Explicit Exact Solution of Damage Probability for Multiple Weapons against a Unitary Target

Abstract We study the damage probability when M weapons are used against a unitary target. We use the Carleton damage function to model the distribution of damage probability caused by each weapon. The deviation of the impact point from the aimpoint is attributed to both the dependent error and independent errors. The dependent error is one random variable affecting M weapons the same way while independent errors are associated with individual weapons and are independent of each other. We consider the case where the dependent error is significant, non-negligible relative to independent errors. We first derive an explicit exact solution for the damage probability caused by M weapons for any M. Based on the exact solution, we find the optimal aimpoint distribution of M weapons to maximize the damage probability in several cases where the aimpoint distribution is constrained geometrically with a few free parameters, including uniform distributions around a circle or around an ellipse. Then, we perform unconstrained optimization to obtain the overall optimal aimpoint distribution and the overall maximum damage probability, which is carried out for different values of M, up to 20 weapons. Finally, we derive a phenomenological approximate expression for the damage probability vs. M, the number of weapons, for the parameters studied here.

Average Damage Caused by Multiple Weapons against an Area Target of Normally Distributed Elements

This paper investigates the effect of launching multiple weapons against an area target of normally distributed elements. We provide an analytical form of the average damage fraction and then apply it to obtain optimal aimpoints. To facilitate the computational efforts in practice, we also consider optimizations over given constrained patterns of aimpoints. Finally, we derive scaling laws for optimal aimpoints and optimal damage fraction with respect to the radius of the area target.