The simplest model possible for bouncing systems consists of a point mass bouncing passively on a mass-less spring without viscous losses. This type of spring–mass model has been used to describe the stance period of symmetric running gaits. In this study, we investigated the interaction between horse and rider at trot using three models of force-driven spring (–damper)–mass systems. The first system consisted of a spring and a mass representing the horse that interact with another spring and mass representing the rider. In the second spring–damper–mass model, dampers, a free-fall and a forcing function for the rider were incorporated. In the third spring–damper–mass model, an active spring system for the leg of the rider was introduced with a variable spring stiffness and resting length in addition to a saddle spring with fixed material properties. The output of the models was compared with experimental data of sitting and rising trot and with the modern riding technique used by jockeys in racing. The models show which combinations of rider mass, spring stiffness and damping coefficient will result in a particular riding technique or other behaviours. Minimization of the peak force of the rider and the work of the horse resulted in an ‘extreme’ modern jockey technique. The incorporation of an active spring system for the leg of the rider was needed to simulate rising trot. Thus, the models provide insight into the biomechanical requirements a rider has to comply with to respond effectively to the movements of a horse.
All authors were involved in the conception, design and execution of the study, the interpretation of the findings, and the drafting and revising of the article. P.d.C. and H.M.C. executed the experimental work, P.d.C. and M.M. constructed the simple model and P.d.C. and J.L.v.L constructed the extended models.
Supplementary material available online at http://jeb.biologists.org/cgi/content/full/216/10/1850/DC1
No competing interests declared.
This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.
LIST OF SYMBOLS AND ABBREVIATIONS
- damping coefficient
- frequency of a bounce
- amplitude of the forcing function
- magnitude of the gravitational acceleration
- horse (subscript)
- spring stiffness
- active spring system of the leg of the rider (subscript)
- rider (subscript)
- saddle spring of the rider (subscript)
- z, ,
- vertical displacement, velocity and acceleration
- phase difference of the forcing function
- static deflection due to the weight of the mass acting on the spring
- force contact factor
- angular frequency of the forcing function
- © 2013. Published by The Company of Biologists Ltd