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: \(D_{c}\sim(\rho_{b}{D_{b}}^{3}H)^{1/4}\). 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.