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 ${\mathrm{R=S(\gamma )(E/\rho }}_0{)}^{\text{1/4}}{t}^{\text{1/2}}$ , 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 ${\mathrm{R=(D/\rho }}_0{)}^{\text{1/4}}{\mathrm{(x/V)}}^{\text{1/2}}$ where D and V denote the total drag and the velocity of the missile, respectively, and x is the distance behind the missile.