Analytical solution in the problem of constructing axisymmetric noses with minimum wave drag

Abstract

An analytical procedure for determining the axisymmetric nose shapes that ensure minimum wave drag is developed. The solution is constructed as an improving variation on the conical shape. The target function is built up in an approximate form on the basis of the assumption that the relationship between the geometric and gasdynamic parameters is local in nature. It is shown that the optimal bodies are truncated power-law bodies with an exponent equal to 2/3. The bodies thus obtained are compared with those constructed in accordance with an exact formulation of the problem.

The construction of a nose shape of minimum drag for specified external dimensions and volume using Euler equations

“…Thus, for Newton's problem truncated nose shapes are obtained having a power generatrix with an exponent of 2/3. 31 For M ∞ = 2 and M ∞ = 4 their C x exceed C x of the optimum nose shapes by no more than 3% and 1% respectively. As the aspect ratio increases the diameter of the front face approaches zero, while the power contour with exponent 2/3, as in the case of Newton's formula, is independent of M ∞ .…”

Wave drag reduction due to a self-aligning aerodisk

“…The analytical and experimental investigations of [1] showed that for noses with a ¦xed length, a pointed geometry with a blunt nose tip is most bene¦cial to minimize the wave drag. The more recent investigation of [2] supports the advantage of the ¤power law-bodies¥ in supersonic §ight. If aerodynamic heating is considered, then, especially for hypersonic §ow, a blunt nose like a semisphere with a large radius r is preferred since the heat §ux ' q is reciprocally proportional to the square root of r [3].…”

Minimum drag and heating 0.3-caliber projectile nose geometry

“…His results suggest that blunt nose shapes minimize drag within a narrow range of geometries, where the first segment makes an angle between 54° and 58° with respect to the nose axis. Similarly, Takovitskii 14 discusses an analytical method to minimize the aerodynamic wave drag. He concluded that a 2/3-power law nose shape would be the best.…”