Exploring dynamic similarity in human running using simulated reduced gravity

The Froude number (a ratio of inertial to gravitational forces) predicts the occurrence of dynamic similarity in legged animals over a wide range of sizes and velocities for both walking and running gaits at Earth gravity. This is puzzling because the Froude number ignores elastic forces that are crucial for understanding running gaits. We used simulated reduced gravity as a tool for exploring dynamic similarity in human running. We simulated reduced gravity by applying a nearly constant upward force to the torsos of our subjects while they ran on a treadmill. We found that at equal Froude numbers, achieved through different combinations of velocity and levels of gravity, our subjects did not run in a dynamically similar manner. Thus, the inertial and gravitational forces that comprise the Froude number were not sufficient to characterize running in reduced gravity. Further, two dimensionless numbers that incorporate elastic forces, the Groucho number and the vertical Strouhal number, also failed to predict dynamic similarity in reduced-gravity running. To better understand the separate effects of velocity and gravity, we also studied running mechanics at fixed absolute velocities under different levels of gravity. The effects of velocity and gravity on the requirements of dynamic similarity differed in both magnitude and direction, indicating that there are no two velocity and gravity combinations at which humans will prefer to run in a dynamically similar manner. A comparison of walking and running results demonstrated that reduced gravity had different effects on the mechanics of each gait. This suggests that a single unifying hypothesis for the effects of size, velocity and gravity on both walking and running gaits will not be successful.