Shape of impact craters in granular media

We present the results of experiments studying the shape of craters formed by the normal impact of a solid spherical projectile into a deep noncohesive granular bed at low energies. The resultant impact crater surfaces are accurately digitized using laser profilometry, allowing for the detailed investigation of the crater shape. We find that these impact craters are very nearly hyperbolic in profile. Crater radii and depths are dependent on impact energy, as well as the projectile density and size. The precise crater shape is a function of the crater aspect ratio. While the dimensions of the crater are highly dependent on the impact energy, we show that the energy required to excavate the crater is only a tiny fraction (0.1%-0.5%) of the kinetic energy of the projectile.