The lifting force of an airplane wing when flying horizontally at high speeds. Explanation of the vortex trail.

Abstract In this paper, an explanation is given of the lift force of an airplane during horizontal flight. It is shown that during a flight, five vertical forces act on the airplane: gravity; pressure gradient with a minus sign; Archimedes force; potential force and the vortex force obtained from the action minimum. The first three forces were known before. The potential force was also known from the Bernoulli equation, but its effect on the airfoil from the air had not previously been taken into account. The vortex force obtained from the minimum action in the application to a continuous medium was not taken into account in aerodynamics. In horizontal flight the vortex force is directed upwards, it compensates for the gravity of the airplane at high speed commensurate with the speed of sound. The paper provides an explanation of the vortex trail behind the airplane, mentioned in the Millennium problem Navier-Stokes equation.