New Theory of Flight

Abstract

We present a new mathematical theory explaining the fluid mechanics of subsonic flight, which is fundamentally different from the existing boundary layer-circulation theory by Prandtl–Kutta–Zhukovsky formed 100 year ago. The new theory is based on our 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 3d rotational slip separation arising from a specific separation instability of potential flow, into turbulent flow with nonzero drag/lift. For a wing this 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 of size 15–20 for a small propeller plane at cruising speed with Reynolds number \({Re\approx 10^{7}}\) and a jumbojet at take-off and landing with \({Re\approx 10^{8}}\) , which allows flight at affordable power. The new mathematical theory is supported by computed turbulent solutions of the Navier–Stokes equations with a slip boundary condition as a model of observed small skin friction of a turbulent boundary layer always arising for \({Re > 10^{6}}\) , in close accordance with experimental observations over the entire range of angle of attacks including stall using a few millions of mesh points for a full wing-body configuration.

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Correspondence to Johan Hoffman.

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Editorial Foreword The special character of this article requires some comments by the editors on the purpose of its publication. Though, its mathematical content does not meet the degree of mathematical rigor usually expected by articles in this journal, the implications of the argument and the accompanying novel numerical computations are of such far reaching importance for technical fluid dynamics, particularly for the computation of certain features in turbulent flow, that it deserves serious consideration. The main purpose of this publication is therefore to stimulate critical discussion among the experts in this area about the relevance and justification of the view taken in this article and its possible consequences for modeling and computation of turbulent flow.

Communicated by R. Rannacher

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Hoffman, J., Jansson, J. & Johnson, C. New Theory of Flight. J. Math. Fluid Mech. 18, 219–241 (2016). https://doi.org/10.1007/s00021-015-0220-y

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Mathematics Subject Classification

  • 76G25
  • 76E09

Keywords

  • Flight
  • lift theory
  • d’Alembert’s paradox