Low-speed impact craters in loose granular media

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.

experiment; 4 pages, 3 figures

References in corpus (2)

• Granular Shear Flow Dynamics and Forces : Experiment and Continuum Theory
• Granular Drag on a Discrete Object: Shape Effects on Jamming

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