Drag minimization for wings in supersonic flow, with various constraints

Max A. Heaslet, Franklyn B. Fuller
naca-tn-4227
Feb 1958


The minimization of inviscid fluid drag is studied for thin aerodynamic shapes subject to imposed constraints on lift, pitching moment, base area, or volume. The problem is transformed to one of determining a two-dimensional potential flow satisfying either Laplace's or Poisson's equations with boundary values fixed by the imposed conditions. By means of Kelvin's minimum energy theorem for harmonic fields, a method is given for approximate drag minimization in the case of given lift. For supersonic-edged wings with straight trailing edges, perfect analogies are established between cases involving lifting and nonlifting shapes. Particularly simple results are derived for a family of wings with curved leading edges with lift specified and center of pressure fixed at the 60-percent-chord position. General relations involving span load distribution and integrated loading along oblique cutting lines are derived. The minimum drag for other plan forms is determined and, in the case of nonlifting wings, difficulties associated with unreal shapes are discussed.

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