DETERMINING THE GROUND REACTION FORCE EXPERIENCED IN BEACH RUNNING

INTRODUCTION: Running on a beach is a popular fitness activity, as well as a critical component in the professional sport of ironman. In this event, ironmen athletes run over terrain ranging from wet compacted sand to dry uncompacted sand, as their distance from the ocean surf line increases. The dynamic loading response of sand surfaces at the extremes of this range has been investigated recently by Barrett et al. using a force plate, and variables such as the peak impact force and the surface stiffness were calculated. In this study we demonstrate how the time response of the ground reaction force (GRF) experienced in beach running can be predicted from the measured plate reaction force, for either wet or dry sand surfaces. METHODS: The ground reaction force experienced in beach running can be measured directly using an accelerometer attached to the runner’s lower extremity. However it is often more convenient to sample the reaction force from a sandcovered force plate in a controlled environment. This idea motivated us to consider the resulting problem of determining the GRF indirectly using the measured plate force. In the measurement process, the instrument response of the force plate, which can be described in the linear regime by a transfer function, is convoluted with the GRF in the time domain. Thus in order to reconstruct the GRF we need to apply the reverse process: a deconvolution of the measured plate force using a known transfer function. The deconvolution is performed in the frequency domain. The transfer function corresponding to the force plate has to be determined a priori by „calibrating“ direct GRF measurements with plate force measurements. RESULTS: The reconstruction of the GRF allows us to estimate any physical quantity we are interested in, such as the time of delay between the moment of impact and the trigger of the plate force reaction, or the peak GRF. We have also determined that the frequency characteristics of the force plate transfer function depend on the impact mass, the impact energy and the effective depth of the sand, and have investigated the changes apparent in this parameter space. CONCLUSIONS: The transfer function approach presented in this study reconstructs the time response of the GRF experienced in beach running conditions, using plate force measurements. Thus, with the exception of calibration measurements, we can eliminate the need to attach an accelerometer to the runner when taking GRF measurements. REFERENCES: Barrett, R.S., Neal, R.J., Roberts, L.J. (1998). The Dynamic Loading Response of Surfaces Encountered in Beach Running. Journal of Science and Medicine in Sport 1, 3-13, 1998

Quantum risk-sensitive control

The purpose of this paper is to describe some recent results concerning optimal feedback control of quantum systems using risk-sensitive performance criteria. We employ quantum stochastic models to describe an important class of quantum systems and define a risk-sensitive criterion for these models. A suitable information state is introduced to solve the optimal control problem using dynamic programming. The results are illustrated by examples