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Low-speed impact craters in loose granular media

J. S. Uehara·M. A. Ambroso·R. P. Ojha·D. J. Durian
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Abstract

We report on craters formed by balls dropped into dry, non-cohesive, granular media. By explicit variation of ball density $ρ_{b}$, 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: $D_{c}\sim(ρ_{b}{D_{b}}^{3}H)^{1/4}$. Against expectation, a different scaling law is discovered for the crater depth: $d\sim({ρ_{b}}^{3/2}{D_{b}}^{2}H)^{1/3}$. 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.

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J. S. Uehara, M. A. Ambroso, R. P. Ojha, D. J. Durian. 2003-03-25. Low-speed impact craters in loose granular media. https://doi.org/10.1103/physrevlett.90.194301

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