Theory of flight prelim

INTRODUCTION
• Aerodynamics as explained in this may also be
termed “ Theory of Flight” because the flight of
any aircraft or any object moving through the air
depends upon the laws of aerodynamics.
• Aero means “ pertaining to air, aircraft, aviation,
or aeronautics”.
• Dynamics is that branch of physics which consider
bodies in motion and the forces that produce or
change such motion.

• Aero is derived from Greek word meaning air
And Dynamics comes from the Greek word
dynamics meaning power.
AERO + DYNAMICS = Aerodynamics meaning
“the science relating to the effect produced by
air or other gases in motion”

• Aerodynamically, an aircraft can be defined as
an object traveling through space that is
affected by the changes in atmospheric
conditions. To state it another way,
aerodynamics covers the relationships
between the aircraft, relative wind, and
atmosphere.

PHYSICS OF THE ATMOSPHERE
• Before examining the fundamental laws of
flight, several basic facts must be considered.
An aircraft operates in the air. Therefore,
those properties of air that affect the control
and performance of an aircraft must be
understood

• The air in the earth’s atmosphere is
composed mostly of nitrogen and
oxygen.

• Air is considered a fluid because it fits the
definition of a substance that has the ability to
flow or assume the shape of the container in
which it is enclosed. If the container is heated,
pressure increases; if cooled, the pressure
decreases.

• The weight of air is heaviest at sea level where
it has been compressed by all of the air above.
This compression of air is called atmospheric
pressure

PRESSURE
• Atmospheric pressure is usually defined as
the force exerted against the earth’s surface
by the weight of the air above that surface.

• Weight is force applied to an area that results
in pressure. Force (F) equals area (A) times
pressure (P), or F = AP. Therefore, to find the
amount of pressure, divide area into force (P =
F/A). A column of air (one square inch)
extending from sea level to the top of the
atmosphere weighs approximately 14.7
pounds; therefore, atmospheric pressure is
stated in pounds per square inch (psi). Thus,
atmospheric pressure at sea level is 14.7 psi.
F = AP
P = F/A

Figure 1-1. The weight exerted by a 1 square inch column of air stretching from
sea level to the top of the atmosphere is what is measured when it is said that
atmospheric pressure is equal to 14.7 pounds per square inch.

• Atmospheric pressure is measured with an
instrument called a barometer, composed of
mercury in a tube that records atmospheric
pressure in inches of mercury ("Hg). (Figure 1-
2) The standard measurement in aviation
altimeters and U.S. weather reports has been
"Hg. However, world-wide weather maps and
some non-U.S. manufactured aircraft
instruments indicate pressure in millibars
(mb), an SI metric unit

Figure 1-2. Barometer used to measure
atmospheric pressure

• Aviators often interchange references to
atmospheric pressure between linear
displacement (e.g., inches of mercury) and units
of force (e.g., psi). Over the years, meteorology
has shifted its use of linear displacement
representation of atmospheric pressure to units
of force. The unit of force nearly universally used
today to represent atmospheric pressure in
meteorology is the hectopascal (hPa). A pascal is
a SI metric unit that expresses force in Newtons
per square meter. A hectoPascal is 100 Pascals. 1
013.2 hPa is equal to 14.7 psi which is equal to
29.92 "Hg. (Figure 1-3)

Figure 1-3. Various equivalent
representations of atmospheric
pressure at sea level.

• If a block weighs 60 N and is lying on a side
with area 2m by 3m, what is the pressure
exerted on the surface?

• Atmospheric pressure decreases with
increasing altitude. The simplest explanation
for this is that the column of air that is
weighed is shorter. How the pressure changes
for a given altitude is shown in Figure 1-4. The
decrease in pressure is a rapid one and, at
50,000 feet, the atmospheric pressure has
dropped to almost one-tenth of the sea level
value.

• As an aircraft ascends, atmospheric pressure
drops, the quantity of oxygen decreases, and
temperature drops. These changes in altitude
affect an aircraft’s performance in such areas
as lift and engine horsepower. The effects of
temperature, altitude, and density of air on
aircraft performance are covered in the
following paragraphs.

Figure 1-4. Atmospheric pressure decreasing with
altitude. At sea level the pressure is 14.7 psi,
while at 40,000 feet, as the dotted lines show, the
pressure is only 2.72 psi.

DENSITY
• Density is weight per unit of volume. Since air is a
mixture of gases, it can be compressed. If the air
in one container is under half as much pressure
as an equal amount of air in an identical
container, the air under the greater pressure
weighs twice as much as that in the container
under lower pressure. The air under greater
pressure is twice as dense as that in the other
container. For the equal weight of air, that which
is under the greater pressure occupies only half
the volume of that under half the pressure.

• The density of gases is governed by the
following rules:
• 1. Density varies in direct proportion with the
pressure.
• 2. Density varies inversely with the
temperature.
• Thus, air at high altitudes is less dense than air
at low altitudes, and a mass of hot air is less
dense than a mass of cool air.

Compression and expansion of air

• Changes in density affect the aerodynamic
performance of aircraft with the same
horsepower. An aircraft can fly faster at a high
altitude where the density is low than at a low
altitude where the density is greater. This is
because air offers less resistance to the
aircraft when it contains a smaller number of
air particles per unit of volume.

HUMIDITY
• Humidity is the amount of water vapor in the
air. The maximum amount of water vapor that
air can hold varies with the temperature. The
higher the temperature of the air, the more
water vapor it can absorb.

• 1. Absolute humidity is the weight of water
vapor in a unit volume of air.
• 2. Relative humidity is the ratio, in percent, of
the moisture actually in the air to the
moisture it would hold if it were saturated at
the same temperature and pressure.

• Assuming that the temperature and pressure
remain the same, the density of the air varies
inversely with the humidity. On damp days, the
air density is less than on dry days. For this
reason, an aircraft requires a longer runway for
takeoff on damp days than it does on dry days.
• By itself, water vapor weighs approximately five
eighths as much as an equal amount of perfectly
dry air. Therefore, when air contains water vapor,
it is not as heavy as dry air containing no
moisture.

Effect of humidity on take off distance

TEMPERATURE AND ALTITUDE
• Temperature variations in the atmosphere are
of concern to aviators. Weather systems
produce changes in temperature near the
earth’s surface. Temperature also changes as
altitude is increased

• The troposphere is the lowest layer of the
atmosphere. On average, it ranges from the
earth’s surface to about 38,000 feet above it.
Over the poles, the troposphere extends to
only 25,000 - 30,000 feet and, at the equator,
it may extend to around 60,000 feet. This
oblong nature of the troposphere is illustrated
in Figure 1-5.

• Most civilian aviation takes place in the
troposphere in which temperature decreases
as altitude increases. The rate of change is
somewhat constant at about –2 °C or –3.5 °F
for every 1,000 feet of increase in altitude.
The upper boundary of the troposphere is the
tropopause. It is characterized as a zone of
relatively constant temperature of –57 °C or –
69 °F.

• Above the tropopause lies the stratosphere.
Temperature increases with altitude in the
stratosphere to near 0 °C before decreasing again
in the mesosphere, which lies above it. The
stratosphere contains the ozone layer that
protects the earth’s inhabitants from harmful UV
rays. Some civilian flights and numerous military
flights occur in the stratosphere. Figure 1-6
diagrams the temperature variations in different
layers of the atmosphere.

• As stated, density varies inversely with
temperature or, as temperature increases, air
density decreases. This phenomenon explains
why on very warm days, aircraft takeoff
performance decreases. The air available for
combustion is less dense. Air with low density
contains less total oxygen to combine with the
fuel.

INTERNATIONAL STANDARD
ATMOSPHERE
• The atmosphere is never at rest. Pressure,
temperature, humidity, and density of the air are
continuously changing. To provide a basis for
theoretical calculations, performance
comparisons and instrumentation parity,
standard values for these and other characteristic
of the atmosphere have been developed. ICAO,
ISO, and various governments establish and
publish the values known as the International
Standard Atmosphere. (Figure 1-7)

Figure 1-7. The International Standard Atmosphere.

AERODYNAMICS
• The law of conservation of energy states that
energy may neither be created nor destroyed.
Motion is the act or process of changing place
or position. An object may be in motion with
respect to one object and motionless with
respect to another.

• For example, a person sitting quietly in an
aircraft flying at 200 knots is at rest or
motionless with respect to the aircraft;
however, the person and the aircraft are in
motion with respect to the air and to the
earth.

• Air has no force or power, except pressure,
unless it is in motion. When it is moving,
however, its force becomes apparent. A
moving object in motionless air has a force
exerted on it as a result of its own motion. It
makes no difference in the effect then,
whether an object is moving with respect to
the air or the air is moving with respect to the
object. The flow of air around an object
caused by the movement of either the air or
the object, or both, is called the relative wind.

VELOCITY AND ACCELERATION
• The terms speed and velocity are often used
interchangeably, but they do not have the
same meaning. Speed is the rate of motion in
relation to time, and velocity is the rate of
motion in a particular direction in relation to
time.

• An aircraft starts from New York City and flies 10 hours
at an average speed of 260 kilometers per hour (kph).
At the end of this time, the aircraft may be over the
Atlantic Ocean, Canada the Gulf of Mexico, or, if its
flight were in a circular path, it may even be back over
New York City. If this same aircraft flew at a velocity of
260 kph in a southwestward direction, it would arrive
in Dallas, TX in about 10 hours. Only the rate of motion
is indicated in the first example and denotes the speed
of the aircraft. In the last example, the particular
direction is included with the rate of motion, thus,
denoting the velocity of the aircraft.

• Acceleration is defined as the rate of change
of velocity. An aircraft increasing in velocity is
an example of positive acceleration, while
another aircraft reducing its velocity is an
example of negative acceleration, or
deceleration.

NEWTON’S LAWS OF MOTION
• The fundamental laws governing the action of
air about a wing are known as Newton’s laws
of motion.

• Newton’s first law is normally referred to as
the law of inertia. It simply states that a body
at rest does not move unless force is applied
to it. If a body is moving at uniform speed in a
straight line, force must be applied to increase
or decrease the speed.

• According to Newton’s law, since air has mass,
it is a body. When an aircraft is on the ground
with its engines off, inertia keeps the aircraft
at rest. An aircraft is moved from its state of
rest by the thrust force created by a propeller,
or by the expanding exhaust, or both. When
an aircraft is flying at uniform speed in a
straight line, inertia tends to keep the aircraft
moving. Some external force is required to
change the aircraft from its path of flight.

• Newton’s second law states that if a body
moving with uniform speed is acted upon by
an external force, the change of motion is
proportional to the amount of the force, and
motion takes place in the direction in which
the force acts. This law may be stated
mathematically as follows:
• Force = mass × acceleration (F = ma)

• ExampleWhere, F is the force and its unit is
Newton, m is mass and has the unit kg and a
is the acceleration has unit m/s².
• Find the acceleration of the block given in the
picture below.

• If an aircraft is flying against a headwind, it is
slowed down. If the wind is coming from
either side of the aircraft’s heading, the
aircraft is pushed off course unless the pilot
takes corrective action against the wind
direction.

• Newton’s third law is the law of action and
reaction. This law states that for every action
(force) there is an equal and opposite reaction
(force). This law can be illustrated by the
example of firing a gun. The action is the
forward movement of the bullet while the
reaction is the backward recoil of the gun.

• The three laws of motion that have been
discussed apply to the theory of flight. In
many cases, all three laws may be operating
on an aircraft at the same time.

BERNOULLI’S PRINCIPLE AND
SUBSONIC FLOW
• Bernoulli’s principle states that when a fluid
(air) flowing through a tube reaches a
constriction, or narrowing, of the tube, the
speed of the fluid flowing through that
constriction increases and its pressure
decreases.

• The cambered (curved) surface of an airfoil
(wing) affects the airflow exactly as a
constriction in a tube affects airflow. (Figure 2-
2) Diagram A of Figure 2-1 illustrates the
effect of air passing through a constriction in a
tube. In B, air is flowing past a cambered
surface, such as an airfoil, and the effect is
similar to that of air passing through a
restriction.

• An airfoil is a surface designed to obtain lift from
the air through which it moves. As the air flows
over the curved upper surface of an airfoil, its
velocity increases and its pressure decreases; an
area of low pressure is formed. There is an area
of greater pressure on the lower surface of the
airfoil, and this greater pressure tends to move
the wing upward. The difference in pressure
between the upper and lower surfaces of the
wing is called lift. Three-fourths of the total lift of
an airfoil is the result of the decrease in pressure
over the upper surface. The impact of air on the
lower surface of an airfoil produces the other
one-fourth of the total lift.

• Free stream airflow is air flowing without
obstruction before it engages the aircraft
structure. The velocity of the free stream flow is
equal to the speed aircraft. The pressure of the
free stream airflow is static pressure. When the
free stream flow arrives at the aircraft structure,
such as the wing, it must flow around the surface
areas. As it does so, the pressure and velocity of
the air change depending on the shape of the
wing. There is a point in front of the structure,
however, where the velocity of the air is zero.
This is known as the point of stagnation.

• Typical airflow patterns show the relationship
between static pressure and velocity defined by
Bernoulli. In aerodynamics, when positive
pressure is mentioned, it refers to pressures
above atmospheric pressure. Negative pressure
or suction pressure is lower than atmospheric
pressure. Any object placed in an airstream will
have the air impact or stagnate at some point
near the leading edge. The pressure at this point
of stagnation will be an absolute static pressure
equal to the total pressure of the airstream. In
other words, the static pressure at the stagnation
point will be greater than the atmospheric
pressure by the amount of the dynamic pressure
of the airstream

• As the flow divides and proceeds around the
object, the increases in local velocity produce
decreases in static pressure. This procedure of
flow is best illustrated by the flow patterns
and pressure distributions

• Note that the "streamlines" in the diagram
show the velocity of the airflow. When they
are close together, high velocity exists at that
point and when they are far apart, low
velocity exists at that point. The vector arrows
in the diagram show the magnitude and
direction of the low pressure caused by the
increased velocity of the airflow.

BOUNDARY LAYER AND FRICTION
EFFECTS
• In the study of physics and fluid mechanics, a
boundary layer is that layer of fluid in the
immediate vicinity of a bounding surface. In
relation to an aircraft, the boundary layer is
the part of the airflow closest to the surface of
the aircraft. In designing high-performance
aircraft, considerable attention is paid to
controlling the behavior of the boundary layer
to minimize pressure drag and skin friction
drag.

• Because air has viscosity (internal resistance
to flow), air encounters resistance to flow over
a surface. The viscous nature of airflow
reduces the local velocities on a surface and
accounts for the drag of skin friction

• The retardation of air particles due to viscosity
is greatest immediately adjacent to the
surface. At the very surface of an object, the
air particles are slowed to a relative velocity of
near zero. Above this area other particles
experience successively smaller retardation
until finally, at some distance above surface,
the local velocity reaches the full value of the
airstream above the surface.

• This layer of air over the surface which shows
local retardation of airflow from viscosity is
the boundary layer. The characteristics of this
boundary layer are illustrated in Figure 2-4
with the flow of air over a smooth flat plate.

• The beginning flow on a smooth surface gives
evidence of a very thin boundary layer with the
flow occurring in smooth laminations, The
boundary layer flow near the leading edge is
similar to layers or laminations of air sliding
smoothly over one another and the obvious term
for this type of flow is the “laminar” boundary
layer as mentioned previously. This smooth
laminar flow exists without the air particles
moving from a given elevation above the surface.

• As the flow continues back from the leading edge,
friction forces in the boundary layer continue to
dissipate energy of the airstream and the laminar
boundary layer increases in thickness with distance
from the leading edge. After some distance back from
the leading edge, the laminar boundary layer begins an
oscillatory disturbance which is unstable. A waviness
occurs in the laminar boundary layer which ultimately
grows larger and more severe and destroys the smooth
laminar flow. Thus, a transition takes place in which the
laminar boundary layer decays into a “turbulent”
boundary layer. The same sort of transition can be
noticed in the smoke from a cigarette in still air. At,
first, the smoke ribbon is smooth and laminar, then it
develops a definite waviness and decays into a random
turbulent smoke pattern.

• As soon as the transition to the turbulent
boundary layer takes place, the boundary layer
thickens and grows at a more rapid rate. (The
small scale, turbulent flow within the boundary
layer should not be confused with the large scale
turbulence associated with airflow separation.)
The flow in the turbulent boundary layer allows
the air particles to travel from one layer to
another producing an energy exchange. However,
some small laminar flow continues to exist in the
very lower levels of the turbulent boundary layer
and is referred to as the “laminar sub-layer.”

• The turbulence which exists in the turbulent
boundary layer allows determination of the point
of transition by several means. Since the
turbulent boundary layer transfers heat more
easily than the laminar layer, frost, water, and oil
films will be removed more rapidly from the area
aft of the transition point. Also, a-small probe
may be attached to a stethoscope and positioned
at various points along a surface. When the probe
is in the laminar area, a low “hiss” will be heard;
when the probe is in the turbulent area, a sharp
“crackling” will be audible.

• In order to compare the characteristics of the
laminar and turbulent boundary layers, the
velocity profiles (the variation of boundary layer
velocity with height above the surface) should be
compared under conditions which could produce
either laminar or turbulent flow. The typical
laminar and turbulent profiles are shown in
Figure 2-4. The velocity profile of the turbulent
boundary layer shows a much sharper initial
change of velocity but a greater height (or
boundary layer thickness) required to reach the
free stream velocity.

As a result of these differences, a
comparison shows:
• ( 1) The turbulent boundary layer has a fuller velocity profile and
has higher local velocities immediately adjacent to the surface. The
turbulent boundary layer has higher kinetic energy in the airflow
next to the surface.
• (2) At the surface, the laminar boundary layer has the less rapid
change of velocity with distance above the surface. Since the
shearing stress is proportional to the velocity gradient, the lower
velocity gradient of the laminar boundary layer is evidence of a
lower friction drag on the surface. In conditions of flow where a
turbulent and a laminar boundary layer can exist, the laminar skin
friction is about one-third that for turbulent flow. And while the low
friction drag of the laminar boundary layer is desirable, the
transition to turbulent boundary layer flow is natural and largely
inevitable.

PLANFORM AND VORTICES
• The previous discussion of aerodynamic forces
concerned the properties of airfoil sections in two-
dimensional flow with no consideration given to the
influence of the plan form. The plan form is the shape
or outline of an aircraft wing as projected onto a
horizontal plane. (Figure 2-5) When the effects of wing
plan form are introduced, attention must be directed
to the existence of flow components in the span-wise
direction. In other words, the airfoil section properties
considered thus far deal with flow in two dimensions.
Plan form properties consider flow in three
dimensions.

• The pressure above the wing is less than
atmospheric pressure, and the pressure below
the wing is equal to or greater than atmospheric
pressure. Since
• fluids always move from high pressure toward
low pressure, in addition to the movement of air
over the wing from front to rear, there is also a
spanwise movement of air from the bottom of
the wing outward from the fuselage and upward
around the wing tip. This flow of air results in
spillage over the wing tip, thereby setting up a
whirlpool of air called a “vortex.” [Figure 2-6] The
plural of vortex is vortices.

• As the difference in the pressure between the
air on the bottom and top of the wing
increases, more lift is generated. This
increased pressure differential also causes
more violent vortices. Small aircraft pilots
must be especially vigilant when flying behind
large aircraft. The vortices coming off the
wingtips of a transport category aircraft could
cause loss of control if encountered before
they have had time to dissipate into the
atmosphere.

• Note that the air on the upper surface of the
wing planform has a tendency to move in
toward the fuselage and off the trailing edge
as shown by the blue arrows in Figure 2-6.
This air current forms a similar vortex to a
wingtip vortex but at the inner portion of the
trailing edge of the wing. All vortices increase
drag because of the turbulence produced, and
constitute induced drag. Vortices increase as
lift (and drag) increase. Drag will be discussed
in further detail later in this module.

• Just as lift increases by increasing of the angle
of the airfoil into the wind, drag also increases
as the angle becomes greater. This occurs
because, within limits, as the angle is
increased, the pressure difference between
the top and bottom of the wing becomes
greater. This causes more violent vortices to
be set up, resulting in more turbulence and
more induced drag.

AERODYNAMIC TERMS
• Before continuing the discussion on
aerodynamics, some terms are defined and
illustrations considered. The chord of a wing is
the width of the wing from the leading edge apex
to the trailing edge. A chord line is a line
depicting the chord which extends forward of the
leading edge. It is used for angular reference to
the chord. (Figure 2-9) The average chord is the
area of the wing divided by the wing span. The
mean aerodynamic chord is they average
distance from the leading edge to the trailing
edge of the wing

• Due to the many wing planform designs, the
mean aerodynamic chord is not necessarily
half way from the fuselage to the wing tip as it
is on a perfectly rectangular wing. However,
the mean aerodynamic chord has half of the
surface area of the wing on each side of it.
(Figure 2-7) The mean aerodynamic chord is
used by aerodynamicists when calculating
stability and other design factors.

• The acute angle the wing chord makes with
the longitudinal axis of the aircraft is called
the angle of incidence, or the angle of wing
setting. (Figure 2-8) The angle of incidence in
most cases is a fixed, built-in angle. When the
leading edge of the wing is higher than the
trailing edge, the angle of incidence is said to
be positive. The angle of incidence is negative
when the leading edge is lower than the
trailing edge of the wing.

AIRFOILS
• Since an airfoil is a surface designed to obtain
lift from the air through which it moves, it can
be stated that any part of the aircraft that
converts air resistance into lift is an airfoil. The
profile of a conventional wing is an excellent
example of an airfoil. (Figure 2-10) Notice
that the top surface of the wing profile has
greater curvature than the lower surface.

• The difference in curvature of the upper and
lower surfaces of the wing creates the lifting
force. Air flowing over the top surface of the wing
must reach the trailing edge of the wing in the
same amount of time as the air flowing under the
wing. To do this, the air passing over the top
surface moves at a greater velocity than the air
passing below the wing because of the greater
distance it must travel along the top surface. This
increased velocity, according to Bernoulli’s
Principle, means a corresponding decrease in
pressure on the upper surface. Thus, a pressure
differential is created between the upper and
lower surfaces of the wing, forcing the wing
upward in the direction of the lower pressure.

SHAPE OF THE AIRFOIL
• Individual airfoil section properties differ from
those properties of the entire wing or aircraft
as a whole because of the effect of the wing
planform. A wing may have various airfoil
sections from root to tip, with taper, twist, and
sweepback. The resulting aerodynamic
properties of the wing are determined by the
action of each section along the span.

• The shape of the airfoil determines the amount
of turbulence or skin friction that it produces,
consequently affecting the efficiency of the wing.
Turbulence and skin friction are controlled mainly
by the fineness ratio, which is defined as the ratio
of the chord of the airfoil to its maximum
thickness. If the wing has a high fineness ratio, it
is a very thin wing. A thick wing has a low
fineness ratio. A wing with a high fineness ratio
produces a large amount of skin friction. A wing
with a low fineness ratio produces a large amount
of turbulence. The best wing is a compromise
between these two extremes to hold both
turbulence and skin friction to a minimum. Figure
2-11 illustrates a wide variety of airfoil shapes.

AIRFOIL CONTAMINATION
• All discussion of aerodynamic behavior of airfoils
assumes that the aircraft airfoils are free of
contamination. Some of the most common forms of
contamination are ice, snow and frost. Each of these, if
accumulated on the aircraft, will reduce its capacity to
develop lift. Ice commonly changes the shape of the
airfoil which disrupts airflow and make it less efficient.
Snow, ice, and especially frost, alter the smooth even
surface that normally promotes laminar airflow.
Laminar airflow is required to set up the pressure
differential between the lower and upper wing surfaces
that creates lift. All snow and ice must be completely
removed from any aircraft

• before flight. Frost must also be removed.
While it appears insignificant, the disruption
to airflow caused by frost is possibly the most
dangerous. before flight. Frost must also be
removed. While it appears insignificant, the
disruption to airflow caused by frost is
possibly the most dangerous.

Theory of flight prelim

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Theory of flight prelim