The amazing stability of bicycles

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.


  1. colnago80 says

    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

    Actually, there are two factors here. In addition to the caster (sometimes called the head angle), there is the trail which is defined as the horizontal distance between the front dropouts and the projection of the front forks just below the headset. Modern bikes with carbon forks have little or no trail and consequently have a larger head angle then old style bikes. My 33 year old Colnago Superissimo has a very steep head angle which makes the bike very responsive to steering adjustments, important in road racing, and a a fairly large trail. In fact, it is barely stable and attempting to ride with hands off the handlebars is a dicey proposition.

    Another important factor is the adjustment of the headset. If the cups are too tight or too loose, the bike will be unstable. This is less of a problem with modern sealed bearing headsets, such as the Chris King.

  2. mnb0 says

    Allow me to complicate things a little. As a Dutchman I have ridden my bike almost my entire life. Sometimes the Dutch roads are very slippery in winter because of freezing rain. On such days I still ride my bike, which still is pretty stable provided that my speed is high enough to follow a fairly straight line. That’s counterintuitive as higher speeds feel more dangerous. Making a turn, let alone a sharp one, is nearly impossible -- I solve this by slowing down a bit and stretching one leg, usually ending getting off my bike.
    Any comment on this, MS?

  3. Mano Singham says

    My suggestion would be to not ride a bike on icy surfaces. It is an accident waiting to happen.

  4. dean says

    I rode in RAGBRAI (an annual late July across Iowa) through the 90s and early 2000s. Lots of enjoyable memories and interesting times.
    Each year the main branches of the armed forces, Air Force, Marines, Army, and Navy, had fairly large teams doing the ride. One year (yes, there is a point here) one of the members of the Army team rode the entire week, nearly 500 miles that year, on a “penny farthing” -- one of the old bicycles with a large front wheel, small rear, and no gears -- pedals directly connected to the front wheel. It was especially fascinating to see him go down the hills: he would pedal until he was going too fast to keep up, then splay his legs away form the bike let it go. If there was no stop or cross road at the bottom he just rolled along: if there was need to stop he would steer the bike off the road and (most often safely, without a crash) slow down and stop in a field or a yard.
    I thought then, and still think, it was an interesting, but odd, feat.

  5. Wylann says

    Rake and trail are important to bicycle stability and steering (see this image ). It’s also important to how maneuverable a bike or motorcycle is.

    I ride a recumbent with a 20 inch front tire, and a slightly odd weight distribution (55/45 roughly, front/rear) which makes it feel rather twitchy, but once I got used to it, it rides like a dream, and with the lower cg, is very maneuverable as well. It’s my main commuter (11 miles each to work, almost every day).

  6. kyoseki says

    Gyroscopic forces at the front wheel generally only result in making the bike’s steering “heavier” at higher speeds -- this is most noticeable on motorcycles which have much heavier wheels spinning at much higher speeds, as you increase your speed, the force required to turn the fork becomes much greater.

    There was an experimental motorcycle a few years back that had the brake rotors geared to spin in the opposite direction to the wheel, canceling out the gyroscopic effects at speed, the result was a motorcycle that required far less force to steer the thing at higher speeds, making it more agile.

    The stability side of things is, again, easier to notice on motorcycles than bicycles. One basic technique that you get taught when learning to ride a motorcycle is named “countersteering”, whereby to make a right handed turn, you actually steer the forks to the left (this is not to be confused with countersteering in a car, whereby you turn into a skid/slide to retain control, the mechanics of both are completely different).

    The way counter steering works is when you steer left, you’re effectively moving the bike out from under the center of gravity, which continues in a straight line, consequently the bike LEANS to the right (just as a car leans towards the outside of a turn because the mass wants to continue in a straight line). Because of the way rake & trail are arranged, what happens next is that the weight of the bike starts forcing the front wheel to steer into the turn, which attempts to steer the bike back under the center of gravity -- it’s a self stabilizing effect that applies to both heavy motorcycles and light bicycles -- you notice this mostly as a dramatic increase in the force applied at the inside handlebar (countersteering is generally taught as “pushing” the inside bar, the harder you push, the faster the bike falls over and the sooner you start to turn).

    … obviously this only works with the toroidal shape of motorcycle & bicycle tires, which steer into the direction they’re falling (the slice made by sweeping the contact patch around the axle best being though of as a slice through a cone of decreasing height).

    Steeper head angles and shorter trail distances reduce the amount of this force felt at the handlebars, making the bike feel twitchy, but more agile, conversely shallower head angles (like custom choppers) dramatically increase this force at the bars, making the bike feel sluggish but stable.

    Bikes with negative trail are, apparently, still self stable, but if a bike’s reaction to leaning over is for the steering to react in such a way that it worsens the lean, then it’s not going to be stable, the rider will have to constantly override the bike’s tendencies, so I’d like to see exactly which bikes they have that do this.

    … at least, that’s my understanding of the mechanisms involved, if you’re aware of them, it’s relatively easy to notice them whilst riding.

  7. Lofty says

    I wonder how much damping has to do with stability? The human body adds significant damping to a bicycle. There are also some badly designed bicycles prone to high speed shimmy, the ‘death wobbles” that aren’t found on old relaxed geometry steel bikes.

  8. colnago80 says

    Although bicycles, especially with too soft frames, can be inherently unstable, for most commercial bikes purchased at a reputable dealer, this is usually not a problem. The major manufacturers, like Trek or Specialized, are well aware of bike frame design. Wobbling is usually caused by a loose headset, or front wheels out of true due to loose or broken spokes.

  9. Acolyte of Sagan says

    Interestingly (to me, at least) is the fact that a rider-less cycle will remain stable when given a push -- but only forwards. Try it backwards and it falls over immediately. If you have a cycle and want to test this for yourself but don’t want to risk damaging it, just ‘walk’ it forwards a few steps with your hand on the saddle, then try it backwards. It seems that a cycle is only inherently stable when the steered wheel is at the front.

  10. Wylann says

    I believe this has mostly to do with the rake and trail geometry of the forks, as mentioned by kyoseki, above. The angle of the forks make it self correcting. I suspect it’s possible to do that for a rear wheel steering bike, but I don’t know how off the top of my head.

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