## Calculated effects of body shape on the bow-shock overpressures in the far field of bodies in supersonic flowDonald L. Lansing, Langley Research Center, United States. National Aeronautics and Space Administration 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. |

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ambient pressure analytic expression area distributions axisymmetric basic hypothesis bodies having various body axis body of revolution body shapes shown body surface body-wake combination bow shock bow-shock overpressures characteristic curve characteristic field coefficient for bodies constant cross section cross-sectional-area distribution curved characteristics cylinder of constant determined downstream effect of body EFFECT OF NOSE equa equivalent bodies evaluated expression is available families of body family of shapes far-field conditions far-field pressure flight flow field free-stream pressure front shock given distance integral large distances linear theory lines of linear location of maximum maximum cross section MODIFIED THEORY nose angle nose shock obtained parameters PRESSURE AS PREDICTED pressure discontinuity pressure jump projectile radius of body regions Rmax shapes having various shapes treated shock waves showing the radius shown in figure Simpson's rule sonic boom straight Mach lines strength supersonic area rule supersonic flow tion upstream wake shapes Whitham's theory x/l)max increases