The mysterious physics of bicycles

I’m pretty sure I’ve been doing that on my bicycle without realizing it consciously. I provide the higher weight and power myself.

Your argument doesn’t explain why a bike pushed forward and let go will topple quite quickly.

What you’re describing disagrees with the experience of at least some of the other people here. If you tried the experiment yourself, and had this result, you might have used a bike with geometry different from the ones the rest of us used.

Personally, I got in a heck of a lot of trouble as a kid with a new 10-speed, by rolling my old Huffy down a hill over and over again, just amazed at how powerfully it tended to remain upright while rolling and riderless. I don’t think we ever found a way to knock it over without first stopping it.

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I know so little physics, I’m not even going to try to argue with the physics and engineering folks… but I do want to mention the experience of Bob Mellin in his book about railbiking:

He was a unicyclist with excellent balance… so he figured he could balance a bike on a rail without an outrigger. Wrong. He said he learned very quickly, we don’t balance (rolling) bicycles by shifting our weight… we balance them by steering in the direction we’re falling. Subtly. And we’re falling all the time.

Constraining the bike’s wheels to go in a straight line is, I think, an interesting manipulation of the variables…

Personally, I ride a tricycle. Problem solved.


Thanks, I have argued this with others who question my credibility versus the article. As a cyclist, I’m aware of this - it’s obvious but I couldn’t quite articulate it as you have. Thanks for posting.

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The same has been shown on regular bicycles. And it makes sense.

If you want to go around a corner, you need to lean into the corner. If you don’t you fall over, away from the curve.

To initiate the lean towards the direction you want to steer, you have to begin a topple in that direction. We do it instinctively by counter steering.

Watch little kids learning to ride without training wheels. They don’t know to counter steer, so they wipe out at the first turn, usually away from the direction they were trying to go. Somehow we pick up that little trick and never think about it.

Friction, on a moving bike, it takes more effort/energy/momentum to break friction and fall over than it does to keep rolling, on a stationary bike, it’s just as easy to fall over sideways.

The idea that there is a hole in our (collective) understanding of how bicycles work, or more precisely, why they remain stable for certain configurations and speeds, is utter rubbish. It’s actually not hard for a well-prepared scientist or engineer to derive the equations of motion and determine stability. Indeed, the standard model for bicycle dynamics is the Whipple model, was developed in the undergraduate thesis of Francis John Welsh Whipple at Cambridge University in 1899 (albeit apparently with one sign error in the equations).

The difficulty is that as in many areas of science, the explanation is reductive, leading to a description that has more explanatory power for the scientist or engineer, but less power for the layman. The logic goes like this: The nonlinear equations of motion can be developed using Newton’s laws, or more advanced methods ultimately based on Newton’s laws. The derivation is slightly complicated by the fact that the dynamics are nonholonomic because of the rolling tires. (As an aside, it would not be possible for the bicycle to be asymptotically stable if it weren’t nonholonomic.) The equations of motion admit an equilibrium solution, namely a vertical pose at constant velocity and zero steering angle. The stability of the equilibrium can be determined by linearizing the equations of motion and determining the stability of the simpler linear equations. In turn, the stability of the linear equations can be determined using the Routh criterion, which gives a binary answer for stability based on the coefficients in the linear dynamics.

It turns out that the stability of the bicycle depends on the interplay of about two dozen parameters, such as wheel size, wheel base, caster angle, front wheel trail, etc. If you “turn off” the gyroscopic effect for a stable configuration, it will change the stability range, but in ways that may not be intuitive. The problem is not that the dynamics of bicycles isn’t understood, or that there’s a hole in our understanding, it’s that the interplay is complicated enough that there’s no single, prescriptive rule that is easily stated to a layman that will tell you why a bike is stable.

See the video of Richard Feynmann on the problem of “why” in science.

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Um, nobody who understood the first thing about physics and has ever ridden a bicycle thought that they stayed upright via gyroscopic effect, so I don’t hold a lot of faith in this guy’s opinion.

It’s pretty easy to understand how bicycles stay upright. The rider balances them by continually moving the front wheel to steer the contact points of the tires directly under the center of gravity. This is why you can’t balance if the bike doesn’t move at all, you can’t cause the tires to shift under you with no forward movement.

To steer, the rider actually intentionally unbalances the bike by steering in the opposite direction, causing the tire contact point to move away from the desired direction of travel so the center of gravity “falls” in the desired direction, then the rider returns the wheel to “follow” the fall through the turn. At the end of the turn, a steering maneuver in the opposite direction returns the bike upright.

Yeah a motorbike riding friend introduced me to countersteering, and I realised I had been doing it all my life on bicycles. Its why when I am out riding with my son I have to take care when turning. He can’t turn as fast as me because he hasn’t learned that trick.

There are “ghost bike” challenges at some cycling events, the idea being to set a riderless bike off down a hill and see whose stays up the farthest. Usually this involves bikes no one cares about.

Old school high-wheelers actually did have considerable gyroscopic effects, with heavy wheels and a long radius. If you ride a “penny farthing” at any speed you’ll feel it. The stability of a modern diamond frame bicycle was arrived at through thousands of actual experiments. Trial and error produced a design that embodies the optimum stability and/or maneuverability that the bike’s purpose requires.

As mentioned ad nauseum, bicycle stability is a combination of a number of factors, each of whose importance varies slightly with differences in wheelbase, fork rake and trail, frame design and so on. Apparently a general formula integrating all factors is elusive, but people who build bikes are generally aware of what each trade-off involves.

Humans can learn to ride anything, regardless of its stability. A unicycle is not exactly stable, but people can ride them. Nobody should be able to stand on a slack line, but people do. A stable design just makes bike riding easier.

Figuring out how a bike stays upright is theoretical physics. Riding one is practical physics.

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Yeah this is why tram tracks on roads are so dangerous, along with raised markers on bicycle lanes. Our local council started putting raised plastic strips (a few cm high) along bike lanes. In wet weather you could get trapped on one side of the marker and that a guaranteed crash.

True, the old penny farthings are a very different beast from modern bicycles (or the diamond frame bikes of the day). Leaning to steer is the wrong instinct, they turn more like a bus, and the gyroscopic effects are pretty strong (but don’t necessarily help you because they can cause it to “dive” into turns). Very fun to ride, but I’m glad that the diamond frame took over.

Fun tidbit - in penny farthing days, the only way to get a higher gear as you became stronger was to buy a larger wheel. So if you were new you might ride a 50", but a stronger cyclist may move up to a 60" to go faster. We still use that measurement today as a way to compare the relative ratio of different gear and wheel choices, called “gear-inches” - A bicycles “gear inches” are calculated using the chainring, the cassette sprocket, and the wheel size to determine the equivalent diameter single wheel for each gear option - for instance my single speed bike has two sprocket options - one gives me 72 gear inches for flat terrain, and the other closer to 60 gear inches for hilly terrain. Pennyfarthings are also why we call a higher gear ratio a “taller” gear - because you would be physically taller on a pennyfarthing of that gear!


It’s not actually friction. It’s actually the geometry of the front fork and the tube that holds it. And it takes a bit of weight to activate it, and that’s why a bike without a rider won’t stay up for long.

The geometry part can be seen this way. Sit on a bike but don’t ride it (yet). Just balance with your toes on the ground. Now turn the handlebars one way and notice what happens. The front of the bike lifts. Lets it go and your weight will help it to return to straight-ahead. Friction on the tire limits the effect a bit but the action is easy to see.

If you see sketches of very early bikes you’ll see that the front fork is vertical, and that bike is very hard to ride. Racing bikes still have only a small angle there - harder to ride but quicker to respond. Bikes for easy riding have more angle and are more stable, but don’t turn quickly. Check out “Easy Rider” motorcycle for a rather extreme example.

The same thing happens in cars and it’s why steering is self-centering. The mechanism in behind each wheel has a device that is similar to the steering tube. In a car it’s known as the “kingpin”. Cars these days do not have an actual kingpin but the suspension mechanism performs the same function. And “kingpin inclination” is a critical piece of suspension design.


Whilst friction is important (hard to stay upright on ice), it isn’t really the “reason”. The main mechanism is that the geometry of the steering ( fork rake, trail, offset, caster etc) causes the front wheel to naturally steer the bike back under its centre of gravity if it leans over. A bike with no steering is very hard (close to impossible) to ride. Take any bike and hold it by the seat. Lean it to one side and you will see the front wheel turn to the downside as if trying to steer back under itself.

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So the net conclusion here is that this should have been subjected to

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In strong cross winds my two 26 inch wheels feel the wind as if they are disks. I hate to think what that would be like on a big 60 inch wheel.

well… the way I think of it… if a bike was just pushed down the road, with no one to balance it or steer it, then it wouldnt get too far. Its the people on the bike that keep it upright and rolling.

The number of comments here with different ideas makes it clear that this isn’t well understood. Part of this is the way the question is stated. The answers involving corrections made by the rider are missing the real point, which is why a riderless bicycle stays upright. Those claiming riderless bicycles don’t stay upright can’t really have experimented much. The answer is in counter-steering, as described by many here. When a bike with sensible steering geometry falls to one side a bit, it steers in that direction so centripetal forces, acting against the friction between the tyres and the ground, pull it back upright and it stops steering in that direction. If you lock the steering on this bike, it immediately ceases to do this and, with or without a rider, it won’t get very far. If you manage to configure the steering geometry so that this doesn’t happen (e.g. no rake and no trail) then it won’t get far without a rider.

This, incidentally, is why training wheels are a bad idea: they turn a bike into a trike, which doesn’t counter-steer, so you learn exactly the wrong way to steer. As mentioned by someone else here, when you take them off the first thing that happens is an attempt to steer in the opposite direction to what’s required, with inevitable, demoralising consequences. Teach your kids to ride on pedal-less bicycles!

The answer is simple: mad skillz.

IIRC, we only found out how bugs stayed in the air a few years ago. I think the thing was that at the scale of a bug the air has the viscosity of oil! Now, that’s a pretty damn counterintuitive effect of scale, and not very far away at that.

But yeah, with bikes it’s obviously not something like that; it’s hard to see how the explanation could be hiding…

I guess the question hasn’t ever stuck in the mind of someone sufficiently brilliant.

Just want to chime in on the non-mysteriousness of bicycle stability. It’s mainly friction between the wheels and ground + geometry of linkage between front wheel and body = restoring force if bicycle starts to tip over sideways. A second contribution is ‘castering’-- the effect that pushes the wheels of a cart into lining up in the direction you are pushing the cart, which is also due to friction. Gyroscopic stability is minor for a bicycle, not so minor for a motorcycle. But, repeat, not a mystery.