Cylindrical Shock Waves Produced by Instantaneous Energy Release

TLDR

Taylor’s analysis of intense spherical explosions has been extended to cylindrical geometries. The study derives that a strong cylindrical shock wave from a sudden energy release per unit length expands as \(R=S(\gamma)(E/\rho_0)^{1/4}t^{1/2}\), with \(S(\gamma)\approx1\) for \(\gamma=1.4\), the post‑shock pressure decaying as \(p_1=0.216E/R^2\), and the shock envelope behind a hypersonic missile approximated by a paraboloid \(R=(D/\rho_0)^{1/4}(x/V)^{1/2}\).

Abstract

Taylor's analysis of the intense spherical explosion has been extended to the cylindrical case. It is found that the radius R of a strong cylindrical shock wave produced by a sudden release of energy E per unit length grows with time t according to the equation R=S(γ)(E/ρ0)1/4t1/2, where ρ0 is the atmospheric density and S(γ) is a calculated function of the specific heat ratio γ. For γ=1.4, S(γ) is found to be approximately unity. For this case, the pressure p1 behind the shock wave decays with radius R according to the relation p1=0.216E/R2. Applying the results of this analysis to the case of hypersonic flight, it can be shown that the shock envelope behind a meteor or a high-speed missile is approximately a paraboloid given by R=(D/ρ0)1/4(x/V)1/2 where D and V denote the total drag and the velocity of the missile, respectively, and x is the distance behind the missile.