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

## Description

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.