Maximal muscle power output in cycling: A modelling approach

This study sought to find the optimal design parameters for a bicycle-rider system (crank length, pelvic inclination, seat height and rate of crank rotation) that maximise the power output from muscles of the human lower limb during cycling. The human lower limb was modelled as a planar system of five rigid bodies connected by four frictionless pin joints and driven by seven functional muscle groups. The muscles were assumed to behave according to an adapted form of Hill's (1938) equation, incorporating the muscle force-length relation. The force-length relation and the values of length that served as input into the relations of the various muscles were defined in the following two ways: (1) the force-length relation was parabolic, based on the experiment of Woittiez et al. (1984), and the length was defined as the whole muscle length; and (2) the force-length relation was expressed as a combination of lines, based on the cross-bridge theory, and the length was defined as muscle fibre length. In the second definition, the joint configurations at which four of the seven muscle groups reached optimal length (i.e. the length at which the muscle can exert maximal isometric force) were further given in two ways. The first way was consistent with a previous study from this laboratory (Yoshihuku and Herzog, 1990); the second way relied on unpublished experimental data. The dependence of the average power on the design parameters and definitions of the force-length relation and muscle length was examined. Maximal average power for one full crank rotation with a crank length of 0.17 m was found to be about 1300 W for definition 1 and 1000 W for definition 2. The average power was more sensitive to changes in design parameters in definition 2 than definition 1. The optimal rate of crank rotation with a crank length of 0.17 m was 18.4 rad s(-1) (176 rev min(-1)) for definition 1 (this value is different from the result of the previous study due to revisions in input for two muscle groups), and 15.2 rad s(-1) (145 rev min(-1)) and 14.6 rad s(-1) (139 rev min(-1)) for definition 2.