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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 Increased velocity, Relative decreased Airflow 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 Total Lift

Drag Increases as Angle Of Attack And Total Lift Increases

Fig. 3.4

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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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