18 Superelevation and Spiral Curves.ppt

1
Quiz Answers
What can be done to improve the safety of a
horizontal curve?
 Make it less sharp
 Widen lanes and shoulders on curve
 Add spiral transitions
 Increase superelevation

2
Quiz Answers
5. Increase clear zone
6. Improve horizontal and vertical
alignment
7. Assure adequate surface drainage
8. Increase skid resistance on downgrade
curves

3
Some of Your Answers
 Decrease posted speed
 Add rumble strips
 Bigger or better signs
 Guardrail
 Better lane markers
 Sight distance
 Decrease radius

4
Superelevation and Spiral
Curves
CE 453 Lecture 18

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Objectives
1. Define superelevation runoff length and
methods of attainment (for simple and
spiral curves)
2. Calculate spiral curve length

6
Other Issues Relating to
Horizontal Curves
1. Need to coordinate with
vertical and topography
2. Not always needed
MAXIMUM CENTERLINE DEFLECTION
NOT REQUIRING HORIZONTAL CURVE
Design Speed, mph Maximum Deflection
25 5°30'
30 3°45'
35 2°45'
40 2°15'
45 1°15'
50 1°15'
55 1°00'
60 1°00'
65 0°45'
70 0°45'
Source: Ohio DOT Design Manual, Figure 202-1E

7
Attainment of Superelevation -
General
1. Tangent to superelevation
2. Must be done gradually over a distance without
appreciable reduction in speed or safety and
with comfort
3. Change in pavement slope should be consistent
over a distance
4. Methods (Exhibit 3-37 p. 186)
a. Rotate pavement about centerline
b. Rotate about inner edge of pavement
c. Rotate about outside edge of pavement

8
Superelevation
Transition Section
• Tangent Runout Section +
Superelevation Runoff Section

9
Tangent Runout Section
• Length of roadway needed to
accomplish a change in outside-lane
cross slope from normal cross
slope rate to zero
For rotation about
centerline

10
Superelevation Runoff
Section
• Length of roadway needed to
accomplish a change in outside-lane
cross slope from 0 to full
superelevation or vice versa
• For undivided highways with cross-
section rotated about centerline

11
Source: A Policy
on Geometric
Design of
Highways and
Streets (The
Green Book).
Washington, DC.
American
Association of
State Highway
and
Transportation
Officials, 2001
4th Ed.

12
Source: A Policy
on Geometric
Design of
Highways and
Streets (The
Green Book).
Washington, DC.
American
Association of
State Highway
and
Transportation
Officials, 2001
4th Ed.

14
Source: CalTrans Design Manual online,
http://www.dot.ca.gov/hq/oppd/hdm/pdf/chp0200.pdf

15
Source: Iowa DOT Standard Road
Plans
Same as point E of GB

16
Attainment Location -
WHERE
1. Superelevation must be attained over a
length that includes the tangent and the
curve (why)
2. Typical: 66% on tangent and 33% on
curve of length of runoff if no spiral
3. Iowa uses 70% and 30% if no spiral
4. Super runoff is all attained in Spiral if
used (see lab manual (Iowa Spiral length =
Runoff length)

17
Minimum Length of Runoff
for curve
• Lr based on drainage and
aesthetics
• rate of transition of edge line
from NC to full superelevation
traditionally taken at 0.5% ( 1
foot rise per 200 feet along the
road)
• current recommendation varies
from 0.35% at 80 mph to 0.80%
for 15mph (with further
adjustments for number of lanes)

18
Minimum Length of Tangent Runout
Lt = eNC x Lr
ed
where
• eNC = normal cross slope rate (%)
• ed = design superelevation rate
• Lr = minimum length of superelevation
runoff (ft)
(Result is the edge slope is same as for
Runoff segment)

19
Length of Superelevation
Runoff
α = multilane adjustment factor
Adjusts for total width
r

20
Relative Gradient (G)
• Maximum longitudinal slope
• Depends on design speed, higher
speed = gentler slope. For example:
• For 15 mph, G = 0.78%
• For 80 mph, G = 0.35%
• See table, next page

21
Maximum Relative
Gradient (G)
Source: A Policy on Geometric Design of
Highways and Streets (The Green Book).
Washington, DC. American Association of
State Highway and Transportation Officials,
2001 4th Ed.

22
Multilane Adjustment
• Runout and runoff must be adjusted for
multilane rotation.
• See Iowa DOT manual section 2A-2 and
Standard Road Plan RP-2

23
Length of Superelevation
Runoff Example
For a 4-lane divided highway with cross-
section rotated about centerline, design
superelevation rate = 4%. Design speed
is 50 mph. What is the minimum length
of superelevation runoff (ft)
Lr = 12eα
G
•

24
Lr = 12eα = (12) (0.04) (1.5)
G 0.5
Lr = 144 feet

25
Tangent runout length
Example continued
• Lt = (eNC / ed ) x Lr
as defined previously, if NC = 2%
Tangent runout for the example is:
LT = 2% / 4% * 144’ = 72 feet

26
From previous example, speed = 50 mph, e = 4%
From chart runoff = 144 feet, same as from calculation
Source: A Policy on Geometric
Design of Highways and
Streets (The Green Book).
Washington, DC. American
Association of State Highway
and Transportation Officials,
2001 4th Ed.

28
Spiral Curve Transitions
• Vehicles follow a transition path as
they enter or leave a horizontal
curve
• Combination of high speed and sharp
curvature can result in lateral shifts
in position and encroachment on
adjoining lanes

29
Spirals
1. Advantages
a. Provides natural, easy to follow, path
for drivers (less encroachment,
promotes more uniform speeds), lateral
force increases and decreases
gradually
b. Provides location for superelevation
runoff (not part on tangent/curve)
c. Provides transition in width when
horizontal curve is widened
d. Aesthetic

30
Minimum Length of Spiral
Possible Equations:
Larger of (1) L = 3.15 V3
RC
Where:
L = minimum length of spiral (ft)
V = speed (mph)
R = curve radius (ft)
C = rate of increase in centripetal acceleration
(ft/s3) use 1-3 ft/s3 for highway)

31
Minimum Length of Spiral
Or (2) L = (24pminR)1/2
Where:
L = minimum length of spiral (ft)
pmin = minimum lateral offset between the
tangent and circular curve (0.66 feet)

32
Maximum Length of Spiral
• Safety problems may occur when
spiral curves are too long – drivers
underestimate sharpness of
approaching curve (driver
expectancy)

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Maximum Length of Spiral
L = (24pmaxR)1/2
Where:
L = maximum length of spiral (ft)
pmax = maximum lateral offset between the
tangent and circular curve (3.3 feet)

34
Length of Spiral
o AASHTO also provides recommended spiral
lengths based on driver behavior rather
than a specific equation. See Table 16.12
of text and the associated tangent runout
lengths in Table 16.13.
o Superelevation runoff length is set equal
to the spiral curve length when spirals are
used.
o Design Note: For construction purposes,
round your designs to a reasonable values;
e.g.
Ls = 147 feet, round it to
Ls = 150 feet.

35
Source: Iowa DOT
Design Manual

36
Source: Iowa DOT
Design Manual

37
Source: Iowa
DOT Design
Manual

38
Source: Iowa DOT Design Manual
SPIRAL TERMINOLOGY

39
Attainment of superelevation
on spiral curves
See sketches that follow:
Normal Crown (DOT – pt A)
1. Tangent Runout (sometimes known as crown
runoff): removal of adverse crown (DOT – A to B)
B = TS
2. Point of reversal of crown (DOT – C) note A to B =
B to C
3. Length of Runoff: length from adverse crown
removed to full superelevated (DOT – B to D), D =
SC
4. Fully superelevate remainder of curve and then
reverse the process at the CS.

40
Source: Iowa DOT Standard Road Plans RP-2
With Spirals
Same as point E of GB

41
With Spirals
Tangent runout (A to B)

42
With Spirals
Removal of crown

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With Spirals
Transition of
superelevation
Full superelevation

45
Transition Example
Given:
• PI @ station 245+74.24
• D = 4º (R = 1,432.4 ft)
•  = 55.417º
• L = 1385.42 ft

46
With no spiral …
• T = 752.30 ft
• PC = PI – T = 238 +21.94

47
For:
• Design Speed = 50 mph
• superelevation = 0.04
• normal crown = 0.02
Runoff length was found to be 144’
Tangent runout length =
0.02/ 0.04 * 144 = 72 ft.

48
Where to start transition for superelevation?
Using 2/3 of Lr on tangent, 1/3 on curve for
superelevation runoff:
Distance before PC = Lt + 2/3 Lr
=72 +2/3 (144) = 168
Start removing crown at:
PC station – 168’ = 238+21.94 - 168.00 =
Station = 236+ 53.94

49
Location Example – with spiral
• Speed, e and NC as before and
•  = 55.417º
• PI @ Station 245+74.24
• R = 1,432.4’
• Lr was 144’, so set Ls = 150’

50
See Iowa DOT design manual for more
equations:
http://www.dot.state.ia.us/design/00_toc.ht
m#Chapter_2
• Spiral angle Θs = Ls * D /200 = 3 degrees
• P = 0.65 (calculated)
• Ts = (R + p ) tan (delta /2) + k = 827.63 ft

51
• TS station = PI – Ts
= 245+74.24 – 8 + 27.63
= 237+46.61
Runoff length = length of spiral
Tangent runout length = Lt = (eNC / ed ) x Lr
= 2% / 4% * 150’ = 75’
Therefore: Transition from Normal crown begins
at (237+46.61) – (0+75.00) = 236+71.61

52
With spirals, the central angle for the
circular curve is reduced by 2 * Θs
Lc = ((delta – 2 * Θs) / D) * 100
Lc = (55.417-2*3)/4)*100 = 1235.42 ft
Total length of curves = Lc +2 * Ls = 1535.42
Verify that this is exactly 1 spiral length
longer than when spirals are not used
(extra credit for who can tell me why,
provide a one-page memo by Monday)

53
Also note that the tangent length with
a spiral should be longer than the
non-spiraled curve by approximately ½
of the spiral length used. (good check
– but why???)

54
Notes – Iowa DOT
Source: Iowa DOT Standard Road Plans
Note: Draw a sketch and think about what the last para is saying

18 Superelevation and Spiral Curves.ppt

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18 Superelevation and Spiral Curves.ppt