Thanks for the new web links! For people interested in the analysis of wings and other airfoils, Iíll include here a link to your previous posting of many very nice links to detailed descriptions of how airfoils work. Links about how airplane lift really works
Bernoulliís principle isnít wrong at all, but it is not a convenient way to describe lift, as your original sites correctly point out. Instead, wings turn airflow downwards, creating an action-reaction pair of forces, and there is suction on top of the wing. One talk I saw which nicely dismissed Bernoulliís principle as a practical explanation of lift showed rather graphically the underside of an F-16ís wing, fully loaded with hanging fuel tanks and missiles. It really doesnít matter much what you put on the bottom of the wing -- the top of the F-16ís wings was smooth and polished. That thing flies?
Much of the flow turning comes from a vacuum created above the wing. So your postings I hope will help people think more about lift than the usual Bernoulli explanation.
In regards to your latest postings, these are great! However, here the usual Bernoulliís principle as you may see it in introductory texts cannot be used at all because the flow is at least in places supersonic. This creates a shock wave which meets the wing. The design of wings for supersonic flight (and also wings for which some portion of the airflow around them might be supersonic) centers on minimizing the drag created by these shock fronts, while of course maintaining stability for safety. The simplest form of Bernoulliís principle requires that the flow is incompressible, and a supersonic shock wave is a big compresson of the air. Of course there is the full version of Bernoulliís equation which incorporates the heat function of the air (when you compress the air it has higher energy in the form of heat and the enthalpy is the right variable). The proper way to do all this is with numerical simulations using the Euler equation. The continuity equation also is more complicated for compressible flow. div(v) = 0 is no longer true -- div(rho*v) + d(rho)/dt = 0 where rho is the gas density and v is the velocity vector field and div is the divergence is the full continuity equation and applies whenver the total number of gas molecules remains constant (not true when there are chemical reactions or phase transitions -- liquid to vapor, for instance).
(republished on 07/30/06)