Elastic energy savings and active energy cost in a simple model of running
Fig 8
Unified model energy cost vs. speed and spring stiffness, including force-rate cost.
(A) Energetic cost per time versus speed is shown for the Actuated Spring-mass model (k* of 35.6 kN m-1, ε* of 0.5∙10−3; red curve) and for empirical metabolic data of human subjects running on a treadmill (mean ± standard deviation; [48]). Model cost includes costs for work and force-rate, plus a constant offset associated with human resting metabolism (dashed horizontal line). (B) The model’s energetic cost is shown for three speeds v (2.5–3.5 m s-1) and with parameter variation of spring stiffnesses k (13.7–109.5 kN m-1), with total cost (black lines), force-rate cost (difference between offset and magenta lines), and actuator work cost (difference between total and magenta lines). The unified model’s spring nominal stiffness k* is indicated (red line in A, red symbol in B).