Theory
As with bicycles, unicycles lack stability when stationary, and under most circumstances can only remain upright when moving. Experimentation and mathematical analysis have shown that a unicycle stays upright when it is steered to keep its wheel beneath its center of mass (inverse pendulum control theory). This steering is supplied by a rider. Long-standing hypotheses and claims that gyroscopic effect is the main stabilizing force have been discredited. Unicycles are also a nonholonomic system because its outcome is path-dependent. The problem of controlling a self-balancing unicycle forms an interesting problem in control theory. (See Segway.)
In order to ride the unicycle a proficient rider subconsciously notices they are falling and corrects it (bringing the wheel under their centre of gravity) before the unicycle moves far from its unstable equilibrium. While remaining upright may be the primary goal of beginning riders, they must (in order to voluntarily turn, accelerate or decelerate) allow themselves to 'fall' in the appropriate direction, before correcting it.
The horizontal distance between the centre of gravity and the contact point (between the wheel and the floor) determines the acceleration in a particular direction. The speed and direction of the wheel's rotation (pedalling) then determines the relative position of the contact point (and thus the increase/decrease in acceleration).
If a unicyclist is (far) off balance they can't move their centre of gravity to the other side of the wheel (the base of which is the fulcrum) without pushing off a wall (or similar)—so in order not to fall over, they must turn the wheel (with their lower body) and move it (by pedalling) underneath their centre of gravity.
Voluntary movement in a particular direction involves allowing a rider's centre of gravity to 'fall' in the direction they desire to move, generally this begins by subtle arm motions or leaning. Once more proficient, a rider may twist their hips (and counter rotate their body) in order to line up the wheel with the direction, they are going to fall toward, before they begin 'falling' in that direction, and thus they can immediately begin riding in that direction despite any sudden change in velocity.
Once a rider is in motion they shift their centre of gravity forward of the wheel's contact point to accelerate, shift it behind to decelerate, and keep their centre of gravity over the contact point to maintain a constant velocity. But significantly (and counter intuitively) the most significant way to affect the acceleration acting on the rider's centre of gravity is by adjusting their pedalling speed and direction, and thus the contact point, not by leaning their body.
Read more about this topic: Unicycle
Famous quotes containing the word theory:
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—Camille Paglia (b. 1947)
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—Rheta Childe Dorr (1866–1948)