FYFD

One of the most vexing topics for fluid dynamicists and their audiences is the subject of how wings generate lift. As discussed in the video above, there are a number of common but flawed explanations for this. Perhaps the most common one argues that the shape of the wing requires air moving over the top to move farther in the same amount of time, therefore moving faster. The flaw here, as my advisor used to say, is that there is no Conservation of Who-You-Were-Sitting-Next-To-When-You-Started. Nothing requires that air moving over the top and bottom of a wing meet up again. In fact, the air moving over the top of the wing outpaces air moving underneath it. 

In the Sixty Symbols video, the conclusion presented is that any complete explanation requires use of three conservation principles: mass, momentum, and energy. In essence, though, this is like saying that airplanes fly because the Navier-Stokes equations say they do. It’s not a terribly satisfying answer to someone uninterested in the mathematics. 

Part of the reason that so many explanations exist -- here’s one the video didn’t touch on using circulation -- is that no one has presented a simple, intuitive, and complete explanation. This is not to say that we don’t understand lift on fixed wings -- we do! It’s just tough to simplify without oversimplifying. 

Here’s the bottom line, though: the shape of the wing forces air moving around it to change direction and move downward. By Newton’s 3rd law (equal and opposite reactions), that means the air pushes the wing up, thereby creating lift. (Video credit: Sixty Symbols)

One of the topics in fluid dynamics almost everyone has come across is the explanation of how airplanes produce lift. Using Bernoulli's principle--which relates velocity and pressure--and a picture of an airfoil, your average science text will say that a bit of air going over the top of the airfoil has to travel farther than a bit of air going under the airfoil, and that, therefore, the air over the top travels faster than the air under the airfoil.

Unfortunately, this is misleading and, depending on the wording, outright wrong! The hidden assumption in this explanation is that air that goes over the top and air that goes under the bottom have to reach the trailing edge of the airfoil at the same time. But why would that be? (As one of my profs once said, "There is nothing in physics that says there is Conservation-Of-Who-You-Were-Sitting-Next-To-When-You-Started.")

Take a look at the video above. It shows an airfoil in a wind tunnel using smoke visualization to show how the air moves. Around the 0:25 mark, the video slows to show a pulse of smoke traveling over the airfoil. What happens at the trailing edge? The smoke going over the top of the airfoil is well past the trailing edge by the time the smoke going under the airfoil reaches the trailing edge!

It's true that air goes faster over the top of the airfoil than the bottom and that this causes a lower pressure on top of the airfoil (as Bernoulli tells us it should) and that this causes an upward force on the airfoil. But which causes which is something of a chicken-and-egg problem.

A more straightforward way, in my opinion, of explaining lift on an airplane is by thinking about Newton's 3rd law: for every action, there is an equal and opposite reaction. Take a look at the air's movement around the airfoil as the angle of attack is increased around 1:00 on the video. Just in front of the airfoil, the air is moving upward. Just after the airfoil, the air is pointed downward. A force from the airfoil has pushed the air down and changed its direction. By Newton's 3rd law, this means that the air has pushed the airfoil up by the same amount. Voila! Lift!