Back in April, 1970, I came across an article in Physics Today, the journal of the American Institute of Physics, on bicycle stability by an amateur home experimenter. My Xeroxed copy had disappeared, but to my surprise, I was able to track it down with a Google search. Google usually does not go back that far, but the article had a cult following and Physics Today republished it in September, 2006.
The author, David E. H. Jones, a young Englishman with a Ph.D. in chemistry, had a long, gently sloping driveway and an old bicycle he didn’t mind destroying. He found that the bicycle would remain upright when coasting down the entire driveway without anyone on it. Not only that, if he had someone give it a sideways punch partway down, it wobbled a bit, but it quickly righted itself and coasted smoothly to the bottom as if nothing had happened.
What could account for this incredible stability? If he could find the reason, he thought, he could then build a bicycle without this stability to see if it could be ridden by just the skill of the rider.
The stability obviously had something to do with the front wheel because the bike would immediately crash if it started down the driveway facing backwards. Also, the bike had to be moving to be stable. As we all know, a non-moving bike will fall right over.
People often believe the thickness of the tires is a factor. Years ago, I, myself, was a little cautious in going from my old balloon-tired bike to an English bike with the narrow tires, but anyone with a little experience knows they are equally easy to ride.
The most common and reasonable belief is that the large, revolving wheel has a gyroscopic action that stabilizes the bike. A rolling hoop is known to stay upright by this principle, and a bicycle could be thought of as a hoop with a trailer. This would also explain why the bike has to be moving to be stable. The author first tested this by using a furniture caster as a front wheel which would have negligible gyroscopic force. The experiment was inconclusive, however, because the caster quickly overheated and stopped working. Besides, even the smallest bump in the driveway upset the bike.
Jones abandoned this approach and instead mounted a duplicate wheel beside the front wheel, but an inch or two higher so it did not touch the ground. Then, when he released the bike on the driveway, he spun the duplicate wheel in the opposite direction so any gyroscopic forces would cancel out. The bicycle did fall over, as did a similar arrangement with a hoop. When he tried to ride the bike, however, it felt almost normal. He concluded gyroscopic action was a factor in bicycle stability, but not the whole story.
He then presented the main reason for a bicycle’s stability, which I suspect he knew all along. If, when you are sitting on a bike, you lean forward and sight down the axis of the handlebar stem, you will see the projected line intersects the street an inch or two in front of the point where the tire touches the street. This slight difference is the key. When a bicycle leans to one side or the other, this difference twists the wheel in the direction into the lean so it automatically steers itself back into a fully upright position. You can see this for yourself by holding a bike steady and tilting it one way or another. The front wheel will turn by itself into the lean. I have used this principle myself many times when walking my bike up a hill. I hold it by the saddle and steer it by tilting it right or left to turn the wheel.
The front forks of most bicycles curve forward to bring the two points closer together. Too far apart and the bicycle will be overly stable. Jones found this to be true by mounting the fork backwards so the curve increased the distance between the points. It was very stable coasting by itself on the driveway, but very difficult to control when he rode it and tried to steer in different directions. Too much stability is undesirable. Any successful bicycle has to be a compromise between stability and nimbleness .
He then wrote a FORTRAN program where he could test various geometries without risking life and limb. (FORTRAN was an early programming language for constructing mathematical models and is still used for these applications.)
His final unridable bicycle had extensions on the fork that moved the point where the tire touches the street forward of the projected steering axis, well into the region where the lean twisted the wheel in the opposite direction for stability. However, it proved to be a bit disappointing as an unridable bicycle. He says, “It was indeed very dodgy to ride, although not as impossible as I had hoped—perhaps my skill had increased in the course of this study.”
You can see the full article at http://www.phys.lsu.edu/faculty/gonzalez/Teaching/Phys7221/vol59no9p51_56.pdf, or simply Google “Jones bicycle stability.”
The article has diagrams and photos of Jones on his bicycle, who looks exactly as you would expect. English to the core.