Testing of Rigid Two- and Three-Wheeled Vehicle Pitch-Over Threshold Models

The phenomenon of bicycle pitch-over is simple in concept, yet determining threshold criteria for pitch-over has yet to be well established, particularly with respect to determining whether or not a bicycle’s front wheel will roll over a particular obstacle or not. Two prior SAE papers have laid out two different analytical approaches to predict this threshold – the Moment-Inversion and Brach Pitch-Over Threshold models - and this paper proposes a modification to the Moment-Inversion model to account for tire deflection. Testing began by measuring the center of gravity locations and moments of inertia for a bicycle with weights and training wheels and for a test rider on a bicycle and tricycle. These physical measurements were used to calculate the predicted pitch-over height for each system for each model. The test systems were then ridden over a series of progressively taller square edge obstacles until they transitioned from rolling over to stopping or pitching over. From this testing, it was demonstrated that the sole bicycle with training wheels stopped rolling over the square edge within one centimeter of the threshold predicted by the original Moment-Inversion model, which was below the height predicted by the other two. However, the rider on the bicycle and tricycle was able to ride repeatedly over obstacles taller than the height calculated by any of the analytical methods. The Brach Maximum Pitch-Over Threshold model (which assumes no upwards impulse from ground contact at the front wheel) consistently predicted the highest pitch-over height, and thus was closest to predicting the critical height for the bicycle and rider system; however, this testing has demonstrated how the dynamics of a bicycle-rider system differ from that of a fully rigid system and that more advanced models or simulations will be required to more accurately predict pitch-over thresholds.