# Would a bicycle stay upright if moving on a treadmill and why?

I suspect not, because moving forward (or backwards for that matter) is an important part, but I would like to confirm.

UPDATE: Clearly it's possible

Can someone explain why?

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## migrated from bicycles.stackexchange.comJan 15 '13 at 22:36

This question came from our site for people who build and repair bicycles, people who train cycling, or commute on bicycles.

This is similar to the interminable airplane on a treadmill question that did the rounds a few years ago, e.g. blog.xkcd.com/2008/09/09/… - I don't think it has much place on bicycles.SE - maybe move to Physics? –  Unsliced Jan 15 '13 at 10:28
No need for the video -- clearly rollers do the same thing. As Alex says, the reason is that you can steer, and steering to keep the bike under you is how you balance. –  Hot Licks Jan 15 '13 at 12:13
@Unsliced: On the contrary it is quite different from the airplane on the threadmill question. The core difference is that in the case of the bicicle, all of the force is applied through the wheels (and thus the threadmill can be used to compensate the forward velocity of the bike), while on the case of the airplane, the thrust is independent on the wheels, and thus the threadmill cannot stop the airplane from moving forward. –  David Rodríguez - dribeas Jan 15 '13 at 14:49
It's the same concept as running. –  ekaj Jan 15 '13 at 18:11
The airplane on a treadmill question has been asked on Phys.SE here. –  Qmechanic Jan 15 '13 at 22:40

Because you can move the bike from left to right, like when you're riding, to balance it.

Whether you're moving or not doesn't matter, just that your wheels are turning so the steering works.

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In some conditions, even a riderless bike could run on a treadmill. The main problem is that the bike has self-balancing, but not self-aligning to an original trajectory (it generally finds a new path after self-balancing). –  heltonbiker Jan 15 '13 at 12:25

When you begin to fall to one side, you are effectively leaning into a turn. Because the contact patch of the front wheel trails slightly behind the center of the steer tube, leaning over causes the steer tube to turn at a more acute angle than the radius of the turn given sole by the lean amount. Because the handle bars are turned into a tight[er] turn, the bike begins to turn under the center of mass of the bike and rider. This animation on from Wikipedia's Bicycle and Motorcycle dynamics article shows this process.

Basically, bicycles are self-righting because they are always turning (or being turned) to stay under the rider's center of mass. At slow speeds, the weaving is noticeable as in the animation. At higher speeds the weaving will become so fast and small that it becomes imperceptible by the rider. In the presence of additional forces on the front wheel (such as a rough surface or wind), additional rider inputs are often needed to counteract these forces and keep the front wheel on the angle it needs to be to keep the bike under the rider.

This article by Dr. Hugh Hunt (University of Cambridge Department of Engineering) does the math on the gyroscopic forces when riding a bicycle and finds that at 12mph they are only strong enough to counter about 2mm of lean and not a significant contribution to stability. Additionally, it catalogs an experimental test where a second counter-rotating wheel is used to cancel the gyroscopic forces -- and the bicycle suffers no noticeable decrease in stability:

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Yes, the geometry of the front fork and steering is set up such that the wheel will tend to turn in the direction that the bike leans. This provides an auto-righting effect. A bike with a straight 90 degree fork, with no "rake", is much harder to ride. –  Hot Licks Jan 16 '13 at 1:26
The wikipedia article from which this graphic is taken discusses a balance between centrifugal forces and gravitational torques in order to maintain the upright position of the bicycle, which is how I had previously understood bicycle balance to work. It seems to me that, on a treadmill, centrifugal forces would no longer be present, and so the balancing procedure would be different insofar as centrifugal forces are important in the non-treadmill case. Can you comment on this? –  kleingordon Jan 21 '13 at 2:53
Maybe centrifugal forces are still playing role, if you consider the treadmill surface's rest frame? It seems like that must be the answer, but for some reason I'm still bothered by it and would appreciate confirmation. –  kleingordon Jan 21 '13 at 3:12
This is not really why bikes stay upright. The real reason is that the front wheel acts like a gyroscope. Leaning is precession, which cause the wheel to pivot around the steering mechanism so that it steers into the turn. –  Olin Lathrop May 16 '14 at 18:04
@OlinLathrop Sorry, but the gyroscopic forces are not significant (only able to counter 2mm of lean at 12mph). Please see this article: www2.eng.cam.ac.uk/~hemh/gyrobike.htm –  Adam Franco May 17 '14 at 19:19

The main reason is not balancing, but a physical phenomenon called gyroscopic effect. In principle this is the fact that a rotating body tries to keep the axis of its rotation fixed in space and also the reason why a spinner stays upright as long as it spins. The gyroscopic effect makes rotating things self-balancing an works better the faster the rotation is -- hence it is much harder to not fall down as you cycle very slow (which means the wheel rotate only slowly) compared to higher speeds.

If you had to balance the whole thing just by actively balancing, you wouldn't stay up for long. Compare trial cyclists: they invest hours of practice into balancing on their bike while standing and even then have to work a lot on their bike with rolling or hopping slightly back and forth or aside to keep their center of gravity balanced over their bike. You could not do this on a treadmill if you neglected the gyroscopic effect.

So what is now happening on a treadmill that keeps you up? As you tend to tilt to one side, the gyroscopic effect jumps in with some rather unintuitive behavior: if you apply a force perpendicular to the rotation axis (which is what you do when you try to tilt the bike) the gyro reacts on this with another force that is perpendicular to both the rotation axis and the initial force. So if you consider the rotation axis to be parallel to the ground (and perpendicular to the wheel plane) and the tilting force perpendicular to the ground, the resulting force will be perpendicular to both of them, i.e. lies in the plane of the wheel and parallel to the ground. This force will turn the wheel out of its initial direction like you do when you turn the handle bar to steer.

But (and here comes the magic) this will again result in another force that is again perpendicular to the ground and therefore a tilting force but in the opposite direction as the initial tilting force and therefore it will make the bike get more upright. This will again induce a "steering" force and as long as the tilting is rather small it goes back and forth resulting in some oscillation where the bike tilts slightly right and left but always stays nearly upright.

Important security notice: As already said it's quite unintuitive. Even if one in theory knows how it works, one should not try to forcefully probe some of the implications. I know of a physics professor that had a nice crash on thinking he knew how it works.

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Whilst gyroscopic effect is certainly what would keep the wheels upright, I am not convinced it's the main force when it comes to the whole bike. Thank you for the explanation though, it's very thorough. –  Shagglez Jan 15 '13 at 15:19
Just having the gyroscopic effect isn't enough, which is why it's so hard to ride on rollers. On a bike you have both forward momentum, and the gyroscopic effect. If you remove the forward momentum, even though the wheels are spinning, and you can steer to keep the wheels under you, it's still quite hard to ride. The combination of steering, forward momentum, and angular momentum of the wheels all work together to make the bike easier to balance. Remove any one of those and the stability is compromised. Anybody with ultralight wheels care to chime in on if they are any harder to balance on? –  Kibbee Jan 15 '13 at 16:32
The significance of the gyroscopic effect has been shown to be negligible. –  Hot Licks Jan 15 '13 at 16:42
As Daniel R. Hicks mentions, gyro not needed. Good article: news.cornell.edu/stories/April11/bicycle.html –  Ken Hiatt Jan 15 '13 at 20:44
A very nice explanation of a negligible effect. Sorry for the downvote, but you are just helping preserve the myth. On normal bikes, it is caster, a.k.a. trail, the main culprit, although recently they have built self stabilizing bicycles without caster or gyroscopic effects, see Ken's link. And see also the photos on this 1970 article of an unrideable bicycle with a custom fork, and rideable bicycles with gyroscopic effect cancelled: socrates.berkeley.edu/~fajans/Teaching/MoreBikeFiles/… –  Jaime Jan 15 '13 at 22:18

Centrifugal force or inertia is the main reason that keeps the bike balanced. Gyroscopic and caster effect are minor and not sufficient by themselves to mantain balance. Therefore it's very hard to balance a bike on a treadmill.

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