Penetration drag in loosely packed granular materials

The drag coefficient for penetration of granular materials by conical-nosed penetrators was computed by assuming the particles are non-interacting and rebound elastically off of the advancing penetrator. The solution was C $=$4 [sin(theta)]**2, where theta is the half angle of the cone. Experiments were conducted in which the drag coefficient was measured over the range 30 to 80 m/s for four types of sand: Ottawa silica sand, crushed quartz glass, coral sand, and aragonite sand. The sands were tested at relative densities of 40 and 80{\%}. The drag coefficients for the low density materials were in excellent agreement with this simple model. The high density material had a drag considerably larger than predicted, presumably because of particle-to-particle interactions.