Tsai Hsuan-Wei, Tsai Hsieh-Chen, Wu Wen-Fang, Lai Chun-Liang
Department of Mechanical Engineering, National Taiwan University, Taipei, 10617, Taiwan, ROC.
Sci Rep. 2022 Sep 30;12(1):16372. doi: 10.1038/s41598-022-19992-x.
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.
继之前发表的一篇关于研究打水漂过程的论文之后，本文展示了详细的实验数据。还提供了一个数学模型来解释观察到的现象和测量数据。该模型将跳跃过程分为几个阶段。特别强调了撞击阶段和滑动阶段，并且在其公式中还包括了毛细重力波阻力。在这两个阶段中，首先应用尺度分析来评估作用在石头上的各种力之间的相对重要性。经过合理简化后，建立了一个数值算法来描述石头从首次接触水面到最终下沉的运动。据此可以预测在指定初始投掷条件下的跳跃总数。分析结果与实验结果之间的一致性表明了所提出模型的适用性。
