Wobble of a racing bicycle with a rider hands on and hands off the handlebar

Abstract

So far fundamental papers on the understanding of the wobble mode at motorcycles have been published, but in contrast, little research has been published on the wobble mode at bicycles. Wobble denotes a characteristic unstable oscillatory mode dominated by oscillations of the front wheel about the steering axis. The wobble mode of a trekking bicycle at low speeds has already been analysed, where no influence of the rider's hands on the steering system is taken into account. The wobble mode of a racing bicycle at higher speeds has not been addressed in more detail so far. The paper points out the difference between a trekking bicycle and a racing bicycle in particular with respect to the wobble mode. Different geometry, mass and stiffness properties of both types of bicycles and different characteristic positions of the rider are considered. As the wobble at racing bicycles often occurs at high speeds, when riding down a grade with hands on a dropped handlebar, a passive rider model, that takes into account the movement of the rider's arms, is presented.

The effect of tyre and rider properties on the stability of a bicycle

“…Notable is that he did not incorporate the twisting torque into the tyre model. In return, Plo¨chl et al 10 and Klinger et al 13 did include the twisting torque and found a significant effect of their tyre model on the capsize and weave mode. In agreement with the results presented in this article, they found that the capsize mode becomes stable and the weave mode significantly destabilizes by implementing the realistic tyre model.…”

“…6,12 However, modelling the rider's arms on the steer does drastically change the dynamic properties. 12,13 In Doria and Tognazzo, 12 it was reported that a small amount (25.7 N m/rad) of passive arm stiffness is able to destroy the stability by making the steer-roll combination ineffective. However, in Doria and Tognazzo, 12 tyre dynamics were not considered and this significantly changes the influence of the rider's impedance on the handlebars.…”

“…This might be caused by the twisting torque that generates a yaw torque in the direction of the fall. In Klinger et al, 13 the tyre dynamics were considered, but a very small value of passive arm stiffness (3.2 N m/rad) was used in their basic hands-on model, and therefore they did not find an unstable capsize mode.…”

“…The Magic Formula tyre model (case 6) destabilizes the weave mode (weave speed increases to 9.3 m/s), but stabilizes the capsize mode. It is worth highlighting that in Klinger et al, 13 which considers a linear model of tyre forces and torques, weave speed is about 9.5 m/s and capsize mode is always stable. When the full model is used (which includes the new tyre model, passive rider and arms), the capsize mode is always stable and weave speed increases a bit more with respect to case 6.…”

“…Recently, Doria and Tognazzo 12 experimentally determined the passive properties of the rider's body and integrated the derived models in the benchmark model. Klinger et al 13 combined a realistic tyre model with a passive rider model and studied the effect of different postures of the rider on the wobble mode, in the case of a racing bicycle.…”