A model for gymnastics vaulting.

A mathematical model describing the motion of a gymnast represented by a planar three-segment link system is developed for the airborne and horse-support phases of vaulting. Four handspring vaults performed by advanced-level female gymnasts were analyzed and the results were used to verify the model. In order to describe observed performance, it was found necessary to consider the period of support on the vaulting horse as being comprised of two distinct phases: a compression phase and a repulsion phase. Solutions of the model are presented graphically enabling the relationships of important variables to be readily observed, and predictions to be made. Good agreement between observed performance and the model was obtained in all cases. The take-off velocity and initial distance from the horse were found to be the principal variables affecting the outcome of the vault. The model indicated that in the case of a good vault, a decrease of 7% in the take-off horizontal speed would cause a reduction of 13% in after-flight distance, and a similar decrease in the vertical speed would produce a 25% reduction in after-flight distance. Also, the force exerted by the performer during the repulsion phase has only a minimal effect on the after-flight characteristics of the vault. The take-off velocity requirements for an excellent vault were investigated for varying take-off distances from the horse. As the distance was decreased, the necessary velocity was decreased, but the angular velocity of the body required during the pre-flight phase was found to increase very rapidly.