Application of Flexible Spring Characteristics to Sport Engineering (Fundamental Study on Pole-vaulting)

Abstract

The record of pole-vaulting has been improving rapidly by the appearance of a flexible fiberglass. The fiberglass pole has large elasticity. In analysis of the dynamics of the pole-vaulting, it is necessary to consider a high flexibility of pole. This paper deals with a large deformation problem of pole subjected to concentrated loads by the vaulter at two supporting points near the upper end. A simple combination model consisted of a mass (vaulter) and a pole was introduced in this analysis. Several analytical formulae are derived for vertical and horizontal displacements of the vaulter and so on in terms of elliptic integrals. Furthermore, a time progress of pole deformation is investigated. From the results, it is clarified that the initial conditions (e.g., vertical and horizontal velocities of the vaulter) and the applied bending moment during the vault play important roles.