### Why Don't Airplanes Fall Down?

#### Abstract

What causes the lift on the wing of an airplane? Surprisingly, this problem is still poorly understood mathematically and perhaps also physically. The Kutta's formula for the lift force works in the case of airfoil with a sharp rear but not generally. Taha and Gonzales proposed a variational principle based on so called Appellian, in which hydrodynamic acceleration replaces velocity. The predicted expression for the velocity circulation associated with the vortex around the wing is reported to work in more general situations than Kutta's formula. In this article, I will concentrate on the question of what creates the vortex. The TGD based quantum hydrodynamics leads to a view about how vortices are generated and how they decay. The vortex around the airfoil would be accompanied by magnetic flux structure, which is quantum coherent in the scale of the object. The generation of the vortex would compensate for the momentum loss of fluid as the boundary layer is formed. The variational principle of Taha can be translated to the TGD framework. Also a simpler variational principle based on *Z ^{0}* magnetic energy is considered. In the TGD framework the velocity field is assumed to be proportional to

*Z*gauge potential: This assumption generalizes a similar assumption in superconductivity. This implies a quantization of velocity circulation as multiplies of effective Planck constant

^{0}*h*

_{eff}_{ }=

*nh*having as largest values the gravitational Planck constant

_{0}*h*=

_{gr}*GMm*/

*β*for Earth and Sun.

_{0}