曲球與滑球運動軌跡的數值模擬及知識輔助訓練

Numerical Simulation of the Trajectory of Curveball and Slider and Knowledge-Aided Training

張憲國(Hsien-Kuo Chang) ； 黃杉楹(Shan-Ying Huang) ； 陳蔚瑋(Wei-Wei Chen)

《大專體育學刊》 22卷1期 (2020/03) Pp. 53-67

https://doi.org/10.5297/ser.202003_22(1).0004

摘要

具多變球種及控球能力的優秀投手是棒球比賽輸贏的關鍵，投手常利用曲球及滑球的尾端銳利下墜來有效壓制打者的出棒。本研究目的為提出一個數值計算方法來模擬曲球及滑球的球體運動特性，並探討兩種球路的放球速率及轉速對運動軌跡及進壘位置的影響。由研究結果顯示15 km/hr的放球球速差異會影響進壘高度約20.0 cm的差異，而300 rpm的球轉速差異影響進壘高度差異僅約1.5 cm。本研究的結論為空氣阻力是延長球體飛行時間，約0.02 s，而馬格納斯力大小是決定球體進壘側向偏移及更多下墜的重要因素。本文提供的放球起始條件及進壘位置的量化運動科學知識可有效輔助投手訓練。

關鍵字

運動科學 ； 阻力 ； 馬格納斯力 ； 進壘位置

並列摘要

An excellent pitcher with abundant repertoire and dominant ball control are the decisive factors in a baseball game. Curveballs and sliders that veer laterally or downwardly through the batter's hitting zone are 2 examples of breaking the balls for a pitcher to suppress the batter’s hot hitting. This study aimed to analytically study the trajectory of these 2 breaking balls. In the attempt to study control techniques of curveballs and sliders, we used numerical computation to simulate the trajectory motions and investigated the effect of initial velocity and rotating speed at the base entry. The results showed that 15 km/hr difference in the release velocity ends up with an averaged difference of entry height by 20.0 cm, but a 300-rpm release angular speed difference makes a slight change of only 1.5 cm in entry height. We concluded that the drag force increases the flight time of a pitch by about 0.02 s, and the Magnus force induces the lateral movement and achieves more drop. The obtained quantitative relationship between the initial conditions and entry positions will offer pitchers necessary academic knowledge-aided pitching training in sports science.

並列關鍵字

sports science ； drag force ； Magnus force ； entry position

參考文獻

李中傑（2011）。由流體力學之觀點看作用在飛行棒球上的力。物理教育學刊，12 卷 1 期，57-72頁。doi:10.6212/CPE.2011.1201.04[Lee, C.-C. (2011). Forces on a flying baseball from the viewpoint of fluid dynamics: Where are those forces coming from? and how large are they? Chinese Physics Education, 12(1), 57-72. doi:10.6212/CPE.2011.1201.04]

高英傑、江昆達（2008）。棒球縫線對飛行軌跡與球速之影響。大專體育學刊，10 卷 1 期，99-109 頁。doi:10.5297/ser.200803_10(1).0008[Kao, Y.-C., & Chiang, K.-D. (2008). The effects of the baseball seams on flying trajectories and velocities. Bulletin of University Physical Education & Sports, 10(1), 99-109. doi:10.5297/ser.200803_10(1).0008]

Barkla, H. M., & Auchterlonie, L. J. (1971). The Magnus or Robins effect on rotating spheres. Journal of Fluid Mechanics, 47(3), 437-447. doi: 10.1017/S0022112071001150

Bray, K., & Kerwin, D. (2003). Modelling the flight of a soccer ball in a direct free kick. Journal of Sports Science, 21(2), 75-85. doi:10.1080/0264041031000070994

Escalera Santos, G. J., Aguirre-López, M. A., Díaz-Hernández, O., Hueyotl-Zahuantitla, F., MoralesCastillo, J., & Almaguer, F-J. (2019). On the aerodynamic forces on a baseball, with applications. Applied Mathematics and Statistics, 4, 66. doi:10.3389/fams.2018.00066