Hypersonic minimum-drag slender bodies of revolution.

Abstract

Slender bodies of revolution with minimum inviscid pressure drag are derived using the hypersonic small-disturbance approximation to the shock-expansion method. Solutions are examined for each of the six classical optimization criteria based on length, diameter, surface area, and volume. By use of a method developed by Miele, each optimization problem is reduced to that of numerically minimizing a product of nondimensional integrals. Minimumdrag coefficients and the corresponding optimum body shapes are computed over a range of the hypersonic Mach number similarity parameter at specific-heat ratios of jand %. The minimum-drag coefficients for high hypersonic speeds and a specific-heat ratio of •§• are bracketed by Newtonian theory with and without centrifugal effects. The minimum-drag coefficients increase with decreasing Mach number similarity parameter and increasing specificheat ratio. The optimum body shapes vary slowly with Mach number similarity parameter. They are weakly dependent on specific-heat ratio and are approximated by those derived from Newtonian impact theory. The most rapid variations of minimum-drag coefficient and optimum body shape with Mach number similarity parameter occur in the moderate supersonic flow regime.