The shapes of bodies with maximum lift-to-drag ratio in supersonic flow

Analytical solutions for variational problems on con¦gurations of threedimensional (3D) bodies with the maximal lift-to-drag ratio at a given base area or a planform area are found within the limits of a localised interaction between the supersonic §ow and the body surface. Functionals of considered variational problems depend on derivatives of the desired function with respect to independent variables only, and this simpli¦es the solution and allows studying the structure of the extremal surface. It is shown that the lower surface of optimal bodies is planar. If a base area is given, the upper surface is cylindrical with the generating line parallel to the oncoming §ow velocity vector. If a planform area is given, the optimal body is a §at plate with the highest possible value of the liftto-drag ratio at a prescribed Mach number and friction coe©cient. The optimal body with a planar upper surface is a wedge. These results are valid if the base pressure is taken into account and also for zero base pressure.

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“…The equations of extremal surfaces are de¦ned by the system: ∂F ∂u = 0 ; ∂F ∂w = 0 , which has two families of solutions [9]:…”

Section: Analysis Of Extremal Surfacesmentioning

confidence: 99%

“…The analysis of deduced extremal surface has shown that the K maximum is realized at α 2 → 0, and the formulation of the problem should include the surfaces with α = 0 [9].…”

Section: Analysis Of Extremal Surfacesmentioning

confidence: 99%