Low-speed impact craters in loose granular media

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: $D_c\sim ({\rho }_b{D_b}^{3}H{)}^{1\mathrm{/}4}$. Against expectation, a different scaling law is discovered for the crater depth: $d\sim ({{\rho }_b}^{3\mathrm{/}2}{D_b}^{2}H{)}^{1\mathrm{/}3}$. 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.