A Class of Three-Dimensional Optimum Wings in Hypersonic Flow

Author: Zien, Tse-Fou

Year: 1967

Degree: Dissertation (Ph.D.)

Advisor: Cole, Julian D.

Committee Member: Unknown, Unknown

Option: Aeronautics

DOI: 10.7907/X1J8-JK85

Abstract

The idea of using streamlines of a certain known flow field to construct generally three-dimensional lifting surfaces together with the method of evaluating the aerodynamic forces on the surfaces, developed by Nonweiler, Jones and Woods, has been extended and applied to axisymmetric hypersonic flow fields associated with a class of slender power-law shock waves of the form r ~ τxn in the limit of infinite free stream Mach number. For this purpose, the basic flow fields associated with concave shocks (n > 1) have first been calculated numerically at a fixed value of the ratio of specific heats γ = 1.40, and the results are presented in tabulated form, covering a wide range of values of n. The method of constructing a lifting surface either by prescribing its leading edge shape on the basic shock or by specifying its trailing edge shape in the plane x = 1 is then discussed. Expressions for lift and drag on the surface are derived. A class of optimum shapes giving minimum pressure drag at a fixed value of lift has been determined for every basic flow field with n ranging from 1/2 to 10 at γ = 1.40.

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