A new approach to modelling the ground reaction force from a runner

The impact force experienced by a runner when his/her foot makes contact with the ground has been the subject of much research. This force is called the ground reaction force (GRF), and has been measured by several groups. In parallel with this, mathematical models have been developed to simulate GRFs in order to investigate various effects on this, such as the parameters of the human body and types of running shoe soles. Lumped parameter models have been developed by several researchers with limited success, because they are either constrained to model translational motion, or become complicated if they include rotational motion. This paper proposes a new approach based on modes of vibration, which encompasses the simplicity of the lumped parameter approach, without the motion constraints. The GRF is decomposed into contributions due to the various vibration modes of the system. To achieve this, a linear system is required, so a Zener model, which is used to model viscoelastic materials, is employed as the ground reaction model. The modal modelling approach is described in detail using established lumped parameter models used to predict the GRF. It is then applied to four experimental data sets from the literature, where it is shown that at most three modes are required to model GRF data accurately. Two of these modes are oscillatory modes and one is a non-oscillatory exponentially decaying mode. In general, it is shown that the modal model can capture the dynamics of each measured GRF independently of speed and running style.