Poncelet coefficients of granular media

We have developed a new technique for precise measurement of deceleration of projectiles in sand. It uses a PDV to observe the back of a sphere. Impacts were conducted up to 300 m/s, and trajectories were observed for more than 10 projectile diameters. The precise measurements allow us to calculate Poncelet parameters for spheres in dry and saturated sand and fused quartz. We find that the coefficients needed to describe the data change at about 100 m/s, and Poncelet values that give accurate estimates of deceleration will usually fail to predict ultimate penetration depth. For comparing materials, we find sand is harder to penetrate than fused quartz. Dense materials are harder to penetrate than less dense materials. Dry materials are harder to penetrate than saturated materials.