Hamilton G R, Reinschmidt C
Human Performance Laboratory, The University of Calgary, Alberta, Canada.
J Sports Sci. 1997 Oct;15(5):491-504. doi: 10.1080/026404197367137.
Using a theoretical approach, we studied the basketball free throw as a function of angle, speed and spin at release. The ball was constrained to the sagittal plane bisecting the hoop and normal to the backboard, and was permitted to bounce and change spin on both backboard and hoop. Combinations of angle, speed and spin resulting in a successful shot were calculated analytically. Standard deviations for a shooter's angle and speed were used to predict the optimal trajectory for a specific position of release. An optimal trajectory was predicted which had an initial angle and speed of approximately 60 degrees and 7.3 m s(-1) respectively over the domain of spins (-2 to +2 m s(-1) surface speed; -16 to +16 rad s[1]). The effect of air resistance and the sagittal plane constraint on the predicted optimal trajectory were discussed and quantified. The optimal trajectory depended on both the anthropometric characteristics and accuracy of the shooter, but generally a high backspin with an angle and speed combination which sent the ball closer to the far rim of the basket than the near rim was advantageous. We provide recommendations for shooters as a function of the height of ball release.
我们采用理论方法，研究了篮球罚球时出手角度、速度和旋转之间的函数关系。球被限制在将篮筐二等分且垂直于篮板的矢状面内，并允许在篮板和篮筐上反弹及改变旋转。通过解析计算得出了能成功投篮的角度、速度和旋转的组合。利用射手角度和速度的标准差来预测特定出手位置的最佳轨迹。预测出一条最佳轨迹，在旋转范围（表面速度为 -2 至 +2 m s(-1)；角速率为 -16 至 +16 rad s[1]）内，其初始角度和速度分别约为 60 度和 7.3 m s(-1)。讨论并量化了空气阻力和矢状面约束对预测的最佳轨迹的影响。最佳轨迹取决于射手的人体测量特征和准确性，但一般来说，高后旋且角度和速度的组合使球更靠近篮筐远边缘而非近边缘是有利的。我们根据球出手高度为射手提供了相关建议。
