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Why does the bike fall when its speed is very low or close to zero and is balanced when going with a high speed?

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Note that this isn't really physics related for the most part. When you ride your bike you constantly make tiny movements with your wheel in order to balance it, and the size these corrections need to be get smaller with momentum, as @David explained. –  Arda Xi Nov 10 '10 at 16:53
This question might be of interest to you. –  Vortico Nov 26 '10 at 17:02
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8 Answers

The surprising answer is that the stability of the modern bicycle has little or nothing to do with centrifugal force or gyroscopes or any of that. Look up "bicycle stability" on Google. Experiments show that the sloped angle of the front fork is very important, e.g. If the fork pointed backwards it is very difficult to stay upright at any speed.

At higher speeds a very slight turn of the handles moves the bicycle under the center of gravity of the rider quicker, so that the dynamical stability is improved. As usual experiment corrects theory here.

See the answer of Tristan at Does leaning (banking) help cause turning on a bike? as well for an even better answer

See the comment of nibot below for a reference to an actual definitive article.

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I've made about 30,000 kilometers on my bikes throughout the years, most of which was in a hands-free model, so I assure you that the existence of the handles doesn't have much to do with the stability of my bike when I am riding it. The angular momentum goes in the left horizontal direction; when the bike is falling, it would go slightly up or down. So the change of the angular momentum or torque would have to be in the vertical direction. But that's exactly the direction of torque that the contact with the road can't offer us because it's down from the center-of-mass. –  Luboš Motl Feb 2 '12 at 6:34
The angular momentum from the rotating bikes is rather small in absolute sense but it doesn't matter because the vertical torque that can be obtained from the road - the lowest point of the tires - is even smaller, essentially zero. By moving the center of mass of the person, one may change what is the allowed "quasivertical" direction in which the conditions above hold and in which stability is maintained. At any rate, the stability does increase with the speed of the bike, exactly as the "angular momentum based" theory predicts. –  Luboš Motl Feb 2 '12 at 6:37
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A report appeared in Science today which addresses this exact question: Kooijman et al., Science 332 (6027): 339-342, "A Bicycle Can Be Self-Stable Without Gyroscopic or Caster Effects."

The abstract reads:

A riderless bicycle can automatically steer itself so as to recover from falls. The common view is that this self-steering is caused by gyroscopic precession of the front wheel, or by the wheel contact trailing like a caster behind the steer axis. We show that neither effect is necessary for self-stability. Using linearized stability calculations as a guide, we built a bicycle with extra counter-rotating wheels (canceling the wheel spin angular momentum) and with its front-wheel ground-contact forward of the steer axis (making the trailing distance negative). When laterally disturbed from rolling straight, this bicycle automatically recovers to upright travel. Our results show that various design variables, like the front mass location and the steer axis tilt, contribute to stability in complex interacting ways.

There is also a blurb in ScienceNOW that you can read without subscription.

Here is a free-to-read preprint.

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This problem was solved in 1970 already by E.H. Jones. Google for "unridable bicycle". –  Georg Apr 14 '11 at 21:11
@Georg: actually, the solution is opposite of what Jones found. The unridable bicycle Jones constructs tries to remove the caster effect. But the recent paper showed that you can have a stable bicycle without the caster effect anyway. –  Willie Wong Apr 15 '11 at 2:33
The E.H. Jones (1970) story is referenced in a comment to David Zaslavsky's answer. –  nibot Apr 15 '11 at 3:54
Covered this week in New Scientist: newscientist.com/article/… –  nibot Jun 3 '11 at 19:37
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When you walk on stilts or skate, you don't balance by being very careful. You don't even balance. You're continually out of balance, and you keep moving your point of support so that you arrest your fall in one direction and start falling in another.

If you're on a bicycle moving very slowly, you do the same thing. You keep moving your point of support left or right to arrest your fall in that direction. If you're moving slowly, it takes more steering motion to accomplish this, so you "wiggle about". At higher speed, it takes less steering motion to do that. That works even in the absence of gyroscopic precession, caster, or rake angle. Just watch a scooter with tiny wheels, or a ski-bike, or a unicycle.

Now, throw in rake angle. Turning the handlebars to the right moves the point of support to the left, even if you're moving very slowly, so that helps.

Now, switch to a high-speed motorcycle with a nice, heavy, gyroscopic front wheel. When it's traveling at a good speed, that thing precesses, no matter what people say, and its precession goes in exactly the right way to powerfully maintain stability.

So it's not an all-or-nothing single-explanation deal.

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The basic concept (at least, as I've heard it) is angular momentum. As a bike wheel turns, it has an amount of angular momentum proportional to its rotational speed, associated with the plane of rotation of the wheel. This makes it act basically like a gyroscope: it "resists" any change in the amount or direction of that angular momentum, in the same sense that mass "resists" any change in the amount or direction of its velocity. This basically slows down the tipping of the bike to the point where you are able to prevent it by pushing down on the opposite side pedal.

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The article "The stability of the bicycle" (physik.uni-regensburg.de/forschung/fabian/pages/mainframes/…) suggests that angular momentum has little to do with bicycle stability. –  nibot Nov 10 '10 at 18:32
Interesting, I'd never heard about that, although I had a feeling angular momentum might be one of those popular but incorrect explanations (like the Bernoulli effect with airplane wings). Although, I'm certainly not claiming that it's angular momentum alone that keeps the bike up, only that it makes it easier for other effects to maintain stability. –  David Z Nov 10 '10 at 20:15
The gyroscopic inertia explanation doesn't really explain why those scooters with the really tiny wheels can stay upright. It's got everything to do with the angle of the fork. If you lean to the right, the angle between the fork and the point of contact with the ground will cause the wheel to turn to the right. This in turn causes the bike to turn right, which, from the now-rotating frame of reference of the bike, causes a leftward centrifugal force that rights the bike. –  Tristan Nov 10 '10 at 21:05
I think your answer is correct and I don't understand the down votes. Let's put it another way: Why is it so hard to remain upright on a stationary bicycle compared to when it's moving? Because it's wheels are turning around and lots of lovely angular momentum. This point will convince people if you edit it into your answer. –  John McVirgo Feb 12 '11 at 22:21
we're both wrong - I'm shocked. Dr Hugh Hunt from Cambridge has written an article, "on the insignificance of the gyroscopic effect when riding a bicycle" and demonstrates that it's the "trail" which matters most. –  John McVirgo Feb 13 '11 at 14:33
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Here's an interesting talk on the subject, from the point of view of control theory:

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oneat's answer is correct (I would have commented but I think I'm going to need more space)

Imagine a vector (line) starting at your center of gravity. The line represents all the forces acting on you. When you are standing still, the direction of the line is straight down (gravity is the single force present).

To not fall over whens standing still on a bike, you have to keep the point where the line intersects the ground (let's call it point A), between the two wheels of the bike. If you don't, you'll start tipping over.

When standing still, the only way to affect that point is to move your center of gravity which you do by shifting your weight.

Now let's say you're moving. If you're moving in a straight line, at a constant speed, everything is the same, the only force acting on you is gravity. But if you change direction, you get centrifugal force (as oneat correctly pointed out), the same as what you get when you make a sharp turn in a car moving at speed. The value of that force is proportional with your speed, your weight and the speed of the turn.

This centrifugal force is added to the gravity, and changes the direction of the resulting force acting on you.

Remember point A? If you're riding your bike and it starts to lean to the right, point A starts to move to the right and the bikes leans even more, and so on. But, you instinctively know to turn your bike to the right. This causes a centrifugal force, pointing left, to appear). If point A is still between your wheels then you're fine.

If you're moving slowly, the centrifugal force is small, so you have to take the turn more sharply to compensate. If you're moving fast, you might only need to nudge your bike a little to compensate.

It's explained in more detail here. (I actually thought of looking it up in wikipedia only after writing this answer, I don't have time to read the article now, hopefully I'm not too wrong)

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Then you should thought of reading wikipedia in more details. And this: "you get centrifugal force (as oneat correctly pointed out)" is in no way true: imagine yourself in the inertial frame moving with the bike: no speed, so what ? @Davis answer is short but correct. –  Cedric H. Nov 10 '10 at 17:38
just to be a bit provocative: You are standing upright on your bike, you violently lean on one side, just at the beginning what is the direction of the centrifugal force ? –  Cedric H. Nov 10 '10 at 17:44
If your standing still, or moving at constant speed in a straight line, the effect is the same there is no centrifugal force (there might be one because technically you're moving around an axis, but in that case it's negligible). Did you actually read the wikipedia article? –  Adrian Mester Nov 11 '10 at 10:17
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We have a series of papers on exactly the topic of this discussion, but a bit more narrowly defined. That is, how and why can a bicycle balance itself?

In short, how does a moving bicycle balance itself? For a variety of complicated reasons it steers in the same direction as it falls. And, if you will excuse the sloppy informal physics language, because of the resulting curved path, thecentrifugal forces, push it back upright. What complicated reasons? Partially from the trail (or castor effects), partially from the angular momentum of the spinning wheels, and partially from other effects related to geometry and mass distribution. But there is no simple single necessary mechanism that we know of. For example, our paper in Science Magazine shows that a bicycle can be self-stable without no castor (no trail) and with no spin angular momentum of the front wheels.

We have written several papers and supporting documents. And we have in these a pretty exhaustive coverage of the literature. So if you want to know what we think, what others have thought, and what we think about what they thought, it's all there. I don't think you will know of some important reference that we have not reviewed and described. You can start with my www page http://ruina.tam.cornell.edu (or google ruina bicycle or google schwabb bicycle.

The www site includes photos and videos including simple explanations of some of these things.

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The answer is "Centrifugal force"

The biger your speed is the biger this force is too.

You can notice that when you steer left you make your bike's slope on left side. And Contrifugal force don't let you fall (when your steer angle is constant at the end bike will make a circle). Then when you make your bike steer more left your bike returns to the balance because you increase that force (it comes from equation).

When your speed is smaller contrifugal force is smaller and bike is harder to steer so you can fall easier.

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This is a very misleading answer: there is no "centrifugal force", just a centrifugal pseudo-force in a rotating frame. When you look at a bike you generally do not consider a rotating frame, and even if you do, how would you relate the rotational speed of the frame, leading to a centrifugal term to the speed of the bike ? –  Cedric H. Nov 10 '10 at 17:08
I think centrifugal force is correct. The object's inertia "tries" to keep the object moving in a straight line, the same thing that happens when you swing a rock tied to a rope. –  Adrian Mester Nov 10 '10 at 17:36
@Adrian: you are saying "inertia" because... there is no force... In the case of the rope, the rope is providing a centripetal force. –  Cedric H. Nov 10 '10 at 17:48
If you're moving in a car and the car take a sharp left turn, the force that you feel can be explained either a inertia or centrifugal force. Inertia: your body is trying to continue going in a straight line, centrifugal force: the friction between the wheels of the care and ground acts as a centripetal force on the car. –  Adrian Mester Nov 11 '10 at 14:06
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