Cratering experiments in sands and a trial for general scaling law

The results of the vertical impacts of aluminum projectiles into quartz sand are reported. The impacts are at velocities of 35 to 830 m/sec with a single-stage powder gun. The morphology of craters formed in loose sands is generally conical, whereas that of craters formed in self-compacted sands varies with increasing impact velocity from a flat-floor type to a double-ring type. The present data, together with previous experimental data and the 'late-stage equivalence' of Dienes and Walsh, are seen as indicating that the crater diameter is expressed by a function of the 'late-stage effective energy' but not of the impact kinetic energy. The diameter of a crater formed in a noncohesive sand is found to be proportional to one-fourth the power of the late-state effective energy. For general impact cratering in a target with a finite strength, a relation is given between the velocity and the diameter, suggesting that there are four regimes in the crater diameter versus kinetic energy relation.