we discuss here are spheres and the granular substrate is comprised of particles that are much smaller than the projectile.

Our granular substrate is dry playground sand. As irregularities in a fine medium are less likely affect the projectile trajectory, and craters are easier to see in a fine medium, we chose fine sand to facilitate measurement of projectile stopping times, crater sizes, depths and morphology. The sand was passed through a sieve, giving only particles less than 0.5 mm in diameter. Density of our sand is $\rho_s = 1.6$ g/cm$^3$. The porosity of our sand was 0.4. We measured the porosity by filling a volume of sand with water until the voids were filled and taking the ratio of the volumes. Prior to each impact the substrate is raked and then scraped flat. It is not pressed or compacted. The rake consists of a linear row of 2 cm long nails. The separation between each pair of neighboring nails is 1 cm. The rake and a close up view of the sand tray is shown in Figure \[fig:setup\_close\]. The low packing fraction of the sand and shallow penetration regime of our impacts suggests that interstitial air would not have 