We investigate the condition for the bounce of circular disks which obliquely impacts on the fluid surface. An experiment [C. Clanet, F. Hersen, and L. Bocquet, Nature (London) 427, 29 (2004)] revealed that there exists a “magic angle” of 20° between a disk’s face and water surface in which the condition of the lowest impact speed necessary for a bounce is minimized. We perform a three-dimensional simulation of the disk-water impact by means of the smoothed particle hydrodynamics. Furthermore, we analyze the impact with a model of the ordinary differential equation (ODE). Our simulation is in good agreement with the experiment. The analysis with the ODE model gives us a theoretical insight into the “magic angle” of stone skipping.

• Received 22 November 2004

DOI:https://doi.org/10.1103/PhysRevLett.94.174501