New Theory of Flight

We present a new mathematical theory explaning the mircale of flight which is fundamentally different from the existing theory by Kutta-ZhukovskyPrandtl formed 100 year ago. The new theory is based a new resolution of d’Alembert’s paradox showing that slightly viscous bluff body flow can be viewed as zero-drag/lift potential flow modified by a specific separation instability into turbulent flow witn nonzero drag/lift. For a wing the separation mechanism maintains the large lift of potential flow generated at the leading edge at the price of small drag, resulting in a lift to drag quotient in the range 10− 70 which allows flight at affordable power. The new mathematical theory is supported by computed turbulent solutions of the Navier-Stokes equations with small friction boundary conditions in close accordance with observations. 1 Why is it Possible to Fly? What keeps a bird or airplane in the air? How can the flow of air around a wing generate large lift L (balancing gravitation) at small drag D (requiring forward thrust) with a lift to drag ratio also referred to as finesse L D ranging from 10 for short wings to 70 for the long thin wings of extreme gliders, which allows flying at affordable power for both birds and airplanes? An albatross with finesse L D = 50 can glide 50 meters upon losing 1 meter in altitude. A 525 ton Airbus 380 with L D = 15 is carried by a thrust of 35 tons, corresponding to 1 4 of maximal thrust with 3 4 required for accelleration at takeoff. The dream of human-powered flight came true in 1977 on 60 m wings of the Gossamer Albatross generating a lift of 100 kp at a thrust of 5 kp (thus with L D = 20) at a speed of 5m/s supplied by a 0.3hp human powered pedal propeller.