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Lippisch shows in the linke video at 22:40-23:29. By the time the lower particle arrives at the trailing edge, the upper particle may have gone another 50% of the wing chord farther, as Dr.
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In fact, as has been observed in wind tunnels, the two particles of air that separate at the leading edge do not arrive at the trailing edge at the same time. The assumption that “the oncoming airflow traveling over the upper surface has a greater distance to travel in the same amount of time than the lower air flow, so it travels faster” is simply not true, there is no basis for this statement other than ignorant assumption.
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It is not valid to compare two different fluid flow streams or a moving stream with ambient static air. It says the total energy will be the same at both cross sections. The principle applies to two cross sections of a single fluid stream in steady flow.
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The usual discussion contains a misstatement and misapplication of the Bernoulli principle. Tietgens, Applied Hydro- and Aeromechanics, Dover Publications, New York, 1934, 1957. It is the physical condition of the forces around the sharp trailing edge that determine the Kutta condition that defines the circulation strength that produces lift. It creates the shearing forces that create circulation. This random jiggling permits transfer of momentum within a fluid. Real fluids are made of molecules that jiggle around at random with what is known as Brownian motion. Chapter VI, Airfoil Theory.) The pattern of flow around a wing and the resulting forces derive from the molecular nature of real fluids. It gave no explanation of how the circulation came into being or what determined its strength. This provided a theory that was in agreement with observation at least for small angles of attack. Prandtl proposed the circulation theory of flow around a wing, following observations by Rayleigh, Lanchester and Montgomery. D’Alembert showed in 1752 that no such force could exist in the ideal fluid. For a force to exist on a moving object requires a transfer of energy, energy is not conserved in the fluid. The Bernoulli ideal fluid is continuous and frictionless. The Bernoulli principle makes the rational assumption that energy is conserved in a moving fluid. Air has very different properties than those postulated for the ideal fluid. The ideal fluid is postulated to be continuous and frictionless. The Bernoulli principle is part of the classical theory of ideal fluids which is based on rational, logical postulates which are wrong when applied to real air. In the pioneer years of aviation, journalists would ask experts, physicists with PhD degrees and Nobel Prizes in physics, what they thought about flying machines and the universal response was something to the effect that “Mechanical flight is physically and mathematically impossible.” There is a mathematical proof, based on the Bernoulli principle, that a body moving through an ideal fluid would experience no resultant force. It is based on assumptions which directly contradict the possibility of flight. Actually Bernoulli’s principle has absolutely nothing whatsoever to do with the lift on a wing. The higher pressure underneath and the lower pressure above produces the lift on the wing. We are told that according to the Bernoulli principle, where the velocity is high, the pressure is low. It is said that the air going over the top of the wing must go farther than the air going under the wing and to get to the trailing edge in the same time it must go faster. Many discussions of the lift on a wing appeal to the Bernoulli principle.