Point mass impulse-momentum model of the equine rotational fall

Rotational falls are a serious cause of injury and death to horse and rider, particularly in the cross-country phase of eventing. The forces involved when horses galloping cross-country strike an immovable fence are unknown. The objective of this study was to mathematically model those forces using existing kinematic data measured from jumping horses. Data were obtained from published research using motion capture to measure mechanics about the center of gravity of the jumping horse at take-off. A convenience method from video evidence of rotational falls was used to estimate time of collision (δt). A point mass model using equations of impulse-momentum and incorporating key variables was systematically implemented in Matlab (r2016a). The mean collision time (δt=0.79s) produced horizontal, vertical, and resultant impact forces of 8,580, 8,245, and 12,158 N, respectively. Reference curves of impact forces were created for ranges of relevant input variables including collision time. Proportional relationships showed that shorter impact duration led to higher magnitude of force transfer between horse and obstacle. This study presents a preliminary range of collision forces based on a simplified model and numerous assumptions related to input variables. Future research should work to build upon these estimates through more complex modelling and data collection to enhance applicability for the design of cross-country safety devices.