An empirical analytical method to determine the human walking ground reaction force at known speeds

The experimental analysis of biomechanical energy harvesting is typically conducted at known speeds. However, the theoretical mapping of walking speed to the ground reaction force is often constrained by the inherent complexity of the energy conservation method commonly applied to solve the spring roller foot model in engineering applications. Consequently, an empirical analytical method has been proposed to address this challenge. This analytical method mathematically models human walking using time-varying spring stiffness. The empirical analytical method is developed based on an empirical gait division ratio of 3:1 and further refined by incorporating the leg swing effect. A comparison between the proposed method and the energy conservation method reveals that the proposed method offers several advantages, including a simple solving process, accurate and unique solutions, and predictions that are independent of prior data. Finally, the proposed empirical analytical method is validated using four distinct datasets, demonstrating its superior capability in predicting ground reaction forces during human walking at known speeds.