M2 Running spring-mass model

Topic

The athlete's running gait includes an aerial phase within each cycle—during which neither foot touches the ground—a phase that serves as a defining criterion distinguishing running from walking. The runner's center of mass follows a spring-mass trajectory; consequently, the leg acts as a linear spring that stores and subsequently releases elastic energy during ground contact. The leg's stiffness—defined as the ratio of maximum force to maximum spring elongation—determines both the ground contact time and the vertical oscillation of the center of mass. At moderate running speeds, this elastic recovery contributes a significant portion of the energy for each stride—primarily through the Achilles tendon and the femur—characterized by the extraordinary tension within the Achilles tendon. The optimal stride frequency minimizes the runner's metabolic cost. The vertical ground reaction force exhibits a single peak during the mid-stance phase—a temporal pattern distinct from the double-peak pattern observed in walking—and this single peak can reach magnitudes several times the runner's body weight, reflecting the extraordinary vertical forces characteristic of elite runners. Consequently, with this model—characterized by the aerial phase and the spring-mass system that define it—the final cost of running depends on both the collision work required to redirect the center of mass during each footstrike and the additional work needed to recover the energy dissipated in each cycle. The runner's final maximal aerobic speed thus serves as a global performance parameter, integrating maximal oxygen consumption, the lactate threshold, and running economy (which, in another model within this framework, is linked to metabolic efficiency). Therefore, if the runner's running economy improves, their final maximal aerobic speed will also increase for any given level of maximal oxygen consumption.

ID:446