Three-Dimensional Bobsled Turning Dynamics

Abstract

We have developed a mathematical model and computer simulation of three-dimensional bobsled turning. It is based on accurate descriptions of existing or hypothetical tracks and on dynamic equations of motion including gravitational, normal, lift, drag, ice friction, and steering forces. The three-dimensional track surface model uses cubic spline geometric modeling and approximation techniques. The position of the sled on the track is specified by the two variables α and β in the along-track and cross-track directions, differential equations for which govern the possible motions of the sled. The model can be used for studies involving (a) track design, (b) calculation of optimal driver control strategies, and (c) as the basis for a real-time bobsled simulator. It can provide detailed quantitative information (e.g., splits for individual turns) that is not available in runs at actual tracks. The model also allows for comparison of driver performance with the numerically computed optimum performance, and for safe experimentation with risky driving strategies.