When is a sphere flat?

Water impact events are characterized by large, short-lived impulses during the early stages of water entry. For sphere impacts, the analytical force model of Shiffman and Spencer from 1945 has been repeatedly confirmed by experiments for a range of sphere radii r. The transient force is driven by added mass as a growing surface area of the sphere becomes wetted. On the other extreme, the transient force on a flat disk impacting water is so fast that the impact physics are altered (Jain et al. 2021). However, as a sphere looks increasingly disk-like as , this raises the question of when and how sphere impact behavior transitions to disk impact behavior. Here, we vary the nose curvature on a cylindrical body from hemispherical (r = R_cyl) to flat (r => infinity) and experimentally measure the water impact forces on free-falling bodies. We show that the classical sphere model of Shiffman and Spencer explains the measured forces until the nose curvature reaches . Near this nose curvature, the body forms a depression on the water surface prior to impact, resulting in a trapped air layer whose dynamics play a significant role in the impulsive force. Because this depression has finite curvature, we hypothesize that the largest impact force will not be on a perfectly flat nose, but rather a nose with slight positive curvature, which is supported by our experiments. We thus explain the mechanisms by which sphere impactors behave as flat disks and demonstrate the implications for water entry forces.