Direction of spin axis and spin rate of the pitched baseball
Direction of spin axis and spin rate of the pitched baseball
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DOI：
10.1080/14763140608522874
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发表时间：
2006-07-01
影响因子：
2.2
通讯作者：
Sakurai, Shinji
中科院分区：
文献类型：
--
作者：
Jinji, Tsutomu;Sakurai, Shinji
在这项研究中，我们的目的是确定自转轴的方向和投球的自旋速率，并估计相关的空气动力。此外，还评估了自旋轴方向和自旋速率对投球轨迹的影响。使用4台同步摄像机（60 Hz）记录投手和投球机投出的棒球轨迹，并使用直接线性变换（DLT）程序进行分析。利用最小二乘法建立多项式函数，推导出每节球在飞行过程中球坐标的时间位移关系。使用高速摄像机（250 Hz）拍摄棒球在球释放后的瞬间，并根据球上标记的位置变化计算出自转轴的方向和旋转速率（omega）。升力系数与omega sin alpha密切相关（r = 0.860），其中alpha为自转轴与俯仰方向之间的夹角。sin表示速度矢量的竖直分量。升力是由于球的旋转而产生的马格努斯效应，它垂直于旋转轴。马格努斯效应在角速度与平动速度矢量相互垂直时最大，当角速度与平动速度矢量之间的夹角接近0度时，投出的棒球的断裂越小。投球机投出的球比实际投球手投出的球更容易破碎。当我们在击球练习中使用投球机时，有必要考虑这些差异。
In this study, we aimed to determine the direction of the spin axis and the spin rate of pitched baseballs and to estimate the associated aerodynamic forces. In addition, the effects of the spin axis direction and spin rate on the trajectory of a pitched baseball were evaluated. The trajectories of baseballs pitched by both a pitcher and a pitching machine were recorded using four synchronized video cameras (60 Hz) and were analyzed using direct linear transform (DLT) procedures. A polynomial function using the least squares method was used to derive the time-displacement relationship of the ball coordinates during flight for each pitch. The baseball was filmed immediately after ball release using a high-speed video camera (250 Hz), and the direction of the spin axis and the spin rate (omega) were calculated based on the positional changes of the marks on the ball. The lift coefficient was correlated closely with omega sin alpha (r = 0.860), where alpha is the angle between the spin axis and the pitching direction. The term omega sin alpha represents the vertical component of the velocity vector. The lift force, which is a result of the Magnus effect occurring because of the rotation of the ball, acts perpendicularly to the axis of rotation. The Magnus effect was found to be greatest when the angular and translational velocity vectors were perpendicular to each other, and the break of the pitched baseball became smaller as the angle between these vectors approached 0 degrees. Balls delivered from a pitching machine broke more than actual pitchers balls. It is necessary to consider the differences when we use pitching machines in batting practice.