I was bored whilst working on my thesis, and found this delightful article in the American Journal of Physics. Unicycling.org was the first reference used in the paper!
The author suggests a new metric with which to judge a rider’s skill. He has come up with the “unicycle equation of motion,” a second-order linear diff. eqn., which has terms that describe the rider’s reaction time and ability to “self-excite” and control oscillations about equilibrium.
Leave it to scientists to take something fun and make it as dry as burnt toast.
There is no real mystery about how unicyclists stay
upright—they pedal so as to keep their point of contact with
the ground under their center of gravity.
But pedaling is confined to the plane of the wheel, and so
a sideways fall has to be countered by first turning the wheel plane. This may be done by upper-body rotation, using angular momentum conservation and wheel/ground friction.
As a result, a competent rider can control the machine near
upright by continual small adjustments of the wheel plane
plus minor pedaling to and fro. This may be either static
balancing (‘‘idling’’) or a subsidiary component of steady
Looks like this is the citation: R. C. Johnson (Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, United Kingdom), “Unicycles and bifurcations,” American Journal of Physics – July 1998 – Volume 66, Issue 7, pp. 589-592
To answer Ben, this is the correct article, however, it is only available for access with a subscription. Most university libraries subscribe to online journal services; if you can’t find the journal in their stacks, ask a librarian about accessing the journal online.
That’s why I always find it so interesting when someone tries to break down unicycling from a physics/math perspective. Those equations spell out some of the forces and movements involved in unicycling, but impart no physical understanding of the process. If you want to really know what balancing a unicycle is like, you need to get on one. It’s a lot more rewarding.
When adults are learning to ride, I always make a point of reminding them not to think too much. I tell them that if they try to analyze what it’s going to take to ride from point A to B, they’re never going to get anywhere. It’s so complicated it will get your brain telling your body it’s not worth it. The only analyzing a beginning rider should be doing is noting which direction they fell off, and keep that in mind for the next attempt. That’s how the kids learn so much faster.
But even while all of this is going on, I appreciate the people who put unicycling into scientific terms. It provides them a nice, juicy, complex problem, and helps to underscore just how interesting unicycling can be.
Actually, there are lots of exceptions, and there are lots of riders that also think about the physics of unicycling, including the folks that design the equipment you ride on (assuming you’re riding on top notch equipment). For example, what allows the new KH frames to switch to aluminum, remain as strong, and get significantly lighter than their predecessors? Attention to physics. There are many other examples. It’s great that your riding is all “on instinct”, but that doesn’t mean others don’t take a different approach.
Tom (blackwood): Physicists don’t design useful things. Engineers design useful things. A physicist would never lower himself to actually design a useful object like a unicycle. They have more important things to do. Harper can confirm this.
gerblefranklin: I think Kris gets a lot of help from Norco on the engineering work for his frames and other parts. I don’t think Kris is doing the engineering analysis and design himself. Kris would be the idea man. The engineers and other technical people turn those ideas into reality.
John, I disagree, although I know you are semi-joking. I build every experimant I want, and I think I can speak for at least a few of the physicits I know when I sya I wouldn’t trust an engineer to build it for me.
I don’t think for something as simple as a unicycle frame you need to worry about actually calculating things such as fatigue analasys. The frame is simple enough that you can understand and predict the direction and magnitude of the forces involved simply by looking at it. A simple Ferramie estimate is often adaquate. This leads me to believe that Kris didn’t ask an engineer to design the frame for him. But of course there’s a simple way to resolve this. Kris, did you design the frame or did an engineer?