桌球不同弧圈球軌跡數值模擬與分析

Numerical simulation and analysis of loop-drive trajectories in table tennis

緒論：在政府的體育政策下，各級學校及地方單位有系統且積極地推動桌球運動，桌球目前已成為國人熱門運動項目之一。桌球弧圈球因多變的技巧是現今桌球技術分類的主流，選手若可理解弧圈球運動特性也是精進球技的一種手段。因此，本文主要目的為建立一個可量化描述弧圈球的飛行速度及運動軌跡的模式。方法：使用的方法為基於球體運動的六個變數封閉型非線性控制方程式組及以高精度的龍格－庫塔法－斐伯格法獲得數值計算結果，並探討前衝弧圈、高吊弧圈及側拉弧圈的軌跡及關鍵運動特性的差異比較。結果：研究結果發現側拉弧圈比前衝弧圈及高吊弧圈有因更多的側向旋轉率所產生側向的馬格納斯力，造成的接觸點側偏可達0.21 m，且當時偏移角度約為8.07度。當球體起始旋轉越快及擊球點越外側，均會使桌球下墜越快，而接觸點越近桌端，且其側偏量增加。結論：本研究已量化比較指定幾種側旋轉角速率及擊球位置的側拉起始值所產生側偏及下墜量的差異，未來也可應用至新發展球技或特殊條件下球體運動特性的模擬計算。

Introduction: To comply with the government's sports policy, schools at all levels and localities have systematically and actively promoted the game of table tennis, which has become one of the most popular sports in Taiwan. Loop ball is a current table tennis practice method that can improve table tennis skills. Players who master the techniques associated with loop ball can improve their fine scoring skills in table tennis. Therefore, the main purpose of this study was to establish a model for quantifying the flight speed and trajectory of the looping ball. Methods: A closed-form set of six-variable nonlinear control equations was established to estimate the movement of a table tennis ball.Numerical calculations were conducted using the high-precision Runge-Kutta-Feiberg method, and differences between trajectories and key kinematic properties were discussed. Results: The results of the study found that side-spin drive generates more lateral Magnus force due to the lateral rotation rate than the other two loops. The lateral deviation of the landing point can reach 0.21 meters, with an offset angle of approximately 8.07°. A ball with a faster initial rotation of the sphere that was hit from a more outside contact point will fall faster with a drop point closer to the end of the table, increasing the amount of side deviation. Conclusion: This study quantitatively compared the degree of lateral deviation and drop in response to various angular side-spin rates relative to the initial position of the ball at the point of contact. In the future, this model can also be applied to calculations of table tennis ball movement characteristics under various conditions or circumstances.