DEM modeling and simulation of post-impact shotgun pellet ricochet for safety analysis

Abstract

Shotguns have increasingly used case-hardened steel pellets, as opposed to “classical” lead, owing to food safety and environmental concerns. Correspondingly, there is increasing concern about unintended ricochet of pellets and subsequent bodily harm, such as eye damage. Correspondingly, this paper focuses on the impact of pellets with a surface and the post-impact ricochet range. Equations for general three-dimensional inelastic impact with unilateral stick–slip conditions are derived for pellets and a post-impact trajectory analysis is performed. Qualitatively, with increasing friction, ranges of ricochet decrease because most of the pre-impact translational energy of the pellets is converted upon impact into rotational energy, which reduces the post-impact ricochet range. For slippery surfaces, wide ranging trajectory distributions occur owing to the mix of stick and slip conditions among the pellets. In the case of slip, the pellets retain much of their translational energy and the post-impact linear velocities are greater than high-friction cases, which leads to much larger post-impact trajectory ranges. The model enables analysts to make more quantitative decisions on the choices of parameters associated with shotgun use and can reduce trial-and-error procedures in testing.