Low-speed impact craters in loose granular media
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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.
experiment; 4 pages, 3 figures
experiment; 4 pages, 3 figures