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 ρb, diameter Db, and drop height H, the crater diameter is confirmed to scale as the 1/4 power of the energy of the ball at impact: Dc∼(ρbD3bH)1/4. Against expectation, a different scaling law is discovered for the crater depth: d ∼ (ρ3/2bD2bH)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.