# Why do we lose balance in a bike when at a standstill?

sophiecentaur
Gold Member
It doesn't. It just says that there is more to it, and that there are others ways to achieve self stability.

Sounds like you simply don't understand the "gyro theory" here. The precession is not supposed to bring the bike upright directly, it merely turns the front wheel into the direction in which the wheel falls over.
But, once the bike starts to lift and right itself, won't that change the couple on the wheel so it steers out? I am confused.

A.T.
But, once the bike starts to lift and right itself, won't that change the couple on the wheel so it steers out?
At the moment when the bike starts to right itself the steering is turned into the lean. So before it steers out, it has to get straight first. While the leaned bike lifts itself towards vertical, the gyro effect works to straighten the steering back to straight ahead.

The gyro theory makes sense qualitatively, and plays some role in normal bikes. But it is not the whole story, and is not necessary to achieve self-stability.

sophiecentaur
Gold Member
I see your explanation but is there not the possibility of instability as the sign of the gyro moment could take the bike wildly past the upright position before the original direction of travel is reached.
Incidentally. You had to put me right about the true gyro effect. I bet I wasn't the only one!!

A.T.
I see your explanation but is there not the possibility of instability as the sign of the gyro moment could take the bike wildly past the upright position before the original direction of travel is reached.
Yes it possible if the bike is too fast. That is true for all those different effects. There is only a certain range of velocities, at which a bike is self stable. Check out the plot at 14:00 in this lecture:
http://techtv.mit.edu/collections/l...cle-smarts-stability-translation-and-rotation

The self-stable range for typical unmaned bike is 4-6 m/s according to this plot.

ETA: There are similar plots in the document linked by rcgldr:

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rcgldr
Homework Helper
I see your explanation but is there not the possibility of instability as the sign of the gyro moment could take the bike wildly past the upright position before the original direction of travel is reached.
Even if the bike is returned to vertical, the direction is usually changed.

There is only a certain range of velocities, at which a bike is self stable. Check out the plot at 14:00 in this lecture: The self-stable range for typical unmaned bike is 4-6 m/s according to this plot. There are similar plots in the document linked by rcgldr:

However as noted in my previous post although the plot showed a stability range with an upper limit below 8 m/s or 28.8 kph, where at faster speeds, there should be undercorrection with the bike falling inwards (capsize), the actual treadmill tests for the same bicycle showed it to be "very stable" at 30 kph.

http://www.tudelft.nl/live/pagina.jsp?id=0cc5c910-a1ee-40a8-92cb-bf4a2ac54bd0&lang=en [Broken]

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A.T.
However as noted in my previous post although the plot showed a stability range with an upper limit below 8 m/s or 28.8 kph, where at faster speeds, there should be undercorrection with the bike falling inwards (capsize), the actual treadmill tests for the same bicycle showed it to be "very stable" at 30 kph.

http://www.tudelft.nl/live/pagina.jsp?id=0cc5c910-a1ee-40a8-92cb-bf4a2ac54bd0&lang=en [Broken]
I assume 30km/h is the max speed for their treadmill. And when you push it above 30km/h on the ground, then it slows down due to drag. The capsize mode in the plot gets positive at fast speed but stays pretty close to zero. So it is not very unstable there and a small inaccuracy in the model could shift the upper range significantly. But on the video it is indeed very stable and not just semi stable.

Physics might need yet another 100 years to fully understand... a bicycle. :-)

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rcgldr
Homework Helper
But on the video it is indeed very stable and not just semi stable.
I was thinking that since the tires are not infinitely thin, the contact patch moves to the same side as the lean, which would create a small corrective torque. With the relatively thin tires used on the test bike, I'm now thinking it's unlikely that small amount of corrective torque would explain the difference between reality and a mathematical model, even if that model assumed infinitely thin tires. I'm also wondering how much effect camber thrust has in terms of self stability, and if that was included in the mathematical model.

I wonder about the capsize effect (slowly falling inwards) at higher speed since I've never witnessed this or seen any videos of this, although it's predicted by the mathematical model. I do know that motorcycles at high speeds (100+ mph, 160+ kph), tend to hold a lean angle as opposed to changing lean angle inwards or outwards, but this could be due to a rate of change of lean angle that is so small that it's imperceptible in a normal situation (race track).

Getting back to basics, it seems that trail is a key factor for stability. Too little trail and the minimum speed for self stability is increased and at high speeds there's an increased speed wiggle (not quite a full wobble) issue. Increasing trail seems to increase the range of stability rather than just shift the range upwards or downwards.

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A.T.
Increasing trail seems to increase the range of stability rather than just shift the range upwards or downwards.
But why is the front wheel fork often bend forward at the lower ends? This seems to be done in order to prevent too much trail.

rcgldr
Homework Helper
But why is the front wheel fork often bend forward at the lower ends? This seems to be done in order to prevent too much trail.
It reduces steering effort, and also allows the forks to flex, acting a bit like a suspension. On motorcycles, the two triple clamps that hold the front forks also locate them forward, which reduces trail. For the early Honda 900RR's, they moved them a bit too far forwards, resulting in some speed "wiggle" at high speeds, especially when used for racing, and it was common to replace the clamps to move the forks back a bit. Eventually Honda changed the triple clamps to move them 3/8 inch back, similar to the replacement kits used by racers.

Hi:

Andy Ruina here. I am the fat bald bearded guy with a lisp in the 7 minute video that A.T. posted.

A. Reading the whole discussion here I think one gets a sense of a consensus that I agree with.

1) Bicycles are balanced by steering.
2) Moving bicycles can balance themselves.
3) Gyroscopic torques contribute to this self-steering for balance,
so do trail (castor) effects.
4) There are other effects that contribute
5) Our (Delft+Cornell) TMS bike and related calculations show that gyroscopic and trail effects are not necessary for bike balance.

B. In the video of me gabbing and gasping away I say one word wrong. In the video I incorrectly say "our calculations showed that trail and gyro terms were not important". I meant to say "were not necessary". They are important.

C. I would like to think that the much of the text in our various papers, just glaze over the math if that's not your thing, is readable by people who read this forum. You could start by looking at the photos and videos on these pages and then lightly read the various papers:
http://ruina.tam.cornell.edu/research/topics/bicycle_mechanics/stablebicycle/. In our papers we pretty thoroughly review most all other papers on this topic.

D. One misconception in posts here, which I have seen on other forums: Opposite spinning gyros that are linked together (like the wheels on our TMS bike) do in fact cancel. The stiffness from spinning doesn't add, it cancels. Angular momentum is a vector. So when you have two opposite angular momenta stuck together they add to zero. It's not like red mass and blue mass make more colored mass. It's like going North and going South is going nowhere.

The main reason is that when you are moving, steering allows you to move your point of support around. In particular, you need to keep the support vertically in line with your centre of gravity. When you are stopped, you can no longer do this. It's like standing on one foot. If you are not allowed to hop, and you start falling sideways, you cannot recover. But if you can hop to relocate the foot with respect to the c.of.g, you will recover balance.
Krab’s explanation is correct. The scenario is akin to balancing an upside down broom in one’s hand; so long as you can move your hand around as required, the broom can remain in an essentially balanced upright state. Likewise when steering the bicycle, even at low speeds, steering allows redirection of the bicycle to allow balancing corrections. Zero bicycle velocity fails to provide an means to correct the bicycle's balance.

haruspex
Homework Helper
Gold Member
The question of what makes a bike rideable has been properly researched at least twice - once in Loughborough, UK, back in the 60s, and again independently (apparently in ignorance of the earlier work) in the US a year or so back.
For each theory, the investigators built a bicycle which lacked the theoretically key element (e.g. contrarotating wheel to cancel any gyroscopic effect).

Result: gyroscopic effects are useful, but the critical item is the steering geometry.
If you take a line down through the steering column to where it hits the road, you'll see it is in front of the point of contact of tyre with road. As a result, if the bicycle leans to the left the front wheel turns to the left. You can observe this with a stationary bike, though of course it doesn't help you stay upright unless moving forward.
This is why bicycles with small wheels are still rideable.
The gyroscopic effect does the same, but not as strongly in standard designs.

rcgldr
Homework Helper
5) Our (Delft+Cornell) TMS bike and related calculations show that gyroscopic and trail effects are not necessary for bike balance.
True, but the TMS bike located some mass in front of and above the front wheel to produce an effect similar to trail.

Still wondering why the mathematical model for the Delft bicycle predicted capsize (near neutral stability) speed at 8 m/s when the actual bike being modeled ended up being "very stable" at 8.33 m/s (30 kph).

http://home.tudelft.nl/index.php?id=13322&L=1 [Broken]

link to pdf file with diagram showing capsize (near neutral stability just above 0) speed at 8 m/s or higher, figure 1.3 on page 4:

video is the last one on the page, the 30kph run.
http://bicycle.tudelft.nl/schwab/Bicycle/index.htm

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True, but the TMS bike located some mass in front of and above the front wheel to produce an effect similar to trail.

Still wondering why the mathematical model for the Delft bicycle predicted capsize (near neutral stability) speed at 8 m/s when the actual bike being modeled ended up being "very stable" at 8.33 m/s (30 kph).
Hi,

Arend Schwab one of the co-authors of the Science paper and PhD adviser to Jodi Kooijman here.

The oscillatory weave mode is very stable, which is clearly visible in the video where we see the lateral oscillation die out quickly. The capsize mode (falling over like a ship with no steering involved) is very mildly unstable, an eigenvalue of say +0.1, then for things to double it takes a long time, exp(0.1*T)=2 so aprox T=7 seconds, which is a long time indeed and that is why you don't see this capsize happen in the video. Due to the change in heading after the lateral perturbation, it would have rolled of the treadmill by then anyway.

Arend Schwab

rcgldr
Homework Helper
The capsize mode (falling over like a ship with no steering involved) is very mildly unstable, an eigenvalue of say +0.1, then for things to double it takes a long time, exp(0.1*T)=2 so aprox T=7 seconds, which is a long time indeed and that is why you don't see this capsize happen in the video. Due to the change in heading after the lateral perturbation, it would have rolled of the treadmill by then anyway.
OK, but in the video at 30 kph (8.33 m/s), the bike quickly returns to vertical after being disturbed (the direction changes, but that heppens even when in stable mode due to the distrubance).

I'm thinking that once in capsize mode, the bike would tend to hold the lean angle induced by the disturbance unless the trail / caster effect is still dominant when the bike is disturbed in that manner (tapping the bike sideways just behind the seat).

For motorcyles at sufficient speed, they tend to hold a lean angle as opposed to tending to straighten up. This could be a very mildly unstable capsise mode, one where the time for the bike to fall inwards is so long that it's not perceptible to the rider. The width of the front tire profile could be producing just enough outwards torque when leaned (contact patch on side of tire) to counter the slight inwards torque of capsize mode to prevent a motorcycle from falling inwards.

haruspex
Homework Helper
Gold Member
The question of what makes a bike rideable has been properly researched at least twice - once in Loughborough, UK, back in the 60s, and again independently (apparently in ignorance of the earlier work) in the US a year or so back.
I have been justly taken to task by Andy Ruina of the Cornell team for suggesting they were unaware of the earlier work in the UK. Andy suggests I'm thinking of DEH Jones around 1970 at Imperial, London; possibly, though I recall it as a team at Loughborough ca. 1965.
More importantly, the Cornell work takes matters further than Jones did, finding that the whole answer is rather more complex.
My sincere apologies to Andy.