Application of a Projection Model Including the Effect of Run-Up to Sports Activities

Abstract

We investigate the projection model with the effect of run-up that includes three variables: projection speed and angle, and also a horizontal speed at projection. These variables express the least effect for the multi-degree of freedom of a human body. In the model with three variables, a constraint between initial speed and initial angle is derived, and it presents the adequate function for projection with the run-up effect. We attempt to determine the function by comparing its shape with that of the given constraints in shot put and long jump. Consequently, the function derived from the model with three variables reproduces successfully the measured results, and estimated values of the model variables predict the optimum values of the initial speed and initial angle. This means that the model with three variables includes a constraint between initial speed and initial angle, and therefore we conclude that it provides theoretical ground for projection with the run-up effect in sports activities.