What Holds Up a Plane ?

To the Editor: Bob Colwell’s discussion of lift (“Leave Bernoulli Out of This,” At Random, May 2003, pp. 10-12) is better informed than many elementary texts on the subject, but it leaves out a more interesting question about how wings fly. Colwell points out the errors in the usual explanation—the one that depends on a wing’s greater curvature on top. His excellent counterexamples are that flat wings generate lift and that planes can fly upside down. It was making those very arguments in grade school—and having my teacher tell me to shut up—that helped turn me into a scientist. Logic told me I was right even though the teacher said I was wrong. Although, like Colwell, I prefer a Newtonian approach, it is possible to correctly explain lift in terms of Bernoullian pressure differences. In Life in Moving Fluids (Princeton University Press, 1994), an authoritative yet entertaining book, Steven Vogel explains flight from a Bernoullian standpoint and applies it to a wide variety of physical and biological phenomena. Colwell says that Richard von Mises “obtains his formulas for lift by applying Newton’s second law.” In fact, von Mises uses circulation and Bernoulli’s law to explain lift in the traditional way (Theory of Flight, Dover Publications, 1959, p. 174)—although he does it properly, and not in the naive way that Colwell correctly criticizes. Colwell notes that “what holds up a plane” is that its wings “deflect a large mass of air downward; the reaction is to push the wing upward.” It can be shown that most of the air that is deflected downward is acted on by the top of the wing. It is easy to say the plane rises due to the wing’s reaction to this action, but we need to ask how it does this and to physically link the motion of the air to the resultant force on the wing. Jef Raskin Pacifica, Calif. [email protected]