A simple analytical model for predicting locomotive ground reaction forces

Equine models are useful in biomechanics research of locomotion due to their similarity in musculoskeletal tissue to humans, their athletic nature, and rapid skeletal development which permits ontogenetic studies. However, a continuing challenge in musculoskeletal models for large animal biomechanics is measuring the ground reaction force (GRF) during locomotion. This gap has resulted in a lack of reporting of gait measures such as joint torques. Here we propose an analytical method for predicting ground reaction forces in foals (growing horses) based on the Froude number. Motion capture, GRF, and subject mass data during walking and trotting gaits were collected longitudinally. To account for differences in subject size, we calculated the dimensionless Froude number (Fr=v2/(g*l)). The walk-trot transition speed occurred near Fr=0.5, v=1.75-2.15 m/s and was consistent for all evaluated ages. Of the analytical regression models tested, linear regression models had the best performance for predicting vertical GRF data in foals with an average absolute error percent of 7.97% during trotting and 2.39% during walking, compared to a non-linear logistic model with an error of 8.38%. The model was converted to Python and implemented to predict GRF data for foals using the subject velocity and limb length as input. Our resulting analytical model can be used to estimate the GRF profile of equine gait enabling comparative studies of locomotion.