A Model for Determining Rider Induced Energy Losses in Bicycle Suspension Systems

The energy dissipated by the suspension systems used for off-road bicycles is a major concern due to the limited power source in cycling. Rider induced energy losses are those that arise from the muscular action of the rider. The purpose of this study was to develop and verify a dynamic model of a seated cyclist riding an off-road bicycle up a smooth road. With the absence of terrain irregularities, all suspension motion was rider induced. Knowing the stiffness and dissipative characteristics of the suspension elements, the power dissipated by the suspensions was calculated.

Simulation results were compared to suspension deflections that were experimentally measured for a cyclist riding a commercially available dual suspension bicycle up a 6% grade at 6.5m/s. For this particular case, no fork motion was observed in the experiments which was consistent with the simulation results. For the rear suspension, the mean and amplitude of the largest harmonic were experimentally determined to be 6.6 and ±2.7 mm respectively. Simulation results were within 0.7mm of the mean and within 0.3mm of the amplitude. The only major discrepancy between the experiments and the simulations was the presence of a phase lag in the simulation results which was attributed to inter-subject variability. The power dissipated by the rear suspension was calculated to be 6.9 Watts or 1.3% of the total power input by the rider. Given the grade and forward velocity, this translated into an equivalent mass of 1.8 kg. Thus, the bicycle appeared to be roughly 12% heavier than it actually was.     

Minimization of Pedaling Induced Energy Losses in Off-road Bicycle Rear Suspension Systems

This paper presents the results of an optimization analysis performed on off-road bicycles in which the energy loss induced as a result of pedaling action was minimized. A previously developed computer-based dynamic system model (Wang and Hull, Vehicle System Dynamics, 25:3, 1996) was used to evaluate the power dissipated by a single pivot point rear suspension while pedalling uphill on a smooth surface. By systematically varying the location of the pivot point, the relationship between power dissipated and pivot location was determined. The optimal location was defined as the location which resulted in the least power dissipated. The simulation results show that the power dissipated was very dependent on the height above the bottom bracket but not the fore-aft location of the pivot point. If the pivot point is constrained to the seat tube, then the optimal pivot point was found to be 11 cm above the bottom bracket. Compared to a commercially available design, the optimal pivot point reduced the power dissipated from 6.9 to 1.2 Watts. Furthermore, the optimal pivot point was found to be very insensitive to pedaling mechanics, and both the spring and damping parameter values. The optimal pivot point did, however, have a linear dependence on the height of the chainline; as the chainline height increased so too did the optimal pivot point height.