Fig 7 Direction of air movement around a wing as seen by an observer on the ground.
In the mathematical aerodynamics description of lift this rotation of the air around the wing gives rise to the "bound vortex" or "circulation" model. The advent of this model, and the complicated mathematical manipulations associated with it, leads to the direct understanding of forces on a wing. But, the mathematics required typically takes students in aerodynamics some time to master.
One observation that can be made from figure 7 is that the top surface of the wing does much more to move the air than the bottom. So the top is the more critical surface. Thus, airplanes can carry external stores, such as drop tanks, under the wings but not on top where they would interfere with lift. That is also why wing struts under the wing are common but struts on the top of the wing have been historically rare. A strut, or any obstruction, on the top of the wing would interfere with the lift.
Air has viscosity
The natural question is "how does the wing divert the air down?" When a moving fluid, such as air or water, comes into contact with a curved surface it will try to follow that surface. To demonstrate this effect, hold a water glass horizontally under a faucet such that a small stream of water just touches the side of the glass. Instead of flowing straight down, the presence of the glass causes the water to wrap around the glass as is shown in figure 8. This tendency of fluids to follow a curved surface is known as the Coanda effect. From Newton’s first law we know that for the fluid to bend there must be a force acting on it. From Newton’s third law we know that the fluid must put an equal and opposite force on the object that caused the fluid to bend.
Fig 8 Coanda effect.
Why should a fluid follow a curved surface? The answer is viscosity: 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. The relative velocity between the surface and the nearest air molecules is exactly zero. (That is why one cannot hose the dust off of a car and why there is dust on the backside of the fans in a wind tunnel.) Just above the surface the fluid has some small velocity. The farther one goes from the surface the faster the fluid is moving until the external velocity is reached (note that this occurs in less than an inch). Because the fluid near the surface has a change in velocity, the fluid flow is bent towards the surface. Unless the bend is too tight, the fluid will follow the surface. This volume of air around the wing that appears to be partially stuck to the wing is called the "boundary layer".
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Lift as a function of angle of attack
There are many types of wing: conventional, symmetric, conventional in inverted flight, the early biplane wings that looked like warped boards, and even the proverbial "barn door." In all cases, the wing is forcing the air down, or more accurately pulling air down from above. What all of these wings have in common is an angle of attack with respect to the oncoming air. It is this angle of attack that is the primary parameter in determining lift. The lift of the inverted wing can be explained by its angle of attack, despite the apparent contradiction with the popular explanation involving the Bernoulli principle. A pilot adjusts the angle of attack to adjust the lift for the speed and load. The popular explanation of lift which focuses on the shape of the wing gives the pilot only the speed to adjust.
To better understand the role of the angle of attack it is useful to introduce an "effective" angle of attack, defined such that the angle of the wing to the oncoming air that gives zero lift is defined to be zero degrees. If one then changes the angle of attack both up and down one finds that the lift is proportional to the angle. Figure 9 shows the coefficient of lift (lift normalized for the size of the wing) for a typical wing as a function of the effective angle of attack. A similar lift versus angle of attack relationship is found for all wings, independent of their design. This is true for the wing of a 747 or a barn door. The role of the angle of attack is more important than the details of the airfoil’s shape in understanding lift.
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