A generalized empirical analysis of cratering

Abstract

A general empirical analysis of chemical and nuclear explosive cratering is presented. This analysis makes use of the concepts of efficiency and scaling formalism. Efficiency is assumed to depend on type of explosive, medium, and depth of burst. Scaling formalism is generalized in terms of experimentally determined yield exponents associated with each pertinent dimension. Experimental procedures are specified that determine the efficiency and yield exponents. Applying these methods to chemical explosive cratering data in desert alluvium, the crater radius and depth yield exponents are both 1/3.4. The standard deviation is 3 per cent. The depth-of-burst yield exponent is 1/3.6 with a standard deviation of 5 per cent. Thus the principle of similitude is not rigorously obeyed. Assuming that nuclear craters are best described by the above exponents, the percentage efficiency of nuclear cratering in desert alluvium is determined as follows: Based on Based on Crater Radius Crater DepthJangle S 2.6±1.2 4.6±2.1Jangle U 78±35 146±66Teapot Ess 43±19 208±94 This behavior of the efficiency indicates that the relative contributions of various crater-forming mechanisms differ in chemical and nuclear cratering. Therefore the cratering capabilities of nuclear explosives cannot be related to those of chemical explosives by means of a single parameter. The prediction of nuclear crater dimensions from data obtained from low-yield chemical explosives is examined. The prediction error depends on yield extrapolation and depth-of-burst as well as the errors in the yield exponents and efficiency. For depths of burst near the surface or the maxima of the depth-of-burst curves the prediction error is a minimum. The accuracy of the depth-of-burst yield exponent q is much less important than that of the crater dimension exponents pi. The relationships between the precision that should be attempted for pi and that for E is σpi=σE|lnEW| where EW is the yield extrapolation. For yield extrapolations of 105 the accuracy of pi should be an order of magnitude better than that of E.