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CHAPTER 3
THEORY OF FLIGHT
To understand how forces act on an aircraft in flight, it is necessary to understand
Bernoulli's Theorem and Newton's Laws of Motion.
Bernoulli's Theorem - In any system, total energy must remain constant. In a
fluid, we are talking about pressures and speed. If one is increased, the other must
decrease to maintain a constant energy (C = p * s).
Newton's First Law of Motion - An object in motion remains in motion, or an
object at rest remains at rest, unless an external force is applied to it.
Newton's Second Law of Motion - A force must be applied to alter the state of a
given mass.
Newton's Third Law of Motion - For every action, there is an equal and
opposite reaction.
FORCES ACTING ON AN AIRPLANE
Lift
Bernoulli's Theorem and Newton's Laws all combine to produce lift on an airfoil.
Lift
Upwash
Relative
Airflow
Increased
velocity,
decreased
pressure
Deflected
Air
Downwash
Fig. 3.1
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Newton's First Law is encountered when we move a wing through the air. The
moving wing deflects some air downward illustrating Newton's Second Law. The
downwards deflected air forces the wing upward - Newton's Third Law. The air going
over the wing must travel a greater distance due to the wings shape and angle of attack.
This air is therefore accelerated, causing a decrease in pressure over the upper surface of
the wing (Bernoulli). The wing then rises into the area of lower pressure.
Airspeed then, directly affects lift. Higher airspeed increases acceleration over the
wing, causing decreased pressure and more lift. Higher airspeed also increases the
downward deflection under the wing, increasing lift. Lift increases as the square of the
increase in airspeed.
Weight
The weight of the aircraft is caused by gravity. All aircraft are designed to be
flown at, or under, a specific maximum allowable weight. This weight acts downward
through a point called the centre of gravity (C of G). The position of the C of G depends
upon the weight distribution of the aircraft. The farther back the load, the farther back the
C of G.
Lift
Drag
Thrust
Weight
Fig. 3.2
Thrust
Thrust is produced by the engine and propeller, which follows Newton's Third
Law. Pushing a mass of air backward propels the aircraft forward.
When power is added and thrust is greater than drag, the excess thrust is
immediately translated into lift. There will be decreased pressure over the wing as the air
will have to move even faster to fulfill Bernoulli’s Theorem, and increased pressure
under the wing due to the increased airflow.
To increase airspeed when power is added, the angle of attack of the wings must
be reduced to maintain altitude, allowing the excess thrust to be converted to airspeed.
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Drag
Drag is the resistance an aircraft encounters as it moves through the air, and it
directly opposes thrust. There are two primary types of drag, induced drag and parasite
drag.
Induced drag is the result of the wing generating lift. The airflow over the upper
surface of a wing tends to flow in toward the fuselage as it has less pressure than the air
around it. The airflow under a wing tends to flow away from the fuselage as it has more
pressure than the air around it. The two airflows meet at the trailing edge of the wing on
an angle creating turbulence and drag.
The higher pressure air from under the wing also tends to flow around the tip of
the wing to take the place of the lower pressure air above the wing. These wing tip
vortices also cause drag.
Induced Drag
Fig. 3.3
Induced drag increases as the angle of attack of a wing increases. Induced drag
therefore increases as airspeed decreases, as the angle of attack must increase to maintain
the lift required for level flight. Induced drag also increases as aircraft weight or wing
loading increases, as the angle of attack must increase to produce the lift required to
maintain level flight.
Induced drag
Induced Drag
Effective Lift
Total Lift
Effective Lift
Drag Increases as Angle Of Attack And Total Lift Increases
Fig. 3.4
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Total Lift
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Parasite drag is produced by all parts of the aircraft that do not produce lift landing gear, wing struts, antennae, etc. It is also caused by spaces, gaps or openings at
the wing routes, control surfaces, and cowls. Parasite drag has little effect at low speeds,
however it increases as airspeed increases. Parasite drag is further divided into form, skin,
and profile drag.
Form drag results from passing any solid object through the air. The amount of
form drag depends upon the shape of the object. Form drag occurs both fore and aft of the
object.
Form Drag
Fig. 3.5
Skin friction is produced by the friction between the air and the aircraft. The
smoother the surface of the wing, the less is the friction.
Profile drag is a combination of the skin friction and the form drag of the wing.
Total Drag Chart
Total Drag
Drag
Stall
Parasite Drag
Induced Drag
0
Airspeed
Fig. 3.6
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Streamlining is the reduction of drag through design.
Lift/Drag Ratio
Both lift and drag increase as you increase the angle of attack of an airfoil, to a
point. Beyond that point drag continues to increase, but lift decreases. The best lift/drag
ratio occurs at the angle of attack that gives the most lift for the least drag - usually about
18 degrees angle of attack. In the following diagram, CD is the coefficient of drag, CL is
the coefficient of lift, and L/D is lift over drag.
Lift and drag depend directly on the angle of attack of the aircraft and on the wing
shape, the wing area (S), the square of its velocity or TAS (V squared) and the air density
(P).
Lift = CL x 1/2 P x V(V) x S
Drag = CD x 1/2 P x V(V) x S
CD
CL
L/D
-8%
0%
8%
16%
24%
32%
Angle of Attack (Degrees)
Fig. 3.7
Equilibrium
An aircraft is in equilibrium whenever thrust and drag are equal. If one of these
forces becomes greater than the other, the aircraft will climb or descend (see Thrust). An
aircraft is also in equilibrium when lift and weight are equal. If one of these forces
becomes greater than the other the aircraft will climb or descend.
Couple
A Couple occurs when two forces are equal and opposite, but are parallel. Thrust
and drag can form a Couple, and lift and weight can form a Couple.
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