It was started by a famous paper from Ludwig Prandtl, in ?1920?. The math is easy, if vortex-shedding is removed, and our wing has infinite span. Nobody realizes that an infinite wing is permanently trapped in ground-effect mode, and only works by instant ground-forces, just like a venturi. Just like those snow-speeders from Star Wars.
Other Prandtl papers analyze short, non-infinite wings. But they avoid all the insoluable equations by having the wing fly at infinite velocity! This way, no air moves downwards on average. Prandtl forgets that if the tip-vortices don't move downwards, then also the vortex-shedding goes to zero, and the tip-vortices vanish! By flying at infinite velocity, then pretending that tip-vortices are still created, Prandtl is "searching for car-keys under bright streetlights, where the job is easier" when the actual explanation of lifting force is still hidden elsewhere, out in the darkness.
Heh, another of Prandtl's papers rigorously described the equal-transit-time theory, giving us diagrams, and including it as the explanation for lifting-force. Yet nobody could contradict the Great Prandtl, since his papers were huge walls of interlocking equations, which were all correct. Only his initial assumptions were wrong, and it took about seven decades before physics teachers started seeing the problem.
There's a longstanding interest in the acadame in finding "clean" closed-form analytical explanations for all sorts of real-world problems, which mostly speaks to the historical lack of computing power to do a complete simulation leading to acceptance of bad approximations. Economics is also full of these kinds of equations, and many of the ones taught in undergrad are barely beyond a working hypothesis.
Other Prandtl papers analyze short, non-infinite wings. But they avoid all the insoluable equations by having the wing fly at infinite velocity! This way, no air moves downwards on average. Prandtl forgets that if the tip-vortices don't move downwards, then also the vortex-shedding goes to zero, and the tip-vortices vanish! By flying at infinite velocity, then pretending that tip-vortices are still created, Prandtl is "searching for car-keys under bright streetlights, where the job is easier" when the actual explanation of lifting force is still hidden elsewhere, out in the darkness.
Heh, another of Prandtl's papers rigorously described the equal-transit-time theory, giving us diagrams, and including it as the explanation for lifting-force. Yet nobody could contradict the Great Prandtl, since his papers were huge walls of interlocking equations, which were all correct. Only his initial assumptions were wrong, and it took about seven decades before physics teachers started seeing the problem.
See: http://amasci.com/wing/Weltner1a.gif