One (and perhaps the most important) force vector applies at the contact point of the tire and the road. There are several force vectors in a problem involving a unicycle and rider but this is the one to which I think you are referring.
A line drawn from the center of mass of the entire system to the center of the earth, while moving forward at a constant velocity, intersects a point in the road that lies in front of the contact point of the tire and the road. This is the point to which I think you are referring.
Energy needed to stay in balance? You need energy to correct your balance. Imagine a small tree in a tub - it stands there, requiring no energy to stay in balance. It wobbles a little bit, and takes only a small amount of energy to re-stabilise it. It wobbles a lot and starts to fall, and it takes a lot of energy to stand it up again.
The perfect unicyclist expends very little energy staying in balance because (s)he is always balanced. Beginners wear themselves out trying to stay balanced.
On a longish ride this evening, I found myself forgetting I was riding, and contemplating all sorts of irrelevancies. I can now ride on auto pilot almost indefinitely. When I took up riding, one of the things that attracted me to it was the 100% focus it required - at a time when I needed a diversion from problems in my life.
> A line drawn from the center of mass of the entire system to the center
> of the earth, while moving forward at a constant velocity, intersects a
> point in the road that lies in front of the contact point of the tire
> and the road.
Such a force constitutes to a torque acceletaring the wheel in
the forward direction. If the rider opposes such a torque (by
opposing the natural motion of the pedals), then the rider will move
forward relative to the wheel.
Unless there is another external force (wind?) acting on the system,
the unicycle is not in balance when the center of mass is not directly
above the contact patch.
Re: Re: Investigating The Energy Needed to Stay in Balance
Yes, you are correct. I would at least have to change “velocity” to “acceleration” to make my statement correct. To get the point across and not be incorrect, I would have to word it entirely differently. Who wants to move a unicycle forward with constant acceleration? Away we go, faster and faster.