A bicycle is a good example of something that is commonplace and yet quite extraordinary. It seems such an unlikely mode of transportation. One has to wonder how someone came up with the bizarre idea that by sitting astride a bar that connects two wheels one behind the other, one could propel oneself forward without falling. And yet everyone who has ridden a bike knows that it feels remarkably stable and as long as it is moving, it stays upright and seems to almost ride itself. ‘Look, no hands’ is the common exultation expressed by new learners as they discover for themselves that the bike can be ridden with minimal action on their part other than to keep it moving.
Even a robot can ride a bike.
From the scientific point of view, the stability of bikes has been a puzzle for a long time and the dynamics are extremely complicated. It turns out to be easier to show what is not important for stability than what is. What we have learned is that seemingly obvious explanations turn out to not be valid. One popular explanation is that the rider continuously makes minor bodily adjustments so that the combined center of mass of the system always falls vertically above the line of contact of the wheels along the ground, thus avoiding a sideways fall. This is not true. Anyone who has ridden a bike knows that while one has to make bodily adjustments, one of the pleasures of bike riding is that the adjustments can be done in a quite leisurely manner.
In an article titled The stability of the bicycle that was published in April 1970 in Physics Today (vol. 23, no. 4, p. 34), David E. H. Jones reported the results of his experiments on the stability of bikes. He developed a novel approach. He tried to make bikes that would be difficult, if not impossible, to ride, by adding features that neutralized the effects of the more common explanations for stability. His article describing his efforts is amusingly written (for a technical article). He found it surprisingly hard to manufacture bikes that could not be ridden.
Most mechanics textbooks or treatises on bicycles either ignore the matter of their stability, or treat it as fairly trivial. The bicycle is assumed to be balanced by the action of its rider who, if he feels the vehicle falling, steers into the direction of fall and so traverses a curved trajectory of such a radius as to generate enough centrifugal force to correct the fall. This theory is well formalised mathematically by S. Timoshenko and D. H. Young who derive the equation of motion of an idealized bicycle, neglecting rotational moments, and demonstrate that a falling bicycle can be saved by proper steering of the front wheel. The theory explains, for example, that the ridability of a bicycle depends crucially on the freedom of the front forks to swivel (if they are locked, even dead ahead, the bicycle can not be ridden), that the faster a bicycle moves the easier it is to ride (because a smaller steering adjustment is needed to create the centrifugal correction) and that it can not be balanced when stationary.
Nevertheless this theory cannot be true, or at least it cannot be the whole truth. You experience a powerful sense, when riding a bicycle fast, that it is inherently stable and could not fall over even if you wanted it to. Also a bicycle pushed and released riderless will stay up on its own, traveling in a long curve and finally collapsing after about 20 seconds, compared to the 2 sec it would take if static. Clearly the machine has a large measure of self-stability.
For example, it was thought that it was the gyroscopic action of the turning front wheel that made the bike stable, just the way that a rolling hoop was stable. But while the hoop’s stability is in fact due to gyroscopic action, and does play a greater role for a bike that is light and has no rider, this is not true for a bike with a rider on it. Jones showed this by manufacturing a bike that had a third wheel mounted on the front fork that was clear of the ground but could be rotated so that it exactly countered the gyroscopic effects of the wheel. He found that the bike rode just fine whether the extra wheel turned in the same or opposite direction of the front wheel. He concluded, “The light, riderless bicycle is stabilized by gyroscopic action, whereas the heavier ridden model is not-it requires constant rider effort to maintain its stability. A combination of the simple theories accounts neatly for all the facts.”
In a more recent article in the American Journal of Physics (December 1982 — Volume 50, Issue 12, pp. 1106) J. Lowell and H. D. McKell followed up the work of Jones and showed that moving bikes are almost self-stable, in that they remain upright with little action required by the rider.
But this still left open the question of what makes the bicycle feel so stable. What seems to be important is the front wheel. The ability to make tiny adjustments to the front wheel is important in the bike’s stability. Jones claimed that the ‘caster’ (the angle made by the front fork with the vertical), played a crucial role in stability. An even more recent article in 2011 claimed that the caster effect was not as important as Jones thought.
We also have a ‘bicymple’, a bicycle made simple that seems to break some of the other rules of bicycle construction and yet works.
The amazing stability of bikes has led to the construction of all manner of weird contraptions. Via Boing Boing I came across another bizarre, yet workable, bike.
Then of course, we have the physics of unicycles, another fascinating topic.