How do you turn corners?

[gauss]

I stayed out of this a while, but now i'll come in. I thought Klaas was going to hit what I was thinking as he set it up the same way. That is, how will a unicycle spontaneously turn when no in plane torque is applied?
I think you can get this by looking at the wheel's contact patch versus your center of mass. Think of a unicycle riding straight down the road with the rider centered up on it. If he leans over without turning he falls. I attached an image that shows why. The left half shows this situation when viewed from behind. The red block is your center of mass. the black block is the tire. when riding straight there is your force down and because of newton's third law the road pushes up on the tire with the same force and there is a balance. Immediately to the right of that there is a leaning unicycle. Here the center of mass has moved away from the contact patch. the forces are still equal but now there is what is called a "moment". A moment is when two equal and opposite forces are applied but there is a distance between them. I included what this disatnce is in this case, but that isn't important. A moment is torque and makes things twist, and is the force times the disance between them (think of torque in your car. That is why the units are ft lbs it is the force times the distance). Anyway, so the second two pictures are viewed from above. The top one is again a lean. there is a force pulling out and since the contact patch is below, there is a torque tipping the unicycle. Now, in the lower picture, the unicyclist shifts his weight foward. There is still the force pulling in, but now he is ahead of the contact patch. So there is a distance between the reaction force and there is a resulting torque making the uni twist. It is a little more complicated than this, but that is pretty much it. If anyone wants to fight about it, let me know, I'll give you my email. I'll not be responsible for another "wheel puzzle" thread of doom.
-gauss