A Unicycle on a Slope
By Juan Reyero, Jaime Fernández and Utpal Sarkar. What is the maximum slope that a unicycle can climb? Trying to answer this question leads to some elegant results, and sheds some light on the dynamics of unicycle riding. Assumptions We shall assume the rotational inertia of the wheel, pedals and legs to be negligible. A further simplifying assumption is that the rider is putting all his weight into the pedal throughout its trajectory as it is going down, and that this is the only impulsion force. Which implies that the rider is not pulling up from the saddle, nor accelerating the body upwards with respect to the unicycle, nor making a horizontal force in the pedals. We know this assumption to be too stringent for expert unicyclists, who will typically be able to do all these things, but we hold it to be a reasonable approximation to what a unicyclist of normal skill would do when pressed to climb a slope at the limit of the unicycle’s possiblities. ...