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THEORY OF FLIGHT

Airfoils and Lift

The angle of incidence is the angle at which the wing is attached to the fuselage.

An airfoil gets useful reaction from air moving above its surface. When airfoil  moves through the air, it is produces lift. Wings, horizontal tail surfaces, vertical tails surfaces, and propellers are all airfoils.

The front part of an airfoil is known as leading edge. The aft part which is narrow and tapered and is the trailing edge. An imaginary straight line joining the extremities of the leading and trailing edges is called the chord.

Angle of Incidence: The angle of incidence is formed by the longitudinal axis of the airplane and the chord of the wing. Longitudinal axis is the imaginary line that extends lengthwise through the fuselage from front portion to tail most portion. The angle of incidence is fixed and cannot be changed by the pilot.

Bernoulli's Principle: To know how lift gets produced, we should examine the phenomenon discovered many years ago by scientist Bernoulli and later called Bernoulli's Principle: The pressure of a fluid (liquid or gas) decreases at points where the speed of the fluid increases. In other words, Bernoulli found that within the same fluid, in this case air, high speed flow is associated with low pressure, and low speed flow with high pressure. 

Application of this phenomenon is made in giving lift to the wing of an airplane.. The airfoil is made to increase the velocity of the airflow above its surface so it decreases pressure above the airfoil. Also impact of air on lower portion of the airfoil also increases the pressure which is below. Combination of pressure decreasing above and increasing below gives lift.

Lift: Hold your flattened hand out of a moving automobile window. If you inclined your hand towards the wind, force of air pushes against it which in turn forces your hand to rise. Your hand in this case was deflecting the wind creating an equal and opposite dynamic pressure on the lower surface of hand, forcing it tomove up and back. The upward part of this force is lift; the backward part is drag .

Pressure get reduced with the smaller space the air has above the wing than below. Air cannot pierce the wing, so it needs to push around the wing. Surface air molecules push between the wing and outer layers that is found in air. Space being smaller and also the bump in the airfoil, molecules are forced to go faster. Bernoulli's Law states that faster air has lower air pressure, and thus the high pressure beneath the wing pushes it up to cause lift.

LIFT

Everyone today might have flown in an airplane at some point of life. Almost all ask the question "what makes this to fly"? The answer one gets is misleading and often wrong. The answers provided here will clarify many wrong about lift. Lift is easier to understand if you start with Newton and not Bernoulli. Popular explanation we were taught is misleading and that lift is due to the wing diverting air down.

There are three descriptions of lift used in textbooks and training manuals. The first one is the Mathematical Aerodynamics Description used by aeronautical engineers. This description is using to explain lift with complex mathematics  calculations. They are design good tools which are powerful for computing lift but cannot lend themselves to an efficient understanding of flight.

Another description is the Popular Explanation based on Bernoulli principle. This description is easy to understand and were taught for many years. Its simplicity, has forced it to describe lift in most flight training manuals. It relies on the "principle of equal transit times" which is a disadvantage since it is wrong. It focuses on the wing shape and prevents one from understanding  other important phenomena as inverted flight, power, ground effect, and the dependence of lift on the angle of attack of wing.

Another description is the Physical Description of lift. It is based on Newton’s laws. It is useful in understanding flight, and is easily accessible to those who are curious.

The popular explanation of lift

Students of physics and aerodynamics are being taught,  airplanes fly as a result of Bernoulli’s principle, that if air speeds up the pressure is lowered helping the wing to generate lift because the air goes faster over the top creating a region of low pressure, and producing lift.  You ask the question why the air goes faster over the top of the wing and there the popular explanation of lift falls apart.

To describe the same many have resorted to geometric argument that the distance the air must travel is directly connected to its speed. The usual claim is  when the air separates at the leading edge, the part going over the top must converge at the trailing edge with the part going under the bottom. This is the called "principle of equal transit times".

Look at wing of a small plane, which has a top surface that is 1.5 - 2.5% longer than the bottom, in which case Cessna 172 would have to fly at over 400 mph to generate required lift. Clearly, something is flawed in this description..

This explanation also reiterates that inverted flight is not possible. It does not address acrobatic airplanes, with symmetric wings (both top and bottom surfaces are of the same shape), or how wing adjusts for the great changes in load while pulling out of a dive or in a sharp turn.

But this explanation has prevailed for so long.  The basic reason being Bernoulli principle is easy to understand. Nothing is wrong with Bernoulli principle and the statement that the air goes faster over the top of the wing. Our understanding is not complete with this explanation. We are missing certain vital piece of information when we apply Bernoulli’s principle. We can calculate the pressures around the wing if we know the speed of the air over and under the wing, but how do we determine the speed?

Another basic fault in the popular explanation is it ignores the work already done. Lift needs power. An understanding of power is key to the understanding the phenomena of lift.

Newton’s laws and lift

How does a wing generate lift? To begin to understand lift we must read basic school physics and go through Newton’s first and third laws once again. Newton’s first law states a body at rest will remain at rest, and a body in motion will continue in straight-line motion unless subjected to an external applied force. If one sees a bend in the flow of air, or if air originally at rest is accelerated into motion, there is a force acting on it. Newton’s third law states that for every action there is an equal and opposite reaction. Air in this scenario is the action while lift is reaction.

The wing as a pump

Newton’s laws suggest that wing must change something of the air to get lift. Changes in the air’s momentum will result in some force on the wing. To get a force of lift a wing must divert air down, chunk of air.

Estimating that the average vertical component of the downwash of a Cessna 172 traveling at 110 knots to be about 9 knots, then to generate the needed 2,300 lbs of lift the wing pumps a whopping 2.5 ton/sec of air! This means that the amount of air pumped down for a Boeing 747 to create lift for its roughly 800,000 pounds takeoff weight is incredible indeed.

Pumping so much air down is an argument against lift being just a surface effect. In order to pump 2.5 ton/sec the wing of the Cessna 172 must accelerate all of the air within 9 feet above the wing.

Then how does a thin wing divert that much air? When the air is bent around the top of the wing, it pulls on the air above it accelerating that air down, otherwise there would be voids in the air left above the wing. To prevent voids air is pulled from above. This pulling causes pressure to become lower above wing. It is the acceleration of air above wing in downward direction that gives lift.

Air has viscosity

The general question is "how does the wing divert the air down?" When a moving fluid, such as air or water, comes into contact with curved surface it tries to follow the same surface.

Viscosity is the resistance to flow which also gives the air a kind of "stickiness." Viscosity in air is very small but it is enough for the air molecules to want to stick to the surface. Relative velocity between surface and nearest air molecules is zero. (That is why one cannot hose the dust of a car and there is dust accumulated on the backside of the fans in a wind tunnel.) Above surface the fluid has some small velocity. The farther one goes from surface, faster the fluid is moving until the external velocity is reached (this happens in less than an inch) Since fluid near the surface has change in velocity, the fluid flow is bent towards surface. Unless bend is too tight, fluid follows the surface. Volume of air around wing that appears to be partially stuck to the wing is called "boundary layer".

The wing as air "scoop"

One is used to thinking of wing as thin blade that slices though air and develops lift like magic. As plane increases its speed, the scoop diverts more air.

Axis of an Airplane in Flight.

An airplane can turn about three axes. Whenever the altitude of the airplane changes in flight, it will rotate about one or more of these axes. The three axes intersect at center of gravity and each one is perpendicular to other two.

Longitudinal Axis: The imaginary line extending lengthwise through the fuselage, from nose to tail, is the longitudinal axis.

Lateral Axis: The imaginary line extending crosswise,  one side wing tip to other side wing tip, is the lateral axis.

Vertical Axis: The imaginary line passing vertically through the center of gravity is the vertical axis. Motion about the vertical axis is known as yaw.

An airplane in straight-and-level unaccelerated flight is flying with the help of four forces. The four forces are lift, gravity, thrust and drag.

The airplane in straight-and-level unaccelerated flight is acted on by four forces--lift, the upward acting force; weight, or gravity, the downward acting force; thrust, the forward acting force; and drag, the backward acting, or retarding force of wind resistance.