Zhukovsky`s theorem says ;) it is circulation (closed contour integral of velocity). But it will be a huge vortex, maybe a tornado :) in order to lift, say Airbus A-320 or Boeing 737??!!! I have two questions.
1. Why this huge vortex is stable? For any passenger it looks like amazing or thrilling or awful, we should die..:) :)! Is there strong physical theoretical proof of this stability?
2. How does the vortex (or, maybe a tornado ;) ) influence the wings? Are they polished at least :) :) :)?? Usual tornado in the US easy "handles" with american suburban homes (which to the first approximation can be a model of aluminum wings) :) :)......:) :)
Units: rho v^2 is the order of magnitude of the pressure. rho for air is about 1 (kg/m^3), so the pressure is of the order of v^2, with v in m/s. For an airplane going about Mach 1 (typical, it is usually going a bit less), we get a pressure of 10^5 Pa, so 10^4 kg/square meter. So to lift an airplane just requires that for each ton of material you provide 0.1 square meter of wing, take 1 square meter to be on the safe side. Of course, these numbers are *very* approximate, but show that the thing can be done.
The stability of the vortex is probably a bit more complex to be certain of.
Dear Mr. F. Leyvraz,
I see you have forgotten Zhukovsky`s theorem of lifting force of infinite wing. But you do not answer to my two questions!
All wing have two surfaces. Upper and lower. The run of the air (fluid) over the upper surface is longer than over the lower surface, then the velocities are higher in the upper surface than the lower. Bernoulli law states that pressure and velocity (square) behaviour are opposite. Thus pressures are low on the upper surface and high on the lower surface. This pressure against area produces a net lifting force that sustain the airplane.
See Bernoulli law P+rho*V^2/2 = constant or review this
https://www.academia.edu/11942882/Mec%C3%A1nica_y_Termodin%C3%A1mica_de_Sistemas_Materiales_Continuos Chpt.IX, Sect.1.4.1, pag.190
Dear Sirs,
Why you talk me about the reasons of aircraft flight? I asked you about the STABILITY of the huge vortex which is around wings! I can not believe in the vortex stability and consequently I am starting to think about validity and conditions of Zhukovsky`s theory of lifting force! That is why I entitles my question in such a way.
Did anyone can answer me to my TWO QUESTIONS OR NOT at this brilliant researchgate...:) :). German prof. Ludwig Prandtl did not talk to all the world for about 20 years about his pioneering theory of boundary layer...
The air plane wings has a dihedral angle that assures the stability.
Dear prof. Andrés Granados,
Thank you very much for technical answer.
1. You mean a wing with sharp edge or not? Due to the sharp edge new vortices come off the wing periodically due to the detachment of the boundary layer. So the vortex persists all the time. AM I RIGHT?
2. But I read the monography in which the wing with two blunt edges have also the lifting force. So maybe the wing sharp edge is not the main reason of the constant vortex persistence around the wing.
Could you provide some references on the solid physical theory of this phenomenon (classical articles, maybe Prandtl or his group)? Thank you very much for an advance.
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