Optimal jumping strategies from compliant surfaces: a simple model of springboard standing jumps.

A simple model of standing dives is used to investigate optimal jumping strategies from compliant surfaces and applied to springboard diving. The human model consists of a massless leg actuated by knee torque, and a lumped torso mass centered above the leg. The springboard is modeled as a mass-spring system. Maximum jump height for a male and a female is calculated by controlling knee-torque activation level as a function of time. The optimization includes constraints on minimum and maximum knee angle, rate of change of normalized activation level, and contact duration. Simulation results for maximal springboard depression and diver takeoff velocity agree reasonably with experimental data, even though larger board tip velocities are necessarily predicted earlier during the contact period. Qualitatively similar multiple pulse knee-torque activation patterns are found over various conditions and are different from those in rigid-surface jumping. The model is less able to predict accurately jump height at high fulcrum number since jumpers may have difficulty behaving optimally at non-preferred fulcrum settings. If strength is proportional to the product of mass and leg length, increasing leg length is more effective in increasing jump height than is increasing mass.