Dynamics of the long jump

A mechanical model is proposed which quantitatively describes the dynamics of the centre of gravity (c.g.) during the take-off phase of the long jump. The model entails a minimal but necessary number of components: a linear l eg spring with the ability of lengthening to describe the active peak of th e force time curve and a distal mass coupled with nonlinear visco-elastic e lements to describe the passive peak. The influence of the positions and ve locities of the supported body and the jumper's leg as well as of systemic parameters such as leg stiffness and mass distribution on the jumping dista nce were investigated. Techniques for optimum operation are identified: (1) There is a minimum stiffness for optimum performance. Further increase of the stiffness does not lead to longer jumps. (2) For any given stiffness th ere is always an optimum angle of attack. (3) The same distance can be achi eved by different techniques. (4) The losses due to deceleration of the sup porting leg do not result in reduced jumping distance as this deceleration results in a higher vertical momentum. (5) Thus, increasing the touch-down velocity of the jumper's supporting leg increases jumping distance. (C) 199 9 Elsevier Science Ltd. All rights reserved.