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.

由于食品安全和环境问题，弹枪越来越多地使用表面硬化的钢丸，而不是“经典”铅。相应地，人们越来越担心意外的药丸弹跳以及随后的诸如眼部伤害之类的人身伤害。相应地，本文重点讨论了具有表面和撞击后弹跳范围的弹丸的影响。推导了具有单边粘滑条件的一般三维非弹性冲击方程，并进行了碰撞后轨迹分析。定性地，随着摩擦的增加，跳弹的范围减小，这是因为丸粒的大部分撞击前平移能在撞击时转换为旋转能，从而减小了撞击后的跳弹范围。对于光滑的表面，由于小球之间的粘滑条件的混合，出现了大范围的轨迹分布。在打滑的情况下，丸粒保留了其大部分平移能量，并且撞击后的线速度大于高摩擦情况，这导致了撞击后的轨迹范围大得多。该模型使分析人员可以对与shot弹枪使用相关的参数选择做出更多定量决策，并可以减少测试中的反复试验程序。