Weapon effectiveness and the shapes of damage functions

This paper provides a review of methods of assessing a fragmentation weapon's effectiveness against a point target or an area target with keeping the focus on the necessity of using the Carleton damage function with the correct shape factor.First,cookie-cutter damage functions are redefined to preserve the shape factor of and to have the same lethal area as the corresponding Carleton damage function.Then,closed-form solutions of the effectiveness methods are obtained by using those cookie-cutter damage functions and the Carleton damage function.Finally,the closed-form solutions are applied to calculate the probability of damaging a point target and the expected fractional damage to an area target for several attack scenarios by using cookie-cutter damage functions and the Carleton damage functions with different shape factors.The comparison of the calculation results shows that using cookie-cutter damage functions or the Carleton damage function with a wrong shape factor results in quite signifi-cant differences from using the original Carleton damage function with a correct shape factor when weapon's delivery error deviations are less than or comparable to the lengths of the lethal area and the aim point is far from a target.The effectiveness methods improved in this paper will be useful for mission planning utilizing the precision-guided munitions in circumstances where the collateral damage should be reduced.