How do airplanes fly, really?

aerodave replies:

You’d think that after a century of powered flight we’d have this lift thing figured out. Unfortunately, it’s not as clear as we’d like. A lot of half-baked theories attempt to explain why airplanes fly. All try to take the mysterious world of aerodynamics and distill it into something comprehensible to the lay audience–not an easy task. Nearly all of the common “theories” are misleading at best, and usually flat-out wrong.

You mention a couple concepts that provide part of the answer but are incomplete in fundamental ways. To hear some tell it, wings work due to angle of attack and little else. Angle of attack (AOA) is the difference between the orientation of a surface and the direction of the air flowing over it. If you hold your hand horizontally out the window of a moving car, and then start to point your fingers toward the sky, you’re giving your hand a positive AOA. That generates a significant amount of upward force on your arm. It makes sense that this same force should keep a plane in the air, and to some degree it does. A wing’s angle of attack helps it deflect air downward, and Newton’s Third Law–every action has an equal and opposite reaction–says this downward push on the air must result in an upward push on the wing. But there’s more to it, since the force generated by this deflection alone is far short of what we see in real life.

The problem is that the AOA explanation ignores the cross-sectional shape of the wing–the quintessential aerodynamic form known as the airfoil. In particular, it suggests that it doesn’t matter how the top of the wing is shaped, and that a thin flat plate would do just fine. Not so. Cambered airfoils–those with the characteristic upward hump that most wings have–can generate lift without any positive AOA at all, or even a slightly negative angle!

Of all the flawed explanations of why planes fly, the one most people have heard involves the Bernoulli principle and “equal transit times.” The curved upper surface of the wing is longer than the bottom one, we’re told, and the air above the wing must therefore speed up to keep pace with its counterpart below. Start with this increased velocity on the top of the wing, mix in Bernoulli’s principle, and you find lower pressure above. This pressure differential sucks the airplane upward and voilà! A quarter-million pounds of jumbo jet stays aloft.

This logic is taught to students of all ages, and finds its way into many respectable science textbooks. Its only problem is its complete lack of resemblance to reality. A given “piece” of upper-surface air has no compelling reason to keep pace with its estranged sibling below; it can’t know and doesn’t care what’s happening on the other side of that aluminum partition.

That’s not to say this model totally misses the mark; it just underestimates the effect. The air really does accelerate over the top of the wing, but actually far outpaces the lower-surface air. It’s a good thing, too–if the air stayed in sync over the minuscule difference between the upper and lower paths, a Cessna 152 would have to fly at over 300 mph just to stay in the air! (In reality, it’s about 55 mph.)

By this point I’m sure you’re tired of hearing all the non-reasons airplanes fly and would like a real answer. Where does lift come from? One important fact is that fluids have a tendency to adhere to curved surfaces as they flow past. This is called the Coanda effect. The explanation for it is outside the scope of this article, so you’ll have to take my word for it or check out the references. The bottom line is that if you correctly shape the top of the wing, the air will keep hugging the surface as it passes.

The next step is realizing that when a fluid is made to curve, its pressure is “thrown” to the outside by centrifugal force (that’s the simplest way of describing it). As the air crests the hill at the top of the airfoil, it pulls away from the wing surface, creating a slight vacuum next to the metal. The pressure differential helps push the wing up. In addition, the wing causes the flow behind it to move downward. Some of the downward flow is caused by air deflected by the lower surface, and some comes from air that is forced down as it rounds the top. (That’s where the missing lift we mentioned in connection with the AOA explanation comes from!) In short, an airfoil generates lift up by deflecting the air flow down, a clear example of Newton’s Third Law. This illustration makes the notion of downward deflection a little clearer.

Is it wrong to invoke the Bernoulli principle when explaining how an airfoil works? No, but it tends to confuse matters for the non-technical audience. In fact, airfoils can be explained in two ways. I’ve just given the “Newton” explanation–a wing generates lift because it deflects the airflow. The “Bernoulli” explanation has to do with pressure differentials. For complex reasons we needn’t get into (other than to say they have little to do with equal transit times), air moves faster over the top of a wing than beneath it. Bernoulli’s principle tells us that the higher the velocity of an airstream, the lower its static pressure. Because the static pressure below the wing is higher than that above, the wing generates lift. If you don’t quite follow all that, don’t worry–the Newton explanation is perfectly adequate.

That’s the simple explanation of lift. Using that knowledge to design anything useful is a little messier. There’s a big set of equations that in principle can be solved to fully describe the behavior of a moving fluid. They’re called the Navier-Stokes equations, and they’ve got more Greek letters than the Athens phone book. (Check out this page to see what I mean.) When applied to anything approaching reality, they get so hairy they gag the world’s fastest computers. So engineers make lots of simplifying assumptions to produce results that are “good enough.” That’s why we have a hard time predicting how real bodies will behave, and why experimentation is so important in aeronautics.

How can aviation be grounded in such a muddy understanding of the underlying physics? As with many other scientific phenomena, it’s not always necessary to understand why something works to make use of it. We engineers are happy if we’ve got enough practical knowledge to build flying aircraft. The rest we chalk up to magic.

Further reading:

Gale M. Craig’s 2002 book Introduction to Aerodynamics does an excellent job of breaking down the misconceptions of flight and explaining the reality with enough math for the techies, but plenty of great description for the non-engineer.

NASA’s Glenn Research Center has an educational site that covers these topics (and lots of others, like propulsion) at a basic level, with interactive Java applets. The incorrect theories of lift start at: http://www.grc.nasa.gov/WWW/K-12/airplane/lift1.html

References:

Langewiesche, W., Stick and Rudder, 1990.

Jane’s All the World’s Aircraft 2004-2005, Jane’s Information Group, 2004.

aerodave

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