Experimental results and mathematical formulation of non-spinning stone-skipping process

Abstract

Abstract Following a previously published paper in studying stone-skipping processes, detailed experimental figures are revealed in this paper. A mathematical model is also provided to explain the observed phenomena and measured data. The model separates the skipping process into several stages. It emphasizes, in particular, a hitting stage and a sliding stage, and also includes capillary-gravity wave resistance in its formulation. During these two stages, scale analysis is applied first to evaluate the relative importance among various forces acting on the stone. After reasonable simplification, a numerical algorithm is established to depict motion of the stone starting from its first hit of water to final sink. The total number of skips under specified initial throwing conditions can be predicted accordingly. The agreement between the analytical and experimental results indicates the applicability of the proposed model.