臺灣博碩士論文加值系統

緒論：棒球打擊被視為是運動中最困難的運動技巧之一，必須要透過大量打擊訓練才能有效提升打擊能力。但現階段缺乏較好的打擊訓練方法，能幫助打者模擬比賽真實情況的球路。因此本研究希望透過空氣動力學計算棒球飛行過程中所受的各種力，模擬與真實情況相吻合的飛行軌跡。方法：本研究經電腦數值運算模擬的棒球軌跡，與下列兩者比較進行驗證。(1)實體實驗：以棒球發球機將球發出，並透過高速攝影機捕捉球上的反光貼紙位置，進而計算球飛行的運動學參數 (2)其他研究團隊(Nathan等人)之軌跡模型。並透過最佳化的方式，求取飛行過程中最佳的CD (阻力係數)與CY (橫向力係數)。結果：實體實驗因器材限制而導致X方向的分量偏移過大，以致無法參與比對，因此僅以方法2進行最佳化及軌跡比對。在假設CD為常數的情況下，最佳CY (0.00339)與速率、速度平方以及雷諾數成高度負相關 (相關係數R分別為-0.825，-0.823，與-0.825)；而在假設CY為常數的情況下，最佳CD (0.27700)與速率及速度平方亦呈負相關 (R分別為-0.474與-0.475)。若同時計算最佳CY與CD值，則得最佳CY=0.00254、CD=0.27603。軌跡比對部分，則以模擬過程中有加入最佳CD時的位置誤差最小，其X、Z與總偏移量的誤差皆明顯下降 (誤差分別為0.031m，-0.033m，0.102m)，至於該軌跡中EVf的誤差 (1.38%)是否會造成打者打擊判斷上的影響，則有待探討。結論：最佳CY與速率以及雷諾數在本實驗中呈高度負相關，需透過更大範圍的球速測試，才能確認其於各範圍球速下之間的相關性。而由於CY值很小，對於模擬軌跡影響有限，因此於忽略橫向力的情況下，透過加入會隨雷諾數變化的CD值，應可模擬出貼近真實飛行情況的軌跡。

This study simulated baseball flight trajectories by considering all the forces applied to the ball, including the gravitational force and aerodynamic forces. Calculation of the lift coefficient was based on previous studies, while the drag coefficient CD and side force coefficient CY were obtained by applying optimization methods. Simulated flight trajectories were verified by (1) Using high-speed cameras to record the trajectories of markers on a baseball for calculating the kinematic parameters of ball flight, and (2) Inputting the initial conditions to the Trajectory Calculator (TC) developed by another research group to obtain the data of trajectories. Moreover, when the CY and CD were not assumed to be constant, their optimal values were calculated by minimizing the overall difference in trajectory between the present simulation and TC. When the CD was assumed to be constant, the optimal CY was found to highly correlate with ball speed V, V2 and the Reynolds number Re. Optimal CD was moderately correlated with V and V2 when the side force was ignored. On the other hand, dispensing with the assumption of constant CY and CD allowed their optimal values to be calculated as 0.00254 and 0.27603, respectively. When employing optimal CD in the simulation, the deviation in the trajectory was the smallest and ΔX, ΔZ, ΔR were considerably reduced. To sum up, the small value of CY implies diminutive influence on trajectories and therefore realistic trajectories might be simulated by solely using suitable CD values. However, it still requires further research to investigate the effect of the deviation of EVf on batters’ reactions.

摘要 i
致謝 ix
目錄 x
表目錄 xii
圖目錄 xiii
第壹章 緒論 1
第一節 研究背景 1
第二節 研究目的 3
第三節 研究假設 3
第四節 名詞解釋 4
第貳章 文獻探討 5
第一節 棒球飛行的空氣動力學 5
第二節 阻力 5
第三節 升力 7
第四節 其他作用力 9
第五節 總結 9
第參章 研究方法 11
第一節 儀器設備 11
第二節 實驗設置 12
第三節 Trajectory Calculator 17
第四節 電腦模擬 19
第五節 實驗流程 20
第六節 資料處理與分析 21
第肆章 研究結果 25
第一節 電腦模擬與Trajectory Calculator 26
第二節 最佳CY與CD 26
第三節 位移變化量 30
第四節 末速誤差率與飛行時間差 31
第伍章 討論 33
第一節 實體實驗 33
第二節 原模擬軌跡差異比較 33
第三節 CY與CD對飛行軌跡之影響 34
第陸章 結論與建議 37
參考文獻 38

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