Exact Three Dimensional Mathematical Model for Evaluation of Antipersonnel and Antimaterial Effectiveness of Fragmenting/ Preformed Conventional Warhead

The basic theory for the evalution of warhead-target interaction in three dimensional space on the concept of partitioning the target surface into sub-target surfaces having atleast two such mathematically defined boundaries which are projections of randomly fragmenting shapiro rings of the exploding shell with respect to the point of burst or preferably the centre of gravity of the shell lying on the shell-axis is presented. The equation for any given orientation of the shell-axis to the family of cones around the shell-axis has been derived for the cases: (i) when both the warhead and the target are stationary, (ii) when the warhead is moving and the target is stationary, and (iii) when both the warhead and the target are moving. Expressions for the conditional probability of kill for at least one lethal hit, and for a finite number of lethal hits, p, among a group of r hits (r >- p) on a tactical target by fragments/projectiles of an exploding warhead for use in the above three cases have been derived