Optimization of penetration into geological and concrete shields by impactor with jet thruster

Abstract

High-speed penetration into soil, rock, concrete, and ice by impactors equipped with a jet thruster is optimized using analytical and numerical methods. It is shown that using a jet thruster with optimum burning programs bears considerable promise for increasing the depth of penetration. In this study, we used modified Young’s penetration equations with a smooth approximation of the dependence between the depth of penetration and impact velocity for the description of impactor-shield interaction. Optimization of jet propulsion in media with drag was considered mainly with applications to planes and missiles. Surveys of the obtained results and references can be found in the studies by Leitmann [1962], Kosmodemiansky [1966], and Tertychny-Dauri [2004]. Using jet thrusters for increasing the depth of penetration into solid media was analyzed in only a few publications. Sagomonyan [1988] formulated two problems. In the first problem, a jet thruster was assumed to operate during a fixed time interval, and, in order to maximize the depth of penetration (DOP) of penetrator into soil, it was necessary to determine the moment at which the jet thruster must be switched on. In the second problem, a jet thruster could operate along a fixed length of the trajectory, and, in order to provide the maximum DOP, it was necessary to determine the depth at which the jet thruster must be switched on. The second problem was solved for a penetrator with a conical nose, assuming that the mass of the penetrator remains constant. Gould [1997] suggested engineering designs whereby a rocket motor is attached to the penetrator and operates during penetration. Ben-Dor et al. [2007] considered maximization of the DOP as an optimization problem for a penetrator with a variable mass. They noticed a similarity between this problem and maximization of the distance of a horizontal flight in the atmosphere. Various formulations of the latter problem were considered in the past [Hibbs 1952; Cicala and Miele 1956; Miele 1957; Miele 1962; Krotov 1995]. However, it transpired that this similarity had limited applications because of different drag laws in the atmosphere and soil. Only general properties of the solutions obtained for an arbitrary dependence of drag force upon the instantaneous mass and velocity, DD D.m;v/, can be used for solving penetration optimization problems. Consequently, optimization of the penetrator with a jet thruster must be analyzed separately. In the study by Ben-Dor et al. [2007], the authors employed the simplest penetration model in which the drag force is a linear function of a squared velocity. Combining analytical and numerical methods, they determined the optimum burning programs and compared the obtained results with more simple burning programs for controlling the motion of a penetrator.