The Attenuation of Spherical Shock Waves in Air

Abstract

The peak pressure of spherical shock waves from small explosive charges has been determined as a function of distance by measuring the velocity of propagation and applying the velocity-pressure relation derived from the Rankine-Hugoniot equations. The charges were composed of TNT or pentolite (TNT/PETN 50/50 by weight), weighed from 1.45 to 8 lb., and were spherical or cylindrical in shape, except for one series of small rectangular blocks. Measurements on the non-spherical charges were made in the plane through the center of the charge, perpendicular to the axis. The pressure-distance relations for the four principle charge types are given by the following fitted equations, in which Π represents excess peak pressure in atmospheres, and the distance, scaled according to charge weight, is given by the non-dimensional variable Z=R/(ρτ)⅓ where R is the distance from a charge of volume τ and specific gravity ρ: ½-lb. rectangular blocks, TNT, ΠQ=13.50/Z−769.9/Z2+36280/Z3;8-lb. cylinders, Pentolite, ΠA=10.49/Z−135.5/Z2+21070/Z3;4-lb. cylinders, TNT, ΠB=11.34/Z−185.9/Z2+19210/Z3;3.75-lb. spheres, Pentolite, ΠC=8.63/Z+295.1/Z2+7823/Z3. These equations are valid for values of Z between approximately 18 and 110. The indicated probable error of the fitted curves is of the order of one percent for intermediate distances, increasing to from two to seven percent at the extremes of the distance range covered. The curve for spherical charges is in agreement with the Kirkwood theory, and the results for cylinders having various length/diameter ratios indicate large dependence of pressure on charge shape for values of Z up to 50 at least.