An Analysis of the Applicability of the Hypersonic Similarity Law to the Study of Flow About Bodies of Revolution at Zero Angle of Attack

The hypersonic similarity law as derived by Tsien has been investigated by comparing the pressure distributions along bodies of revolution at zero angle of attack. In making these comparisons, particular attention was given to determining the limits of Mach number and fineness ratio for which the similarity law applies. For the purpose of this investigation, pressure distributions determined by the method of characteristics for ogive cylinders for values of Mach numbers and fineness ratios varying from 1.5 to 12 were compared. Pressures on various cones and on cone cylinders were also compared in this study. The pressure distributions presented demonstrate that the hypersonic similarity law is applicable over a wider range of values of Mach numbers and fineness ratios than might be expected from the assumptions made in the derivation. This is significant since within the range of applicability of the law a single pressure distribution exists for all similarly shaped bodies for which the ratio of free-stream Mach number to fineness ratio is constant. Charts are presented for rapid determination of pressure distributions over ogive cylinders for any combination of Mach number and fineness ratio within defined limits

NACA Technical Notes

Note presenting an investigation of the accuracy and range of applicability of the linearized theory, second-order theory, tangent-cone method, conical-shock-expansion theory, and Newtonian theory for predicting pressure distributions on pointed bodies of revolution at zero angle of attack. Three shapes, cone, ogive, and a modified optimum body, are investigated over a wide range of fineness ratios and Mach numbers. The results indicated that for most combinations of fineness ratio and Mach number, one of the approximate methods will give reasonable results