Using the Spring-Mass Model for Running: Force-Length Curves and Foot-Strike Patterns

Abstract Background The spring-mass model is commonly used to investigate the mechanical characteristics of human running. Underlying this model is the assumption of a linear force-length relationship, during the stance phase of running, and the idea that stiffness can be characterised using a single spring constant. However, it remains unclear whether the assumption of linearity is valid across different running styles. Research Question: How does the linearity of the force-length curve vary across a sample of runners and is there an association between force-length linearity and foot-strike index/speed? Methods Kinematic and kinetic data were collected from twenty-eight participants who ran overground at four speeds. The square of the Pearson’s correlation coefficient, R2, was used to quantify linearity; with a threshold of R2 ≥ 0.95 selected to define linear behaviour. A linear mixed model was used to investigate the association between linearity and foot-strike index and speed. Results Only 36-46 % of participants demonstrated linear force-length behaviour across the four speeds during the loading phase. Importantly, the linear model showed a significant effect of both foot-strike index and speed on linearity during the loading phase (p =  0.003 and p  Significance This study showed that the assumption of a linear force-length relationship is not appropriate for all runners. These findings suggest that the use of the spring-mass model, and a constant value of stiffness, may not be appropriate for characterising and comparing different running styles. Given these findings, it may be better to restrict the use of the spring-mass model to individuals who exhibit linear force-length dependence. It would also be appropriate for future studies, characterising stiffness using the spring-mass model, to report data on force-length linearity across the cohort under study.