We all know how an airplane wing works: the top surface is longer than the bottom, so the air across the top must flow faster than the air across the bottom. Just look in any basic physics text. (Bernoulli, and all that.) The calculation involved is easy. Using Bernoulli's principal, we know that the difference in pressure (top vs bottom) is equal to the difference in the squares of the velocities. [If you look up the formula, you will find one of those funny looking letters, rho, which stands for the mass density of air. In English units, that measurement is in slugs per cubic foot, and at STP, its value is .0024. In doing the math below, you probably won't need that, because it cancels out (given that the top and bottom of the wing are flying on the same day through the same conditions.) But you may find that you want to double check by calculating the actual pressures.]
So here is the challenge, which probably seems a little elementary to many of you (it doesn't require any calculus, and doesn't even require algebra, unless substituting numbers for letters counts.) But even if it seems elementary, go ahead and try it; it won't take long, and you'll win the admiration of your peers if you can get this to work out right. All you need to do, is run the numbers (which you can darn near do in your head) to show that my old Beech Sport would be capable of supporting its own weight at 49 knots, the published stall speed (the speed at which it essentially stops flying and begins to sink like a stone) . Here are some actual measurements. The top surface of the wing is 1.008 times longer than the bottom: but use 1.01 for ease: we're trying to prove the thing can fly, not that it can't. 49 knots = 83 FPS. Consider the velocity across the bottom of the wing to be 83 FPS, and that across the top to be 83.83 (1 percent higher). My plane's weight, with fuel and me (assuming 1G): 2000#. Wing area: 146 square feet. SP = 14.7 psi, and the wing area, in sq inches, for the lazy among you is 21,024. (To those of you who work in metric units, I'd say "Hey, your units already make more sense, and the numbers are simpler, so to avoid giving you an advantage, you have to do the conversions yourself.")
So all you need to do is show that the differential pressure is about 1/10 psi, and you've shown that we can lift 2102 pounds, which is enough above the weight of my plane that I'll feel safe in flying it, knowing the physics work. Post your answers, and a clear (maybe step-by-step) rationale, to impress your peers. If you come up with an answer that doesn't seem to work, just google for Bernoulli's principle to make sure you have the right formula. You might even separately calculate the pressures top and bottom, just to convince yourself that you are doing the math right. Warning: I know some pretty good mathematicians who must have goofed up somehow, because they couldn't get the numbers to work out.
Extra credit: for those of you who were able to get the right answer: My friend has a Pitts Special, which flies ever so much better than my own plane, especially aerobatically. Do the math to show how this is possible with its symmetrical wing profile, in which the top surface and bottom surface are the same length.