# What makes a bike stay upright when moving?

What makes a bike stay upright when it is in motion? What is the relationship between speed and stability? Is it a linear relationship?

I could ask this on the physics site however I am hoping for a relatively simple answer. I took an introductory class in physics in University so basic physics is appreciated but nothing too gnarly.

I think that it is not the spinning mass of the wheel that is keeping the bike upright. I read a study recently stating that if you have a wheel with identical mass spinning backwards beside the bike the bike will not lose stability. (I am not sure where I read the study).

Why do bikes stay upright when on a roller?

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In short, the Bicycle GODS. – Moab Jul 5 '11 at 21:39
Little secret antigravity modules under the seat. That's why seats are so expensive. – Daniel R Hicks Jul 5 '11 at 23:00
@ Daniel, I thought it was the "space age" Gel that drove up the price...I think I will make my next seat out of a coconut shell, that will turn some heads. – Moab Jul 6 '11 at 13:57
My bikes are kept upright by conceit and a sense of self-importance. – Neil Fein Jul 6 '11 at 14:53
I think it might be called pedaling. – zenbike Aug 7 '11 at 14:51

It should be as simple as this:

• action = reaction. If the bike is upright, it will stay upright unless there are sideway forces. This is true even when the bike is not moving.
• if there's some force that disrupt the balance, there needs to be an equal amount of counteracting force to maintain balance.
• when the bike is moving, steering will translate some of forward momentum into sideways force, so steering can be used to balance the bike.
• on a roller, the bike can move sideways to balance.
• moving the weight of the rider shouldn't generate sideway force because to move to one side, the rider needs to push the bike on the other direction with same amount of force. Any success with this can be attributed to inefficiencies in the system.

Then there's the gyroscopic effect of the wheels that can alter the amount and direction to forces that work on the system.

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There has been some more recent research on this: http://www.science20.com/news_articles/why_does_moving_bicycle_stay-78139

It was previously thought that the rotating wheels of the bicycle provide stability through gyroscopic effects; and that the ‘trail’ (the distance by which the contact point of the front wheel trails behind the steering axis, plays an important part).

However:

A new study in Science claims to have settled the issue - gyroscopic effects and trail help, says researcher Dr Arend Schwab of the 3mE faculty at TU Delft, but are not necessary above a certain speed . In a 2007 Proceedings of the Royal Society article (doi:10.1098/rspa.2007.1857), a mathematical model with around 25 physical parameters was developed at the time which appeared to predict whether, and at what speeds, a particular design of bicycle would be stable.

The authors designed and constructed a Two Mass Skate bicycle, with small and counter-rotating wheels, which means there is no gyroscopic effect to speak of, and a small negative trail (in other words, where the point of contact of the front wheel is marginally in front of the steering axis). Yet the bicycle remained stable when moving.

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This 7-minute video gives an explanation of bicycle stability, discussing gyroscopic, caster, and steering effects. In particular, it shows examples of (riderless) bicycles that can balance even when one or more of the sources of stability are canceled out. Thus, there are several design features that enable stability -- including the rider.

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Bicycles are inherently stable because of their geometry. The geometry causes the bicycle to always turn into the direction it begins to lean, which keeps it upright. The reason is best illustrated through a concept known as counter-steering.

Counter steering is how all two wheel vehicles turn. When you want to turn towards the left, you turn the handlebars a little to the right. The friction of the wheels pulls the bottom of the bike towards the right, which initiates a lean towards the left. The handle bars then begin to swing towards the left to track through the turn.

When it's time to stop the turn, you turn the handlebars a little more to the left. That pulls the bottom of the bike further towards the left, which brings the bottom of the bike directly under the center of gravity and thus stopping the turn.

On many bikes and at low speeds, the counter steering effect can be unnoticed by many riders. However, at high speeds, or with heavier vehicles such as motor cycles it is more significant.

So, how does this work where there is no rider? It is because of the rake in the fork and the rail it causes. If you trace an imaginary line through the axis of your fork to the ground, it will hit the ground ahead of where the wheel contacts the ground.

Because the wheel contacts the ground behind the steering axis, the wheel will always feel a force from the road trying to bring it to center, pointing straight ahead. When the bike is tipped to one side, the forces begin to push the wheel to the side that the bike is tipped.

So all these forces add up. The rake in the fork makes the bike want to go straight forward. And when it feels a bump in one direction or the other, the counter steering will tend to bring the bike the other direction. Then the fork rake will begin pushing the front wheel further away, which will then straighten the bike out, because of the counter steering.

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Its like balancing a broom on you hand, you steer to move the wheels under you. Bike manufacturers help by designing the steering geometry so that the bike will stay upright on its own, if you don't mess with it.

The gyroscopic forces help but are not essential.

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Great example. I think that your description of "steering to keep the bike under you" is very interesting. – sixtyfootersdude Jul 6 '11 at 14:41

The basic answer without getting too much into the physics is angular momentum. Basically a spinning object (your wheels) exert a force in the opposite direction if you try to "tip" them. To try this at home, take off your front wheel. Hold onto the axle with both hands and spin the wheel. Now try to tip the wheel. Notice how the wheel pulls back. Try the same with the wheel not spinning and notice how it doesn't pull back. The faster the wheel is spinning, the harder it pulls back. I'm not sure if the relationship is linear or not. Take a look here for a more basic look at angular momentum. It shows a video doing a demonstration using a bike tire.

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-1. Gyroscopic forces (which is from angular momentum) have been conclusively shown not to significantly influence bicycle stability. – whatsisname Aug 8 '11 at 15:58

Bike geometry provides some degree of self-stability. The angle and rake of the fork produce a situation where the front tire will tend to turn into a lean, and so correct a tendency to fall to one side.

The gyroscopic effect of the wheels by itself is likely not that strong, but the gyroscopic effect on steering works with the angle/rake of the fork to turn the tire in the direction of the "fall" and provide even more self-stabilization.

In theory rollers are no different from the street -- the front tire will turn towards the direction of lean, either until the edge of the rollers produces a crash or the bike stabilizes.

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+1. A bike's natural ability to stay upright when you "ghost ride" one, or send it off rolling without a rider, is largely due to the rake (or caster) of the front wheel. If it was mounted vertically (your wheel axel was directly below the head tube, and the head tube was vertical) then the bike would fall over fairly easily. This is similar to the caster of a car's front wheels, which helps stability and to center the steering wheel on its own (let go of a car steering wheel in a turn and it comes back toward center) and the dihedral of an aircraft wing which helps it from rolling over. – rally25rs Sep 7 '11 at 19:17

Aided by the characteristics of self-stability, as noted above, the basic reason a bike stays upright while you are riding it is that you are actively balancing by keeping the contact points of the bike under your center of mass. As you are riding, you are making subtle turning motions to keep the bike underneath you - when the bike falls to the left, you turn left, which moves the front wheel and puts the bike back underneath you. On rollers you can see this as the bike moving back and forth across the roller - and when it can't do that, you fall over.

You are able to do this so unconsciously after learning to ride that it's quite a challenge to ride a bike with the steering reversed.

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But then why is it so much harder to balance when the bike is stationary (ie, doing a track stand) than when you are travelling down the road. – Kibbee Jul 6 '11 at 0:03
+1 for the mention of a reversed steering bike. I've tried one just couldn't stay upright. – Mac Jul 6 '11 at 0:05
@Kibbee I think the main difference is how quickly the corrections you make take effect. At speed, a small change in the angle of the front wheel results in the bike changing angle in a very small amount of time. However when travelling slowly, it takes a longer time to change the angle of the bike, and that is time that the bike has to exaggerate it's current lean angle – Mac Jul 6 '11 at 1:11
-1, because physicists have shown (per matthew's answer) that a rider making subtle corrections is not a prerequisite for a bike to self-balance. – Stephen Touset Aug 8 '11 at 16:43
It's not a prerequisite when the bike travels along a free path, but you need it when you want the bike to follow an arbitrary path or overcome an obstacle... – Jahaziel Jan 31 '12 at 0:33

This question was recently the subject of a lengthy article in New Scientist magazine. To summarize:

"Why does this bicycle steer the proper amounts at the proper times to assure self-stability?" the paper asks. "We have found no simple physical explanation."

http://www.newscientist.com/article/mg21028141.700-bike-to-the-drawing-board.html

This article also cites the study that you could not quite place - gyroscopic forces, for so long thought to be the be all and end all of bicycle stability - have been scientifically proven to not be of the consequence popularly imagined.

As for staying upright on a roller, that is not covered by the article, however, it does discuss what happens when you send a bike off down the street with nobody on it - seemingly the weight and steering adjustments made by the rider have nothing to do with it.

I don't think that the New Scientist article is the last word on the subject. However it is recent (a few weeks old) and is a good introduction to the mystery. Enjoy!

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Its funny, the more scientists study something the less they know, they discover more questions than answers. – Moab Jul 5 '11 at 21:40
@ʍǝɥʇɐɯ: except that the study talked about in the article replicates similar work in the 1980's, and there are pictures of equivalent apparatus from the 1930's. So it's more a case of "once again, scientists have re-discovered that an urban legend if false". I wouldn't class it as IG-Nobel quality, but it's nothing like as exciting as they claim. I'm told that using Bill Wassisname's equations on their test bikes gives answers that agree with their experiments, for instance. – Мסž Jul 5 '11 at 21:56
@Мסž - I read the article a few weeks back now and it smelt a bit of 'popular science', but did get me thinking and talking with a cycling neighbour. Personally I believe it to be Jedi 'the Force' (lesser described as the 'fear of the rider experiencing gravel rash') that keeps the bike upright. – ʍǝɥʇɐɯ Jul 5 '11 at 22:48
@ʍǝɥʇɐɯ: what annoys me is that they don't seem to have published their solution (the equations), so I can't compare their results to Bill "Lords of the Chainring" ones, so it's all just fluff. It's not science if you can't reproduce the results. – Мסž Jul 6 '11 at 2:30
New Scientist is certainly NOT a credible source of scientific information. – MarkovCh1 Aug 8 '11 at 16:40

## protected by zenbike♦Apr 17 '12 at 3:50

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