Abstract
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.
Highlights
Accurate throwing is a skilled motor task in humans that has inspired many studies of motor control [1,2,3,4,5,6]
We have focused on the simplest physical problem of how errors in the release parameters are amplified by the parabolic trajectory of a thrown projectile to determine optimal strategies for throwing
Throwing is a complicated motor task, the predictions of our model for overarm versus underarm throwing styles are consistent with extant experimental data that show a dependence of style on the target location as well as on planning uncertainty
Summary
Accurate throwing is a skilled motor task in humans that has inspired many studies of motor control [1,2,3,4,5,6]. One has to learn strategies from an iterative process of error estimation and correction from one trial to the This has led to studies of error propagation via the throwing actions used in specific sports, such as basketball [4,15,16], darts [3] or pétanque [1], where the analyses treat throwing as a problem of shooting, i.e. the arm plays no role. We complement these by studying optimal strategies in throwing using a simple model of the arm as a finite object, and an analysis of error propagation through the dynamics of an ideal projectile flight This allows us to address the qualitative selection of overarm versus underarm styles, as well as the quantitative selection of the release angle and speed, and their dependence on the target geometry, location and throwing speed. We look at the role of planning uncertainty in characterizing how errors are amplified, and what this implies for a measured approach to learning the optimal strategy for throwing
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