Journal of Mathematical Fluid Mechanics

, Volume 18, Issue 2, pp 219–241

New Theory of Flight


DOI: 10.1007/s00021-015-0220-y

Cite this article as:
Hoffman, J., Jansson, J. & Johnson, C. J. Math. Fluid Mech. (2016) 18: 219. doi:10.1007/s00021-015-0220-y


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.


Flight lift theory d’Alembert’s paradox 

Mathematics Subject Classification

76G25 76E09 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.School of Computer Science and CommunicationKTHStockholmSweden
  2. 2.Basque Center for Applied Mathematics (BCAM)BilbaoSpain

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