Stuart Quayle
Theory Of Flight
The aerofoil on a wing is used to obtain
a reaction from air moving over its surface. When an aerofoil is moved through
the air, lift can be produced. Wings, horizontal tail surfaces, vertical tail
surfaces, and propellers are all examples of airfoils.
Below is a picture of what the aerofoil shape wing of a small aircraft would
look like. The forward part of the aerofoil is rounded and is called the leading
edge. The rear part is narrow and tapered and is called the trailing edge.
The chord is an imaginary straight line joining the leading and trailing
edges.
In this example the angle of incidence is the angle formed by the longitudinal axis of the aeroplane and the chord of the wing. The longitudinal axis is a line that extends lengthwise through the fuselage from the nose to the tail. The angle of incidence is measured by the angle at which the wing is attached to the fuselage.
Bernoulli's
Principle
Many years ago a scientist by the name of Bernoulli discovered that the pressure of a liquid or a gas decreases at points where the speed of the liquid or gas increases. What he found was that with the same fluid, air in this case, high-speed flow is associated with low pressure and low speed flow is associated with high pressure.
His
ideas were originally used to explain changes in the pressure of fluid flowing
within a pipe whose cross-sectional area varied. In the wide section of the
gradually narrowing pipe, the fluid moves at low speed, producing high pressure.
As the pipe narrows it must contain the same amount of fluid. In this narrow
section, the fluid moves at high speed, producing low pressure.
This is where the
idea for giving lift to the wing of an aeroplane came from. The aerofoil is
designed to increase the velocity of the airflow above its surface; this
decreases the pressure above the aerofoil. At the same time, the impact of the
air on the lower surface of the aerofoil increases the pressure below it. This
combination of pressure decrease above and increase below produces lift.
A good example of lift occurring would be if you were to hold your flattened hand out of the window of a moving car. As you inclined your hand to the wind, the force of air pushed against it forcing your hand to rise. Your hand acting as an aerofoil was deflecting the wind, which, created an equal, and opposite dynamic pressure on the lower surface of the aerofoil, forcing it up and back. The upward component of this force is lift; the backward component is drag.
It is often taught that Students that aeroplanes fly as a result of Bernoulli’s principle. This explanation usually satisfies the curious and few challenge the conclusions. But why does the air go faster over the top of the wing and this is where the popular explanation of lift falls apart.
To explain why the air goes faster over the top of the wing, it is often said that the distance the air must travel is directly related to its speed. It is usually said that when the air separates at the leading edge, the part that goes over the top must meet at the trailing edge with the part that goes under the bottom. This is the so-called "principle of equal transit times".
Bernoulli’s principle is a good start at explaining lift, but it is the whole truth. The average speeds of the air over and under the wing are easily determined because we can measure the distances and the speeds can be calculated. From Bernoulli’s principle, we can then determine the pressure forces and the lift. If we do a simple calculation we would find that in order to generate the required lift for a typical small airplane, the distance over the top of the wing must be about 50% longer than under the bottom. Figure 1 shows what such an airfoil would look like. Now, imagine what a Boeing 747 wing would have to look like
Shape of wing predicted by principle of equal transit time.
A good example of this theory not quite working is if we look at the wing of a typical small plane, which has a top surface that is 1.5 - 2.5% longer than the bottom, you find that a Cessna 172 would have to fly at over 400 mph to generate enough lift. So it is becoming obvious that something in this description of lift is not quite correct.
So the next thing to look at is why the air passing over the top and bottom of the wing should need to meet again at the converging edge of the wing at the same time. In the next picture a drawing of a wind tunnel experiment in which coloured smoke is fed in at set intervals.
It can be clearly seen that the air is not meeting at the same time when it reaches the converging edge of the wing. An obvious problem in the popular explanation is that it ignores the work that is done. Lift requires power.
How does a wing generate lift?
To begin lets review Newton’s first and third laws. 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 force. That means, 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. As an example, an object sitting on a table exerts a force on the table (its weight) and the table puts an equal and opposite force on the object to hold it up. In order to generate lift a wing must do something to the air. What the wing does to the air is the action while lift is the reaction.
The next two pictures show the streams of air running over wings. In the first picture the air comes straight at the wing, bends around it, and then leaves the wing horizontally, this is not very realistic and no lift is created. The next figure shows the streamlines, as they should be. The air passes over the wing and is bent down. The bending of the air is the action, and the reaction is the lift on the wing.
As Newton’s laws states, the wing must change the air to get lift. Changes in the air’s momentum will result in forces on the wing. To generate lift a wing must divert air down, lots of air.
The lift
of a wing is equal to the change in momentum of the air it diverts down.
Momentum comes from mass and velocity. The lift of a wing is proportional to
the amount of air diverted down times the downward velocity of that air.
It’s that simple. We have used
Newton’s second law that relates the acceleration of an object to its mass and
force on it, F=ma. For more lift the wing can either divert more air (mass) or
increase its downward velocity. This downward velocity behind the wing is called
"downwash". To the pilot
the air is coming off the wing at roughly the angle of attack (the angle it goes
in at). To the observer on the ground, if he or she could see the air, it would
be coming off the wing almost vertically. The greater the angle of attack, the
greater the vertical velocity. For the same angle of attack, the greater the
speed of the wing the greater the vertical velocity. Both the increase in the
speed and the increase of the angle of attack increase the length of the
vertical arrow. It is this vertical velocity that gives the wing lift.
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