Physics of unicycling video

What do you make of this explanation (uni riding starts at 3:40)

I think the first part seems wrong about always pedaling back to get started moving forward, but the rest of the explanation seems semi-reasonable.

He’s just stopping and starting and of course you will automatically lean forward in that case. But you can start from a stand-still by just leaning forward, no need to ‘pedal back’ (whatever that means).


He doesn’t mean necessarily to pedal backwards but rather to apply pressure to the back pedal. You won’t truly appreciate this until you try to freewheel unicycle. But it would have been good to add one of those in that video for comparison since you either accelerate forwards, balance with body movement only, or brake(if you’re me the braking phase is just an instant upd but maybe one day I’ll figure it out).

I assume that by a stand still you mean being stationary with your centre of gravity exactly above the tyre contact patch. This is a so-called unstable equilibrium, but according to classical mechanics theory this situation can last forever. Now how do you go from there to a forward lean? I guess through a little bit of ‘pedal back’. This type of thing (moving the bottom end to one side to initiate a lean to the other side) is exactly the point of this video. So IMHO the need for ‘pedal back’ is correct.

Hey riders? Who gives a crap about unicycle physics? We do, right?
Well, I just watched this video.
My comments:

  1. The video presenter cannot communicate effectively. He say “…pedal back to go forwards…” WTF, is that? What, what…whattttttt? Bad explanation. Here’s what he should say. Let’s translate.

2.) Pedal back = driving one pedal down creates an action = rider “tilts back or whiplashes”

3.) An additional force needs to be applied to prevent falling on your back, either:
a.) A constant lean forwards.
b.) A momentary forward rock synchronized to each pedaling action

This should have been mentioned.

Oh there’s actually a lot more. Save it for another topic.
Especially about steering and lateral balance, which is “pedal clock drive direction and timing” controlled, as well as weight distribution from pedal to seat.

Not super complicated, but I hate how scientists need to “minimize” everything to a 2 dimensional sketch and a 5 minute lecture about CG and contact patch…slam

Oh, oh…, I’m one of those nerds interested in unicycle physics :wink:

I’ve read quite a few papers on the subject. A nice quote from a very old (1989) MIT thesis by David W Voss is:

“Physically, in order for the unicyclist to change forward velocity, the wheel speed is slowed in order to generate a pitch error and then in recovery of this error, the new forward (increased) velocity is set. Similar reasoning is valid for the lateral motion - a heading change to the left is achieved by initially incurring a roll error by turning to the right, before recovering on the desired heading.”

[btw, I agree that the simple “pedal backwards to go forwards” sounds pretty silly].

I have a personal project on the back burner to develop a scripted SVG showing a schematic of a unicycle rider with animated pedal force graph as they maintain balance while moving forward at an approximately constant speed with minor bumps in the road (2D only, tire friction taken into account, but no body twisting, camber or gyro forces included).

In researching for this, I found a rather useful and concise paper, in case anyone is interested, for the maths:

[“The development of self-balancing controller for one-wheeled vehicles” by CN Huang in 2010 - pitch control only!]

The interesting/convincing thing is that several people have built controllers based on the theory, and they actually work.