The mysterious physics of bicycles


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I didn’t know we weren’t sure why bikes moved. Interesting stuff!

Hi Maggie, look, I saw this article published a few years ago on Ars and, frankly, I was appalled. I posted there at the time, but I’d like to set the situation straight, here, again. People DO know how bikes ‘right’ themselves. Its not magic, its physics. Specifically, its friction. Why does a car ‘right’ itself? FRICTION! Its the same concept. The interface between the tires and the road cause the phenomenon. It literally takes MORE ENERGY to turn a wheel then keep driving along the same vector. Likewise, if you blow a tire in your car, it will vear off to that direction. A first year Engineering student can impart these basic facts. The real scandal here is that these people were allowed to graduate.

So, Maggie, feel free to post this response to Boing Boing on my behalf. Together we could blow the top off Bikey-Stay-Uppy-And-Go-Straighty Phenomenon!


So, okay, to prove my ‘theorem’, lets build a bike tire with a front profile of LJ. sharp L rubber of the left, standard J shape on the right. The left side is in constant contact with the road, the right is a normal bike tire and tapers off from the middle where it would normally interface. Bike will never right itself. Will always pull towards the L where the most friction is.

I realize the authors of the study threw a bunch of bike configurations at the investigation, but clearly, they didn’t have the foresight to alter the wheel uniformity; that said, test this against any bicycle configuration. Doesn’t matter. Case closed.

We had a whole room of modified bikes at UIUC in the early 90’s. Many probably dated to before this. Including several that had canceled gyroscopic effects. They rode just fine.

The collection was created by a professor, Richard Klein. I worked with him and took one of his classes. His specialty was bicycle dynamics and control, so the subject came up a time or two. Most certainly, the gyroscopic effect was debunked as critical for riders. The bikes rode just fine.

A big part of his study was how much control was required to keep systems stable. What I gleaned by osmosis was that, for a bike, the mass location and steer axis tilt was within a certain range was important to stability. Just what this article states.

Here’s a nice article that has some nice discussion and pics:


That article, even though it was written by a physicist, sounds a lot like that apocraphal story about “scientists prove that a bumble bee can’t fly! haha dumb scientists” but which is actually a story about a scientist describing how simplified models only work within the scope they were intended to apply, and fail when applied to other systems (aerodynamics models meant to apply to aircraft don’t work when applied to something that flies like a bee).

Of course we know how bicycles work. People have known for a long time that gyroscopic effects don’t keep bicycles upright - in fact precession would actually tend to make the bike LESS stable during steering. The study with the counter-rotating wheels just put the nail in the coffin on that one.

Tire friction matters, as mentioned, as does the geometry of a bicycle - due to the rake and trail of the fork, a bicycle in a “turning” position has a higher center of gravity than a bicycle in a “straight” position, so gravity literally pulls the bicycle straight again, by lowering it’s center of gravity.

I’ve made and ridden a lot of “freak bikes” and you realize pretty quickly how small changes, like making a bike with no rake and trail, make it nearly unrideable, since it is no longer dynamically stable.

I suppose it may be true that no one has written up the whole model that describes the bicycle (and motorcycle’s) behavior, but that doesn’t mean that it is some kind of mystery, just that it hasn’t all been generalized yet.


Take a bike and roll it down the street. Notice how it falls over. Bikes don’t stay upright while they move, people on bikes stay upright when they move. For goodness sakes, people can sit on bikes and balance when they aren’t moving. People can right unicycles across tightropes.


Actually the bike pushed down the street will stay upright for quite a long time, even making “steering corrections” on it’s own, which is part of the anomalous effect. It isn’t the giant mystery the author makes it out to be, though - it is just a variety of little effects contributing, like the steering geometry, tire friction, etc.


When a bicycle leans over, the wheel turns in the direction of the lean. I don’t know why; I’d guess it has something to do with the shape of the tyre, the middle being fatter than the edges and having further to travel. Then the turned wheel pulls the bicycle into a turn, and the forward momentum pulls it upright. Right?

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You seem to know a lot more about it than I do, so I will concede you are probably right, but this is not how I recall things working. I guess I’ll just have to go try it out (for science!).

A good, on-line book on the subject: “The Physics of Bicycle Riding”, by Hans Rudolf Zeller. No nonsense kinematics and dynamics with clear diagrams.

I always liked this page, where the author creates a bike with a wheel spinning in reverse:

It references this article, where a number of URBs (unridable bikes) are discussed:

In general, though, most of the reason why a regular bike is ridable is because a human is doing the riding, and making corrections. A regular bike just pushed and let go will topple quickly. A bike with fixed handlebars ridden by a human will also topple quickly. But a regular bike ridden by a human can stay upright at any speed, even stationary (though usually with a bit of (necessary) back-and-forth).

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Your argument doesn’t explain why a bike pushed forward and let go will topple quite quickly. Even a rolling wheel alone will usually fall before its forward momentum has been given up, so clearly it does not take “more energy” for it to fall than for it to keep going.

I have gotten good at trackstands from riding a fixed gear bike for several years. I can assure you that it takes very little motion to keep the bike upright. The geometry of the bike is the major contributing factor, along with the human’s ability to inject balancing motions. It’s all very supercomputer-solvable.

My experience agrees with phidauex: An unoccupied bike will stay stable for quite some time unless you pushed it badly when you jumped off or released it badly when you pushed. It’s clear that there’s a feedback process whereby the bike is inclined to turn into the direction it’s leaning.

Past experimentation with moving the front wheel’s axle forward or backward from the standard suggests that the sideways force exerted upon the wheel as a lean starts has a lot to do with that. Those experiments also demonstrated that the ridability of bikes was affected by this – they weren’t often made completely unridable, but the ease with which one can ride them was indeed affected.

Not gyro, but feedback governor none the less.

Claims that it isn’t understood have got to be bogus. It’s too easy to experiment with and/or simulate.


I don’t think you’re contradicting what I said even a little bit.

Certainly try it out! You can even do things like turn the handlebars all the way around (may have to loosen some of the cables to make it work) and then try it. “For Science” is a great reason to play around with things.


But if it’s not gyroscopic, why is it harder to stay upright on a still bike than a moving one?

I’ll add another aspect to this - motorcycles steer using the same dynamics as a bicycle, just on different scales, and much research has been done on them (I might ride a contraption around the block without knowing how it works, but I bet BMW wouldn’t build a $30,000 motorcycle without knowing how it works).

An interesting phenomenon to google is “countersteering” which is a technique for motorcycle riding where at moderate to high speeds you turn the handlebars RIGHT to start a LEFT turn. It sounds totally counter intuitive until you actually do it and feel it happening. Pressing forward on the right grip initiates a right turn. The dynamics are understood - you are initiating a lean by imbalacing the front wheel, which pulls the two wheels into different tracks, which helps carry the turn. The technique only works because of the same geometric and friction principles that keeps the motorcycle stable. Countersteering can be felt on bicycles, but it is much more obvious on a motorcycle with higher weight and more power.

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It isn’t gyroscopic, but it does require momentum - a bike pushed alone will self-correct for a while, but only because the movement gives it energy by which to self correct (the tire pulls itself back into alignment by using up some of the momentum). A person can still balance on a still bike, but that is more due to our ability to correct with tiny movements, like balancing on one foot, though the bike geometry still helps (if you watch people trackstanding, you’ll see they usually have the wheel turned slightly, it really does help).

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