Data for: Mach number scaling of impact craters in unconsolidated granular materials

The formation of impact craters in unconsolidated granular materials is a topic of enduring interest in solid-earth geophysics, planetary science, and several branches of engineering science. In particular, a general relationship between crater size, impact parameters, and target material properties is often sought. This paper presents a new empirical relationship, based on dimensional analysis and inspired by gas-dynamic shock physics, for the diameters of low- and high-speed impact craters in dry granular materials based on the hypothesis that surface-gravity- and shock-wave phenomena primarily set crater size. The final relationship involves the impacting object’s kinetic energy and speed; the target material’s density, angle of repose, and sound speed; and the gravitational acceleration at the impact location. It is formulated in terms of a dimensionless crater diameter, an algebraic combination of Froude number, Mach number, and the tangent of the target material’s angle of repose, using an analogy to gas dynamics and an empirical power law for the dependence of granular-material sound speed on gravitational acceleration. The coefficient of determination for the final fit is 0.969 based on experimental impact data from 325 individual impacts spanning parametric ranges of more than 400 in crater diameter, 10^10 in impact energy, 500 in gravitational acceleration, and 40 in target material density for two different angles of repose. The final formula provides insight into how impact energy conversion depends on Mach number and may be useful for predictive and forensic analysis of planetary impact craters and for granular-flow code validation.松散颗粒物质中的撞击坑形成过程，是固体地球物理学、行星科学以及多门工程科学领域长期备受关注的研究课题。尤为关键的是，学界长期致力于探寻撞击坑尺寸、撞击参数与靶材物理性质之间的普适关联。本文基于量纲分析（dimensional analysis），并受气体动力学冲击物理（gas-dynamic shock physics）的启发，针对干燥颗粒物质中的低速与高速撞击坑直径，提出了全新的经验关联式，其核心假设为：表面重力与冲击波现象是决定撞击坑尺寸的主导因素。该最终关联式涵盖了撞击体的动能与速度、靶材的密度、休止角、声速，以及撞击位置的重力加速度。该式以无量纲撞击坑直径为基础构建，通过类比气体动力学，并基于颗粒物质声速随重力加速度变化的经验幂律关系，将弗劳德数（Froude number）、马赫数（Mach number）与靶材休止角的正切值进行代数组合，得到了上述关联式。基于325组独立撞击实验数据得到的最终拟合模型，其决定系数为0.969；该实验数据集覆盖的参数范围包括：撞击坑直径跨度超400倍、撞击能量跨度达10^10倍、重力加速度跨度达500倍，靶材密度跨度达40倍，且涵盖两种不同的休止角工况。该最终公式揭示了撞击能量转换与马赫数之间的依赖关系，可用于行星撞击坑的预测分析与取证分析，同时也可用于颗粒流动数值模拟代码的验证工作。