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 are investigated. Pressure distributions and integrated pressure drag obtained by these methods are compared with standard values obtained by the method of characteristics and the theory of Taylor and Maccoll. Three shapes, cone, ogive, and a modified optimum body, are investigated over a wide range of fineness ratios and Mach numbers.
It is found that the linearized theory is accurate only at law values of the hypersonic similarity parameter (the ratio of free-stream Mach number to body fineness ratio) and that second-order theory appreciably extends the range of accurate application. The second-order theory gives good results on ogives when the ratio of the tangent of maximum surface angle to the tangent of the Mach angle is less than 0.9. Tangent-cone methods cannot be widely applied with good accuracy. In general, the conical-shock-expansion theory predicts pressure and drag within engineering accuracy when the hypersonic similarity parameter is greater than 1.2. Although Newtonian theory gives good accuracy, except for cones, at the highest values of the hypersonic similarity parameter investigated, it is less accurate than the conical-shock-expansion theory.