Slender body theory and optimization procedures for transonic lifting wing bodies

Limit process asymptotic expansion has been applied to develop an unsteady equivalence rule for transonic speeds The rule characterizes the near field of the flow over a transonic body as harmonic in cross planes perpendicular to the freestream direction, and the far field as a pulsating nonlinear line source Derived ex pressions for the loading indicate a substantial simplification of the prediction problem for three dimensional transonic unsteady airfoils using the theory In another application of transonic slender body asymptotics, substantial reductions in wave drag have been demonstrated using a parametric inverse method The procedure leads to a nearly shockless equivalent body of revolution for a slender airplane using iteration concepts and elimination of jump discontinuities in the equivalent body surface pressure distributions Multiple constraints such as fixed volume and base area are satisfied in the method by correlation of the equivalent body geometry with features of the smoothed surface pressure distribution