Dynamic optimization analysis for equipment setup problems in endurance cycling

The goals of the work reported by this article are two-fold. The first is to develop a dynamic optimization framework for analysis of equipment setup problems in endurance cycling. The second is to illustrate the application of the approach by determining an optimal chainring shape. To achieve these goals, a mathematical model of the pedaling motion for given trajectories of the net joint moments and the rate of change of the chainring radius was derived, and chainring optimization was posed as an optimal control problem. The cost functional produced a chainring shape that reduced the cost of endurance cycling at 250 W and 90 rpm, apparently by taking advantage of mechanical interactions that arise as a natural consequence of the movement. However, the predicted joint moments required larger peak values during phases of significantly increased joint velocity. Thus, the ‘optimal’ performance predicted by the cost functional appears opposed to expectations based on muscle mechanics and illustrates the need for further analysis of endurance cycling with a physiologically based cost functional.