Low-speed impact craters in loose granular media

TL;DR

This study investigates the formation of craters by low-speed impacts in dry granular media, confirming a known scaling law for crater diameter and discovering a new scaling law for crater depth, with implications for granular mechanics.

Contribution

It introduces a new scaling law for crater depth in granular impacts, expanding understanding beyond the established diameter scaling.

Findings

Crater diameter scales as the 1/4 power of impact energy.

Crater depth follows a different 1/3 power law involving impact properties.

Crater depth relates to the stopping force on impacting objects.

Abstract

We report on craters formed by balls dropped into dry, non-cohesive, granular media. By explicit variation of ball density $\rho_{b}$, diameter $D_{b}$, and drop height $H$, the crater diameter is confirmed to scale as the 1/4 power of the energy of the ball at impact: $D_{c}\sim(\rho_{b}{D_{b}}^{3}H)^{1/4}$. Against expectation, a different scaling law is discovered for the crater depth: $d\sim({\rho_{b}}^{3/2}{D_{b}}^{2}H)^{1/3}$. The scaling with properties of the medium is also established. The crater depth has significance for granular mechanics in that it relates to the stopping force on the ball.