标题： 成功执行一次三段式挑高球技术在匹克球中的应用 显示英文标题

标题： Executing a Successful Third Shot Drop in Pickleball

摘要： 我们通过构建pickleball球空气动力学的数值模型来定义和研究pickleball中的成功第三拍吊球。 我们的总体目标是研究导致成功第三拍吊球的初始速度、角度和自旋范围。 我们得出结论，初始速度必须在直线击球范围内$10.9~ms^{-1}$到$13~ms^{-1}$，以及在斜线击球范围内$13.3~ ms^{-1}$到$16~ms^{-1}$。 初始角度对于直线击球必须在$15.5$度到$22.5$度的范围内，对于斜线击球则必须在$12.5$度到$18$度的范围内。 我们得出结论，旋转对第三拍落点的影响是次要的。 我们认为这些结果可能对希望提升乒乓球这项运动这一关键环节的教练和选手有所帮助。 显示英文摘要

摘要： We define and investigate a successful third shot drop in pickleball using a numerical model of pickleball ball aerodynamics. Our overall objective is to investigate the ranges of initial speeds, angles and spins that result in a successful third shot drop. We conclude that the initial speed must be in the range $10.9~ms^{-1}$ to $13~ms^{-1}$ for down-the-line shots and $13.3~ ms^{-1}$ to $16~ms^{-1}$ for cross-court shots. The initial angle must be in the range $15.5$ degrees to $22.5$ degrees for down-the-line shots and $12.5$ degrees to $18$ degrees for cross-court shots. We conclude that the effects of spin on the third shot drop are of secondary importance. We believe these results could be useful as a guide to coaches and players wanting to develop this crucial aspect of the game of pickleball.