Unicycle Turn Theory

Anybody know of some good articles on how unicycles turn? Even without Gyroscopic Precession, Body Twist, and Tire Coning, I still think it is possible to turn. Once leaned over, if you merely increase your pedaling torque, the uni should turn into the lean.

Have any of you noticed yourself using this technique as a turning aid? What about when entering spins?

Chris Reeder
the Ex-Unicyclist

Re: Unicycle Turn Theory

With the Primo The Wall tire, the tire is almost torical, so there is no coning. Assuming you have a lean, simply pedaling at the proper speed will put you “in orbit” horizontally about a point. The vector forces balance out just like the Space Shuttle in orbit. The size of the orbit depends only on your speed and degree of lean. Getting into the lean simply requires a temporary hip twist which allows the wheel to track away from the body’s direction. Ditto for getting “out of orbit”.

So Chris, does this mean you’re back?

Re: Re: Unicycle Turn Theory

You make it sound like it’s impossible to fall. Yet I do! I think I grasp your model of it though. One thing I wonder is, when I need to turn into the lean, do I just need to pedal faster (and allow the wheel to pass me up, as it were), or do I need to lean forward first, then pedal faster so I accelerate with the wheel. Maybe it depends on the rest of the situation…

I do believe that even toric tires cone, because there is a finite width contact patch, one side of the contact patch having a larger radius (from the unicycle’s axle) than the other side of the contact patch. I expect coning in a torical tire to decrease as inflation pressure increases. Not to say that coning is therefore the dominant (or even significant) factor in a turn, just saying that coning is present.

Alas, no. I am trying to understand how to keep my motorcycle under me.:smiley: I do this weaving back and forth thing, which usually ends up in me nearly running off the road, so I have to set her back down. It seems less weavy at 15mph than it does at 10, yet 10 is still the goal eventually. Conditions are: some loose pebbles on top of hard dirt, rounded slick rear tire, some wind from the side, '81 XR200R.

Unibiker, where are you?

Chris Reeder
the Ex-Unicyclist

Having a motorcycle makes the situation more difficult because in the intiation into the turn you have to also get the entire motorcycle rotating like the moon; so that when you have done one orbit, the motorcycle has also done one rotation. This is also true of unicycle but the mass is much less and much closer to the center of the uni.


While upright, yes, our mass is close to the center of rotation. Just like a pencil that you stand on end and spin. But the further we lean over “into orbit”, the more we become like a pencil on its side, requiring much more torque to initiate the spin about a vertical axis.

So the uni and the motorcycle may still be in the same ballpark, at least for medium to steep banks.

Now for the real question: Have you been able to pull out of orbit merely by adjusting pedaling torque (and speed)? As in no hip adjustments. Motorcycles don’t have much in terms of hips.

I personally haven’t thought of it while riding a unicycle. Theoretically increasing your speed only would only increase the size of your orbit. I suppose for the motorcycle you’re going to have to use your hips and arms and wrestle a little.

Re: Unicycle Turn Theory

cjreeder <cjreeder@NoEmail.Message.Poster.at.Unicyclist.com> writes:

> Now for the real question: Have you been able to pull out of orbit
> merely by adjusting pedaling torque (and speed)? As in no hip
> adjustments. Motorcycles don’t have much in terms of hips.

Your question implies that “adjusting pedaling torque” is a simple
process. I think there’s a lot going on when you pedal in a turn.
Obviously, there is an average torque that is applied to the wheel
which determines your speed, but to really understand a turn, I think
you have to look at how the torque is applied throughout the pedaling

First consider this question: What do unicycle tracks look like?
Specifically, what does the track left behind a low friction
(i.e. high pressure tire on hard surface) unicycle pedalled straight
look like? The answer is a sine wave (or close enough) - the wheel
oscillates from side to side as we ride. At least that’s the answer
at my level of ability. (Clearly riders can control the amount of
oscillation, and maybe even overcome it with effort, but the unicycle
naturall oscillates.)

Maybe you see where I’m going with this. Pedalling naturally turns a
unicycle wheel, though the turns cancel out each revolution when going
straight. Maybe we turn largely by pedalling asymmetrically (assuming
necessary leaning takes place, of course). If you experiment with
your unicycle, you will quickly see that pedal pressure at the right
crank angles will cause the unicycle to pivot.

So. I think you can succeed in turning by adjusting pedalling torque,
but not simply by increasing the power of a straight ahead cadence.
You need to push harder on the inside leg to turn.

I’m not very good at turning - I’ve done a tight 360 turn only a
handful of time and only then because I’ve over shot an attempted 180.
I’d love to hear from more accomplished riders to learn whether
tighter or more elegant turns use different techniques.


Re: Re: Re: Unicycle Turn Theory

Hello Chris, and uni world,

I’m still around, barely. I’ve been working way too much and trying to recuperate from the back injury I sustained at work shortly after being relocated to Louisiana. After a year of therapy and limping, it looks like I’m headed for back surgery.

Anyway Chris, the problem with the weaving on the motorcycle is a common one. You probably don’t notice it much while under power. But when you get near the balance point to maintain a constant speed, things get wobbly. The balance is a little more critical at this point, but the larger problem is that you can’t see through the handlebars as you fall backward. This causes you to look to one side, which causes the motorcycle to fall that way, which causes you to lean the other way to correct. Except you have to lean too far in order to be able to see around the other side; hence, the perpetual weaving. The correction is similar to that which is needed to fight a cross-wind on a bicycle. It’s a combination of body lean, frame lean (side-to-side pressure on the bars), and handlebar turning. The correct combination will keep you going straight, while allowing you to lean to one side enough to see where you’re going.

As I previously mentioned with regards to the bicycle, the steering is easier behind the balance point if your comfortable with coasting. When the weaving gets out of control, you can throw it over the balance point and it will straighten out and become much more steer-able. Until you get more comfortable with controlling the weaving at the balance point, you might try to stay either in front of it - under power, or behind it - on the brakes. Either situation will be more stable and steer-able than being right at the balance point.

One more point. Loose pebbles on dirt is not ideal for learning. When you depend on the brakes to keep 400 pounds of bike and rider from falling over backwards, you need to consider the traction! I have used my hide for traction more than once. It doesn’t work too well.

Extra, Extra - I’ve owned the older XR’s. The brake drums do not hold up well. Shortly after replacing the first set of brake shoes, you will probably find that the brakes begin locking up do to the cam turning sideways between the shoes, caused by the larger diameter of the worn out drum. Replacing the drum or the wheel, is not only time consuming (if you can find the part), but will leave you with the same design problem and repeat repairs in the future. For wheelying, you should consider looking for a bike with a rear disc, or a non-Honda drum.

Good luck, have fun, and be safe!


I’ve decided I’ve had enough of the loose pebbles (and with summer coming,the roads just keep getting drier and pebblier). So I’ve done some wheelies on the street, but the XR200 isn’t much of a street machine if you want to go for group rides. So it’s for sale in hopes of getting a proper stunt bike. (Must go at least 85mph, must wheelie, should stoppie, must be cheap enough I can drop it a couple times.)

Anyway, thanks for the input. I won’t get to put it to use till I get something else to ride, but hopefully it will make the difference.


I asked a question like this a while back and created a web page with links to some of the related information:

Unicycle maths, physics & robots, a collection of references:



I read an article in Motorcycle Consumer News this weekend and thought of you. One of the editors went to a one day “wheelie school” and was favorably impressed.

Here’s the school’s website:

They use Triumph’s Speed Triple for a trainer bike because of it’s exceptional midrange power. Consequently they can have their students bring the front end up without using the clutch.

The bike is equipped with a wheelie bar that kills the spark in one cylinder and/or applies the rear brake if the front end gets too high.

more wheelie stuff!

Chris and others,

This impressed me a lot and might be of interest to a few of you out there.

Found here:

Don’t miss the fender bender!

Chris, sorry I don’t have anything really to add on getting more stable at slow speeds on the motorbike, but it’s great to hear from you nonetheless. Beaming you thoughts of killer balance all the way from California…


PS The guy in the wheelie cliip from George sure looked comfortable doing that - just ride like him!

Holy gear reduction!

It’s hard to see, but look at the size of his rear sprocket! Yikes!

Hi All,

I thought I’d bring this thread to the forefront again because it seems that there have been quite a few questions about turning lately!
Good info!