The influence of pedalling on the lateral dynamics of cycling

Abstract

There are still important knowledge gaps regarding stability and safety of bicycle riding. Every year around 60,000 people need hospital treatment for single sided accidents in the Netherlands alone. Supporting the need for understanding lateral bicycle dynamics. One of the prominent disturbances on lateral bicycle and rider behaviour is pedalling. However, although there is a good understanding of the determinants effecting the forward or propulsive behaviour of the bicycle associated with pedalling, the effect on the lateral bicycle and rider behaviour is still poorly understood. This study focusses on determining what the effect of pedalling is on the lateral behaviour of the bicycle-rider system. This determination is three fold. First the nature of the pedalling disturbance and parameters influencing it is ascertained. This is used to develop a pedalling disturbance model which can be easily applied to any dynamical bicycle-rider model, by applying harmonic external torques on the steering and roll of the bicycle. Secondly the direct response of this pedalling disturbance of the bicycle-rider system is ascertained for a variety of models and cycling conditions. This is achieved by applying the pedalling disturbance to multiple bicycle-rider models for multiple cycling conditions. Methods, with various model complexity and solution approaches, are evaluated. Based on this evaluation we propose a simple and effective method of analytically obtaining a periodic solution based on a linearised time-invariant bicycle-rider system. This periodic solution represents the open loop lateral bicycle response corresponding to the periodic pedalling disturbance. Thirdly the overall effect of pedalling, the closed loop response, is ascertained using experimental data. Specific cycling conditions are chosen to validate the open loop response of the model, since these cycling conditions should be only minimally effected by control. The experimental data corresponding to other cycling conditions are explored for parameter dependence and influence of control and upper body motions. The nature of the pedalling disturbance is now understood. The pedalling disturbance is determined by vertical and the forward acceleration of the left and right leg centre of mass, the leg mass, the hip width and the cadence. This motion of mass promotes roll and yaw disturbances, where the yaw disturbance can be translated to a steering disturbance by bicycle parameters defining yaw-steering coupling. The direct lateral response and the overall lateral bicycle-rider behaviour due to pedalling are explored. This uncovered parameter dependencies of the bicycle-rider system, differences due to rider upper body movements, rider control and cycling conditions such as forward speed and cadence. We developed and validated a simple method of ascertaining the direct effect of a pedalling disturbance on the lateral behaviour of a bicycle-rider system. This is done by applying harmonic steering and roll toques to an easily obtained time-invariant linearised bicycle model. Some bicycle-rider combinations exhibit resonance behaviour due to pedalling within the normal cycling range, this model could be used to slightly change bicycle design parameters such that this dangerous behaviour is avoided.