Venkadesan M, Mahadevan L
Department of Mechanical Engineering and Materials Science, Yale University, New Haven, CT 06520, USA.
Department of Physics, Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, USA.
R Soc Open Sci. 2017 Apr 26;4(4):170136. doi: 10.1098/rsos.170136. eCollection 2017 Apr.
The accuracy of throwing in games and sports is governed by how errors in planning and initial conditions are propagated by the dynamics of the projectile. In the simplest setting, the projectile path is typically described by a deterministic parabolic trajectory which has the potential to amplify noisy launch conditions. By analysing how parabolic trajectories propagate errors, we show how to devise optimal strategies for a throwing task demanding accuracy. Our calculations explain observed speed-accuracy trade-offs, preferred throwing style of overarm versus underarm, and strategies for games such as dart throwing, despite having left out most biological complexities. As our criteria for optimal performance depend on the target location, shape and the level of uncertainty in planning, they also naturally suggest an iterative scheme to learn throwing strategies by trial and error.
在游戏和体育运动中，投掷的准确性取决于规划和初始条件中的误差如何通过抛射体的动力学进行传播。在最简单的情况下，抛射体路径通常由确定性抛物线轨迹描述，这种轨迹有可能放大有噪声的发射条件。通过分析抛物线轨迹如何传播误差，我们展示了如何为要求准确性的投掷任务设计最优策略。我们的计算解释了观察到的速度与准确性的权衡、上手投掷与下手投掷的偏好投掷方式，以及诸如飞镖投掷等游戏的策略，尽管我们忽略了大多数生物学复杂性。由于我们的最优性能标准取决于目标位置、形状以及规划中的不确定性水平，它们自然也暗示了一种通过试错来学习投掷策略的迭代方案。
