Air travel is one of the great triumphs of the twentieth century. Every day hundreds of thousands of people are carried through the air to destinations all around the world. In every case the flight of heavier-than-air craft results from the flow of air around their wings.

Before their first powered flight in December 1903, the Wright brothers tested many different wing shapes in a wind tunnel to find the shape that produced the most lifting force. This shape is often called an airfoil. The fluid moving over the top travels a greater distance than that moving just under the bottom of the wing. Consequently, the fluid moving over the top must travel faster in order to conform with the shape of the wing and still maintain the natural streamline. The shape of the wing also crowds the streamlines together above the wing, just as in the case of a constricting pipe. The result is that the region immediately above the wing experiences reduced pressure relative to the region immediately below the wing. Because the downward force on the top of the wing is less than the upward force on the bottom, a net upward force, or lift, arises from the air flow. (Beyond the airfoil the flowing air has a downward component of velocity. By Newton's third law, the reaction force to the net downward force exerted on the air is the lift.) Note that for lift to occur, a flow of air is required relative to the wing. The lift occurs equally well for a wing moving through stationary air or for air moving past a stationary wing.

You can demonstrate this effect with a small piece of paper, about 10x15 cm. Hold the short edge close below your lower lip and blow vigorously across the top of the paper. The motion of the air above the paper will cause it to rise. This same effect helps to lift a plane into the air.

In addition, the angle of attack, or tilt of the wing relative to the air flow, can be changed to get additional lift from the deflection of the air stream. If the leading edge of the wing is higher than the trailing edge, the force of air against the underside of the wing is greater than its force against the upper side. In this case lift occurs even for a flat wing. However, if the angle of attack becomes too great, the streamline flow gives way to turbulence and the pressure difference is reduced. If the turbulence is great enough, the lift diminishes and the plane stalls.

In general, as the flow of air past the wing increases, both the lift force and the drag force (the resistance to forward motion) increase. Aircraft wings are designed so that pilots can change the wing shape during flight, producing greater lift for the slower speeds of takeoff and landing and producing less drag at cruising speeds. During takeoff and landing, flaps are extended backward and downward from the trailing edge of the wing, increasing lift by imparting a greater downward velocity to the air. On some planes, extending the flaps increases the wing area as much as 25%, resulting in a much increased drag. At the same time, the leading edge of the wing may be moved forward, creating a slot that directs a high-speed layer of air over the top surface of the wing to reduce turbulence and increase lift. At higher speeds, the pilot closes the slot and retracts the flaps to reduce the drag forces. Passengers in commercial aircraft can easily see these changes in the wing during flight.

We should point out that lift is not in strict accord with Bernoulli's equation. The reason is that the Bernoulli equation holds exactly only for incompressible nonviscous fluids, yet air is both compressible and viscous. However, the pressure difference, and hence the lift, does occur in air, even if the amount is not in exact agreement with the Bernoulli equation.