Calculated Effects Of Body Shape On The Bow Shock Overpressures In The Far Field Of Bodies In Supersonic Flow

The theory developed by G.B. Whitham (Communications on Pure and Applied Mathematics, August 1952) for the supersonic flow about bodies in uniform flight in a homogeneous medium is reviewed and an integral which expresses the effect of body shape upon the flow parameters in the far field is reduced to a form which may be readily evaluated for arbitrary body shapes. This expression is then used to investigate the effect of nose angle, fineness ratio, and location of maximum body cross section upon the far-field pressure jump across the bow shock of slender bodies. Curves are presented showing the variation of the shock strength with each of these parameters. It is found that, for a wide variety of shapes having equal fineness ratios, the integral has nearly a constant value. Hence, to a first order, the pressure jump in the far field is independent of the shape and depends only upon the fineness ratio.