The way I see it, a bicycle in motion is always falling. Stability is the ability to recover from the fall, which we do by steering towards the fall to get the wheels under the center of gravity; maneuverability is the ability to increase the fall, by steering away from it, so that we can take a path where the forces of gravity and centripetal acceleration combine at an angle. These actions can in principle be taken effectively with a center of gravity at any height, but as that gets lower we run into human limitations in perception, response time and reaction precision.
That's how I understand bicycling to work at most speeds - but I will say that as I ride down a long hill on one of my wonderful recumbent bicycles, I don't really perceive that process, and rather it seems like there are gyroscopic and whatever other forces in play that might make center of gravity height less significant, or even possibly change the ideal height.
That's how I understand bicycling to work at most speeds - but I will say that as I ride down a long hill on one of my wonderful recumbent bicycles, I don't really perceive that process, and rather it seems like there are gyroscopic and whatever other forces in play that might make center of gravity height less significant, or even possibly change the ideal height.