SYME, D.A.*; STRUTHERS, C.N.; University of Calgary, Alberta; University of Calgary, Alberta: How Much Can Tendons Improve Jump Height? Computer simulated jumping with a muscle-tendon-load complex

Inserting a compliant tendon between a muscle and a load results in an increase in the height to which the muscle can lift the load. What are the limits and why? An iterative mathematical model was developed to explore how tendons with different physical characteristics affect the work and power output of a linear muscle-tendon-load system, and ultimately on the height the load can be lifted during simulated vertical jumping. Muscle force was based on physiological length-tension, force-velocity and activation-time characteristics of frog muscle. The tendon was a Hookean spring with no viscosity and was defined by its length, cross-sectional area and Young’s modulus. The inertial load was 20% of isometric force and its movement was modeled using ballistic equations. Use of a ‘catch’ mechanism to enhance performance was modeled by forcing the load to remain stationary for a defined period while the muscle contracted before being released. The simulation began with the load on the ground and the muscle relaxed. Work done by the muscle, energy absorbed and released by the tendon, and displacement of the load were measured during each simulated jump. A comprehensive series of muscle lengths, tendon lengths, tendon compliances and delays before release of the load were tested. It was revealed that adding a tendon with an appropriate length/stiffness ratio would improve jump height by maximally 4% above what a muscle alone could do. If the muscle was first stretched by 20% an 82% improvement was observed (with an appropriate tendon). A stretch, tendon, and ‘catch’ resulted in a 2.55 fold increase in jump height and 3.6 fold increase in peak power. The improvements in jump height resulted from an increase in work done by the muscle and were only loosely related to increased power output.