Supersonic flow past slender bodies of elliptic cross-section

Abstract

The theories of supersonic flow past slender, smooth, pointed bodies of arbitrary cross-sectional shape, due to Ward, and of the flow past slender bodies of revolution with discontinuities in profile slope, due to Lighthill, are applied and extended to calculate first approximations for the aerodynamic forces on bodies of elliptic cross-section with discontinuities in profile slope. Open-nose bodies are included in this class, but only the external forces are considered. The investigation is restricted to bodies the major axes of whose cross-sections are co-planar and whose cross-sections have constant eccentricity. General expressions are deduced for the wave drag, lift, induced drag, and pitching moments of such bodies. The drag formula bears a marked resemblance to that for the equivalent body of revolution (i.e., the body of revolution with the same axial distribution of cross-sectional area), but the discontinuities introduce a slight difference in one term. The lift formula is identical with that already deduced by Ward for a particular case of the present problem. The general theory is applied to elliptic cones, and a comparison is made with Squire's solution of this problems. Numerical results for the wave drag of bodies of revolution having straight and parabolic profiles are also extended to bodies of elliptic cross-section.