Author: Arpan Dey
So, how does an aircraft fly? You have asked this question at some point. Some of you have been satisfied by a simple non-mathematical explanation, while some of you have not got the chance to pursue the question properly. In this article, we will not discuss how does an airplane maneuver in air. We will only discuss how does it generate the lift force required to become airborne. For a start, an airplane flies by manipulating, with the help of movable control surfaces, the flow of air around it. The wings are designed such that the air above the wings would flow faster that the air below, and thus create a region of low air pressure above the wings – thus generating a lift force upward. But to understand this better and more rigorously, you will need some fluid mechanics. Air is a fluid, remember?
Before that, four forces act on an airplane. The weight of the plane tends to bring it down. This is balanced by the lift force generated by the wings. The thrust of the engines tend to push the plane forward. This is balanced by air resistance, or drag. Thus, all we need to do is generate more lift than weight and more thrust than drag, if we are to remain airborne and move forward.
But how do we generate lift? We have the wings to generate them. Anyone who has travelled by air is aware of the huge surface area of the main wings. The wings are specially shaped to maximize lift force. The airfoil shape of the wings curves the air that is flowing on top of it, and slows down the air that is flowing below. This creates a difference in air pressure above and below the wings – with a greater pressure below. This is responsible for generating the force that pushes the wings (and thus, the entire airplane) upward.
A common but flawed explanation of how the wings produce lift is the equal transit theory. When air strikes the front edge of the wings, it is divided into two groups of streamlines, one group which flows above the wing, and one which flows below. The curvature of the wings is such that the streamlines of air flowing above the wings need to travel a greater distance than the streamlines below to meet at the backward edge of the wings. And since the streamlines need to meet at the same time, the streamlines above the wings travel faster to cover more distance within the same time. And since the wind travels faster above the wings, there is a region of low pressure above the wings and a region of high pressure below the wings. To stabilize this pressure difference, the wings are forced to move upward.
However, it should be noted that the equal transit theory is flawed since the airflows above and below the wings need not meet at the trailing edge. Also, contrary to what is stated in the equal transit theory, velocity difference does not give rise to pressure difference, rather the opposite.
To understand what actually happens, let’s get down to some fluid mechanics. The flow of a fluid is steady if at any given point, the velocity of each passing fluid particle remains constant in time. The path taken by a fluid particle under a steady flow is a streamline.
Now, we need to learn the equation of continuity. When a fluid is in motion, it must move in such a way that mass is retained. Consider the steady flow of fluid through a pipe (i.e., the inlet and outlet flows don’t vary with time).
This is the continuity equation for steady one-dimensional flow. The equation shows that the greater the area, the lower the velocity and vice-versa. This is precisely why water from a pipe rushes out at a greater velocity if the mouth of the pipe is pinched, thus decreasing the area of cross-section.
Now, Bernoulli’s equation. Look at the figure below.
Now consider this system.
Now, we need to know what is the Magnus effect. Take a non-spinning ball moving relative to a fluid. The streamlines around this ball are symmetrical above and below the ball, and the velocity of the fluid above and below at corresponding points is the same. Thus, there is no pressure difference. The ball moves neither up nor down. Now, take a ball in a fluid which is moving toward the right and spinning anticlockwise. This ball drags the fluid with it. The ball is moving forward and relative to it, the fluid is moving backward. The velocity of the fluid above the ball relative to it is greater than that below the ball since the streamlines get crowded above and there is a pressure difference above and below the ball. The result is a net upward force.
Now, the airplane wings are shaped like an airfoil. From the side, it looks as shown in the figure below.
The airfoil shape is such that it can generate lift when it moves horizontally through a fluid (it need not spin). Since the upward surface of the wings is curved outward, and due to the Coanda effect, the streamlines are more crowded above the wings. Now, what is the Coanda effect? It’s simply the tendency of a fluid to stick to the surface over which it is flowing, even if the surface is curved. It is due to the Coanda effect that the streamlines above the wings curve with the curvature of the wings and stick to the surface of the wings. Otherwise, the streamlines could just travel in a straight line and there would be no crowding of the streamlines above the wings.
Now, since the streamlines are more crowded above the wings, the velocity of the fluid above the fluid is more, and thus, the pressure above is lesser than the pressure below. There is a pressure difference, and this is responsible for generating the lift force which pushes the wings upward. Thus, now we have a basic understanding of how the airplane wings generate lift force.
Aviation has improved a lot since Wilbur and Orville Wright’s first flight. Concludingly, it can be said that, as William Boeing said, “We are embarked as pioneers upon a new science and industry in which our problems are so new and unusual that it behooves no one to dismiss any novel idea with the statement that ‘It can’t be done!’”