The role of body shape and mass in skimming on water

Over many years, there has been great practical interest in how solid bodies interact with and skim on liquid layers. In the present investigation, the focus is on the important role of body mass and shape in such skimming motions. Considering a thin two-dimensional solid body that impacts obliquely and then rebounds on a shallow inviscid water layer, we develop a mathematical model to predict quantitatively the duration and evolution of the body and fluid motions and indeed the success or failure of the whole skim. In the current setting, the shallow water layer thickness is small relative to the representative body length. The combined roles of increased mass and shape are found to be crucial, governed by a similarity solution. The relationship $C∼M^{2/3}$ between scaled body curvature and mass is identified and highlighted. In particular, increased convex curvature of the underbody is found to alter the interactive pressure in such a way that it inhibits the occurrence of a super-elastic response in the exit vertical velocity and height of the body, and in effect enables a much heavier body to skim successfully provided the above relationship is maintained.