Originally Posted by
StephenH
The speed at which the front of the bike moves sideways when you steer is proportional to your speed.
Here is another angle. Suppose you are tipping over a bit. Then to avoid falling over you will want to steer in a circle so that the forcing pulling you over is the same as the centripetal force keeping you in a circle. Centripetal force is v^2/r - so the radius of the turn required will be proportional to the square of your velocity. Go twice as fast and the radius becomes four times as much. At high speed you can stay up with wide shallow arcs while at low speed you'll need sharper zig-zags.