Low-speed impact craters in loose granular media

We report on craters formed by balls dropped into dry, noncohesive, 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 similar to (rho(b)D(b)(3)H)(1/4). Against expectation, a different scaling law is discovered for the crater depth: d similar to (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.