Control of exterior ballistic properties of spin-stabilized bullet by optimizing internal mass distribution

Abstract

This paper introduces a novel approach for controlling the exterior ballistic properties of spin-stabilized bullets by optimizing their internal mass distributions. Specifically, the properties of interest are the bullets’ stability characteristics that are examined through dynamic and gyroscopic stability parameters. New analytical expressions for aerodynamic quantities are also derived to address the compressibility of air. These expressions are utilized in a bullet model that enables efficient computation of the stability parameters for a given mass distribution. The bullet model is used in the formulation of nonlinear optimization problems that provide optimal mass distributions with respect to given goals, i.e., desired stability characteristics. The bullet types investigated in this paper are a long range bullet and a limited range training bullet. In the optimization of the mass distribution of the long range bullet, the goal is that the bullet stays stable for as long as possible. The mass distribution of the training bullet is optimized such that the bullet is stable at launch but becomes unstable shortly afterwards. The global optimal solutions obtained with the new approach fulfill the desired stability characteristics better than currently used uniformly filled bullets. Overall, the optimization approach reveals a new goal focused philosophy for bullet design compared to current trial and error design practices. Keywords: Aerodynamics, Bullet, Exterior ballistics, Mass properties, Optimization, Stability