n g t h is i n c r e a s e d by 10-12%, and f l i g h t s a f e t y i n c a s e of an engine f a i l u r e i s decreased. The t a k e o f f weight i n f l u e n c e s t h e t a k e o f f r u n l e n g t h as f o l l o w s : 1) with an i n c r e a s e i n weight, t h e s e p a r a t i o n speed i n c r e a s e s ; 2) w i t h t h e same engine t h r u s t , an i n c r e a s e i n weight l e a d s t o a d e c r e a s e i n perform ance, and consequently t o a d e c r e a s e i n a c c e l e r a t i o n d u r i n g t h e takeoff run. As a r e s u l t , t h e l e n g t h o f t h e r u n i s i n c r e a s e d . The a i r temperature i n f l u e n c e s t h e t a k e o f f run l e n g t h i n two d i r e c t i o n s . F i r s t of a l l , t h e a i r temperature i n f l u e n c e s t h e t h r u s t of t h e engine, and, secondly, i t i n f l u e n c e s t h e t r u e s e p a r a t i o n speed. I n c r e a s i n g t h e temperature aauses a d e c r e a s e i n t h r u s t , and consequently o f a c c e l e r a t i o n d u r i n g t h e t a k e o f f r u n , which i n c r e a s e s t h e t a k e o f f run l e n g t h . Also, i n c r e a s i n g t h e temperature causes a d e c r e a s e i n d e n s i t y a n d , consequently, an i n c r e a s e i n t h e s e p a r a t i o n speed. For. example, an i n c r e a s e /lo5 i n a i r temperature of 10" i n c r e a s e s t h e t a k e o f f run l e n g t h by 6 - 7 % . - P r e s s u r e and d e n s i t y of t h e a i r . I f t h e a i r temperature i s c o n s t a n t , b u t t h e p r e s s u r e changes, t h e d e n s i t y of t h e a i r w i l l a l s o change; a s t h e p r e s s u r e changes, t h e d e n s i t y changes by t h e same f a c t o r , s i n c e p = o 0473 f, 98
- 108. I where p i s t h e a i r p r e s s u r e , mm Hg; T = 273 + t i s t h e a b s o l u t e temperature; t i s t h e temperature of t h e surrounding a i r i n degrees Centigrade. This formula allows us t o determine t h e d e n s i t y i n case o f a simul taneous change of t e m p e r a t u r e and a i r p r e s s u r e . A d e c r e a s e i n d e n s i t y l e a d s t o an i n c r e a s e i n t h e s e p a r a t i o n speeds and a d e c r e a s e i n t h e t h r u s t o f t h e engine due t o t h e d e c r e a s e i n t h e a i r flow by weight through t h e engine. With d e c r e a s i n g t h r u s t , t h e mean a c c e l e r a t i o n j d e c r e a s e s and, i n t h e x av f i n a l a n a l y s i s , t h e t a k e o f f run l e n g t h i n c r e a s e s . A d e c r e a s e i n p r e s s u r e of 10 mm Hg l e a d s t o an i n c r e a s e i n t a k e o f f run l e n g t h o f 3-4%. Thus, d u r i n g t a k e o f f under nonstandard c o n d i t i o n s ( t = +3OoC and p = 730 mm Hg) t h e t a k e o f f r u n l e n g t h i s i n c r e a s e d by 30-32%. Wind speed and d i r e c t i o n . The l e n g t h of t h e t a k e o f f run with a wind i s determined by t h e f o l l o w i n g formula: where W i s t h e head wind component o f t h e wind ( t h e "plus'' s i g n i s taken with a t a i l wind, "minus" - - with a head wind). The t a k e o f f , a s a r u l e , i s performed a g a i n s t t h e wind, s o t h a t t h e run l e n g t h and t a k e o f f d i s t a n c e a r e minimal. S e p a r a t i o n occurs a t a given a i r speed V SeP . With a head wind, t h e s e p a r a t i o n speed of t h e a i r c r a f t r e l a t i v e t o t h e ground i s decreased by t h e v a l u e of t h e wind speed. T h e r e f o r e , l e s s time i s r e q u i r e d f o r a t a k e o f f run with a head wind t h a n i n calm a i r , and t h e t a k e o f f run l e n g t h i s decreased; whileewith a t a i l wind i t i s i n c r e a s e d . F o r example, i f t h e head wind speed i s 5 m/sec (18 km/hr), t h e a i r c r a f t need b e a c c e l e r a t e d t o only 2 2 2 km/hr ground speed, a t which time t h e a i r speed w i l l be 240 km/hr, i . e . , t h e s e p a r a t i o n speed i s reached, and t h e t a k e o f f run i s s h o r t e n e d . A headwind o f 5 m/sec decreases t h e t a k e o f f run length by an average of 15-17%, while a t a i l wind of t h i s same speed i n c r e a s e s t h e l e n g t h by 18-20%. When t a k i n g o f f w i t h a s i d e wind, t h e a i r c r a f t t e n d s t o t u r n i n t o t h e wind, p a r t i c u l a r l y during a c c e l e r a t i o n with t h e f r o n t landing g e a r up. The reason f o r t h i s r o t a t i o n is t h e f a c t t h a t a i r c r a f t with t u r b o j e t engines have l a r g e v e r t i c a l t a i l s u r f a c e a r e a , l o c a t e d a t a c o n s i d e r a b l e d i s t a n c e from t h e main landing g e a r . A q u a n t i t a t i v e e s t i m a t e of t h e i n f l u e n c e o f v a r i o u s f a c t o r s on t h e /lo6 l e n g t h o f t h e t a k e o f f run can be made u s i n g nomograms, w i t h which t h e p i l o t can determine t h e t a k e o f f r u n l e n g t h under t h e c o n c r e t e t a k e o f f c o n d i t i o n s involved.
- 109. 98. Methods of Improving Takeoff C h a r a c t e r i s t i c s As we analyzed above, t h e l e n g t h .of t h e t a k e o f f r u n depends on t h e s e p a r a t i o n speed and a c c e l e r a t i o n d u r i n g t h e t a k e o f f run. I n t u r n , t h e s e p a r a t i o n speed depends on t h e s p e c i f i c loading p e r 1 m2 o f wing a r e a and C while t h e a c c e l e r a t i o n depends on t h e excess t h r u s t a v a i l a b l e . Y sep’ A decrease i n s p e c i f i c loading on t h e wing i s t h e most e f f e c t i v e method o f decreasing V and Ltor. However, t h i s always i n v o l v e s a d e c r e a s e i n seP t h e u s e f u l weight c a r r i e d , s i n c e with t h e s u r f a c e area of t h e wing c o n s t a n t , a decrease i n t a k e o f f weight can b e achieved only by d e c r e a s i n g t h e u s e f u l load. A decrease i n t h e weight c a r r i e d i n a passenger a i r c r a f t means a d e c r e a s e i n o p e r a t i o n a l economy. Therefore, t h i s means o f decreasing t h e t a k e o f f run length i s used t o a l i m i t e d e x t e n t , p a r t i c u l a r l y s i n c e t h e tendency t o u s e t h e maximum p o s s i b l e f l i g h t range r e q u i r e s an i n c r e a s e i n s p e c i f i c loading on t h e wing. The most a c c e p t a b l e method of d e c r e a s i n g t h e t a k e o f f run length i s an i n c r e a s e i n t h e l i f t i n g f o r c e of t h e wing u s i n g t h e wing mechanisms. A s w e know, t h e main means of mechanization o f t h e wing c o n s i s t s of t h e f l a p s . A l l modern j e t passenger a i r c r a f t have extendable ( s l i d i n g ) s l i t t y p e wing f l a p s 1 . The ef?�ectiveness o f t h e f l a p s (magnitude o f i n c r e a s e i n A c ) i n c r e a s e s as t h e s l i d e (outward movement) of t h e f l a p s and angle o f Y f l a p d e f l e c t i o n a r e i n c r e a s e d . With low angles o f f l a p d e f l e c t i o n , t h e l i f t i n g f o r c e i s p r i m a r i l y i n c r e a s e d without any e s s e n t i a l i n c r e a s e i n drag, and t h e aerodynamic q u a l i t y i s decreased o n l y i n s i g n i f i c a n t l y . These angles can be used f o r t a k e o f f d u r i n g high temperature c o n d i t i o n s , when t h e length o f t h e t a k e o f f run can b e r e t a i n e d w i t h i n t h e r e q u i r e d l i m i t s i n s p i t e of t h e decrease i n q u a l i t y . The lower drag during t h e t a k e o f f run allows a considerable a c c e l e r a t i o n t o b e achieved. Usually, attempts a r e made t o produce t h e maximum a i r c r a f t aerodynamic q u a l i t y with t h e f l a p s d e f l e c t e d t o t h e t a k e o f f p o s i t i o n , s i n c e t h e q u a l i t y determines t h e t h r u s t consumed and t h e excess t h r u s t which a c c e l e r a t e s t h e a i r c r a f t during t h e t a k e o f f run. For a i r c r a f t with t a k e o f f weights of 55-80 and aerodynamic q u a l i t y o f 12-14, a t h r u s t o f consumption of 5000 6000 kg i s r e q u i r e d , and with a t o t a l a v a i l a b l e t h r u s t o f 13,000-28,000 kg, t h e excess t h r u s t provides r a p i d (25-30 sec) a c c e l e r a t i o n of t h e a i r c r a f t t o /= t h e s e p a r a t i o n speed; t h e t a k e o f f run l e n g t h i s 1000-1200 m . Long experience of passenger a i r c r a f t o p e r a t i o n h a s proven t h e u s e f u l ness of t h e method o f d e c r e a s i n g t a k e o f f run l e n g t h by i n c r e a s i n g t h e a v a i l a b l e power ( g r e a t e r excess t h r u s t ) . The Boeing 727 a i r c r a f t c a r r i e s a . . I S M Yege r-, Proyektirovaniye Passazhirskikh Reaktivnikh SumoZetov [Design of Passenger J e t A i r c r a f t ] , Mashinostroyeniye P r e s s , 1964. 100
- 110. t h r e e - s l i t f l a p (Figure 73) which, t o g e t h e r with t h e s l i t t y p e s l a t and Kruger s l a t ( f r o n t f l a p ) makes i t p o s s i b l e t o produce c = 2 . 7 with t h e Y m a maximum angle o f f l a p d e f l e c t i o n . T h i s i n t u r n allows r a t h e r high v a l u e s of c t o b e achieved with lesser a n g l e s of d e f l e c t i o n , corresponding t o t h e Y t a k e o f f p o s i t i o n of t h e f l a p s ( c = 1.6-1.8). Y sep aJ - . =% - ti . % Figure 73. Diagram of Extendable Flaps: a , S i n g l e - s l i t (flow s e p a r a t i o n b e g i n s a t 6 3 = 35 4 0 " ) ; b , c , M u l t i - s l i t (flow s e p a r a t i o n delayed t o 6 3 - 50-60") Th.e m u l t i - s l i t f l a p , due t o t h e i n c r e a s e i n c u r v a t u r e of t h e p r o f i l e and t h e pumping e f f e c t of t h e s l i t s , delays flow s e p a r a t i o n t o l a r g e r angles of a t t a c k , which allows r a t h e r high values of c t o be produced during t a k e o f f and landing. The i n c r e a s e i n t h e l i f t i x g f o r c e of t h e wing with f l a p s down r e s u l t s from a change i n c i r c u l a t i o n around t h e wing with i n c r e a s i n g flow speed over t h e upper s u r f a c e of t h e wing. However, a t l a r g e angles of a t t a c k , flow s e p a r a t i o n a t t h e upper s u r f a c e begins a t t h e f r o n t of t h e wing p r o f i l e , which i s combatted u s i n g f r o n t s l a t s o r d e f l e c t a b l e leading edges of t h e wing. S l i t t y p e s l a t s (Figure 7 4 , a ) , which allow a i r t o flow through t h e f r o n t s l i t , i n t e n s i f y t h e boundary l a y e r behind t h e peak of r a r e f a c t i o n on t h e wing p r o f i l e and i n c r e a s e t h e energy of t h e flow, s o t h a t s e p a r a t i o n of t h e flow i s delayed a t high angles o f a t t a c k . When Kruger s l a t s a r e opened (Figure 74, c ) t h e e f f e c t i v e aerodynamic c u r v a t u r e of t h e p r o v i l e i s increased i n t h e f r o n t p o r t i o n , as a r e s u l t o f which t h e load-bearing c h a r a c t e r i s t i c s of t h e p r o f i l e a r e improved. Since / l o8 t h i s i n c r e a s e s t h e s u c t i o n f o r c e p u l l i n g forward, t h e drag of t h e wing with t h e f r o n t s l a t open i n c r e a s e s only s l i g h t l y , and t h e aerodynamic q u a l i t y of t h e wing remains e s s e n t i a l l y unchanged. 10 1
- 111. The same effect can a l s o b e achieved by t i l t i n g t h e forward edge o f t h e wing downward (Figure 74, b ) . Thus, t h e r e i s a r a t h e r l a r g e number o f methods o f i n c r e a s i n g c and, Y consequently, d e c r e a s i n g t h e s e p a r a t i o n speed and l e n g t h o f t h e a i r c r a f t takeoff run. One promising method i s t h e usage o f t h e g a s streams from t h e j e t e n g i n e s . Experiments have shown t h a t i f t h e gas stream i s d i r e c t e d down ward, i t can supplement t h e l i f t i n g f o r c e of t h e wings. As a r e s u l t , t h e a i r c r a f t can be s e p a r a t e d from t h e e a r t h almost without a t a k e o f f r u n . During t h e l a n d i n g , t h i s same gas stream c a r r i e s a p o r t i o n of t h e f l y i n g weight o f t h e a i r c r a f t and allows t h e a i r c r a f t t o be landed a t low speeds PI , Slat UP Slat out 1 - Figure 7 4 . Diagram of S l i t T y p e Front S l a t ( a ) , D e f l e c t a b l e Front P o r t i o n of A i r c r a f t Wing of "Trident" A i r c r a f t ( b ) and Kruger Front S l a t ( c ) The r e a c t i o n f l a p (Figure 7 5 ) , a device c o n s i s t i n g o f a s l i t along t h e r e a r edge o f t h e wing through which a stream o f a i r flows a t a c e r t a i n angle 6 t o t h e chord, d r i v e n by t h e compressor of t h e j e t e n g i n e , i s q u i t e important f o r heavy t r a n s p o r t a i r c r a f t . This d e v i c e changes t h e n a t u r e of flow around t h e wing, causing a s i g n i f i c a n t i n c r e a s e i n l i f t i n g f o r c e . The v a l u e o f c i n c r e a s e s due t o t h e pumping o f gas j e t s i n t h e boundary l a y e r Y from t h e upper s u r f a c e of t h e wing and t h e r e a c t i o n o f t h e outflowing gas stream. The f o r c e o f t h e r e a c t i o n of t h e s t r e a m i s d i v i d e d i n t o components N and N x . The component N i n c r e a s e s t h e l i f t o f t h e wing, while N Y Y X produces a d d i t i o n a l t h r u s t . The l i f t i n g f a c t o r o f a wing with a r e a c t i v e f l a p i s equal t o t h e sum of t h e l i f t f a c t o r s of t h e aerodynamic e f f e c t o f /- 109 t h e flow o v e r t h e wing and from t h e r e a c t i o n of t h e outflowing g a s e s . 102
- 112. The usage o f t h e r e a c t i v e f l a p allows a broad range o f f l i g h t speeds t o b e used and s i m p l i f i e s t h e problem o f t a k e o f f and l a n d i n g . Systems a r e known f o r c o n t r o l l i n g t h e boundary l a y e r , which e i t h e r remove o r i n j e c t a i r . A s w e know, flow s e p a r a t i o n o f t h e wing due t o an i n c r e a s e d boundary l a y e r t h i c k n e s s d e c r e a s e s c o e f f i c i e n t c By u s i n g Y' removal o r i n j e c t i o n i n t h e boundary l a y e r , t h e beginning of s e p a r a t i o n can b e delayed t o h i g h e r a n g l e s of a t t a c k , which makes it p o s s i b l e t o i n c r e a s e t h e l i f t of t h e wing, d e c r e a s e t h e t a k e o f f and l a n d i n g speed o f t h e a i r c r a f t and reduce t h e t a k e o f f and landing r u n l e n g t h (and consequently t h e l e n g t h of t h e runway). F o r example, a boundary l a y e r blowing d e v i c e decreases t h e landing speed by 20 - 25%. This t y p e of boundary l a y e r c o n t r o l system (BLAC) was used on t h e C-130C "Hercules" heavy turboprop t r a n s p o r t . With t h i s system, t h e l i f t i n g f o r c e o f t h e wing i s i n c r e a s e d more t h a n when t h e boundary l a y e r is drawn o f f b y s u c t i o n . Four gas t u r b i n e r e a c t i o n engines l o c a t e d i n two gondolas beneath t h e wing were used t o supply compressed a i r t o t h e system. The a i r i s c o l l e c t e d i n t h e r e a r p o r t i o n s of t h e gondola and f e d by f o u r c e n t r i f u g a l compressors t o a network o f a i r l i n e s (common system f o r wing and t a i l s u r f a c e ) . Many small l i n e s connect t h e main d i s t r i b u t i n g l i n e with a common c o l l e c t i n g chamber, from which t h e a i r i s e j e c t e d on t h e upper s u r f a c e s of t h e f l a p s and a i l e r o n s through s l i t s . The landing speed of- t h e a i r c r a f t was decreased from 170 t o 110 km/hr, while t h e t a k e o f f d i s t a n c e was reduced from 1280 t o 853 m , and t h e l a n d i n g d i s t a n c e was reduced from 427 t o 250 m . D i s t r i b u t i ng Figure 75. Reactive Flap on Wing ( a ) and Air F e e d System f o r Boundary Layer I n j e c t i o n a t Wing Surface ( b ) A BLAC system i s a l s o i n s t a l l e d on t h e English Blackburn NA39 "Buckaneer" m i l i t a r y t u r b o j e t a i r c r a f t . The experimental Boeing 707 a i r c r a f t used a system f o r boundary l a y e r i n j e c t i o n i n t h e a r e a of t h e f l a p s u s i n g a i r taken from t h e engine compressors. During t h e t e s t s , a d e c r e a s e i n l a n d i n g speed from 220-240 t o 150-160 km/hr was achieved, i . e . , by /110 approximately 30%. 103 I
- 113. Turbofan engines expand t h e p o s s i b i l i t y f o r u s i n g BLAC i n passenger j e t a i r c r a f t , s i n c e t h e removal of c o n s i d e r a b l e masses of a i r from t h e o u t e r channel does not d i s r u p t t h e o p e r a t i o n o f t h e engine. The placement of a s l a t on t h e f r o n t edge of t h e wing and i n j e c t i o n o f t h e boundary l a y e r a t t h e f l a p s and a i l e r o n s can produce a c o n s i d e r a b l e decrease i n landing and t a k e o f f speeds and allow t h e l e n g t h of runways t o be decreased by 30-40%. The placement of a s l a t on t h e wing o f a j e t a i r c r a f t , i n a d d i t i o n t o decreasing t a k e o f f and landing speeds, a l s o improves i t s maneuverability a t high speeds, s i n c e i t d e l a y s t h e p o i n t o f flow s e p a r a t i o n t o higher angles o f a t t a c k . P r a c t i c e has shown t h a t s l a t s can be used up t o M = 0.9. A laminar flow c o n t r o l system i s i n t h e s t a g e of development. I t has been experimentally e s t a b l i s h e d t h a t t h e t r a n s i t i o n o f laminar flow t o t u r b u l e n t flow can be prevented by sucking t h e slow, t u r b u l i z a t i o n - i n c l i n e d boundary l a y e r away from t h e wing s u r f a c e through a l a r g e number of t h i n s l o t s c u t i n t h e wing covering. This i s c a l l e d laminar flow c o n t r o l . I n v e s t i g a t i o n s performed i n t h e USA' have shown t h a t t h i s method can. i n c r e a s e t h e p r o f i l e d r a g c o e f f i c i e n t of a swept wing t o a v a l u e n e a r t h e drag c o e f f i c i e n t of a p l a t e with laminar flow, i . e . , decrease i t by approx imately s i x t i m e s . Laminar flow c o n t r o l by sucking away t h e boundary l a y e r , n a t u r a l l y , i n c r e a s e s t h e load-carrying c a p a c i t y of t h e wing. However, t h e usage o f l f c t o i n c r e a s e c alone i s not expedient, s i n c e t h i s problem can be more Y simply solved by i n j e c t i o n i n t o t h e boundary l a y e r . The production of high aerodynamic q u a l i t y ( i n c r e a s e d by a f a c t o r of 1 . 5 times) b o t h during t a k e o f f and during f l i g h t , allows t h e t a k e o f f and o t h e r c h a r a c t e r i s t i c s of t h e a i r c r a f t t o be improved. C a l c u l a t i o n s have shown t h a t f o r an a i r c r a f t l i k e t h e Lockheed C-141 with a t a k e o f f weight of about 120 t and a c r u i s i n g speed o f 850 km/hr, laminar flow c o n t r o l can i n c r e a s e t h e f l i g h t range by 30-33%. With t h i s f l i g h t range, t h e t a k e o f f weight of t h e a i r c r a f t can be decreased by 18-20% by decreasing t h e f u e l r e s e r v e s c a r r i e d . In conclusion f o r t h i s c h a p t e r , we n o t e t h a t an improvement of t a k e o f f ( a s well as landing) c h a r a c t e r i s t i c s of passenger j e t a i r c r a f t - - decreased t a k e o f f run l e n g t h and s e p a r a t i o n speed -- makes i t p o s s i b l e t o expand t h e network of a i r f i e l d s and connect a r e a and a d m i n i s t r a t i v e c e n t e r s . I t i s always e a s i e r t o f i n d a r e a s f o r small a i r f i e l d s t h a n f o r l a r g e a i r f i e l d s . /111 - B e t t e r t a k e o f f and landing c h a r a c t e r i s t i c s of a i r c r a f t w i l l a l s o provide a lower "minimum weather" (see Chapter I X , S8). A t t h e p r e s e n t time, c o n s i d e r a b l e a t t e n t i o n i s being turned t o t h e c r e a t i o n of s p e c i a l passenger j e t a i r c r a f t with s h o r t t a k e o f f and landing characteristics. ~ _ -_ S. M. Yeger , Proyektirovaniye Passazhirskikh Reaktivnykh ShoZetov [Design of Passenger J e t A i r c r a f t ] , Mashinostroyeniye P r e s s , 1964. 104
- 114. I I Chapter V I . Climbing §l. Forces A c t i n g on A i r c r a f t Climbing refers t o s t r a i g h t and even (constant v e l o c i t y ) f l i g h t of an a i r c r a f t i n an ascending t r a j e c t o r y . During t h e climb, t h e f o r c e s a c t i n g on t h e a i r c r a f t i n c l u d e t h e f o r c e o f g r a v i t y G , t h e f o r c e of t h e t h r u s t P', l i f t i n g f o r c e Y and drag Q (Figure 7 6 ) . Forces Y and Q a r e a r b i t r a r i l y considered t o be a p p l i e d t o t h e c e n t e r of g r a v i t y o f t h e a i r c r a f t , although t h e y a r e a c t u a l l y a p p l i e d a t t h e c e n t e r of p r e s s u r e . This a r b i t r a r i n e s s i s p e r m i t t e d f o r f o r c e s Y and Q, s i n c e ' t h e a i r c r a f t i s balanced by d e f l e c t i o n of t h e e l e v a t o r . Force P f o r s i m p l i c i t y of d i s c u s s i o n w i l l b e considered t o b e a p p l i e d through t h e c e n t e r of g r a v i t y . The d i r e c t i o n o f t h e e f f e c t of t h e f o r c e s i s as follows: f o r c e G a c t s v e r t i c a l l y downward, f o r c e P - - forward a t a c e r t a i n angle f3 t o t h e d i r e c t i o n of f l i g h t , f o r c e Y - - p e r p e n d i c u l a r t o t h e d i r e c t i o n of f l i g h t and f o r c e Q - - o p p o s i t e t o t h e d i r e c t i o n of f l i g h t . Figure 76. Diagram of Forces Acting on A i r c r a f t i n S t a b l e C 1 i m b : 1 , C l i m b t r a j e c t o r y ; 2 , Longitudinal a x i s of a i r c r a f t ; 3 , Chord o f w i n g The f l i g h t t r a j e c t o r y o f t h e a i r c r a f t is i n c l i n e d t o t h e h o r i z o n t a l a t a c e r t a i n angle 0 , c a l l e d t h e climbing angle. The following dependence e x i s t s between t h e p i t c h a n g l e 9, t h e climbing a n g l e 0, angle o f a t t a c k a and a n g l e of wing s e t t i n g ( a n g l e i n c l u d e d between l o n g i t u d i n a l a x i s of /112 a i r c r a f t and wing chord) : 9 + 4 = 0 + a. For modern a i r c r a f t , a n g l e 4 = 1-3", angle a = 2 . 5 - 5 " , t h e p i t c h angle ( t h e angle included between t h e a x i s of t h e f u s e l a g e and t h e h o r i z o n t a l ) i n f l i g h t can b e determined u s i n g t h e gyrohorizon. During a climb, t h e climbing angle i s less t h a n t h e p i t c h angle. 105
- 115. Force P does n o t correspond t o t h e f l i g h t t r a j e c t o r y , forming with it a c e r t a i n angle 8 . The magnitude o f t h i s a n g l e i s i n f l u e n c e d .by t h e angle of motor s e t t i n g r e l a t i v e t o t h e l o n g i t u d i n a l a x i s o f t h e a i r c r a f t . As w e e x p l a i n e d e a r l i e r ( c h a p t e r 4, 58) t h e a n g l e of motor s e t t i n g may b e from zero t o f i v e d e g r e e s . Angle B can b e determined as f o l l o w s . L e t us a n a l y z e t h e climb d u r i n g t h e f i r s t moments a f t e r t a k e o f f . Let us assume t h a t f o r c e P forms an a n g l e o f 5" w i t h t h e l o n g i t u d i n a l axis o f t h e a i r c r a f t , t h e v e l o c i t y i n t h e climb i s 520 km/hr, and t h e v e r t i c a l speed i s 16 m/sec. The climbing a n g l e can be determined as f o l l o w s (Figure 76): i . e . , 0 = 6.5". Then p i t c h a n g l e 4 = 0 .t ci - 4 = 6.5" + 3" - 1" = 8.5" (we assume ci = 3" f o r Vr = 520 km/hr, and t h e a n g l e of wing s e t t i n g $ = 1"). S i n c e t h e d i f f e r e n c e between angles 4 and 0 f o r t h i s c a s e i s 2 " , f o r c e P corresponds t o t h e climbing t r a j e c t o r y , a n g l e B = 7". I n t h i s c a s e , t h e component P s i n B i s added t o t h e l i f t i n g f o r c e . The magnitude o f t h i s component may b e r a t h e r high. For t h e q u a n t i t i e s h e r e b e i n g analyzed i n an a i r c r a f t with f o u r motors with a t h r u s t of each motor o f 8,000 kg, w e produce P s i n B = 32,000*0.122 = 3900 kg. This f o r c e i s added t o t h e l i f t Y = 80-85 t . As t h e a l t i t u d e i n c r e a s e s , t h e v e r t i c a l speed d e c r e a s e s , b u t t h e t r u e v e l o c i t y i n t h e climb i n c r e a s e s . Therefore, t h e l i f t a n g l e i s c o n t i n u a l l y decreased. W can t h e r e f o r e w r i t e t h e f o l l o w i n g two e q u a t i o n s f o r a s t a b l e e climb : Y=G COS 9; P=Qf G sin 0. W can see from t h e f i r s t e q u a t i o n t h a t t h e l i f t d u r i n g a climb e q u a l i z e s e only a p o r t i o n o f t h e weight of t h e a i r c r a f t . The o t h e r p o r t i o n of t h e a i r c r a f t weight (G s i n 0) i s balanced by t h e motor t h r u s t . For example, f o r an a i r c r a f t weighing 38 t with a climbing angle 0 = 7 " , component G s i n 0 = 38,000-0.122 = 4630 kg, and f o r an a i r c r a f t weighing 80 t t h i s f i g u r e i s 9770 kg. If t h e a v a i l a b l e engine t h r u s t f o r an a i r c r a f t with a t a k e o f f weight of 38 t i s 6700-7000 kg i n t h e nominal o p e r a t i n g mode ( n e a r t h e e a r t h ) , more t h a n one h a l f o f t h i s t h r u s t i s expended t o b a l a n c e t h e weight o f t h e a i r c r a f t , while t h e remaining t h r u s t is expended i n overcoming drag. The climbing a n g l e 0 can a l s o b e determined from t h e second f o r c e equation: 106
- 116. I /113 c _ - where P - Q = AP is t h e excess t h r u s t ; P is t h e t h r u s t f a c t o r of t h e a i r c r a f t : t h e r a t i o o f engine t h r u s t t o a i r c r a f t weight; Q/G i s a q u a n t i t y i n v e r s e to quality. A t climbing angles of 6-8', t h e v a l u e o f cos 0 1, and t h e f i r s t equation can b e w r i t t e n as follows: In o r d e r t o determine a n g l e 0, w e must u s e t h e Zhukovskiy curves f o r consumed and a v a i l a b l e t h r u s t . Figure 77 shows t h e d e f i n i t i o n of APmax, a t which t h e maximum climbing angle i s achieved. The maximum excess t h r u s t is produced a t t h e m o s t f a v o r a b l e f l i g h t v e l o c i t y , corresponding t o t h e maximum aerodynamic q u a l i t y of t h e a i r c r a f t and t h e s t e e p e s t climbing angle. For a i r c r a f t with s p e c i f i c loads of 350-370 kg/m2, t h e most s u i t a b l e speed i s 360-370 km/hr, f o r s p e c i f i c loads of 500-550 kg/m2 - - 400-450 km/hr. The excess t h r u s t produced under t h e s e c o n d i t i o n s a t nominal engine o p e r a t i o n w i l l provide a climbing angle 0 = 6-8'. 52. Determination o f Most S u i t a b l e C1 imbing Speed The v e r t i c a l speed i n a climb i s determined by t h e formula V = V s i n 0. Y Replacing s i n 0 with t h e excess t h r u s t and weight (we know from aerodynamics t h a t AP/G = s i n 0, we produce VAP V Y = 7 m/sec F i g u r e 77. Determination o f Maximum Excess Thrust U s i n g Zhukovskiy Curves I n o r d e r t o produce t h e maximum r a t e of a l t i t u d e i n c r e a s e ( s i n c e it i s t h i s q u a n t i t y , not t h e climbing angle which i s of t h e g r e a t e s t p r a c t i c a l i n t e r e s t ) , w e must know t h e maximum value of t h e product APV, which r e p r e s e n t s t h e excess power: AN = APV. 107
- 117. For t u r b o j e t a i r c r a f t , t h e maximum v a l u e s of t h e product APV kg*m/sec i s determined, and t h e v e r t i c a l v e l o c i t i e s are c a l c u l a t e d (Figure 78). I f we have t h e maximum v a l u e s of t h e product APV/3.6(kg-m/sec), we can /114 determine t h e maximum V f o r v a r i o u s weights. Y The v e l o c i t y along t h e t r a j e c t o r y a t which t h e maximum r a t e o f a l t i t u d e i n c r e a s e is achieved i s c a l l e d t h e climbing speed V I t i s higher than t h e cl' speed a t s t e e p e s t climb which, as w e showed i n t h e preceding paragraph, c o r r e sponds t o t h e most s u i t a b l e a i r c r a f t v e l o c i t y (maximum q u a l i t y ) . The climbing speed can be e a s i l y determined a l s o u s i n g Zhukovskiy curves f o r power consumed and a v a i l a b l e (Figure 79) ( t h e a v a i l a b l e t h r u s t power was analyzed i n Chapter IV,§7, and t h e graph of power consumption f o r v a r i o u s f l i g h t a l t i t u d e s i s c o n s t r u c t e d l i k e t h e graph f o r t h r u s t consumed). I n o r d e r t o do t h i s , we must draw a tangent p a r a l l e l t o l i n e N o f power t o t h e curve P f o r power consumed. A t t h e p o i n t of c o n t a c t , t h e excess AN = PAV and max v e l o c i t y corresponding t o t h i s excess power are determined. k g , m/se_c f 885000 825000 Figure 78. Excess Power Figure 79. Zhukovskiy As a Function of F l i g h t Curves f o r Power Velocity ( G t L = 52 T , spec i f i c 1 oad 390 kg/m2) F o r a i r c r a f t with wings swept a t 30-35", t h e maximum r a t e o f a l t i t u d e i n c r e a s e i s produced f o r p r a c t i c a l l y a l l t a k e o f f weights ( f r o m t h e maximum p e r m i s s i b l e t o t h e minimum with small commercial load) i s produced a t i n d i c a t e d speeds o f 480-550 km/hr a t t h e e a r t h . This speed must be maintained up t o 5000-6000 m . I f t h i s i s done, t h e maximum r a t e o f a l t i t u d e i n c r e a s e w i l l be achieved a t a l l a l t i t u d e s . A s t h e a l t i t u d e i n c r e a s e s , t h e t r u e f l i g h t speed w i l l i n c r e a s e ( f o r example a t H = 6000 m and V = 520 km/hr, ind Vtr = 700 km/hr). 108
- 118. Many f l y i n g i n v e s t i g a t i o n s have shown t h a t i n order t o r e t a i n maximum v e r t i c a l speed, t h e i n d i c a t e d speed must be decreased beginning a t 6000-7000 m /1 15 by an average of 15-20 km/hr p e r 1000 m. Figure 78 shows t h a t t h e product APV has a smoothly s l o p i n g upper p o r t i o n i n t h e zone of maximum v a l u e s , s o t h a t a d e v i a t i o n of t h e i n d i c a t e d climbing speed o f * 2 0 km/hr from t h e most f a v o r a b l e v a l u e ( p i l o t e r r o r ) changes t h e v e r t i c a l speed i n s i g n i f i c a n t l y , and t h e time t o climb and f u e l expenditure over t h e climb remain p r a c t i c a l l y unchanged from t h e most f a v o r a b l e v a l u e s . The maximum v e r t i c a l speeds of a i r c r a f t with two and t h r e e motors a r e 17-25 m/sec ( a t t h e e a r t h ) , decreasing with i n c r e a s i n g a l t i t u d e t o 8-10 m/sec a t 8000-9000 m. For a i r c r a f t with f o u r motors, t h e v e r t i c a l speeds a r e 12-15 m/sec a t low a l t i t u d e and 5-8 m/sec a t high a l t i t u d e s . The g r e a t e s t decrease i n v e r t i c a l speeds i s observed a t a l t i t u d e s of over 10,000 m. The f l i g h t a l t i t u d e a t which t h e v e r t i c a l speeds equal 0 . 5 m/sec co.rresponds t o t h e p r a c t i c a l c e i l i n g of t h e a i r c r a f t . The height of t h e p r a c t i c a l c e i l i n g of a passenger a i r c r a f t i s 12,000-13,500 m. The h e i g h t of t h e p r a c t i c a l c e i l i n g (without c o n s i d e r a t i o n of maneuvering i n t h e a r e a of t h e a i r f i e l d a f t e r t a k e o f f ) can be reached by an a i r c r a f t i n 43-45 min. Figure 80. Vertical Speed and Time o f C l i m b f o r An A i r c r a f t w i t h Two Motors (nominal mode, power f a c t o r P = 0.3) Climbing a t t h e nominal engine mode i s t h e most economical (Figure SO), s i n c e t h e maximum d i f f e r e n c e between a v a i l a b l e and consumed power i s produced, - / 116 and t h e s p e c i f i c f u e l consumption w i l l be near minimal. A decrease i n t h e o p e r a t i n g mode o f t h e engines i n a climb leads t o an i n c r e a s e i n s p e c i f i c f u e l consumption, a decrease i n a v a i l a b l e power and r a t e o f a l t i t u d e i n c r e a s e of t h e a i r c r a f t , an i n c r e a s e i n climbing time, and as a r e s u l t an i n c r e a s e i n t h e t o t a l f u e l expenditure r e q u i r e d t o perform t h e climb. A modern passenger 109
- 119. I a i r c r a f t reaches an a l t i t u d e o f 10,000-11,000 m i n 18-25 min, covering 200-250 km and expending 2000-4000 kg of f u e l ( t h e h i g h e r . v a l u e s correspond t o t h r e e - and four-motor a i r c r a f t ) . S3. Velocity Regime o f C l i m b Climbing a t t h e maximum r a t e o f a l t i t u d e i n c r e a s e i s most economical. In t h i s case, up t o 10,000-11,000 m t h e climb occurs a t an i n d i c a t e d speed of 460-440 km/hr (with corresponding lower t r u e v e l o c i t y ) , and upon reaching t h e i n d i c a t e d a l t i t u d e t h e p i l o t a c c e l e r a t e s t h e a i r c r a f t a t t h e nominal regime t o an i n d i c a t e d speed o f 500-550 km/hr i n 4-5 min f o r subsequent h o r i z o n t a l f l i g h t a t t h e maximum c r u i s i n g regime. Thus, a c c e l e r a t i o n of t h e a i r c r a f t a t t h e s e a l t i t u d e s , where t h e excess t h r u s t is s l i g h t , r e q u i r e s a d d i t i o n a l time. Operational t e s t s of many t u r b o j e t passenger a i r c r a f t have shown t h a t a t times it i s more expedient (from t h e p o i n t o f view o f c o s t ) t o climb t o a l t i t u d e i n t h e s o - c a l l e d h i g h speed regime. To do t h i s , t h e a i r c r a f t i s turned i n i t s f i n a l f l i g h t d i r e c t i o n , t h e n a c c e l e r a t e d t o an i n d i c a t e d speed of 600-670 km/hr and t h e climb i s performed a t t h i s speed u n t i l t h e a i r speed reaches 800-880 km/hr (according t o t h e t h i n needle). A t t h i s p o i n t , t h e r a t e of a l t i t u d e i n c r e a s e o f t h e a i r c r a f t i s .de creased t o 12-14 m/sec, while t h e i n d i c a t e d speeds a r e considerably h i g h e r than t h e most f a v o r a b l e speed. When an a i r speed of 800-880 km/hr i s reached, f u r t h e r climb i s continued a t t h i s speed. The r a t e o f a l t i t u d e i n c r e a s e decreases t o 2 - 3 m/sec as a l t i t u d e s of 10,000-11,000 m a r e reached. The a i r c r a f t a r r i v e s a t i t s assigned a l t i t u d e with s u f f i c i e n t t r u e v e l o c i t y , so t h a t almost no a d d i t i o n a l acceleration is required. After t h e t r a n s i t i o n t o horizontal f l i g h t , t h e c r u i s i n g o p e r a t i n g regime of t h e motors i s i n s t i t u t e d . Climbing a t t h e high speed regime d e c r e a s e s t h e d u r a t i o n of t h e f l i g h t , b u t i n c r e a s e s s l i g h t l y t h e f u e l expenditure. The problem i s t h a t a5 speeds o f 600-880 km/hr are maintained, t h e v e r t i c a l speed i s decreased a t a l l a l t i t u d e s and t h e time which t h e a i r c r a f t spends a t low a l t i t u d e s i s i n c r e a s e d , l e a d i n g t o an i n c r e a s e i n f u e l expenditure i n t h e climb. Therefore, t h e high speed climb method is g e n e r a l l y recommended f o r f l i g h t s over s h o r t d i s t a n c e s , SO-60% of t h e maximum range of t h e a i r c r a f t with f u l l f u e l load. The a d d i t i o n a l /I17 f u e l expenditure i n t h e s e f l i g h t s r e q u i r e s no d e c r e a s e i n commercial l o a d , The d i s t a n c e which t h e a i r c r a f t t r a v e l s i n t h e h o r i z o n t a l d i r e c t i o n d u r i n g t h e climb i n t h e high speed regime i s 50-100 km g r e a t e r t h a n d u r i n g t h e climb a t maximum r a t e o f a l t i t u d e i n c r e a s e . The p o l a r curve on Figure 81 c h a r a c t e r i z e s t h e s e two climbing methods. A s w e can s e e from t h e f i g u r e , t h e v e c t o r corresponding t o t h e speed of 500 km/hr is d i r e c t e d more s t e e p l y upward, corresponding t o v e r t i c a l speeds o f 15-17 m/sec, while a t 650 km/hr t h e v e r t i c a l speeds produced a r e l e s s , but t h e h o r i z o n t a l range i s g r e a t e r . 110
- 120. S4. Noise R e d u c t ion Methods The n o i s e of t u r b o j e t passenger a i r c r a f t i s caused by: o s c i l l a t i o n s o f -- 0 $KN/h; c o l d a i r flowing around t h e a i r c r a f t and mixing o f t h e cold a i r w i t h t h e - p u l s a t i n g , h o t gas j e t s from t h e engines and o s c i l l a t i o n s of a i r com- F i g u r e 81. Polar Curve o f p r e s s e d i n t h e compressors of t h e C 1 imb i ng S p e e d s engines. The frequency spectrum o f t h i s n o i s e i s s i g n i f i c a n t l y d i f f e r e n t from t h e n o i s e c r e a t e d by p i s t o n and turboprop motors. Whereas t h e n o i s e spectrum of turboprop engines i s c h a r a c t e r i z e d by high sound p r e s s u r e s i n t h e low f r e q u e n c i e s , t h e n o i s e spectrum o f t u r b o j e t engines c o n t a i n s predominantly high frequency sound. This makes t h e n o i s e c r e a t e d by a t u r b o j e t engine more unpleasant t o human h e a r i n g . The n o i s e c r e a t e d by an o r d i n a r y t u r b o j e t a t over 35% t h r u s t i s g r e a t e r t h a n t h e n o i s e r e s u l t i n g from t h e e f f l u x o f t h e jets. The usage of two c i r c u i t t u r b o j e t motors allows t h e n o i s e l e v e l t o be decreased during t a k e o f f by 8-10 db ( d e c i b e l s ) , although t h e n o i s e l e v e l i s s t i l l q u i t e high. E x i s t i n g engineering methods of n o i s e r e d u c t i o n - - dampers a t t h e i n p u t p i p e s (JT8D engine) and exhaust nozzles (JTSD and Conway engines, e t c . ) are n o t e f f e c t i v e , and d e c r e a s e t h e n o i s e very s l i g h t l y . F o r example, a m u f f l e r on t h e output nozzle c o n s i s t i n g of n i n e t u b e s d e c r e a s e s t h e n o i s e l e v e l by 5 . 5 db, b u t a l s o d e c r e a s e s t h e e f f i c i e n c y o f t h e engine. I n s t a l l a t i o n o f p e r f o r a t e d s h e e t s and a s c r e e n around t h e a i r i n t a k e a l s o provide some decrease i n n o i s e l e v e l a t t h e i n p u t t o t h e compressor o r f a n . Therefore, i n o r d e r t o decrease t h e n o i s e t o t h e r e q u i r e d l e v e l ( a t high /118 power, t h e n o i s e from t h e t u r b i n e and exhaust j e t , a t low power - - from t h e compressor), s p e c i a l methods of p i l o t i n g a f t e r s e p a r a t i o n and d u r i n g landing must b e used. A s we know, f o r e i g n a i r c r a f t ( t h e Boing 7 0 7 , C a r a v e l l e , e t c . ) employ t h e s o - c a l l e d low n o i s e t a k e o f f and landing method ( t a k e o f f and landing u s i n g t h e s t e e p e s t t r a j e c t o r i e s with engines t h r o t t l e d over l i s t e n i n g check p o i n t s ) , i . e . , t h e d e c r e a s e of n o i s e a t ground l e v e l is based on r a p i d removal o f t h e n o i s e source from ground l e v e l . The i n i t i a l climb i s achieved on s t e e p t r a j e c t o r i e s a t s a f e speed with decreased engine power. This i s aided by improved engine design and high mechanization o f t h e wing. I n o r d e r t o determine t h e i n f l u e n c e of t h e n o i s e of an a i r c r a f t t a k i n g o f f on t h e population i n t h e r e g i o n of an a i r p o r t , t h e q u a n t i t y known as perceived n o i s e l e v e l i s o f t e n used. I t has been e s t a b l i s h e d t h a t t h e maximum p e r m i s s i b l e perceived n o i s e l e v e l a c t i n g on t h e organs of h e a r i n g f o r s e v e r a l seconds P = 1 1 2 PN db (here PN db i s t h e u n i t o f measurement of "ax t h e n o i s e ) . Noise l e v e l s over 1 1 2 PN db i s s a i d t o b e above t h e " t o l e r a n c e l i m i t " f o r man. 111
- 121. A t many l a r g e a i r p o r t s i n Europe and t h e USA, l i m i t a t i o n s have been p l a c e d on t h e n o i s e c r e a t e d by a i r c r a f t t a k i n g o f f and landing!. The a p p a r a t u s measuring t h e n o i s e l e v e l i s p l a c e d d i r e c t l y beneath t h e f l i g h t p a t h o f t h e a i r c r a f t . I f t h e maximum p e r m i s s i b l e n o i s e l e v e l i s exceeded, t h e a i r l i n e companies are f o r b i d d e n t o c o n t i n u e o p e r a t i n g t h e a i r c r a f t . L e t u s a n a l y z e t h e s p e c i f i c s o f a i r c r a f t f l i g h t along a s t e e p t r a j e c t o r y . As w can s e e from t h e formula s i n 0 = V /V, e i n o r d e r t o produce t h e maximum Y a n g l e 0, w e must p r o v i d e a combination of v e r t i c a l speed and speed along t r a j e c t o r y such t h a t t h e v a l u e of s i n 0 is maximal. F l i g h t t e s t s are u s u a l l y performed t o determine t h e s t e e p climbing speed, d u r i n g which t h e f l a p s are l e f t down a t low speeds a f t e r t a k e o f f i n o r d e r t o i n c r e a s e f l i g h t s a f e t y . T h e r e f o r e , t h e s t e e p climbing speed i s g e n e r a l l y 40-50 km/hr h i g h e r t h a n t h e s e p a r a t i o n speed and p r a c t i c a l l y corresponds t o maximum a i r c r a f t aerodynamic q u a l i t y f o r t h e t a k e o f f wing s e t t i n g angle. As i s known, t h e f l i g h t regime with maximum t r a j e c t o r y i n c l i n a t i o n 0 corresponds t o t h e maximum excess t h r u s t AP and, consequently, t h e maximum v a l u e of s i n 0: sin8,,,=-- ARnax- . G Therefore, i f t h e most f a v o r a b l e a i r c r a f t speed (K ) i s about max 9 Omax 350-360 km/hr f o r f l a p s up, due t o t h e placement of t h e f l a p s i n t h e i r landing / 119 p o s i t i o n , t h i s speed i s decreased t o 300-310 km/hr. The climb a f t e r t a k e o f f on t h e s t e e p t r a j e c t o r y i s performed a t t h e most f a v o r a b l e speed w i t h f l a p s down. During t e s t i n g o f one a i r c r a f t , t h e following method was developed f o r s t e e p climbing (Figure 8 2 ) . With f l a p s down i n t h e t a k e o f f p o s i t i o n ( l o " ) , V = 260 km/hr. A f t e r s e p a r a t i o n , a t an a l t i t u d e of 5-10 m , t h e landing S eP g e a r was r a i s e d and t h e speed i n c r e a s e d t o 300 km/hr ( a t 50-60 m ) . The climb was continued t o 300 m a t t h i s speed with t h e motor o p e r a t i n g i n t h e t a k e o f f mode, a f t e r which t h e motor was s h i f t e d t o t h e nominal regime. Whereas t h e climbing a n g l e o f t h e t r a j e c t o r y a t t h e t a k e o f f regime 0 = a t t h e nominal regime i t i s decreased t o 6.5-7". A t an a l t i t u d e of 500 m, t h e a i r c r a f t was d e c e l e r a t e d by d e c r e a s i n g t h e v e r t i c a l speed and t h e f l a p s were r a i s e d . The f l i g h t was performed a t a p i t c h angle o f 14-16". During t h e l a n d i n g , i t i.s impossible t o reduce n o i s e by i n c r e a s i n g t h e s t e e p n e s s o f t h e g l i d i n g t b a j e c t o r y , s i n c e t h e r a t e o f descent i s f i x e d by t h e o p e r a t i n g c o n d i t i o n s of t h e l a n d i n g system. However, s i n c e t h e engines a r e o p e r a t i n g a t reduced power, t h e i n i t i a l n o i s e l e v e l i s decreased. 112 I
- 122. 500 --- H,fl 450 - 300 - 1.50 - 0 - Figure 82. Optimal C l i m b i n g Tra e c t o r i e s f o r Noise Reduction a t Ground L e v e l : a , S e p a r a t i o n , V = 260 km/hr; b, B e g i n n i n g of 1 f t i n g of landing g e a r ; c , Landing g e a r u p ; d , Accelera t i o n t o V = 300 km/hr; e , F1 i g h t s e c t o r a t V = 300 km/hr; 6 3 = 10"; f , B e g i n n i n g o f a c c e l e r a t i o n f o r r a i s i n g of f l a p s ; g , L i s t e n i n g p o i n t ; h , F l i g h t t r a j e c t o r y w i t h continuous a c c e l e r a t i o n ; i , Point o f b e g i n n i n g of l i f t i n g f l a p s ; j , End o f l i f t i n g of f l a p s The i n f l u e n c e of noi'se from an a i r c r a f t t a k i n g o f f i s p a r t i c u l a r l y n o t i c e a b l e i f t h e r e i s a populated p o i n t along t h e f l i g h t p a t h a t l e s s t h a n 4-5 km from t h e s t a r t i n g p o i n t of t h e a i r c r a f t . I n such c a s e s , t e s t s must b e made t o determine under which c o n d i t i o n s and o p e r a t i n g modes o f t h e engines p e r m i s s i b l e n o i s e l e v e l s can be provided ( i n p a r t i c u l a r , 110-112 PN db f o r t a k e o f f d u r i n g t h e day and 102 PN db a t n i g h t , t h e " t o l e r a n c e l i m i t " f o r n o i s e being c o n s i d e r a b l y lower a t n i g h t ) . The nomogram on Figure 83 i s /120 c o n s t r u c t e d from t h e r e s u l t s of f l y i n g t e s t s on a i r c r a f t with two engines with maximum t a k e o f f weight under s t a n d a r d c o n d i t i o n s of 38 T . The s l o p i n g l i n e s of t h e nomogram a r e t h e t r a j e c t o r i e s i n s t e e p climb s i t u a t i o n s . The z e r o p o i n t on t h e nomogram corresponds t o t h e beginning of t h e a i r c r a f t t a k e o f f r u n . O t h e r i g h t we have a t a b l e of o p e r a t i n g regimes of n t h e engines and t h e corresponding n o i s e l e v e l s perceived on t h e ground. The d o t t e d l i n e shows an example of d e t e r m i n a t i o n o f t h e a l t i t u d e of change i n engine o p e r a t i n g regime and t h e necessary regime d u r i n g t a k e o f f o f an a i r c r a f t weighing 38 T when t h e edge of a populated p o i n t i s l o c a t e d 3 . 3 km from t h e beginning o f t h e t a k e o f f r u n ( t h e t a k e o f f is performed d u r i n g t h e day, s t a n d a r d c o n d i t i o n s , no wind). To do t h i s , w e draw a l i n e from p o i n t A, corresponding t o a d i s t a n c e o f 3 . 3 km, upward t o t h e p o i n t o f i n t e r s e c t i o n with t h e 38 T weight l i n e ( p o i n t B ) , t h e n draw a h o r i z o n t a l l i n e . Point C determines t h e a l t i t u d e (230-240 m) a t whichlhe o p e r a t i n g regime of 113
- 123. t h e engines must b e reduced t o 88-89% ( p o i n t D), corresponding t o t h e maximum p e r m i s s i b l e n o i s e l e v e l f o r daytime, 1 1 2 PN db. If t h e regime i s n o t changed, t h e n o i s e l e v e l i s 117 PN db ( p o i n t D). After f l y i n g over t h e populated p o i n t o r an i n c r e a s e i n a l t i t u d e of 500 m , t h e engines must be s h i f t e d t o t h e nominal o p e r a t i n g regime. % U 1 2 3 4 5 6 7 8 9 Distance from s t a r t o f rup, KM Figure 83. Nomogram f o r Determination of A l t i t u d e of Change i n Operating Regime o f Motor (con ditions of i n i t i a l c l i m b : V = 300 km/hr, i nd n = 97%, 63 = IOo) A s we can s e e from t h e same nomogram, with t h e same a i r c r a f t , b u t with a /I21 s e p a r a t i o n d i s t a n c e t o t h e populated p o i n t o f 3 . 8 km ( p o i n t E ) , i t i s s u f f i c i e n t t o e s t a b l i s h t h e nominal regime ( p o i n t I ) and maintain an a l t i t u d e o f 300 m ( p o i n t F) i n o r d e r t o produce a n o i s e l e v e l o f 1 1 2 PN db i n t h e daytime. When t h e a i r temperature and p r e s s u r e are changed o r when t h e r e is a wind, s p e c i a l graphs must b e used t o determine t h e c o r r e c t e d a i r c ' r a f t weight, s i n c e t h e f l y i n g d a t a change. These graphs change f o r each a i r c r a f t i n t h e handbook on f l y i n g o p e r a t i o n s . For example, f o r t h e example above a t t = +25"C, p = 760 mm H with a head wind component o f 2 m/sec, t h e c o r r e c t e d g weight Gcor = 40 t w i t h an a c t u a l weight of 38 t . The i n c r e a s e d c o r r e c t e d weight r e q u i r e s a lower a l t i t u d e f o r t h e beginning of motor t h r o t t l i n g . However, t h e decreased o p e r a t i n g regime o f t h e engines a f t e r r a i s i n g t h e landing g e a r is not p e r m i t t e d a t an a l t i t u d e o f l e s s t h a n 150 m. I n c o n c l u s i o n , we n o t e t h a t t h e f l i g h t speed d u r i n g a s t e e p climb t o a l t i t u d e w i t h f l a p s down should provide a s u f f i c i e n t r e s e r v e a g a i n s t 114
- 124. s e p a r a t i o n . The a k r c r a f t speeds a t which h o r i z o n t a l f l i g h t with s u f f i c i e n t c o n t r o l l a b i l i t y i s p o s s i b l e i s c a l l e d t h e maneuvering speed; it must b e 1.15 times t h e minimum speed corresponding t o s e p a r a t i o n . F o r example, f l y i n g t e s t s i n d i c a t e a minimum speed of 200 km/hr, s o t h a t t h e maneuvering speed i s 230 km/hr. The r e s e r v e a g a i n s t s e p a r a t i o n with a s t e e p climb speed o f 300 km/hr i s 70 km/hr, and t h e r e s e r v e t o s t a l l i s about 100 km/hr. S5. C l i m b i n g w i t h O n e Motor Not Operating If t h e s i t u a t i o n r e q u i r e s a p i l o t t o f l y t o a r e s e r v e a i r f i e l d a f t e r a motor f a i l u r e on t a k e o f f , with t h e r e s e r v e a i r f i e l d l o c a t e d 350-400 k m d i s t a n c e , a climb must b e performed. I t w i l l b e shown i n Chapter V I 1 t h a t t h e most f a v o r a b l e a l t i t u d e f o r ranges of 300-400 k i s 5700-6000 m; m however, f o r f l i g h t w i t h one motor n o t o p e r a t i n g , t h e most f a v o r a b l e a l t i t u d e i s 2500-3000 m. An a i r c r a f t w i t h a motor o u t , when climbing a t t h e nominal regime, can a t t a i n a v e r t i c a l v e l o c i t y component o f 3-6.5 m/sec a t ground l e v e l . This speed d e c r e a s e s with a l t i t u d e and a t 4500-7000 m , t h e r a t e of a l t i t u d e i n c r e a s e i s about 0 . 5 m/sec. I t i s considered t h a t a t t h i s p o i n t t h e a i r c r a f t reaches i t s p r a c t i c a l f l i g h t c e i l i n g w i t h one motor n o t o p e r a t i n g . F o r a i r c r a f t with t h r e e motors, t h e f l i g h t a l t i t u d e with one nonoperating motor, n a t u r a l l y , i s g r e a t e r t h a n f o r a i r c r a f t with two motors. The time t o climb t o t h i s a l t i t u d e i s 45-50 min and depends s t r o n g l y on t h e a c t u a l temperature of t h e surrounding a i r . The climbing speed i n such c a s e s i s 70-100 km/hr l e s s , explained by t h e d e c r e a s e i n a v a i l a b l e t h r u s t of 30-SO%, s o t h a t t h e maximum of product APY is d i s p l a c e d toward lower v a l u e s of i n d i c a t e d ( a s w e l l as t r u e ) speed. I t i s recommended t h a t as t h e a l t i t u d e i s i n c r e a s e d , t h e i n d i c a t e d speed be decreased by 5 km/hr p e r 1000 m a l t i t u d e . T r a n s i t i o n of engines from nominal t o t a k e o f f regime i n c r e a s e s t h e excess t h r u s t and allows t h e r a t e of a l t i t u d e i n c r e a s e o f t h e a i r c r a f t t o b e i n c r e a s e d t e m p o r a r i l y , although t h e time of o p e r a t i o n i n t a k e o f f regime i s 1i m i t e d . 115
- 125. Chapter V I I . Horizontal F1 i g h t /122 91. Diagram of Forces A c t i n g on A i r c r a f t H o r i z o n t a l f l i g h t means s t r a i g h t l i n e , s t a b l e a i r c r a f t f l i g h t without i n c r e a s e o r d e c r e a s e of a l t i t u d e . The f o r c e s a c t i n g on t h e a i r c r a f t were shown i n c h a p t e r V I . W add t h a t e t h e t o t a l aerodynamic f o r c e R ( e q u a l i z i n g f o r c e s Y and Q) i s a p p l i e d a t t h e c e n t e r of p r e s s u r e , and i s d e f l e c t e d from f o r c e Y by c e r t a i n angle 0 (Figure 8 4 ) . I n c l i n a t i o n of f o r c e R i s changed by t h e p i l o t by u s i n g t h e e l e v a t o r , d e f l e c t i n g it enough so t h a t f o r c e R p a s s e s through t h e c e n t e r o f g r a v i t y . T h e r e f o r e , we w i l l c o n s i d e r f o r h o r i z o n t a l f l i g h t , as f o r climbing, t h a t a l l f o r c e s a r e a p p l i e d t o t h e c e n t e r of g r a v i t y o f t h e a i r c r a f t . Figure 84. Diagram of Forces Acting on A i r c r a f t i n Horizontal F l i g h t : 1 , Longitudinal a x i s of a i r c r a f t ; 2 , Chord l i n e ; 3 , D i r e c t i o n of a i r c r a f t ; 4 , Direction of t h r u s t As we know, i n o r d e r t o achieve s t a b l e h o r i z o n t a l f l i g h t , i t i s n e c e s s a r y t h a t t h e following e q u a t i o n b e f u l f i l l e d : G=Y+Psinp; Q=Pcosp. These e q u a l i t i e s show t h e c o n d i t i o n s o f h o r i z o n t a l f l i g h t . The f i r s t e q u a l i t y shows t h a t t h e movement o f t h e a i r c r a f t i s l i n e a r and occurs i n t h e h o r i z o n t a l p l a n e . The second i s t h e c o n d i t i o n of evenness of motion, i . e . , f l i g h t a t c o n s t a n t v e l o c i t y . If t h i s c o n d i t i o n were n o t f u l f i l l e d , t h e f l i g h t would be /123 u n s t a b l e (with a c c e l e r a t i o n o r d e c e l e r a t i o n ) . 116
- 126. I t w a s s t a t e d above t h a t f o r c e P may make a c e r t a i n angle w i t h t h e chord o f t h e wing. If w e assume as an average a = 3", t h e wing s e t t i n g a n g l e $I = 1" and t h e motor s e t t i n g a n g l e ( i n t h e t a i l p o r t i o n of t h e f u s e l a g e ) i s z e r o , a s w e see from F i g u r e 84 a n g l e B = 2O. T h e r e f o r e , t h e force, P cos B w i l l b e less t h a n f o r c e P . I n p r a c t i c e , w i t h angle B = 2-7", t h e v a l u e of cos B d i f f e r s l i t t l e from u n i t y , s o t h a t it can b e considered t h a t Q = P. W can a l s o e c o n s i d e r t h a t Y = G , s i n c e w e can i g n o r e t h e component P s i n 6 , which f o r c r u i s i n g t h r u s t v a l u e s w i l l b e less t h a n one p e r c e n t of t h e mean f l y i n g weight. For example, w i t h an average f l y i n g weight o f 70 t and a q u a l i t y of 14, t h e r e q u i r e d t h r u s t Pr = 5000 kg, and P s i n 2" = 5000*0.035 = 175 kg, i . e . , 0.25% of t h e average weight. Even i f $Ien = 5" (with engines i n t h e rear p o r t i o n o f t h e wing) and a = 3" and B = 7", = 5000 kg w e w i t h t h e same P r produce P s i n 7" = 5000-0.122 = 610 kg. T h i s i s 0.87% of t h e weight o f 70 t . 52. Required T h r u s t f o r H o r i z o n t a l F1 i g h t An a i r c r a f t i s capable of performing f l i g h t a t v a r i o u s angles of a t t a c k w i t h i n t h e speed range from t h e minimum t o t h e maximum, i . e . , a t v a r i o u s regimes. Each o f t h e s e regimes corresponds t o a c e r t a i n a i r speed (angle of a t t a c k ) , providing t h e l i f t i n g f o r c e equal t o t h e weight of t h e a i r c r a f t . This v e l o c i t y has come t o be c a l l e d t h e r e q u i r e d v e l o c i t y f o r h o r i z o n t a l f l i g h t , and t h e t h r u s t n e c e s s a r y f o r t h e performance of h o r i z o n t a l f l i g h t a t t h i s angle o f a t t a c k i s t h e r e q u i r e d t h r u s t f o r h o r i z o n t a l f l i g h t . Thus, i n h o r i z o n t a l f l i g h t a given angle of a t t a c k corresponds t o a d e f i n i t e r e q u i r e d v e l o c i t y and t h r u s t . I n o r d e r t o c a l c u l a t e t h e graphs o f r e q u i r e d t h r u s t on Figure 85, a graph o f t h e dependence c = f ( a ) and t h e p o l a r curve o f t h e a i r c r a f t with a wing without geometricYtwist i s used. The c a l c u l a t i o n was performed i n t h e f o l l o w i n g o r d e r : t h e r e q u i r e d t h r u s t i n h o r i z o n t a l f l i g h t i s s e t equal t o t h e d r a g : Pr = Q. S e t t i n g v a r i o u s f l i g h t speeds, we determine f o r each of them t h e impact p r e s s u r e and c Y' - u s i n g t h e p o l a r curve ( f o r v a r i o u s M numbers) w e f i n d t h e v a l u e o f c corresponding t o t h e s e speeds. X Using t h e formula Pr = Q = cxSp(V2/2) = cxSq, w e determine t h e r e q u i r e d thrust . As w e can s e e from F i g u r e 85, with t h e most f a v o r a b l e angle o f a t t a c k OL = 6" and H = 0 , we produce t h e minimum r e q u i r e d t h r u s t , corresponding t o hv t h e most f a v o r a b l e speed of 360 km/hr and q u a l i t y K = 15 (from t h e formula = G / K w e produce K = G/Pr = 35,000/2330 = 1 5 ) . An i n c r e a s e o r d e c r e a s e i n 'r speed l e a d s t o an i n c r e a s e i n r e q u i r e d t h r u s t , s i n c e w i t h angles of a t t a c k g r e a t e r t h a n o r l e s s t h a n 6", t h e aerodynamic q u a l i t y d e c r e a s e s . /124 For f l i g h t a t 360 km/hr n e a r t h e e a r t h t h e motors must b e t h r o t t l e d back so as t o achieve e q u a l i t y P = Pr. I n t h i s c a s e , t h e curve o f a v a i l a b l e P 117
- 127. t h r u s t touches t h e curve o f r e q u i r e d t h r u s t a t p o i n t B , corresponding t o a = 6'. As w e can see from F i g u r e 85, f o r f l i g h t with lower speed (V = 300 km/hr) as w e l l as f o r f l i g h t w i t h h i g h e r speed (600 km/hr), an i n c r e a s e i n engine t h r u s t i s r e q u i r e d ( p o i n t s C and A ) . --- i.g. 3000 2500 Figure 85. Required T:lrust As a Function of F l i g h t S p e e d ( f l y i n g w e i g h t 35 T I : 1 , Thrust f o r f l i g h t w i t h = 360 km/hr; 2 , Thrust f o r f l i g h t w i t h 'hv 1 . g . = landing g e a r V = 600 km/hr W know t h a t f o r a i r c r a f t with t u r b o j e t engines, t h e maximum excess e t h r u s t corresponds t o t h e most f a v o r a b l e speed and, i n t h e example h e r e analyzed Vhv = 360 km/hr. I n o r d e r t o achieve APmax a t t h e t a k e o f f o r nominal regime, an i n d i c a t e d f l i g h t speed of 360 km/hr must be maintained. As t h e f l y i n g a l t i t u d e i s i n c r e a s e d ( f o r t h e same weight, i n o u r example. 35 t ) , t h e r e q u i r e d t h r u s t remains unchanged i f t h e q u a l i t y i s t h e same. I n p r a c t i c e , however, as t h e i n d i c a t e d speed i s r e t a i n e d , Kmax d e c r e a s e s s l i g h t l y with i n c r e a s i n g a l t i t u d e (by 0 . 4 - 0 . 6 ) , s o t h a t Pr i s somewhat h i g h e r . I n our example (Figure 85), t h e i n d i c a t e d speed o f 360 km/hr a t 10,000 m corresponds t o a t r u e speed of 592 km/hr (M = 0.5) and a maximum q u a l i t y of 1 4 . 5 , i . e . , t h e q u a l i t y i s decreased by 0.5. The angles of a t t a c k corresponding t o Kmax are a l s o d i f f e r e n t f o r d i f f e r e n t a l t i t u d e s due t o t h e i n f l u e n c e of t h e M number on t h e p o l a r curve of t h e a i r c r a f t . F o r example, f o r H = 0 , t h e /125 angle of a t t a c k corresponding t o t h e minimum r e q u i r e d t h r u s t i s 6 " , and f o r H = 10,000 m -- 4.8". 118
- 128. A d e c r e a s e i n f l y i n g weight r e s u l t s i n a d e c r e a s e i n r e q u i r e d t h r u s t f o r t h e same angles of a t t a c k (and t h e r e f o r e , f o r t h e same a l t i t u d e s ) . As w e can see on Figure 85, a t H = 10,000 m f o r G = 30 t , t h e minimum Pr i s less t h a n t h e minimum P f o r G = 35 t , and a l s o t h e speed corresponding t o t h e minimum r r e q u i r e d t h r u s t i s less - - 575 km/hr (Vind = 350 km/hr). 9000 C I I Figure 86. Required Thrust As a Function of F l i g h t Speed ( a i r c r a f t w i t h three e n g i n e s ) If w e c o n s t r u c t curves of r e q u i r e d t h r u s t s f o r a i r c r a f t with h i g h weight and s p e c i f i c load ( f o r example with G = 80 t and G/S = 432 kg/m2), t h e most f a v o r a b l e speed is i n c r e a s e d t o 400 km/hr a t H = 0 and 625 km/hr a t H = 10,000 m (Figure 8 6 ) . I n o r d e r t o c a l c u l a t e t h e curves on Figure 86, w e used t h e dependence c = f ( a ) and t h e p o l a r curve of t h e a i r c r a f t shown on F i g u r e s 16 and 27. The Y i n c r e a s e d ah,, i s explained by t h e geometric t w i s t of t h e wing, about 3". F o r /126 c l a r i t y , Figure 86 shows t h e r e q u i r e d t h r u s t as a f u n c t i o n of f l i g h t speed f o r an a i r c r a f t w i t h landing g e a r and f l a p s down, when t h e r e q u i r e d t h r u s t i s i n c r e a s e d due t o t h e decreased q u a l i t y . 119
- 129. S3. Two Horizontal F l i g h t Regimes The p o i n t s o f i n t e r s e c t i o n of t h e curves o f r e q u i r e d and a v a i l a b l e t h r u s t correspond t o t h e e q u a l i t y P = P a consequently, f o r c e s P and Q, as w e l l as r P’ Y and G w i l l a l s o b e e q u a l . On Figure 85 f o r H = 0, t h e s e p o i n t s are marked by t h e l e t t e r s a , b and c. Due t o t h e s p e c i f i c f d a t u r e s of p i l o t i n g d u r i n g t r a n s i t i o n from one v e l o c i t y t o a n o t h e r , t h e s e p o i n t s d i f f e r considerably. For example, a t p o i n t a t h e t r a n s i t i o n t o a d i f f e r e n t speed r e q u i r e s s i m p l e r c o n t r o l t h a n a t p o i n t c. Thus, i n o r d e r t o i n c r e a s e t h e speed t o over 600 km/hr, a c c e l e r a t i o n must b e performed by i n c r e a s i n g t h e t h r u s t (P > Q ) . I n o r d e r t o decreas.e t h e speed, t h e a v a i l a b l e t h r u s t should be decreased, s i n c e t h e r e q u i r e d t h r u s t i n h o r i z o n t a l f l i g h t i n t h i s case i s l e s s t h a n f o r 600 km/hr. However, i n o r d e r t o move t o a d i f f e r e n t speed a t p o i n t c, f o r example, i n o r d e r t o i n c r e a s e t h r u s t over 300 km/hr, t h e c o n t r o l s t i c k must b e pushed forward t o t r a n s f e r t h e a i r c r a f t t o a lower angle of a t t a c k and, i n o r d e r t o maintain t h e same f l i g h t a l t i t u d e , t h e t h r u s t must b e i n i t i a l l y decreased, t h e n t h e n e c e s s a r y regime s e t when t h e speed begins t o i n c r e a s e . The same t h i n g must b e done t o d e c r e a s e t h e f l i g h t speed: t h e t h r u s t must b e t e m p o r a r i l y decreased, t h e n once more i n c r e a s e d , s i n c e a d e c r e a s e i n speed causes an i n c r e a s e i n r e q u i r e d t h r u s t . Point a corresponds t o t h e f i r s t f l i g h t regime, p o i n t c t o t h e second. The main p e c u l i a r i t y o f t h e second regime i s t h e n e c e s s i t y o f double a c t i o n with t h e c o n t r o l l e v e r o f t h e motor when f l i g h t speed i s changed. Therefore, f l i g h t should n o t be performed i n t h e second regime. s i n c e i t decreases c o n t r o l l a b i l i t y and makes flow s e p a r a t i o n on t h e a i r c r a f t wing p o s s i b l e . The boundary between t h e f i r s t and second f l i g h t regimes i s t h e most f a v o r a b l e angle o f a t t a c k f o r a t u r b o j e t a i r c r a f t ( f o r a p i s t o n powered a i r c r a f t it i s t h e most economical). Whereas f l i g h t s i n t h e second regime had no p r a c t i c a l s i g n i f i c a n c e f o r p i s t o n powered c r a f t , s i n c e f l i g h t s a t angles of a t t a c k g r e a t e r t h a n t h e economical angle of a t t a c k were almost never performed since a was n e a r t h e maximum p e r m i s s i b l e a n g l e o f a t t a c k , f l i g h t s of j e t ec a i r c r a f t ( p a r t i c u l a r l y a t a l t i t u d e s n e a r t h e p r a c t i c a l c e i l i n g ) may occur a t regimes n e a r t h e most f a v o r a b l e . The e s t a b l i s h e d minimum p e r m i s s i b l e o p e r a t i n g speed on t h e b a s i s of t h e values c i s u s u a l l y 50-70 km/hr less t h a n t h e most f a v o r a b l e speed. W e Y Per should n o t e t h a t i n t h e f o l l o w i n g i n our a n a l y s i s o f examples w e w i l l n o t c o n s i d e r a l t i t u d e l i m i t a t i o n s r e l a t e d t o t h e f l y i n g weight of t h e a i r c r a f t ( s e e 58 of t h i s c h a p t e r ) . I n t h e examples on F i g u r e s 85 and 86, t h e d i v i s i o n between t h e two f l i g h t /127 regimes a t low a l t i t u d e c o n s i s t s o f t h e most f a v o r a b l e speeds of 360 km/hr and 400 km/hr. I n h o r i z o n t a l f l i g h t with Vhv t h e motors must b e t h r o t t l e d back s o t h a t f l i g h t occurs a t speeds corresponding t o t h e p o i n t of c o n t a c t of t h e curves of a v a i l a b l e and r e q u i r e d t h r u s t (on F i g u r e 85, p o i n t b ) . As t h e f l y i n g weight i s d e c r e a s e d , t h e most f a v o r a b l e speed d e c r e a s e s ; f o r example, 120
- 130. a t 30 t , Vmf = 350 km/hr i n d i c a t e d (Figure 85). Lowering t h e landing g e a r and f l a p s d i s p l a c e s t h e boundary between f i r s t and second regimes c o n s i d e r a b l y toward lower speeds (Figure 8 6 ) . For example, with f l a p s down t h e speed d e c r e a s e s t o 325 km/hr ( a = 8.5") and with f l a p s mf down 25", t o 265 km/hr (amf = 7 . 8 " ) . A s a r u l e , t h e a i r c r a f t i s brought i n f o r a l a n d i n g i n t h e f i r s t regime. I n o r d e r t o avoid t r a n s f e r r i n g t o t h e second regime with t h e a i r c r a f t wing mechanics i n t h e t a k e o f f and l a n d i n g p o s i t i o n , t h e p i l o t must r e c a l l t h e i n d i c a t e d speed corresponding t o t h e boundary between t h e two f l i g h t regimes. 94. Influence o f External Air Temperature on Required Thrust A s was noted, a change i n t h e temperature of t h e surrounding a i r l e a d s t o a change i n engine t h r u s t ( c h a p t e r V I , § 6 ) . Also, temperature o f t h e s u r rounding a i r i n f l u e n c e s t h e n a t u r e of t h e dependence of r e q u i r e d t h r u s t on f l i g h t speed, which appears a s a displacement of t h e curve t o t h e l e f t (with d e c r e a s i n g t ) o r t o t h e r i g h t (with i n c r e a s i n g t ) and i n f l u e n c e s t h e v a l u e of r e q u i r e d speed f o r h o r i z o n t a l f l i g h t . The e x t e r n a l a i r temperature does n o t i n f l u e n c e t h e r e q u i r e d t h r u s t , s i n c e P = G / K , and K = c / c depends only on r Y X t h e angle of a t t a c k . Let US analyze t h e reason why t h e curve P = (V,t") i s r d i s p l a c e d . W know t h a t i n h o r i z o n t a l f l i g h t with unchanging a n g l e o f a t t a c k e ( o r c ) a t d i f f e r e n t temperatures t h e following c o n d i t i o n should be f u l f i l l e d : Y A s t h e temperature i s decreased with c o n s t a n t p r e s s u r e , t h e d e n s i t y of t h e a i r i s i n c r e a s e d . I n t h i s c a s e , i n o r d e r f o r e q u a l i t y Y = G t o be f u l f i l l e d , t h e r e q u i r e d h o r i z o n t a l f l i g h t speed must be decreased ( c unchanged). As t h e Y v e l o c i t i e s a r e decreased, t h e curves of r e q u i r e d t h r u s t w i l l be s h i f t e d t o t h e l e f t . A s t h e temperature i s i n c r e a s e d , on t h e o t h e r hand, t h e curves o f required t h r u s t a r e displaced t o t h e r i g h t , s i n c e t h e required v e l o c i t i e s i n c r e a s e (Figure 8 7 ) . A s w e can s e e from t h e f i g u r e , t h e same Prl corresponds t o a g r e a t e r r e q u i r e d t h r u s t f o r a temperature 10" h i g h e r t h a n t h e s t a n d a r d t e m p e r a t u r e , /128 __. since f o r t we have Vcrl, and f o r tst + 10" v e l o c i t y V st Vcrl. The curves of r e q u i r e d t h r u s t f o r c o n d i t i o n s o t h e r t h a n s t a n d a r d a r e c a l c u l a t e d as f o l l o w s . A t f i r s t we f i n d t h e a i r d e n s i t y under t h e new condi t i o n s . For example, when t h e o u t s i d e a i r temperature i s i n c r e a s e d by 10" with p r e s s u r e unchanged f o r H = 10,000 m y T = 223°K and p = 198 mm Hg, w e produce 1 21
- 131. T = 223 + 10 = 233', p = 0.0473 p/T = 0.0473*198/233 = 0.0403 kg*sec2/m4. This v a l u e o f p , according t o t h e s t a n d a r d t a b l e , i s e q u i v a l e n t t o a f l i g h t a l t i t u d e o f 10,300 m. Then, f i x i n g t h e f l i g h t speed, w e determine c then take c from t h e YY X p o l a r curve o f t h e a i r c r a f t w i t h v a r i o u s M (Figure 28). Using t h e formula Pr = cxSq, w e determine t h e r e q u i r e d t h r u s t . I n d e t e r m i n i n g t h e M number, w e b a s e o u r c a l c u l a t i o n s on t h e f a c t t h a t a t T = 233'K, t h e speed o f sound a = 306 m/sec. W must n o t e t h a t as t h e e t e m p e r a t u r e is i n c r e a s e d by more . - t h a n lo', t h e d e c r e a s e i n d e n s i t y ( i n c r e a s e i n speed) w i l l b e g r e a t e r . For example, w i t h A t = +30° a t H = 10,000 m y t h e tS decrease i n d e n s i t y i s e q u i v a l e n t t o an i n c r e a s e i n f l y i n g a l t i t u d e t o approximately 11,000 m. Let u s now a n a l y z e t h e graphs o f r e q u i r e d t h r u s t (Figure 87). f i g u r e 87. Influence o f Surrounding Air Temperature o n Required and With s t a n d a r d t e m p e r a t u r e , Ava i 1 ab le A i r c r a f t Thrust ( s p e c i f i c i n o r d e r t o produce t h e v e l o c i t y 1 oad i ng 340 kg/m2) a t H = 10,000 m , we must 'crl u s e engine speed n O At this 1"' speed, t h e a v a i l a b l e t h r u s t w i l l be equal t o t h e r e q u i r e d t h r u s t ( p o i n t A ) . A s t h e temperature i s i n c r e a s e d by 10' (by 4.2% o f 233'K) , t h e curve o f r e q u i r e d t h r u s t i s d i s p l a c e d t o t h e r i g h t , and t h e curve of P i s d i s p l a c e d downward. The a v a i l a b l e t h r u s t , depending on t h e t y p e and d e s i g n o f t h e motor, may be decreased by 5-8% (curve 2 ) . The i n t e r s e c t i o n o f t h e curves of a v a i l a b l e and r e q u i r e d t h r u s t d e f i n e s t h e speed Vcr2 w i t h unchanged engine o p e r a t i n g - /129 regime. As we can see from t h e f i g u r e , t h e t r u e f l i g h t speed has decreased, s o t h a t t h e M number i s a l s o decreased, s i n c e t h e speed o f sound i s n o t 300, b u t r a t h e r 306 m/sec (M = Vcr2/306). Thus, as t h e a i r temperature i s i n c r e a s e d by lo', t h e f l y i n g regime changes s i g n i f i c a n t l y . If we must maintain t h e previous M number ( i . e . , corresponding t o t s t ) ' w e must i n c r e a s e t h e o p e r a t i n g speed of t h e engines and, as w can see on Figure 87, s e t i n engine speed n3% ( p o i n t B ) . e The t r u e f l i g h t speed i n c r e a s e s and becomes V cr3 = aM = 306 M. 122
- 132. . . a,, , , ' I , 0' ! I: , .;(, , : '. If t h e p i l o t does not change t h e o p e r a t i n g regime of t h e engines, as t h e . 1 , , f l i g h t speed i s decreased from Vcrl t o Vcr2, t h e angle o f a t t a c k and c , ' , .II ,', * Y .' . , , ' . I <;' , i n c r e a s e . Allowing t h e aircraft t o f l y a t h i g h e r angles of a t t a c k i s danger- ' I ,*,' x.:. ,.. .., ous due t o t h e approach toward c and t h e s e p a r a t i o n l i m i t . Also, under '.., Y Per : .,$,',,.-. e. . -. r e l a t i v e l y h i g h temperature c o n d i t i o n s , t h e v e r t i c a l gust reserve i s r , I: 3 , . -.< . _.. ' ;,,:', : ,': decreased. Therefore, i n case such c o n d i t i o n s are encountered, t h e r o t a t i n g ' . _ I . speed o f t h e engine should b e i n c r e a s e d by .an -avecage of 5% f o r each 5-10" k - . , I,:, .:. , , 8. , , -. : /. -. < , I. ; o f i n c r e a s e i n temperature, o r if t h i s i s impossible, a lower f l y i n g a l t i t u d e s ),, .. ~ should be requested. I ,.I . 1.' ' ? I' . As t h e temperature d e c r e a s e s , t h e a v a i l a b l e t h r u s t i n c r e a s e s (curve 4) ' I ad; ' and t h e curve of r e q u i r e d t h r u s t i s d i s p l a c e d t o t h e l e f t . The p o i n t of t h e i r .;. , ' ' , , , ,x. ., ' ' . . > 1 i n t e r s e c t i o n c d e f i n e s t h e new f l i g h t . s p e e d . ':~,, I '; .>, .I, . .. I : 95. Most Favorable Horizontal F l i g h t Regimes. Influence of A l t i t u d e and .. ! .,_ ' , ' ) " .r :'- ,. . > ..> . . . The f l i g h t range i s t h e d i s t a n c e t r a v e l e d by t h e a i r c r a f t during t h e , h o r i z o n t a l f l i g h t and descent. If f l i g h t i s performed u n t i l t h e f u e l i s completely exhausted, t h e d i s t a n c e t r a v e l e d i s c a l l e d t h e t e c h n i c a l range. F o r . p a s s e n g e r a i r c r a f t , t h e f l i g h t range given i s u s u a l l y t h a t with one hour's ' f u e l reserve i f t h e f l i g h t schedule i s maintained. (recommended regimes). t h e r e are v a r i o u s ways w h i c h - t h e aircraft can l e a v e t h e area of t h e e l d and climb after t a k e o f f , t h e range o f f l i g h t covered during t h e climb t o assigned a l t i t u d e changes s i g n i f i c a n t l y . However, t h e range covered during t o a l t i t u d e i s r e l a t i v e l y . s l i g h t , s o t h a t i n t h e following w e w i l l d i s c u s s t h e range of h o r i z o n t a l f l i g h t . The range of t h e h o r i z o n t a l f l i g h t s e c t o r depends on t h e f u e l r e s e r v e f o r h o r i z o n t a l f l i g h t and on t h e rate a t which it i s expended, i . e . , t h e kilometer expenditure c -- t h e expenditure of f u e l p e r kilometer of f l i g h t path. k ',:,;* Before going over t o h o r i z o n t a l f l i g h t , t h e a i r c r a f t must t a k e o f f and climb. ' , ' The f u e l expenditure during t h e time of t a k e o f f and climb t o 9-11 k f o r two- m ': ! and three-engine aircraft is 1600-4000 kg. ' The f u e l expended d u r i n g t a k e o f f and establishment of nominal f l i g h t , ' . j regime (without c o n s i d e r a t i o n o f climb) i s 250-350 kg, t h e f u e l expended - /130 , , . : during t h e descent and landing i s 700-1000 kg. I n o r d e r t o determine t h e ! q u a n t i t y o f f u e l t o be used i n t h e h o r i z o n t a l f l i g h t s e c t o r Gf her, w e must ,- '!{ s u b t r a c t from t h e q u a n t i t y of f u e l t a k e n on board a l l supplementary expend- ,,,',: i t u r e s and t h e n a v i g a t i o n a l reserve. For example, with a t a k e o f f weight o f . . - ... . .. ,',; t h e aircraft o r 44,000 kg and an i n i t i a l f u e l weight of 13,000 kg, 7000 '>, 7700 kg o f f u e l remain f o r h o r i z o n t a l f l i g h t a t H = 10,000 m, s i n c e about " 2000 kg are expended i n ' t a k e o f f and climbing, 800-1000 kg f o r descent and I , , ! landing and 2500 kg are h e l d as n a v i g a t i o n a l reserve. 123
- 133. For s h o r t e r range f l i g h t s a t t h e same a l t i t u d e , t h e o n l y change i s i n t h e q u a n t i t y of f u e l r e q u i r e d f o r t h e h o r i z o n t a l s e c t o r , while t h e remaining f u e l expenditure norms remain approximately unchanged. The d u r a t i o n of h o r i z o n t a l f l i g h t i s determined from t h e r e l a t i o n s h i p where 5 is t h e hourly f u e l expenditure. The hourly f u e l e x p e n d i t u r e i s t h e q u a n t i t y of f u e l expended by t h e a i r c r a f t i n one hour of h o r i z o n t a l f l i g h t . For example, f o r an a i r c r a f t with t h r e e engines with a r e q u i r e d t h r u s t o f 6000 kg and a s p e c i f i c expenditure of 0 , 8 kg/kg.hr, t h e h o u r l y r a t e i s 4800 kg/hr. The r e l a t i o n s h i p between h o u r l y and kilometer e x p e n d i t u r e s i s e s t a b l i s h e d from t h e f o l l o w i n g c o n s i d e r a t i o n s : i n one hour of f l i g h t , t h e engines burn kg o f f u e l . However, d u r i n g t h i s same time t h e a i r c r a f t covers a d i s t a n c e numerically e q u a l t o t h e f l i g h t speed V ( i n calm a i r ) . Therefore, t h e f u e l expenditure p e r k i s m where V i s t a k e n i n km/hr. If V i s taken i n m/sec, ch cK=- * 3.6V For V = 880 km/hr and ch = 4800 kg/hr, w produce ck = 5.46 kg/km. e Both t h e hourly and k i l o m e t e r e x p e n d i t u r e s depend g r e a t l y on t h e s p e c i f i c e x p e n d i t u r e o f t h e engines c The r e l a t i o n s h i p between t h e P‘ s p e c i f i c and h o u r l y e x p e n d i t u r e s i s e s t a b l i s h e d as f o l l o w s : f o r each 1 kg of t h r u s t and one hour of engine o p e r a t i o n , cp kg of f u e l are expended, while a t h r u s t o f P kg r e q u i r e s t h e e x p e n d i t u r e o f P times more f u e l . Therefore, 124
- 134. I n Chzpter I V w e s t a b l i s h e d t h a t t h e s p e c i f i c fuel expenditure depends e on t h e r o t a t i n g speed o f t h e engine, a l t i t u d e and v e l o c i t y of f l i g h t . - /131 L e t u s now go over t o an a n a l y s i s o f f l i g h t range. With i d e n t i c a l f u e l reserve w i t h i n t h e l i m i t s of p o s s i b l e speeds, v a r i o u s ranges w i l l b e produced. For example, i n t h e example o u t l i n e d above with a f u e l load of 13,000 kg, a t a k e o f f weight o f 44,000 kg, f l i g h t a t 10,000 m with a t r u e speed of 810 km/hr (M = 0.75-0.76) and an hourly fue1,expenditure of 2500 kg/hr, i n calm a i r a range on t h e or-der of 2800-3000 k can be produced. With f l i g h t a t m a high M number (V > 810 km/hr), t h e range is decreased t o 2200-2500 km. Figure 88 shows. a f l i g h t p r o f i l e f o r , an a i r c r a f t c a l c u l a t e d f o r various h o r i z o n t a l ' f l i g h t speeds, which a l s o i l l u s t r a t e s t h e above. A head wind o r t a i l wind changes t h e f l i g h t range. Let u s analyze t h e i n f l u e n c e of f l i g h t speed on t h e hourly and kilometer f u e l expenditures. W can explain t h i s e f o r f l i g h t a t one and t h e same a l t i t u d e , using t h e Zhukovskiy curves f o r r e q u i r e d and a v a i l a b l e t h r u s t (Figure 89). F i g u r e 88. C h a r a c t e r i s t i c I n order t o achieve h o r i z o n t a l f l i g h t F l i g h t P r o f i l e of A i r c r a f t a t any given speed (Vmax' '1, 2 and vmf) ' to Range a t Fixed A l t i t u d e it i s r e q u i r e d t h a t P = P,'. This means P t h a t i n o r d e r t o f l y a t less than Vma, t h e engine must b e t h r o t t l e d back s o t h a t t h e curve o f P passes through P p0int.s AI, A and A r e s p e c t i v e l y (Figure 89 a ) . 2 3 The hourly f u e l expenditure 5= cpP P' b u t s i n c e a t any v e l o c i t y o f - /132 h o r i z o n t a l f l i g h t Pr = Pp > Ch 5 cppr. I n order t o decrease t h e f l y i n g speed, t h e r o t a t i n g speed of t h e engine must be decreased. This r e s u l t s i n an i n c r e a s e i n s p e c i f i c consumption. However, as t h e f l y i n g speed i s decreased, t h e value of Pr = G/K i s a l s o decreased. Thus, as t h e engine is t h r o t t l e d back, cp i n c r e a s e s , b u t Pr decreases. The hourly expenditure w i l l depend on t h e way i n which cp and P change. W f i n d t h a t as t h e f l i g h t speed i s decreased, t h r u s t P decreases e . more i n t e n s i v e l y than cp i n c r e a s e s . Therefore, c a l s o decreases; t h e minimum h 125
- 135. "h min w i l l correspond t o Vmf, a t which Pr min - G/Kma. With V < Vmf, 5 begins t o i n c r e a s e , s i n c e P increases. Consequently, t h e g r e a t e s t f l i g h t r d u r a t i o n a t any a l t i t u d e w i l l occur when f l y i n g at t h e most f a v o r a b l e speed. F i g u r e 89. Explanation of Influence of F l i g h t Speed on Hourly and Kilometer F u e l Expenditures Let us e x p l a i n how t h e f l y i n g a l t i t u d e i n f l u e n c e s t h e hourly expenditure. I n 92 of t h i s chapter we showed t h a t t h e r e q u i r e d t h r u s t i s almost i d e n t i c a l for t h e same weight a t a l l f l y i n g a l t i t u d e s up t o 10,000 m. However, t h e r e q u i r e d speed i n c r e a s e s with a l t i t u d e . Therefore, t h e curves of r e q u i r e d t h r u s t a r e d i s p l a c e d toward t h e a r e a of h i g h e r speeds with i n c r e a s i n g a l t i t u d e ( s e e Figure 85). Since t h e a v a i l a b l e t h r u s t of t h e engine decreases with a l t i t u d e , t h e curves o f t h e change i n t h r u s t with v e l o c i t y are displaced downward with an i n c r e a s e i n a l t i t u d e . Therefore, whereas a t low a l t i t u d e t h e engines must be t h r o t t l e d back, t h u s considerably i n c r e a s i n g t h e s p e c i f i c expenditure, a t 10,000 m l e s s t h r o t t l i n g i s r e q u i r e d and t h e s p e c i f i c expenditure i n c r e a s e s only s l i g h t l y . When f l y i n g a t t h e c e i l i n g , t h e engines need not be t h r o t t l e d back a t a l l . Therefore, as t h e f l y i n g a l t i t u d e i n c r e a s e s t h e product cpPr min decreases, which e x p l a i n s t h e decrease i n hourly expenditure. Also, t h e decrease i n with a l t i t u d e f a c i l i t a t e s a decrease i n s p e c i f i c expenditure a t constant o p e r a t i n g speed. Therefore, t h e l o n g e s t f l i g h t d u r a t i o n f o r an a i r c r a f t with a t u r b o j e t engine i s produced n e a r t h e c e i l i n g . F l i g h t d u r a t i o n a t high a l t i t u d e i s 2-2.5 times g r e a t e r than a t low a l t i t u d e . The regime of lowest hourly expenditure i s used when f l y i n g i n a holding p a t t e r n o r with a s t r o n g t a i l wind (150-200 km/hr) i n o r d e r t o maintain t h e scheduled time of arrival. Let u s now analyze t h e way i n which t h e s e l e c t i o n o f f l i g h t speed i n f l u e n c e s t h e kilometer expenditure. I t was shown above t h a t ck = eh//3.6 V. S u b s t i t u t i n g t h e value = cpPr i n t h i s formula, we produce 126
- 136. If t h e p i l o t does n o t change t h e o p e r a t i n g regime of t h e engines, as t h e f l i g h t speed i s decreased from Vcrl t o Vcr2, t h e angle of a t t a c k and c ch=L Y i n c r e a s e . Allowing t h e a i r c r a f t t o f l y a t h i g h e r angles of a t t a c k is danger cI(=Ch= ous due t o t h e approach toward c and t h e s e p a r a t i o n l i m i t . Also, under Y Per r e l a t i v e l y h i g h temperature c o n d i t i o n s , t h e v e r t i c a l g u s t r e s e r v e i s decreased. T h e r e f o r e , i n c a s e such c o n d i t i o n s a r e encountered, t h e r o t a t i n g speed of t h e engine should b e i n c r e a s e d by an average of 5% f o r each 5-10' In C h W e r I V w e established t h a t t h of i n c r e a s e i n temperature, o r i f t h i s i s impossible, a lower f l y i n g a l t i t u d e on t h e r o t a t i n g speed o f t h e engine, a l t should b e r e q u e s t e d . L e t u s now go over t o an a n a l y s i s o A s t h e temperature d e c r e a s e s , t h e a v a i l a b l e t h r u s t i n c r e a s e s (curve 4) r e s e r v e w i t h i n t h e l i m i t s of p o s s i b l e s p and t h e curve of r e q u i r e d t h r u s t i s d i s p l a c e d t o t h e l e f t . The p o i n t of t h e i r For example, i n t h e example o u t l i n e d abo: i n t e r s e c t i o n c d e f i n e s t h e new f l i g h t speed. t a k e o f f weight o f 44,000 kg, f . l i g h t a t 1 810 km/hr (M = 0.75-0.76) and an h o u r l y calm a i r a range on t h e o r d e r o f 2800-30 95. M o s t Favorable Horizontal F l i g h t Regimes. Influence o f A l t i t u d e and a high M number (V > 810 km/hr), t h e r a n S p e e d Figure 88 shows a f l i g h t p r o f i l e f o r an h o r i z o n t a l f l i g h t speeds, which a l s o i l l The f l i g h t range i s t h e d i s t a n c e t r a v e l e d by t h e a i r c r a f t d u r i n g t h e climb, h o r i z o n t a l f l i g h t and d e s c e n t . I f f l i g h t i s performed u n t i l t h e f u e l i s completely exhausted, t h e d i s t a n c e t r a v e l e d i s c a l l e d t h e t e c h n i c a l range. f l i g For passenger a i r c r a f t , t h e f l i g h t range given i s u s u a l l y t h a t with one h o u r ' s V= 75-OK+, f u e l r e s e r v e if t h e f l i g h t schedule i s maintained. (recommended regimes). S i n c e t h e r e a r e v a r i o u s ways which t h e a i r c r a f t can l e a v e t h e a r e a of t h e f l i g a i r f i e l d and climb a f t e r t a k e o f f , t h e range of f l i g h t covered d u r i n g t h e climb f u e l t o assigned a l t i t u d e changes s i g n i f i c a n t l y , However, t h e range covered d u r i n g f o r climb t o a l t i t u d e i s r e l a t i v e l y s l i g h t , s o t h a t i n t h e following w e w i l l u s i n d i s c u s s t h e range of h o r i z o n t a l f l i g h t . U 2800 L m and The range of t h e h o r i z o n t a l f l i g h t s e c t o r depends on t h e f u e l r e s e r v e f o r Figure 88. C h a r a c t e r i s t i c h o r i z o n t a l f l i g h t and on t h e r a t e a t which it i s expended, i . e . , t h e k i l o m e t e r F l i g h t P r o f i l e of A i r c r a f t at a e x p e n d i t u r e c - - t h e e x p e n d i t u r e of f u e l p e r k i l o m e t e r of f l i g h t p a t h . t o Range a t Fixed A l t i t u d e k it Before going over t o h o r i z o n t a l f l i g h t , t h e a i r c r a f t must t a k e o f f and climb. t h a t The f u e l e x p e n d i t u r e d u r i n g t h e t i m e of t a k e o f f and climb t o 9-11 km f o r two- and t h r e e - e n g i n e a i r c r a f t i s 1600-4000 kg. t h e engine must b e t h r o t t l e d back s o tha - p o i n t s A1, A and A3 r e s p e c t i v e l y (Figur 2 The f u e l expended d u r i n g t a k e o f f and e s t a b l i s h m e n t of nominal f l i g h t regime (without c o n s i d e r a t i o n o f climb) i s 250-350 kg, t h e f u e l expended - /130 The h o u r l y f u e l e x p e n d i t u r e ch = E d u r i n g t h e d e s c e n t and l a n d i n g i s 700-1000 kg. I n o r d e r t o determine t h e ' i q u a n t i t y of f u e l t o be used i n t h e h o r i z o n t a l f l i g h t s e c t o r Gf her, w e must h o r i z o n t a l f l i g h t Pr = P p , ch = c p P r . s u b t r a c t from t h e q u a n t i t y of f u e l t a k e n on board a l l supplementary expend- 1 I n o r d e r t o d e c r e a s e t h e f l y i n g s p i t u r e s and t h e n a v i g a t i o n a l r e s e r v e . F o r example, with a t a k e o f f weight of must be decreased. This r e s u l t s i n an , t h e a i r c r a f t o r 44,000 kg and an i n i t i a l f u e l weight of 13,000 kg, 7000 However, as t h e f l y i n g speed i s decreasc 7700 kg of f u e l remain f o r h o r i z o n t a l f l i g h t a t H = 10,000 m , s i n c e about 2000 kg a r e expended i n t a k e o f f and climbing, 800-1000 kg f o r descent and decreased. Thus, a s t h e engine is t h r o ; l a n d i n g and 2500 kg are h e l d as n a v i g a t i o n a l r e s e r v e . d e c r e a s e s . The hourly expenditure w i l l 1 c 1 change. W f i n d t h a t a s t h e f l i g h t spef e more i n t e n s i v e l y t h a n c P i n c r e a s e s . 'Thl I I 123
- 137. For s h o r t e r range f l i g h t s t h e q u a n t i t y of f u e l r e q u i r e d f ' w i l l correspond t o Vmf, a t which Pr min - G/Kmm. With V < Vmf, ch f u e l expenditure norms remain ch min b e g i n s t o i n c r e a s e , s i n c e Pr i n c r e a s e s . Consequently, t h e g r e a t e s t f l i g h t The d u r a t i o n of h o r i z o n t a l d u r a t i o n a t any a l t i t u d e w i l l occur when f l y i n g a t t h e most f a v o r a b l e speed. where % i s t h e h o u r l y f u e l expc The h o u r l y f u e l expenditurc a i r c r a f t i n one hour of horizon: t h r e e engines with a r e q u i r e d t l 0 , 8 kg/kg-hr, t h e h o u r l y r a t e i t The r e l a t i o n s h i p between hc from t h e f o l l o w i n g c o n s i d e r a t i o r Figure 89. Explanation o f I n f l u e n c e o f F l i g h t % kg of f u e l . However, d u r i n g S p e e d o n Hourly and K i lometer F u e l Expend i t u r e s numerically e q u a l t o t h e f l i g h t expenditure p e r km i s Let u s e x p l a i n how t h e f l y i n g a l t i t u d e i n f l u e n c e s t h e h o u r l y e x p e n d i t u r e . I n 9 2 o f t h i s c h a p t e r w e showed t h a t t h e r e q u i r e d t h r u s t i s almost i d e n t i c a l f o r t h e same weight a t a l l f l y i n g a l t i t u d e s up t o 10,000 m. However, t h e r e q u i r e d speed i n c r e a s e s w i t h a l t i t u d e . T h e r e f o r e , t h e curves of r e q u i r e d t h r u s t a r e d i s p l a c e d toward t h e area of h i g h e r speeds w i t h i n c r e a s i n g a l t i t u d e ( s e e Figure 8 5 ) . where V i s taken i n km/hr. If L S i n c e t h e a v a i l a b l e t h r u s t of t h e engine d e c r e a s e s with a l t i t u d e , t h e curves o f t h e change i n t h r u s t w i t h v e l o c i t y a r e d i s p l a c e d downward w i t h an i n c r e a s e i n a l t i t u d e . T h e r e f o r e , whereas a t low a l t i t u d e t h e engines must b e t h r o t t l e d back, t h u s c o n s i d e r a b l y i n c r e a s i n g t h e s p e c i f i c e x p e n d i t u r e , a t 10,000 m l e s s t h r o t t l i n g i s r e q u i r e d and t h e s p e c i f i c e x p e n d i t u r e i n c r e a s e s only s l i g h t l y . When f l y i n g a t t h e c e i l i n g , t h e engines need n o t be t h r o t t l e d back a t a l l . T h e r e f o r e , as t h e f l y i n g a l t i t u d e i n c r e a s e s t h e product cpPr min F o r V = 880 km/hr and ch = d e c r e a s e s , which e x p l a i n s t h e d e c r e a s e i n h o u r l y e x p e n d i t u r e . Also, t h e Both t h e hourly and kilomet d e c r e a s e i n w i t h a l t i t u d e f a c i l i t a t e s a d e c r e a s e i n s p e c i f i c expenditure a t s p e c i f i c expenditure o f t h e engi c o n s t a n t o p e r a t i n g speed. T h e r e f o r e , t h e l o n g e s t f l i g h t d u r a t i o n f o r an s p e c i f i c and h o u r l y e x p e n d i t u r e s a i r c r a f t with a t u r b o j e t engine i s produced n e a r t h e c e i l i n g . F l i g h t d u r a t i o n 1 kg of t h r u s t and one hour of e a t high a l t i t u d e i s 2-2.5 times g r e a t e r t h a n a t low a l t i t u d e . The regime of lowest h o u r l y e x p e n d i t u r e i s used when f l y i n g i n a h o l d i n g p a t t e r n o r w i t h while a t h r u s t o f P kg r e q u i r e s a s t r o n g t a i l wind (150-200 km/hr) i n o r d e r t o m a i n t a i n t h e scheduled time of Therefore , arr i v a 1. Let u s now analyze t h e way i n which t h e s e l e c t i o n o f f l i g h t speed i n f l u e n c e s t h e k i l o m e t e r e x p e n d i t u r e . I t was shown above t h a t ck = ch/3.6 V. S u b s t i t u t i n g t h e v a l u e ch = cpPr i n t h i s formula, we produce 124 126
- 138. I n o r d e r t o s i m p l i f y o u r d i s c u s s i o n s , l e t u s assume t h a t c remains P c o n s t a n t with changing f l i g h t speed, i . e . , c o n s i d e r t h a t n e i t h e r a d e c r e a s e i n engine t h r u s t n o r a d e c r e a s e i n t h e v e l o c i t y i t s e l f i n f l u e n c e s c Then i t P' f o l l o w s from t h e l a s t e x p r e s s i o n f o r c t h a t t h e minimum k i l o m e t e r e x p e n d i t u r e - ,133 k w i l l occur a t t h e speed f o r which t h e q u a n t i t y P / V i s minimal. In order t o r determine t h i s speed, we u s e t h e graph on Figure 89 b . The q u a n t i t y P / V = t a n $ ( a n g l e $ i s formed by t h e h o r i z o n t a l a x i s and a r a y from t h e r c o o r d i n a t e o r i g i n t o any p o i n t on curve P ) . When f l y i n g a t Vmf, r tan $ = P and when f l y i n g a t Vmm, t a n $ = P / V r minlVmf' r max' W can s e e from t h e f i g u r e t h a t w i t h d e c r e a s i n g f l i g h t speed, a n g l e 4 e d e c r e a s e s and reaches a minimum a t a speed corresponding t o t h e p o i n t of c o n t a c t o f t h e r a y t o t h e curve o f r e q u i r e d t h r u s t . This speed, a t which Pr/V i s minimal, w i l l be c a l l e d speed V With a f u r t h e r d e c r e a s e i n speed, angle 3' $ b e g i n s t o i n c r e a s e , i . e . , P / V i s i n c r e a s e d . Thus, i f we c o n s i d e r t h e r s p e c i f i c e x p e n d i t u r e c o n s t a n t a s t h e speed i s changed, (Pr/V)min and conse q u e n t l y a l s o t h e minimal k i l o m e t e r expenditure w i l l be produced a t speed V 3' A s we can s e e , V i s always g r e a t e r t h a n Vmf. 3 Let us now c o n s i d e r t h a t t h e s p e c i f i c expenditure i s n o t c o n s t a n t with changing speed and c o n s i d e r t h e i n f l u e n c e of t h r o t t l i n g of t h e motor on c I f f l i g h t i s performed a t V w e have high P / V and nominal motor P' max' r o p e r a t i n g speed, s o t h a t c h e r e i s minimal. When we d e c r e a s e t h e speed P ( d e c r e a s e motor o p e r a t i n g s p e e d ) , we d e c r e a s e P / V , but due t o t h e t h r o t t l i n g r o f t h e motors, c i n c r e a s e s . A t V3, t h e v a l u e of P / V i s minimal, b u t h e r e P r c i s i n c r e a s e d , s i n c e t h e engines are c o n s i d e r a b l y t h r o t t l e d . Comparing P t h e s e two extreme p o s i t i o n s , we might conclude t h a t somewhere between Vmax and V t h e r e should be a speed a t which c P / V i s minimal. This speed i s s l i g h t l y 3 P r g r e a t e r t h a n V3 and i s c a l l e d t h e speed of minimal k i l o m e t e r e x p e n d i t u r e . For H = 0 w i t h a s p e c i f i c l o a d i n g o f 350-420 kg/m2, t h i s speed i s approximately 450- 52 0 km/hr . W can see from Figure 90 t h a t as t h e a l t i t u d e i n c r e a s e s , t h e t r u e speed e corresponding t o t h e minimal k i l o m e t e r e x p e n d i t u r e a l s o i n c r e a s e s . W can see e from F i g u r e 91 t h a t t h e minimal k i l o m e t e r expenditure d e c r e a s e s up t o 10,800 m , t h e n b e g i n s t o i n c r e a s e . The d e c r e a s e i n k i l o m e t e r e x p e n d i t u r e of 127
- 139. , f u e l with i n c r e a s i n g a l t i t u d e i s f a c i l i t a t e d by t h e d e c r e a s e i n t h e q u a n t i t y P /V r e s u l t i n g from t h e i n c r e a s e d f l i g h t speed and decreased s p e c i f i c f u e l /134 r expenditure. I n t h i s example, t h e a l t i t u d e of 10,800 m a t which t h e minimum k i l o m e t e r e x p e n d i t u r e i s produced i s c a l l e d t h e most f a v o r a b l e a l t i t u d e . For t u r b o j e t a i r c r a f t it i s 1000-1200 m below t h e p r a c t i c a l c e i l i n g , a t which a c o n s i d e r a b l e wave d r a g i s c r e a t e d due t o t h e high a n g l e s o f a t t a c k . T r a n s i t i o n t o lower a l t i t u d e , i . e . , t o lower angles o f a t t a c k , d e c r e a s e s t h i s drag component s i g n i f i c a n t l y and i n c r e a s e s t h e aerodynamic q u a l i t y . Let u s show t h a t t h e k i l o m e t e r e x p e n d i t u r e depends on q u a l i t y : Figure 90. S p e e d of M i n Figure 91. Influe.nce of imal Kilometer Expend F l i g h t A l t i t u d e on M i n i t u r e o f F u e l As a imal Kilometer F u e l Function of F l y i n g Expend i t u r e Altitude (aircraft w i t h two e n g i n e s ) W can see from t h e formula t h a t t h e k i l o m e t e r e x p e n d i t u r e i s i n v e r s e l y e p r o p o r t i o n a l t o t h e q u a l i t y . Now w e can f o r m u l a t e a d e f i n i t i o n of most favorable f l i g h t a l t i t u d e : t h e a l t i t u d e corresponding t o (KV) called t h e max ’ most f a v o r a b l e a l t i t u d e o r t h e a l t i t u d e o f l e a s t k i l o m e t e r e x p e n d i t u r e . The dependence o f t h e a l t i t u d e of t h e p r a c t i c a l c e i l i n g and t h e a l t i t u d e of minimal k i l o m e t e r e x p e n d i t u r e on f l y i n g weight of a TU-124 a i r c r a f t i s shown on Figure 9 2 , w h i l e F i g u r e 93 shows t h e dependence o f t h e minimal k i l o m e t e r e x p e n d i t u r e f o r t h i s a i r c r a f t on f l i g h t speed. W can s e e from t h i s e l a s t graph t h a t t h e minimal k i l o m e t e r e x p e n d i t u r e i s produced a t 128
- 140. V = 752 km/hr. T h i s i s t h e speed V a t t h e most f a v o r a b l e a l t i t u d e . C k min F l i g h t s a t lower and h i g h e r speeds and a t o t h e r a l t i t u d e s cause i n c r e a s e s i n k i l o m e t e r expenditure. I t has been e s t a b l i s h e d t h a t a t speeds 5-8% (30-50 km/hr) h i g h e r t h a n , t h e k i l o m e t e r e x p e n d i t u r e i s i n c r e a s e d by an average of 1%( f o r "k min example, i f ck min = 3 kg/km, i t w i l l be i n c r e a s e d t o 3.03 kg/lcm), and t h a t t h i s i s t h e optimal regime f o r l o n g - d i s t a n c e f l i g h t s . T h i s c r u i s i n g regime i s t h e most economical as concerns t o t a l t r a n s p o r t a t i o n c o s t , s i n c e i t - / 135 consumes l i t t l e f u e l , allowing h i g h e r commercial load t o b e c a r r i e d . For medium range f l i g h t s (1300-1500 km), t h e h i g h e s t c r u i s i n g regime i s recommended, i n which t h e k i l o m e t e r e x p e n d i t u r e s a r e h i g h e r b u t t h e i n c r e a s e d f u e l load does n o t r e q u i r e a d e c r e a s e i n commercial l o a d , b u t t h e i n c r e a s e i n speed does d e c r e a s e t h e f l y i n g t i m e , as a r e s u l t of which t h e c o s t o f t r a n s p o r t a t i o n i s decreased. These regimes correspond t o f l y i n g a l t i t u d e s o f 7000-9000 m and maximal i n d i c a t e d speeds, o r maximum p e r m i s s i b l e M number a t higher a l t i t u d e s . rre 700 752 800 K M / ~r Figure 9 2 . Height of Figure 93. Minimal Kilo P r a c t i c a l C e i l i n g and meter Expenditure of F u e l H e i g h t of Minimal Kilometer As a Function of F l i g h t Expenditure o f F u e l As a S p e e d ( a i r c r a f t w i t h two Function of F l y i n g W e i g h t eng i nes) (TU-124 a i r c r a f t ) 56. D e f i n i t i o n of Required Q u a n t i t y of F u e l I n o r d e r t o determine t h e f u e l expenditure i n f l i g h t s t o v a r i o u s d i s t a n c e s a t v a r i o u s a l t i t u d e s w i t h v a r i o u s winds, a s p e c i a l graph must be used (Figure 9 4 ) . I n c a l c u l a t i n g t h i s graph, we assume t h e mean c r u i s i n g regime of engine o p e r a t i o n , with a k i l o m e t e r expenditure of one p e r c e n t 129
- 141. I1 I I 1 g r e a t e r than t h e minimal. This i s s u f f i c i e n t t o provide a f u e l r e s e r v e i n case t h e f l i g h t i s performed a t h i g h e r o r lower speed t h a n t h e minimal expenditure speed. The climbing and descending regimes f o r t h e a i r c r a f t a r e i d e n t i c a l i n p r a c t i c a l l y a l l c a s e s . Therefore, t h e expenditures o f time and f u e l f o r t h e s e p o r t i o n s of t h e f l i g h t can be considered c o n s t a n t , dependent only on t h e f l y i n g a l t i t u d e . The d i s t a n c e t r a v e l e d by t h e a i r c r a f t during t h e climb and descent a l s o depends only on a l t i t u d e . When it i s necessary t o determine t h e f l i g h t range o r f u e l r e s e r v e p r e c i s e l y under s p e c i a l c o n d i t i o n s ( s p e c i a l f l i g h t s ) , a graph of t h i s t y p e must be c o n s t r u c t e d f o r t h e regime s e l e c t e d . Figure 94 allows us t o determine - /136 without c a l c u l a t i o n s t h e range of an a i r c r a f t f o r a given q u a n t i t y of f u e l f o r any p o i n t . For example, p o i n t 4 corresponds t o a f u e l r e s e r v e of 7750 kg and a f l i g h t range (calm wind) of 2220 km a t H = 10,000 m. The lower p o r t i o n o f t h e graph p r e s e n t s c o r r e c t i o n s c o n s i d e r i n g t h e i n f l u e n c e of wind. Distance between a i r p o r t s (S), Figure 94. Total Fuel Expenditure As a Function o f Distance, A l t i t u d e and Wind I f we must determine t h e f u e l expenditure f o r f l i g h t o f 1700 km a t 8000 m with a t a i l wind of 175 km/hr, we move from p o i n t 1, corresponding t o s = 1700 km along t h e i n c l i n e d l i n e s f o r wind t o p o i n t 2 ' corresponding t o a t a i l wind of 175 km/hr. Then we move v e r t i c a l l y upward t o t h e assigned a l t i t u d e of 8000 m ( p o i n t 3 ' ) and h e r e read t h e f u e l expenditure: 5500 kg. Adding t h e n a v i g a t i o n a l r e s e r v e , we produce t h e q u a n t i t y o f f u e l which must be placed i n t o t h e f u e l t a n k s of t h e a i r c r a f t . For a f l i g h t of t h e same range with a head wind o f 80 km/hr (point 2) a t 7000 m, 8000 kg w i l l be required (point 3 ) . 130
- 142. I n p r o c e s s i n g t h e m a t e r i a l o f f l y i n g t e s t s with r e s p e c t t o f u e l r e s e r v e s , w e u s u a l l y determine t h e f l y i n g a l t i t u d e most s u i t a b l e as concerns t o t a l f l i g h t Cost. Table 9 p r e s e n t s t h e s e a l t i t u d e s f o r one passenger a i r c r a f t . A s w e can see from t h e t a b l e , even a t 200-400 km range, t h e f l i g h t should b e performed at 4500-7000 m, s i n c e t h i s w i l l produce minimum f u e l e x p e n d i t u r e . /137 F l i g h t s o v e r t h e s e ranges a t 1200-1500 m ( t h e a l t i t u d e of t h e IL-14 a i r c r a f t ) - are i n e f f i c i e n t , s i n c e due t o t h e comparatively low t r u e f l y i n g speeds ( 5 7 0 600 km/hr, i n d i c a t e d speed 480-550 km/hr) t h e k i l o m e t e r expenditure i s r a t h e r high. TABLE 9 - . .. ~~ . . ~ * &-- __ - Distance, km Most favor able a l t i t u d e , m 57. F l i g h t a t t h e "Ceilings" With d e c r e a s i n g f l y i n g weight of t h e a i r c r a f t , t h e h e i g h t of minimal k i l o m e t e r e x p e n d i t u r e (most f a v o r a b l e a l t i t u d e ) i n c r e a s e s (Figure 9 2 ) . This dependence i s used when f l y i n g a t t h e " c e i l i n g s . " The weight o f t h e a i r c r a f t when f l y i n g t o maximum range can be reduced by 10-25 t (by 10-30% of i n i t i a l w e i g h t ) . I n o r d e r t o keep t h e a i r c r a f t f l y i n g a t a l l times a t ck min, t h e a l t i t u d e must be g r a d u a l l y i n c r e a s e d as t h e f u e l i s consumed. The d e n s i t y should b e decreased i n p r o p o r t i o n t o t h e d e c r e a s i n g f l y i n g weight. This t y p e of f l i g h t i s c a l l e d f l i g h t a t t h e c e i l i n g s . This i s t h e way i n which maximum range can b e a t t a i n e d . During t h e p r o c e s s o f such a f l i g h t , t h e a i r c r a f t w i l l remain c o n t i n u o u s l y a t 1000-1200 m below i t s c u r r e n t p r a c t i c a l c e i l i n g . W should n o t e t h a t c i v i l a i r c r a f t perform f l i g h t s a t assigned a l t i t u d e s . e However, it i s of i n t e r e s t t o t h e p i l o t t o know t h e s p e c i f i c n a t u r e of f l i g h t a t t h e c e i l i n g s , s i n c e he may f i n d t h i s f l i g h t n e c e s s a r y , f o r example, when f l y i n g along o t h e r t h a n e s t a b l i s h e d a i r l a n e s and i n o t h e r cases when maximum range must be a t t a i n e d . Let us analyze t h e performance of a f l i g h t a t t h e c e i l i n g s ( F i g u r e 95) u s i n g a TU- 1_24 a i r c r a f t . The i n i t i a l a l t i t u d e f o r t h i s t y p e o f f l i g h t w i l l b e 10,500 m. This a l t i t u d e ( p e r m i s s i b l e on t h e b a s i s o f t h e c o n d i t i o n o f t h e e f f e c t on t h e a i r c r a f t o f a 1 0 - s / s e c v e r t i c a l g u s t ) w i l l correspond t o an a c t u a l a i r c r a f t weight a t t h e i n n i n g of t h e f l i g h t o f 36 t (we w i l l c o n s i d e r t h a t t h e f l i g h t i s nc- along an e s t a b l i s h e d a i r l a n e ) . A t t h i s a l t i t u d e ( p = 0.0395 kg*sec2/m4, f u e l weight 8400 k g ) , t h e p i l o t 131
- 143. should e s t a b l i s h a h o r i z o n t a l f l i g h t speed of Vc , which i n t h i s c a s e k min * corresponds t o M = 0.7. T h i s a i r speed w i l l b e maintained throughout t h e e n t i r e f l i g h t . A f t e r approximately 2 h r 36 min, t h e p i l o t h a s expended about 5200-5400 kg f u e l , i . e . , 15.5% of t h e i n i t i a l weight. The a i r d e n s i t y should b e decreased by t h e same f a c t o r : 0.0395.84.5 = 0.0334 kg.sec2/m4 (84.5% d e n s i t y a t H = 10,500 m), meaning t h a t t h e a i r c r a f t w i l l a c t u a l l y have r i s e n t o an a l t i t u d e o f 11,800 m ( s e e s t a n d a r d atmosphere t a b l e ) , i . e . , w i l l have climbed by 1300 m, w i t h a v e r t i c a l v e l o c i t y component o f 1300/156-60 = = 0.139 m/sec. I t i s d i f f i c u l t t o m a i n t a i n t h i s speed u s i n g t h e v a r i o m e t e r , p i l o t i n g t h e a i r c r a f t by r e f e r r i n g t o t h e t h i n . n e e d l e o f t h e KUS-1200 speed i n d i c a t o r . In p r a c t i c e , i t i s e a s i e r t o maintain t h e M number s t e a d y u s i n g t h e M number i n d i c a t o r , s i n c e t h e v a l u e of a scale d i v i s i o n of t h i s instrument i s 0.01. A t 10,000-12,000 M, t h e a i r temperature, and consequently t h e speed of sound, remains p r a c t i c a l l y unchanged, so t h a t with c o n s t a n t M number, t h e t r u e speed w i l l a l s o remain c o n s t a n t . I n t h i s example as t h e weight i s changed f o r each 1000 kg t h e flying altitude is i n c r e a s e d by 200-220 m. For a i r c r a f t with h o u r l y f u e l expend i t u r e s of 4000-5000 kg, t h e increase i n a l t i t u d e w i l l be 50-70 m . In f l i g h t a t the ceilings, the r o t a t i n g speed of t h e engines and t h e M 36 min+28min = 3 h r 29 m i n number must b e kept c o n s t a n t . If t h e a i r Figure 95. P r o f i l e of F l i g h t a t t h e temperature changes, c e i l i n g s : a , A t most f a v o r a b l e a l t i t u d e s ; t h e engine r o t a t i n g b, C e i l i n g ; c , W i t h a l t i t u d e l i m i t e d speed should be changed according t o f l y i n g w e i g h t by one p e r c e n t f o r each So ( d e c r e a s i n g w i t h d e c r e a s i n g temperature and i n c r e a s i n g with i n c r e a s i n g t e m p e r a t u r e ) . Flying t e s t s have e s t a b l i s h e d t h a t f l i g h t a t t h e c e i l i n g s can i n c r e a s e t h e range by 3-8%. F l i g h t a t t h e c e i l i n g s can b e p r i m a r i l y used i n c a s e o f engine f a i l u r e , when it i s necessary t o c o n t i n u e f l y i n g t o t h e assigned d e s t i n a t i o n . I t i s h e r e t h a t t h e advantages o f t h i s t y p e o f f l y i n g a r e most notable. 132
- 144. 98. P e r m i s s i b l e F l y i n g A l t i t u d e s . Influence o f A i r c r a f t W e i g h t / 139 The o p e r a t i o n of j e t a i r c r a f t with high p r a c t i c a l c e i l i n g s (11,500 13,000 m h a s shown t h a t i t i s n o t always p o s s i b l e t o f l y a t t h e s e a l t i t u d e s , ) o r even a t t h e a l t i t u d e o f minimal kilometer expenditure (most f a v o r a b l e a l t i t u d e , Figure 92). The problem i s t h a t t h e f l y i n g a l t i t u d e of a high speed a i r c r a f t is s e l e c t e d on t h e b a s i s o f t h e c o n d i t i o n o f maintenance of a reserve f o r overloads i n case a v e r t i c a l wind gust is encountered. ChapterXI w i l l p r e s e n t an a n a l y s i s o f t h e e f f e c t o f a v e r t i c a l g u s t on an a i r c r a f t , and now l e t u s analyze t h e i n f l u e n c e o f a i r c r a f t weight on t h e s e l e c t i o n of p e r m i s s i b l e f l i g h t a l t i t u d e , u s i n g t h e combined graphs c = f(M) and Y Per C = f(M). Yhf Let u s analyze t h e f l i g h t o f a TU-124 weighing 34 t a t 10,000 m a t a speed corresponding t o M = 0.75, and e x p l a i n t h e p e r m i s s i b l e overload i n case o f a v e r t i c a l maneuver from t h e s t a n d p o i n t of s a f e t y . As we can see from t h e CY hF f i g u r e , f o r t h e s e a l t i t u d e s and M numbers t h e a i r c r a f t will have = 0.3 and c = 0.715. 'yh f Y Per Consequently, t h e r e s e r v e with r e s p e c t t o c will be AC = c y- = 0.715 Y Y Per CYhf - 0 . 3 = 0.415. I n case a v e r t i c a l gust i s encountered o r i n case of maneuver, t h i s r e s e r v e may be expended and t h e a i r c r a f t w i l l find i t s e l f a t c . This Y Per r e q u i r e s t h a t t h e overload C per 0.715 N per = Y = - 2.4. Y C h.f. 0 .. 3 Y Figure 96. Combined Graphs o f Dependences o f Coef f i c i e n t s c Yhf This w i l l be t h e value of and c on M Number of F l i g h t p e r m i s s i b l e overload. Each Y Per M number (with unchanged weight) corresponds t o a d e f i n i t e B j o i n i n g t h e p o i n t s corresponding t o t h e s e v a l u e s , we y Of CYhf' produce t h e dependence c = f(M) (Figure 9 6 ) . A s w e can s e e from Figure 96, Y f h i n t h e range of numbers M = 0.7-0.75, t h e r e s e r v e with r e s p e c t t o c i s Y maximal. With high M numbers, p a r t i c u l a r l y a t M > 0 . 8 , t h e r e s e r v e of c i s Y decreased. This r e s e r v e i s a l s o decreased with i n c r e a s i n g f l i g h t a l t i t u d e (with unchanged weight) and i n c r e a s i n g a i r c r a f t weight ( a t constant a l t i t u d e ) . 133
- 145. The r e s e r v e of c i s e q u i v a l e n t t o r e s e r v e a g a i n s t a v e r t i c a l g u s t . I n Y - /140 p a r t i c u l a r , it i s r e q u i r e d f o r a passenger a i r c r a f t t h a t i f an e f f e c t i v e i n d i c a t o r g u s t o f 10 m/sec i s encountered, t h e a i r c r a f t w i l l r e a c h only C n o t encountering s t a l l ( s e e d e f i n i t i o n i n C h a p t e r X I ) . Therefore; i n Y Per o r d e r t o avoid exceeding c and c a u s i n g t h e a i r c r a f t t o s t a l l , p e r m i s s i b l e Y Per f l y i n g a l t i t u d e s are e s t a b l i s h e d as a f u n c t i o n o f f l y i n g weight (Figure 9 7 ) . I f t h e s e l i m i t a t i o n s are n o t observed, a v e r t i c a l g u s t o f lower magnitude w i l l bring t h e aircraft t o c or stall. Y Per The d e c r e a s e i n weight r e s u l t i n g from consumption o f f u e l i n c r e a s e s t h e r e s e r v e w i t h r e s p e c t t o c and, t h e r e f o r e , t h e r e s e r v e f o r v e r t i c a l g u s t s ; Y t h e r e f o r e , t h e f l y i n g a l t i t u d e can b e i n c r e a s e d . I n t h e same way as t h e a l t i t u d e i s decreased ( f o r example t o 5000 m), t h e r e s e r v e with r e s p e c t t o c Y and gusts i n c r e a s e s . For M = 0.6 (V = aM = 32000.6 = 198 m/sec) , c - yhf = 0.24 and c = 0.92 (Figure 96). I n t h i s case, t h e overload p e r m i s s i b l e Y Per with r e s p e c t t o c w i l l b e n = 0.92/0.24 = 3.83. Y Y Per Figure 97 shows a graph o f p e r m i s s i b l e f l y i n g a l t i t u d e ( f o r t h i s example) as a f u n c t i o n of f l y i n g weight. The s t a n d a r d p r a c t i c e of assigning a l t i t u d e intervals of I f 500 1000 m a t a l t i t u d e s above 6000 m rmu -r - - - reduces t h e " r e s o l v i n g capacity" o f ----I- -- - 3- a i r c r a f t as t o p e r m i s s i b l e a l t i t u d e ; fUz0D tom -1- -I- - - 4 -- t h e r e f o r e , i t would b e more d e s i r a b l e t o u s e s e p a r a t i o n s o f 600 m a l t i t u d e . 29 ' 32 '' 354 The h e i g h t s o f f l i g h t a t t h e c e i l i n g s correspond t o p e r m i s s i b l e f l y i n g Figure 97. P e r m i s s i b l e F l y i n g altitudes. A l t ' i t u d e A s a Function o f Air c r a f t Weight The l i m i t a t i o n on f l y i n g a l t i t u d e i s n o t t h e only l i m i t a t i o n f o r a high speed passenger a i r c r a f t . The second l i - m i t a t i o n i s t h e p e r m i s s i b l e M number f o r f l i g h t s a t high a l t i t u d e s (Chapter X$ 512). AS f l y i n g o p e r a t i o n s have shown, t h e most f a v o r a b l e c r u i s i n g f l i g h t regimes as t o M number and a l t i t u d e f o r t h e f i r s t g e n e r a t i o n of a i r c r a f t d i f f e r s l i g h t l y from safe regimes as concerns t h e c o n d i t i o n s of encountering powerful ascending g u s t s . 59. E n g i n e F a i l u r e During Horizontal F1 i g h t I n c a s e of engine f a i l u r e , i f c a n a i r c r a f t cannot c o n t i n u e f l y i n g a t a l t i t u d e s o r d i n a r i l y used (8000-11,000 m). As we know, i n f l i g h t s a t a l t i t u d e s below t h e c e i l i n g a t speeds lower t h a n t h e maximal, t h e engines a r e 134
- 146. t h r o t t l e d t o some e x t e n t . This i s a l s o t r u e of c r u i s i n g f l i g h t regimes a t 8000-11,000 m . The n e c e s s i t y of reducing engine speed i n t h e s e regimes causes /141 an i n c r e a s e i n t h e s p e c i f i c f u e l e x p e n d i t u r e . I n case of f a i l u r e of one engine, t h e p i l o t w i l l b e forced t o s e t t h e remaining engines a t t h e nominal regime (which i s permitted f o r long term o p e r a t i o n ) , which should reduce t h e s p e c i f i c e x p e n d i t u r e . However, i n t h i s case t h e d r a g i s increased due t o a u t o r o t a t i o n of t h e compressor and t u r b i n e o f t h e engine which has f a i l e d ( f o r example, a t V = 600-620 km/hr a t 4000-5000 m a l t i t u d e , t h e a u t o r o t a t i o n drag i s 150-300 kg), l e a d i n g t o an i n c r e a s e i n t h e k i l o m e t e r and h o u r l y e x p e n d i t u r e s . I n c a s e o f an engine f a i l u r e , h o r i z o n t a l f l i g h t a t a l t i t u d e s above 6000-7000 m i s impossible, and t h e a i r c r a f t w i l l descend t o 5500-6000 m (two-engine a i r c r a f t , Figure 9 8 ) . For a i r c r a f t with t h r e e and f o u r engines i n c a s e of f a i l u r e o f one engine, t h e d e c r e a s e i n a l t i t u d e i s not s o g r e a t . The a l t i t u d e a t which a t h e a i r c r a f t can f l y without f u r t h e r descent w i l l be e s s e n t i a l l y t h e i n i t i a l a l t i t u d e of f l i g h t a t t h e c e i l i n g s with one nonoperating motor, i f long range f l i g h t must be Derformed and a landing " 0 500 I0 00 m-0 L, KM cannot be made immediately a f t e r t h e motor f a i l s . Figure 98. P r o f i l e of F l i g h t of A i r c r a f t . w i t h Two E n g i n e s i n Case of F a i l u r e of O n e I n case of a motor E n g i n e A f t e r 45 m i n F l y i n g Time: a , Point f a i l u r e , i t i s necessary of f a i l u r e ; b , Descending t r a j e c t o r y ( t i m e f i r s t of a l l t o achieve 37 m i n , L = 400 km); c , F l i g h t w i t h t h e l e a s t p o s s i b l e r a t e of increasing a l t i t u d e v e r t i c a l descent and secondly t o decrease t h e weight of t h e a i r c r a f t r a p i d l y (using up f u e l ) i n o r d e r t o make i t p o s s i b l e t o continue h o r i z o n t a l f l i g h t with one nonoperating engine a t high a l t i t u d e . Therefore, t h e descent should be made a t t h e nominal regime, g r a d u a l l y decreasing t h e v e r t i c a l v e l o c i t y component, which a t t h e beginning of t h e descent w i l l be V = 3-5.5 m/sec. The i n d i c a t e d speed f o r each a i r c r a f t depends on t h e Y s p e c i f i c loading on t h e wing and t h e power f a c t o r . For exam l e , f o r an 8 a i r c r a f t with two engines and a s p e c i f i c loading of 350 kg/m , an i n d i c a t e d speed of 430 km/hr was produced. The descent from 10,000-11,000 m t o t h e /142 p r a c t i c a l c e i l i n g of t h e a i r c r a f t with one nonoperating engine occurs i n 35-45 min. Over t h i s time, t h e a i r c r a f t covers 350-500 km. I f i t i s necessary t o continue t h e f l i g h t , t h e p i l o t should s h i f t t h e a i r c r a f t t o t h e regime o f f l y i n g a t t h e c e i l i n g s ; then i n 60-70 min t h e a i r c r a f t w i l l cover another 650-750 km, with an i n c r e a s e i n a l t i t u d e of 800-1000 m and an average r a t e of a l t i t u d e i n c r e a s e of 0.15-0.2 m/sec. F l i g h t 135 , .., . . I
- 147. should b e performed a t M = 0.50-0.55, corresponding a t 5500-6500 m a l t i t u d e t o a t r u e speed o f 600-650 km/hr. The mean k i l o m e t e r f u e l e x p e n d i t u r e f o r an a i r c r a f t with two engines a t t h i s s t a g e w i l l b e about 3 . 5 kg/km, which i s approximately 0 . 5 kg/km g r e a t e r t h a n a t 10,000 m with two engines o p e r a t i n g . Thus, t h e f l i g h t range with one engine n o t o p e r a t i n g i s always l e s s . A g a i n i n f l y i n g range with one engine n o t o p e r a t i n g can be produced only if t h e i n i t i a l f l y i n g weight was planned (due t o u n a v a i l a b i l i t y o f h i g h e r a l t i t u d e s o r o t h e r reasons) f o r a low a l t i t u d e , f o r example 6000-7000 m. F o r example, f o r t h e TU-104 a i r c r a f t a t t h i s a l t i t u d e a t 800 km/hr, t h e h o u r l y f u e l e x p e n d i t u r e i s 3100 kg/hr, and t h e k i l o m e t e r e x p e n d i t u r e i s 3100/800 = = 3.88 kg/km. I n case one engine f a i l s , it i s p o s s i b l e t o f l y a t 5000 m and 620 km/hr, t h e second engine o p e r a t i n g a t t h e nominal regime w i t h an h o u r l y e x p e n d i t u r e of 2200-2300 kg/hr. I n t h i s c a s e t h e k i l o m e t e r expenditure w i l l be about 3.6 kg/km, i . e . , l e s s t h a n i n f l i g h t w i t h both engines ( f o r t h i s a l t i t u d e ) and t h e p o s s i b l e f l y i n g range i n c r e a s e s . In a l l c a s e s i n case of f a i l u r e o f one engine, t h e crew should r e t u r n t o t h e a i r f i e l d o f o r i g i n i f p o s s i b l e o r land a t t h e n e a r e s t a v a i l a b l e a i r f i e 1d . 010. M i n i m u m P e r m i s s i b l e Horizontal F1 i g h t S p e e d The most f a v o r a b l e h o r i z o n t a l f l i g h t speed i s t h e d i v i s i o n between t h e two f l i g h t regimes. However, i n e s t a b l i s h i n g t h e minimum p e r m i s s i b l e speed, t h e most f a v o r a b l e speed i s not t a k e n i n t o c o n s i d e r a t i o n , b u t c a l c u l a t i o n s a r e based on c produced ?or low M numbers. The v a l u e of c which Y per’ y max’ i s used t o determine t h e s t a l l speed, i s a l s o n o t used i n t h i s c a s e . Let u s determine t h e minimum speed o f h o r i z o n t a l f l i g h t , i . e . , t h e speed corresponding t o c assuming t h a t t h e wing a r e a i s 120 m 2 , t h e a i r c r a f t Y per’ weight i s 50 t , and c = 1 . 2 (from t h e graph on F i g u r e 9 6 ) : Y Per When v a l u e s o f c > c are achieved, t h e s t a b i l i t y o f an a i r c r a f t /143 Y Y Per with a smooth wing ( f l a p s up) may be d i s r u p t e d . I n o r d e r t o prevent a l o s s of speed and a s t a l l , t h e minimum p e r m i s s i b l e h o r i z o n t a l f l i g h t speed should be .50-60 km/hr g r e a t e r t h a n t h e a b s o l u t e l y minimal speed. I n o u r example, t h i s w i l l be 320 km/hr. A f t e r 10 t of f u e l have been expended (Ginst = 40 t ) w e produce (according t o t h e l a s t formula) t h e minimal p o s s i b l e speed of 240 km/hr, s o t h a t t h e minimal p e r m i s s i b l e speed w i l l b e 300 km/hr. 136
- 148. Frequently, i n o r d e r t o avoid t h e n e c e s s i t y o f memorizing many v a l u e s o f minimal p e r m i s s i b l e speed, f l y i n g handbooks show o n l y t h e v a l u e f o r m a x i m u m weight. I n our example, t h i s w i l l b e 320 km/hr. When f l y i n g a t t h i s speed, an a i r c r a f t weighing 40-50 t o r l e s s w i l l have c < c by 30-40%. With Y Y Per normal o p e r a t i o n o f t h e a i r c r a f t , f l y i n g a t 320 km/hr is n o t p e r m i s s i b l e , s i n c e even f o r c i r c l e f l i g h t s t h e speed a t t h i s weight (S = 120 m2) should be 350-370 km/hr. T h i s l i m i t a t i o n w i l l provide f l i g h t s a f e t y . 137
- 149. Chapter V I I I . Descent / 143 91. General Statements. Forces Acting on A i r c r a f t During Descent Descent refers t o s t e a d y , s t r a i g h t l i n e f l i g h t o f t h e a i r c r a f t on a descending t r a j e c t o r y . Descent a t low power, when t h e t h r u s t a t 8000 10,000 m i s f l i g h t , w i l l b e c a l l e d g l i d i n g . Usually, passenger a i r c r a f t descend with t h e engines o p e r a t i n g a t 80-86% r e v o l u t i o n s , a t which t h e t h r u s t is g r e a t e r t h a n a t t h e i d l e ( f o r example, t h e i d l e a t H = 10,000 m might correspond t o 72-74% r e v o l u t i o n ) . The p r e s e n c e o f motor t h r u s t i n c r e a s e s t h e descent range and d e c r e a s e s t h e a n g l e of i n c l i n a t i o n o f t h e t r a j e c t o r y . Following h i s a s s i g n e d a l t i t u d e (9000-11,000 m) t h e p i l o t begins h i s descent a t 250-300 km from t h e a i r f i e l d a t a h i g h i n d i c a t e d speed (550-650 km/hr). The time f o r t h e beginning o f t h e d e s c e n t i s c a l c u l a t e d by the navigator. I n t h o s e c a s e s when t h e f l i g h t range i s n o t over 1000-1200 km and f u e l economy i s of l e s s s i g n i f i c a n c e t h a n f l y i n g time economy, t h e descent i s performed a t t h e g r e a t e s t p e r m i s s i b l e i n d i c a t e d speed o r M number. Figure 99 shows t h e f o r c e s a c t i n g on an a i r c r a f t d u r i n g t h e descent with engines o p e r a t i n g . The angle of i n c l i n a t i o n of t h e t r a j e c t o r y of t h e d e s c e n t from 9000-11,000 m w i l l be 0 = 2.5-3', t h e p i t c h a n g l e = 2-2.5'. I t must b e /144 b e noted t h a t a n g l e 0 does n o t remain c o n s t a n t , b u t r a t h e r changes as a f u n c t i o n of t h e v e r t i c a l component of t h e d e s c e n t , which i s maintained by t h e p i l o t by s e t t i n g t h e corresponding engine o p e r a t i n g regime. Operational e x p e r i e n c e has shown t h a t d u r i n g a descent from 9000 1 1 , 0 0 0 m with t r u e speeds o f 850-900 km/hr, a t f i r s t a v e r t i c a l speed o f 8-10 m/sec must be maintained, t h e n g r a d u a l l y decreased s o t h a t by 5000-6500 m , when t h e p r e s s u r e i n t h e c a b i n i s c o n s t a n t (Figure 100) t h e v e r t i c a l speed i s n o t over 5-6 m/sec. A t a l t i t u d e s o f l e s s t h a n 5000 m , t h e v e r t i c a l speed can b e i n c r e a s e d t o 10 m/sec. W w i l l consider t h a t t h e e t h r u s t of t h e engines P a c t s i n t h e d i r e c t i o n o f movement o f t h e a i r c r a f t , although as was s t a t e d above t h e r e i s a c e r t a i n angle B between f o r c e P and t h e d i r e c t i o n of movement of t h e a i r c r a f t . The l i f t i n g f o r c e Y i s perpen d i c u l a r t o t h e d i r e c t i o n of movement of t h e a i r c r a f t , and t h e drag 0 a c t s i n t h e d i r e c t i o n o p p o s i t e t o a i r c r a f t movement. For a s t a b l e d e s c e n t , it i s necessary t h a t t h e a i r c r a f t weight component G cos 0 b e balanced by f o r c e Y , and t h a t f o r c e Q be balanced by t h e weight component G s i n 0 and f o r c e P , i . e . , t h a t t h e f o l l o w i n g e q u a l i t y be f u l f i l l e d : 138
- 150. Y=G cos 0 ; Q . = P f G sin 8. rd Horizon L i n e Figure 99. Diagram o f Forces Acting on A i r c r a f t During Descent: 1 , Longitudinal a x i s o f a i r c r a f t ; 2 , Descent t r a j e c t o r y ; 6 , P i t c h a n g l e ; 0, , F l i g h t - p a t h a n g l e ; 4 , R i g g i n g a n g l e of . incidence; a, Angle o f attack The f i r s t e q u a l i t y i s t h e c o n d i t i o n f o r s t r a i g h t l i n e movement, while t h e /145 - second i s t h e c o n d i t i o n f o r c o n s t a n t v e l o c i t y on t h e t r a j e c t o r y . 92. Most Favorable Descent Regimes I n o r d e r t o analyze t h e most f a v o r a b l e descent regimes from t h e s t a n d p o i n t of f u e l economy, l e t us use t h e formula Q = P + G s i n @, which char a c t e r i z e s t h e c o n d i t i o n of c o n s t a n t v e l o c i t y . Let u s analyze a t f i r s t descent with engines t h r o t t l e d . W w i l l c o n s i d e r t h a t when t h e engines o p e r a t e a t t h e i d l e , t h e descent e occurs only under t h e i n f l u e n c e of t h e component G s i n 0, when Q = G s i n 0. Let u s assume t h a t t h e f l y i n g weight of t h e a i r c r a f t G = 33,000 kg, f o r c e Q = 3000 kg with a q u a l i t y of 11 and t h e f l i g h t speed i s 810 km/hr. Then s i n 0 = Q/G = 3000/33,000 = 0.091 and t h e a n g l e of i n c l i n a t i o n o f t h e trajectory 0 So. I n o r d e r t o m a i n t a i n t h i s angle 0, w i t h a forward speed of V = 810 km/hr ( 2 2 5 m/sec) it i s n e c e s s a r y t o m a i n t a i n a v e r t i c a l speed 139
- 151. As t h e f l y i n g a l t i t u d e is decreased, t h e t r u e speed o f t h e a i r c r a f t w i l l d e c r e a s e and, consequently, i n o r d e r t o r e t a i n t h e c o n s t a n t t r a j e c t o r y a n g l e , t h e v e r t i c a l v e l o c i t y component must be i n c r e a s e d t o 15-17 m/sec. With t h i s s o r t o f v e r t i c a l speed, t h e t o t a l d e s c e n t time t o t h e h o l d i n g a l t i t u d e w i l l b e 10-12 min, and t h e t o t a l f u e l e x p e n d i t u r e 300-400 kg, t h e descent range 120-170 k ( c o n s i d e r i n g t h e c o n s i d e r a b l e d e c r e a s e i n v e r t i c a l m speed involved a t low a l t i t u d e s ) . T h i s method of d e s c e n t i s used when t h e c a b i n a i r p r e s s u r e r e g u l a t i o n can provide normal c o n d i t i o n s f o r crew and p a s s e n g e r s . Another descent regime i s t h a t i n which t h e engine speed i s maintained o v e r t h e i d l e ( i n p r a c t i c e i n passenger a i r c r a f t t h e d e s c e n t a t i d l i n g regime i s j u s t b e i n g i n t r o d u c e d ) . When t h i s regime i s used f o r t h e d e s c e n t , t h e f u e l expended i s 400-500 kg g r e a t e r t h a n i n t h e regime d e s c r i b e d above, b u t Z a t i s f a c t o r y c o n d i t i o n s a r e maintained f o r passenger and crew. Table 1 0 shows t h e c h a r a c t e r i s t i c s of t h e descent regime with l e a s t e x p e n d i t u r e of f u e l f o r a TU-124 a i r c r a f t . In comparison with t h e descent regime a t t h e i d l e , t h e d e s c e n t t i m e is almost doubled, and t h e range i s i n c r e a s e d by 50-100 km. The v e r t i c a l v e l o c i t y components are s e l e c t e d from t h e c o n d i t i o n o f maintenance o f a constant p r e s s u r e drop i n t h e passenger c a b i n . The d u r a t i o n o f t h e l a n d i n g - /146 maneuver (approximately from t h e r e g i o n of t h e t h i r d t u r n , see Chapter IX) i s taken as 6 min (according t o s t a t i s t i c a l d a t a from scheduled f l i g h t s ) . The next method i s d e s c e n t a t t h e h i g h e s t speed, i n which p i l o t i n g i s performed a t t h e c r u i s i n g (maximum p e r m i s s i b l e ) M number o r maximum i n d i c a t e d speed. I n t h i s regime, t h e descent must be begun 270-300 km from t h e landing p o i n t . The f u e l e x p e n d i t u r e during t h e descent i s i n c r e a s e d , s i n c e t h e engines o p e r a t e a t a regime n e a r t h e c r u i s i n g regime f o r h o r i z o n t a l f l i g h t . /147 - Table 11 shows t h e c h a r a c t e r i s t i c s of t h e regime o f descent a t g r e a t e s t speed (TU-124 a i r c r a f t ) . 53. Provision o f Normal Conditions i n Cabin During H i g h A l t i t u d e F l y i n g The c a b i n o f a passenger t u r b o j e t a i r c r a f t i s s e a l e d . I n t h e c a b i n , t h e temperature (20-22°C) , r e l a t i v e humidity and a i r p r e s s u r e a r e maintained s o a s t o support normal v i t a l a c t i v i t y o f t h e crew and passengers d u r i n g high altitude flight. 140
- 152. TABLE 10 V m/sec Eng i n e Des cen t Range, k m F u e l expend Y' "ind' speed, % and i t u r e , kg km/h r landing time, min 1 440 so 31' -1 1 1 000 8.0 10 OOO 7,5 450 80 28,s 9000 '. 70 455 80 26,1 8 000 6,s 460 73 23,s 7 OCO 6,O 460 75 . 21,l 6000 5,5 465 75 1. 82 5 000 5-10 470 60 15,l 4 000 10 475 60 13,4 3 000 10 480 60 11,s 2 000 10 490 60 10,2 500 60 S.3 1000 landing 10 - - 6.0 maneuver from H=500m A excess p r e s s u r e over t h e atmospheric p r e s s u r e i s i a i n t a i n e d i n t h e n cabin (Figure 100). A t . a l t i t u d e s between zero and 12,000 m , two p r e s s u r e r e g u l a t i o n regimes a r e g e n e r a l l y used: a) The regime of c o n s t a n t a b s o l u t e p r e s s u r e , during which from ground l e v e l t o 4500-65'00 m y a p r e s s u r e of 760 mm H i s maintained; g b) A regime o f c o n s t a n t p r e s s u r e drop ( d i f f e r e n c e between p r e s s u r e i n cabin and atmosphere), i n which a t a l t i t u d e s over 4500-6500 m , t h e p r e s s u r e i n t h e cabin i s 0.5-0.65 kg/cm2 h i g h e r t h a n t h e atmospheric p r e s s u r e . With Ap = 0.5 kg/cm2 a t 8000 m, t h e cabin a l t i t u d e i s 1493 m, a t 10,000 m - - 2417 m ; with Ap = 0.6, t h e cabin a l t i t u d e a t t h e s e a l t i t u d e s w i l l be 500-600 m lower. Each of t h e s e regimes h a s a c h a r a c t e r i s t i c r a t e of change o f p r e s s u r e as a f u n c t i o n of a l t i t u d e . I n t h e c o n s t a n t a b s o l u t e p r e s s u r e regime, t h e a l t i t u d e i n t h e c a b i n remains unchanged d u r i n g a s c e n t and d e s c e n t , equal t o zero. T h e r e f o r e , a t a l t i t u d e s from z e r o t o 4500-6500 m a t any v e r t i c a l speeds p r a c t i c a l l y p o s s i b l e (climb o r d e s c e n t ) t h e r a t e of change o f a l t i t u d e i n t h e c a b i n i s equal t o z e r o . I n t h e c o n s t a n t excess and v a r i a b l e a b s o l u t e p r e s s u r e regime, t h e r a t e of change of p r e s s u r e i n t h e c a b i n i s of e s s e n t i a l s i g n i f i c a n c e f o r high a l t i t u d e passenger a i r c r a f t d u r i n g a climb and p a r t i c u l a r l y d u r i n g a d e s c e n t , d u r i n g which v e r t i c a l speeds may r e a c h 45-70 m/sec ( i n an emergency s i t u a t i o n ) . 141
- 153. A t a l t i t u d e s Over 5000-6000 m, t h e v e r t i c a l climbing speeds are u s u a l l y huch less t h a n descending speeds, 10-15 m/sec. /14 TABLE 1 1 - . _I_- .- ~ -~ H ,m V m/sec Eng i n e Descent Range, km F u e l expend Y' 'ind' speed, % and i t u r e , kg km/hr landing time, min 11 000 8,O 480 84 31 270 960 10 OGO 7.5 520 83 28,8 240 900 9 cm 7.0 555 83 26,4 210 830 8 oco 6.5 595 82 23.8 175 760 7 000 690 600 82 21,l I0 4 680 6 GOO 5,5 600 81 18,2 105 600 5 000 5-10 600 80 15,1 65 500 4 000 10 600 79 13.4 45 460 3 000 10 600 77 11,8 30 400 2000 10 600 76 10,2 20 340 1 000 10 600 75 8,O 10 280 1 and i ng - - 6,O 0 250 m neuve r a from H-500m The comfort o f most passengers v a r i e s s t r o n g l y w i t h t h e r a t e o f change i n b a r o m e t r i c p r e s s u r e . During r a p i d p r e s s u r e changes ( p a r t i c u l a r l y during descent) t h e passengers experience unpleasant and p a i n f u l s e n s a t i o n s i n t h e i r e a r s . Therefore, t h e r a t e of change of c a b i n p r e s s u r e W should be cab = 0.18-0.20 mm Hg/sec, according t o medical requirements. Maintenance 'cab o f Wcab w i t h i n t h e s e l i m i t s a t a l l a l t i t u d e s o v e r which p r e s s u r e changes w i l l a s s u r e an even r a t e o f p r e s s u r e i n c r e a s e . The r a t e o f change of cabin p r e s s u r e i s equal t o W cab = V y - A p H , where V i s t h e v e r t i c a l r a t e of descent (climb); Y A H i s t h e v e r t i c a l p r e s s u r e g r a d i e n t o f t h e atmosphere, mm Hg/m. p For H = 0, t h e g r a d i e n t Ap = 0.09, f o r H = 8000 m - - 0.038 and f o r H H = 10,000 m -- 0 . 0 3 mm Hg/m. 142
- 154. T h i s dependence can b e used t o d e t e r mine t h e v e r t i c a l r a t e o f descent o r climb f o r any h e i g h t , on t h e b a s i s of t h e c o n d i t i o n o f maintenance of normal s e n s a t i o n s of t h e passengers. For example , l e t u s determine t h e v e r t i c a l r a t e of d e s c e n t o f an a i r c r a f t f o r W = cab = 0.18 mm Hg/sec: F i g u r e 100. P r e s s u r e i n Sealed Cabin A s a F u n c For H = 0 tion o f F l y i n g Altitude ( p r e s s u r e drop Ap = = 0.5k0.02 kg/cm2) : 1 , Pressure i n cabin; 2 , Atmospheric p r e s s u r e For H = 10,000 m v 0,18 =-- - 6 0,03 mlsec Let u s now determine t h e p e r m i s s i b l e " v e r t i c a l speed" o f t h e descent i n a passenger a i r c r a f t with s e a l e d c a b i n a t H = 10,000 m, i f t h e c a b i n a l t i t u d e i s 2417 m and t h e v e r t i c a l p r e s s u r e g r a d i e n t f o r t h i s a l t i t u d e Ap = H = 0.07 mm Hg/m: V = 0.18/0.07 = 2 . 5 m/sec. However, f l y i n g t e s t s have shown Y t h a t an i n c r e a s e i n t h e v e r t i c a l v e l o c i t y component a t 10-12 km t o 8-9 m/sec and a corresponding i n c r e a s e i n t h e v e r t i c a l i r e l o c i t y o f c a b i n a l t i t u d e t o 3-3.2 m/sec has almost no i n f l u e n c e on t h e f e e l i n g s o f t h e p a s s e n g e r s . Therefore, t h e descent can be begun a t 250-300 k from t h e a i r f i e l d , i n o r d e r m t o provide normal landing maneuver. A improvement i n t h e v a l v e s o f t h e cabin a l t i t u d e system allows V n t o be Y i n c r e a s e d and t h e r e f o r e allows t h e descent t o be i n i t i a t e d 100-120 km from t h e landing p o i n t with t h e engines o p e r a t i n g a t t h e i d l e , which w i l l provide a s a v i n g s o f 350-600 kg f u e l ( t h e descent a t t h e l e a s t f u e l e x p e n d i t u r e regime, t h e i d l i n g regime, analyzed above). The p e r m i s s i b l e " v e r t i c a l v e l o c i t i e s " i n t h e s e a l e d passenger cabin o f a t u r b o j e t a i r c r a f t a r e p r e s e n t e d i n Table 1 2 . 143
- 155. TABLE 12 Flying altitude, km V i n cab i n , Y m/sec I t f o l l o w s from t h e above t h a t descent from high a l t i t u d e s should b e performed a t a v e r t i c a l r a t e o f 8-9 m/sec down t o 4500-6500 m, t h e n w i t h any v e r t i c a l r a t e r e q u i r e d , a s long a s t h e p e r m i s s i b l e i n d i c a t e d speed i s n o t exceeded, s i n c e t h e p r e s s u r e i n t h e cabin w i l l be made c o n s t a n t a t 760 mm Hg. S4. Emergency Descent W have n o t e d t h a t i n s e a l e d cabins of t u r b o j e t a i r c r a f t t h e a i r p r e s s u r e e i s 640-540 mm H w i t h a p r e s s u r e drop Ap = 0.50-0.62 kg/cm2 ( c o n s t a n t excess g p r e s s u r e r e g u l a t i o n regime). The change i n t h e primary a i r parameters ( p r e s s u r e , weight d e n s i t y , temperature and humidity) a s a f u n c t i o n of " a l t i t u d e t t i n a s e a l e d c a b i n i s of c o n s i d e r a b l e s i g n i f i c a n c e f o r l i f e support o f man i n f l i g h t . O f primary s i g n i f i c a n c e i s any change i n p a r t i a l oxygen p r e s s u r e (p ) and i t s p e r c e n t O2 content . The p a r t i a l p r e s s u r e o f a gas included i n t h e composition of any gas mixture i s t h a t p o r t i o n o f t h e t o t a l p r e s s u r e o f t h e mixture produced by t h e s h a r e o f t h e gas i n q u e s t i o n . Oxygen e n t e r s t h e human organism, as w e know, through t h e lungs, t h e a l v e o l i o f which are covered by a network o f blood v e s s e l s . The p e n e t r a t i o n ( d i f f u s i o n ) of oxygen through t h e walls o f t h e blood v e s s e l s i n t o t h e blood can occur o n l y i f t h e p a r t i a l p r e s s u r e exceeds t h e p r e s s u r e o f t h e oxygen i n t h e blood. S i m i l a r l y , removal o f carbon d i o x i d e from t h e organism r e q u i r e s t h a t t h e p a r t i a l p r e s s u r e of carbon d i o x i d e i n t h e blood b e h i g h e r t h a n i n t h e a i r i n t h e a l v e o l i o f t h e l u n g s . Thus, whereas t h e p a r t i a l oxygen p r e s s u r e a t which normal gas exchange i s a s s u r e d under s u r f a c e c o n d i t i o n s f o r t h e a i r i n h a l e d i s 159 mm Hg, t h i s f i g u r e f o r a l v e o l a r a i r i s 105-110 mm Hg. The minimum p e r m i s s i b l e p a r t i a l p r e s s u r e o f oxygen i n a l v e o l a r a i r , a t which blood s a t u r a t i o n of 80-85% w i l l occur i s 37-50 mm Hg. T h i s p r e s s u r e corresponds t o an a l t i t u d e o f 4 . 5 km, and t h i s a l t i t u d e cannot b e exceeded without s p e c i a l d e v i c e s t o i n c r e a s e t h e p a r t i a l p r e s s u r e /150 without oxygen s t a r v a t i o n . This a l t i t u d e i s t h e p h y s i o l o g i c a l l i m i t f o r 144
- 156. f l i g h t i n nonpressurized c a b i n s without oxygen d e v i c e s . Oxygen s t a r v a t i o n , which causes s o - c a l l e d a l t i t u d e s i c k n e s s , may occur b e f o r e t h i s a l t i t u d e , s i n c e it depends t o a g r e a t e x t e n t on t h e work performed by man. The symptoms of a l t i t u d e s i c k n e s s a r e headache, s l e e p i n e s s , decreased a c u i t y o f v i s i o n and h e a r i n g , d i s r u p t i o n of d i g e s t i o n and metabolism. These symptoms b e g i n t o appear q u i t e a c u t e l y beginning a t 4 . 5 km due t o t h e d e c r e a s e i n oxygen supply t o t h e c e r e b r a l c o r t e x . I t i s d i f f i c u l t f o r t h e organism t o compensate f o r a d e c r e a s e i n t h e q u a n t i t y o f oxygen i n t h e blood. T h e r e f o r e , t h e a l t i t u d e zone from 4 t o 6 k i s c a l l e d t h e zone of incomplete compensa m t i o n . Above 6 km t h e c r i t i c a l zone b e g i n s , i n which t h e d i s r u p t i o n of mental a c t i v i t y , and f u n c t i o n s of t h e organism becomes q u i t e dangerous f o r s u r v i v a l . I n t h i s zone, man l o s e s consciousness and can only b e saved by immediate descent o r supplementary oxygen supply. The c r i t i c a l zone ends a t an a l t i t u d e o f 8 km. I n c a s e of a sudden s h a r p drop o f p r e s s u r e i n t h e cabin ( l o s s of cabin p r e s s u r e ) , oxygen s t a r v a t i o n may occur. The t i m e from t h e beginning of oxygen s t a r v a t i o n t o l o s s of consciousness i s c a l l e d t h e r e s e r v e t i m e . I t must b e used t o descend t o an a l t i t u d e p r o v i d i n g s u f f i c i e n t oxygen c o n c e n t r a t i o n . I n c a s e of a l o s s of c a b i n p r e s s u r i z a t i o n o r i n o t h e r cases ( i n p a r t i c u l a r i n case of f i r e on t h e a i r c r a f t ) r e q u i r i n g a r a p i d d e s c e n t , t h e a i r c r a f t commander should d e c r e a s e t h e f l y i n g a l t i t u d e t o 5000 m ( s a f e a l t i t u d e ) i n 2.5-3 min o r should perform an emergency l a n d i n g . An emergency descent should be performed a t t h e maximum p o s s i b l e v e r t i c a l speed. This can b e achieved by i n c r e a s i n g t h e forward speed and t h e angle of i n c l i n a t i o n o f t h e t r a j e c t o r y . The g r e a t e r t h e forward speed and t h e g r e a t e r t h e a n g l e o f i n c l i n a t i o n , of t h e t r a j e c t o r y , t h e g r e a t e r w i l l b e t h e v e r t i c a l speed. However, t h e speed of an a i r c r a f t i s u s u a l l y l i m i t e d a t high a l t i t u d e s by t h e p e r m i s s i b l e M number, and a t a l t i t u d e s below 6000-7000 m by t h e p e r m i s s i b l e i n d i c a t e d speed. T h e r e f o r e , u n l i m i t e d i n c r e a s e s i n forward speed cannot be used, and t h e forward speed must be maintained w i t h i n permissible l i m i t s . The next p o s s i b i l i t y f o r i n c r e a s i n g t h e v e r t i c a l speed i s t o i n c r e a s e t h e angle o f t h e t r a j e c t o r y 0 . The l o n g i t u d i n a l f o r c e s must be equal d u r i n g descent a t c o n s t a n t speed. I t should be kept i n mind t h a t i n a t u r b o j e t a i r c r a f t d u r i n g an emergency d e s c e n t , t h e engines o p e r a t e a t t h e i d l e , c r e a t i n g i n s i g n i f i c a n t t h r u s t . W can s e e from t h e e q u a t i o n P + G s i n 0 = Q e t h a t s i n 0 = (Q - P ) / G , i . e . , t h e a n g l e of i n c l i n a t i o n of t h e descent t r a j e c t o r y (with c o n s t a n t a i r c r a f t weight) i s g r e a t e r , t h e g r e a t e r t h e drag of t h e / 151 a i r c r a f t . A i n c r e a s e i n t h e d r a g of a t u r b o j e t a i r c r a f t can be achieved by n lowering t h e l a n d i n g g e a r and s p o i l e r s . F o r example, during an emergency d e s c e n t , c o f t h e a i r c r a f t i s 0.024-0.026 f o r M = 0.84-0.86. Lowering t h e X l a n d i n g g e a r i n c r e a s e s c o f t h e a i r c r a f t by 0.015-0.020. Lowering t h e X s p o i l e r s can i n c r e a s e cX s t i l l more. I n s p i t e of t h e high f l y i n g a l t i t u d e s (9000-11,000 m), t h e impact p r e s s u r e r e a c h e s h i g h v a l u e s ( f o r example, f o r 145
- 157. v = 900 km/hr a t H = 10,000 m y q = 1300 k /m2, while a t 6000-7000 m w i t h 'ind 5 = 650-700 km/hr it i s over 2000 kg/m ) , which makes it d i f f i c u l t t o lower and lock t h e l a n d i n g - g e a r if t h e y are r a i s e d w i t h t h e flow, o r t o lower them if t h e y are r a i s e d a g a i n s t t h e flow. Therefore, i n o r d e r t o lower t h e l a n d i n g g e a r t h e i n d i c a t e d speed must b e decreased by 40-60 km/hr. The l o s s o f t i m e t o a c h i e v e t h i s i s compensated f o r by t h e c o n s i d e r a b l e i n c r e a s e i n a n g l e of i n c l i n a t i o n o f t h e descent t r a j e c t o r y and, t h e r e f o r e , t h e d e c r e a s e i n time r e q u i r e d f o r t h e emergency d e s c e n t . A t t h e same time, r a i s i n g t h e s p o i l e r i s p r a c t i c a l l y independent o f t h e impact p r e s s u r e . Emergency d e s c e n t o f an a i r c r a f t can b e d i v i d e d i n t o t h r e e main stageso! 1) t r a n s i t i o n t o descent with a t t a i n m e n t o f t h e maximum v e r t i c a l v e l o c i t y of 35-40 m/sec with l a n d i n g g e a r up o r 65-70 m/sec w i t h l a n d i n g g e a r down; 2) s t a b l e descent w i t h t h e s e v e r t i c a l v e l o c i t i e s without exceeding t h e maximum p e r m i s s i b l e M number a t h i g h a l t i t u d e s o r p e r m i s s i b l e i n d i c a t e d speed a t low a l t i t u d e s ; 3) b r i n g i n g t h e a i r c r a f t out o f t h e d e s c e n t . E n e r g e t i c t r a n s i t i o n from i n i t i a l c r u i s i n g regime t o t h e descent a t M = 0.78-0.80 i s performed with an overload n = 0.6-0.55, and t h e c o n t r o l Y should b e performed u s i n g t h e overload i n d i c a t o r of t h e AUAP d e v i c e (Chapter X I , 915). During t h i s t r a n s i t i o n , V = 35-40 m/sec can b e achieved r Y i n 12-15 sec, with t h e M number i n c r e a s i n g only t o 0.82-0.84 (with landing g e a r u p ) . With a smooth t r a n s i t i o n with an overload o f 0.9-0.8, t h e v e r t i c a l speed w i l l o n l y reach 25-28 m/sec a f t e r 35-40 s e c , and t h e M number w i l l be approximately 0.85-0.86, i . e . , t h e r a t e of i n c r e a s e i n M number exceeds t h e r a t e of i n c r e a s e i n v e r t i c a l v e l o c i t y . If t h i s mode of t r a n s i t i o n i s used, t h e a i r c r a f t may q u i c k l y reach t h e maximum p e r m i s s i b l e M number o r exceed i t . I f t h e t r a n s i t i o n i s performed w i t h n = 0.4-0.3 o r l e s s , it becomes d i f f i c u l t Y t o c o n t r o l t h e i n c r e a s e i n v e r t i c a l v e l o c i t y , and t h e a i r c r a f t may reach Vv > 35-40 m/sec and subsequently exceed t h e p e r m i s s i b l e M number. Therefore, I t h e t r a n s i t i o n t o t h e descent should be performed with n = 0.6-0.55, which Y ( a s w i l l be s e e n below) corresponds t o attainment o f a v e r t i c a l speed of 15-17 m/sec i n t h e f i r s t 5-6 s e c . The second s t a g e o f t h e descent c o n s i s t s of maintaining a v e r t i c a l speed of 35-40 m/sec with l a n d i n g g e a r up o r 65-70 m/sec with l a n d i n g g e a r down, w i t h t h e M number i n c r e a s i n g t o t h e m a x i m u m p e r m i s s i b l e v a l u e a t t h e same time. The a i r c r a f t should continue d e s c e n t a t t h i s M number down t o 6500- /152 6000 m. The p r a c t i c a l l y p e r m i s s i b l e M number i s r e t a i n e d f o r 50-60 s e c , t h e n d e c r e a s e s as t h e maximum i n d i c a t e d speed i s reached. S u b s e q u e n t l y , as descent i s continued a t c o n s t a n t i n d i c a t e d speed, t h e M number drops (by approximately 0.08-0.1 by 5000 m), and t h e v e r t i c a l speed d e c r e a s e s from 35-40 t o 20-25 m/sec. Flying t e s t s have shown t h a t it i s n o t n e c e s s a r y t o attempt t o b r i n g t h e a i r c r a f t up t o t h e p e r m i s s i b l e M number, b u t r a t h e r descent can be formed a t an M number 0.02-0.04 less t h a n t h e p e r m i s s i b l e , s i n c e i f t h e p e r m i s s i b l e 146
- 158. M number i s exceeded, subsequent d e c e l e r a t i o n o f t h e a i r c r a f t w i l l s h a r p l y d e c r e a s e t h e v e r t i c a l speed. I t cannot be excluded t h a t d u r i n g t h e p r o c e s s of a descent t h e v e l o c i t y of t h e a i r c r a f t w i l l exceed t h e p e r m i s s i b l e v a l u e ( e i t h e r p e r m i s s i b l e M number o r i n d i c a t e d s p e e d ) . I n t h e s e c a s e s , i t i s n e c e s s a r y f i r s t of a l l t o h a l t f u r t h e r i n c r e a s e i n M number, by s l i g h t l y d e c r e a s i n g t h e v e r t i c a l speed (by 5-7 m/sec), t h e n once more d e c r e a s e t h e v e r t i c a l speed by 5-7 m/sec, and when t h e M number reaches i t s p e r m i s s i b l e v a l u e , t o r e - e s t a b l i s h t h e c o n s t a n t v e r t i c a l speed o f 35-40 m/sec ( o r 65-70 m/sec with landing g e a r down). The t h i r d s t a g e i n t h e descent i s a smooth t r a n s i t i o n back t o h o r i z o n t a l f l i g h t . This must be performed when t h e safe a l t i t u d e i s reached w i t h an ~ overload n = 1 . 1 - 1 . 2 , corresponding t o a l o s s of 350-400 m a l t i t u d e . The Y t r a n s i t i o n from t h e d e s c e n t ( c r e a t i o n o f n n o t o v e r 1 . 2 ) i s achieved by Y observing t h e change i n a l t i t u d e , overload and v e r t i c a l speed, not allowing t h e maneuver t o b e performed i n l e s s t h a n 300-400 m. As we can s e e from Figure 101, t h e f l y i n g a l t i t u d e of t h e a i r c r a f t with landing g e a r up d e c r e a s e s by an average o f 1000 m each 30-32 sec, and t h e t o t a l time of descent i s 2 min 30 sec-2 min 40 s e c . With t h e l a n d i n g g e a r down, descent from 10,000 t o 5000 m occurs i n approximately 2 min. The i n d i c a t e d speed g r a d u a l l y i n c r e a s e s from t h e c r u i s i n g speed (480-500 km/hr) t o t h e maximum p e r m i s s i b l e speed (700 km/hr) r e t a i n i n g t h i s l a t t e r speed f o r 20-25 s e c from 6500 down t o 5000 m ( l a n d i n g g e a r u p ) . The M number i s i n c r e a s e d from t h e c r u i s i n g v a l u e of 0.78-0.82 t o 0.85 ( f o r t h i s c o n c r e t e c a s e ) which i t r e t a i n s f o r 50-52 s e c , t h e n d e c r e a s e s . The v e r t i c a l speed i n c r e a s e s over 17-20 s e c t o a v a l u e of 35-40 m/sec ( l a n d i n g g e a r u p ) , t h e n r e t a i n s t h i s r a t e down t o 7000-7200 m , a f t e r which (due t o t h e a t t a i n m e n t of an i n d i c a t e d speed of 700 km/hr, which must be maintained by d e c e l e r a t i n g t h e a i r c r a f t with t h e e l e v a t o r ) it i s decreased. With t h e landing g e a r , t h e v e r t i c a l speed reaches 65-70 m/sec and r e t a i n s t h i s l e v e l f o r 50-60 s e c . The overload i s decreased d u r i n g 5-6 sec of t h e i n i t i a l t r a n s i t i o n from / 153 i t s i n i t i a l v a l u e (n = 1) t o 0.6-0.4, then i n c r e a s e s t o i t s i n i t i a l v a l u e and Y f u r t h e r (depending on t h e p i l o t ' s o p e r a t i o n o f t h e s t i c k ) , remaining between 1.1 and 0 . 9 . The p i t c h a n g l e 6 v a r i e s from ' ( c r u i s i n g f l i g h t ) t o -(7-8O) w i t h 2 landing g e a r up o r -(20-2Zo) with landing g e a r down. The angle of i n c l i n a t i o n o f t h e t r a j e c t o r y i n a s t a b l e descent i s 0 = 19 + $I - a. For example, l e t u s determine a n g l e 0 i f t h e descent i s performed a t M = 0.86 w i t h V = 38 m/sec, where H = 8000 m , t h e weight o f t h e Y a i r c r a f t i s 34 t , t h e wing s e t t i n g angle $I = l o ; w e know from c a l c u l a t i o n t h a t f o r t h e s e c o n d i t i o n s c = 0.171, a = l o , q = 1885 kg/m2. Then Y 147
- 159. V = a = 308-0.86 = 265 m/sec = 955 km/hr, and a n g l e 0 = 29 = 8 " , s i n c e M I n o r d e r t o achieve a d e s c e n t with l a n d i n g g e a r down w i t h a v e r t i c a l speed of 70 m/sec and a forward speed o f 955 km/hr, a n g l e 0 = 15-16". - /154 Figure 101. Recording of Parameters During Emergency Descent of Turbojet A i r c r a f t : y - W i t h landing g e a r u p from H = 10,000 m y M i n i t = 0.78; ----- , W i t h landing gear down and preliminary d e c e l e r a t i o n from H = 11,200 m , M i n i t = 0.8 The method of p i l o t i n g an a i r c r a f t w i t h landing g e a r up d u r i n g an emergency descent c o n s i s t s of t h e following. Before beginning t h e d e s c e n t , engines a r e s e t a t t h e i d l e and, by moving t h e s t i c k r a p i d l y forward, t h e p i l o t p u t s t h e a i r c r a f t i n a d e s c e n t . During t h i s maneuver, t h e p i l o t must check t h e i n d i c a t i o n s of t h e v a r i o m e t e r , overload i n d i c a t o r and M number indicator. 148
- 160. A t t h e moment when V = 15-17 m/sec i s a t t a i n e d , p r e s s u r e on t h e s t i c k must be reduced, p u l l i n g Y t g e n t l y back s o as t o r e t a r d t h e i n c r e a s e i n v e r t i c a l speed s l i g h t l y . When V = 25-30 m/sec i s achieved, t h e s t i c k must b e Y p u l l e d back smoothly t o r e t a r d t h e i n c r e a s e i n v e r t i c a l v e l o c i t y s t i l l more, g r a d u a l l y going over t o a s t a b l e descent a t a constant speed of 35-40 m/sec. During t h e p r o c e s s o f i n c r e a s i n g V from 30 t o 35-40 m/sec, t h e M number Y i n d i c a t o r must be'watched, t o avoid exceeding t h e maximum p e r m i s s i b l e v a l u e . Subsequently, a c o n s t a n t v e r t i c a l speed of 35-40 m/sec is maintained u s i n g t h e variometer, and t h e M number i s not allowed t o exceed t h e maximum p e r m i s s i b l e u n t i l t h e maximum p e r m i s s i b l e i n d i c a t e d speed i s reached ( a t approximately 6500 m). When t h e maximum p e r m i s s i b l e i n d i c a t e d speed i s achieved, t h e descent i s continued a t t h i s speed u n t i l a safe a l t i t u d e i s reached. The load can b e r e l i e v e d u s i n g t h e e l e v a t o r trimmer i n t h e process o f s t a b l e descent when an i n d i c a t e d speed of 580-620 km/hr i s achieved, so t h a t a p r e s s u r e o f 5-10 kg i s maintained on t h e c o n t r o l s t i c k . I f t h e f o r c e i s not r e l i e v e d by t h e t r i m m e r , i t w i l l reach 50-60 kg. A s t h e i n d i c a t e d speed i n c r e a s e s from 480-490 (beginning of descent) t o 680-700 km/hr, t h e e l e v a t o r trimmer i s moved away by 2.5-3", and t h e d e f l e c t i o n of t h e trimmer reaches 4-4.5" by t h e time an i n d i c a t e d speed of 700 km/hr i s reached. A s t h e assigned a l t i t u d e i s reached, t h e a i r c r a f t i s brought out of t h e descent i n such a way t h a t i t l o s e s no more than 300-350 m a l t i t u d e i n t h e maneuver. T h i s corresponds t o an overload of n = 1.16-1.2. A t a v e r t i c a l speed of 5-6 m/sec, t h e engines can be t r a n s f e r y e d t o t h e r e q u i r e d regime. P i l o t i n g t h e a i r c r a f t during an emergency descent with landing gear down d i f f e r s only s l i g h t l y from t h e above. A f t e r t h e engines a r e s h i f t e d t o t h e i d l e , t h e landing g e a r c o n t r o l l e v e r i s moved t o t h e "downT1p o s i t i o n , and t h e a i r c r a f t i s d e c e l e r a t e d u n t i l t h e landing g e a r a r e completely down ( a t high impact p r e s s b r e s , t h i s may r e q u i r e 20-22 s e c ) , a f t e r which t h e a i r c r a f t i s put i n t o t h e descent by smoothly but f o r c e f u l l y moving t h e s t i c k forward. Due t o t h e i n c r e a s e i n drag r e s u l t i n g from lowering t h e landing g e a r , t h e overload involved i n t h e t r a n s i t i o n may be s l i g h t l y l e s s t h a n i n t h e preceding c a s e ( t h e value may reach 0.3-0.4), s i n c e t h e a c c e l e r a t i o n of t h e a i r c r a f t t o t h e /155 maximum p e r m i s s i b l e M number occurs somewhat more slowly. When a v e r t i c a l speed of 22-24 m/sec i s reached, t h e p r e s s u r e on t h e s t i c k must be decreased, and a t V = 35-40 m/sec t h e r a t e of i n c r e a s e i n Y v e r t i c a l speed must be decreased, and a v e r t i c a l speed must be gradually brought up t o 65-70 m/sec. 149 I
- 161. Chapter IX. The Landing §1. Diagrams o f L a n d i n g Approach /155 The d e s c e n t of an a i r c r a f t i n t h e r e g i o n of t h e a i r f i e l d t o t h e a l t i t u d e o f c i r c l i n g f l i g h t i s g e n e r a l l y performed u s i n g t h e o u t e r marker beacon (OMB) o r t h e e n t r a n c e c o r r i d o r beacon u s i n g t h e d i r e c t i o n f i n d e r - r a n g e f i n d e r system, t h e on-board and ground based r a d a r s . During t h e p r o c e s s of t h e d e s c e n t , t h e a i r c r a f t i s guided t o t h e a i r f i e l d s o t h a t t h e f l y i n g t i m e i n t h e r e g i o n o f t h e a i r p o r t i s 5-6 min. This allows t h e f u e l e x p e n d i t u r e t o be decreased ( t h e a i r c r a f t f l i e s f o r a s h o r t p e r i o d o f time with l a n d i n g g e a r down), and decreases t h e f l y i n g t i m e and c o s t of a i r travel. Therefore, t h e approach i s e i t h e r d i r e c t o r u s e s t h e s h o r t e s t p a t h , i n which t h e a i r c r a f t i s brought i n i n t h e r e g i o n of t h e t h i r d t u r n (Figure 102). I f t h e approach i s d i r e c t , a t 25-30 km from t h e a i r f i e l d t h e a i r c r a f t descends /156 t o 400-600 m and d e c r e a s e s i t s speed t o t h e landing g e a r down speed. When t h i s a l t i t u d e i s reached, t h e landing g e a r a r e lowered a t 12-15 km from t h e OMB ( t h i s range i s checked u s i n g t h e range f i n d e r o r by commands from t h e e a r t h ) , and t h e f l a p s a r e lowered by 15-20". The f l a p s a r e lowered completely before entering the glide. During a descending approach, t h e speed o f t h e a i r c r a f t i s decreased i n t h e r e g i o n of t h e t h i r d t u r n d u r i n g t h e p r o c e s s o f descent t o t h e c i r c l i n g a l t i t u d e , and t h e landing g e a r a r e lowered. The f l a p s are dropped by 15-20" between t h e t h i r d and f o u r t h t u r n s . The f o u r t h t u r n i s performed with t h i s f l y i n g c o n f i g u r a t i o n , u s u a l l y a t 12-16 km from t h e runway, t h e f l a p s a r e d e f l e c t e d f u l l y and t h e a i r c r a f t follows t h e course t o t h e runway a t c o n s t a n t a l t i t u d e u n t i l it enters the glide path. With forward movement speeds i n t h e d e s c e n t of 350-500 km/hr and landing speeds of 200-250 km/hr, a j e t a i r c r a f t w i l l cover c o n s i d e r a b l e d i s t a n c e d u r i n g t h e p r o c e s s o f descent and speed r e d u c t i o n . T h e r e f o r e , t h e e x t e n t o f t h e t u r n s and p a r t i c u l a r l y of t h e s t r a i g h t l i n e . s e c t o r s between t u r n s w i l l be correspondingly i n c r e a s e d . A s a r e s u l t , a f t e r t h e f o u r t h t u r n t h e a i r c r a f t w i l l be a t a c o n s i d e r a b l e d i s t a n c e from t h e runway (12-16 km). The i n c l i n a t i o n of t h e g l i d e p a t h i s g e n e r a l l y 2" 40 min-4', as a r e s u l t of which t h e t r a j e c t o r y of t h e a i r c r a f t ( a f t e r i t e n t e r s t h e g l i d e p a t h ) i s smooth. The g l i d e p a t h i s e n t e r e d a t 7.5-8.5 km from t h e runway. The OMB i s g e n e r a l l y l o c a t e d 4 km from t h e runway, t h e boundary marker beacon (BMB) a t 1000 m from t h e runway. The a l t i t u d e over t h e OMB should be 200 m a over t h e BMB - - 60 m . For t h e s e f l y i n g a l t i t u d e s , t h e v e r t i c a l v e l o c i t y component o f t h e a i r c r a f t should b e 3-3.5 m/sec. 150
- 162. Figure 102. Diagram o f Approach t o Landing ( a ) and G1 i d e ( b ) 52. F l i g h t A f t e r E n t r y i n t o G l i d e Path. Selection o f G l i d i n g Speed According t o t h e norms of ICAO, t h e g l i d i n g speed d u r i n g t h e d e s c e n t on t h e g l i d e p a t h should be 30% g r e a t e r t h a n t h e s t a l l speed f o r t h e l a n d i n g c o n f i g u r a t i o n of t h e a i r c r a f t , i . e . , V = 1 . 3 Vs (where V is the s t a l l gl 0 speed with f l a p s i n t h e g l i d i n g p o s i t i o n ) . A s w can s e e from Figure 16, f o r a maximum f l a p angle of 38", flow e s e p a r a t i o n on t h e wing begins a t c = 1 . 8 5 . For a mean landing weight o f 35 t Y and a wing a r e a of 110 m2, t h i s corresponds t o a s t a l l speed = 1 4 . 4 ~ 3 5 , 0 0 0 / 1 1 0 * 1 . 8 5= 190 km/hr. Vs 0 Then t h e g l i d i n g speed i s Before t h e beginning o f l e v e l i n g o f f , g l i d i n g i s performed a t c o n s t a n t speed, i n t h i s c a s e 250 km/hr. With t h e s t a n d a r d a n g l e o f i n c l i n a t i o n of t h e - /157 151
- 163. 2 O 40 min, t h e v e r t i c a l r a t e o f descent V = V s i n 0 = 69.5.0.0466 = Y gl = 3.24 m/sec ( h e r e s i n 2" 40 min = 0.0466, V = 250 km/hr = 69.5 m/sec) gl . Establishment of a c o n s t a n t g l i d i n g speed a f t e r complete lowering of t h e f l a p s f a c i l i t a t e s p i l o t i n g , s i n c e i t does not r e q u i r e a change i n t h e o p e r a t i n g regime o f t h e engines o r a d e c r e a s e i n t h e speed from t h e moment of e n t r y i n t o t h e g l i d e p a t h u n t i l t h e a i r c r a f t p a s s e s o v e r t h e OMB, BMB and 500-m mark, s o t h a t t h e p i l o t i s less d i s t r a c t e d from t h e i n s t r u m e n t s . I f t h e a i r c r a f t e n t e r s t h e g l i d e p a t h a t 400 m a l t i t u d e and 8 km range from t h e runway (Figure 102), f l i g h t t o t h e OMB i n calm a i r ( t h e a i r c r a f t c r o s s e s t h e beacon a t 200 m a l t i t u d e ) r e q u i r e s t = 2 0 0 : 3.24 = 61 s e c . The d i f f e r e n c e i n a l t i t u d e s of f l i g h t over t h e OMB and BMB i s 140 m, and t h e time of d e s c e n t f o r t h i s d i f f e r e n c e t = 140: 3.24 = 43 s e c . The f l y i n g speed of 250 km/hr corresponds t o an angle of a t t a c k ci = 5" (Figure 1 6 ) . Let u s now determine, assuming I$ = l o , t h e p o s i t i o n of t h e a i r c r a f t concerning t h e landing g l i d e p a t h , i . e . , t h e p i t c h a n g l e : i = -2" 40 min + 5' - l o = 1' 20 min. ? Thus, t h e a i r c r a f t a x i s h a s a p o s i t i v e angle w i t h n e g a t i v e descent angle 0. I f , due t o high mechanization of t h e wing ( t h r e e s l i t f l a p s and secondary c o n t r o l s u r f a c e s ) t h e g l i d i n g speed i s decreased (240-220 km/hr), t h e p i t c h angle i n c r e a s e s . Therefore, t h e f l y i n g time from t h e moment t h e a i r c r a f t e n t e r s t h e g l i d e p a t h u n t i l it f l i e s over t h e OMB and BMB a t lower speeds i s i n c r e a s e d , and t h e p i l o t ' s r e s e r v e time i n c r e a s e s . As a r e s u l t , t h e f o u r t h t u r n can be formed c l o s e r t o t h e end o f t h e runway. As t h e g l i d i n g speed i s decreased a t t h e same t r a j e c t o r y a n g l e , t h e v e r t i c a l speed i s decreased, and with t h e i n c r e a s i n g angle of a t t a c k t h e p i t c h angle i n c r e a s e s , worsening t h e view from t h e p i l o t ' s c a b i n . Let u s analyze t h e engine o p e r a t i o n regime r e q u i r e d f o r g l i d i n g f l i g h t of t h e a i r c r a f t . With t h e landing g e a r down, f l a p s down and a i r b r a k e extended, t h e aero dynamic q u a l i t y o f t h e a i r c r a f t K = 5-6 and t h e g l i d i n g angle 0 = 9-10" ( t a n 0 = 1 / K = 1 / 5 . 5 = 0.183, 0 10") , b u t i n t h i s c a s e t h e engine t h r u s t should be n e a r zero. A c t u a l l y , t h e a i r c r a f t descends along t h e g l i d e p a t h with engines o p e r a t i n g a t angle 0 = 2" 40 min. This a n g l e corresponds t o q u a l i t y 152
- 164. For c = 1.06 ( a n g l e of a t t a c k So, Figure 1 6 ) , we produce c = 0.19 Y X (without a i r b r a k e ) . From t h i s v a l u e o f c we must s u b t r a c t t h e v a l u e of X c o e f f i c i e n t cR o f r e q u i r e d engine t h r u s t , i n o r d e r t o m a i n t a i n K = 21.5 where c = 1.06: Y /158 from which This v a l u e of t h r u s t c o e f f i c i e n t corresponds t o a t h r u s t consumption P = c qS = 0.141*300*110 = 4650 kg, i . e . , 2325. kg t h r u s t f o r each engine R (with a two-engine a i r c r a f t ) . This t h r u s t i s s e v e r a l times g r e a t e r t h a n t h e i d l i n g t h r u s t (300-500 k g ) . I f t h e a i r b r a k e i s extended, t h e t h r u s t must be i n c r e a s e d ( t o m a i n t a i n t h e g l i d i n g angle unchanged, s i n c e c i s i n c r e a s e d t o X 0.226) : c --*- 1 % -0.226=@~0493-0,226.= 10,1771; R-21.5 P=O ,177 -300-110=5840 kg As we can see, t h e t h r u s t i s i n c r e a s e d by almost 25%. I f a f t e r t h e a i r b r a k e i s extended t h e engine o p e r a t i n g regime i s l e f t unchanged, t h e angle o f i n c l i n a t i o n o f t h e d e s c e n t t r a j e c t o r y w i l l be i n c r e a s e d t o 4" 30 min and t h e a i r c r a f t may come down b e f o r e t h e beginning of t h e runway. In o r d e r t o determine t h e new angle of d e s c e n t , we must f i r s t f i n d t h e q u a l i t y of t h e a i r c r a f t from t h e e q u a t i o n c = (1.06/K) - 0 . 2 2 6 = R = -0.141 : and t h e n f i n d t h e d e s c e n t angle 153
- 165. .. The e f f e c t i v e n e s s o f t h e a i r b r a k e i s q u i t e h i g h , s i n c e as c is increased X t h e l i f t of t h e wing remains p r a c t i c a l l y t h e same. T h e r e f o r e , as t h e landing g e a r a r e lowered t h e a i r c r a f t h a s no tendency t o wing s t a l l , b u t only shows a change i n t h e i n c l i n a t i o n o f t h e t r a j e c t o r y . 53. Stages i n t h e Landing The f l i g h t of t h e a i r c r a f t (descent) from 15 m (according t o t h e ICAO norms) c o n s i s t o f t h e f o l l o w i n g main s t a g e s : I) g l i d i n g from 15 m a l t i t u d e a t . V = 1 . 3 Vs u n t i l l e v e l i n g o f f i s begun; 2 ) l e v e l i n g o f f u n t i l t h e moment of gl 0 l a n d i n g and 3) t h e l a n d i n g run. F i g u r e 103 shows a diagram of t h e d e f i n i t i o n of r e q u i r e d runway l e n g t h and a p r o f i l e o f a i r c r a f t f l i g h t from 15 m downward. The t o t a l l e n g t h o f t h e h o r i z o n t a l p r o j e c t i o n o f t h e t r a j e c t o r y of t h e a i r b o r n e s e c t o r and t h e landing run i s c a l l e d t h e l a n d i n g d i s t a n c e . The I 59 1 r e q u i r e d runway l e n g t h i s determined f o r s t a n d a r d and d e s i g n m e t e o r o l o g i c a l c o n d i t i o n s with t h e maximum landing weight of an a i r c r a f t and d r y runway. Gliding - - s t r a i g h t l i n e f l i g h t of the a i r c r a f t on a descending t r a j e c t o r y at constant velocity. Gliding i s usually 1 performed a t 250 220 km/hr i n d i c a t e d , anding d i s t a n c e with an angle o f a t t a c k requ i red runway l e n g t h = c1 = 5-5.5" and landing d i s t x 1.43 c = 0.95-1.1. Y Figure 103. P r o f i l e of Descent o f A i r c r a f t Prelanding g l i d i n g from H = 15 m i s not gliding i n its p u r e form, s i n c e t h e engines c r e a t e approximately 1800-2000 kg t h r u s t each. This t h r u s t i s r e q u i r e d t o r e t a i n t h e a i r c r a f t speed and r e t a i n good motor r e a d i n e s s i n c a s e i t becomes necessary t o c i r c l e once more o r f o r a d d i t i o n a l t h r u s t t o c o r r e c t t h e landing p a t t e r n . If t h e a i r b r a k e i s extended, t h e engine o p e r a t i n g regime must b e i n c r e a s e d by 5-6%, i n c r e a s i n g t h e s a f e t y i n case a second c i r c l e i s r e q u i r e d . 154
- 166. When g l i d i n g from 15 m t o t h e h e i g h t where t h e l e v e l i n g i s begun, t h e a i r c r a f t t r a v e l s 150-200 m. The v e r t i c a l speed i n t h e s e c t o r i s 3-5 m/sec. With t h e a i r b r a k e extended, t h e q u a l i t y i s decreased t o 4.5-5, and t h e angle o f i n c l i n a t i o n o f t h e t r a j e c t o r y can b e i n c r e a s e d when n e c e s s a r y t o 9-11'. I n t h i s c a s e , t h e l e n g t h of t h e g l i d i n g s e c t o r from 15 m down d e c r e a s e s t o 100-150 m. The v e r t i c a l speed can b e i n c r e a s e d t o 8-9 m/sec. Extending t h e f u s e l a g e a i r b r a k e c r e a t e s p i t c h i n g moment and f a c i l i t a t e s b a l a n c i n g t h e a i r c r a f t , s i n c e t h e f l a p s t e n d t o c r e a t e a p i t c h i n g moment i n t h e o p p o s i t e d i r e c t i o n . The a i r c r a f t must b e balanced s o t h a t s l i g h t p u l l i n g loads are f e l t on t h e c o n t r o l s t i c k a t a l l times. Leveling o f f . During l e v e l i n g o f f , which begins a t an a l t i t u d e o f 8-10 m, t h e movement o f t h e a i r c r a f t i s curved and t h e speed d e c r e a s e s . By p u l l i n g t h e s t i c k back, t h e p i l o t i n c r e a s e s t h e l i f t , which becomes g r e a t e r t h a n t h e weight component and t h e r e f o r e t h e t r a j e c t o r y i s curved. I n /160 p r a c t i c e , d u r i n g l e v e l i n g o f f t h e a i r c r a f t does n o t f l y h o r i z o n t a l l y , b u t r a t h e r a t a s l i g h t a n g l e t o t h e ground (0.5-0.8'). I n performing t h i s oper a t i o n , t h e p i l o t d e c r e a s e s t h e angle of i n c l i n a t i o n of t h e t r a j e c t o r y and t h e v e r t i c a l r a t e of d e s c e n t t o t h e p o i n t t h a t a l T s o f t l f touchdown i s provided. T h i s d e c r e a s e i n speed r e s u l t s from two f a c t o r s : f i r s t o f a l l , t h e angle of a t t a c k i s i n c r e a s e d , i n c r e a s i n g d r a g Q ( f o r s t a b l e l a n d i n g a n g l e s of a t t a c k 9-10", t h e drag i n c r e a s e s by 25-30%) and, secondly, b e f o r e t h e beginning of l e v e l i n g o f f t h e p i l o t t h r o t t l e s back t h e engines and t h e r e b y d e c r e a s e s t h e i r t h r u s t . Leveling o f f i s completed a t an a l t i t u d e of 1-0.5 m , s o t h a t t h e touchdown occurs on t h e main wheels a t l a n d i n g speed with s l i g h t p a r a c h u t i n g . I n o r d e r t o r e t a i n l i f t d u r i n g t h e process of l e v e l i n g o f f , t h e angle of a t t a c k must b e i n c r e a s e d t o t h e landing a n g l e of a t t a c k . During p a r a c h u t i n g , t h e l i f t i s less t h a n t h e weight of t h e a i r c r a f t by 25-30%. When an a i r c r a f t l a n d s w i t h a i r b r a k e r e t r a c t e d , t h e l e n g t h of t h e l e v e l i n g s e c t o r i s i n c r e a s e d , while i f t h e a i r b r a k e i s extended, due t o t h e b e t t e r braking t h e l e n g t h of t h e landing s e c t o r i s decreased by 50-100 m. During t h e l e v e l i n g s e c t o r , t h e speed of t h e a i r c r a f t i s decreased from The l e n g t h o f t h e l e v e l i n g o p e r a t i o n depends on t h e d i f f e r e n c e g l to "w between t h e s e speeds. With a d i f f e r e n c e of 30 km/hr, i t amounts t o 350-400 m . The g r e a t e r t h e landing angle of a t t a c k (8-lo'), t h e longer t h e b r a k i n g of t h e a i r c r a f t and t h e g r e a t e r t h e l e n g t h o f t h e l e v e l i n g s e c t o r . As a r e s u l t , t h e landing d i s t a n c e i n c r e a s e s , i n s p i t e of t h e f a c t t h a t t h e l e n g t h of t h e run i s decreased s l i g h t l y by landing a t h i g h angle of a t t a c k . As f l y i n g t e s t s have shown, i t i s more s u i t a b l e t o "brake" on t h e ground ( d u r i n g t h e run) t h a n i n t h e a i r , when t h e aerodynamic q u a l i t y is r a t h e r h i g h (6-7). This l e a d s us t o t h e following conclusion: i n o r d e r t o avoid l e n g t h e n i n g t h e h o l d i n g s e c t o r u n n e c e s s a r i l y , l a n d i n g should b e performed with V = V - 20 km/hr. 1dg gl The run. The speed a t which t h e a i r c r a f t t o u c h e s t h e ground i s c a l l e d t h e landing speed. I t can b e determined from t h e f o l l o w i n g formula: 155
- 167. B i where c i s t h e l i f t i n g c o e f f i c i e n t a t t h e moment t h e a i r c r a f t touches t h e Y 1dg ground. The run begins from t h e moment t h e a i r c r a f t wheels touch t h e l a n d i n g s t r i p . The movement o f t h e a i r c r a f t d u r i n g t h i s s e c t o r i s s t r a i g h t and slow. A t f i r s t t h e run i s accomplished on t h e main wheels, t h e n by moving t h e s t i c k forward t h e p i l o t lowers t h e nose wheels. Most of t h e r u n occurs on t h r e e p o i n t s with a low a n g l e of a t t a c k . On t h e p o l a r curve, t h i s corresponds t o t h e s t a n d i n g angle o f a t t a c k 1-3" (Figure 6 5 ) . Immediately a f t e r grounding, when t h e a i r c r a f t i s r o l l i n g on two p o i n t s , /161 t h e s p o i l e r s are d e f l e c t e d and wheel b r a k i n g b e g i n s . Whereas a t t h e moment of landing c o e f f i c i e n t c = 1 . 4 - 1 . 7 , a f t e r t h e s p o i l e r s a r e extended, due t o t h e Y flow s e p a r a t i o n on t h e wing, it i s decreased t o 0.08-0.12. The l i f t d e c r e a s e s s h a r p l y and complete loading o f t h e l a n d i n g g e a r wheels o c c u r s . I t should b e noted t h a t a t t h e moment t h e s p o i l e r s are extended a n e g a t i v e p i t c h moment i s a c t i n g on t h e a i r c r a f t and t h e p i l o t must push t h e s t i c k forward s l i g h t l y t o h o l d t h e a i r c r a f t a t t h e l a n d i n g a n g l e of a t t a c k . Extending t h e s p o i l e r s d e c r e a s e s t h e speed o f t h e a i r c r a f t by 40-50 km/hr, which causes t h e a i r c r a f t t o t e n d t o drop i t s nose r a p i d l y , t o which t h e p i l o t must r e a c t by p u l l i n g t h e s t i c k back t o allow t h e nose wheel t o drop smoothly. Figure 104 shows an a i r c r a f t d u r i n g t h e l a n d i n g r u n w i t h s p o i l e r s extended and b r a k i n g p a r a c h u t e o u t . During t h e p r o c e s s of t h e r u n , t h e a i r c r a f t i s d e c e l e r a t e d by t h e drag o f t h e a i r c r a f t and t h e f r i c t i o n o f t h e wheels on t h e ground. The s l i g h t engine t h r u s t d e c r e a s e s t h i s d e c e l e r a t i n g force. The diagram of f o r c e s a c t i n g on t h e a i r c r a f t d u r i n g t h e landing run i s t h e same as during t h e t a k e o f f run (Figure 8-6). The only d i f f e r e n c e i s t h a t d u r i n g t h e landing run t h e t h r u s t P i s c o n s i d e r a b l y less than t h e sum o f d e c e l e r a t i n g f o r c e s F and Q. f During t h e l a n d i n g r u n , t h e summary b r a k i n g f o r c e i s d e f i n e d as t h e d i f f e r e n c e between d e c e l e r a t i n g f o r c e s and t h e t h r u s t of t h e engines: Rbr = Q + Ff - P . A s a r e s u l t of t h e e f f e c t s o f t h e b r a k i n g f o r c e , a n e g a t i v e a c c e l e r a t i o n ( i . e . , d e c e l e r a t i o n ) appears 156
- 168. I t f o l l o w s from t h e formula t h a t t h e g r e a t e r t h e sum Q + F the greater /162 f' w i l l be jx. The f r i c t i o n f o r c e F depends on t h e c o e f f i c i e n t o f f r i c t i o n o f f wheels w i t h t h e s u r f a c e o f t h e e a r t h f and t h e f o r c e o f normal p r e s s u r e o f t h e a i r c r a f t on t h e e a r t h N . I t h a s been determined by t e s t i n g t h a t f o r a i r - c r a f t with d i s k brakes and s p o i l e r s running on d r y c o n c r e t e f = 0.2-0.3 . . ( c o n s i d e r i n g braking) Force N depends on t h e l a n d i n g weight o f t h e a i r c r a f t and t h e l i f t : N = G - Y. The f o r c e of f r i c t i o n can b e expressed by t h e following formula: then A t t h e beginning o f t h e landing r u n , when t h e l i f t i s only s l i g h t l y less than t h e weight, t h e f o r c e of f r i c t i o n w i l l be low (low difference G - Y ) . For example, a t 200-220 km/hr, t h e f o r c e of f r i c t i o n i s 4000-5000 kg ( f o r an a i r c r a f t w i t h a landing weight of 35-40 t ) . A t t h e end of t h e r u n , when t h e l i f t i s s l i g h t , t h e f o r c e of f r i c t i o n i n c r e a s e s . Figure 104. A i r c r a f t During Run w i t h S p o i l e r s Extended and Braking Parachute O u t ( a ) and Diagram of O p e n i n g of S p o i l e r ( b ) : 1 , Inner s p o i l e r s ; 2 , Outer s p o i l e r s ; 3 , S p o i l e r ; 4 , Front f l a p ; 5 , Door; 6 , Flap The f o r c e o f a i r c r a f t d r a g a t t h e beginning of t h e landing r u n (when t h e speed i s n e a r t h e l a n d i n g speed, and angle of a t t a c k a = 9-10"> i s r a t h e r g r e a t (Q = 5000-6000 kg f o r t h e same w e i g h t s ) . T h i s i s f a c i l i t a t e d by t h e lowered f l a p s and t h e a i r b r a k e . 157
- 169. I 1 The l a n d i n g d i s t a n c e (Figure 103) i s t h e summary l e n g t h of t h e s e c t o r s of g l i d i n g , l e v e l i n g and l a n d i n g ~ r u n . For a i r c r a f t w i t h two-engines i n t h e t a i l p o r t i o n o f t h e f u s e l a g e , t h e l a n d i n g d i s t a n c e i s 1000-1200 m, and t h e r e q u i r e d runway l e n g t h (according t o ICAO) i s 1400-1700 m. S4. L e n g t h of Post-landing Run and Methods of Shortening It The k i n e t i c energy of t h e a i r c r a f t a t t h e moment of touchdown i s d i s s i p a t e d and absorbed by t h e work o f t h e b r a k i n g f o r c e s : t h e aerodynamic drag, .the f r i c t i o n of t h e wheels on t h e s u r f a c e o f t h e runway, t h e d r a g o f b r a k i n g p a r a c h u t e s , t h r u s t r e v e r s a l , e t c . The dependences o f t h e s e b r a k i n g f o r c e s on t h e speed o f t h e run a r e shown on F i g u r e 105. The u n i t o f b r a k i n g f o r c e (drag f o r c e ) used i s t h e aerodynamic d r a g of t h e a i r c r a f t a t touchdown. /163 - For example, f o r t h e TU-124, a t t h e moment o f touchdown w i t h f l a p s a t 30" and a i r b r a k e extended a t 225 km/hr, cx = 0.18, t h e aerodynamic drag Q = 4600 kg, t h e p a r a c h u t e d r a g i s approximately 5500 kg and t h e b r a k i n g f o r c e o f t h e wheels i s about 2500 kg. A s t h e speed o f t h e landing r u n d e c r e a s e s , t h e d r a g f o r c e of t h e p a r a c h u t e and t h e aerodynamic d r a g of t h e a i r c r a f t drop s h a r p l y , while t h e f o r c e o f f r i c t i o n o f t h e wheels i n c r e a s e s . Thrust r e v e r s a l o f t h e engines i s p r a c t i c a l l y independent o f t h e r a t e o f movement o f t h e a i r c r a f t . j .- m t:p= 45 The l e n g t h o f t h e l a n d i n g run o f an a i r c r a f t can b e determined u s i n g t h e f ormu 1a Y m I 3 I al m 0 36 72 ro8 r08 144 f80 YKMJ hr Figure 105. Nature of Change i n Braking Forces During Post-landing Run where j i s t h e mean a c c e l e r a t i o n o f xmlr of Aircraft (calculated) : braking (deceleration) o f t h e a i r c r a f t 1 , Braking f o r c e ; during t h e landing r u n , m/sec2. 2 , Aerodynamic drag o a i r c r a f t ; 3 , Drag o f As we can s e e from t h e formula, with braking parachute; f i x e d l a n d i n g speed t h e l e n g t h of t h e run 4 , Thrust reversa can b e decreased by i n c r e a s i n g t h e mean braking acceleration. During t h e f i r s t h a l f o f t h e l a n d i n g run [Figure 105) t h e d e c e l e r a t i o n of ~I a i r c r a f t movement i s achieved under t h e i n f l u e n c e of a l l t h e s e d e c e l e r a t i n g f o r c e s , a f t e r which t h e main r o l e i s played by t h e b r a k i n g f o r c e of t h e wheels and t h r u s t r e v e r s a l ( i f t h e r e i s a t h r u s t r e v e r s e r on t h e a i r c r a f t ) . A t t h e p r e s e n t t i m e , braking wheels are equipped w i t h s p e c i a l automatic b r a k i n g d e v i c e s , t h e p r i n c i p l e of o p e r a t i o n of which i s based on t h e usage o f t h e f o r c e o f i n e r t i a of a flywheel r o t a t i n g i n p a r a l l e l w i t h t h e wheel. 158
- 170. If t h e wheel r o t a t e s without s l i p p i n g , t h e flywheel i n t h e automatic d e v i c e r o t a t e s i n synchronism with t h e l a n d i n g wheel. I f t h e wheel begins t o s l i d e , t h e flywheel i n t r o d u c e s an a c c e l e r a t i o n and, working through a s p e c i a l d e v i c e , i n t e r r u p t s t h e supply o f p r e s s u r e t o t h e b r a k e , as a r e s u l t of which t h e b r a k i n g f o r c e on t h e wheel i s decreased. A f t e r t h e r o t a t i n g speed of t h e wheel i s i n c r e a s e d once more and synchronism i s e s t a b l i s h e d between r o t a t i o n o f wheel and flywheel, t h e p r e s s u r e t o t h e brakes i s j n c r e a s e d t o t h e r e q u i r e d l e v e l and t h e wheel i s once more braked. I n o p e r a t i o n , t h i s c y c l e i s u s u a l l y r e p e a t e d q u i t e r a p i d l y and a c t u a l l y t h e p r e s s u r e i n t h e brakes never d e c r e a s e s completely. Thus, t h i s d e v i c e p r o v i d e s optimal b r a k i n g , pumping a t t h e boundary of s l i d i n g 1 . When t h i s d e v i c e i s t u r n e d on, t h e p i l o t immediately provides f u l l p r e s s u r e i n t h e b r a k e s ( d e p r e s s e s b r a k e p e d a l s completely). Smoothly d e p r e s s i n g t h e b r a k e s , a s i s recommended f o r nonautomatic b r a k i n g , i n t h i s c a s e o n l y i n c r e a s e s t h e l e n g t h o f t h e l a n d i n g run, s i n c e t h e maximum b r a k i n g regime will n o t be used. The usage of automatic brakes has allowed t h e l e n g t h o f t h e l a n d i n g run /164 t o be decreased by an a d d i t i o n a l 20-25%.. The s e r v i c e l i f e o f t h e pneumatic system h a s a l s o been i n c r e a s e d . The mean a c c e l e r a t i o n of automatic b r a k i n g i s 1 . 7 - 1 . 8 m/sec2 ( d i s k b r a k e s ) . In a i r c r a f t with s p o i l e r s opened a t t h e moment of touchdown, t h e e f f e c t i v e n e s s of t h e brakes i s even g r e a t e r and = 2.25-2.5 m/sec2. For example, i n an a i r c r a f t with s p o i l e r s Jxmlr ( j m = 2.25 m/sec2) with a l a n d i n g speed o f 216 km/hr (60 m/sec), Llr = 800 m. For t h e TU-104 a i r c r a f t (no s p o i l e r s ) with V = 240 km/hr (66.7 m/sec) w i t h 142 an average b r a k i n g a c c e l e r a t i o n of 1 . 3 m/sec2 (drum brake) t h e l a n d i n g run l e n g t h i s 1700 m. For t h e TU-104 w i t h d i s k brakes (with an average a c c e l e r a t i o n o f 1.55 m/sec2) t h e l a n d i n g run l e n g t h i s 1430 m . Even g r e a t e r b r a k i n g a c c e l e r a t i o n (drag) can b e produced by r e l e a s i n g a b r a k i n g p a r a c h u t e . For example, i f t h e p a r a c h u t e i s open a t 225-215 km/hr, t h e drag i s i n c r e a s e d by 4600-4900 kg (TU-124 a i r c r a f t ) . Figure 106a shows a diagram of t h e usage o f a braking p a r a c h u t e . A f t e r touchdown, a b u t t o n i s p r e s s e d dropping t h e p a r a c h u t e from i t s c o n t a i n e r through h a t c h 1. A f t e r t h i s , t h e p i l o t chute p u l l s t h e braking chute o u t , c r e a t i n g r e s i s t a n c e t o t h e movement of t h e a i r c r a f t . The p a r a c h u t e i s connected t o t h e a i r c r a f t by c a b l e 3 through c a t c h 2 . A t t h e end of t h e r u n , t h e braking p a r a c h u t e s a r e disconnected. Braking p a r a c h u t e s 4 a r e s t r i p t y p e , and t h e s t r e n g t h o f t h e l i n e s and canopy i s s u f f i c i e n t f o r run /165 - speeds of 260-230 km/hr. In a s t r i p type parachute, the a i r p a r t i a l l y passes through t h e canopy and t h e r e f o r e f o r t h i s t y p e o f chute Acx = 0.25-0.55 ( f o r an o r d i n a r y p a r a c h u t e A c = 1 . 2 - 1 . 3 ) . For example, one f o r e i g n b r a k i n g X p a r a c h u t e with a canopy diameter of 9 . 7 6 m and A c = 0.55 c r e a t e s a b r a k i n g X A. V. C h e s t n o v , Letnaya Ekspzuatatsiya S h o Z e t a [ F l y i n g Operation of Air c r a f t ] , Voyenizdat. P r e s s , 1962. 159 J
- 171. f o r c e of 17.25 t a t 296 km/hr ( m i l i t a r y t r a n s p o r t a i r c r a f t ) . The l e n g t h of t h e l a n d i n g r u n on an i c e covered runway can be reduced by 30-40% by u s i n g a b r a k i n g p a r a c h u t e . Under t h e s e c o n d i t i o n s , i t s e f f e c t i v e n e s s i s p a r t i c u l a r l y n o t i c e a b l e . However, t h e less t h e speed, t h e less t h e e f f e c t i v e n e s s of t h e p a r a c h u t e . For example, t h e b r a k i n g p a r a c h u t e s on a TU-104 d e c r e a s e t h e run l e n g t h by 25-30% (wet o r i c e covered s t r i p ) . Thus, under s t a n d a r d c o n d i t i o n s f o r a l a n d i n g weight o f 58 t , t h e r u n l e n g t h i s 1730 m, w h i l e t h e usage o f t h e p a r a c h u t e reduces t h i s f i g u r e t o 1250-1350 m. The b r a k i n g f o r c e i s 10-14 t . Figure 06. Usage of t h e Braking Parachute ( a ) and Diagram of I n s t a l l a t i o n and Operation of Thrust Reverse s ( b ) o n Two External A i r c r a f t Engines: 1 , V i e w from r e a r , reversed flow i n c l i n e d by 20" from v e r t i c a ; 2 , Apertures f o r gas o u t l e t d i r e c t e d a t a n g l e o p p o s i t e t o f l i g h t ; 3 , A t moment of touchdown, r e v e r s e doors c l o s e d , during braking t h e y d i r e c t g a s i n d i r e c t i o n o p p o s i t e movement. During t a x i i n g , doors s e t i n i n t e r m e d i a t e p o s i t i o n . One d e f e c t of t h i s method of reducing t h e r u n l e n g t h i s t h e f a c t t h a t with a s i d e wind s t r o n g e r t h a n 6-8 m/sec a t an a n g l e of o v e r 45" t o t h e runway, t h e p a r a c h u t e w i l l be d e f l e c t e d from t h e a x i s of t h e a i r c r a f t and w i l l tend t o t u r n t h e a i r c r a f t i n t o t h e wind. AS t h e s i d e wind i n c r e a s e s i n speed, t h e p r o b a b i l i t y o f r o t a t i o n a l s o i n c r e a s e s . However, even i n t h i s c a s e i t i s recommended t h a t t h e b r a k i n g chute b e used d u r i n g t h e f i r s t h a l f o f t h e landing r u n , b e i n g extended immediately a f t e r touchdown ( i n p r a c t i c e with a d e l a y o f 5-7 s e c ) . Another d e f e c t i s t h e f a c t t h a t t h e d i s c a r d e d p a r a c h u t e must b e r a p i d l y removed from t h e runway, t r a n s p o r t e d , checked and packed. The s e r v i c e l i f e of a b r a k i n g p a r a c h u t e (with an average a c c e l e r a t i o n o f 1.55 m/sec2) i s 40-50 l a n d i n g s . C a l c u l a t i o n o f t h e d r a g produced by t h e p a r a c h u t e i s performed u s i n g t h e formula 160
- 172. I-l-11 1 1 .11 IIIIII.-1111111IIIII I 1 1 . 11 11111 1 I I 11111111111111=~111~111111111.1111111111ll I I I I I 11111 111111111 I II I I where Acx i s t h e drag of t h e parachute r e l a t e d t o t h e wing area o f t h e aircraft; S i s t h e wing area; q i s t h e impact p r e s s u r e . , For example, f o r t h e b r a k i n g parachute o f a TU-124 with Scan = 40 m2, = 0.54 (S = 105.35 m2) : - C x par 0.54s 0.54.40 Acx pa -9.205. S 105.35 E j e c t i o n of t h e braking parachute a t lower speed i s l e s s e f f e c t i v e . A t t h e end of t h e landing run, due t o t h e d e c r e a s e i n speed and t h e angle of a t t a c k , which w i l l b e equal t o t h e parked angle, f o r c e Q i s p r a c t i c a l l y equal t o zero. I t i s considered t h a t i n t h e process of t h e e n t i r e landing run, an average braking f o r c e a c t s on t h e a i r c r a f t , c r e a t i n g a average n e g a t i v e acceleration j xav = . . 1 95- br . G The g r e a t e s t v a l u e o f n e g a t i v e a c c e l e r a t i o n i s achieved a f t e r t h e braking /166 parachute i s extended and amounts t o 4.4-4.2 m/sec2. I n c r e a s i n g t h e landing speed by 5% (from 210 t o 220 km/hr) i n c r e a s e s t h e l e n g t h o f t h e landing run by approximately 1 0 % . Therefore, a d e c r e a s e i n landing speed i s t h e most e f f e c t i v e means of decreasing t h e run l e n g t h . A n increase i n j by t h e usage o f s p o i l e r s and a braking parachute o r t h r u s t xav r e v e r s a l o f t h e engines can s i g n i f i c a n t l y s h o r t e n t h e landing run. When t h e engine t h r u s t i s r e v e r s e d , t h e r e a c t i o n j e t i s d i r e c t e d forward and e x i t s upward and downward a t an angle t o t h e h o r i z o n t a l . For example, i n t h e two outboard engines of t h e English "Comet" t u r b o j e t a i r c r a f t , t h e r e a c t i o n j e t e x i t s upward and downward a t 45" t o t h e h o r i z o n t a l . The r e v e r s e r ( t h e d e v i c e which d e f l e c t s theflow) i s r o t a t e d a t 20" t o t h e v e r t i c a l , i n o r d e r t o d i r e c t t h e j e t away from t h e f u s e l a g e and landing gear (Figure 106 b ) . 161
- 173. With s u f f i c i e n t l y r a p i d movement of t h e a i r c r a f t , t h e j e t w i l l be d e f l e c t e d rearward and w i l l not e n t e r t h e a i r i n t a k e s , while a t very low speeds o r a t r e s t of t h e a i r c r a f t t h e stream w i l l move f a r forward. The o p e r a t i n g time o f t h e r e v e r s e r i n a landing i s g e n e r a l l y n o t over 15 s e c . The doors of t h e r e v e r s i n g device a r e operated pneumatically. The r e v e r s e r i s put i n o p e r a t i o n by'moving a s p e c i a l l e v e r forward. The t h r o t t l e s c o n t r o l l i n g t h e outboard engines must f i r s t be p u t i n t h e i d l e p o s i t i o n and l i f t e d . The e f f e c t i v e n e s s of t h r u s t r e v e r s a l i s decreased with decreasing a i r c r a f t speed. However, when necessary t h r u s t r e v e r s a l can be used u n t i l t h e a i r c r a f t comes t o a complete s t o p . Thrust r e v e r s a l should be a p p l i e d t h e moment t h e a i r c r a f t touches t h e runway. The maximum r e v e r s e t h r u s t t h e o r e t i c a l l y i s 70% of t h e forward t h r u s t , b u t i n p r a c t i c e only about 50% i s r e a l i z e d . The usage of t h r u s t r e v e r s a l makes it p o s s i b l e t o decrease t h e landing run l e n g t h by 20-25%. Also, i n t h e "Comet-4B" a i r c r a f t t h e s i z e o f t h e f l a p s i s i n c r e a s e d and t h e i r angle of d e f l e c t i o n i s i n c r e a s e d t o 8 0 ° , g r e a t l y reducing t h e landing speed. I n a i r c r a f t with engines l o c a t e d i n t h e wing and n e a r t h e f u s e l a g e , t h e usage of t h r u s t r e v e r s a l i s d i f f i c u l t due t o t h e thermal e f f e c t s of t h e reversed j e t s on t h e f u s e l a g e . I t i s e a s i e s t t o u s e t h r u s t r e v e r s e r s on engines mounted on p i l o n s , as on t h e Boeing 707, DC-8, e t c . I f t h e r e a r e f o u r engines mounted on t h e t a i l of t h e f u s e l a g e , t h e r e v e r s e r s a r e i n s t a l l e d only i n t h e outboard engines. A s was noted, i n a d d i t i o n t o braking p a r a c h u t e s , motor switch off during t h e landing run, and t h r u s t r e v e r s a l , s p o i l e r s and a i r b r a k e s a r e a l s o used. The s p o i l e r s a r e p l a t e s which can be extended o r d e f l e c t e d , mounted on t h e upper s u r f a c e of t h e wings. One, two o r t h r e e s p o i l e r s can be used on each / 167 wing. The s p o i l e r s a r e extended a f t e r t h e a i r c r a f t wheels touch t h e runway. By s e p a r a t i n g t h e flow from t h e upper wing s u r f a c e , t h e s p o i l e r s decrease t h e l i f t i n g f o r c e s h a r p l y and c r e a t e considerable a d d i t i o n a l drag. The graph on Figure 107 shows t h a t with t h e s p o i l e r s closed t h e aero dynamic q u a l i t y of t h e a i r c r a f t decreases from 6 t o 4.4 upon t r a n s i t i o n from t h e landing p o s i t i o n ( a = l o " ) t o t h e landing run p o s i t i o n (a = 1 " ) ; opening of t h e s p o i l e r s during t h e run decreases t h e aerodynamic q u a l i t y by a n a d d i t i o n a l f a c t o r of 4 (from 6 t o 1 . 5 ) . Extending t h e s p o i l e r s has approximately t h e same i n f l u e n c e on t h e dependence c = f ( a ) . Y 162
- 174. S5. Length o f Landing Run A s a Function o f Various Operational Factors The l e n g t h o f t h e landing run i s e s s e n t i a l l y i n f l u e n c e d by t h e a i r c r a f t weight, c o n d i t i o n of t h e runway, d i r e c t i o n and speed o f wind, a i r temperature, e t c . The l e n g t h o f t h e l a n d i n g r u n a l s o depends on t h e actions of t h e p i l o t i n control of the aircraft . The weight of t h e a i r c r a f t i n f l u e n c e s t h e l e n g t h of t h e landing run p r i m a r i l y through t h e l a n d i n g speed. A s t h e weight of t h e a i r c r a f t i s i n c r e a s e d , t h e square o f t h e Figure 107. C o e f f i c i e n t c.. As l a n d i n g speed i s a l s o i n c r e a s e d and Y consequently t h e l e n g t h o f t h e landing a Function of A n g l e o f Attack run i s i n c r e a s e d t o t h e same e x t e n t . and Polar Curve o f A i r c r a f t For example, w i t h landing weight o f During Landing ( f l a p s down, 30,000 kg, t h e l e n g t h o f t h e landing A i rbrake and Spoi 1 e r s extended) r u n under s t a n d a r d c o n d i t i o n s is 930 m , whereas with a landing weight of 32,000 kg, i . e . , i n c r e a s e d by 1.065 times, t h e run l e n g t h i s i n c r e a s e d by t h e same number o f times and w i l l be 930-1.065 = 990 m . Thus, i f t h e a i r c r a f t weight i s i n c r e a s e d by 6.5%, t h e run l e n g t h w i l l be i n c r e a s e d by t h e same f a c t o r . The temperature of t h e surrounding a i r i n f l u e n c e s t h e run l e n g t h p r i m a r i l y through t h e d e n s i t y . As t h e t e m p e r a t u r e i s i n c r e a s e d with unchanged p r e s s u r e , t h e d e n s i t y o f t h e a i r i s decreased.2 I f t h e temperature i s i n c r e a s e d by a c e r t a i n f a c t o r , t h e v a l u e of v Idg i s i n c r e a s e d by t h e same /168 f a c t o r . Thus, i f t h e t e m p e r a t u r e i s i n c r e a s e d by 5% o v e r t h e s t a n d a r d temperature, V2 w i l l b e i n c r e a s e d by approximately t h e same p e r c e n t . 1dg A decrease i n d e n s i t y leads t o a decrease i n t h e drag Q during t h e run. Also, d u r i n g t h e r u n t h e engines c r e a t e a s l i g h t t h r u s t and a s t h e temperature i s i n c r e a s e d , t h i s t h r u s t i s decreased, which h e l p s t o reduce t h e run l e n g t h . I f w e i g n o r e t h e i n f l u e n c e o f temperature on d r a g and t h r u s t , w e can approx i m a t e l y c o n s i d e r t h a t an i n c r e a s e i n t e m p e r a t u r e o f 5% ( f o r example from 15 t o 3OoC (from 288 t o 303OK) w i l l r e s u l t i n an i n c r e a s e i n run l e n g t h o f approximately 5%. I t should be noted t h a t under c o n d i t i o n s o t h e r t h a n t h e s t a n d a r d c o n d i t i o n s , t h e l a n d i n g speed i n d i c a t e d by t h e instrument ( t h e broad 163
- 175. arrow) w i l l b e t h e same as a t s t a n d a r d c o n d i t i o n s , s i n c e w i t h a change i n a i r d e n s i t y t h e v e l o c i t y i n d i c a t o r d e c r e a s e s t h e i n d i c a t e d speed due t o methodic e r r o r . The f i n e n e e d l e o f t h e i n d i c a t o r shows t h e t r u e speed i n t h i s c a s e . The i n f l u e n c e o f head winds and t a i l winds on t h e l e n g t h of t h e landing r u n i s t h e same a s t h i s i n f l u e n c e on t h e l e n g t h of t h e t a k e o f f r u n . The b r a k i n g e f f e c t i s always g r e a t e s t with t h e maximal speeds of u t i l i z a t i o n of s p o i l e r s and p a r a c h u t e . Therefore, a d e l a y i n u s i n g t h e s p o i l e r s of 1.5-2 s e c i n c r e a s e s t h e run l e n g t h by 100-150 m, w h i l e e j e c t i o n of t h e p a r a c h u t e a t 180-140 km/hr decreases i t s b r a k i n g e f f e c t by 35-50%. The wheel b r a k e s should be a p p l i e d immediately a f t e r t h e s p o i l e r s are extended, i . e . , a t 250-220 km/hr. 56. S p e c i f i c Features of Landing R u n s on Dry, Ice o r Snow Covered Runways A t t h e p r e s e n t t i m e we s t i l l do not have s u f f i c i e n t d a t a on methods of determining t h e e f f e c t o f b r a k i n g on wet o r snow covered runways. I n s p i t e of t h e v a r i e t y of means of b r a k i n g , t h e p r i n c i p a l means remains t h e d i s k wheel b r a k e s . I t has been e s t a b l i s h e d t h a t when l a n d i n g on a d r y c o n c r e t e runway, about 70% of t h e energy o f movement of t h e a i r c r a f t i s absorbed by t h e b r a k e s , and 30% by aerodynamic d r a g of t h e a i r c r a f t (usage of f l a p s and a i r b r a k e s ) . When landing on a wet runway, o n l y about 50% of t h e k i n e t i c energy i s absorbed by t h e b r a k e s , o r i f t h e t i r e s a r e worn -- even l e s s . The wheel b r a k e s have an important r o l e t o p l a y d u r i n g a landing run i f f l i g h t i s t e r m i n a t e d a t speeds less t h a n t h e s e p a r a t i o n speed by 15-20%, i n which t h e s p o i l e r s and landing p a r a c h u t e are less e f f e c t i v e . The p r e s s u r e i n t h e t i r e s has a g r e a t i n f l u e n c e on t h e e f f e c t i v e n e s s of b r a k i n g : t h e l e s s t h e p r e s s u r e , t h e g r e a t e r t h e c o n t a c t a r e a and t h e more r e l i z b l y t h e brakes operate . A t t h e p r e s e n t time, t h e runway l e n g t h r e q u i r e d f o r a i r c r a f t o p e r a t i o n i s determined e i t h e r on t h e b a s i s of t h e c o n d i t i o n of t h e p r o v i s i o n of s a f e t y of i n t e r r u p t e d o r extended t a k e o f f ( s e e Figure 7 1 ) , o r from t h e c o n d i t i o n s of t h e /169 c o n d i t i o n s of t h e landing c h a r a c t e r i s t i c s of t h e a i r c r a f t ( s e e Figure 1 0 3 ) . These c h a r a c t e r i s t i c s a r e g e n e r a l l y c a l c u l a t e d f o r a d r y runway s u r f a c e . However, a t most a i r p o r t s due t o c l i m a t i c c o n d i t i o n s o v e r one t h i r d of t h e y e a r o r perhaps even. more t h e runway s u r f a c e s are m o i s t , snow covered o r f r o z e n . S t a t i s t i c s show t h a t on t h e world s c a l e , one l a n d i n g of twelve i s performed on a wet runway’. ’[Technical Information Department, S tAa tier T rcai n snpt ofrit c ResearchONTIs tGOSNIIf GAr I _____I_ .__ Zarubezhnyy Aviatransport , (Foreign --- S e i -- ) No. 7, In itute o C i v i l A v i a t i o n ] , 1965. 164
- 176. The experience o f o p e r a t i o n of domestic t u r b o j e t and turboprop a i r c r a f t , as w e l l as d a t a from f o r e i g n p r a c t i c e i n d i c a t e t h a t t h e p r e s e n c e of s l u s h (wet snow, water) on runway s u r f a c e s h a s t h e following n e g a t i v e i n f l u e n c e on t h e design o f a i r c r a f t and landing o p e r a t i o n s : 1) a d d i t i o n a l d r a g appears as t h e s l u s h s t r i k e s t h e a i r c r a f t , p a r t i c u l a r l y i n t h e c a s e o f a i r c r a f t with heavy l a n d i n g g e a r ; 2 ) t h e danger arises t h a t l i q u i d may e n t e r t h e engine a i r i n t a k e ; 3) c o n t r o l l a b i l i t y of t h e a i r c r a f t i s reduced; and 4) t h e 1andiv.g run l e n g t h i s s i g n i f i c a n t l y i n c r e a s e d . Pavements f o r runways i n c l u d e c o n c r e t e , a s p h a l t , etc. On a moist o r wet runway, t h e wheel r o l l d r a g i n c r e a s e s , b u t t h e coupling f o r c e between wheel and runway d u r i n g b r a k i n g d e c r e a s e s ( i n comparison t o d r y pavement). This r e s u l t s i n an i n c r e a s e i n t h e l a n d i n g run l e n g t h of t h e a i r c r a f t . This i n c r e a s e i s so g r e a t t h a t i n many c a s e s t h e length of t h e runway may be i n s u f f i c i e n t t o complete t h e l a n d i n g r u n . A moist r u n w a y ’ i s understood t o b e t h e c o n d i t i o n i n which t h e pavement i s moistened w i t h water ( a f t e r r a i n ) , while a w e t runway means t h a t t h e r e i s a l a y e r o f water on t h e runway 2 - 3 mm t h i c k . T e s t s performed i n t h e U A S showed t h a t w i t h a c e r t a i n t h i c k n e s s o f water on t h e runway and with c e r t a i n parameters of t h e t i r e s , t h e c r i t i c a l speed can be reached a t which t h e t i r e s a r e completely s e p a r a t e d from t h e s u r f a c e of t h e road by hydrodynamic f o r c e s c r e a t e d by t h e l i q u i d between t h e t i r e and t h e s u r f a c e o f t h e runway (Figure 108 a ) . This speed i s c a l l e d t h e s k i d d i n g speed o r speed o f hydro planing. The e f f e c t o f aquaplaning s i g n i f i c a n t l y i n c r e a s e s t h e landing run l e n g t h on a w e t runway. I n v e s t i g a t i o n s have shown t h a t aquaplaning a r i s e s a t speeds averaging o v e r 160 km/hr. When t h i s o c c u r s , t h e c o n t a c t between wheels and pavement i s l o s t and a f l i m o f water appears between them. This r e s u l t s i n a l o s s of e f f e c t i v e n e s s of b r a k e s and makes i t d i f f i c u l t t o m a i n t a i n t h e d i r e c t i o n of t h e landing r u n . The phenomenon of aquaplaning i s explained by t h e f a c t t h a t a hydrodynamic f o r c e a c t i n g on t h e s u r f a c e of t h e pavement a r i s e s as t h e a i r c r a f t moves over t h e runway. When i t s v e r t i c a l component / 170 becomes equal t o o r g r e a t e r t h a n t h e weight of t h e a i r c r a f t , c o n t a c t o f t h e wheels with t h e runway i s l o s t . The graph on Figure 108 b was produced t h e o r e t i c a l l y and confirmed e x p e r i m e n t a l l y . Using t h i s graph (with known p r e s s u r e i n t h e t i r e s ) , we can e s t a b l i s h t h e l i m i t i n g speed, above which usage of t h e wheel b r a k e s during a landing on w e t s u r f a c e i s u s e l e s s , o r even dangerous i n c a s e of a s t r o n g s i d e wind, so t h a t o n l y aerodynamic brakes should b e used. A s soon as t h e speed drops below t h e aquaplaning speed, t h e wheel brakes can b e u s e d . A t t h e moment t h e b r a k e s a r e a p p l i e d , a f r i c t i o n coupling f o r c e appears between a i r c r a f t wheels and runway. I n some c a s e s b r a k i n g may r e s u l t i n wheel lockup (100% s k i d ) i . e . , a s i t u a t i o n i n which t h e movement o f t h e a i r c r a f t with n o n r o t a t i n g wheels ( s k i d ) causes t h e f o r c e of f r i c t i o n t o d e c r e a s e , i n c r e a s i n g t h e l e n g t h of t h e landing run. The i n t e r a c t i o n of t h e b r a k i n g wheel w i t h t h e runway s u r f a c e i s g e n e r a l l y e v a l u a t e d by t h e coupling 165 I
- 177. c o e f f i c i e n t o r c o e f f i c i e n t of f r i c t i o n , equal t o t h e r a t i o o f t h e t a n g e n t i a l b r a k i n g f o r c e t o t h e normal l o a d i n g on t h e wheel. .q D i r e c t i o n of movement 320 [I Wheelf f e c t i v e ine brakes I n f -0 a, a, C r i t i c a l speed f o r a i r c r a f t i n question / Whee 1 brakes effective 6M G i ven a m 0 1 I 1 2 I 3 1 4 Mdl 5 6 7 2 3 pressure i n t i r e s , k d c m D 5 - - Figure 108. Formation of Hydrodynamic L i f t i n g Force A s Wheels Roll Along W t Runway ( a ) and Aquaplaning S p e e d e A s a Function of P r e s s u r e and T i r e s ( b ) : 1-2, Hydro dynamic l i f t and d r a g O a c l e a n , d r y s u r f a c e , t h e coupling c o e f f i c i e n t o f t h e t i r e s i s q u i t e n high and, i f t h e r u b b e r does n o t melt o r burn due t o t h e h i g h temperature a t t h e p o i n t o f c o n t a c t with t h e runway s u r f a c e , t h i s c o e f f i c i e n t may v a r y between 0 . 7 and 0.8 depending on t h e t r e a d p r o f i l e (dry c o n c r e t e ) . As t h e speed of t h e a i r c r a f t i s i n c r e a s e d , t h e c o e f f i c i e n t d e c r e a s e s by 2-3 t i m e s . T h e r e f o r e , t h e mean v a l u e of coupling c o e f f i c i e n t f o r a d r y c o n c r e t e runway i s 0.15-0.25; f o r a moist runway t h i s f i g u r e i s 0.1-0.21 and f o r a w e t /171 runway, about 0 . 2 l 1 . For an a s p h a l t runway (according t o t h e d a t a of t h e S t a t e Planning I n s t i t u t e and t h e S c i e n t i f i c Research I n s t i t u t e f o r C i v i l Aviation) 2 , t h e coupling c o e f f i c i e n t f o r a l l of t h e pavement c o n d i t i o n s analyzed above is somewhat h i g h e r : from 0.33 t o 0.23; f o r snow covered cement and a s p h a l t pavements i t i s 0.3-0.25. Therefore t h e c a l c u l a t e d l a n d i n g run l e n g t h o f an a i r c r a f t on t h e s e pavements i s 15-20% l e s s . When landing on an i c e covered runway, t h e e f f e c t i v e n e s s o f t h e b r a k e s i s s h a r p l y decreased, by an average of 25-30% i n comparison w i t h a l a n d i n g on a d r y , c o n c r e t e runway. Due t o t h i s , i t i s g e n e r a l l y recommended t h a t a b r a k i n g p a r a c h u t e be used, t h a t one o r two engines be s h u t down, e t c . I t i s known t h a t r a p i d dropping o f t h e f r o n t wheel o n t o t h e runway a f t e r touchdown c r e a t e s t h e b e s t c o n d i t i o n s f o r b r a k i n g . However, as a r u l e , t h i s method i s most s u i t a b l e f o r a d r y runway pavement, s i n c e on w e t pavement, f r o z e n o r ~~ ~ ~ ~- ~.. ~ .. .. . . .~ ~ - .- .. ~. ._ _ - .--__._ - .. . . . - , . Chestnov, A. V . , Letnaya EkspZuatatsiya S m o Z e t a [Flying Operation of t h e A i r c r a f t ] , Voyenizdat. P r e s s , 1962. GPI and NIIGA. 166
- 178. snow covered pavement, t h e b r a k i n g e f f e c t of t h e wheels i s reduced. Under t h e s e c o n d i t i o n s , we must keep i n mind t h e f a c t t h a t running with t h e f r o n t wheel up c r e a t e s a d d i t i o n a l aerodynamic d r a g , which i s t h e main b r a k i n g e f f e c t d u r i n g t h i s p o r t i o n of t h e run. I t i s p a r t i c u l a r l y d i f f i c u l t t o perform a landing ( o r t a k e o f f ) on a runway covered with w e t snow. Experience h a s shown t h a t a l a y e r of wet snow 25 mm t h i c k i n c r e a s e s t h e t a k e o f f run l e n g t h by 60%, and t h a t a l a y e r 75" t h i c k makes a t a k e o f f impossible. The maximum p e r m i s s i b l e depth of a l a y e r of l i q u i d o r water h a s been e x p e r i m e n t a l l y e s t a b l i s h e d a s 12.7 mm. This depth w i l l r e q u i r e an i n c r e a s e i n t a k e o f f r u n l e n g t h of 20-30%. 57. Landing w i t h S i d e Wind The s i d e wind means t h e wind v e l o c i t y component d i r e c t e d p e r p e n d i c u l a r t o t h e runway. A t t h e p r e s e n t t i m e , l a n d i n g s w i t h s i d e winds a r e made by t h e method of course l e a d , i . e . , d r i f t o f t h e a i r c r a f t i s compensated f o r by c r e a t i n g a c e r t a i n l e a d angle E i n t h e course of t h e a i r c r a f t a f t e r e x i t from t h e f o u r t h t u r n (Figure 109). I f t h e c o u r s e of t h e a i r c r a f t i s changed by angle E , determined from t h e r e l a t i o n s h i p t a n E = W/Vg, t h e ground speed V w i l l be g d i r e c t e d along t h e runway. Thus, i f V = 250 km/hr, while W = 10 m/sec, t h e g l e a d angle E = 8 " . However, d u r i n g l e v e l i n g o f f and holding t h e speed o f t h e a i r c r a f t w i l l d e c r e a s e and t h e i n i t i a l l e a d angle w i l l become t o o low; t h e a i r c r a f t w i l l begin t o d r i f t o f f of t h e runway. T h e r e f o r e , a t t h e moment of touchdown, t h e l e a d angle must be i n c r e a s e d by approximately 1-1.5". The crew should have good v i s i b i l i t y from t h e c o c k p i t a t l e a d angles of /172 - 10-15", which a r e r e q u i r e d with a s i d e wind above 15 m/sec. When d r i f t i s compensated f o r by a v a r i a t i o n i n landing c o u r s e , t h e l o n g i t u d i n a l a x i s of t h e a i r c r a f t does n o t correspond t o t h e d i r e c t i o n of movement, and f l i g h t i s performed without s l i p p i n g o r bank. A t t h e moment of touchdown, t h e c o n t r o l wheel should be t u r n e d i n t h e d i r e c t i o n o f t h e d r i f t , r o t a t i n g t h e a i r c r a f t along t h e runway by l e a d a n g l e E . I f when t h i s maneuver i s performed t h e l o n g i t u d i n a l a x i s s t i l l makes a c e r t a i n angle with t h e d i r e c t i o n of t h e runway, s i d e f o r c e Z w i l l a c t a g a i n s t t h e wheels, t e n d i n g t o r o t a t e t h e a i r c r a f t along t h e runway, s i n c e it i s a p p l i e d behind t h e c e n t e r o f g r a v i t y of t h e a i r c r a f t ; however, t h i s e f f e c t i s n o t dangerous f o r t h e landing organs. A s w e can s e e from Figure 110, t h e nose wheel p r e s e n t s no moment, s i n c e i t i s o r i e n t e d f r e e l y along t h e d i r e c t i o n of movement while t h e s i d e f r i c t i o n f o r c e on t h e main wheels c r e a t e s s t a b i l i z i n g moment, t e n d i n g t o r o t a t e t h e a i r c r a f t t o l i n e up with t h e runway. With a s i d e wind, g l i d i n g should be performed a t h i g h e r speeds (10 km/hr h i g h e r ) , and t h e landing speed should be 5-10 km/hr h i g h e r t h a n t h e normal recommended speed. The p i l o t must c o n t r o l h i s a i r c r a f t on t h e approach t o t h e l a n d i n g s t r i p c a r e f u l l y , being s u r e n o t t o l e v e l o f f high o r touchdown h a r d . The f r o n t l e g must be lowered 167
- 179. immediately a f t e r l a n d i n g i n o r d e r t o avoid zooming and t o m a i n t a i n t h e d i r e c t i o n from t h e l a n d i n g run u s i n g t h e c o n t r o l wheel. The c o n t r o l s t i c k should b e pushed forward t o t h e s t o p i n o r d e r t o b r i n g t h e nose wheel down t o t h e pavement. When l a n d i n g w i t h a s i d e wind, t h e l e n g t h o f t h e landing run i s i n c r e a s e d - /173 by 10-15%. The maximum p e r m i s s i b l e v a l u e o f s i d e wind component (90" t o runway a x i s ) i s 12-15 m/sec. I n case o f a l a r g e r o t a t i o n a l moment, t h e down wind engine may b e switched o f f , t h e b r a k i n g p a r a c h u t e can b e r e l e a s e d , t h r u s t r e v e r s a l and b r a k i n g can b e used.. 58. T h e "Minimum" Weather f o r Landings and Takeoffs The t a k e o f f - l a n d i n g c h a r a c t e r i s t i c s of an a i r c r a f t determine t h e l i m i t i n g m e t e o r o l o g i c a l c o n d i t i o n s ("minimum weather") f o r which o p e r a t i o n of t h e a i r c r a f t ( t a k e o f f and landing) can be p e r m i t t e d . The c o n d i t i o n s i n c l u d e : a) minimum c e i l i n g ; b) minimum v i s i b i l i t y a t runway l e v e l ; c) minimum l a t e r a l component o f wind speed Wz. The minimum c e i l i n g determines t h e f l y i n g a l t i t u d e t o which t h e a i r c r a f t should come down o u t o f t h e clouds and c l e a r v i s i b i l i t y of r e f e r e n c e p o i n t s on t h e ground o r runway l i g h t s should be e s t a b l i s h e d . A t t h i s a l t i t u d e , t h e crew can guide t h e a i r c r a f t down on t h e landing l i n e v i s u a l l y . For t u r b o j e t a i r c r a f t landing a t a i r f i e l d s equipped w i t h IL S, w i t h a g l i d e p a t h angle o f 2" 40 min, t h e minimum cloud cover c e i l i n g i s 60-100 m. The minimum v i s i b i l i t y i s considered t h e range a t which t h e crew o f an a i r c r a f t begins t o s e e r e f e r e n c e p o i n t s on t h e ground and t h e beginning of t h e runway during t h e daytime, o r landing l i g h t s and t h e i l l u m i n a t e d runway s u r f a c e a t n i g h t . This range should be s u f f i c i e n t t o make it p o s s i b l e t o c o r r e c t i n a c c u r a c i e s i n a i r c r a f t course and s e p a r a t i o n from runway a x i s . The accuracy of guidance o f t h e a i r c r a f t r e l a t i v e t o t h e c e n t e r l i n e o f t h e runway depends on t h e accuracy of o u t p u t of c o u r s e d a t a by on-board and ground b a s e apparatus and t h e p r e c i s i o n of p i l o t i n g according t o t h e i n d i c a t o r on board t h e a i r c r a f t . Experiments performed by GOSNII G A 1 have e s t a b l i s h e d t h a t f o r passenger j e t a i r c r a f t t h e mean v a l u e of t o t a l d e v i a t i o n from t h e runway a x i s i s 560 m. Coming down out of t h e clouds with t h i s amount of e r r o r , t h e p i l o t must c o r r e c t t h e e r r o r with two s e q u e n t i a l t u r n s (Figure 1 1 1 ) . During t h i s t i m e , t h e a i r c r a f t continues t o descend on t h e g l i d e p a t h , g e n e r a l l y between 2" 40 min and 4" ( t h e h i g h e r v a l u e f o r a i r f i e l d s w i t h d i f f i c u l t approaches). The time r e q u i r e d t o c o r r e c t l a t e r a l d e f l e c t i o n i s i n f l u e n c e d c o n s i d e r a b l y by t h e i n e r t i a of t h e a i r c r a f t , i t s d e l a y (4-5 s e c ) t o movements . S M. Yeger Proyektirovaniye Passazhirskikh Rgaktivnykh Smnozetov [Design of J e t Passenger A i r c r a f t ] Mashinostroyeniye P r e s s , 1964. 168
- 180. of t h e c o n t r o l organs and t h e c h a r a c t e r i s t i c s o f l a t e r a l and t r a n s v e r s e s t a b i l i t y . Furthermore, an a d d i t i o n a l 2-3 sec is r e q u i r e d f o r crew r e a c t i o n from t h e t i m e when t h e runway can f i r s t be s e e n . T h e r e f o r e , it i s r e q u i r e d /174 t h a t upon approach t o t h e BMB o r a f t e r f l y i n g over t h e BMB t h e crew o f t h e a i r c r a f t must b e a b l e t o see t h e beginning of t h e runway from t h e p o i n t o f beginning of l e v e l i n g o f f down t o t h e touchdown (which i n p r a c t i c e i s 250-300 m from t h e beginning o f t h e runway). Minimum v i s i b i l i t y i s t h e n 800-1200 m y o r 1500 m f o r n i g h t l a n d i n g s . Thus, t h e t r a n s i t i o n t o v i s u a l f l i g h t ( e x i t from t h e cloud cover a t 60-100 m f o r a g l i d e p a t h a n g l e o f 2' 40 min) occurs a t 1250-1500 m from t h e beginning o f t h e runway and d u r i n g t h e subsequent 6-7 s e c o f f l i g h t (240 250 km/hr v e l o c i t y ) t h e crew must have a c l e a r view of t h e runway, t h e p o i n t o f beginning of l e v e l i n g off and t h e p o i n t of touchdown. During t h i s t i m e , t h e p i l o t can perform c o u r s e maneuvers i f t h e a i r c r a f t i s coming i n a t an a n g l e , completing h i s maneuvers by t h e t i m e he reaches an a l t i t u d e o f 40-50 m ( a t 600-800 m from t h e runway). Below an a l t i t u d e of 50 m y it i s forbidden f o r a j e t a i r c r a f t t o p u l l up f o r a second c i r c l e . This a l t i t u d e corresponds approximately t o f l i g h t over t h e BMB, and t h e crew should t a k e a l l s t e p s t o a s s u r e a normal landing from t h i s p o i n t . Figure 109. Elimination Figure 110. Diagram o f of Landing D r i f t by Landing R u n After Touch Course Lead Method down w i t h Lead A n g l e E ( f l i g h t w i t h leading course) 169
- 181. Figure 1 1 1 . Determination o f "Minimum Weather" With l a t e r a l d e v i a t i o n s of '60 m and a g l i d i n g speed o f 250-240 km/hr, t h e r e q u i r e d ground l e n g t h t o b r i n g t h e a i r c r a f t over t o t h e landing l i n e i s 800-900 m. If t h e a i r c r a f t comes o u t o f t h e clouds a t 100 m a l t i t u d e and 1800-1900 m range from t h e runway and t h e p i l o t , upon s e e i n g t h e runway, d e c i d e s t o t u r n t h e a i r c r a f t , h e can complete h i s maneuver a t 600-700 m from t h e runway and b r i n g t h e a i r c r a f t onto t h e l a n d i n g course. With g r e a t e r d e v i a t i o n s (70-100 m) t h e r e q u i r e d ground l e n g t h i s 1000-1200 m and t h e p i l o t w i l l not be a b l e t o b r i n g t h e a i r c r a f t onto t h e course l i n e and perform h i s landing i n t h e s p a c e a v a i l a b l e . T h e r e f o r e , t h e r a d a r c o n t r o l l e r guiding t h e a i r c r a f t i n t o a landing, upon determining t h i s abnormal d e v i a t i o n of t h e a i r c r a f t from i t s c o u r s e , should f o r b i d t h e l a n d i n g ( b e f o r e t h e a i r c r a f t g e t s down t o 50 m a l t i t u d e ) and r e q u i r e t h e a i r c r a f t t o go i n t o a second c i r c l e . The "minimum weather" i s e s t a b l i s h e d n o t o n l y from c o n s i d e r a t i o n s of s a f e t y of l a n d i n g o f t h e a i r c r a f t under poor weather c o n d i t i o n s , b u t a l s o from c o n s i d e r a t i o n s of t a k e o f f s a f e t y . As was s t a t e d above, t h e h e i g h t a t which t h e a i r c r a f t f l i e s over t h e BMB i n c a s e of extended t a k e o f f with one non o p e r a t i n g motor i s 20-25 m . I f t h e h e i g h t o f o b s t a c l e s i n t h i s f l i g h t s e c t o r i s not o v e r 11-14 m , t h e r e i s no l i m i t on t h e c e i l i n g . H o r i z o n t a l v i s i b i l i t y should b e a t l e a s t 600-800 m. This q u a n t i t y i s determined as f o l l o w s . During a climb a f t e r t a k e o f f , t h e p i t c h a n g l e 9 = 6-8" (depending on t h e angle of t h e climbing t r a j e c t o r y 0). The a n g l e of view downward from t h e crew's cabin f o r modern a i r c r a f t i s 15-20". A f t e r t a k e o f f a t 60-70 m a l t i t u d e (when t h e l a n d i n g g e a r and f l a p s a r e r a i s e d ) t h e crew should see t h e runway o r o r i e n t a t i o n p o i n t s on t h e s u r f a c e such as approach l i g h t s ( i n o r d e r t o maintain t h e t a k e o f f course) a t l e a s t 400-500 m i n f r o n t o f t h e a i r c r a f t . The a d d i t i o n a l v i s i b i l i t y r e s e r v e due t o 170
- 182. t h e slower r e a c t i o n o f t h e p i l o t i s g e n e r a l l y 2-3 sec, corresponding t o an a d d i t i o n a l 200-300 m. Thus, t h e minimum v i s i b i l i t y d u r i n g a t a k e o f f should b e 600-800 m. S9. Moving into a Second Circle An a i r c r a f t may move i n t o a second c i r c l e d u r i n g any s t a g e of t h e landing approach, i n c l u d i n g t h e l e v e l i n g o f f . High power r e s e r v e makes it p o s s i b l e t o move o f f i n t o a second c i r c l e even w i t h one motor o u t o f o p e r a t i o n (TU-104, TU-124, TU-134). The decreased pickup of t u r b o j e t engines does i n f l u e n c e t h e behavior o f t h e a i r c r a f t a t t h e moment t h e t r a n s i t i o n i s made t o t h e second c i r c l e . The problem i s t h a t t h e t i m e r e q u i r e d f o r t h e engine t o s h i f t from t h e i d l i n g regime (300-600 kg t h r u s t ) t o t h e nominal t h r u s t regime o r h i g h e r i s 15 1 8 sec, while i n p r a c t i c e a f t e r 6-7 s e c , i . e . , a f t e r t h e t h r o t t l e i s p l a c e d i n t h e "maximum t h r u s t " p o s i t i o n , t h e engine t h r u s t reaches a v a l u e s u f f i c i e n t t o provide n o t o n l y h o r i z o n t a l f l i g h t , b u t some climb. On t h e b a s i s o f t h i s , a u n i f i e d method of p i l o t i n g i n c a s e it becomes n e c e s s a r y t o make a second c i r c l e h a s been developed (by Candidate of Technical Sciences M. V . Rozenblat). A f t e r deciding t o e n t e r a second c i r c l e , t h e p i l o t s e t s t h e t h r o t t l e t o t h e maximum p o s i t i o n . I f t h e a i r b r a k e has been extended, i t s switch i s s h i f t e d t o t h e " r e t r a c t " p o s i t i o n . The a i r c r a f t i s brought out o f t h e descent and t h e speed i s r e t a i n e d unchanged u n t i l t h e a i r c r a f t begins t o /176 climb. S i x t o e i g h t sec a f t e r t h e t h r o t t l e s a r e pushed i n t o t h e maximum p o s i t i o n , t h e engines w i l l develop t h r u s t equal t o 75-80% of t h e maximum (Figure 1 1 2 , p o i n t 2 ) , which w i l l overcome t h e d r a g of t h e a i r c r a f t with some excess power a v a i l a b l e . When t h e a v a i l a b l e power exceeds t h e r e q u i r e d power, t h e a i r c r a f t w i l l begin t o climb. When necessary ( f o r example with i n c r e a s e d v e r t i c a l d e s c e n t r a t e ) i n o r d e r t o d e c r e a s e t h e r a t e o f d e s c e n t , immediately a f t e r t h e engines a r e s h i f t e d t o t h e maximum regime t h e f l i g h t speed can be smoothly reduced by 10-15 km/hr, b u t never below t h e e s t a b l i s h e d g l i d i n g speed. A f t e r t h e a i r c r a f t i s s h i f t e d i n t o a climb and t h e engines reach t h e m a x i m u m regime, t h e landing g e a r a r e brought up, causing t h e f l y i n g speed t o i n c r e a s e s h a r p l y . When a s a f e speed i s achieved and an a l t i t u d e o f 80-100 m i s reached, t h e f l a p s are r a i s e d , and t h e engines a r e s h i f t e d t o t h e nominal o r c r u i s i n g regime. The landing g e a r should n o t be r a i s e d u n t i l t h e engines r e a c h a regime p r o v i d i n g s u f f i c i e n t t h r u s t f o r f l i g h t , s i n c e t h e drag o f t h e a i r c r a f t is i n c r e a s e d when t h e l a n d i n g g e a r s t o r a g e bay doors a r e opened causing t h e r a t e of d e s c e n t t o i n c r e a s e . The graph o f F i g u r e 1 1 2 shows t h a t t h e a i r c r a f t continues t o descend u n t i l t h e engines r e a c h t h e r e q u i r e d regime; when t h e v e r t i c a l v e l o c i t y component V = 3.5-4 m/sec, t h e a d d i t i o n a l descent Y w i l l b e 15-20 m . With V = 5-7 m/sec, t h e a d d i t i o n a l d e s c e n t w i l l be 30-40 m Y i f t h e speed i s r e t a i n e d t h e same, o r 20-25 m i f t h e f l i g h t speed i s decreased 171
- 183. by 10-15 km/hr. T h e r e f o r e , t h e lowest s a f e a l t i t u d e f o r t h e d e c i s i o n t o make a second c i r c l e with l a n d i n g g e a r down, f l a p s i n t h e landing p o s i t i o n and airbrake on i s u s u a l l y 50 m. With t h e a d d i t i o n a l d e s c e n t o f up t o 30 m, an altitude r e s e r v e i s t h u s guaranteed. If t h e speed of the aircraft is decreased by lo-. 15 km/hr i n t h e range of g l i d i n g speeds 240-260 km/hr, t h e a d d i t i o n a l climb r e s u l t i n g from k i n e t i c energy i s 18-25 m. F i g u r e 112. Change i n A l t i t u d e and F l i g h t S p e e d of TU-124 A i r c r a f t upon T r a n s i t i o n t o Second C i r c l e from A l t i t u d e of 75 m (average weight 33 t , 6f = 30" and A a b = 4 0 " ) : 1 , Moment of t h r o t t l e s h i f t and beginning of r e t r a c t i o n of a i r b r a k e ; 2 , Moment of achieve ment of 75-80% maximum t h r u s t b y e n g i n e s ; 3 , Moment of t r a n s i t i o n of e n g i n e s t o takeoff regime and b e g i n n i n g of r a i s i n g of landing g e a r ; 4 , B e g i n n i n g of r a i s i n g of f l a p s 172
- 184. Chapter x. Cornering - /177 91. Diagram o f Forces Operating D u r i n g Cornering O f a l l of t h e curved t r a j e c t o r y maneuvers i n t h e h o r i z o n t a l and v e r t i c a l p l a n e s , t h e t r a n s p o r t a i r c r a f t i s p e r m i t t e d t o perform o n l y t h e c o r n e r i n g maneuver -- f l i g h t i n a curved t r a j e c t o r y i n t h e h o r i z o n t a l p l a n e w i t h a 360-degree t u r n . A p o r t i o n o f a c o r n e r i n g maneuver i s c a l l e d a t u r n . A s t a b l e c o r n e r i n g maneuver without s l i p p i n g i s considered p r o p e r . I n o r d e r t o perform c o r n e r i n g it i s n e c e s s a r y t h a t an unbalanced f o r c e a c t on t h e a i r c r a f t , curving t h e t r a j e c t o r y , and d i r e c t e d perpendic u l a r t o the trajectory (Figure 113). This f o r c e i s a component o f t h e l i f t i n g f o r c e Y s i n y (where y i s t h e bank a n g l e ) , produced when t h e a i r c r a f t i s banked. T h i s force is called centripetal; i t r e s u l t s i n t h e appearance o f a f o r c e equal and o p p o s i t e t o the centrifugal force: G V:! -m-,? V pcF-L'7- r Figure 113. Forces Acting on A i r c r a f t D u r i n g Cornering: a , Proper c o r n e r i n g ; b , Cornering w i t h outward s l i p (nose where m i s t h e mass of t h e of a i r c r a f t d e f l e c t e d toward i n t e r i o r aircraft; of turn) V i s t h e speed i n t h e turn ; r i s t h e r a d i u s of t h e turn. As t h e banking angle i s i n c r e a s e d i n a proper t u r n , t h e l i f t i n g f o r c e /178 must be i n c r e a s e d so t h a t i t s v e r t i c a l component Y cos y c o n t i n u e s t o b a l a n c e t h e weight o f t h e a i r c r a f t . The f o r c e s a c t i n g on t h e a i r c r a f t d u r i n g a h o r i z o n t a l t u r n should s a t i s f y t h e following e q u a l i t i e s 173
- 185. If Y i s expressed through t h e overload n = Y/G, t h e n This formula shows t h e r e l a t i o n s h i p between overloading, which must be used t o perform t h e h o r i z o n t a l t u r n and t h e banking a n g l e y (Figure 1 1 4 ) . As we can y- see from t h e graph, i n o r d e r t o perform a h o r i z o n t a l t u r n a t y = 6 0 " , we must create n = 2. Y I n passenger a i r c r a f t , t h e bank angle i s u s u a l l y s e t a t 2 0 - 3 0 ° , which a f f o r d s t h e necessary maneuverab i 1i t y . 40 I During an approach t o landing under i n s t r u w 1 I ment f l i g h t r u l e s , t h e bank cannot exceed 15'. I .I 'f 2 3 4 5 -67 With most modern a i r c r a f t , h o r i z o n t a l t u r n s a r e performed u s i n g t h e a i l e r o n s a l o n e , almost Figure 114. Over- without u s i n g t h e r u d d e r , with t h e a i r c r a f t load A s a F u n c t i o n " i t s e l f " s e l e c t i n g an a n g u l a r t u r n i n g r a t e s o of Banking Angle t h a t t h e r e w i l l be no s l i p p a g e . This has become p o s s i b l e due t o t h e high degree o f d i r e c t i o n a l s t a b i l i t y , which g r e a t l y f a c i l i t a t e s maintenance of s o - c a l l e d "coordination," i . e . , a combination o f o p e r a t i o n s o f t h e a i l e r o n s and rudder f o r which t h e v e l o c i t y v e c t o r remains i n t h e p l a n e of symmetry of t h e a i r c r a f t and no s l i p p i n g occurs1. 52. Cornering Parameters Cornering parameters i n c l u d e t h e r a d i u s o f t h e h o r i z o n t a l t u r n , time of t h e t u r n , angular v e l o c i t y of t h e t u r n , e t c . The following formulas are known f o r t h e r a d i u s and time o f a h o r i z o n t a l turn : m a r S t a b i 1 i t y of t h e A i r c r a f t ," Letchiku o Prakticheskoy Aerod?k"ke [ P r a c t i c a l Aerodynamics f o r t h e P i l o t ] , Voyenizdat. P r e s s , 1961. 174
- 186. I I1 I I I l l 11.11 11111 where V i s t h e speed d u r i n g t h e c o r n e r i n g maneuver; cor g is the acceleration of gravity; /179 n i s t h e overload; y is t h e bank a n g l e o f t h e a i r c r a f t . W can see from t h e formula t h a t t h e r a d i u s of t h e t u r n depends s t r o n g l y e on t h e f l i g h t speed, i n c r e a s i n g r a p i d l y with i n c r e a s i n g speed. The r a d i u s of t h e h o r i z o n t a l t u r n can be d e c r e a s e d by i n c r e a s i n g t h e overloading, i . e . , by i n c r e a s i n g t h e bank a n g l e of t h e a i r c r a f t . During c o r n e r i n g , t h e a i r c r a f t has an angular v e l o c i t y o f Let us c a l c u l a t e t h e r a d i u s of t u r n s performed d u r i n g t h e landing approach around a l a r g e , r e c t a n g u l a r course ( y = 1 S 0 , t a n 15" = 0.268). If t h e bank a n g l e s and t h e t u r n s a r e g r e a t e r t h a n 15", t h e maneuver a b i l i t y of t h e a i r c r a f t i n c r e a s e s and t h e landing approach time d e c r e a s e s ( t h e r e s e r v e of p i l o t ' s time i n c r e a s e s ) . F o r a l l a i r c r a f t , t h e f i r s t t u r n i n t h e approach t o landing begins according t o t h e diagram a t 2800 m a l t i t u d e and 450 km/hr i n d i c a t e d speed. Let u s d e f i n e t h e r a d i u s o f t h e f i r s t t u r n f o r a mean a l t i t u d e o f 2000 m , keeping i n mind t h a t t h e i n d i c a t e d speed of 450 km/hr corresponds t o a mean a i r speed of 486 km/hr (135 m/sec): Where y = 20" ( t a n 20" = 0.363), w e produce r = 5100 m. Let us determine t h e r a d i u s o f t h e t h i r d t u r n when f l y i n g a t V 1nd = . = 350 km/hr and y = 15": Note: Tg = Tan 175
- 187. r= m 9480 - ~ 3 6 0 0 9 -81-0,268 A t a n g l e y = 20" and t h e same speed, t h e r a d i u s o f t h e t u r n w i l l b e 2660 m. On t h e f o u r t h t u r n a t Vind = 320 km/hr and y = 15" ( l a n d i n g g e a r down, f l a p s down 1 5 " ) , r = 3000 m, and a t 20" bank, r = 2200 m . Let us determine t h e time f o r a t u r n w i t h a bank a n g l e o f 15". A n i n c r e a s e i n t h e r a d i u s of a t u r n a l s o r e s u l t s i n an i n c r e a s e i n time r e q u i r e d t o perform t h e t u r n . The formula p r e s e n t e d f o r t i s used t o c a l c u l a t e cor t h e time f o r a complete c o r n e r i n g maneuver, i . e . , a 360-degree t u r n . Usually, t h e a i r c r a f t performs t u r n s o f 180, 90 o r fewer d e g r e e s . The time r e q u i r e d f o r a 180-degree t u r n ( f i r s t and second t u r n s performed together) is f=0;64. -.3' 1 0.5=161.5 sec=2 min 41.5 sec. 0.265 The t i m e f o r t h e t h i r d t u r n i s /180 97.2 t-0.64. -- .0.25=58 S ~ G . 0-268 The time f o r t h e f o u r t h t u r n i s t=0.64.L-OO25=53 89 0 S ~ C . 0.265 The a n g u l a r v e l o c i t y o f r o t a t i o n d u r i n g t h e performance of t h e f o u r t h turn i s w- V --=0.03rad/sec=1.7 89 deg/sec; r 3000 176
- 188. CHAPTER X I STABILITY AND C O N T R O L A B I L I T Y OF A I R C R A F T §1. General Concepts on A i r c r a f t Equilibrium I n studying t h e s t a b i l i t y and c o n t r o l l a b i l i t y o f an a i r c r a f t , it i s r e p r e s e n t e d as a body moving under t h e i n f l u e n c e o f e x t e r n a l f o r c e s and r o t a t i n g under t h e i n f l u e n c e of t h e moments o f t h e s e f o r c e s . I n any f l i g h t , e q u i l i b r i u m o f f o r c e s and moments a c t i n g on t h e a i r c r a f t must be observed. Equilibrium of t h e a i r c r a f t i n f l i g h t i s what w e c a l l t h e s t a t e i n which t h e f o r c e s and moments a c t i n g on t h e a i r c r a f t cause no r o t a t i o n , i . e . , t h e given s t a t e i s n o t d i s r u p t e d . I n a l l f l i g h t modes, t h e a i r c r a f t should be balanced both i n t h e l o n g i t u d i n a l and l a t e r a l d i r e c t i o n s . Balancing means achievement o f equi l i b r i b r i u m of moments u s i n g t h e c o n t r o l s u r f a c e s i n any f l i g h t mode. Equilibrium of f o r c e s and moments a c t i n g on t h e a i r c r a f t i s analyzed r e l a t i v e t o t h e t h r e e c o o r d i n a t e axes passing through i t s c e n t e r of g r a v i t y . The coordinate axes used (Figure 115) are t h e l o n g i t u d i n a l a x i s of t h e a i r c r a f t ox, t h e t r a n s v e r s e axis oz and t h e v e r t i c a l a x i s oy. Figure 115 a l s o shows t h e following moments: M i s t h e yaw o r t r a c k angle, r o t a t i n g t h e a i r c r a f t about a x i s oy, and i s Tonsidered p o s i t i v e i f t h e a i r c r a f t r o t a t e s i t s bow t o t h e l e f t ; M i s t h e bank moment o r t h e t r a n s v e r s e X moment, r o t a t i n g a i r c r a f t around t h e ox a x i s , and i s considered p o s i t i v e i f t h e a i r c r a f t r o t a t e s toward t h e r i g h t wing; M i s t h e p i t c h moment o r t h e Z l o n g i t u d i n a l moment, r o t a t i n g t h e a i r c r a f t about t h e oz a x i s , and i s c a l l e d p o s i t i v e i f t h e a i r c r a f t tends t o l i f t i t s bow. Equilibrium o f t h e a i r c r a f t about t h e s e axes i s divided i n t o longitud i n a l e q u i l i b r i u m (about t h e a x i s oz) , t r a n s v e r s e e q u i l i b r i u m (about t h e a x i s ox) and t r a c k e q u i l i b r i u m (about t h e a x i s oy). Three c h a r a c t e r i s t i c forms o f body e q u i l i b r i u m are known: s t a b l e , u n s t a b l e and n e u t r a l e q u i l i b r i u m . A example i l l u s t r a t i n g t h e s e forms of n e q u i l i b r i u m might b e t h e behavior o f a b a l l on s u r f a c e s of v a r i o u s forms. The behavior of a b a l l on a concave curved s u r f a c e c h a r a c t e r i z e s s t a b l e equilibrium, on a convex s u r f a c e -- u n s t a b l e e q u i l i b r i u m and on a f l a t s u r f a c e -- n e u t r a l e q u i l i b r i u m . 177 I
- 189. - 'r - 'r r P > O i f r Figure 115. S y s t e m of A i r c r a f t Axes and Symbols Used f o r Moments of Angular V e l o c i t i e s , D e f l e c t i o n o f Control Surfaces and Forces on Command Levers Although a i r c r a f t e q u i l i b r i u m i s a more complex phenomenon t h a n t h e e q u i l i b r i u m of a b a l l , i n f l i g h t an a i r c r a f t may b e i n t h e s t a b l e , u n s t a b l e o r n e u t r a l s t a t e s . I n correspondence with t h e s e forms o f e q u i l i b r i u m , t h e a i r c r a f t i s c a l l e d s t a b l e , u n s t a b l e o r n e u t r a l . An u n s t a b l e o r n e u t r a l a i r c r a f t cannot s a t i s f y t h e requirements o f normal c o n t r o l i n f l i g h t . 52. S t a t i c and Dynamic S t a b i l i t y The s t a b i l i t y o f an a i r c r a f t i s i t s a b i l i t y t o r e t a i n i t s f l i g h t regime o r r e t u r n t o i t s i n i t i a l balanced regime i n c a s e of an a r b i t r a r y d e v i a t i o n r e s u l t i n g from e x t e r n a l p e r t u r b a t i o n s , without t h e a i d of t h e p i l o t . A t t h e p r e s e n t t i m e , books on aerodynamics f r e q u e n t l y d i v i d e s t a b i l i t y a r b i t r a r i l y i n t o s t a t i c and dynamic s t a b i l i t y , although i n a c t u a l i t y an a i r c r a f t simply h a s s t a b i l i t y , meaning t h e a b i l i t y of t h e a i r c r a f t t o r e t u r n t o movement a t t h e i n i t i a l kinematic parameters ( v e l o c i t y , angle o f a t t a c k , e t c . ) a f t e r a p e r t u r b a t i o n i s removed o r , as t h e y s a y , t h e a b i l i t y o f t h e a i r c r a f t t o r e t a i n t h e i n i t i a l f l i g h t regime. T h e r e f o r e , t h e s t a b i l i t y o f an a i r c r a f t c o n s i s t s o f s t a t i c s t a b i l i t y and good damping p r o p e r t i e s , which determine and c h a r a c t e r i z e t h e q u a l i t y of t h e t r a n s i e n t p r o c e s s when t h e e q u i l i b r i u m of t h e a i r c c r a f t i s d i s r u p t e d . This i s f r e q u e n t l y c a l l e d dynamic s t a b i l i t y . 178
- 190. .-. .. . . .. . . , ,, ..., Let us analyze t h e s e p r o p e r t i e s o f an a i r c r a f t i n d i v i d u a l l y i n somewhat more d e t a i l . I n f l i g h t , an a i r c r a f t i s s u b j e c t t o t h e effects of t u r b u l e n c e of t h e atmosphere, a s w e l l as s h o r t d u r a t i o n p e r t u r b a t i o n s c r e a t e d by random devi a t i o n s o f t h e c o n t r o l s u r f a c e s by t h e p i l o t , e t c . The p e r t u r b i n g moments d i s r u p t t h e e q u i l i b r i u m of f o r c e s , causing t h e t r a j e c t o r y of t h e a i r c r a f t t o curve and t h e v e l o c i t y of t h e a i r c r a f t t o change. The summary movement of t h e a i r c r a f t produced by adding t h e i n i t i a l unperturbed and supplementary motions, i s c a l l e d t h e p e r t u r b e d movement. S t a t i c s t a b i l i t y means t h e p r o p e r t y o f an a i r c r a f t causing it t o create s t a b i l i z i n g moments when e q u i l i b r i u m i s d i s r u p t e d . For example, i f a n e g a t i v e p i t c h i n g moment arises and acts on t h e a i r c r a f t when t h e angle of a t t a c k i s i n c r e a s e d , t h i s w i l l b e a s t a b i l i z i n g moment. Also, on t h e r i g h t wing causes a moment t o a r i s e t e n d i n g t o t u r n t h e a i r c r a f t t o t h e r i g h t , it w i l l a l s o b e a s t a b i l i z i n g moment. Thus, i f when e q u i l i b r i u m i s d i s r u p t e d , moments a r i s e tending t o r e s t o r e t h e i n i t i a l e q u i l i b r i u m p o s i t i o n of t h e a i r c r a f t , t h e a i r c r a f t i s c a l l e d s t a t i c a l l y s t a b l e . The presence of s t a t i c s t a b i l i t y makes it p o s s i b l e f o r t h e p i l o t t o c o n t r o l t h e a i r c r a f t normally, and t o t a k e proper c o n t r o l a c t i o n s i n emergency s i t u a t i o n s . Dynamic s t a b i l i t y means t h e tendency o f an a i r c r a f t , a f t e r a p e r t u r b i n g f o r c e i s removed, t o r e s t o r e t h e i n i t i a l f l i g h t regime ( v e l o c i t y , a l t i t u d e , overloading, f l i g h t d i r e c t i o n ) without i n t e r f e r e n c e from t h e p i l o t . Dynamic s t a b i l i t y of t h e a i r c r a f t i s c h a r a c t e r i z e d by: t h e period of damping o f o s c i l l a t i o n s T, t h e t i m e of damping of o s c i l l a t i o n s Td (during which time t h e i n i t i a l amplitude of o s c i l l a t i o n s i s decreased by a f a c t o r o f 2 0 ) , t h e d e c r e a s e i n o s c i l l a t i n g amplitude A i n one p e r i o d md = A1/A3 (Figure 116) and t h e r e l a t i v e o s c i l l a t i o n damping c o e f f i c i e n t 6. C o e f f i c i e n t 5 determines t h e q u a l i t y of t h e t r a n s i e n t process o r , i n o t h e r words, t h e i n t e n s i t y o f damping o f o s c i l l a t i o n s from a p e r t u r b i n g movement. I n a dynamically s t a b l e a i r c r a f t , p e r t u r b e d movement must b e damped. The movement may b e e i t h e r a p e r i o d i c ( n o n o s c i l l a t i n g ) , i n which a p e r t u r b e d - /183 movement i s r a p i d l y damped, o r p e r i o d i c ( o s c i l l a t i n g ) , i n which damping occurs with a c e r t a i n amplitude and r e q u i r e s somewhat more time (Figure 117). A n e u t r a l a i r c r a f t shows no tendency toward damping o r i n c r e a s e i n p e r t u r b a t i o n s (Figure 117 b ) , while a dynamically u n s t a b l e a i r c r a f t shows a tendency toward i n c r e a s e d amplitude of p e r t u r b a t i o n s with t i m e (Figure 117 c ) . Weak damping and o s c i l l a t i n g p e r i o d s which are t o o long are c h a r a c t e r i s t i c s of poor a i r c r a f t s t a b i l i t y . A s t h e p e r i o d i s i n c r e a s e d , t h e perturbed movement o f t h e a i r c r a f t i s " s t r e t c h e d out," i . e . , extends over a longer p e r i o d of t i m e . 179
- 191. As w e can see from Figure 118, t h e behavior of a d namically u n s t a b l e a i r c r a f t d i s c h a r a c t e r i e by an a p e r i o d i c i n c r e a s e i n t h e p i t c h angle, t h a t of a dynamically s t a b l e a i r c r a f t by damping o s c i l l a t i o n s . If n e i t h e r s t a b i l i z i n g ilor d e s t a b i l i z i n g moments a r i s e when t h e a i r c r a f t /184 - d e v i a t e s from t h e e q u i l i b r i u m s t a t e , t h e aircraft is called s t a t i c a l l y neutral Figure 116. Determin (Figure 118 c ) . stion of Characteristics o f Short Period Damping S t a t i c s t a b i l i t y alone i s i n s u f f i c i e n t Perturbed Movement t o i n s u r e t h a t t h e a i r c r a f t w i l l have ( A I , A 2 a r e amplitudes) dynamic s t a b i l i t y . This r e q u i r e s a d d i t i o n a l damping and i n e r t i a l p r o p e r t i e s , as w e l l as a p r o p e r r e l a t i o n s h i p of c h a r a c t e r i s t i c s of s t a t i c s t a b i l i t y r e l a t i v e t o t h e various axes. a) b) The damping moments formed when the aircraft is r o t a t e d have a tremendous r o l e t o p l a y i n suppression of o s c i l l a t i o n s and p r o v i s i o n o f good c o n t r o 11a b i li t y f o r example, 1ong it ud i na1 damping ( p i t c h damping) i s c r e a t e d p r i m a r i l y by the horizontal t a i l s u r f aces, while yaw damping ( t r a c k Figure 117. C h a r a c t e r i s t i c s o f Perturbed Move damping) i s produced m e n t o f S t a b l e ( a ) , Neutral ( b ) and Unstable ( c ) by t h e v e r t i c a l t a i l A i r c r a f t (arrow shows i n i t i a l equilibrium surfaces of the pos i t ion) a i r c r a f t . When r o t a t i o n about t h e ox a x i s occurs, t h e wings c r e a t e a t r a n s v e r s e damping moment. With weak damping, a i r c r a f t o s c i l l a t i o n s w i l l b e a t t e n u a t e d slowly, p a r t i c u l a r l y a t a l t i t u d e s of 10,000-11,000 m , and a g r e a t d e a l o f t i m e w i l l b e r e q u i r e d f o r r e s t o r a t i o n of e q u i l i b r i u m . With t o o s t r o n g damping, t h e r e t u r n t o t h e e q u i l i b r i u m s t a t e i s a l s o delayed. The i n e r t i a l p r o p e r t i e s of an a i r c r a f t a r e c h a r a c t e r i z e d by i t s a b i l i t y t o r e t a i n t h e s t a t e of e q u i l i b r i u m o r i t s previous angular r o t a t i o n a l 180
- 192. v e l o c i t y . The g r e a t e r t h e moment o f i n e r t i a , t h e more slowly t h e a i r c r a f t r e a c t s t o d e f l e c t i o n s o f t h e s t i c k and p e d a l s . J e t a i r c r a f t have high moments of i n e r t i a r e l a t i v e t o t h e y and z axes, s i n c e t h e y have a r e l a t i v e l y long f u s e l a g e , i n which t h e main mass o f t h e load i s c o n c e n t r a t e d about t h e c e n t e r o f g r a v i t y . The moment of i n e r t i a r e l a t i v e t o t h e x a x i s i s less, s i n c e t h e wing span i s less t h a n t h e l e n g t h o f t h e f u s e l a g e . a) w i n i gust wind gust wind g u s t Figure I 18. Behavior of Dynamical l y Unstable ( a ) , S t a b l e ( b ) and Neutral ( c ) A i r c r a f t During Perturbed Mot ion §3. C o n t r o l l a b i l i t y of an A i r c r a f t The c o n t r o l l a b i l i t y o f an a i r c r a f t i s an important p i l o t i n g c h a r a c t e r i s t i c , and means i t s c a p a b i l i t y t o respond t o t h e p i l o t ' s movements o f t h e rudder and a i l e r o n s with corresponding movements i n space o r , as t h e y s a y , t h e / 185 a b i l i t y o f t h e a i r c r a f t t o "follow t h e c o n t r o l s u r f a c e s . " I n c o n t r o l l i n g t h e a i r c r a f t , t h e p i l o t moves t h e s t i c k and p e d a l s and e v a l u a t e s t h e behavior of t h e a i r c r a f t by t h e f o r c e s on t h e c o n t r o l s u r f a c e s . By moving t h e v a r i o u s s u r f a c e s , t h e p i l o t overcomes t h e i n e r t i a l , damping and r e s t o r i n g moments a c t i n g on t h e a i r c r a f t . I f t h e f o r c e s a r e extremely h i g h , t h e p i l o t w i l l become f a t i g u e d d u r i n g maneuvering. Such a i r c r a f t a r e d e s c r i b e d as being heavy t o c o n t r o l . Unnecessarily l i g h t c o n t r o l should a l s o b e avoided, s i n c e it makes p r e c i s e c o n t r o l of movements o f c o n t r o l s u r f a c e s d i f f i c u l t and may cause t h e a i r c r a f t t o shake. The c o n t r o l s u r f a c e s should make it p o s s i b l e t o balance t h e a i r c r a f t i n a l l f l i g h t regimes used. This i s e v a l u a t e d u s i n g b a l a n c i n g c u r v e s , which c h a r a c t e r i z e t h e change i n b a l a n c e angles of c o n t r o l s u r f a c e d e f l e c t i o n (and correspondingly t h e p o s i t i o n o f t h e c o n t r o l l e v e r s , a s w e l l a s t h e f o r c e s on them) a t v a r i o u s s t a b l e f l i g h t regimes as a f u n c t i o n of a change i n one of t h e parameters determining t h e regime ( f o r example, f l i g h t speed, M number, angle of a t t a c k o r s l i p a n g l e , e t c . ) . The p i l o t a l s o judges t h e c o n t r o l l a b i l i t y of an a i r c r a f t from t h e r e a c t i o n of t h e a i r c r a f t t o d e f l e c t i o n s of "the c o n t r o l l e v e r s during maneuvering. C o n t r o l l a b i l i t y i s d i v i d e d i n t o t h r e e forms: l o n g i t u d i n a l , directional and t r a n s v e r s e . The a b i l i t y of t h e a i r c r a f t t o r o t a t e about t h e ox a x i s under t h e i n f l u e n c e o f t h e a i l e r o n s i s c a l l e d t r a n s v e r s e c o n t r o l l a b i l i t y , about t h e oy a x i s under t h e i n f l u e n c e of t h e r u d d e r i s c a l l e d d i r e c t i o n a l c o n t r o l l a b i l i t y 181
- 193. and about t h e oz a x i s under t h e i n f l u e n c e o f t h e e l e v a t o r i s c a l l e d l o n g i t u d . i n a l c o n t r o 1l a b i l i t y C h a r a c t e r i s t i c s of l o n g i t u d i n a l c o n t r o l l a b i l i t y i n c l u d e t h e amount o f e l e v a t o r and s t i c k t r a v e l r e q u i r e d t o change t h e a i r c r a f t v e l o c i t y by a f i x e d amount, as well a s t h e f o r c e , a p p l i e d t o t h e s t i c k by t h e p i l o t . One of t h e most important c h a r a c t e r i s t i c s i s t h e f o r c e g r a d i e n t w i t h r e s p e c t t o over l o a d i n g APel/An showing t h e f o r c e which must b e a p p l i e d t o t h e s t i c k t o Y' change overloading by one u n i t . The following parameters are used as c h a r a c t e r i s t i c s o f t r a n s v e r s e . c o n t r o 1l,abi 1i t y 1) The f o r c e which must b e a p p l i e d t o t h e s t i c k t o g i v e t h e a i r c r a f t an a n g u l a r r o t a t i o n v e l o c i t y about t h e ox a x i s of 1 r a d / s e c : AP Pa - - A , " box where APa i s t h e f o r c e a p p l i e d t o t h e a i l e r o n c o n t r o l l e v e r ; Amx i s t h e change i n a n g u l a r v e l o c i t y o f 1 r a d / s e c ; 2 ) The f o r c e which must b e a p p l i e d t o t h e c o n t r o l l e v e r t o /186 balance t h e a i r c r a f t i n s t r a i g h t l i n e f l i g h t w i t h a s l i p of one degree o r a bank o f one degree: where A @ i s t h e change i n s l i p angle o f one degree; Ay i s t h e change i n bank angle of one degree; 3 ) The change i n a n g u l a r v e l o c i t y o f a bank when t h e d e f l e c t i o n of t h e a i l e r o n s i s changed by one degree: where Amx i s t h e ehange i n a n g u l a r v e l o c i t y o f t h e bank; A6 i s t h e change a i l e r o n a n g l e of one degree. a 182
- 194. The c h a r a c t e r i s t i c s o f d i r e c t i o n a l c o n t r o l l a b i l i t y are t h e following parameters : 1) The f o r c e which must b e a p p l i e d t ? t h e pedals t o impart an angular v e l o c i t y of 1 r a d / s e c t o t h e a i r c r a f t : where APn i s t h e f o r c e a p p l i e d t o t h e p e d a l s ; Au i s t h e change i n angular v e l o c i t y of 1 r a d / s e c ; Y 2) t h e f o r c e which must be a p p l i e d t o t h e pedals t o d e f l e c t t h e rudder when t h e a i r c r a f t i s balanced i n s t r a i g h t l i n e f l i g h t with a s l i p of one degree o r a bank of one degree; 3 ) t h e change i n angular v e l o c i t y when t h e rudder i s d e f l e c t e d by one degree, i . e . , t h e bank r e a c t i o n of t h e a i r c r a f t t o d e f l e c t i o n of t h e rudder: where A6n i s t h e change i n t h e rudder angle of one degree. We can s e e from t h e d e f i n i t i o n s of a i r c r a f t s t a b i l i t y and c o n t r o l l a b i l i , t y t h a t t h e y c h a r a c t e r i z e opposite p r o p e r t i e s o f t h e a i r c r a f t : s t a b i l i t y must b e p r e s e n t t o maintain t h e f l i g h t regime unchanged, while c o n t r o l l a b i l i t y must be p r e s e n t t o allow it t o b e changed. However, t h e r e i s a c e r t a i n i n t e r r e l a t i o n s h i p between s t a b i l i t y and c o n t r o l l a b i l i t y . O a s t a b l e a i r c r a f t , t h e n a t u r e of t h e movements of t h e c o n t r o l l e v e r s n and r e q u i r e d d e f l e c t i o n s during p i l o t i n g are s i m p l i f i e d , and i t i s e a s i e r t o determine t h e f l i g h t regime. I t h a s been t h e o r e t i c a l l y proven and confirmed by p r a c t i c e t h a t t h e h i g h e r t h e s t a b i l i t y of t h e a i r c r a f t , t h e less t h e delay and g r e a t e r t h e accuracy with which i t follows a d e f l e c t i o n o f t h e c o n t r o l s u r f a c e s . Therefore, s t a b i l i t y and c o n t r o l l a b i l i t y provide f o r complete /187 u t i l i z a t i o n o f t h e maneuvering c a p a c i t y o f t h e a i r c r a f t , a s s u r i n g t h e r e q u i r e d accuracy and s i m p l i c i t y o f p i l o t i n g and are an important c o n d i t i o n f o r f l i g h t safety, 183 I . . . ..- . _ .. . __ .. __ .._. __ . .
- 195. S4. Centering of t h e A i r c r a f t and Mean Aerodynamic Chord The p o s i t i o n of t h e c e n t e r o f g r a v i t y of an a i r c r a f t r e l a t i v e t o t h e wings i s c a l l e d t h e c e n t e r i n g o f t h e a i r c T a f t and i s determined by t h e d i s t a n c e ( i n p e r c e n t ) from t h e o r i g i n of t h e mean aerodynamic cord (Figure 119) : - x -5.100%; -T=: g +.loo %, '- MAC MAC where b i s t h e mean aerodynamic cord o f t h e wing; mac x i s t h e h o r i z o n t a l d i s t a n c e from t h e l e a d p o i n t of t h e mac t o t h e t c e n t e r of g r a v i t y ; y t i s t h e v e r t i c a l d i s t a n c e from t h e mac t o t h e c . g . Figure 119. Diagram f o r Determining MAC of Trapezoidal S w e p t Wing ( r . 1 . f . = r e f e r e n c e 1 i n e of a i r c r a f t ; A , p o s i t i o n of c e n t e r of g r a v i t y corresponding t o t i p p i n g of a i r c r a f t o n t o t a i l ) Since y i s small i n magnitude, xt i s of primary s i g n i f i c a n c e i n an t a n a l y s i s o f s t a b i l i t y and c o n t r o l l a b i l i t y . The c e n t e r of g r a v i t y may b e e i t h e r above o r below t h e r e f e r e n c e l i n e of t h e a i r c r a f t , depending on t h e a c t u a l weight of t h e a i r c r a f t ( f u e l load) and placement of motors. I n f l i g h t , t h e c . g . of t h e a i r c r a f t should b e i n s t r i c t l y defined p o s i t i o n s i n r e f e r e n c e t o t h e mac, guaranteeing continued s t a b i l i t y and c o n t r o l l a b i l i t y as t h e f u e l i s consumed. The f u e l r e p r e s e n t s 25-45% o f t h e 184
- 196. weight o f t h e a i r c r a f t . I n o r d e r t o achieve t h e l e a s t displacement o f t h e c . g . i n f l i g h t , t h e f u e l i s consumed i n a predetermined o r d e r , c o n t r o l l e d by an automatic d e v i c e (Figure 120). As w e can s e e from t h e graph, i n o r d e r t o remain w i t h i n t h e r e q u i r e d range of c e n t e r i n g s t (x= 21-30% MAC), t h e loaded a i r c r a f t without f u e l must have x t = 23.3-28.5% MAC (corresponding t o s e c t o r AB on t h e f i g u r e ) . Then, with any f u e l load c e n t e r i n g , o f t h e a i r c r a f t w i l l n o t go beyond t h e s e l i m i t s . For example, i f a c e n t e r i n g of 26% mac was produced f o r t h e loaded a i r c r a f t without f u e l ( l a n d i n g g e a r down) , when 8.5 t of f u e l is taken on t x = 26.7%, o r with 10.5 t -- 24.3% MAC. A f t e r t h e l a n d i n g g e a r a r e r e t r a c t e d , t h e c e n t e r i n g moves a f t one p e r c e n t and w i l l amount t o 26.7 and 25.2% r e s p e c t i v e l y . With a f u e l remainder of 6.65 t , t h e c e n t e r i n g w i l l b e f u r t h e s t t o t h e r e a r , and with a remainder o f 3.15 t -- f u r t h e s t t o t h e f r o n t . With c e n t e r i n g Yt = 42-50% MAC, f o r a i r c r a f t with motors on t h e wings and 48-53% i f t h e motor i s l o c a t e d i n t h e r e a r p o r t i o n o f t h e fuselage, the c e n t e r o f g r a v i t y i s l o c a t e d i n t h e p l a n e of t h e main landing gear s t r u t s ; with c e n t e r i n g f u r t h e r t o t h e r e a r , t h e a i r c r a f t may t i p onto its t a i l (Figure 119). Figure 120. Change i n Centering of A i r c r a f t i n F l i g h t As a Function o f Quantity of F u e l i n Tanks ( y t = 0.8 g/cm3) S5. Aerodynamic Center o f Wing and A i r c r a f t . Neutral Centering W know t h a t t h e r e i s a p o i n t on t h e cord of t h e wing about which t h e e moment o f aerodynamic f o r c e s does n o t change when t h e angle o f a t t a c k i s changed. For example (Figure 121) with an angle of a t t a c k a l , l i f t i n g f o r c e Y c r e a t e s a l o n g i t u d i n a l moment M Z r e l a t i v e t o a c e r t a i n p o i n t F 1 (Figure 1 2 1 a ) . A s t h e a n g l e of a t t a c k i s changed t o a 2 , t h e l i f t i n g f o r c e /189 -- i n c r e a s e s , b u t i t s arm l e n g t h r e l a t i v e t o p o i n t F i s decreased a s a r e s u l t of displacement of t h e c e n t e r o f p r e s s u r e ( F i g u r e 1 2 1 b ) . The new moment may b e 185 I
- 197. H I I I g r e a t e r t h a n o r less t h a n t h e preceding moment. This depends on t h e way i n which t h e r e l a t i o n s h i p between t h e v a l u e s o f f o r c e and a r m l e n g t h change. I t i s p o s s i b l e t o s e l e c t a p o i n t F such t h a t t h e v a l u e o f t h e arm l e n g t h changes i n i n v e r s e p r o p o r t i o n t o t h e aerodynamic f o r c e . Then, t h e moment r e l a t i v e t o t h i s p o i n t w i l l n o t change as t h e a n g l e o f a t t a c k i s changed. This p o i n t i s c a l l e d t h e aerodynamic c e n t e r o f t h e wing. Thus, i f a3 > c1 > c1 and 2 1 L1 > Z 2 > Z , t h e n YIZl = Y2Z2 = Y Z i s t h e c o n s t a n t moment of aerodynamic ~ 3 3 f o r c e r e l a t i v e t o t h e aerodynamic c e n t e r o f t h e wing with v a r i o u s a n g l e s of a t t a c k . With wing shapes used, t h e aerodynamic c e n t e r i s l o c a t e d 23 t o 25% o f t h e d i s t a n c e along i t s cord. Figure 121. Explanation of Aerodynamic Center o f Wing ( a , b, c) and of A i r c r a f t ( d ) W can draw an important conclusion from t h e d e f i n i t i o n of t h e aero e dynamic c e n t e r : t h e increments o f aerodynamic f o r c e s a r i s i n g when t h e angle o f a t t a c k i s changed a r e a p p l i e d t o t h e aerodynamic c e n t e r . A c t u a l l y , f o r c e Y = Y + AY, a p p l i e d a t cp2, can b e d i v i d e d i n t o f o r c e Y1 a p p l i e d t o cpl and 2 1 f o r c e Y, a p p l i e d a t t h e aerodynamic c e n t e r (Figure 1 2 1 b ) . Since t h e moment o f f o r c e AY r e l a t i v e t o p o i n t F i s equal t o z e r o , t h e l o n g i t u d i n a l moment of t h e wing a t angle o f a t t a c k c1 w i l l be t h e same as a t 2 angle o f a t t a c k a 1' The h o r i z o n t a l t a i l s u r f a c e s , l i k e t h e wing, have t h e i r own aerodynamic /= center. 186 .~ . . .... . . .
- 198. When t h e angle o f a t t a c k i s changed, a d d i t i o n a l l i f t i n g f o r c e a r i s e s on t h e wing, and ends on t h e h o r i z o n t a l t a i l s u r f a c e s , a p p l i e d t o t h e aero dynamic c e n t e r s of t h e wing and h o r i z o n t a l t a i l s u r f a c e s (Figure 1 2 1 d ) . The r e s u l t a n t of p a r a l l e l f o r c e s AYw and AYht i s a p p l i e d a t d i s t a n c e s i n v e r s e l y p r o p o r t i o n a l t o t h e v a l u e s o f t h e s e f o r c e s . The p o i n t o f a p p l i c a t i o n o f t h i s r e s u l t a n t i s c a l l e d t h e aerodynamic c e n t e r of t h e a i r c r a f t . W must n o t e h e r e e t h a t f o r a i r c r a f t o f known t y p e s , b o t h t h e h o r i z o n t a l t a i l s u r f a c e l i f t i n g f o r c e and i t s increment AYht are d i r e c t e d downward, no matter what t h e angle o f a t t a c k of t h e wing. As w e can s e e from t h e f i g u r e , t h e moment of supplementary f o r c e s r e l a t i v e t o t h e a i r c r a f t aerodynamic c e n t e r i s zero; consequently, t h e l o n g i t u d i n a l moment o f t h e aircraft relative t o this 40 c e n t e r does n o t change when t h e angle o f a t t a c k i s changed. 1 ' F.t max r e a r 1 I'Stabi 1 i t y Reserve T h e r e f o r e , t h e p o s i t i o n of t h e a i r c r a f t aerodynamic c e n t e r does n o t change when t h e angle 30 42 43 44 I , ,4 8 M 95 I ,7 4 46 of a t t a c k i s changed. The aerodynamic c e n t e r of Figure 122. Neutral Centering o f Air the a i r c r a f t is shifted t o the c r a f t w i t h Respect t o Overloads As a r e a r under t h e i n f l u e n c e o f Function of M Number (example): aerodynamic f o r c e increments a , Maximal indicated speed 1 imita arising i n the stabilizer, t i o n ; b , Minimum permissible f u s e l a g e and engine c e l l s . For indicated s p e e d l i m i t a t i o n example, i f f o r t h e wing without t h e h o r i z o n t a l t a i l s u r f a c e ) X = 2 0 - 2 2 % mac, f o r F the aircraft xF = 46-50% mac. If t h e loads on t h e a i r c r a f t a r e so d i s t r i b u t e d t h a t t h e c e n t e r of g r a v i t y o f t h e a i r c r a f t corresponds with i t s aerodynamic c e n t e r , t h e a i r c r a f t becomes n e u t r a l i n t h e l o n g i t u d i n a l r e s p e c t . I n t h i s c a s e , t h e c e n t e r i n g i s c a l l e d n e u t r a l . Since i n t h i s c a s e t h e l o n g i t u d i n a l moment of t h e a i r c r a f t w i l l n o t change as a f u n c t i o n of angle of a t t a c k , we must conclude t h a t n e u t r a l c e n t e r i n g i s t h e aerodynamic c e n t e r of t h e e n t i r e a i r c r a f t 1 . N e u t r a l a i r c r a f t c e n t e r i n g s are c a l c u l a t e d f o r v a r i o u s a l t i t u d e s and f l i g h t speeds (Figure 122). r-l-.V. Ostoslavskry, Aerodinamika SamoZeta [Aerodynamics o f t h e A i r c r a f t ] , Oborongiz. P r e s s , 1957. 187 I
- 199. As w e can s e e from t h e f i g u r e , a t Mach numbers M 0.6, n e u t r a l c e n t e r i n g moves somewhat (by 1.1-1.7% mac) forward ( r e l a t i v e t o i t s i n i t i a l v a l u e s o f 45-43% mac), w h i l e a t a l t i t u d e s over 6,000 m i t s h i f t s n o t i c e a b l y t o t h e r e a r as a r e s u l t of t h e effect of t h e compressibility o f t h e a i r . For H = 11,000 m, t h e change i n n e u t r a l c e n t e r i n g from 42 t o 49% mac n o t e d i s explained by a displacement o f t h e c e n t e r o f p r e s s u r e o f t h e wing t o t h e rear a t M numbers g r e a t e r t h a n t h e c r i t i c a l M number of t h e wing p r o f i l e (approximately M > 0.7-0.72). A f t e r determining t h e f a r t h e s t forward p o s i t i o n o f t h e n e u t r a l c e n t e r i n g , t h e l i m i t i n g rearward c e n t e r i n g f o r o p e r a t i o n i s defined 10-12% less t h a n n e u t r a l c e n t e r i n g . The d i s t a n c e between t h e n e u t r a l and l i m i t i n g r e a r c e n t e r i n g i s c a l l e d t h e r e s e r v e of s t a b i l i t y f o r c e n t e r i n g . 96. Longitudinal Equilibrium Figure 123. Diagram o f Forces and Moments Act i n g on A i r c r a f t About Transverse Axis The p i l o t m a i n t a i n s l o n g i t u d i n a l e q u i l i b r i u m o r b a l a n c i n g by u s i n g t h e e l e v a t o r and s e l e c t i n g t h e n e c e s s a r y motor t h r u s t . Any s t a b l e f l i g h t regime i s c h a r a c t e r i z e d by angle of a t t a c k a , f l i g h t speed V , a l t i t u d e H and t h e a n g l e of t r a j e c t o r y i n c l i n a t i o n 0. I n o r d e r t o achieve l o n g i t u d i n a l e q u i l i b r i u m o f t h e a i r c r a f t , t h e f o r c e s a c t i n g i n t h e d i r e c t i o n s o f t h e ox and oy axes and t h e moments o f t h e s e f o r c e s a c t i n g r e l a t i v e t o t h e oz a x i s must be i n e q u i l i b r i u m (Figure 123). I n h o r i z o n t a l f l i g h t , t h r e e c o n d i t i o n s o f e q u i l i b r i u m must b e observed. /192 The f i r s t c o n d i t i o n i s : t h e l i f t i n g f o r c e of t h e a i r c r a f t Y must b e equal t o i t s weight. W know t h a t t h e l i f t i n g f o r c e of an a i r c r a f t i s c r e a t e d by t h e wing, e h o r i z o n t a l t a i l s u r f a c e and p a r t i a l l y by t h e engine n a c e l l e s . The l i f t i n g 188
- 200. f o r c e c r e a t e d by t h i s f u s e l a g e i s r e l a t i v e l y s l i g h t , and i s considered t o b e p a r t o f t h e l i f t i n g f o r c e of t h e wing. As w e can see from t h e f i g u r e , t h e s e f o r c e s create moments about t h e t r a n s v e r s e a x i s which d e c r e a s e o r i n c r e a s e t h e angle o f a t t a c k . The l i f t i n g f o r c e of t h e wing i n c r u i s i n g f l i g h t c r e a t e s n e g a t i v e p i t c h moment MZw = YwZ. The l i f t i n g f o r c e o f t h e h o r i z o n t a l t a i l s u r f a c e i s d i r e c t e d downward, and i n a l l f l i g h t regimes used i n p r a c t i c e c r e a t e s t h e p i t c h moment In o r d e r f o r f o r c e Yht t o b e n e g a t i v e , t h e angle of a t t a c k of t h e h o r i z o n t a l t a i l s u r f a c e aht must a l s o be n e g a t i v e . A s we can see from F i g u r e 124, a < a by t h e angle o f downwash of t h e ht w stream E ( t h e downwash o f t h e s t r e a m r e s u l t s from t h e a c t i o n o f t h e a i r c r a f t ht wing on t h e a i r stream). Also, a i s i n f l u e n c e d by t h e angle of t h e ht s t a b i l i z e r C$ ( g e n e r a l l y zero t o - 4 ' ) . Thus, a = a + C$ - ht w chord stabi 1 izer -4 / wing I di'rection o f chord w i n g chord , / s t a b i 1 i zed chord Figure 124. Determination of A n g l e of Attack of Horizontal Tai 1 S u r f a c e ( r 2 e q u a l s r e f e r e n c e l i n e of a i r c r a f t ; V equals f l i g h t speed; VI equals v e l o c i t y of d i v e r t e d stream) For o r d i n a r y a i r c r a f t with t h e s t a b i l i z e r on t h e f u s e l a g e a t a f l i g h t speed o f M = 0.75-0.85 and c = 0.3-0.4, E = 2-3'. For example, w i t h aw = 3 " , Y E = 2.68' and C$ = -2', a n g l e a = 3' - 2' - 2.68' = - 1.68'. The g r e a t e r t h e angle of a t t a c k ( g r e a t e r t h e l k h i n g c a p a c i t y o f t h e wing), t h e g r e a t e r t h e downwash angle of t h e a i r stream. I n o r d e r t o determine t h e summary l o n g i t u d i n a l moment a c t i n g on t h e - /193 a i r c r a f t , w must add t h e l o n g i t u d i n a l moment r e s u l t i n g from engine t h r u s t e 189
- 201. (M ) t o t h e moments of t h e wings and h o r i z o n t a l t a i l s u r f a c e . z en The axis of an engine l o c a t e d i n t h e r e a r p o r t i o n o f t h e f u s e l a g e is placed above t h e c e n t e r of g r a v i t y of t h e a i r c r a f t ; t h e r e f o r e , t h e t h r u s t o f t h e motors creates a d i v i n g moment M = P 2 Zen en en' Thus, t h e summary l o n g i t u d i n a l moment a c t i n g on t h e a i r c r a f t i s d e t e r mined by t h e sum of t h e l o n g i t u d i n a l moments o f t h e wing, h o r i z o n t a l t a i l s u r f a c e and motor t h r u s t . E q u a l i t y of t h e l o n g i t u d i n a l moment t o zero i s t h e second c o n d i t i o n of e q u i 1ibrium. The t h i r d c o n d i t i o n f o r l o n g i t u d i n a l e q u i l i b r i u m of an a i r c r a f t i s e q u i l i b r i u m o f t h e f o r c e s a c t i n g i n t h e d i r e c t i o n of t h e ox a x i s . I n o r d e r f o r t h i s c o n d i t i o n t o be f u l f i l l e d , t h e t h r u s t o f t h e engines must b e equal t o t h e drag of t h e a i r c r a f t : Pen = Q. I f t h i s c o n d i t i o n i s n o t f u l f i l l e d , t h e movement of t h e a i r c r a f t w i l l be a c c e l e r a t e d o r d e c e l e r a t e d and, consequently, t h e l i f t i n g f o r c e w i l l b e changed and t h e f l i g h t t r a j e c t o r y w i l l curve. These t h r e e c o n d i t i o n s f o r l o n g i t u d i n a l b a l a n c i n g o f t h e a i r c r a f t are f u l f i l l e d by varying t h e p o s i t i o n of t h e e l e v a t o r by t h e r e q u i r e d angle and by a d j u s t i n g engine t h r u s t , depending on v e l o c i t y , a l t i t u d e , f l y i n g weight, c e n t e r i n g , e t c . W n o t e t h a t when e q u i l i b r i u m c o n d i t i o n s a r e f u l f i l l e d , t h e e r e s u l t a n t of t h e aerodynamic f o r c e s and t h e t h r u s t of t h e engines can be considered t o be a p p l i e d t o t h e c e n t e r o f g r a v i t y of t h e a i r c r a f t , and a l l f o r c e s a r e balanced, i . e . , Pen = Q and Y = G . Therefore, t h e s e f o r c e s w i l l n o t be shown on f i g u r e s i n t h e following, o n l y t h e a d d i t i o n a l f o r c e s and moments and t h e i r increments a r i s i n g under t h e i n f l u e n c e o f p e r t u r b a t i o n s being shown. 57. S t a t i c Longitudinal Overload S t a b i l i t y A d i s r u p t i o n i n l o n g i t u d i n a l s t a b i l i t y o f an a i r c r a f t i s accompanied by a change i n t h e angle o f a t t a c k a t f l i g h t speed, t h e angle of a t t a c k changing a t f i r s t more r a p i d l y t h a n v e l o c i t y . Subsequently, on t h e o t h e r hand, t h e speed changes more r a p i d l y . For example, by p u l l i n g t h e s t i c k toward himself q u i c k l y , t h e p i l o t can i n c r e a s e t h e angle o f a t t a c k by a f a c t o r of two o r t h r e e times o r more. However, i n o r d e r f o r t h e a i r c r a f t t o change i t s f l i g h t speed by 1 . 5 times, he must use n o t a f r a c t i o n o f a second, b u t dozens of seconds o r even s e v e r a l minutes. This s h a r p d i f f e r e n c e i n t h e n a t u r e of t h e change i n angle of a t t a c k and v e l o c i t y when l o n g i t u d i n a l e q u i l i b r i u m i s d i s r u p t e d has made it necessary t o d i s t i n g u i s h between l o n g i t u d i n a l angle of a t t a c k s t a b i l i t y (overload s t a b i l i t y ) and v e l o c i t y s t a b i l i t y . The s t a b i l i t y of t h e a i r c r a f t i n t h e f i r s t moment a f t e r e q u i l i b r i u m i s d i s r u p t e d i s c h a r a c t e r i z e d by i t s angle of a t t a c k s t a b i l i t y o r overload 190
- 202. s t a b i l i t y . This name i s given t o t h i s form of s t a b i l i t y s i n c e when t h e angle o f a t t a c k i s i n c r e a s e d o r decreased ( a t c o n s t a n t v e l o c i t y ) t h e l i f t i n g f o r c e i s changed, s o t h a t t h e overload i s a l s o changed. The v a l u e of t h e overload shows t h e e x t e n t t o which t h e e x t e r n a l load i s g r e a t e r t h a n t h e weight of t h e a i r c r a f t . The overload i s always r e l a t e d t o t h e d i r e c t i o n i n which i t i s b e i n g analyzed. I n f l i g h t , t h e e x t e r n a l loads a c t i n g on t h e ox and oz axes a r e s l i g h t . Thus, t h e d r a g o f t h e a i r c r a f t , which i s 10-12 times less t h a n t h e weight o f t h e a i r c r a f t , acts along t h e ox a x i s ; t h e loads a r i s i n g only d u r i n g s l i p p i n g o r as a r e s u l t o f s i d e wind g u s t s act along t h e oz a x i s . - - V __c ---f &kcen te r wing chord f i g u r e 125. Forces Acting on A i r c r a f t Entering a V e r t i c a l Wind Gust Therefore, t h e main overload i s t h a t a c t i n g i n t h e d i r e c t i o n o f t h e oy axis. I n t h i s c a s e , t h e e x t e r n a l load i s t h e l i f t of t h e a i r c r a f t Y and I f c o n s t a n t c i s maintained a t t h e given a i r c r a f t speed, t h e l i f t i n g f o r c e Y w i l l a l s o b e c o n s t a n t . The overload w i l l a l s o be unchanged, equal t o z e r o . A a i r c r a f t i s c a l l e d overload s t a b l e i f it tends t o r e t a i n t h e overload n of t h e i n i t i a l f l i g h t regime independently, without i n t e r f e r e n c e by t h e p i l o t . I f an a i r c r a f t i s overload s t a b l e , when t h e angle of a t t a c k i s changed t h e moments change so t h a t t h e r o t a t i o n of t h e a i r c r a f t which t h e y cause r e s u l t s i n disappearance of t h e a d d i t i o n a l overload. Let us assume t h a t an a i r c r a f t i n s t r a i g h t and l e v e l f l i g h t with an overload n = 1 and v e l o c i t y V Y e n t e r s an ascending c u r r e n t with v e l o c i t y W (Figure 125). This causes t h e d i r e c t i o n of t h e r e s u l t i n g v e l o c i t y t o b e changed, causing an i n c r e a s e i n t h e angle of a t t a c k and an i n c r e a s e i n l i f t i n g f o r c e AY (always a t t h e aerodynamic 191
- 203. c e n t e r ) o r an i n c r e a s e i n overload An = AY/G. I f f o r c e AY causes a d i v i n g Y r o t a t i o n o f t h e a i r c r a f t , t h e a i r c r a f t i s s t a b l e . A s w e can s e e from t h e - /195 f i g u r e , t h i s w i l l r e s u l t i f t h e c e n t e r of g r a v i t y o f t h e a i r c r a f t i s l o c a t e d i n f r o n t of t h e aerodynamic c e n t e r . Consequently, t h e appearance of a d i v i n g moment when t h e a n g l e of a t t a c k i s i n c r e a s e d i s a c h a r a c t e r i s t i c o f overload s t a b i l i t y of t h e a i r c r a f t . If t h e e x t e r n a l a c t i o n l e d t o a d e c r e a s e i n t h e a n g l e of a t t a c k , a p i t c h i n g moment would a r i s e which would t e n d t o i n c r e a s e t h e a n g l e o f a t t a c k , i . e . , r e s t o r e t h e i n i t i a l overload regime. With a c e r t a i n p o s i t i o n of t h e c e n t e r of g r a v i t y ( a t t h e aerodynamic c e n t e r ) , t h e a i r c r a f t w i l l n o t r e a c t t o d i s r u p t i o n of e q u i l i b r i u m and w i l l show no tendency e i t h e r t o r e t u r n t o i n i t i a l o v e r l o a d o r t o f u r t h e r movement away from t h e i n i t i a l v a l u e . This p o s i t i o n o f t h e c e n t e r o f g r a v i t y , as was d i s c u s s e d above, i s c a l l e d n e u t r a l c e n t e r i n g . Movement of t h e c e n t e r of g r a v i t y t o t h e r e a r , behind n e u t r a l c e n t e r i n g , r e s u l t s i n t h e appearance of overload i n s t a b i l i t y of t h e a i r c r a f t , s i n c e f o r c e AY w i l l cause an i n c r e a s e i n t h e p i t c h moment a r i s i n g when e q u i l i b r i u m i s d i s r u p t e d . Thus, overload s t a b i l i t y of t h e a i r c r a f t w i l l b e c h a r a c t e r i z e d by t h e p o s i t i o n of t h e c e n t e r o f g r a v i t y of t h e a i r c r a f t r e l a t i v e t o t h e n e u t r a l c e n t e r i n g o r t h e aerodynamic c e n t e r . T h e r e f o r e , i n a d d i t i o n t o l e a d i n g c e n t e r i n g , which d e f i n e s t h e c a p a b i l i t y of b a l a n c i n g o f t h e a i r c r a f t i n f l i g h t and during landing w i t h maximum displacement of t h e e l e v a t o r , we a i s 0 determine p e r m i s s i b l e rear c e n t e r i n g from t h e c o n d i t i o n of p r o v i s i o n of normal overload s t a b i l i t y f o r t h e a i r c r a f t ' . W can see from our a n a l y s i s t h a t a change i n overload s t a b i l i t y i n e f l i g h t may r e s u l t from a change i n t h e p o s i t i o n of t h e c e n t e r of g r a v i t y , as well as a change i n n e u t r a l c e n t e r i n g - - t h e aerodynamic c e n t e r of t h e a i r c r a f t . The n e u t r a l c e n t e r i n g o f t h e a i r c r a f t may change i n f l i g h t as t h e v e l o c i t y o r engine o p e r a t i n g mode i s changed, a s w e l l as when c o n t r o l i s r e l e a s e d . I f overload s t a b i l i t y i n c r e a s e s with unchanged c e n t e r of g r a v i t y , t h i s i n d i c a t e s an i n c r e a s e i n t h e d i s t a n c e between t h e c e n t e r of g r a v i t y and n e u t r a l c e n t e r i n g . On t h e o t h e r hand, i f overload s t a b i l i t y d e c r e a s e s , t h e d i s t a n c e between t h e c e n t e r of g r a v i t y and n e u t r a l c e n t e r i n g must b e decreased. A s a r u l e , n e u t r a l c e n t e r i n g s a r e determined f o r a i r c r a f t with f i x e d e l e v a t o r ; i f t h e c o n t r o l i s r e l e a s e d , c e n t e r i n g i s moved forward by approx imately 1-2% mac. The o p e r a t i n g mode o f t h e engine i n f l u e n c e s t h e l o n g i t u d i n a l s t a b i l i t y of t h e a i r c r a f t t o o v e r l o a d s . I n j e t a i r c r a f t , t h e downwash of t h e a i r stream i n t h e a r e a of t h e s t a b i l i z e r changes n o t only under t h e i n f l u e n c e of t h e wing, b u t a l s o due t o t h e e f f e c t of t h e exhaust gases of t h e j e t engine on t h e surrounding medium. The stream l e a v i n g t h e engine a t high v e l o c i t y a t t r a c t s a c e r t a i n amount o f t h e surrounding a i r along with i t . This surrounding a i r changes t h e d i r e c t i o n o f t h e s t r e a m a s it approaches i t . Usually, t h e 192
- 204. h o r i z o n t a l t a i l s u r f a c e i s l o c a t e d above t h e stream (Figure 126), and t h e r e s u l t a n t of t h e a i r flow toward t h e stream d e c r e a s e s t h e a n g l e of a t t a c k of t h e h o r i z o n t a l t a i l s u r f a c e (makes t h e stream downwash more n e g a t i v e ) . /196 During a climb, t h e o p e r a t i n g regime of t h e engines i s nominal and t h e stream l e a v i n g t h e motor i s a t i t s h i g h e s t power l e v e l . The downwash of t h i s stream i s t h e n maximal and d e c r e a s e s t h e angle o f a t t a c k o f t h e h o r i z o n t a l t a i l s u r f a c e s i g n i f i c a n t l y (makes t h e a n g l e of a t t a c k a considerably ht negative). When t h e angle o f a t t a c k o f t h e wing i s i n c r e a s e d ( a i r c r a f t e n t e r s a v e r t i c a l wind g u s t ) t h e a n g l e of a t t a c k o f t h e ' h o r i z o n t a l t a i l s u r f a c e becomes more n e g a t i v e due t o t h e i n c r e a s e d downwash o f t h e stream r e s u l t i n g from t h e change i n l i f t o f t h e wing and a l s o from t h e stream o f gases. The r e s u l t a n t of t h e i n c r e a s e i n l i f t i n g f o r c e of t h e h o r i z o n t a l t a i l s u r f a c e AYht, a p p l i e d a t i t s aerodynamic c e n t e r and d i r e c t e d downward, w i l l d e c r e a s e t h e r e s t o r i n g moment of t h e h o r i z o n t a l t a i l s u r f a c e and make t h e a i r c r a f t less e f f e c t i v e i n r e t u r n i n g t o i t s i n i t i a l f l i g h t regime. This i n d i c a t e s t h e d e c r e a s e i n l o n g i t u d i n a l s t a b i l i t y r e s e r v e , i . e . , t h e aerodynamic c e n t e r of t h e a i r c r a f t i s moved forward along t h e cord a s a r e s u l t o f t h e engines o p e r a t i n g a t high t h r u s t . F i g u r e 126. P u m p i n g E f f e c t o f J e t Engine Exhaust Gas Stream on Surrounding Air Stream When g l i d i n g a t low engine s e t t i n g , t h e i n f l u e n c e of t h e stream from t h e engines can be ignored. I n t h i s c a s e , t h e downwash of t h e stream on t h e s t a b i l i z e r w i l l b e determined by t h e i n f l u e n c e of t h e wing alone. The angle of a t t a c k of t h e h o r i z o n t a l t a i l s u r f a c e i n c r e a s e s (becomes l e s s n e g a t i v e ) and i t s e f f e c t i v e n e s s i s i n c r e a s e d . Longitudinal o v e r l o a d s t a b i l i t y of t h e a i r c r a f t is increased. This increase i n a i r c r a f t s t a b i l i t y i s equivalent t o a displacement o f t h e n e u t r a l c e n t e r i n g of t h e a i r c r a f t (aerodynamic c e n t e r ) backward along t h e mac. This i s why a i r c r a f t s t a b i l i t y i s s l i g h t l y lower i n a climb t h a n i n a g l i d e . Overload s t a b i l i t y of t h e a i r c r a f t can b e e s t i m a t e d by t h e overload f o r c e g r a d i e n t APel/Any. 193
- 205. 58. Diagrams of Moments /197 The degree of l o n g i t u d i n a l s t a b i l i t y o f an a i r c r a f t i s determined by wind t u n n e l t e s t i n g . Models are t e s t e d w i t h v a r i o u s d e f l e c t i o n s of t h e e l e v a t o r , and t h e l o n g i t u d i n a l moment M i s measured u s i n g s p e c i a l scales. By Z determining moment M a t s e v e r a l s e q u e n t i a l a n g l e s o f a t t a c k , w e can c o n s t r u c t Z graphs c a l l e d moment diagrams mZ = f(a) f o r v a r i o u s M numbers (Figure 127). m*ipi 4’ tch M=qS Figure 127. C o e f f i c i e n t o f Longitudinal Moment mZ A s a Function of A n g l e o f Attack ( 6 e l = 0) The l o n g i t u d i n a l moment c o e f f i c i e n t ( a dimensionless q u a n t i t y such as cx and c ) can b e determined u s i n g t h e following formula: Y The p i t c h moments may b e e i t h e r p o s i t i v e o r n e g a t i v e . A c t u a l l y , i n f l i g h t t h e e l e v a t o r always h a s some b a l a n c i n g d e f l e c t i o n . The angle of a t t a c k a t which mZ = O ( M = 0 ) i s c a l l e d balanced, s i n c e a t t h i s Z angle a t h e a i r c r a f t i s i n t h e s t a t e of e q u i l i b r i u m . As we can s e e , as t h e angle of a t t a c k i s i n c r e a s e d t o c1 ) the a i r c r a f t acts stably, since sup(cy sup t h e d i v i n g moment which a r i s e s causes it t o r e t u r n t o i t s i n i t i a l p o s i t i o n . A random d e c r e a s e i n t h e angle o f a t t a c k by -Aa causes a p o s i t i v e p i t c h moment((+m ) which r e t u r n s t h e a i r c r a f t t o i t s i n i t i a l e q u i l i b r i u m p o s i t i o n , c o r r e s p o n h g t o location of t h e center of gravity i n f r o n t o f t h e aero dynamic c e n t e r . S e c t o r AB of curve mZ = f(a) corresponds t o i n s e n s i b l e e q u i l i b r i u m of t h e a i r c r a f t , s i n c e an i n c r e a s e i n t h e angle of a t t a c k causes no change i n t h e l o n g i t u d i n a l moment. S e c t o r BC of t h e moment diagram corresponds t o (over- /198 load) u n s t a b l e behavior of t h e a i r c r a f t : when t h e angle o f a t t a c k changes, an a d d i t i o n a l p o s i t i v e p i t c h moment a r i s e s , t e n d i n g t o i n c r e a s e it s t i l l f u r t h e r . 194
- 206. 59. S t a t i c Longitudinal Velocity S t a b i l i t y A v e l o c i t y s t a b l e a i r c r a f t i s one which r e s t o r e s i t s assigned v e l o c i t y without i n t e r f e r e n c e of t h e p i l o t a f t e r p e r t u r b a t i o n . For s i m p l i c i t y o f d i s c u s s i o n , w e can c o n s i d e r t h a t t h e angle of a t t a c k does n o t change when t h e v e l o c i t y i s changed. L e t u s assume t h a t an a i r c r a f t f l y i n g h o r i z o n t a l l y a t c o n s t a n t v e l o c i t y V begins t o descend f o r some r e a s o n (Figure 128 a ) . Due t o t h e d e s c e n t , it i n c r e a s e s i t s v e l o c i t y by AV. Figure 128. Behavior of A i r c r a f t After Random Descent ( a ) and F1 i g h t T r a j e c t o r y o f Velocity Unstable A i r c r a f t ( b ) I f angle of a t t a c k cy. or c remains unchanged, due t o t h e i n c r e a s e i n Y v e l o c i t y , t h e l i f t i n g f o r c e a l s o i n c r e a s e s by AY. Due t o t h i s , t h e t o t a l l i f t i n g f o r c e becomes g r e a t e r t h a n t h e weight components and t h e a i r c r a f t t r a j e c t o r y begins t o curve upward, t h e v e l o c i t y begins t o d e c r e a s e , and AY a l s o begins t o d e c r e a s e . A f t e r a c h i e v i n g i t s i n i t i a l a l t i t u d e ( p o i n t c) t h e a i r c r a f t w i l l have i t s i n i t i a l v e l o c i t y V , b u t i t s t r a j e c t o r y w i l l be curved s l i g h t l y upward. T h e r e f o r e , t h e a i r c r a f t w i l l c o n t i n u e t o climb. Due t o t h e i n c r e a s e i n a l t i t u d e , t h e v e l o c i t y w i l l begin t o d e c r e a s e , i . e . , AV w i l l become n e g a t i v e . This makes AY n e g a t i v e , and t h e t r a j e c t o r y begins t o curve downward, e t c . T h u s , t h e a i r c r a f t w i l l o s c i l l a t e . I f t h e a i r c r a f t i s v e l o c i t y s t a b l e , t h e s e o s c i l l a t i o n s w i l l be damped and t h e a i r c r a f t w i l l come out o f o s c i l l a t i o n s a t i t s i n i t i a l a l t i t u d e and v e l o c i t y . O s c i l l a t i o n damping occurs due t o t h e f a c t t h a t t h e f o r c e s involved i n t h e o s c i l l a t i n g p r o c e s s a r e always d i r e c t e d s o a s t o even t h e t r a j e c t o r y . As w e can see from t h e figure, when t h e t r a j e c t o r y i s d e f l e c t e d downward and AV i s p o s i t i v e , p o s i t i v e increments AY a r e a l s o produced; when t h e t r a j e c t o r y d e f l e c t s upward and AV i s n e g a t i v e , n e g a t i v e AY r e s u l t s . N a t u r a l l y , i n p r a c t i c e t h e p i l o t w i l l n o t w a i t u n t i l t h e o s c i l l a t i o n s damp o u t of t h e i r own accord. H e t a k e s c o n t r o l of t h e a i r c r a f t and immediately e l i m i n a t e s them. 195
- 207. However, i t sometimes occurs t h a t , i n s p i t e o f an i n c r e a s e i n v e l o c i t y , t h e l i f t i n g f o r c e i s not i n c r e a s e d , b u t r a t h e r decreased, s i n c e t h e l i f t i n g f o r c e depends n o t only on v e l o c i t y , but a l s o on c Y . Due t o t h e i n f l u e n c e of c o m p r e s s i b i l i t y i n f l i g h t a t l a r g e M numbers o r due t o e l a s t i c deformations, c may i n c r e a s e s o s h a r p l y with i n c r e a s e d v e l o c i t y t h a t t h e l i f t i n g f o r c e Y decreases r a t h e r than i n c r e a s e s . I n t h i s c a s e , t h e f l i g h t t r a j e c t o r y w i l l curve e v e r more s h a r p l y downward ( i f t h e p i l o t does not t a k e c o n t r o l o f t h e a i r c r a f t q u i c k l y u s i n g t h e e l e v a t o r ) , t h e speed w i l l i n c r e a s e and t h e a i r c r a f t w i l l go i n t o a d i v e (Figure 128 b ) . No r e t u r n t o t h e i n i t i a l p o s i t i o n occurs. Figure 129. Dependence o f Force on Elevator Control on M Number (nominal mode, h o r i z o n t a l f l i g h t , H = 1 0 , 0 0 0 m y tremor d e f l e c t e d by T = 2 . 3 " ) I t i s e a s i e s t f o r t h e p i l o t t o judge v e l o c i t y s t a b i l i t y from t h e n a t u r e of t h e change i n f o r c e s on t h e c o n t r o l s t i c k when t h e a i r c r a f t v e l o c i t y o r M numher changes. A s we know, balancing o f an a i r c r a f t a t v a r i o u s speeds of h o r i z o n t a l f l i g h t r e q u i r e s varying f o r c e on t h e s t i c k . Figure 129 shows t h e f o r c e s r e q u i r e d t o balance t h e a i r c r a f t a t various M nbmbers (see 510 of t h i s c h a p t e r ) . Thus, where ?- = 28% mac and M = 0.62, t t h e f o r c e on t h e s t i c k i s equal t o zero, s i n c e t h e a i r c r a f t i s balanced by t h e trimmer and, consequently, t h e s t i c k can be r e l e a s e d i n t h i s p o s i t i o n . This i s t h e balanced regime. A s t h e a i r c r a f t a c c e l e r a t e s t o l a r g e M numbers, p r e s s u r e f o r c e s w i l l a r i s e on t h e s t i c k ( i f t h e trimmer i s l e f t i n i t s i n i t i a l p o s i t i o n ) , i n d i c a t i n g t h a t t h e a i r c r a f t i s v e l o c i t y s t a b l e . Actually, suppose t h e M number i n c r e a s e s t o 0 . 7 4 . W can s e e from t h e graph t h a t i n e o r d e r t o hold t h i s new speed (M = 0.74), t h e p i l o t must apply a p r e s s u r e o f - /200 P = +10 kg t o t h e s t i c k , i . e . , c r e a t e a d i v i n g moment with t h e e l e v a t o r i n o r d e r t o balance t h e p o s i t i v e p i t c h which has a r i s e n . W can conclude from t h e above t h a t if a t M = 0.62 with t h e s t i c k e r e l e a s e d , a random i n c r e a s e i n M number t o 0 . 7 4 o c c u r s , a p o s i t i v e p i t c h moment should a c t on t h e a i r c r a f t , i n c r e a s i n g t h e angle of a t t a c k , and t h e a i r c r a f t w i l l r e t u r n without i n t e r f e r e n c e from t h e p i l o t t o i t s i n i t i a l v e l o c i t y (M = 0 . 6 2 ) . Consequently, t h i s a i r c r a f t i s v e l o c i t y s t a b l e . A similar p i c t u r e w i l l occur i f t h e v e l o c i t y i s decreased. 196
- 208. A t Mach numbers M > 0.8, t h e c o m p r e s s i b i l i t y o f a i r begins t o have a s i g n i f i c a n t i n f l u e n c e , and t h e p r e s s u r e f o r c e r e s u l t a n t ( c e n t e r o f p r e s s u r e ) i s d i s p l a c e d rearward; an a d d i t i o n a l n e g a t i v e p i t c h moment begins t o act on t h e a i r c r a f t . Therefore, whereas a t M = 0.74, a f o r c e o f 10 kg must b e a p p l i e d t o t h e s t i c k , a t M = 0.82 t h e f o r c e w i l l only b e 8 kg, i . e . , t h e p r e s s u r e f o r c e on t h e s t i c k i s decreased, and some v e l o c i t y i n s t a b i l i t y appears. However, s i n c e t h e a i r c r a f t wing i s swept, t h e phenomenon o f p u l l i n g i n t o a d i v e (during a c c e l e r a t i o n ) , a p r o p e r t y of v e l o c i t y i n s t a b i l i t y , is not observed . A decrease i n pushing f o r c e i s observed i n a narrow range o f M numbers, then beginning a t M = 0.88-0.9, t h e f o r c e r e q u i r e d i n c r e a s e s once more, i n d i c a t i n g t h e appearance o f a c o n s i d e r a b l e p o s i t i v e p i t c h moment, i n c r e a s i n g with i n c r e a s i n g M number. 910. Longitudinal Controllability Longitudinal overload s t a b i l i t y determines t h e c h a r a c t e r i s t i c s of l o n g i t u d i n a l c o n t r o l l a b i l i t y of an a i r c r a f t , r e l a t e d t o r o t a t i o n of t h e a i r c r a f t about t h e o z a x i s and c r e a t i o n of overloads. I f t h e performance of a maneuver r e q u i r e s t h a t t h e overload be changed, t h e p i l o t should do t h i s by d e f l e c t i n g t h e e l e v a t o r , d i s r u p t i n g t h e equi librium and overcoming t h e moments attempting t o r e t u r n t h e a i r c r a f t t o i t s i n i t i a l overload. The primary moments p r e v e n t i n g r o t a t i o n o f t h e a i r c r a f t about t h e o z a x i s a r e : t h e a i r c r a f t overload s t a b i l i t y moment, t h e damping moment and t h e moment of i n e r t i a . The g r e a t e r t h e s e moments p r e v e n t i n g r o t a t i o n of t h e a i r c r a f t , t h e g r e a t e r t h e angle t o which t h e e l e v a t o r must be d e f l e c t e d and t h e g r e a t e r t h e f o r c e r e q u i r e d a t t h e c o n t r o l s t i c k i n o r d e r t o change t h e overload. Since t h e p i l o t f e e l s t h e value of f o r c e a p p l i e d t o t h e s t i c k and t h e overload r e s u l t i n g from i t , l o n g i t u d i n a l c o n t r o l l a b i l i t y of t h e a i r c r a f t can b e s t be e v a l u a t e d by t h e g r a d i e n t of overload f o r c e APel/Any and t h z e l e v a t o r t r a v e l used A6el/An . Y The overload f o r c e g r a d i e n t i s numerically equal t o t h e r a t i o of /201 a d d i t i o n a l f o r c e AP on t h e s t i c k t o t h e i n c r e a s e i n overload An produced as el Y a result of t h i s force. Let u s assume t h a t t h e a i r c r a f t i s performing h o r i z o n t a l f l i g h t and n = 1 (Figure 130). Then, i n o r d e r t o produce n = 2 , t h e p i l o t must p u l l Y Y t h e s t i c k toward himself with a f o r c e of 40-70 kg ( f o r small M numbers, 40 kg and f o r M = 0.7-0.8, 50-70 k g ) . Since overload s t a b i l i t y c h a r a c t e r i z e s t h e a b i l i t y of t h e a i r c r a f t t o r e t a i n t h e i n i t i a l overload regime, obviously t h e higher t h e s t a b i l i t y t h e g r e a t e r t h e force required at t h e control s t i c k t o 197
- 209. change t h e overload. W can a l s o see on e Figure 130 t h a t i f t h e c e n t e r i n g moves f u r t h e r forward, t h e f o r c e r e q u i r e d t o change n i n c r e a s e s . Y This i s explained by an i n c r e a s e i n t h e d i s t a n c e between t h e c e n t e r o f g r a v i t y of t h e a i r c r a f t and i t s aerodynamic c e n t e r . Thus, t h e f u r t h e r forward t h e centering of the a i r c r a f t , t h e h e a v i e r it i s t o c o n t r o l . The l i m i t i n forward c e n t e r i n g is s e l e c t e d from t h e c o n d i t i o n of a i r c r a f t b a l a n c i n g d u r i n g t a k e o f f and l a n d i n g . Figure 120. Overload Force Gradient AP /An and Elevator Travel I n o r d e r t o exclude (during el Y t a k e o f f ) s t r e a m s e p a r a t i o n from A6el/An As a Function of M Number the horizontal t a i l surface, the Y e l e v a t o r can be d e f l e c t e d 20-25" ( H = 10,000 m) upward. During landing, t h e p i l o t should i n c r e a s e c t o Y C B p u l l i n g t h e s t i c k toward h i m s e l f , h e i n c r e a s e s t h e angle of a t t a c k , y Y 1dg' c r e a t i n g p o s i t i v e p i t c h moments. When t h e angle o f a t t a c k i s i n c r e a s e d , an i n c r e a s e i n l i f t Ay o c c u r s , a p p l i e d t o t h e aerodynamic c e n t e r and c r e a t i n g a n e g a t i v e p i t c h moment opposing t h e p i l o t . The g r e a t e r t h e d i s t a n c e between t h e aerodynamic c e n t e r and t h e c e n t e r of g r a v i t y , t h e g r e a t e r t h i s h i n d e r i n g moment w i l l be. Since t h e movement of t h e e l e v a t o r i s c o n s i d e r a b l e a t low v e l o c i t i e s , i t may b e found t h a t t h e l i m i t n g d e f l e c t i o n of t h e e l e v a t o r i s i n s u f f i c i e n t t o t i l t t h e a i r c r a f t t o i t s landing a n g l e . Therefore, t h e maximum rearward p o s i t i o n of t h e c e n t e r of g r a v i t y i s f i x e d s o t h a t t h e p e r m i s s i b l e d e f l e c t i o n of t h e e l e v a t o r i s s u f f i c i e n t t o allow t h e p i l o t t o land. The usage of an a.djustable s t a b i l i z e r makes i t p o s s i b l e t o f l y i n a i r c r a f t with more forward c e n t e r i n g , s i n c e i n t h i s case t h e e f f e c t i v e n e s s of the elevator is increased. Usually, some r e s e r v e i n e l e v a t o r d e f l e c t i o n ( 3 - 4 " , b u t no l e s s t h a n 10% o f t h e complete d e f l e c t i o n o f t h e e l e v a t o r ) i s i n s t a l l e d . Let us now analyze t h e d e f l e c t i o n o f t h e e l e v a t o r A6el/Any necessary t o c r e a t e an a d d i t i o n a l u n i t of overload. A s we can s e e from Figure 130, as t h e v e l o c i t y i n c r e a s e s , t h e e f f e c t i v e n e s s of t h e e l e v a t o r s a l s o i n c r e a s e s s h a r p l y . 198
- 210. c For example, whereas a t M = 0.5, t h e e l e v a t o r must be d e f l e c t e d by 8" i n o r d e r t o cause a double overload, a t M = 0.78 t h e required deflection is only 4". The b a l a n c i n g curves, showing t h e 'h r dependence o f e 1e v a to r de f 1 t i on ec on M number, are a l s o used t o char a c t e r i z e longitud inal controllability Figure 131. Balancing Curves of Elevator (Figure 131). Deflection (produced a s a r e s u l t of f l y i n g t e s t s ) : a , I n s t r a i g h t f l i g h t a t nominal e n g i n e According t o o p e r a t i n g mode; b , Coming i n f o r a landing these curves, f o r example with r e a r c e n t e r i n g s (X = t = 28% mac), maintenance of l o n g i t u d i n a l e q u i l i b r i u m a t M = 0.62 r e q u i r e s t h a t t h e e l e v a t o r b e d e f l e c t e d from i t s n e u t r a l p o s i t i o n by 1 . 2 " downward; a t M = 0.74, 1.5" downward; a t M = 0.82, t h e b a l a n c i n g downward d e f l e c t i o n o f t h e /203 e l e v a t o r i s decreased s l i g h t l y , becoming once again +l. . 2 Thus, as t h e a i r c r a f t a c c e l e r a t e s from M = 0.62 t o M = 0.74, l o n g i t u d i n a l b a l a n c i n g r e q u i r e s t h a t t h e e l e v a t o r d e f l e c t i o n b e moved downward by 0 . 3 " , while f u r t h e r a c c e l e r a t i o n t o M = 0.82 r e q u i r e s t h a t it b e decreased by t h e same amount. Beginning a t M = 0.88-0.9, t h e p o s i t i v e p i t c h moment i n c r e a s e s s h a r p l y , and t h e e l e v a t o r must b e d e f l e c t e d c o n s i d e r a b l y downward. 511. Construction of Balancing Curve f o r Deflection of Elevator Using t h e moment diagrams f o r v a r i o u s d e f l e c t i o n s of t h e e l e v a t o r , we can determine-for t h e s e d e f l e c t i o n s c o e f f i c i e n t s c with mZ = O(cy , c ,... ,c 1 Y 1 y2 Yn and c o n s t r u c t t h e b a l a n c i n g diagram f o r d e f l e c t i o n of e l e v a t o r as a f u n c t i o n of c (Figure 132). The l e f t branch o f t h e graph ( l e f t of c ) can be Y y5 produced by wind t u n n e l t e s t i n g o f a model, while t h e r i g h t branch can only be produced i n t e s t f l i g h t s t e s t i n g t h e s t a b i l i t y and c o n t r o l l a b i l i t y o f t h e a i r c r a f t a t high angles of a t t a c k ; i n t h e s e t e s t s , t h e d e f l e c t i o n o f t h e e l e v a t o r a s a f u n c t i o n o f c i s determined f o r each M number. For t h i s , t h e Y 199
- 211. a i r c r a f t i s p l a c e d i n t h e regime c > c and h e l d i n t h i s regime u n t i l t h e Y Y SUP beginning o f "pickup," allowing US t o determine t h e degree of s t a b i l i t y of t h e a i r c r a f t and s u f f i c i e n c y of t h e e l e v a t o r s t o b r i n g t h e a i r c r a f t out of t h i s regime. The a i r c r a f t i s a l s o braked i n o r d e r t o determine t h e minimum v e l o c i t y and n a t u r e of i t s behavior a t t h i s v e l o c i t y . The b a l a n c i n g curves on Figure 133 g i v e us an i d e a o f t h e n a t u r e o f t h e dependence o f e l e v a t o r d e f l e c t i o n del f o r a i r c r a f t e q u i l i b r a t i o n with r e s p e c t t o l o n g i t u d i n a l moments a t s t a b l e f l i g h t regimes on coefficient c . Y A s we see, t h e s e curves a r e s i m i l a r i n form t o t h e moment diagram, f o r which p r o p o r t i o n a l i t y of the deflection of elevator t o t h e c o e f f i c i e n t of l o n g i t u d i n a l moment m is also characteristic. Z In o r d e r t o r e c o r d t h e d e f l e c t i o n s of t h e e l e v a t o r d u r i n g f l i g h t tests, the a i r c r a f t is accelerated t o Figure 132. Construction o f M = 0.65-0.85, and t h e n /204 Elevator D e f l e c t i o n Balancing a t c o n s t a n t M number, t h e e l e v a t o r i s D i ag ram "fed" toward t h e p i l o t i n o r d e r t o cause t h e a i r c r a f t t o climb. This "feeding" of t h e e l e v a t o r i s performed with c with c o n s t a n t i n c r e a s e i n o v e r l o a d n t o 2-3. Y SUP Y Let us analyze t h e movement of t h e a i r c r a f t upon t r a n s i t i o n t o l a r g e angles of a t t a c k ( c > c ) , when t h e p i l o t i s c o n t r o l l i n g t h e a i r c r a f t . Y Y SUP Let us assume t h a t as a r e s u l t of t h e i n f l u e n c e of a powerful ascending a i r c u r r e n t ( o r as a r e s u l t of c r e a t i o n of an overload i n a t e s t f l i g h t ) t h e aircraft arrives a t c > c (Figure 133). I t was noted i n c h a p t e r I1 t h a t Y1 YU P if c i s exceeded, l o n g i t u d i n a l s t a b i l i t y o f t h e a i r c r a f t may b e d i s - Y SUP r u p t e d , s i n c e as a r e s u l t of r e d i s t r i b u t i o n o f p r e s s u r e on t h e wing, s o - c a l l e d "capture" - - i n v o l u n t a r y p r o g r e s s i v e i n c r e a s e i n t h e angle o f a t t a c k - - occurs. The angle o f a t t a c k n e a r which "capture" occurs i s c a l l e d t h e "capture" angle of a t t a c k ( t h e c o e f f i c i e n t c and overload above which "capture" begins Y a r e named s i m i l a r l y ) . I f a t t h e moment of c a p t u r e t h e p i l o t moves t h e e l e v a t o r downward by , by t h e time t h e angle of a t t a c k c1 ( c ) i s achieved f o r which 6 *'el 1 1 Yl 200 I
- 212. . 8 max gel mac considering deformation t h e balancing /,////////, I , I , . . , ' / I/ / / L .,I'.I11111 / / / / / / / I / / / . I L deflection, further /205 1 i n c r e a s e i n t h e angle min of a t t a c k does n o t - -t4=@75 7 h occur and t h e a i r c r a f t _ _ _ M=a,S 2 :,/k g 1 i s balanced a t angle of -4 : I a t t a c k ct and w i l l 1 ________---- --- r e t a i n t h i s angle2. The behavior of an a i r c r a f t i n t h i s curved f l i g h t with n > 1 w i l l Y b e c h a r a c t e r i z e d by a tendency t o i n c r e a s e t h e p i t c h angle without i n c r e a s i n g t h e angle of attack. In order t o return Figure 133. Required Elevator Deflection As the aircraft t o its a Function of c i n i t i a l f l i g h t regime, Y t h e p i l o t s t i l l has t h e e l e v a t o r r e s e r v e A6 s e p a r a t i n g t h e balancing e l e v a t o r d e f i e c t i o n from t h e maximal d e f l e c t i o n , corresponding t o complete d e f l e c t i o n downward ( t o t h e s t o p ) . T'ne f u r t h e r t h e p i l o t moves t h e e1evato.r downward from t h i s balancing p o s i t i o n , t h e g r e a t e r t h e angular v e l o c i t y with which t h e a i r c r a f t w i l l begin t o decrease t h e angle of a t t a c k , i . e . , t h e more r a p i d l y t h e overload w i l l b e decreased t o u n i t y . A p o s i t i o n should not a r i s e i n which t h e r e q u i r e d downward e l e v a t o r d e f l e c t i o n t o r e s t o r e balancing is g r e a t e r than t h a t a v a i l a b l e , i n c l u d i n g c o n s i d e r a t i o n of deformation of f o r c e t r a n s m i t t i n g hardware. Otherwise, it w i l l be impossible t o balance t h e a i r c r a f t , and t h e p i l o t w i l l not be a b l e t o r e t u r n i t t o t h e i n i t i a l f l i g h t regime. Figure 133 shows t h a t with more forward c e n t e r i n g ( 2 5 % mac) t h e e l e v a t o r r e s e r v e i s g r e a t e r , and t h e c o n t r o l l a b i l i t y i s b e t t e r . This r e s u l t s from t h e f a c t t h a t with forward c e n t e r i n g i n t h e i n i t i a l balancing regime t h e e l e v a t o r c o n t r o l s t i c k must b e h e l d c l o s e r t o t h e p i l o t than with rearward c e n t e r i n g and, consequently, t h e e l e v a t o r r e s e r v e t o maximum d e f l e c t i o n i s i n c r e a s e d . I t has been noted i n t h e p r o c e s s of f l i g h t t e s t s t h a t a f t e r an a i r c r a f t i s put i n a high overload p o s i t i o n , s o a r i n g r e q u i r e s t h a t a p o s i t i v e p i t c h moment be c r e a t e d by applying a f o r c e of 80-100 kg t o t h e s t i c k . This f o r c e , which e q u a l i z e s t h e aerodynamic load a c t i n g on t h e d e f l e c t e d e l e v a t o r , deforms t h e f o r c e t r a n s m i t t i n g elements, s h o r t e n i n g them. A s a r e s u l t , f u l l forward d e f l e c t i o n of t h e s t i c k d i d not r e s u l t i n f u l l d e f l e c t i o n o f t h e e l e v a t o r . With maximum d e f l e c t i o n s o f t h e e l e v a t o r (29-31O) t h e a c t u a l angle of p o s i t i o n M. V . Rozenblat, PiZoter o Peregrazke [To t h e P i l o t Concerning Overloading], k r o f l o t Redizdat P r e s s , 1964. 201
- 213. was only 24-25", due t o deformation (Figure 134). The only method of c r e a t i n g a r e s e r v e o f e l e v a t o r movement f o r a i r c r a f t c o n t r o l i n t h i s case i s unloading of t h e c o n t r o l c a b l e by u s i n g t h e e l e v a t o r trimmer. When t h e trimmer o f t h e e l e v a t o r i s d e f l e c t e d , t h e h i n g e moments d e c r e a s e , and t h e d e f l e c t i o n of t h e e l e v a t o r i s i n c r e a s e d as a r e s u l t of unloading o f t h e c o n t r o l c a b l e s . During t h e p r o c e s s of f l i g h t t e s t s o f an a i r c r a f t a t h i g h a n g l e s of a t t a c k , t h e f o l l o w i n g p e c u l i a r i t y was discovered. W know t h a t when a back- e swept wing moves a t high a n g l e s o f a t t a c k , flow s e p a r a t i o n b e g i n s where t h e a i l e r o n s a r e l o c a t e d . This l e a d s t o a change i n t h e a i l e r o n hinge moment such t h a t b o t h a i l e r o n s t e n d t o move upward by approximately 2-4". This phenomenon /206 h a s come t o be c a l l e d " f l o a t i n g " o f t h e a i l e r o n s . I n i t s e f f e c t , it i s e q u i v a l e n t t o an a d d i t i o n a l d e f l e c t i o n of t h e e l e v a t o r upward, s i n c e it causes an a d d i t i o n a l l o s s i n l i f t a t t h e t e r m i n a l p o r t i o n of t h e wing where the' l i f t p r o p e r t i e s a r e worsened by t h e s e p a r a t i o n . "Floating" o f a i l e r o n s worsens l o n g i t u d i n a l i n s t a b i l i t y o f t h e a i r c r a f t with swept wings a t high a n g l e s o f a t t a c k and makes c a p t u r e of t h e a i r c r a f t even s h a r p e r . The design- aerodynamic measures analyzed i n 53 of Chapter I11 improve t h e overload s t a b i l i t y c h a r a c t e r i s t i c s of a swept wing a i r c r a f t a t h i g h a n g l e s of a t t a c k . mechanical d e v i c e s o r by d e c r e a s i n g t h e s i z e of t h e a i l e r o n s . The c a b l e deformation A p i l o t flying a passenger a i r c r a f t with a swept wing should avoid a r e a s with s t r o n g t u r b u l e n c e , i n which t h e c h a r a c t e r i s t i c s of l o n g i t u d i n a l overload s t a b i l i t y appear s o unfavorably. 202
- 214. 112. Vertical G u s t s . P e r m i s s i b l e M Number i n Cruising F l i g h t During f l i g h t through atmospheric t u r b u l e n c e , i n t e n s i v e and f r e q u e n t v e r t i c a l g u s t s o f a i r r e s u l t i n l a r g e l o n g i t u d i n a l and l a t e r a l o s c i l l a t i o n s of t h e a i r c r a f t . The a c c e l e r a t i o n s a r i s i n g i n t h i s case l e a d t o t h e appearance o f i n e r t i a l f o r c e s c h a r a c t e r i z e d by overloads on t h e a i r c r a f t . A v e r t i c a l /207 g u s t i s a v e r t i c a l a i r movement r e s u l t i n g i n an i n c r e a s e i n overload i n n o t over 2 sec. The h o r i z o n t a l components of wind g u s t s have no e s s e n t i a l s i g n i f i c a n c e f o r t h e movement o f t h e a i r c r a f t . For example, h o r i z o n t a l wind g u s t s up t o 6-15 m/sec cause s l i g h t v e l o c i t y p u l s a t i o n s i n modern a i r c r a f t f l y i n g between 200 and 250 m/sec, and c r e a t e s l i g h t o v e r l o a d s , whereas v e r t i c a l wind g u s t s a t t h e s e speeds cause 10-15 times more overloading 3 . Longitudinal overloading ( o r more a c c u r a t e l y an increment i n overloading) a c t i n g i n t h e h o r i z o n t a l p l a n e can be determined according t o t h e following formula : An,=-, AV gAf where AV i s t h e change i n v e l o c i t y r e s u l t i n g from an oncoming g u s t ; A t i s t h e time of a c t i o n of t h e g u s t . Thus, i f a h o r i z o n t a l wind g u s t causes a v e l o c i t y v a r i a t i o n of 11 m/sec i n two seconds, t h e increment t o t h e l o n g i t u d i n a l o v e r l o a d w i l l be An X = 11/2-9.81 = 0.56; with a t i m e of a c t i o n o f t h r e e seconds, AnX = 0.37. The s i g n of t h e o v e r l o a d w i l l depend on whether t h e g u s t i s a headwind o r t a i l w i n d . I n t h e case of a headwind g u s t , t h e s i g n w i l l b e p l u s ( t h e crew and passengers w i l l b e p r e s s e d a g a i n s t t h e backs of t h e i r s e a t s ) , and with a t a i l w i n d g u s t t h e s i g n w i l l be minus ( t h e crew and passengers w i l l be p u l l e d away from t h e backs of t h e i r s e a t s ) . What must t h e v e l o c i t y of a v e r t i c a l g u s t be i n o r d e r f o r t h e a i r c r a f t t o b e brought t o c o r t o t h e mode of i n v o l u n t a r y i n c r e a s e i n overload Y SUP ("captureIf)? As we can s e e from Figure 135, a t M = 0 . 8 when a g u s t of W i sup' an a i r c r a f t with an i n i t i a l v a l u e of c w i l l reach c while t h e e f f e c t s Y f h Y SUP' of a g u s t a t Wi capt w i l l cause it t o r e a c h c I n t h i s case, t h e y capt' b a l a n c i n g p o s i t i o n of t h e e l e v a t o r w i l l b e i n s u f f i c i e n t t o r e t u r n t h e a i r c r a f t t o i t s i n i t i a l parameters. I n o r d e r t o estimate t h e e f f e c t s of a v e r t i c a l a i r stream on t h e wings of /208 an a i r c r a f t , we must u s e t h e s o - c a l l e d v e l o c i t y o f t h e e f f e c t i v e g u s t . The i n d i c a t o r e f f e c t i v e g u s t Wief d i f f e r s from t h e r e a l i n d i c a t o r g u s t (measured under c o n c r e t e c o n d i t i o n s ) , s i n c e t h e r e are no s h a r p l y d i f f e r e n t i a t e d v e r t i c a l jKu 1 ik M . M . , Obosnovmiye rekomendatsky o P i Z o t i r o v m i y u Sam0 Zetov p& Poleta& v Zonakh Atmospernoy Turbulentnos% [Basis f o r Recommendat ions, f o r P t l g t j n g Aircrzjft on F1 i i h t s i ~ nZones of Atmospheric Turbulence] G Q s N I ( GA P r e s s , 1963. 203 I
- 215. movements i n t h e atmosphere, as a r e s u l t of t h e i n f l u e n c e of v i s c o s i t y of t h e a i r . There i s always a t r a n s i t i o n zone, i n which t h e r a t e of t h e v e r t i c a l component v a r i e s from zero t o some v a l u e Wief. Various a i r c r a f t with t h e i r inherent s p e c i f i c f e a t u r e s of aerodynamics r e a c t d i f f e r e n t l y t o t h e same g u s t . For example, it h a s been e s t a b l i s h e d t h a t f o r Figure 135. Determination of a i r c r a f t with swept wings, - Effective Indicator Vertical 'ief - = 1.11 wi. Gust Bringing A i r c r a f t to C and c * 1 , Initial Y SUP y capt' C a l c u l a t i o n o f t h e v e l o c i t y of an balancing regime; 2 , E f f e c t i v e e f f e c t i v e v e r t i c a l g u s t i s performed d i v i n g moment u s i n g t h e formula where Aa i s t h e i n c r e a s e i n a n g l e of a t t a c k c a l c u l a t e d from ci hf; V. i s t h e i n d i c a t o r v e l o c i t y of t h e a i r c r a f t . 1 Let us assume t h a t t h e p i l o t does not i n t e r f e r e i n c o n t r o l and t h a t t h e e l e v a t o r i s "clamped" i n t h e i n i t i a l balanced p o s i t i o n . L e t us c a l c u l a t e t h e g u s t speed W . required t o bring the a i r c r a f t t o c . The f l i g h t i s ief Y SUP performed a t c = 0.35 and ct = 3' a t M = 0.75 and H = 10,000 m. In t h i s Yhf case c = 0.715 and a = 7.2'. Let us determine: t h e increment of angle Y SUP SUP of a t t a c k Aci = 4 . 2 " o r 0.073 r a d , t h e i n d i c a t o r v e l o c i t y V . = 475 km/hr = 1 = 132.0 m/sec, s o Wief = 1.11 Vi& = 1.11*132.0.073 = 10.7 m/sec. The e f f e c t i v e i n d i c a t o r v e r t i c a l g u s t corresponding t o t h e beginning of i n v o l u n t a r y i n c r e a s e i n overload - - "capture" with f i x e d c o n t r o l -- is c a l c u l a t e d u s i n g t h e same formula, except t h a t t h e i n c r e a s e i n angle of a t t a c k i s s e l e c t e d from ahf t o t h e beginning of "capture." Thus, f o r t h e same c o n d i t i o n s Aa = 7", and Wief = 1.11-132*0.157 = 23 m/sec. When a v e r t i c a l g u s t a t 10.7 m/sec a c t s upon t h e a i r c r a f t , it goes t o C while where Wief = 2 3 m/sec, t h e "capture" regime i s begun, and a Y SUP' s e l f - s u s t a i n i n g i n c r e a s e i n overload and v i b r a t i o n of t h e e n t i r e a i r c r a f t occur. As we can see from Figure 136, a t M = 0.75, t h e r e s e r v e f o r a v e r t i c a l /209 g u s t f o r t h e weight and f l i g h t a l t i t u d e s h e r e analyzed i s maximal. A t 204
- 216. t M = 0.75-0.78, a s l i g h t reduction is -&. W1 e m/sec C=3Zm observed, and a t M > 0.78 t h i s r e s e r v e i s 26 ' Capture somewhat g r e a t e r . Thesefore, f o r t h i s +VOO" 24 22 20 - -: 10 000 _ / a i r c r a f t , t h e maximum p e r m i s s i b l e M number i n h o r i z o n t a l f l i g h t i s 0.78, i n o r d e r t o r e t a i n a s u f f i c i e n t l y high reserve of f8 '- 805 - 5 ! -.; ' v e r t i c a l gust s t a b i l i t y . 16 3% 5', I 14 .- §13. P e r m i s s i b l e Overloads During a 12 V e r t i c a l Maneuver If f 8 I n a d d i t i o n t o v e r t i c a l a i r g u s t s , an 6 , a i r c r a f t may be s u b j e c t e d t o t h e a c t i o n of 7 ---. extended ascending o r descending a i r 4 j_ operation o f , c u r r e n t s , which cause c o n s i d e r a b l e v e r t i c a l 2 AUAP displacement of t h e a i r c r a f t , independent 0 65 47 475 478 4 8 M of p i l o t a c t i o n . I n s t a b l e h o r i z o n t a l f l i g h t , t h e sum Figure 136. P e r m i s s i b l e of v e r t i c a l f o r c e s a c t i n g on t h e a i r c r a f t Effective Indicator i s equal t o zero and t h e overload V e r t i c a l Gust As a F u n c t i o n of M Number of Y n=-=l. F1 i g h t (TU-124 a i r c r a f t ) G When t h e a i r c r a f t c r o s s e s a v e r t i c a l g u s t , t h e angle of a t t a c k i n c r e a s e s r a p i d l y and consequently t h e l i f t i n g f o r c e i n c r e a s e s as w e l l . A l l of t h i s causes v e r t i c a l and a n g u l a r displacement of t h e a i r c r a f t , which i n t u r n once more i n f l u e n c e s t h e a n g l e of a t t a c k . I n t h i s c a s e , t h e overload The increment of overload An occurs as a r e s u l t of t h e summary increment of angle of a t t a c k r e s u l t i n g from t h e i n f l u e n c e of t h e v e r t i c a l gust and a n g u l a r displacement of t h e a i r c r a f t caused by t h e g u s t . The overload a c t i n g on t h e a i r c r a f t can be r e p r e s e n t e d i n t h i s c a s e by t h e following e x p r e s s i o n : 205 I
- 217. ( t h e lrplus'l s i g n r e l a t e s t o an ascending g u s t , t h e "minus" s i g n t o a descending g u s t ) , where ca i s t h e t a n g e n t of t h e a n g l e o f i n c l i n a t i o n o f curve c = f(a), i . e . , Y Y t h e g r a d i e n t o f t h e change i n c o e f f i c i e n t c as a f u n c t i o n o f angle of a t t a c k a; Y V. i s t h e i n d i c a t o r v e l o c i t y o f t h e a i r c r a f t ; 1 W . i s t h e i n d i c a t o r v e l o c i t y of t h e v e r t i c a l g u s t ; 1 K is a coefficient characterizing t h e increase i n t h e v e r t i c a l gust (K = 0.85-0.95). As w e can see from t h e formula, t h e o v e r l o a d a c t i n g on t h e a i r c r a f t depends on t h e f l i g h t speed and f o r c e of t h e v e r t i c a l g u s t . F l i g h t s o f high- speed a i r c r a f t a t high a l t i t u d e s have shown t h a t when t h e a i r c r a f t e n t e r s a v e r t i c a l gust with a c e r t a i n v e l o c i t y W t h e overload n ( r e l a t e d t o t h e - /210 i' W moment o f a c t i o n o f t h e g u s t ) i s much less t h a n na b u t even i n t h i s case y max' s e p a r a t i o n of t h e flow over t h e wing occurs, which may l e a d t o r o l l i n g of t h e a i r c r a f t . Usually, r o l l i n g i s preceded by t h e appearance of a c o n s i d e r a b l e p o s i t i v e p i t c h moment, under t h e i n f l u e n c e o f which t h e a i r c r a f t climbs and l o s e s speed. Therefore, l i m i t a t i o n s on overloads move along two l i n e s : along t h e l i n e of aerodynamics, i . e . , w i t h r e s p e c t t o c and along t h e l i n e of s t r e n g t h Y SUP' o f t h e a i r c r a f t , i . e . , with r e s p e c t t o t h e maximum c o e f f i c i e n t o f o p e r a t i o n a l overload n max.; I n o r d e r t o avoid exceeding c and p r e v e n t t h e a i r c r a f t from going Y SUP i n t o a r o l l , p e r m i s s i b l e f l i g h t a l t i t u d e s are e s t a b l i s h e d as a f u n c t i o n o f f l y i n g weight ( s e e Chapter V I I , 5 8 ) . §14. Behavior of A i r c r a f t a t Large Angles of Attack A t t h e p r e s e n t time, t h e s e p a r a t i o n c h a r a c t e r i s t i c s , r o l l i n g and termin a t i o n of r o l l i n g of a i r c r a f t with low s t a b i l i z e r s and engines i n s t a l l e d on t h e wings have been s t u d i e d r a t h e r w e 1 1. However, t h e r e i s s t i l l very l i t t l e m a t e r i a l a v a i l a b l e on t h e b e h a v i o r of a i r c r a f t w i t h T-shaped t a i l s and motors l o c a t e d i n t h e r e a r p o r t i o n of t h e f u s e l a g e d u r i n g flow s e p a r a t i o n a t high angles of a t t a c k . The b a l a n c i n g c h a r a c t e r i s t i c analyzed i n 5 1 1 r e l a t e d completely t o an a i r c r a f t with load st a b i 1i z e r . L e t us analyze some f e a t u r e s o f t h e behavior of an a i r c r a f t moving i n t o l a r g e angles o f a t t a c k . The f l i g h t speed o f t h e a i r c r a f t corresponding t o C i s c a l l e d t h e minimum speed o r t h e s e p a r a t i o n speed. The problem is Y " 206
- 218. ~- ._. .... .. 1 t h a t when c i s achieved i n f l i g h t , t h e flow s e p a r a t e s , causing a s h a r p y max decrease i n t h e l i f t and a c o n s i d e r a b l e i n c r e a s e i n t h e drag. (The s e p a r a t i o n speed f o r a smooth wing i s r e p r e s e n t e d as V f o r t h e t a k e o f f p o s i t i o n of t h e S' wing mechanism as V , for t h e landing p o s i t i o n -- vs . I s1 0 Due t o t h e asymmetrical development o f s e p a r a t i o n on t h e wings of t h e aircraft, a b,anking moment arises and t h e a i r c r a f t r o l l s . By r o l l , we mean a movement of t h e a i r c r a f t about t h e l o n g i t u d i n a l a x i s such tha't t h e angular velocity of r o t a t i o n wx > 0 . 1 r a d / s e c , i . e . , g r e a t e r t h a n 6" p e r second. I n o r d e r t o determine t h e minimum v e l o c i t y corresponding t o c the y max' a i r c r a f t i s d e c e l e r a t e d a t u n i t overload. Since t h e l i f t i n g f o r c e of t h e wing depends on c V2, as t h e speed is reduced g r a d u a l l y , t h e v a l u e of c should Y Y i n c r e a s e , which does occur, w h i l e t h e p i l o t , g r a d u a l l y p u l l i n g t h e s t i c k toward h i m s e l f , s h i f t s t h e a i r c r a f t i n t o high angles of a t t a c k . The speed a t which s h a r p flow s e p a r a t i o n occurs i s accompanied by r a p i d r o l l i n g of t h e a i r c r a f t , and t h i s i s t h e minimum speed o r t h e speed o f s e p a r a t i o n Vs. A case has been observed i n which an a i r c r a f t developed such a high angular v e l o c i t y /211 w t h a t i t r o t a t e d by 180" i n a few seconds. X With f l a p s down, t h e movement of t h e s t i c k may n o t be s u f f i c i e n t t o achieve V S o r Vs . Then, t h e f l i g h t speed corresponding t o maximum rearward 0 1 p o s i t i o n of t h e s t i c k i s taken as t h e minimum speed. A s w e can s e e from processing o f s t r i p c h a r t r e c o r d e r s (Figure 137) when an a i r c r a f t with a low s t a b i l i z e r i s d e c e l e r a t e d a t an a l t i t u d e o f 1 2 , 0 0 0 m ( f l a p s and landing g e a r up) a f t e r an i n d i c a t e d speed o f 200 km/hr i s achieved, t h e a i r c r a f t maintains almost constant c = 1 . 4 5 and overload n = 1 f o r s e v e r a l seconds. The d e f l e c t i o n of t h e g l e v a t o r "upward" v a r i e g from 3 t o 3.8". A t c = 1 . 5 , a s l i g h t v i b r a t i o n of t h e a i l e r o n s and s t i c k b e g i n s . Y Rolling occurred a t c = 1 . 5 8 toward t h e r i g h t wing. In t h i s case, t h e Y angular banking v e l o c i t y , reached 0.19 r a d / s e c (approximately 11 deg/sec) , + and t h e nose dropped a t 4 deg/sec. During t h e r o l l , t h e a i l e r o n s were observed t o move upward by 2 - 2 . 5 " (negative d e f l e c t i o n ) . A f t e r 0 . 3 - 0 . 5 s e c of r o l l , t h e p i l o t moved t h e s t i c k away from himself (6el = + 2 " ) and t r a n s f e r r e d t h e a i r c r a f t t o lower v a l u e s of c .Y I n 3-4 s e c , t h e v i b r a t i o n s stopped. A f t e r t h e a i l e r o n s were moved t o s t o p t h e bank, t h e a i r c r a f t r a p i d l y stopped r o l l i n g , t h e e f f e c t i v e n e s s o f t h e a i l e r o n s being s u f f i c i e n t . B p u l l i n g t h e s t i c k toward himself ( d e f l e c t i n g t h e e l e v a t o r y "upward" by 2-3.5"), t h e p i l o t brought t h e a i r c r a f t back t o h o r i z o n t a l f l i g h t a t 320-340 km/hr. 207 I
- 219. I n o r d e r t o determine p e r m i s s i b l e v a l u e s of c t h e e l e v a t o r i s lrfedrr Y SUP' a t v a r i o u s v a l u e s of M number (Figure 138). I n o r d e r t o improve s a f e t y , t h i s maneuver i s performed a t h i g h a l t i t u d e (about 12,000 m ) . When t h e s t i c k i s moved e n e r g e t i c a l l y backward, t h e a i r c r a f t i s t r a n s f e r r e d t o angles of a t t a c k (high c1 ) a t which "capture" o r i n v o l u n t a r y p o s i t i v e p i t c h occurs. SUP A s w can s e e from t h e s t r i p c h a r t r e c o r d i n g s , t h e a i r c r a f t f i r s t e a c c e l e r a t e d , t h e n when M = 0.66 was reached, t h e p i l o t began t o i n c r e a s e t h e overload by p u l l i n g t h e s t i c k s h a r p l y back. The a n g u l a r r a t e o f r o t a t i o n about t h e t r a n s v e r s e a x i s reached 1 2 " p e r second ( w = 0.2 r a d / s e c ) z . At this p o i n t , t h e p i l o t slowed t h e r a t e a t which h e was p u l l i n g back t h e s t i c k , and t h e d e f l e c t i o n was l e f t c o n s t a n t a t 3" "upward." The overload i n c r e a s e d s h a r p l y , r e a c h i n g a maximum v a l u e of 2 . 8 , and "capture" began a t n = 2(cy = Y = 0.85) ( s e c t o r a b ) . A s t h e overload i n c r e a s e d t o 2.05-2.2 (c 1 1) , t h e Y a i r c r a f t s t a r t e d v i b r a t i n g and t h e a i l e r o n s began t o " f l o a t " ( d e f l e c t i o n of both a i l e r o n s upward due t o e l a s t i c deformation o f t h e c o n t r o l c a b l e ) . The a i r c r a f t d i d n o t r o l l , b u t a bank d i d occur a t 4-4.3 deg/sec. The maximum /213 ltfloatinglt of a i l e r o n s was 4.5-5". When t h e e l e v a t o r was s h i f t e d a t M = 0 . 7 , v i b r a t i o n was noted a t c = 0.85, while a t M = 0 . 8 - - a t c = 0 . 6 5 . When t h e s t i c k was moved f o r - Y Y ward, t h e maximum b a l a n c i n g d e f l e c t i o n of t h e e l e v a t o r (M = 0 . 8 and c = 0 . 9 ) Y was 5 . 3 ' , and t h e maximum b a l a n c i n g f o r c e r e q u i r e d t o b r i n g t h e a i r c r a f t back t o t h e i n i t i a l regime was 60 kg. I t was noted i n t h e p r o c e s s of t e s t i n g t h a t t h e warning v i b r a t i o n which /214 a r i s e s as t h e minimum f l i g h t speed i s approached i s i n s u f f i c i e n t l y i n t e n s e t o b e n o t i c e d by t h e p i l o t . A s t r o n g e r v i b r a t i o n o c c u r r e d a t t h e moment of "capture" o r a t t h e moment t h e a i r c r a f t s t a r t e d t o r o l l . I n most a i r c r a f t as t h e s e p a r a t i o n regime i s approached, t h e v i b r a t i o n of t h e t a i l s u r f a c e s is noted due t o i n t e r f e r e n c e between t h e t a i l and streams from t h e wings of t h e a i r c r a f t . I n t h o s e c a s e s when v i b r a t i o n was n o t observed, devices have been i n s t a l l e d t o cause a r t i f i c i a l v i b r a t i o n o f t h e s t i c k , warning t h e p i l o t t h a t he was approaching t h e s e p a r a t i o n regime. From t h e p o i n t o f view of formation o f v i b r a t i o n and r o l l i n g o f t h e a i r c r a f t , it i s dangerous t o perform a t a k e o f f i n which d u r i n g t h e f i r s t s t a g e of t a k e o f f t h e a i r speed i s 20% h i g h e r t h a n t h e s e p a r a t i o n speed V , a s w e l l a s landing s1 during which t h e f l i g h t speed o f t h e a i r c r a f t exceeds t h e s e p a r a t i o n speed Vs by 30%. 0 208
- 220. 4 ffA 94 - rac see a,; P tl khrus P E 0 -5 F i g u r e 137. Recording o f S t r i p Chart Recorders During D e c e l e r a t i o n o f A i r c r a f t 209
- 221. Figure 138. Recording o f S t r i p Chart Recorders AS A i r c r a f t I s Transferred t o n > 1 Y I n h o r i z o n t a l f l i g h t ( f l a p s up) a t high a l t i t u d e s when a zone o f s t r o n g t u r b u l e n c e i s e n t e r e d , s e p a r a t i o n may occur. I n t h i s case, i f t h e a i r c r a f t has s a t i s f a c t o r y c h a r a c t e r i s t i c s ( a d i v i n g moment appears) and t h e p i l o t t a k e s control, t h e a i r c r a f t w i l l eliminate t h e disruption of equilibrium. The problem i s somewhat worse a s concerns t h e s e p a r a t i o n c h a r a c t e r i s t i c s of an a i r c r a f t with a high h o r i z o n t a l t a i l s u r f a c e and motors i n t h e t a i l p o r t i o n of t h e f u s e l a g e . If i n a i r c r a f t with low s t a b i l i z e r , high s l i p angles E a r e c r e a t e d immediately b e f o r e s e p a r a t i o n , and t h e s l i p p i n g of t h e stream d i s a p p e a r s 2 10
- 222. immediately a f t e r s e p a r a t i o n , causing an i n c r e a s e i n t h e angle of a t t a c k and l i f t i n g force of the s t a b i l i z e r (a = a 1 , i . e . , an i n c r e a s e i n t h e d i v i n g ht cr moment, i n a i r c r a f t with T-shaped t a i l s u r f a c e s (high s t a b i l i z e r ) a f t e r t h e stream s e p a r a t e s from t h e wing, v o r t e x e s from t h e f u s e l a g e , and t h e stream from t h e wing, engine n a c e l l e s and mounting s t r u t s s t r i k e t h e s t a b i l i z e r , causing a p o s i t i v e p i t c h moment (Figure 139). This decreases t h e n e g a t i v e s i g n i f i c a n c e o f t h e l o n g i t u d i n a l moment c o e f f i c i e n t , and t h e a i r c r a f t has no tendency t o t i p over on i t s nose. When t h e s t a b i l i z e r i s below t h e s e p a r a t e d stream zone, which occurs with v e r y high angles of a t t a c k , t h e h o r i z o n t a l t a i l s u r f a c e c r e a t e s c o n s i d e r a b l e drag and a d i v i n g moment appears. In connection with t h i s , a f t e r s e p a r a t i o n , a p o s i t i v e p i t c h moment may a r i s e , making t h e s i t u a t i o n worse; a f t e r s e p a r a t i o n begins, t h e e l e v a t o r should b e f u l l y d e f l e c t e d "downward. Therefore, i n some a i r c r a f t with T-shaped t a i l s , a d i v i n g moment i s c r e a t e d a r t i f i c i a l l y u s i n g a "pusher" ("recoil" ~ y s t e m ) ~ . This device, working from an angle of a t t a c k t r a n s d u c e r l o c a t e d on t h e /215 f u s e l a g e , c r e a t e s f o r c e s a c t i n g on t h e s t i c k i n t h e d i r e c t i o n of a d i v e a t an angle of a t t a c k n e a r c1 . This f o r c e should be high enough t o overcome t h e m f o r c e a p p l i e d by t h e p i l o t and should continue a c t i n g u n t i l t h e angle of a t t a c k i s decreased. In order t o prevent e l i m i n a t i o n of a) overload by separ a t i o n , t h e "pusherv1 i s - - equipped with a s p e c i a l device with a gyroscope which l i m i t s t h e incEease i n angle b) of a t t a c k as a func t i o n o f t h e angular v e l o c i t y of t h e beginning o f s e p a r ation. The "pusher" can a l s o eliminate t h e s t a b l e r o l l i n g mode "long t e r m p o s i t i v e p i t c h i n g moment), i n Figure 139. Flow Spectra Around A i r c r a f t w i t h which t h e a i r c r a f t T-shaped Tail Surface A f t e r Flow Separation: leaves t h e r o l l only a , A n g l e of a t t a c k 3" g r e a t e r than s e p a r a t i o n a f t e r a considerable a n g l e ; b , A n g l e o f a t t a c k 18" g r e a t e r than decrease i n v e l o c i t y s e p a r a t i o n a n g l e ; 1 , Air stream from w i n g ; and a l t i t u d e . 2 , Air stream from n a c e l l e s and s t r u t s of e n g i nes ..-.-. ...... . . _ _ . _ _ _ .. 4Z&bezhnyy Aviatransport, NO .*-12.; G O S N I - I - G A Pkess-, 1965. ~~ . 211 II
- 223. 515. Automatic A n g l e o f Attack and Overload Device The automatic a n g l e o f a t t a c k and overload d e v i c e (AUAP) i s used t o warn t h e p i l o t t h a t t h e a i r c r a f t i s f l y i n g a t l a r g e a n g l e s of a t t a c k as t h e minimum v e l o c i t y i s approached and d u r i n g f l i g h t s i n bumpy a i r . During f l i g h t s u s i n g t h i s d e v i c e , t h e i n s t a n t a n e o u s angle o f a t t a c k a t which t h e a i r c r a f t i s f l y i n g and t h e v e r t i c a l overload are determined. Also, a t each moment i n time t h e v a l u e of t h e c r i t i c a l a n g l e o f a t t a c k i s determined /* a s a f u n c t i o n of t h e M number of f l i g h t . The d e v i c e c o n s i s t s of a number o f a g g r e g a t e s . The main u n i t s a r e : 1) t h e angle o f a t t a c k measuring d e v i c e , which measures t h e l o c a l angles of a t t a c k i n c o n j u n c t i o n with t h e wind vane on t h e f u s e l a g e ; 2) t h e c r i t i c a l angle measuring d e v i c e which o u t p u t s t h e r e q u i r e d v o l t a g e a s a f u n c t i o n o f t h e M number of t h e f l i g h t ; 3) t h e overload t r a n s d u c e r , i n s t a l l e d i n t h e a r e a of t h e c e n t e r o f g r a v i t y of t h e a i r c r a f t ; 4) an i n d i c a t o r d e v i c e on t h e i n s t r u ment p a n e l i n f r o n t o f t h e p i l o t . Using t h i s d e v i c e , t h e p i l o t can observe t h e c u r r e n t angles of a t t a c k a t which he i s f l y i n g , t h e c r i t i c a l a n g l e of a t t a c k (more p r e c i s e l y , t h e angle of a t t a c k a t which t h e automatic d e v i c e o p e r a t e s under t h e given c o n d i t i o n s ) and t h e v e r t i c a l overload. When t h e a i r c r a f t e n t e r s a c r i t i c a l regime ( t h e o p e r a t i n g regime, which i s somewhat less t h a n t h e p e r m i s s i b l e ) t h e lower s e c t o r o f t h e movable c r i t i c a l angle o f a t t a c k s e c t o r on t h i s instrument corresponds with t h e arrow i n d i c a t i n g t h e i n s t a n t a n e o u s angle of a t t a c k ( F i g u r e 1 4 0 ) . A t t h i s moment, a 1217 lamp with t h e i n s c r i p t i o n "ac: l i g h t s up i n f r o n t o f t h e c o p i l o t . Also, i f t h e a i r c r a f t undergoes overlo-ads g r e a t e r t h a n t h o s e p e r m i s s i b l e t h e arrow i n d i c a t i n g i n s t a n t a n e o u s overload approaches t h e s e c t o r of dangerous overloads and t h e ].amp with t h e i n s c r i p t i o n 'In '' l i g h t s up. Y SUP When e i t h e r of t h e s e lamps l i g h t s up, t h e " a t t e n t i o n " lamp on t h e d i s p l a y begins t o f l a s h . Adjustment of t h i s d e v i c e i s performed i n d i v i d u a l l y f o r o p e r a t i o n i n f l i g h t with a l l f l a p s and g e a r up and f o r f l i g h t with f l a p s down f o r t a k e o f f and f o r l a n d i n g . For example, i n t h e o r d i n a r y f l y i n g mode ( f l a p s u p ) , t h e aCr warning l i g h t s up when a n g l e s o f a t t a c k of 1 . 4 - 2 " less t h a n t h e p e r m i s s i b l e angles a r e reached. These parameters a r e shown f o r one a i r c r a f t equipped with t h e AUAP d e v i c e i n Table 13. W can see from Figure 140 t h a t t h e a n g l e o f a t t a c k r e s e r v e up t o t h e e moment o f o p e r a t i o n i s 1.8-3.2" (M = 0.7-0.82). For example, f o r M = 0 . 8 , t h e r e s e r v e from c1 = 3" t o c1 = 5 . 2 " i s 2 . 2 " , and t h e r e s e r v e t o c i s 4". hf OP Y SUP I n o r d e r t o achieve c = 0 . 7 i n f l i g h t a t M = 0.8, we must c r e a t e an Y SUP overload n = 0 . 7 / 0 . 2 7 5 = 2 . 5 2 . However, a t cx = 5.2" (c = 0.53), i . e . , a t Y OP Y overload n = 0.53/0.275 = 1.93, t h e "n '' l i g h t comes on. The p i l o t ' s Y Y SUP 212
- 224. action i n c o n t r o l l i n g t h e longitudinal a t t i t u d e of t h e aircraft prevents t h e a i r c r a f t from e n t e r i n g t h e dangerous r o l l i n g regime. TABLE 13 .~ 0.8 . .I . . . .~ ao SUP 10,6 9,8 7 aO0per.c r 9,2 8.4 794 6,3 5,2 aohf f o r H= 1 0 km' 5,7 5 4,2 3-5 3 c sup 0,96 0,91 0,84 0,78 0.7 C Y oper - 0,715 0,62 0,53 - 0,355 0,315 0.275 C y hf - 2,O 1,96 1,93 nyope r Note: Commas r e p r e s e n t decimal p o i n t s . The speed r e s e r v e from t h e moment when t h e l i g h t s i g n a l l i n g t h e dangerous regime l i g h t s up u n t i l t h e minimum p e r m i s s i b l e speed i s II ." reached i s u s u a l l y 25-40 km/hr l and t h e r e s e r v e b e f o r e r o l l i n g i s 80-100 km/hr i n d i c a t e d speed. With f l a p s down, t h e automatic device a l s o warns t h e p i l o t i n advance of any d e v i a t i o n from t h e normal regime. F o r example, where ci = 9 - l o o (near t h e angles OP of a t t a c k used i n landing and t a k e o f f ) , t r a n s f e r of t h e a i r c r a f t i n t o t h e nonpermis s i b l e regime i s s i g n a l l e d by l i g h t i n g of t h e ''a ' I lamp. cr 916. Lateral S t a b i l i t y - /218 F i g u r e 140. Operating C h a r a c t e r i s t i c s o f AUAP AS a Function o f M Number: L a t e r a l e q u i l i b r i u m of 1 , Movable s e c t o r of c r i t i c a l angles t h e a i r c r a f t can be d i s r u p t e d ~2 2 , S e c t o r o f dangerous overloads; by two f a c t o r s which a r e 3 , Nonflashing lamp warning o f danger i n t e r r e l a t e d : s l i p p i n g and ous n * 4 , Flashing lamp; 5 , Non- banking. Thus, i f t h e cause Y' o f a d i s r u p t i o n of l a t e r a l f l a s h i n g lamp s i g n a l l i n g c r i t i c a l equilibrium i s banking, as a angles a r e s u l t o f t h e f o r c e of 213
- 225. g r a v i t y an unbalanced l a t e r a l f o r c e w i l l appear, a p p l i e d a t t h e c e n t e r of g r a v i t y , which w i l l d i s t o r t t h e t r a j e c t o r y of movement. The a i r c r a f t b e g i n s t o s l i p . I n t h e same way, i f t h e d i s r u p t i o n o f l a t e r a l e q u i l i b r i u m occurs as a r e s u l t of s l i p p i n g o f t h e a i r c r a f t , an i n c r e a s e i n l a t e r a l f o r c e AZ occurs, a p p l i e d a t t h e l a t e r a l aerodynamic c e n t e r , t h e t r a j e c t o r y i s curved and as a r e s u l t an unbalance t r a n s v e r s e moment AMx a p p e a r s . The a i r c r a f t begins t o bank. Thus, when l a t e r a l e q u i l i b r i u m i s d i s r u p t e d , t h e a i r c r a f t begins t o r o t a t e about t h e axes o f ox and oy simultaneously. The term l a t e r a l s t a b i l i t y means t h e a b i l i t y of an a i r c r a f t t o r e t u r n t o i t s i n i t i a l p o s i t i o n a f t e r any small p e r t u r b a t i o n independently, without p i l o t a c t i o n , except f o r unavoidable course d e v i a t i o n . F o r a b e t t e r understanding o f l a t e r a l s t a b i l i t y , i t i s methodologically expedient t o analyze f i r s t s t a b i l i t y of t h e a i r c r a f t r e l a t i v e t o t h e ox a x i s , t h e n s e p a r a t e l y r e l a t i v e t o t h e oy a x i s . The former is c a l l e d t r a n s v e r s e s t a b i l i t y , the latter -- directional s t a b i l i t y . Simultaneous d i r e c t i o n a l and t r a n s v e r s e s t a b i l i t y r e p r e s e n t l a t e r a l s t a b i l i t y of t h e a i r c r a f t . 517. Transverse Static Stability Transverse s t a b i l i t y i s t h e a b i l i t y o f an a i r c r a f t t o e l i m i n a t e a bank a u t o m a t i c a l l y , o r , i n o t h e r words, t o bank i n t h e d i r e c t i o n o p p o s i t e t o s l i p p a g e . For example, i f t h e a i r c r a f t s l i p s t o t h e r i g h t , t h e a i r c r a f t should bank t o t h e l e f t . I n o r d e r f o r an a i r c r a f t t o e l i m i n a t e bank independently, it i s n e c e s s a r y t h a t a t r a n s v e r s e moment a r i s e on t h e lower wing during s l i p p i n g such as t o cause r o t a t i o n toward t h e h i g h e r wing. The banking o f t h e a i r c r a f t i t s e l f h a s no d i r e c t i n f l u e n c e on t h e magnitude o f t r a n s v e r s e moments. I t s i n f l u e n c e i s f e l t through s l i p p i n g . The bank a n g l e determines t h e s l i p a n g l e which i s t h e d i r e c t cause o f t r a n s v e r s e moments. The degres of t r a n s v e r s e s t a b i l i t y i s e v a l u a t e d according t o t h e v a l u e of t r a n s v e r s e moment Amx r e s t o r e d p e r one degree of s l i p angle B , i . e . , according 6 to t h e v a l u e of mx, c a l l e d t h e c o e f f i c i e n t of t r a n s v e r s e s t a t i c s t a b i l i t y : I n a t r a n s v e r s e l y s t a b l e a i r c r a f t , when s l i p p i n g occurs t o t h e r i g h t wing / 219 ( p o s i t i v e s l i p p i n g ) , a n e g a t i v e t r a n s v e r s e moment appears on t h e l e f t wing, and c o e f f i c i e n t m B i s n e g a t i v e . The v a l u e of t h i s c o e f f i c i e n t i s determined X 2 14
- 226. p r i m a r i l y by t h e form o f t h e wing and t h e h e i g h t o f t h e v e r t i c a l c o n t r o l s u r f a c e . For swept wings with no t r a n s v e r s e V, t h e t r a n s v e r s e s t a b i l i t y c o e f f i c i e n t i s u s u a l l y q u i t e high, and must be decreased by g i v i n g t h e wing a n e g a t i v e t r a n s v e r s e V = -(1-3O). This decreases t h e moment o f t h e bank . s t r i v i n g t o b r i n g t h e a i r c r a f t out of t h e s l i p p i n g s t a t e . Transverse s t a t i c s t a b i l i t y depends both on t h e angle o f a t t a c k and on t h e f l i g h t speed. Mechanization of t h e wing i s a l s o q u i t e important. The increase i n t r a n s v e r s e s t a t i c s t a b i l i t y with increasing c o e f f i c i e n t c i s explained as Y follows. When a Figure 141. Change i n S w e e p A n g l e of Wing swept wing s l i p s , t h e During S l i p p i n g and Influence o f S l i p p i n g on sweep angle o f t h e D e p e n d e n c e o f c on A n g l e of Attack Y wing i s changed (Figure 141). Where t h e sweep angle i s decreased ( r i g h t wing), t h e load b e a r i n g q u a l i t i e s i n c r e a s e . The curve of t h e f u n c t i o n c = f ( a ) f o r t h i s wing i s h i g h e r than f o r t h e wing f o r which t h e sweep angle'increases during t h e s l i p . W s e e from e t h e graph t h a t a t high angles of a t t a c k (more p r e c i s e l y a t high values of c ) Y t h e d i f f e r e n c e i n t h e values f o r t h e wings i n c r e a s e s . Therefore, t h e h i g h e r t h e a n g l e s of a t t a c k a t which f l i g h t i s performed, t h e g r e a t e r t h e banking moment c r e a t e d d u r i n g s l i p p i n g . A s a r e s u l t , t r a n s v e r s e s t a b i l i t y of a swept wing i s h i g h e r , t h e h i g h e r t h e angle of a t t a c k . Whereas during climbing, h o r i z o n t a l f l i g h t and descent (angles o f a t t a c k 2 . 5 - 3 . 3 " ) t h e t r a n s v e r s e s t a t i c s t a b i l i t y i s w i t h i n t h e l i m i t s of normal v a l u e s , during t h e landing regime i t i n c r e a s e s . The i n c r e a s e i n l a t e r a l s t a t i c s t a b i l i t y a t high angles of a t t a c k has a n e g a t i v e influence on t h e prelanding regime and may worsen t h e f l y i n g qual i t i e s of an a i r c r a f t , causing it t o rock and g i v i n g it poor damping char- /220 a c t e r i s t i c s . Therefore, when t h e f l a p s a r e lowered (high values o f c ) , when Y f l i g h t i s being performed a t low speeds, t h e t r a n s v e r s e s t a t i c s t a b i l i t y i s high. A i n c r e a s e i n t r a n s v e r s e s t a b i l i t y of an a i r c r a f t a t low angles of n a t t a c k is aided by aerodynamic d e f l e c t i o n o f t h e wings. Aerodynamic b a f f l e s a l s o extend t h e beginning o f development o f terminal s e p a r a t i o n and h e l p t o i n c r e a s e t h e t r a n s v e r s e s t a b i l i t y of an a i r c r a f t a t high angles of a t t a c k . 215
- 227. 518. Directional S t a t i c S t a b i l i t y D i r e c t i o n a l s t a b i l i t y i s t h e a b i l i t y o f an a i r c r a f t t o e l i m i n a t e s l i p p i n g a u t o m a t i c a l l y . During f l i g h t with s l i p p i n g , as a r e s u l t o f l a t e r a l a i r c u r r e n t a g a i n s t t h e f u s e l a g e , aerodynamic f o r c e Z a r i s e s , t h e moment o f which r e l a t i v e t o t h e c e n t e r o f g r a v i t y c r e a t e s a r o t a t i n g moment M about v e r t i c a l Y a x i s oy. Normally, t h e p o i n t of a p p l i c a t i o n of t h e l a t e r a l f o r c e i s behind t h e c e n t e r o f g r a v i t y o f t h e a i r c r a f t , as a r e s u l t of which f o r c e Z t e n d s t o r o t a t e t h e a i r c r a f t ( l i k e a weather vane) toward t h e wing onto which t h e a i r c r a f t i s s l i p p i n g . Q u a n t i t a t i v e l y , t h e degree o f d i r e c t i o n a l s t a b i l i t y i s determined by t h e v a l u e of s t a b i l i t y c o e f f i c i e n t m B . P h y s i c a l l y , c o e f f i c i e n t Y mB d e f i n e s t h e amount of i n c r e a s e i n r o t a t i o n a l moment M B when t h e s l i p p i n g Y Y angle B changes by one degree, i . e . , +-. Amy A@ The g r e a t e r mB t h e g r e a t e r t h e d i r e c t i o n a l s t a b i l i t y o f t h e a i r c r a f t and t h e Y’ more i n t e n s i v e l y i t e l i m i n a t e s s l i p p i n g . Modern a i r c r a f t have s u f f i c i e n t d i r e c t i o n a l s t a b i l i t y , c o e f f i c i e n t m B i s Y n e g a t i v e , i . e . , when t h e a i r c r a f t s l i p s over onto t h e r i g h t wing ( p o s i t i v e 6) a d i r e c t i o n a l moment appears t o r o t a t e t h e a i r c r a f t t o t h e l e f t . D i r e c t i o n a l s t a b i l i t y o f a i r c r a f t i s provided p r i m a r i l y by t h e v e r t i c a l t a i l surface. 519. Lateral Dynamic Stabi 1 i t y Let us assume t h a t an a i r c r a f t i s banked onto t h e r i g h t wing under t h e i n f l u e n c e of e x t e r n a l p e r t u r b a t i o n . This r e s u l t s i n r i g h t s l i p p a g e , and t h e t r a j e c t o r y o f t h e a i r c r a f t i s bent t o t h e r i g h t . Further movement of t h e a i r c r a f t depends on t h e r a t i o between t r a n s v e r s e and d i r e c t i o n a l s t a b i l i t y . Let us assume t h a t t h e t r a n s v e r s e s t a b i l i t y i s g r e a t e r than t h e d i r e c t i o n a l s t a b i l i t y , i . e . , mB i s g r e a t e r t h a n mB In t h i s case t h e bank is r a p i d l y X Y’ eliminated, t h e a i r c r a f t moves from r i g h t bank t o l e f t bank and begins t o s l i p on t h e l e f t wing. However, s i n c e t h e s l i p p i n g i s n o t completely e l i m i n a t e d , once more a banking moment onto t h e r i g h t wing appears. The a i r c r a f t goes i n t o a r i g h t bank once more. Thus, a rocking of t h e a i r c r a f t occurs, c a l l e d l a t e r a l o s c i 1l a t i n g i n s t a b i l i t y . O t h e o t h e r hand, i f mB i s l e s s than m B i . e . , t h e d i r e c t i o n a l moment i s n X Y’ g r e a t e r than t h e t r a n s v e r s e moment, a f t e r t h e a i r c r a f t i s banked, t h e bank i s r e t a i n e d , but t h e s l i p p i n g i s r a p i d l y eliminated. The remaining bank curves 216
- 228. I t h e t r a j e c t o r y , i . e . , t h e a i r c r a f t descends i n a s p i r a l t o t h e r i g h t . This i s known as l a t e r a l s p i r a l i n s t a b i l i t y . The dynamics o f t h e l a t e r a l movement o f t h e a i r c r a f t under t h e i n f l u e n c e o f e x t e r n a l c o n d i t i o n s and i t s behavior under t h e i n f l u e n c e of t h e p i l o t ' s a c t i o n s a r e determined i n t h e s e examples n o t only by t h e s i g n and magnitude of c o e f f i c i e n t s m' and mB b u t a l s o by t h e presence of c e r t a i n r e l a t i o n s h i p s Y X ' between them. Therefore, t h e magnitude of K, which i s d i r e c t l y dependent on t h e r a t i o mE/mB and numerically equal t o t h e r a t i o of angular v e l o c i t i e s of Y bank and yawing, i s very important i n l a t e r a l dynamic s t a b i l i t y as w e l l as t h e controllability of t h e aircraft. This parameter c h a r a c t e r i z e s t h e l a t e r a l movement of t h e a i r c r a f t . Figure 1 4 2 shows a recording from a s t r i p c h a r t r e c o r d e r when t h e rudder i s moved with (a) and without (b) t h e yaw damper. Recording of c h a r a c t e r i s t i c s w and w a t low f l i g h t speeds was performed with f l a p s f u l l y down. X Y A f t e r t h e rudder impulse was t r a n s m i t t e d , t h e d i r e c t i o n of t h e a i r c r a f t began t o s l i p with a bank. A s we can s e e from t h e recordings, a f t e r 8 . 8 s e c K = 2 , a f t e r 1 2 . 1 s e c , 1.94 and f u r t h e r , as t h e o s c i l l a t i o n s were damped, t h e value decreased. Attenuation of o s c i l l a t i o n s shows t h e dynamic l a t e r a l s t a b i l i t y of t h e a i r c r a f t . The v a l u e of K should l i e between zero and one. W can s e e on e Figure 143 t h a t t h i s c o n d i t i o n i s observed a t various a l t i t u d e s only w i t h i n a d e f i n i t e range of M numbers, f o r example f o r 11 = 10,000 m a t M > 0 . 7 5 . A t s m a l l e r M numbers, K > 1 . When t h e value of K i s extremely high, s o t h a t t h e r a t i o m B / m B i s high, t h e a i r c r a f t w i l l be judged u n s a t i s f a c t o r y by i t s p i l o t s . X Y This i s explained by t h e f a c t t h a t with high t r a n s v e r s e s t a b i l i t y , t h e r e a c t i o n of t h e a i r c r a f t t o s l i p p i n g becomes q u i t e s h a r p . In t h i s c a s e , even small s l i p angles cause t h e a i r c r a f t t o bank s h a r p l y , and banking and yawing movements with comparatively s h o r t r e p e t i t i o n p e r i o d s occur, and a r e n o t always damped. This "rocking" of t h e a i r c r a f t i s u s u a l l y evaluated by p i l o t s /223 as l a t e r a l i n s t a b i l i t y , although a c t u a l l y i t i s an excess o f l a t e r a l s t a b i l i t y , causing t h e a i r c r a f t t o respond e a g e r l y t o t h e s l i g h t e s t random s l i p p i n g . I n landing modes, t h e values o f K produced a r e r a t h e r high (on t h e o r d e r o f of 1.5-23, leading t o yawing and rocking of t h e a i r c r a f t (Figure 144). P i l o t i n g o f t h e a i r c r a f t i s more d i f f i c u l t , and t h e p i l o t must f r e q u e n t l y o p e r a t e t h e c o n t r o l s . F l i g h t i n bumpy a i r becomes p a r t i c u l a r l y u n p l e a s a n t . 217
- 229. The dependence of t h e parameters T , K and mbl , c h a r a c t e r i z i n g t h e l a t e r a l dynamic s t a b i l i t y of the a i r c r a f t , on f l i g h t speed are shown on Figure 144. 520. Yaw Damper W know t h a t an e arrow-shaped a i r c r a f t w i 11 have s a t i s f a c t o r y lateral stability if, i n addition t o trans v e r s e and d i r e c t i o n a l s t a b i l i t y and t h e Figure 142. Determination of Value of optimal combination o f x ( V r = 220 km/hr, 6 n is t h e angle of devi- t h e s e two, it a l s o has a t i o n o f t h e rudder, H = 2000 m, landing gear good damping p r o p e r - and f l a p s down) t i e s , providing intens i v e damping o f l a t e r a l oscillations. a! 1 0 ec 5 U 43 44 Q5 46 97 Q8 M Figure 143. Character- Figure 144. i s t i c s of L a t e r a l Dynamic Characteristics S t a b i l i t y As a Function of L a t e r a l of M Number ( a n g l e x = Dynamic Stabi 1 = 35", landing gear and i t y As Functions Flaps Up); 1 , 2 , Normal- of F l i g h t S p e e d ized values of parameters (1.g. down, f l a p s down, H = = 2100 m) 218
- 230. The i n s t a l l a t i o n of dampers h a s allowed improvement i n t h e damping char a c t e r i s t i c s i n t h e event of p e r t u r b a t i o n s t o b e achieved, p a r t i c u l a r l y during t a k e o f f and l a n d i n g . A t t h e same t i m e , t h e e f f e c t i v e n e s s of t h e a i l e r o n s has been i n c r e a s e d . Thus, t h e s t a b i l i t y of an a i r c r a f t i s i n c r e a s e d and t h e work of t h e p i l o t i s g r e a t l y eased, e s p e c i a l l y i n t r a n s i e n t modes. For example, t h e yaw damper provides automatic damping of a i r c r a f t c o u r s e and bank o s c i l l a t i o n s by a r t i f i c i a l l y i n c r e a s i n g t h e damping c o e f f i c i e n t by a u t o m a t i c a l l y s h i f t i n g t h e rudder t o an angle p r o p o r t i o n a l t o t h e a n g u l a r v e l o c i t y . A s t h e yaw damper o p e r a t e s , t h e i n t e n s i t y of damping o f l a t e r a l o s c i l l a t i o n s i s i n c r e a s e d ; t h i s means t h a t t h e number o f o s c i l l a t i o n s t o complete damping and t h e t o t a l t i m e o f damping a r e decreased. The amplitude of o s c i l l a t i o n s A (Figure 116) during one p e r i o d i s decreased s o g r e a t l y t h a t t h e v a l u e "bn = A / A is decreased by 1 2 s e v e r a l times. Figure 142 b shows a diagram of t h e d e c r e a s e i n a n g u l a r v e l o c i t i e s when t h e yaw damper i s turned on a f t e r a p u l s e i s f e d t o t h e r u d d e r . The p e r i o d of o s c i l l a t i o n i s decreased t o 5-7 s e c , mbl = 5-8 and t h e s e n s e and s i g n i f i c a n c e of parameter K are l o s t . The a c t u a t i n g mechanism of t h e damper (Figure 145) is a t e l e s c o p i c arm. Control of t h e rudder during o p e r a t i o n o f t h e damper i s performed u s i n g a h y d r a u l i c a m p l i f i e r which t r a n s m i t s t h e f o r c e t o t h e r u d d e r . The angular v e l o c i t y t r a n s d u c e r s , which measure wx and w a r e gyroscopes Y' with two degrees of freedom, r e a c t i n g t o t h e a n g u l a r v e l o c i t y o f r o t a t i o n of /224 t h e a i r c r a f t about t h e oy and ox axes. A s t h e a i r c r a f t o s c i l l a t e s about t h e s e a x e s , p e r i o d i c changes i n angular v e l o c i t i e s of yaw w and bank wx o c c u r . Y E l e c t r i c a l s i g n a l s a r e produced which a r e p r o p o r t i o n a l a t each moment t o t h e v a l u e s of t h e s e v e l o c i t i e s , t h e n a r e a m p l i f i e d and s e n t t o t h e t e l e s c o p i n g arms. The t e l e s c o p i n g arms a r e i n s t a l l e d i n t h e arms of t h e r i g i d c o n t r o l system from t h e p e d a l s i n f r o n t o f t h e p i l o t . The h y d r a u l i c a m p l i f i e r d e f l e c t s t h e rudder depending on t h e l i n e a r displacement of t h e s h a f t o f t h e t e l e s c o p i n g arm according t o an e s t a b l i s h e d c o n t r o l law. For example, with t h e landing gear down and f l a p s down, d e f l e c t i o n o f t h e rudder occurs on t h e b a s i s of s i g n a l s from t h e w and wx t r a n s d u c e r s . The c o n t r o l law can be Y r e p r e s e n t e d by t h e f o l l o w i n g formula: A$ = Aoy+ Bo,, where A6r i s t h e d e f l e c t i o n of t h e r u d d e r ; A, B a r e t h e c o e f f i c i e n t s o f p r o p o r t i o n a l i t y corresponding t o t h e adjustment o f t h e damper. With t h e landing g e a r and f l a p s up, t h e s i g n a l from t h e wx t r a n s d u c e r i s disconnected and t h e o p e r a t i o n of t h e damper follows t h e law = Aw Y . 2 19
- 231. The o p e r a t i o n o f t h e t e l e s c o p i c arms has no i n f l u e n c e on t h e movement o f t h e p e d a l s , although t h e rudder i s d e f l e c t e d by an a n g l e p r o p o r t i o n a l t o t h e a n g u l a r v e l o c i t y o f r o t a t i o n of t h e a i r c r a f t . When t h e a i r c r a f t r o t a t e s t o t h e r i g h t , t h e rudder i s d e f l e c t e d t o t h e l e f t and v i c e versa. Let us u s e t h e f o l l o w i n g examples t o analyze when and how t h e rudder is d e f l e c t e d by t h e damper: 1. Let u s assume t h a t i n f l i g h t with landing g e a r and f l a p s down, t h e p i l o t t u r n s t o t h e r i g h t . To do t h i s , h e d e f l e c t s t h e s t i c k t o t h e r i g h t , banking t h e a i r c r a f t t o t h e r i g h t by angle y (Figure 146 a ) . Due t o t h e d i f f e r e n c e i n l i f t i n g f o r c e s on t h e wings, t r a n s v e r s e bank moment +M appears xa from t h e a i l e r o n s , under t h e i n f l u e n c e of which t h e a i r c r a f t begins t o /225 r o t a t e t o t h e r i g h t a t a n g u l a r v e l o c i t y +w X .As i t banks t o t h e r i g h t , t h e a i r c r a f t w i l l s l i p a t a n g l e + B t o t h e r i g h t (lower) wing (Figure 146 b ) , and l a t e r a l moments M and M appear. X Y Figure 145. Diagram of Operation of Yaw Damper i n Rudder S y s t e m : 1 , Pedal; 2 , Spring oad; 3 , Trim m i n g mechanism; 4 , T e l e s c o p i c arm; 5 A m p l i f y i n g u n i t ; 6 , Angular v e l o c i t y transducer 7 , Hydraulic amp1 i f i e r ; 8, Rudder I n a l a t e r a l l y s t a b l e a i r c r a f t , as s l i p p i n g b e g i n s , t r a n s v e r s e moment Mxsl a r i s e s , a c t i n g t o e l i m i n a t e t h e bank, i . e . , a c t i n g t o l i f t t h e wing (Figure 146 c ) . This moment, p r o p o r t i o n a l t o t h e c o e f f i c i e n t o f t r a n s v e r s e B s t a b i l i t y mx and s l i p angle f3 i s : B = -m BC (where C = qSZ, q is t h e -‘xs 1 X v e l o c i t y p r e s s u r e , S i s t h e a r e a of t h e wing, Z is t h e wing span) and a c t s a g a i n s t t h e d e f l e c t e d a i l e r o n s , a s a r e s u l t of which t h e e f f e c t i v e n e s s of t r a n s v e r s e c o n t r o l i s worsened. The g r e a t e r t h e t r a n s v e r s e s t a t i c s t a b i l i t y o f t h e a i r c r a f t (bank s t a b i l i t y ) , which i s a p r o p e r t y of a l l swept wing a i r c r a f t a t low f l i g h t speeds ( V = 240-280 km/hr), t h e more s h a r p l y t h e 220
- 232. a i r c r a f t w i l l react with r e v e r s e bank t o t h e l i f t i n g (lagging) wing during s l i p p i n g , s o t h a t a p o s i t i o n arises i n which t h e a i l e r o n s are i n e f f e c t i v e . Due t o t h e d i r e c t i o n a l s t a b i l i t y , as t h e a i r c r a f t s l i p s t o t h e r i g h t a moment appears p r o p o r t i o n a l t o t h e c o e f f i c i e n t of d i r e c t i o n a l s t a b i l i t y -M = YSl = -m BC, r o t a t i n g t h e a i r c r a f t t o t h e r i g h t a t angular v e l o c i t y - w /226 Y Y (Figure 146 d) i n attempting t o e l i m i n a t e t h e s l i p , s l i g h t l y reducing t h e l o s s o f e f f e c t i v e n e s s of t h e a i l e r o n s . Therefore, t h e l e s s s l i p p i n g a t t h e moment when t h e a i r c r a f t i s banked, t h e less w i l l b e t h e bank i n t h e d i r e c t i o n of t h e r i s i n g wing. Thus, i n o r d e r t o i n c r e a s e t h e e f f e c t i v e n e s s of t h e a i l e r o n s , i t i s necessary when t h e a i r c r a f t i s banked t o r e i n f o r c e r o t a t i n g moment M ysl' adding a moment from t h e rudder r e s u l t i n g from i t s d e f l e c t i o n by angle +A6r3. This d e f l e c t i o n i s c r e a t e d by t h e yaw damper. With f l a p s and landing gear down, t h e d e f l e c t i o n of t h e rudder from t h e yaw damper i s determined from t h e formula: AEr= AwYf Bw,. The s i g n a l wx d e f l e c t s t h e rudder by angle A 6 r l = Bwx. However, due t o t h e appearance of t h e angular r o t a t i o n v e l o c i t y - w ( r o t a t i o n o f t h e r i g h t due Y t o s h i f t i n g o f t h e rudder) t h e rudder w i l l a l s o b e a u t o m a t i c a l l y d e f l e c t e d by t h e damper i n t h e o p p o s i t e d i r e c t i o n by angle -A6r2 = -Aw Y . The summary d e f l e c t i o n of t h e rudder +AAr3 w i l l b e less than from t h e s i g n a l +wx alone (Figure 146 d) s o t h a t t h e e f f e c t i v e n e s s of o p e r a t i o n o f t h e damper w i l l be s l i g h t l y reduced. However, t h e c o n t r o l l a b i l i t y o f t h e a i r c r a f t (more p r e c i s e l y , t h e e f f e c t i v e n e s s of t h e a i l e r o n s ) i s increased s i g n i f i c a n t l y i n comparison t o t h e c o n t r o l l a b i l i t y without t h i s damper. 2. I f t h e d i s r u p t i o n o f e q u i l i b r i u m of t h e a i r c r a f t occurs due t o a g u s t from t h e l e f t (Figure 146 e ) forming a r i g h t bank (we w i l l consider t h a t t h e p i l o t has not y e t had time t o move t h e c o n t r o l s ) , s l i p p i n g onto t h e r i g h t wing occurs a t angle + 8 . A s i n t h e preceding c a s e , l a t e r a l moments occur. Transverse moment -M w i l l b r i n g t h e a i r c r a f t out of t h e bank, and r o t a t i n g X moment -M w i l l act t o reduce t h e s l i p angle. Thus, as a r e s u l t of t h e g u s t Y we have +u X and as a r e s u l t o f t h e s l i p p i n g , - w Y . The rudder i s d e f l e c t e d by A6rl = Bwx i n a d d i t i o n t o A 6 r2 = -Am Y . 22 1
- 233. Actually, t h e o p e r a t i o n of t h e yaw damper i s more complex t h a n what w e have j u s t analyzed. In p a r t i c u l a r , after equilibrium i s d i s rupted, transverse moment -M r e s u l t s X i n angular v e l o c i t y -w (rotation t o the X l e f t ) and t h e rudder is shifted t o the l e f t . However, t h e action of angular v e l o c i t y - w i s much X less t h a n +wx c r e a t e d by a c t i o n o f the p i l o t o r a v e r t i c a l gust, since the i n i t i a l deflec t i o n of t h e rudder rapidly eliminates Figure 146. Explanation o f Operation o f Auto- t h e s l i p p i n g . The mat i c Rudder Control b y Damper summary d e f l e c t i o n o f t h e rudder may b e so great t h a t t h e a i r c r a f t reduces s l i p p i n g o n t o t h e r i g h t wing e n e r g e t i c a l l y , even perhaps beginning t o s l i p o n t o t h e l e f t . I n t h i s c a s e , a bank o n t o t h e r i g h t wing w i l l appear a g a i n , and t h e /227 a i r c r a f t as a r e s u l t w i l l yaw back and f o r t h - s e v e r a l t i m e s , rocking from wing t o wing. The damper causes t h e o s c i l l a t i o n s t o d i e out q u i c k l y , and t h e p i l o t f e e l s no s e n s i b l e rocking. Also i n f l i g h t ( f l a p s up, wx s i g n a l disconnected) w i t h momentary a p p l i c a t i o n o f a s i d e wind g u s t , t h e a i r c r a f t w i l l f i r s t e n e r g e t i c a l l y r o t a t e , and s l i p p i n g occurs a t angle 6. Due t o t h e w s i g n a l , t h e rudder i s d e f l e c t e d Y by t h e damper t o e l i m i n a t e t h e s l i p p i n g , and due t o t h e a c t i o n of t h e damper, i n a d d i t i o n t o t h e damping p r o p e r t i e s of t h e a i r c r a f t , r o t a t i o n under t h e i n f l u e n c e of t h e s i d e wind w i l l b e r e t a r d e d ( f o r s i m p l i c i t y w e w i l l n o t analyze t h e banking moment). When, due t o t h e d i r e c t i o n a l s t a b i l i t y and d e f l e c t i o n of t h e rudder t o reduce s l i p p a g e , t h e a i r c r a f t t r i e s t o r e t u r n t o i t s i n i t i a l p o s i t i o n , w of o p p o s i t e s i g n appears and t h e i n i t i a l d e f l e c t i o n Y of t h e r u d d e r i s decreased. The e f f e c t of t h e d i r e c t i o n a l s t a b i l i t y of t h e a i r c r a f t i s s l i g h t l y reduced. The movement of t h e a i r c r a f t w i l l be d i r e c t e d t o e l i m i n a t e t h e s l i p p i n g , and it r e t u r n s t o i t s i n i t i a l p o s i t i o n , e l i m i n a t i n g 222
- 234. t h e i n i t i a l s l i p p i n g , and may even begin s l i p p i n g on t h e o t h e r wing. However, t h e s e o s c i l l a t i o n s of t h e a i r c r a f t about t h e oy a x i s are r a p i d l y damped and rocking is eliminated. The p i l o t may g e t t h e impression t h a t t h e d i r e c t i o n a l s t a b i l i t y of t h e a i r c r a f t with t h e yaw damper i s worse, and t h a t t h e a i r c r a f t i s l e s s s t a b l e , although i n a c t u a l i t y , t h e yaw damper causes p e r t u r b a t i o n s which a r i s e t o be q u i c k l y a t t e n u a t e d . Thus, each angular v e l o c i t y of r o t a t i o n o f t h e a i r c r a f t about t h e oy and ox axes corresponds t o a d e f i n i t e d e f l e c t i o n o f t h e rudder. I f angular v e l o c i t y w i s 1 deg/sec, d e f l e c t i o n of t h e rudder w i l l be Y Aw degrees, while i f wx = 1 deg/sec -- 6 = Bw degrees (A and B are equal Y r X t o about 1.5-2). I n o r d e r t o i n c r e a s e r e l i a b i l i t y o f damper o p e r a t i o n , u s u a l l y two s e r i e s connected t e l e s c o p i n g arms a r e ' i n s t a l l e d , o p e r a t i n g simultaneously. T h e i r c o n t r o l a c t i o n i s added. The s t r o k e o f each arm i s 6-8 mm, and t h e maximum d e f l e c t i o n o f t h e rudder by t h e damper i s 5-6". When t h e rudder i s t u r n e d off o r when t h e r e i s no angular v e l o c i t y of r o t a t i o n o f t h e a i r c r a f t , t h e t e l e s c o p i n g arm a u t o m a t i c a l l y t a k e s up a n e u t r a l pos it ion. The h y d r a u l i c a m p l i f i e r s of t h e yaw dampers o p e r a t e without r e v e r s e . This means t h a t t h e aerodynamic load a r i s i n g i n f l i g h t on t h e rudder i s not t r a n s m i t t e d t o t h e p e d a l s , and t h e e n t i r e hinge moment from t h e rudder i s absorbed by t h e a m p l i f i e r p i s t o n . The p i l o t need only expend t h e f o r c e r e q u i r e d t o move i t s v a l v e . Since t h i s f o r c e does not g i v e t h e p i l o t any "control" f e e l i n g , " t h e d e s i r e d magnitude and n a t u r e of f o r c e change must be c r e a t e d by i n c l u s i o n of a s p e c i a l s p r i n g loading device i n t h e c o n t r o l system. When t h e pedals are moved (by t h e p i l o t ) t h e load s p r i n g s a r e compressed, /228 i m i t a t i n g t h e aerodynamic load from t h e rudder. The f o r c e from t h e pedal can be removed (during long f l i g h t with d e f l e c t e d rudder) by an electromechanical trimming mechanism which s h i f t s t h e body of t h e s p r i n g loader t o a p o s i t i o n i n which t h e load i s reduced t o zero. In a l l cases of f a i l u r e of t h e yaw damper, c o n t r o l of t h e rudder i s performed by t h e p i l o t with t h e p e d a l s , r e q u i r i n g him t o overcome t h e hinge moment from aerodynamic l o a d s . 921. Transverse C o n t r o l l a b i 1 i ty Transverse c o n t r o l of t h e a i r c r a f t i s performed by t h e a i l e r o n s , and i n c e r t a i n a i r c r a f t by t h e a i l e r o n s t o g e t h e r w i t h i n t e r c e p t o r s . D e f l e c t i o n of t h e i n t e r c e p t o r s ( a i d i n g t h e a i l e r o n s ) i s performed a f t e r t h e a i l e r o n s a r e d e f l e c t e d by 8-10'. This t y p e of c o n t r o l i s c h a r a c t e r i s t i c f o r a i r c r a f t with l a r g e wing areas. The e f f e c t i v e n e s s of t r a n s v e r s e c o n t r o l o f t h e a i r c r a f t i s g r e a t l y augmented. Also, t h e a i l e r o n s are f r e q u e n t l y made i n s e c t i o n s , i n o r d e r t o reduce " f l o a t i n g " i n case of flow s e p a r a t i o n on t h e wing. The a i l e r o n s are u s u a l l y 223
- 235. I d e f l e c t e d by '20' (up and down), and t h e angle o f r o t a t i o n of t h e c o n t r o l wheel i s 120-180'. The a n g l e of a i l e r o n d e f l e c t i o n by t h e a u t o p i l o t averages '2.5-3.5'. I n t h e p o r t i o n of t h e wing where t h e a i l e r o n s are placed t h e r e l a t i v e t h i c k n e s s o f t h e wing p r o f i l e i s s l i g h t , 10-12%, t h e r e l a t i v e curv a t u r e 0.8-1.5%. The comparatively small r e l a t i v e t h i c k n e s s and s l i g h t c u r v a t u r e allows t h e a i l e r o n s t o b e d e f l e c t e d by t h e same angle up and down. The r o t a t i n g moment t h u s produced (as a r e s u l t of d i f f e r e n c e i n t h e d r a g o f t h e wings with a i l e r o n s up and down) i s s l i g h t , even a t l a r g e angles o f a t t a c k and has almost no i n f l u e n c e on t h e behavior o f t h e a i r c r a f t ( r o t a t i o n about vertical axis). A swept wing shape has an unfavorable i n f l u e n c e on t r a n s v e r s e c o n t r o l l a b i l i t y , p a r t i c u l a r l y a t l a r g e angles of a t t a c k . The tendency o f swept wing a i r c r a f t t o r e a c t s h a r p l y by banking t o s l i p p i n g and t o e l i m i n a t e a i r c r a f t banking (by o p e r a t i o n of t h e a i l e r o n s ) s i g n i f i c a n t l y d e c r e a s e s t h e e f f e c t i v e n e s s of t h e a i l e r o n s . T h e i r e f f e c t i v e n e s s i s decreased by s i d e flow of t h e boundary l a y e r along t h e l e n g t h of t h e wing, i n c r e a s i n g t h e i n t e n s i t y of flow s e p a r a t i o n a t i t s ends. Aerodynamic b a f f l e s prevent e a r l y development of flow s e p a r a t i o n i n t h e t e r m i n a l c r o s s s e c t i o n s and t h e r e b y i n c r e a s e t h e e f f e c t i v e ness of a i l e r o n o p e r a t i o n . Let us look upon t h e f o r c e a p p l i e d t o t h e c o n t r o l wheel f o r a i l e r o n s i n o r d e r t o c r e a t e an a n g u l a r banking v e l o c i t y of 1 r a d / s e c , APa/Awx a s a c h a r a c t e r i s t i c of t r a n s v e r s e e o n t r o l l a b i l i t y , a s w e l l a s t h e change i n a n g u l a r /229 banking v e l o c i t y w r e s u l t i n g from a change i n a i l e r o n d e f l e c t i o n of one X degree, AoX/*Aa. During t r a n s v e r s e r o t a t i o n , a damping moment arises which should be e q u a l i z e d by t h e banking moment from t h e a i l e r o n s . A s we can s e e from Figure 147, a t M = 0.7-0.75, t h e f o r c e i s 105-156 kg. This means t h a t i f we must c r e a t e an a n g u l a r w = 3 deg/sec, a f o r c e X "U 4.7 4s $5 46 $7 475 M o f 5.5-7 kg must be a p p l i e d t o t h e wheel. Figure 147. Force on Control Wheel As a The h i g h e r wx, t h e Function of M Number g r e a t e r must be t h e f o r c e on t h e wheel. A s w i s doubled, t h e f o r c e a l s o doubles. As t h e f l i g h t a l t i t u d e i s increased X with c o n s t a n t M number, t h e f o r c e on t h e wheel i n c r e a s e s , s i n c e , due t o t h e decrease i n v e l o c i t y p r e s s u r e , t h e a i l e r o n d e f l e c t i o n angles i n c r e a s e . W can e s e e from t h e f i g u r e t h a t a t 1 0 , 0 0 0 m , t h e f o r c e s a r e g r e a t e r t h a n a t H = 6000 m. 224
- 236. I I I 11-14 The a i l e r o n e f f e c t i v e I 1: ness can be estimated as a f u n c t i o n o f M numbers and a l t i t u d e s u s i n g t h e graph on Figure 148. The h i g h e r t h e $ I a b s o l u t e value o f A W ~ / A ~ ~ , t h e more e f f e c t i v e a r e t h e I I 45 I 46 I I I t 4747518M ailerons. A t speeds /230 n e a r t h e maximum t h e e f f e c t i v e n e s s 0.t t h e Figure 148. Aileron E f f e c t i v e n e s s A s a a i l e r o n s should allow t h e Function of M Number development o f an angular v e l o c i t y of wx = 1 2 deg/sec, with f o r c e s not over 35 kg on t h e wheel (according t o t h e t e c h n i c a l c o n d i t i o n s ) . For example, a t H = 1 0 , 0 0 0 m and ?= I . 7 5 , t h e c r e a t i o n o f w = 1 r a d / s e c (57.3') r e q u i r e s a J0 X f o r c e of Pa = 156 kg a t t h e wheel. I f a f o r c e o f 35 kg i s a p p l i e d , w e produce an angular v e l o c i t y w = 12.8 deg/sec. The a i l e r o n d e f l e c t i o n used i s X deg/s ec rad s e c The q u a n t i t y 2.29 (0.04 ) i s taken from t h e graph of deg deg Figure 148. The a i l - e r o n e f f e c t i v e n e s s i n a landing maneuver ( M = 0.2, Vr = 250 km/hr) can a l s o be estimated using t h e graph of Figure 148. A s we can s e e , with an a i l e r o n d e f l e c t i o n of one degree we produce o = 9.45 deg/sec (Awx/Asa = X = 0.0165). With a f o r c e on t h e wheel o f 90 kg a t t h e s e speeds wx = 1 rad/sec, and t h e production of an angular r o t a t i o n v e l o c i t y of 9.45 deg/sec r e q u i r e s a f o r c e o f 14.8 kg. 522. Directional C o n t r o l l a b i l i t y . Reverse Reaction f o r Banking The rudder i s d e f l e c t e d t o t h e r i g h t and t o t h e l e f t by t h e pedals by 20-2S0, by t h e a u t o p i l o t by an average of '4-5'. Axial compensation of t h e rudder i s g e n e r a l l y 28-29% of i t s a r e a ( i n o r d e r t o produce a c c e p t a b l e f o r c e s ) . O most a i r c r a f t , i t h a s been noted t h a t , due t o i n c r e a s e d a r e a of n a x i a l compensation a t angles o f d e f l e c t i o n of 10-12" o r more (about one t h i r d o f t h e pedal t r a v e l ) t h e t i p of t h e rudder moves out i n t o t h e stream and f o r c e s on t h e pedal begin t o decrease. A phenomenon o f overcompensation 225
- 237. arises. I n o r d e r t o e l i m i n a t e t h i s phenomenon, t h e r u d d e r c o n t r o l system i n c l u d e s s p r i n g l o a d e r s . They compensate f o r t h e d e c r e a s e i n f o r c e on t h e pedals at l a r g e d e f l e c t i o n angles o r during s l i p p i n g . Also, i n t e r c e p t o r s may b e used. They have an a n g u l a r p r o f i l e and a r e f a s t e n e d t o t h e f r o n t o f t h e rudder i n f r o n t o f i t s r o t a t i o n a x i s (Figure 149). The a c t i o n o f an i n t e r c e p t o r can b e reduced t o t h e f o l l o w i n g . When t h e rudder i s d e f l e c t e d by 10-12O, t h e i n t e r c e p t o r on t h e l e f t s i d e e n t e r s t h e stream and c r e a t e s s e p a r a t i o n (and t h e r e f o r e a change i n p r e s s u r e d i s t r i b u t i o n ) i n t h e p o r t i o n o f t h e r u d d e r behind t h e a x i s o f r o t a t i o n . The i n t e r c e p t o r on t h e r i g h t s i d e i s covered by t h e v e r t i c a l t a i l s u r f a c e and does n o t i n t e r f e r e with t h e flow. Due t o t h e r a r e f a c t i o n formed on t h e l e f t s i d e , t h e rudder a t t e m p t s t o move t o t h e l e f t (move with t h e s t r e a m ) , which c r e a t e s an a d d i t i o n a l load on t h e r i g h t pedal as t h e rudder i s h e l d i n i t s d e f l e c t e d p o s i t i o n . As we can see from t h e graph, t h e f o r c e on t h e pedal i n c r e a s e s w i t h - /231 i n c r e a s i n g angle o f d e f l e c t i o n o f t h e rudder, while where t h e r e i s no i n t e r c e p t o r t h e f o r c e b e g i n s t o d e c r e a s e a t d e f l e c t i o n a n g l e s 10-11" (over compensation e f f e c t ) . Thus , i n s t a l l a t i o n of t h e i n t e r c e p t o r causes an i n c r e a s e of t h e hinge moment and produces a d i r e c t f o r c e on t h e pedals , t h i s force being g r e a t e r , t h e g r e a t e r t h e angle of Rudder t o R i g h t inclination of the rudder. Let u s look upon t h e banking r e a c t i o n of the a i r c r a f t t o a Figure 149. Force on Pedals As a Function o f d e f l e c t i o n of t h e Deflection o f Rudder During S t r a i g h t L i n e rudder defined by F l i g h t w i t h O n e Motor Off ( V r = 300 km/hr, AuX/AAr a s a char landing g e a r d o w n , 6 3 = 20", H = 1500-2000 m ) : a c t e r i s t i c of 1 , Vertical t a i l surface; 2, Interceptor; directional control - 3 , Rudder a b i l i t y , where Au i s X t h e change i n a n g u l a r bank v e l o c i t y ; A6 i s a change i n rudder d e f l e c t i o n o f one degree. r As w e can see from Figure 150, up t o M = 0.84-0.85, AuX/AAr i s p o s i t i v e , i . e . , t h e bank follows t h e c o n t r o l . A t high M numbers, t h e s i g n becomes n e g a t i v e , i . e . , t h e bank is o p p o s i t e . This means t h a t a r e v e r s e bank r e a c t i o n - /232 occurs when pedal i s f e d . Let us anaiyze t h i s f e a t u r e o f a i r c r a f t with swept 226
- 238. wings i n more d e t a i l . In a transversely stable a i r c r a f t when l e f t pedal i s a p p l i e d a s l i p t o t h e r i g h t occurs and, as a r e s u l t , a moment a r i s e s t i l t i n g t h e a i r c r a f t onto t h e l e f t wing; conversely, when r i g h t p e d a l i s f e d , a bank t o t h e r i g h t occurs. This r e a c t i o n of t h e a i r c r a f t t o deflec t i o n o f t h e rudder i s c a l l e d normal o r direct. 150. D e p e n d e n c e of However, when an a i r c r a f t with &-/A6 on M Number (H = swept wings f l i e s a t h i g h M number, t h i s x r = 10,000 m; a t M = 0.84, r e g u l a r i t y may b e d i s r u p t e d ( f o r reverse banking r e a c t ion of example, when r i g h t pedal i s f e d , t h e a i r c r a f t banks t o t h e l e f t r a t h e r t h a n t h e a i r c r a f t t o deflection o f rudder b e g i n s ) the right). The appearance of a r e v e r s e bank r e a c t i o n when t h e rudder i s d e f l e c t e d r e s u l t s from t h e i n f l u e n c e o f c o m p r e s s i b i l i t y o f t h e a i r on t h e aerodynamic c h a r a c t e r i s t i c s of t h e wing. A t s u b c r i t i c a l speeds, t h e sweep of t h e wing h e l p s t o i n c r e a s e t h e t r a n s v e r s e s t a b i l i t y o f t h e a i r c r a f t and, consequently, r e i n f o r c e t h e d i r e c t bank r e a c t i o n t o d e f l e c t i o n of t h e r u d d e r . The p i c t u r e is d i f f e r e n t a t s u p e r c r i t i c a l f l i g h t speeds. During s l i p p i n g , t h e e f f e c t i v e sweep angles of t h e r i g h t and l e f t wings change, s o t h a t t h e i r c r i t i c a l M numbers a l s o change (Figure 1 5 1 ) . The wing which i s moved forward shows a d e c r e a s e i n M a s a r e s u l t o f t h e decrease i n cr e f f e c t i v e sweep a n g l e , while t h e lagging wing, on t h e o t h e r hand, shows an increase i n M as a r e s u l t of t h e i n c r e a s e d sweep a n g l e . This change i n Mcr cr means t h a t i n s l i p p i n g t h e wave c r i s i s develops a t d i f f e r e n t times on each wing - - f i r s t on t h e wing on which t h e e f f e c t i v e sweep angle i s l e s s . This t i m e d i f f e r e n t i a l i n development o f t h e wave c r i s i s on t h e l e f t and r i g h t /223 wings and, consequently, t h e asymmetry i n t h e change o f t h e i r l i f t , causes t h e appearance of a r e v e r s e bank r e a c t i o n when p e d a l i s f e d . Figure 152 shows t h e r e g u l a r i t y of d e f l e c t i o n o f a i l e r o n s d u r i n g a c c e l e r a t i o n with s l i p p i n g i n an a i r c r a f t with r e v e r s e bank r e a c t i o n t o s l i p p i n g . I t i s easy t o determine t h e M number a t which t h e degree of normal r e a c t i o n of t h e a i r c r a f t t o s l i p p i n g b e g i n s t o d e c r e a s e ( p o i n t 1) and when t h e normal r e a c t i o n i s t r a n s f e r r e d t o a r e v e r s e r e a c t i o n ( p o i n t 2 ) . A t t h i s same p o i n t 2 , where t h e curve p a s s e s through zero, t h e r e i s n e i t h e r a d i r e c t n o r a r e v e r s e bank r e a c t i o n t o s l i p p i n g . I n o t h e r words, when f l y i n g with M number corresponding t o p o i n t 2 t h e a i r c r a f t does n o t have any bank r e a c t i o n t o s l i p p i n g ; t h e m a n i f e s t a t i o n of t h i s i s t h a t when t h e p e d a l s a r e d e f l e c t e d a p u r e yaw motion occurs without any tendency t o bank. 227
- 239. i I;lt c9 ion ci=2 tYt1eft w i n g X=25" X=jg" I . -(3+.4)O -. I "area o f r e v e r s e r e a c t I on Figure 152. Deflection o f Ailerons During Accel eration w i t h S l i p p i n g on Figure 151. Change i n E f f e c t v e Sweep an A i r c r a f t w i t h Reverse A n g l e and C o e f f i c i e n t c As a Function Bank Reaction t o S l i p p i n g Y of M Number w i t h Constant A n g l e c1 = 2" f o r Wings D i f f e r i n g i n S w e e p A n g l e Between p o i n t s 2 and 3 we f i n d t h e a r e a o f r e v e r s e bank r e a c t i o n t o s l i p p i n g . To t h e r i g h t of p o i n t 3 , d i r e c t r e a c t i o n i s r e s t o r e d once again. Frequently, t h i s p o i n t i s u n a t t a i n a b l e , s i n c e t h e corresponding M number i s beyond t h e l i m i t i n g p e r m i s s i b l e number f o r t h e a i r c r a f t ( a s i s t h e case on Figure 152). The beginning o f t h e r e v e r s e r e a c t i o n can be found by a c c e l e r a t i n g and d e f l e c t i n g t h e rudder. If an a i r c r a f t w i t h a swept wing (x = 35") f l i e s a t a speed corresponding t o M 1 (Figure 151) a t which t h e r e v e r s e r e a c t i o n o c c u r s (M1 > Mrr), when r i g h t pedal i s f e d d u r i n g l e f t s l i p , f o r example w i t h an a n g l e f3 = l o " , t h e e f f e c t i v e sweep angles o f t h e wings change: t h e a n g l e o f t h e l e f t wing i s 25", o f t h e r i g h t wing - - 45". As a r e s u l t of t h i s , t h e development of t h e wave c r i s i s on t h e l e f t wing i s r e i n f o r c e d , while i t i s r e t a r d e d on t h e r i g h t wing. A s a r e s u l t , c o e f f i c i e n t c on t h e l e f t wing i s s h a r p l y decreased, while it is Y s l i g h t l y i n c r e a s e d on t h e r i g h t wing, leading t o h i g h t r a n s v e r s e moments, t e n d i n g t o bank t h e a i r c r a f t i n t h e d i r e c t i o n of t h e s l i p . The g r e a t e r t h e sweep o f t h e wing and t h e t h i n n e r t h e wing p r o f i l e , t h e weaker t h e r e v e r s e bank r e a c t i o n w i l l b e , s i n c e t h e change i n c with M number Y w i l l be smoother. The M number corresponding t o t h e p o i n t of i n t e r s e c t i o n o f curves c = f(M) f o r sweep angles 25 and 45" i s r e p r e s e n t e d by M The p i l o t 1234 Y rr' should know the M number of t h e r e v e r s e r e a c t i o n of h i s a i r c r a f t and r e c a l l 228
- 240. . . . ............ . ,, t h e f a c t o r s which might lead t o improper p i l o t i n g i f he i s forced t o f l y a t M > M rr' W n o t e i n conclusion t h a t i n modern a i r c r a f t t h e rudder i s p r a c t i c a l l y e never used i n f l i g h t . Control of l a t e r a l a i x c r a f t movement (curves, t u r n s , s p i r a l s and o t h e r e v o l u t i o n s ) a r e a c t u a l l y performed by t h e a i l e r o n s alone. Exceptions i n c l u d e t a k e o f f and landing, during which g u s t s o f wind ( p a r t i c u l a r l y s i d e g u s t s ) a r e sometimes countered u s i n g d e f l e c t i o n s of t h e rudder. § 23. Involuntary Banking ("Valezhkal') I n high-speed a i r c r a f t with swept wings, s o - c a l l e d i n v o l u n t a r y banking may occur, which has come t o b e c a l l e d "valezhka." This phenomenon occurs both a t low a l t i t u d e s a t high i n d i c a t e d speeds, and a t high a l t i t u d e s a t high M numbers. Valezhka may occur f o r two reasons: a ) as a r e s u l t o f t h e appearance of a banking moment under t h e i n f l u e n c e of a d i f f e r e n c e i n l i f t i n g f o r c e on t h e l e f t and r i g h t wings and b) due t o a drop i n a i l e r o n e f f e c t i v e n e s s . The d i f f e r e n c e i n l i f t i n g f o r c e on t h e wings i s c r e a t e d due t o geometric o r rigid:-ty asymmetry of t h e a i r c r a f t . Geometric asymmetry i s c h a r a c t e r i z e d by a d i f f e r e n c e i n e f f e c t i v e angles o f a t t a c k of p o r t i o n s of t h e r i g h t and l e f t wings. I f t h e wings have d i f f e r e n t s t r u c t u r a l r i g i d i t y and t h e r e f o r e d i f f e r e n t deformations, a d i f f e r e n c e i n angle of a t t a c k may occur. A l l of t h i s l e a d s t o l a r g e banking moments a t high f l i g h t speeds. However, t h i s banking moment sometimes cannot be countered by d e f l e c t i n g t h e a i l e r o n s , s i n c e under c e r t a i n c o n d i t i o n s t h e i r e f f e c t i v e n e s s i s decreased. Suppose, f o r example, a banking moment on t h e r i g h t wing appears. I n o r d e r t o counter t h i s moment, t h e p i l o t d e f l q c t s t h e r i g h t a i l e r o n downward, t h e l e f t a i l e r o n upward. However, when t h e :tilerons a r e d e f l e c t e d a t high i n d i c a t e d speed (when t h e v e l o c i t y p r e s s u r e i s g r e a t ) moments appear which t w i s t t h e wing. Due t o t h e e l a s t i c i t y o f t h e wing, t h e angle of a t t a c k of t h e r i g h t wing i s decreased, t h a t of t h e l e f t wing increased. This diminishes t h e e f f e c t of a i l e r o n d e f l e c t i o n . The f o r c e s on t h e c o n t r o l wheel i n c r e a s e s h a r p l y . This phenomenon i s c a l l e d a i l e r o n r e v e r s e . A t high a l t i t u d e s , t h e a i l e r o n e f f e c t i v e n e s s drops due t o t h e presence of s u p e r s o n i c zones and compression drops on t h e wing. In a l l c a s e s where valezhka o c c u r s , t h e p i l o t should t a k e measures t o prevent banking of t h e a i r c r a f t , and t h e bank should b e c o r r e c t e d with t h e a i l e r o n s . Countering o f valezhka a t high M numbers by feeding pedal a g a i n s t /235 t h e bank may r e s u l t , i n some a i r c r a f t with swept wings ( a s a r e s u l t of t h e r e v e r s e bank r e a c t i o n ) t o an i n c r e a s e i n t h e bank. 229
- 241. 524. i n f l u e n c e o f C o m p r e s s i b i l i t y of Air on Control Surface E f f e c t i v e n e s s The c o n t r o l l a b i l i t y o f an a i r c r a f t , dependent on t h e o p e r a t i o n o f t h e h o r i z o n t a l c o n t r o l s u r f a c e s , may change e s s e n t i a l l y a t high M numbers. L e t u s analyze t h e o p e r a t i o n o f t h e c o n t r o l s u r f a c e s a t v a r i o u s M numbers. As we know, when t h e s u r f a c e s are d e f l e c t e d a t s u b c r i t i c a l speeds, a change i n t h e flow spectrum and p r e s s u r e d i s t r i b u t i o n o c c u r s throughout t h e e n t i r e p r o f i l e o f t h e c o n t r o l s u r f a c e , as a r e s u l t o f which aerodynamic f o r c e Rht arises (Figure 153 a ) . The change i n p r e s s u r e d i s t r i b u t i o n i s explained by t h e f a c t t h a t d e f l e c t i o n o f t h e c o n f r o l s u r f a c e creates small p e r t u r b a t i o n s , propa g a t i n g i n a l l d i r e c t i o n s a t t h e speed o f sound, i n c l u d i n g a g a i n s t t h e d i r e c t i o n o f flow, which i s subsonic. These small p e r t u r b a t i o n s cause changes i n p r e s s u r e along t h e p r o f i l e of t h e a i r f o i l . Figure 153. Explanation of t h e Influence o f Air Compressibi I i t y on Control Surface E f f e c t i v e n e s s I f f l i g h t i s performed a t s u p e r c r i t i c a l M numbers, a t which t h e wave c r i s i s i s developed on t h e c o n t r o l s u r f a c e , t h e e f f e c t i v e n e s s o f t h e a r t i c u l a t e d s u r f a c e s i s decreased c o n s i d e r a b l y . This o c c u r s f o r t h e f o l l o w i n g reasons. A f t e r s u p e r s o n i c v e l o c i t i e s a r i s e on t h e t a i l s u r f a c e s , when t h e p r e s s u r e jump ends, t h e d e f l e c t i o n of t h e c o n t r o l s u r f a c e can no l o n g e r change t h e n a t u r e of t h e flow around t h e e n t i r e t a i l s u r f a c e , n o r can it change t h e p r e s s u r e d i s t r i b u t i o n over t h e s u r f a c e (Figure 153 b ) . I n t h i s c a s e , t h e p e r t u r b a t i o n s caused by d e f l e c t i o n of t h e a r t i c u l a t e d c o n t r o l s u r f a c e s e c t i o n , propagating a t t h e speed of sound, cannot extend t o t h e p o r t i o n of t h e t a i l s u r f a c e where t h e flow r a t e i s h i g h e r t h a n t h e speed of sound. Therefore, t h e n a t u r e o f t h e flow changes only over t h a t s e c t i o n of t h e t a i l s u r f a c e which i s l o c a t e d behind t h e compression jump. Thus, t h e c r e a t i o n o f a d d i t i o n a l a e r o dynamic f o r c e by d e f l e c t i o n o f t h e a r t i c u l a t e d s u r f a c e i n c l u d e s only a p o r t i o n of t h e t a i l s u r f a c e , s o t h a t t h e magnitude of t h e f o r c e i s decreased. I n o r d e r t o improve t h e e f f e c t i v e n e s s of t h e s u r f a c e s a t high s p e e d s , f o r t h e t a i l s u r f a c e s can b e i n c r e a s e d by u s i n g high-speed p r o f i l e s and 2 30
- 242. g i v i n g t h e t a i l s u r f a c e an arrow;like form i n c r o s s s e c t i o n . I n o r d e r t o prevent e a r l y l o s s o f t a i l s u r f a c e e f f e c t i v e n e s s , Mcr should always b e g r e a t e r f o r t h e t a i l surface than M f o r t h e wing. A l s o , t h e h o r i z o n t a l t a i l s u r f a c e cr should b e removed (upward o r downward) from t h e v o r t e x flow zone behind t h e wing, i n o r d e r t o avoid decreases i n i t s e f f e c t i v e n e s s . 525. Methods o f Decreasing Forces on A i r c r a f t Control Levers In order t o control the aircraft, the p i l o t deflects the control surfaces by applying c e r t a i n f o r c e s t o t h e command l e v e r s . The f o r c e s on t h e l e v e r s depend on t h e hinge moments a r i s i n g as t h e a r t i c u l a t e d s u r f a c e s a r e d e f l e c t e d . I f t h e s e f o r c e s a r e g r e a t and t h e f l i g h t r e q u i r e s a good d e a l of maneuvering, o p e r a t i o n of t h e c o n t r o l organs becomes f a t i g u i n g . A t high speeds, s i g n i f i c a n t hinge moments are c h a r a c t e r i s t i c , s o t h a t g r e a t f o r c e s must be expended t o control the aircraft. YP The hinge moment i s a x i s of r o t a t i o n t h e moment c r e a t e d by t h e aerodynamic f o r c e a r i s i n g x i s of r o t a t i o n on t h e a r t i c u l a t e d s u r f a c e a s it i s deflected relative t o its a x i s o f r o t a t i o n . This axial moment acts a g a i n s t compensation deflection of the surface Mu=aYo= Y H ~ and i s perceived by t h e p i l o t as a f o r c e on t h e control s t i c k o r pedals (Figure 154). The hinge moment i n c r e a s e s with i n c r e a s i n g angle of d e f l e c t i o n of t h e s u r f a c e (from i t s e q u i l i b r i u m Figure 154. Explanation o f H i n g e Moment p o s i t i o n ) , with t h e a r e a and Operation o f Axial Compensation ( a ) , and cord of t h e s u r f a c e and Diagram o f Operation o f Servo- and with v e l o c i t y compensator ( b ) pressure. I n o r d e r t o decrease t h e f o r c e on t h e s t i c k , a x i a l o r i n t e r n a l conpensation, servo-compensators and trimmers a r e used. Axial compensation i s achieved by d i s p l a c i n g t h e p o i n t o f r o t a t i o n of t h e s u r f a c e (hinge) backward , t h u s decreasing t h e hinge moment (Figure 154). Axial compensation of t h e e l e v a t o r covers about 30% o f i t s a r e a , of t h e rudder - - about 28-29% o f i t s area, of t h e a i l e r o n s - - 28-31%. Greater v a l u e s o f a x i a l compensation may l e a d t o overcompensation. I t s essence i s as follows. The hinge moment can b e decreased t o zero, o r i f t h e hinge i s moved 231 I
- 243. even f u r t h e r rearward a hinge moment of t h e "reverge" s i g n may appear. I n t h i s case, t h e hinge moment appearing when t h e s u r f a c e i s d e f l e c t e d w i l l tend t o i n c r e a s e t h e a n g l e of d e f l e c t i o n . This is an u n f o r t u n a t e phenomenon, and i s c a l l e d overcompensation. <-dM - h a - h O t h e TU-104 n a i r c r a f t , i n order t o s a t o r d e c r e a s e loads on t h e ailerons , internal aerodynamic compensa- t i o n i s used h 2-Sect i on (Figure 155) , which Aeleron is similar t o axial compensation b u t Figure 155. I n t e r n a l Aerodynamic Compensation d i f f e r s i n t h a t when ( a ) and I n t e r c e p t o r s f o r Transverse Control on the control surface Wings of DC-8 A i r c r a f t ( b ) i s deflected , compensation does n o t extend beyond t h e wing p r o f i l e . I n t e r n a l aerodynamic compensation i s achieved by a p l a t e f a s t e n e d t o t h e f r o n t o f t h e a i l e r o n . On one end o f t h i s p l a t e t h e r e i s a s e a l i n g s t r i p , t h e o t h e r end of which i s f a s t e n e d t o t h e r e a r w a l l of t h e nonmoving wing. This s t r i p is a b a r r i e r , s e p a r a t i n g t h e i n t e r n a l c a v i t y of t h e r e a r p o r t i o n of t h e wing i n t o two nonconnected c a v i t i e s . When, f o r example, t h e a i l e r o n i s d e f l e c t e d downward, t h e flow r a t e o v e r t h e wing i n c r e a s e s , and t h e p r e s s u r e correspondingly d e c r e a s e s . Due t o t h e d e c r e a s e i n p r e s s u r e , a i r i s pumped out of t h e upper c a v i t y o f t h e chamber and t h e p r e s s u r e i n t h i s c a v i t y d e c r e a s e s . The p r e s s u r e beneath t h e wing and i n t h e lower c a v i t y i n c r e a s e . As a r e s u l t of t h e p r e s s u r e d i f f e r e n c e i n t h e upper and. lower c a v i t i e s , aerodynamic f o r c e Y a c t s on t h e s t r i p and p l a t e . T h i s k f o r c e creates a moment about t h e a x i s of r o t a t i o n o f t h e a i l e r o n which decreases t h e hinge moment. The compensation works s i m i l a r l y when t h e a i l e r o n i s d e f l e c t e d upward. The advantage of i n t e r n a l aerodynamic compensation i s /238 t h a t i t produces a v e r y s l i g h t i n c r e a s e i n d r a g o f t h e wing, s i n c e t h e r e a r e no p r o t r u d i n g p a r t s o f t h e a i l e r o n b e f o r e i t s a x i s of r o t a t i o n . However, i t does have c e r t a i n d e f e c t s a s w e l l . The a i l e r o n p l a t e s w i t h i n t h e wing l i m i t t h e angle of d e f l e c t i o n o f t h e a i l e r o n s . For t h e e l e v a t o r and rudder, which have c o n s i d e r a b l e d e f l e c t i o n , t h e usage o f t h i s compensation i s d i f f i c u l t due t o t h e t h i n t a i l s u r f a c e p r o f i l e s . The f l e x i b l e s t r i p must b e c a r e f u l l y maintained d u r i n g o p e r a t i o n . If t h e s t r i p i s damaged, t h e compensation fails. The servo-compensator ( o r F l e t t n e r ) i s a small supplementary c o n t r o l s u r f a c e l o c a t e d a t t h e r e a r end o f t h e main a r t i c u l a t e d s u r f a c e and hinge connected t o t h e nonmoving p o r t i o n o f t h e t a i l s u r f a c e ( v e r t i c a l t a i l s u r f a c e f o r t h e rudder o r wing f o r t h e a i l e r o n s ) by a t e n s i o n member (Figure 154 b ) . Deflection o f t h e c o n t r o l s u r f a c e a u t o m a t i c a l l y causes t h e servo-compensator t o move i n t h e o p p o s i t e d i r e c t i o n . The aerodynamic f o r c e a r i s i n g on t h e servo-compensator i s o p p o s i t e i n i t s s i g n t o t h e aerodynamic f o r c e on t h e c o n t r o l s u r f a c e . As a r e s u l t o f t h i s , t h e h i n g e moment of t h e s u r f a c e i s 2 32
- 244. decreased. Servo-compensators are i n s t a l l e d on t h e a i l e r o n s and rudder, l e s s f r e q u e n t l y on t h e e l e v a t o r s . Servo-compensators a r e d e f l e c t e d by '3-14". This reduces t h e f o r c e r e q u i r e d t o a c c e p t a b l e l e v e l s . Trimmers allow l o a d s o p e r a t i n g o v e r long p e r i o d s o f time and c o r r e sponding t o d e f i e c t i o n o f t h e rudder o r a i l e r o n t o b e completely o r almost completely removed; t h e y cannot b e used t o d e c r e a s e t h e f o r c e s a r i s i n g during b r i e f d e f l e c t i o n s of t h e s e s u r f a c e s ( f o r example when moving i n t o a new f l i g h t . regime o r when c o u n t e r i n g e x t e r n a l p e r t u r b a t i o n ) The area of t h e e l e v a t o r trimmer o f a modern a i r c r a f t i s 7-10% of t h e a r e a o f t h e e l e v a t o r , t h e a r e a o f t h e r u d d e r trimmer i s 8-10% t h e a r e a o f t h e rudder, while t h e a r e a o f t h e a i l e r o n t r i m m e r i s 6-8% of t h e a r e a of t h e ailerons. The angles of d e f l e c t i o n o f t h e trimmers a r e so s e l e c t e d t h a t i n c a s e of a c c i d e n t a l o p e r a t i o n of t h e e l e c t r i c a l c o n t r o l mechanisms f o r t h e trimmers, r e s u l t i n g i n movement of t h e c o n t r o l s u r f a c e s , t h e p i l o t w i l l be p h y s i c a l l y a b l e t o h o l d t h e c o n t r o l s u r f a c e i n t h e r e q u i r e d p o s i t i o n s . For example, i f t h e trimmer o f t h e rudder i s d e f l e c t e d by '3-4" and t h e r a t e of movement i s 0.5 deg/sec, a c c i d e n t a l o p e r a t i o n o f t h e trimmer w i l l cause it t o d e f l e c t f u l l y ( i n 6-7 s e c ) and a t speeds of 300-350 km/hr, c r e a t e s f o r c e s on t h e p e d a l s of 25-30 kg; a t 500-600 km/hr a t H = 1000 m , t h e f o r c e c r e a t e d i s 70-80 kg. This f o r c e can be overcome by t h e p i l o t and c o p i l o t and r e p r e s e n t s no emergency s i t u a t i o n . The angle o f d e f l e c t i o n o f t h e a i l e r o n trimmers i s a l s o '3-4", and t h e r a t e of movement i s about 0 . 4 deg/sec. With t h e maximum d e f l e c t i o n of t h e trimmer, f o r c e on t h e c o n t r o l l e v e r of 12-36kg r e s p e c t i v e l y i s r e q u i r e d f o r speeds of 300-500 km/hr. The a n g l e of d e f l e c t i o n o f t h e e l e v a t o r trimmers i s - /239 6-8" upward, 8-10" downward, and t h e r a t e o f movement i s 1 deg/sec. Accidental connection of t h e e l e v a t o r trimmer e l e c t r i c d r i v e and d e f l e c t i o n of t h e trimmer by 3-4" c r e a t e s a load of 22-27 kg on t h e s t i c k a t 300 km/hr, 60-70 kg a t 520 km/hr. Consequently, t h i s a l s o c r e a t e s no emergency s i t u a t i o n . 526. Balancing of t h e A i r c r a f t During Takeoff and Landing L e t u s analyze how t h e a i r c r a f t i s balanced d u r i n g t a k e o f f a t 2 0 0 300 km/hr (Figure 1 5 6 ) . A t t h e moment when t h e f r o n t landing g e a r l i f t s (V = 200 km/hr, t a k e o f f w i t h p r e l i m i n a r y l i f t o f f r o n t g e a r ) , t h e a n g l e o f d e f l e c t i o n of t h e e l e v a t o r 6el = -16.7", and t h e f o r c e on t h e s t i c k i s 37.5 kg. A s t h e speed i n c r e a s e s , t h e e f f e c t i v e n e s s of t h e e l e v a t o r i n c r e a s e s and t h e p i l o t d e c r e a s e s i t s d e f l e c t i o n , while t h e f o r c e i n c r e a s e s . A t t h e moment o f l i f t o f f o f t h e a i r c r a f t (V = 240 km/hr), t h e angle of d e f l e c t i o n of t h e e l e v a t o r i s -14" and t h e f o r c e on t h e s t i c k i s 45 kg. A f t e r l i f t o f f a s t h e f l i g h t speed i n c r e a s e s , t h e e l e v a t o r f e e d i s decreased, and t h e f o r c e on t h e s t i c k a l s o decreases. 233
- 245. ' Usage of t h e trimmer reduces t h e f o r c e . For example, a t 200 km/hr, a . d e f l e c t i o n -io -4 of t h e trimmer by one I; degree decreases t h e -20 -8 f o r c e by 3 kg, a t 240 km/hr -- by -3u -12 4.35 kg, a t 300 km/hr -- 3y 7 kg. -4ff - 6 1 As we can s e e from t h e graph, a t 300 km/hr, i n -50 0 o r d e r t o remove t h e force, the elevator trimmer must be d e f l e c t e d by approx- Figure 156. Deflection of Elevator and Force imately 4". Before on S t i c k As a Function o f Velocity During takeoff , t h e e l e v a t o r Takeoff trimmer i s p r e s e t a t 1.5-2" ( t h e wheel i s turned toward t h e p i l o t ) . Further trimmer adjustment i s performed i n f l i g h t a f t e r t h e landing g e a r and f l a p s /240 have been r a i s e d . H-15-25N , t0,uchdowq landing c o n s i s t s of t h e following. As oc I t h e v e l o c i t y i s decreased i n t h e 2'70 is0 250 240 20 Z~RI@$I~ 3 glide, t h e deflection of the elevator -4 ---IO upward and f o r c e on t h e s t i c k i n c r e a s e . As we can s e e from -&-% Figure 157, i f t h e e l e v a t o r i s - P d e f l e c t e d upward by 7 " a t 275 km/hr, - 12 - --3a 'YhePr; and t h e f o r c e i s 28 kg (trimmer 1 - --40 6 n e u t r a l ) , a t 230 km/hr t h e s e q u a n t i t i e s a r e 13' and 38 kg -20 ---50 r e s p e c t i v e l y . A t t h e moment o f c touchdown a t 220 km/hr, t h e angle of d e f l e c t i o n o f t h e e l e v a t o r i s approx- 2 34
- 246. s t i c k . A t 280-300 km/hr, t h e f o r c e on t h e s t i c k is n e a r zero. As t h e v e l o c i t y i s decreased d u r i n g t h e g l i d e and t h e e l e v a t o r d e f l e c t i o n i s i n c r e a s e d t o 15-17", t h e p u l l i n g f o r c e s on t h e s t i c k i n c r e a s e , amounting t o 10-15 kg a t t h e moment of touchdown. An a d j u s t a b l e s t a b i l i z e r allows t h e l o a d s on t h e e l e v a t o r t o be decreased s i g n i f i c a n t l y i f i t i s d e f l e c t e d by - 2 t o -5". 2 35
- 247. Chapter X I I . Influence of I c i n g on Flying C h a r a c t e r i s t i c s §I. General Statements In j e t a i r c r a f t , i c i n g g e n e r a l l y occurs on t h e f r o n t edges of t h e wings, v e r t i c a l t a i l s u r f a c e and s t a b i l i z e r , t h e windshields o f t h e p i l o t and n a v i g a t o r , t h e temperature r e c e p t o r and n a v i g a t i o n a l instrument t u b e s p r o j e c t i n g outward from t h e f u s e l a g e and a l s o t h e edges o f t h e a i r i n t a k e s , engine support p i l o n s , b l a d e s of t h e i n t a k e d i r e c t i n g a p p a r a t u s and f i r s t /241 - compressor s t a g e . I n modern t u r b o j e t a i r c r a f t with high power r e s e r v e , i c i n g of t h e f u s e l a g e , wings and h o r i z o n t a l t a i l s u r f a c e s changes t h e f l y i n g d a t a ( f l i g h t speed, v e r t i c a l v e l o c i t y component, e t c . ) only s l i g h t l y ; t h e main danger t o f l i g h t under i c i n g c o n d i t i o n s does not r e s u l t from an i n c r e a s e i n a i r c r a f t weight due t o d e p o s i t i o n of i c e , b u t r a t h e r from t h e d e t e r i o r a t i o n i n c h a r a c t e r i s t i c s of s t a b i l i t y and c o n t r o l l a b i l i t y of t h e a i r c r a f t . The i c e f i l m s which a r e formed ( i f t h e a n t i - i c i n g system i s not used) may s i g n i f i c a n t l y change t h e wing p r o f i l e and t h e p r o f i l e o f t h e h o r i z o n t a l t a i l s u r f a c e , c r e a t i n g i n c r e a s e d turbulence and flow s e p a r a t i o n , which i s p a r t i c u l a r l y dangerous f o r low speed f l i g h t during t h e approach t o landing. Although i c i n g of t h e wings and f u s e l a g e change t h e f l y i n g c h a r a c t e r i s t i c s but l i t t l e , i c i n g of t h e s t a b i l i z e r , even when t h e i c e i s r a t h e r t h i n , may have an e s s e n t i a l i n f l u e n c e on t h e s t a b i l i t y and c o n t r o l l a b i l i t y o f t h e a i r c r a f t . Flow s e p a r a t i o n on t h e h o r i z o n t a l t a i l s u r f a c e depends p r i m a r i l y on t h e form of t h e i c e deposited and t o a c o n s i d e r a b l y lesser e x t e n t on i t s t h i c k n e s s . Deposition o f i c e on t h e a i r i n t a k e , followed by s e p a r a t i o n of t h e i c e and e n t r y of i c e p a r t i c l e s t o t h e compressor b l a d e s may cause damage t o t h e compressor and t o t h e engine. Therefore, i c i n g o f t h e i n t a k e channels and f i r s t s t a g e of t h e compressor cannot be p e r m i t t e d , n o t due t o t h e d e c r e a s e i n t h r u s t which r e s u l t s , but r a t h e r due t o t h e p o s s i b i l i t y of complete d i s r u p t i o n o f compressor o p e r a t i o n . I c i n g of t h e a i r c r a f t occurs p r i m a r i l y i n clouds ( u s u a l l y a t temperatures below f r e e z i n g ) , c o n s i s t i n g of supercooled water d r o p l e t s which f r e e z e when t h e y s t r i k e t h e s u r f a c e of t h e f l y i n g a i r c r a f t and form i c e d e p o s i t s on v a r i o u s a i r c r a f t p a r t s . The q u a n t i t y of i c e d e p o s i t e d depends on t h e time which t h e a i r c r a f t spends under i c i n g c o n d i t i o n s . For example, i n f l i g h t s o f a TU-104 a i r c r a f t , i c i n g was observed between 3000 and 8000 m a t surrounding a i r temperatures from -8 t o -34" i n c i r r u s , a l t o altocumulus and a l t o s t r a t u s clouds. I c i n g has n o t been observed a t high a l t i t u d e s o u t s i d e t h e clouds. The maximum time of continuous a i r c r a f t o p e r a t i o n under i n t e n s i v e i c i n g c o n d i t i o n s was 12-15 min, and t h e maximum i c e t h i c k n e s s (according t o t h e i n d i c a t o r ) was 46-50 mm. The b r i e f time which t h e j e t a i r c r a f t spends under i c i n g c o n d i t i o n s r e s u l t s from t h e high f l i g h t speeds (650-850 km/hr). Climbs t o 8000-11,000 m occur i n 15-28 min, and t h e a i r c r a f t climbs through t h e main l a y e r of clouds n e a r t h e e a r t h (2000-4000 m) a t high v e r t i c a l speeds 2 36
- 248. I' (12-16 m/sec) i n 3-5 min. The same t h i n g occurs d u r i n g t h e d e s c e n t . The g r e a t e s t p o s s i b i l i t y o f i c i n g o c c u r s d u r i n g c i r c l i n g f l i g h t i n t h e a r e a of an a i r f i e l d , a t which time t h e a i r c r a f t f l i e s a t 350-380 km/hr, spending 10-12 min i n t h e approach t o landing. When f l y i n g a t very high speeds, t h e s u r f a c e o f t h e a i r c r a f t i s heated; /242 which p r e v e n t s i c i n g t o some e x t e n t . The s u r f a c e of t h e wing i s p a r t i c u l a r l y h e a t e d , s i n c e h e a t is l i b e r a t e d due t o i n t e r n a l f r i c t i o n i n t h e boundary l a y e r and t h e temperature of t h e l e a d i n g edge o f t h e wing i s i n c r e a s e d . There i s a p o i n t along t h e p r o f i l e of t h e wing where t h e flow i s completely d e c e l e r a t e d , which i s accompanied by an i n c r e a s e i n temperature AT o f t h e a i r i n r e l a t i o n t o t h e temperature of t h e surrounding a i r . This temperature i n c r e a s e depends on t h e f l i g h t speed and can be c a l c u l a t e d u s i n g t h e formula V2 AT=-- 2000 ' where speed V i s t a k e n i n m/sec. The v a l u e s of temperature i n c r e a s e f o r v a r i o u s f l i g h t speeds a r e shown i n Table 14. T A B L E 14 However, during i c i n g of an a i r c r a f t t h e a c t u a l i n c r e a s e i s 30-50% l e s s . This r e s u l t s from t h e f a c t t h a t t h e water d r o p l e t s which d e p o s i t on t h e s u r f a c e of t h e a i r c r a f t w i l l be p a r t i a l l y o'r completely evaporated and t h e r e f o r e w i l l d e c r e a s e t h e temperature of t h e s u r f a c e . A l s o , h e a t exchange occurs i n t h e boundary s u r f a c e , a l s o reducing t h e temperature. 52. Types and Forms o f Ice Deposition. I n t e n s i t y of Icing The forms of a i r c r a f t i c i n g a r e v a r i o u s and depend p r i m a r i l y on t h e e x t e n t of s u p e r c o o l i n g o f t h e d r o p l e t s i n t h e clouds. The following t y p e s o f ice are differentiatedl : I20. K. Trunov, ObZedeneniye SamoZetov i Sredstva B o r ' b y s N i m i [ I c i n g o f A i r c r a f t and Methods o f I t s C o n t r o l ] , Mashinostroyeniye P r e s s , 1965. 237
- 249. a) Transparent ice ( g l a z e ) -- d e p o s i t e d on a i r c r a f t f l y i n g i n medium w i t h l a r g e , supercooled d r o p l e t s forming even, dense and t r a n s p a r e n t l a y e r (Figure 152 a ) . Ice formation temperature 0 t o -5'. This form of i c i n g i s p a r t i c u l a r l y dangerous, s i n c e it a t t a c h e s i t s e l f f i r m l y t o t h e s u r f a c e of t h e a i r c r a f t . If t h e r e i s a h e a t i n g element on t h e f r o n t edge, b a r r i e r i c e i s formed ,(Figure 158 e ) ; b ) T r a n s l u c e n t mixed i c e -- encountered more f r e q u e n t l y (Figure 158 b ) , formed a t -5 t o -lo", s h a r p l y worsening aerodynamic q u a l i t y o f a i r c r a f t ; c) Hoar f r o s t - - a w h i t e , l a r g e - g r a i n e d c r y s t a l l i n e i c e , formation temperature about -10" (Figure 158 c ) , uneven d e p o s i t i o n form with ragged p r o j e c t i n g edges , making f l i g h t dangerous ( e a r l y flow s e p a r a t i o n p o s s i b l e ) ; d) Rime - - a white, f i n e c r y s t a l l i n e d e p o s i t formed by water vapor f r o z e n upon c o n t a c t with t h e cooled s u r f a c e of t h e a i r c r a f t , r e p r e s e n t i n g no danger f o r j e t a i r c r a f t ; e) Barrier i c e -- d e p o s i t e d on t h e l e a d i n g edge a t temperatures above 0 " , on remaining p o r t i o n s a t lower temperatures ( t h e e f f e c t o f t h e h e a t i n g element a p p e a r s ) , t h e moisture which p r e c i p i t a t e s does n o t f r e e z e , b u t i s blown away by t h e a i r and f r e e z e s t o t h e s u r f a c e of t h e wing ( s t a b i l i z e r ) on both s i d e s o f t h e l e a d i n g edge, forming an i c e d e p o s i t i n a grooved shape along t h e l e a d i n g edge (Figure 158 e ) . When d e p o s i t e d on t h e l e a d i n g edge o f t h e s t a b i l i z e r , may r e s u l t i n complete flow s e p a r a t i o n . Since t h e t e s t i n g o f an a i r c r a f t f o r s t a b i l i t y and c o n t r o l l a b i l i t y w i t h i c i n g of t h e wings and s t a b i l i z e r s represents a certain d i f f i c u l t y, p a r t i c u l a r l y during t h e w a r m season of t h e y e a r , i n e) Heating element r e c e n t times t e s t s have / been made u s i n g models i n wind t u n n e l s with i c i n g imitators fastened t o t h e Figure 158. C h a r a c t e r i s t i c Forms of Ice wings and s t a b i l i z e r . Depos i t s on W i ngs Flying t e s t s o f a i r c r a f t with i c e i m i t a t o r s glued onto t h e f r o n t edge o f t h e s t a b i l i z e r a r e a l s o performed. As wind t u n n e l t e s t s o f model a i r c r a f t have shown, i c i n g i m i t a t o r s p l a c e d on t h e l e a d i n g edge of t h e s t a b i l i z e r cause s l i g h t changes i n t h e c h a r a c t e r i s t i c s o f s t a b i l i t y and c o n t r o l l a b i l i t y . The forms of t h e i m i t a t o r s (Figure 159) are s i m i l a r t o t h e n a t u r a l ' f o r m s of i c e d e p o s i t i o n . For example, i m i t a t o r form 1 r e p r e s e n t s t h e i c e d e p o s i t produced during i n t e n s i v e i c i n g 2 38
- 250. / with poor o p e r a t i o n o f edge h e a t e r ( t h e i c e t a k e s on t h e form of a groove); 2 r e p r e s e n t s b a r r i e r i c e w i t h t h e h e a t i n g element o p e r a t i n g ; 3 r e p r e s e n t s t h e d e p o s i t i o n o f i c e a t temperatures of - 3 t o -go with t h e h e a t i n g system n o t operating. The i n f l u e n c e of i c i n g of t h e s t a b i l i z e r on c h a r a c t e r i s t i c s o f l o n g i t u d - /244 i n a l s t a b i l i t y and controllability w i l l b e d e s c r i b e d below. I n o r d e r t o e s t i m a t e t h e degree o f danger o f i c i n g o f an a i r c r a f t , t h e concept o f t h e i n t e n s i t y o f i c i n g has been i n t r o d u c e d , c h a r a c t e r i z i n g t h e q u a n t i t y o f i c e d e p o s i t e d ( i n nun) p e r min. The f o l l o w i n g scale h a s been .evolved: a) low i n t e n s i t y - - i c e d e p o s i t e d a t 1 mm/min; b) moderate -- from 1 t o 2 mm/min and c ) high - - from 2 mm/min up. Figure 159. Forms of I m i t a t o r s o f I c i n g of Leading Edge of S t a b i 1 i z e r S3. Influence o f Icing on S t a b i l i t y and C o n t r o l a b i l i t y of A i r c r a f t i n Pre landing G u i d e Regime I n o r d e r t o e s t i m a t e t h e i n f l u e n c e o f i c i n g of t h e l e a d i n g edge of wing and s t a b i l i z e r on t h e f l y i n g c h a r a c t e r i s t i c s o f an a i r c r a f t , a s well a s t h e s t a b i l i t y and c o n t r o l l a b i l i t y , s p e c i a l f l y i n g t e s t s a r e performed under c o n d i t i o n s of moderate o r s l i g h t i c i n g a t temperatures of t h e surrounding a i r between -3 and -17'C between 1000 and 2000 m a l t i t u d e w i t h i n d i c a t e d speeds of 400-420 km/hr (speeds n e a r t h o s e used i n t h e landing approach). P i l o t i n g o f an i c e d a i r c r a f t with an i c e t h i c k n e s s of 30-40 mm on t h e c o n t r o l s u r f a c e p r o f i l e ( a n t i - i c i n g system switched o f f ) i n h o r i z o n t a l f l i g h t and d u r i n g a climb with landing g e a r and f l a p s up without t h e c r e a t i o n of any maneuvering loads does not d i f f e r : e s s e n t i a l l y from p i l o t i n g under normal c o n d i t i o n s , i . e . , with no i c i n g . No n o t i c e a b l e changes i n s t a b i l i t y o r c o n t r o l l a b i l i t y of t h e a i r c r a f t were observed. The f o r c e s on t h e c o n t r o l l e v e r s remain p r a c t i c a l l y unchanged; no s e i z i n g o r wedging of t h e e l e v a t o r o r a i l e r o n s was noted. As t h e i c e continued t o i n c r e a s e i n t h i c k n e s s , t h e motor o p e r a t i n g regime had t o be i n c r e a s e d by 4-5% i n o r d e r t o maintain s t e a d y speed. The d a t a produced d u r i n g wind t u n n e l t e s t i n g o f an a i r c r a f t model with i c i n g i m i t a t o r s on t h e l e a d i n g edge o f t h e s t a b i l i z e r i n d i c a t e d t h a t i c i n g of t h e l e a d i n g edge o f t h e s t a b i l i z e r should n o t r e s u l t i n d i s r u p t i o n of s t a b i l i t y o r l o s s of c o n t r o l d u r i n g s h a r p d e f l e c t i o n s o f t h e e l e v a t o r . This allowed f l y i n g t e s t s t o b e performed s a f e l y . 2 39
- 251. Sharp i n p u t s o f e l e v a t o r c o n t r o l ("feed") d u r i n g t h e approach t o landing a t 260-290 km/hr (without i c i n g ) w i t h landing g e a r , f l a p s and a i r b r a k e down showed t h a t t h e a i r c r a f t was s t a b l e i n t h e l o n g i t u d i n a l d i r e c t i o n w i t h overload decreased down t o 0.2. As w e know, t h e p i l o t s e n s e s h i s c o n t r o l o f t h e a i r c r a f t from t h e r e s i s t a n c e which h e f e e l s a t t h e c o n t r o l s t i c k d u r i n g t h e ' /245 p r o c e s s of performance of v a r i o u s maneuvers. I n o r d e r t o c r e a t e a c o n s i d e r a b l e o v e r l o a d , l a r g e f o r c e s must b e a p p l i e d t o t h e s t i c k . When t h e s t i c k i s trfed" forward, t h e p i l o t should f e e l a f o r c e on t h e s t i c k , g r e a t e r t h e less t h e o v e r l o a d c r e a t e d . I n t h o s e c a s e s when t h e p i l o t ceases t o f e e l t h e c o n t r o l of t h e a i r c r a f t , l o n g i t u d i n a l overload s t a b i l i t y of the aircraft is disrupted. A r e d u c t i o n i n t h e f o r c e on t h e c o n t r o l s t i c k d u r i n g i c i n g c o n d i t i o n s r e s u l t s from a change i n t h e hinge moments due t o r e d i s t r i b u t i o n o f p r e s s u r e s on t h e h o r i z o n t a l t a i l s u r f a c e . T h i s i s explained by t h e appearance of l o c a l a i r flow s e p a r a t i o n over t h e lower s u r f a c e of t h e s t a b i l i z e r . W can s e e from t h e graph on Figure 160 t h a t a t 290-260 km/hr a s t h e e overloads d e c r e a s e , t h e f o r c e on t h e c o n t r o l s t i c k i n c r e a s e s , a s does t h e angle of d e f l e c t i o n o f t h e e l e v a t o r . The amount of e l e v a t o r f e e d which must b e a p p l i e d p e r u n i t of overload a t 290 km/hr i s less t h a n z t 250 km/hr. The f o r c e s on t h e s t i c k change a s f o l l o w s . For example, i n o r d e r t o c r e a t e an o v e r l o a d n = 0 . 4 a t V = 260 km/hr, a f o r c e of 2 2 kg i s r e q u i r e d , while a t Y V = 290 km/hr - - 37 kg i s r e q u i r e d . With s h a r p d e f l e c t i o n s of t h e e l e v a t o r , t h e overload ( p a r t i c u l a r l y , 0.2) was r e t a i n e d f o r 3-4 s e c and no drop i n f o r c e on t h e s t i c k was observed. The model t e s t s performed i n t h e wind tunnel using t h e horizontal t a i l surface and n e g a t i v e a n g l e s o f attack (-10 t o -18') showed t h a t when t h e l e a d i n g edge of t h e s t a b i l i z e r i s i c e d ( t h e f a i l u r e of a n t i - i c i n g system), no d i s r u p t i o n of l o n g i t u d i n a l s t a t i c s t a b i l i t y o r change i n hinge moments of t h e e l e v a t o r was observed. A change i n s t a t i c s t a b i l i t y o r hinge moment o f t h e e l e v a t o r i s observed o n l y a t a n g l e s o f a t t a c k corresponding t o n e g a t i v e o v e r l o a d s . For zero overload v a l u e s , t h e graph mZ = f ( a ) i n t h e c a s e of an i c e d l e a d i n g edge o f t h e s t a b i l i z e r , Figure 160. D e f l e c t i o n o f changes i t s i n c l i n a t i o n very s l i g h t l y with Elevator and Force on t h e t h r e e forms of i m i t a t o r s used, i . e . , Control S t i c k As a Func- t h e l o n g i t u d i n a l s t a t i c s t a b i l i t y remained t i o n o f Overloads (pro- p r a c t i c a l l y unchanged. duced i n f l y i n g t e s t s ) The flow angles were measured with f l a p s down, and f o r wing angles of a t t a c k /246 of 2-4", t h e flow a n g l e s were 5-6" (with 240
- 252. qJ = - 2 " ) . As was s t a t e d above, when g l i d i n g i n f o r a landing, t h e wing has a = 3"; t h e r e f o r e , with a flow angle o f about So, we produce a n e g a t i v e v a l u e of angle cr = qJ - E = 3" - 2" - 5" = of a t t a c k o f t h e h o r i z o n t a l t a i l s u r f a c e : a. = a -4". nt With t h e same angle of a t t a c k , flow s e p a r a t i o n on a swept s t a b i l i z e r does n o t occur, s i n e i t s c r i t i c a l angle of a t t a c k d u r i n g i c i n g changes from F 16-17" by only 3-4" . Even with l a r g e flow angles ( i n t h e c a s e o f i c i n g o f t h e leading edge of t h e s t a b i l i z e r by b a r r i e r i c e of c o n s i d e r a b l e t h i c k n e s s ) , t h e angle o f a t t a c k of t h e h o r i z o n t a l s u r f a c e does not change i t s c r i t i c a l value. W analyzed t h e case i n which t h a a n t i - i c i n g system d i d n o t work o r was e not connected, and i n v e s t i g a t e d what might occur i f an a i r c r a f t began i c i n g as i t descended f o r a landing. I n p r a c t i c e , f a i l u r e of t h e a n t i - i c i n g system on t u r b o j e t a i r c r a f t a t Vind = 400-450 km/hr, t h e temperature drops along t h e leading edge of t h e wings (hot a i r h e a t i n g system turned on) decrease only s l i g h t l y , while t h e e l e c t r i c a l s t a b i l i z e r and v e r t i c a l f i n h e a t i n g system o p e r a t e normally with one engine o u t , being independent o f t h e number o f engines i n o p e r a t i o n on t h e a i r c r a f t . Greater d i f f i c u l t i e s can be c r e a t e d by untimely switching on of t h e system h e a t i n g wings, v e r t i c a l t a i l s u r f a c e and s t a b i l i z e r than by f a i l u r e of one engine, with t h e r e s u l t i n g r e d u c t i o n i n hot a i r untake. I t has been noted t h a t when t h e a n t i - i c i n g system on t h e wing i s turned on a f t e r i c e has grown t o 24 mm t h i c k n e s s on a c o n t r o l l e d s u r f a c e t h e i c e was shed from t h e heated leacling edge i n one minute, whi.le when t h e a n t i - i c i n g system of t h e s t a b i l i z e r was turned on, i c e was shed from both halves of t h e s t a b i l i z e r i n 1 - 2 c y c l e s (2-4 min). In o r d e r t o be s a f e during a landing approach with t h e a n t i - i c i n g system not o p e r a t i n g , t h e p i l o t should b r i n g h i s a i r c r a f t down smoothly, not c r e a t i n g overloads l e s s than 1. . . . . -- - -.. . . .- - . . . . . ~ . .. _._~ ~ ' A l l - r e l a t e d t o - a swept s t a b l i z e r w i t h x = 40-45". 1 NASA-Langley, 1969 -1 F-542 241
- 253. i N ATIONAL AERONAUTICS SPACE ADMINISTRATION AND S, I h WASHINGTON,C. 20546 D. OFFICIAL BUSINESS FIRST CLASS MAIL POSTAGE A f J D FEES PA NATIONAL AERONAUTICS SPACE ADMINISTRATIO If Undeliverable (Section POSTMASTER: Postal Manual) Do Nor R " T h e ne1 oiirricticnl nnd spnce cictivities of the Uuited States shnll be coizdzccted so ns t o coiztsibzcte . . . t o the expmzsion of huttian knoavl edge of phenomena in the dmosphese nizd spnce. T h e Adtiiinistrntiolz shdl provide for the widest psrrcticable and @propsiate dissetnhaation of iizfos)iintio?z coixesizing its nctiiijties nizd the seszclts theseof." -NATIONALAERONAUTICS D SPACE ACT OF 1958 AN NASA SCIENTIFIC AND TECHNICAL PUBLICATIONS TECHNICAL REPORTS: Scientific and TECHNICAL TRANSLATIONS: Information technical information considered important, - published in a foreign language considered complete, and a lasting contribution to existing to merit NASA distribution in English. knowledge. SPECIAL PUBLICATIONS: Information TECHNICAL NOTES: Information less broad derived from or of value to NASA activities. in scope but nevertheless of importance as a Publications include conference proceedings, contribution to existing knowledge. . monographs, data compilations, handbooks, sc)urcebooks,and special bibliographies. TECHNICAL MEMORANDUMS: Information receiving limited distribution TECHNOLOGY UTILIZATION because of preliminary data, securjty classifica PUBLICATIONS: Information on technology tion, or other reasons. used by NASA that may be of particular interest in commercial and other non-aerospace CONTRACTOR REPORTS: Scientific and applications. Publications include Tech Briefs, technical information generated under a NASA Ttchnology Utilization Reports and Notes, contract or grant and considered an important and Technology Surveys. contribution to existing knowledge. Details on the availability of these publications may be obtained from: DIVISION SCIENTIFIC AND TECHNICAL INFORMATION NATIONAL AERONAUTICS AND SPACE ADMINISTRATION Washington, D.C. 20546