Cylindrical Shock Waves Produced by Instantaneous Energy Release

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.