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This is page iPrinter: Opaque this The Secret of Flight Applied Mathematics Body & Soul Vol 6 Johan Hoffman, Johan Jansson and Claes Johnson December 23, 2008 ii This is page iiiPrinter: Opaque this Contents I In the Rear Mirror 2 1 Classical Theory of Flight 3 1.1 Early Pioneers . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Cayley . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Lilienthal and Wright . . . . . . . . . . . . . . . . . . . . . 81.4 Status Quo . . . . . . . . . . . . . . . . . . . . . . . . . . . 91.5 New Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.6 A Glimpse of The Secret . . . . . . . . . . . . . . . . . . . . 131.7 The Secret of Lift According to NASA . . . . . . . . . . . . 14 2 Confusion: Lack of Theory of Lift 173 Aristotele 21 3.1 Liberation from Aristotle . . . . . . . . . . . . . . . . . . . 22 4 Medieval Islamic Physics of Motion 23 4.1 Avicenna . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.2 Abu’l-Barakat . . . . . . . . . . . . . . . . . . . . . . . . . . 244.3 Biruni . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.4 Ibn al-Haytham . . . . . . . . . . . . . . . . . . . . . . . . . 254.5 Others . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 iv Contents 5 Leonardo da Vinci 27 5.1 The Polymath . . . . . . . . . . . . . . . . . . . . . . . . . . 285.2 The Notebooks . . . . . . . . . . . . . . . . . . . . . . . . . 285.3 The Scientist . . . . . . . . . . . . . . . . . . . . . . . . . . 295.4 The Mathematician . . . . . . . . . . . . . . . . . . . . . . . 305.5 The Engineer . . . . . . . . . . . . . . . . . . . . . . . . . . 315.6 The Philosopher . . . . . . . . . . . . . . . . . . . . . . . . 32 6 Newton’s Incorrect Theory 337 D’Alembert and his Paradox 35 7.1 d’Alembert and Euler and Potential Flow . . . . . . . . . . 357.2 The Euler Equations . . . . . . . . . . . . . . . . . . . . . . 377.3 Potential Flow around a Circular Cylinder . . . . . . . . . . 387.4 Non-Separation of Potential Flow . . . . . . . . . . . . . . . 41 8 Robins and the Magnus Effect 439 Lilienthal and Bird Flight 4510 Wilbur and Orwille Wright 4911 Lift by Circulation 55 11.1 Lanchester . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5511.2 Kutta . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5611.3 Zhukovsky . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 12 Prandtl and Boundary Layers 59 12.1 Separation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5912.2 Boundary Layers . . . . . . . . . . . . . . . . . . . . . . . . 6012.3 Prandtl’s Resolution of d’Alembert’s Paradox . . . . . . . . 63 II Preparing for Takeoff 65 13 Navier-Stokes Equations 67 13.1 Small or Very Small Viscosity . . . . . . . . . . . . . . . . . 6713.2 The Squeeze . . . . . . . . . . . . . . . . . . . . . . . . . . . 6913.3 The Way Out . . . . . . . . . . . . . . . . . . . . . . . . . . 6913.4 Navier-Stokes with Force BC . . . . . . . . . . . . . . . . . 6913.5 Exponential Instability . . . . . . . . . . . . . . . . . . . . . 7013.6 Energy Estimate with Turbulent Dissipation . . . . . . . . . 7113.7 G2 Computational Solution . . . . . . . . . . . . . . . . . . 7313.8 Wellposedness . . . . . . . . . . . . . . . . . . . . . . . . . . 7413.9 Wellposedness of Mean-Value Outputs . . . . . . . . . . . . 7413.10Stability of the Dual Linearized Problem . . . . . . . . . . . 75
