# Why is it possible to ride a bike?

• rogerk8

#### rogerk8

Hi!

I simply wonder how it is possible to ride a bike.

I do not understand why the pure forward motion cancels the mass-centre offset which I think always should be inherent in riding a bike.

With mass-centre offset I mean that looking at the rider vertically it is impossible to keep the mass-centre perfectly aligned with gravity. Which will make you tilt to either side.

But when you are moving, something miraculously obviously happens.

What?

Does it have something to do with mv (=forward momentum?) or, as a collague said, is there some kind of gyro-effect (remember that I have no clue whatsoever of what that gyro-effect might be).

Looking forward to being educated.

Best regards, Roger

One reason a bike is much easier to keep upright when it is moving than when it is stationary comes from the perpendicular axis theorem. https://en.wikipedia.org/wiki/Perpendicular_axis_theorem. Qualitatively, once the wheels of the bike are spinning, their rotational momentum causes the moment of rotational inertia about the "tipping over" axis to increase. [To keep things straight, imagine you're riding a bike like normal and looking forward. The axis the wheels rotate about would be left-right, whereas the "tipping over" axis would run front-back. Hence these are "perpendicular axes" and so the theorem describes what happens.] Thus a greater torque is required to knock you over when your bicycle wheels are rotating. This is basically an example of gyroscopic effects--we should all remember from playing with gyroscope toys and tops that it is much harder to knock them over when they're spinning quickly.

That's just one easy example of why it's plausible, but there are other interesting aspects of bicycles to consider to fully answer this question.

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Hi Jolb!

One gyroscopic effect my colleague and I talked about was something I've seen on TV which was a man sitting on a turnable chair while holding a spinning wheel.

When he hold it straight he just sat there.

But tilting the weel actually made him turn.

I can't understand this effect.

Even though you so kindly have tried to explain.

I will have to look more into the perpendicular axis theorem.

But I kind of got stuck with elementary theories like Newton's three laws which where presented to me by a 35 minutes long and nice video by MIT's Walter Lewin (https://en.wikipedia.org/wiki/Newton's_Laws_of_Motion#Newton.27s_first_law):

1) A moving object which is not affected by accelrations will continue to move in a straight line.
2) F=ma
3) Action equals -reaction (making the sum of forces upon an object equal to zero)

Have I understood this correctly?

Best regards, Roger

The steering geometry of a bike tends to keep the bike veritcal. Most of this is due to "trail", which means the point of contact between the tire and pavement is "behind" the point where the line corresponding to the steering pivot axis intercepts the pavement. If the bike starts to lean, since the point of contact is behind the pivot axis, the downwards force from gravity at the front wheel axis and the upwards force from the pavement generate a torque that causes the front wheel to steer in the direction of the lean, enough to correct the lean and return to vertical, within a range of speeds. ... the greater the amount of trail, the slower the minimum speed at which self-correction to vertical occurs.

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The steering geometry of a bike tends to keep the bike veritcal. Most of this is due to "trail", which means the point of contact between the tire and pavement is "behind" the point where the line corresponding to the steering pivot axis intercepts the pavement. If the bike starts to lean, since the point of contact is behind the pivot axis, the downwards force from gravity at the front wheel axis and the upwards force from the pavement generate a torque that causes the front wheel to steer in the direction of the lean, enough to correct the lean and return to vertical, within a range of speeds. ... the greater the amount of trail, the slower the minimum speed at which self-correction to vertical occurs.

I always thought it was the gyro effect of the wheels, and that never intuitively seemed adequate. That description really hit the spot! leaning generates torque tending to steer you into the lean.

I always thought it was the gyro effect of the wheels, and that never intuitively seemed adequate. That description really hit the spot! leaning generates torque tending to steer you into the lean.

That explanation about the torque and the steering axis only describes why the steering bar is stable. It has nothing to do with why the bike stays upright. You could also build a bike without a steering bar or axis. Just a stiff frame with two wheels. It would still work. Even with only one wheel a bike can still balance itself.

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That explanation about the torque and the steering axis only describes why the steering bar is stable. It has nothing to do with why the bike stays upright.
Not nothing. The gyroscopic torque steers the wheel into the lean, stabilizing the bike. But it can be stable without this, because there are other stabilizing effects. See this thread

Hi folks!

The answer to this trivial question seems to be harder than I expected.

But I think I now got some kind of knowledge regarding this.

The picture in https://en.wikipedia.org/wiki/Angular_momentum says a bit.

I tend to try to simplify stuff.

And seeing that picture made me think of momentum in the case where you have a simple lever and a length of that lever yielding a momentum/torque eual to the length of lever times the force.

And in case of the spinning wheel we have both mass, radius/length and force to start the spin.

The spinning wheel will have an moment of inertia (I) proportional to its mass.

You will therefore have to put in some energy to actually make the spinning wheel spinn.

And once it spins it will stabilise and not stop until the friction has used up all the rotational energy perhaps called angular momentum (?, L=I*w)

I wonder if this angular momentum can be so large that it somehow generates an "effective mass radius" of zero?

Because the above does not explain why the spinning wheel does not lean/fall while L is along the z-axis.

In the same time, a bicycle wheel isn't really that heavy...

Best regards, Roger
PS
It now strikes me that the centrifugal force of the spinning wheel will tend to point in all r-directions, so to speak. This pulls on the spinning wheel r-wise. And as long as the pull is large, the spinning wheel will stay upright (?)

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In the same time, a bicycle weel isn't really that heavy...
No, and doesn't have to be. See post #8.

I suggest people check out this paper:

P.A. Cleary and P. Mohazzabi, Eur. J. Phys. v.32, p.1293 (2011).

In particular, check out this passage in that paper:

Riding a bicycle on rollers is unique because of the absence of the forward inertia which aids in bicycle handling for stability, instead of isolating and restricting the degrees of freedom in handling. Adopting one’s riding style to ride on rollers is quite difficult, with many avid cyclists falling off their bicycles on the first few attempts. Given that all riders struggle somewhat with the apparatus, but some more than others, the degree of struggle to ride on rollers may also indicate how different riders rely on specific factors for bicycle stability, which has not been addressed in many studies up to now. We use the example of riding bicycles on rollers as a test case on the individual factors that lead to bicycle stability.

Zz.

rogerk8, angular momentum and gyroscopic motion are notoriously counter-intuitive concepts in mechanics. I think that the wonderment children get from watching tops spin upright until suddenly beginning to precess with widening opening angle as the rotation slows is evidence that this is actually a very novel and unexpected aspect of the world around us. Similar rotational motion problems, like the Coriolis force and its effect on Foucault pendula are quite counterintuitive and have amazed people for generations.

The interesting effects that the other posters have added to mine are all true and show the great complexity in "simple" engineering. But the example I gave is, I believe, a good place to begin to understand gyroscopic effects.

Take another example: for a space telescope, like the Hubble, to get a good picture of a distant object, it needs to point directly at that object and remain very stable for a long time. But there is no "ground" beneath it to hold onto! Wind of space dust or collisions with little meteorites would start it spinning unless there were some "rotational inertia" to resist being sent into rotation.

The way engineers solved this was by putting a big gyroscope (actually a few gyroscopes) in each space telescope! Once spinning, these gyroscopes make the satellites more stable because they increase the amount of torque needed to throw the satellite off its target. Check out: http://www.spacetelescope.org/about/general/gyroscopes/ Airplanes and helicopters also contain a "flywheel" for gyroscopic reasons.

Once a torque is applied to a body with a gyroscope in it, the body reacts in interesting ways--you mentioned how a man sitting on a rotating chair will begin to spin if he tries to tip over a rotating wheel. To see how all this works, you need to do math. It is counterintuitive. This sort of effect is related to the other ones mentioned above--such as how leaning a bicycle puts a torque on the front wheel which steers you into the lean, placing you back over your center of gravity. But my example is the most basic, I believe. [It's actually exactly the example they use on the website I linked: "Gyroscopes maintain orientation and provide stability in boats, aircraft and spacecraft based on the principles of angular momentum. You can experience this effect by holding a bicycle wheel by its axle and asking someone to spin the wheel. If you try to move the axle of the spinning wheel, you will feel a force opposing your attempt to move it."]

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gyroscopic effects
One issue being ignored with the "gyro effects" theory, is that once a leaned bike starts to roll back to vertical, that same "gyro effect" steers the front wheel outwards preventing recovery to vertical. The other issue is that gyro effect, if it works at all, would only work at a specific speed, and would only provide a near term tendency to hold a lean angle, as opposed to tending towards a vertical orientation over the long term which is what trail does (within a range of speeds). At very high speeds, even with trail, due to gyro effect, instead of recovering to vertical, a bike tends to hold a lean angle or to fall inwards at a very slow rate (high speed capsize mode).

In the thread linked to in A.T.'s post, the university was able to make a self stable bike with a weight mounted above and in front of the bike on an extended rod in order to cause the front wheel to steer inwards in response to lean without using trail or castor effect. Gyro effect wouldn't be needed either.

I suggest people check out this paper: ... rollers ...
I suspect that the rollers interfere with trail effect, and probably result in a non-self stable bike or at least reduce the range of speed for self-stability. Also, in the case of a treadmill or rollers, in addition to maintaining a vertical orientation (which trail does), the direction also has to be maintained (which trail does not do).

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One issue being ignored with the "gyro effects" theory, is that once a leaned bike starts to roll back to vertical, that same "gyro effect" steers the front wheel outwards preventing recovery to vertical.
As the lean reduces, the gyro torque straightens the steering again. That doesn't necessarily prevent recovery to vertical. It prevents leaning to the other side.

The other issue is that gyro effect, if it works at all, would only work at a specific speed,
It would work optimally at a specific speed. But it doesn't have to work optimally with other mechanisms acting too. It could contribute to stability over a certain speed range.

Hmm, maybe there is a nugget of truth to the idea that gyroscopic forces have nothing to do with balancing a bike. Maybe I have been making a huge mistake!

I guess it is true that the linear motion and steering has a lot to do with balancing on things with small/insignificant wheels (like a scooter) or, say, ice skating on a single ice skate, maybe even water skiing on one ski. So maybe I am totally wrong! Anyway, gyroscopic forces are cool :tongue2:

I would say, however, that you do notice increases in how a bike feels stability-wise that you can't attribute to only steering effects. Even if you are accelerating in a straight line starting from a speed that is more than adequate for steering, you feel an increase in how rigidly upright the bike feels [i.e., against small perturbations.] I guess this is evidenced by the fact that the riders on rollers actually can balance when "riding".

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One issue being ignored with the "gyro effects" theory, is that once a leaned bike starts to roll back to vertical, that same "gyro effect" steers the front wheel outwards preventing recovery to vertical.

As the lean reduces, the gyro torque straightens the steering again. That doesn't necessarily prevent recovery to vertical. It prevents leaning to the other side.
The rate of precession is tied into the rate of roll (and speed of the bike). The response to the rate of roll is the same for increasing or decreasing lean. Take the case of a riderless bike with zero trail that is initially launched with a lean angle. The gyro effects (without any other corrective mechanism) would tend to hold that lean angle over the short term.

The other issue is that gyro effect, if it works at all, would only work at a specific speed ...

It would work optimally at a specific speed. But it doesn't have to work optimally with other mechanisms acting too.
I meant the case where only gyro effects were involved and no other mechanisms were involved such as trail.

No, and doesn't have to be. See post #8.

Thanks A.T!

I saw that video and it fascinated me.

They took away both the gyroscopic and the trail-effect with an experimental bike.

And yet it could balance itself!

But what does he say in the end regarding that one necessary condition for bycycle stability is that "such a bicycle should turn into a "fall"?

Best regards, Roger

But what does he say in the end regarding that one necessary condition for bycycle stability is that "such a bicycle should turn into a "fall"?
What he meant is if the bicycle "falls" over to one side (leans), then the front tire needs to turn into the direction of the "fall" so that the resulting steering effect from the front tire corrects the fall and returns the bike to a vertical orientation.

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The gyro effects (without any other corrective mechanism) would tend to hold that lean angle over the short term.

Doesn't a single rolling wheel have this kind of stability?
Yes (assuming a round tread surface, and within a given range of speeds and while on a horizontal surface, and perhaps other factors, I'm not sure of all the requirements), but a bicycle is a different case.

For a bike, the gyroscopic related steering inputs are a reaction to the rate of roll (rate of change in lean angle), but what is needed for vertical stability is a reaction to the lean angle (as opposed to the rate of change in lean angle), and that is what trail provides.

what is needed for vertical stability is a reaction to the lean angle (as opposed to the rate of change in lean angle)
An input that depends only on the current deviation results in oscillation around zero, due to inertia. A more effective stabilizing input depends on both: current deviation and its first derivative.

An input that depends only on the current deviation results in oscillation around zero, due to inertia. A more effective stabilizing input depends on both: current deviation and its first derivative.
There is some resistance to steering in the pivot axis bearings and at the contact patch, which provides some dampening of the motion. Gyroscopic reactions also dampen steering motion above some minimal speed. Trail also translates into a caster, but I'm not sure of the overall effect. Speed wobble, which is an oscillation as mentioned, can occur depending on the bike and the speed. The usual cure for speed wobble on motorcycles is to increase the trail and/or dampen steering motion using shocks.