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

[rcgldr]

which is mostly correct when learning to ride a bicycle, since when learning, you are initially at a very slow speed. But to proclaim this and use it to sell training videos... people try to make money off anything these days. Myself and my kids learned very efficiently, with no videos (and no training wheels).

Someone else posted a link to the article. I don't think anyone was suggesting buying a video. Somehow we've managed to learn how to ride bikes without any videos for many years. Part of my point is that bicycles self-correct once they're going anything faster than a slow walk.

 

[mathlete]

Can someone explain what exactly the gyroscopic action is?

 

[rcgldr]

Can someone explain what exactly the gyroscopic action is?

When a torque force is applied to a rotating mass, the reaction is along an axis perpendicular to the torque force.

Using a helicopter as example, there's a cyclic control that changed the pitch of the blades as they travel around in a circle. If the cyclic is tilted forwards, creating a pitch down torque force, the helicopter instead responds with a roll towards the rearward rotating blades. If the cyclic is tilted sideways towards the forward rotating blades, the helicopter pitches down.

To keep the pilot from getting confused, the cyclic control is shifted 90 degrees to compensate for this, so the pilot can just push forwards to pitch downwards.

 

[Chi Meson]

If you have ever ridden a bike on rollers, you will find out how very little help "conservation of angular momentum" will be for balance.

As opposed to stationary trainers, rollers are thin barrels that the wheels sit on. The rear wheel spins normally, which turns the rear roller, which is attached to a long band which turns the front roller which turns the front wheel. There is just as much angular momentum as when on the road. The wheels are not kept in place "side-to side" and consequently, a novice bicyclist will fall repeatedly, no matter how fast the wheels are spinning.

The reason why rollers are more difficult than actually riding, is you just can't lean! Leaning will turn the front wheel which will send you 10 inches to the side and off you go!

So angular momentum does connect the lean with the turn of the front wheel, but it does nearly nothing to keep us "gyroscopically" upright.
(Basically, everything Krab has said is Bang on.)

 

[Tullebukk]

The gyroscopic effect is important; it allows one to affect a bike's lean by applying steering force. But it is not the effect that explains why it is possible to balance while moving and practically impossible when stationary. There are in fact 3 phases: 1. When stationary, it is hard to balance; 2. When moving too slowly for gyro effects to matter (below a fast walking pace), you tend to meander around while balancing; 3. When moving above a walking pace, it's easy to balance with hardly any meander, one can also ride with no hands.

Experiments have been done where the gyro effect is canceled by a counter-rotating wheel. It is still possible to ride such a bike.

Another question: let's say we only have a bicycle wheel, a dinner plate or another circular object. If we roll this object pretty slow down the floor, it will very well hold balance. What is the main reason for this? The gyroscopic effect?

 

[rcgldr]

Another question: let's say we only have a bicycle wheel, a dinner plate or another circular object. If we roll this object pretty slow down the floor, it will very well hold balance. What is the main reason for this? The gyroscopic effect?

It doesn't hold balance for very long. Gyroscopic forces will reduce the rate of lean, but a wheel will lean over until camber thrust counteracts the leaning torque due to gravity pulling downwards at the center of mass, and the upwards force at the contact patch, or until the wheel slips and falls.

I don't know if I mentioned this before, but I can balance a 10 speed for about 10 to 30 seconds without moving. This is because steering the front tire translates the contact patch sideways. Steer left, and the contact patch move right if not resisted. With the front tire on the ground, the contact patch doesn't slide much, so steering left moves the front end left. It's enough movement to balance a bike, but it's difficult. Velodrome racers can remain still for very long times, as this is part of the tactic used to try and get the other racer(s) ahead for those racers that want to start from behind (draft).

 

[boit]

Let me throw in a controversial twist to this discussion. Someone pointed out that gyroscopic effects plays no part in bicycle's balancing and threw in the counter rotating added wheels argument to back it up. Someone disagreed with him and said if anything the gyroscopic stability will increase. The first guy insisted that angular momentum is a vector hence this cancels out blah blah blah (they lost me somewhere. I agree with whoever say gyroscopic stability will improve, intuitively though cause my phyisic background is wanting. Now to the twist and this is helped by a chap who said motion in itself yield stability and called to meind ice skaters among other wheel-less locomotion.
Mine is simple. Riding a bike a structured perpetual falling to a particular direction much like a satellite in orbit. Take a flag pole and stand it on a flat surface. It is highly unstable (an inveted pendulam-like) Now tip it to fall to one direction. It is extremely had now to make it fall to any other direction. Left to its own divices it will hit at an exact spot. Slowing a bicycle to a stop is analogous to standing the flag pole on its foot again. how about that for food for thought?

 

[sophiecentaur]

I can't find any comments in this thread, about the effect of castor action and the fact that a line through the top bracket (the steering axis) on all stable bikes, when produced, always meets the ground ahead of the tyre footprint. This will always cause the wheel to steer into a lean. The result, when traveling forward, will be to produce a force on the ground, 'inwards' and a corresponding moment to turn the bike upright. The faster the bike is travelling, the more this effect will be.

Whilst the gyroscopic effect may be significant on morotbikes, it will be very small on light wheeled bikes - particularly with small diameter wheels, whereas the castor effect only depends on the distance between footprint and the forward produced line of the steering axis on the ground. Folding and 'delivery' bikes have very small front wheels but are still stable. It even works on kids' scooters with plastic wheels of less than 10cm diameter where angular momentum is extremely small.
There is more to this than just one mechanism at work, I'm sure.

 

[rcgldr]

I can't find any comments in this thread, about the effect of castor action.

Both Krab and I mention this effect (trail), starting with post 21 in this thread.

 

[A.T.]

gyroscopic effect ... castor effect ...

There is more to this than just one mechanism at work, I'm sure.

There is more indeed. Guys from the TU Delft build a "bike" that eliminates the gyroscopic effect and the castor effect... and it still balances itself:

 

[sophiecentaur]

That link is good and very inventive in its thesis. (I wonder how many takes they did to get that bike to stay up so well) At least it puts to bed the gyro theory, which applies to very few cases and which, I think only applies a damping / reactive force rather than a restoring force. If the gyro action were actually to bring the bike upright, would not the force be downwards again - by the same precession argument- as the rotation would then be the other way? Once a bike has leant into the curve, after the (truly) restoring couple is there until it is actually upright again.
"Turning into a fall" is a very good way of putting things; both "trail" and castor action, will achieve this. Their model has this forward pointing rod, which achieves the same thing. BUT how many of the bicycles we see on the road are loaded that way?

They do not dismiss trail as a mechanism so they are not disagreeing with my contention that it is due to trail on 'real bikes'. They just achieve the 'leaning in' by a different mechanism.
Funny thing is that I tried a 'butcher's delivery' bike, once. That had a large load out over the small front wheel. It was a real mother to ride.

 

[rcgldr]

Guys from the TU Delft build a "bike" that eliminates the gyroscopic effect and the castor effect... and it still balances itself.

As explained in that video, the front wheel was weighted to produce the equivalent of trail effect, using weight distribution to cause the front end to "fall inwards" more than the bike. I would have liked to see a true "2 skate bicycle" being tested on a ice rink, to show gyroscopic forces are not required.

TU Delft also ran into a conflict between their math and their testing of an actual bicycle regarding capsize speed, I don't know if they've since resolved the issue. Link to link to article, showing image of bicycle:

http://www.tudelft.nl/live/pagina.jsp?id=95c52a8b-37c2-4136-ad98-97aea768d9b7&lang=en&binary=/doc/Koo06.pdf

page 4 of this article includes a graph where the upper limit of the "stable" range is just below 8 m/s = 28.8 kph:

http://home.tudelft.nl/fileadmin/UD/MenC/Support/Internet/TU_Website/TU_Delft_portal/Onderzoek/Wetenschapsprojecten/Bicycle_Research/Dynamics_and_Stability/doc/Koo06.pdf

link to treadmill video where 30 kph is described as "very stable", even though it's greater than the 28.8 kph end of the "stable" speed range from the graph in the artitcle linked to above. My guess is this is due to the fact that the tires are not infinitely thin disk, and when leaned, the fact that the contact patch is on the side of the tire results in a outwards torque that keeps the bike from falling inwards as predicted by the capsize speed shown in the graph.

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

 

[sophiecentaur]

Is there any more need to 'prove' that gyro forces are irrelevant?

 

[A.T.]

At least it puts to bed the gyro theory,

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

If the gyro action were actually to bring the bike upright, would not the force be downwards again - by the same precession argument-

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.

Here a more complete explanation of the different theories:

"Turning into a fall" is a very good way of putting things; both "trail" and castor action, will achieve this.

So will the gyro effect. But what is the difference between "trail" and "castor action" again?

They do not dismiss trail as a mechanism so they are not disagreeing with my contention that it is due to trail on 'real bikes'.

On real bikes the gyro effect also plays a role.

 

[rcgldr]

"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.

From what I recall, although precession turns the front tire in the direction of lean, at some speeds, the precession effect produces insufficient turn into correct the lean, so trail is needed as well. Trail alone without gyroscopic effect can be enough to correct a lean angle.

What is the difference between "trail" and "castor action" again?

Trail is the distance from where the pivot axis intercepts the ground back to the contact point between wheel and ground. Trail is normally used to refer to what happens when you lean a castored wheel (the wheel turns in the direction of the lean). Normally castor effect refers to the tendency of a vertical castored wheel to pivot away from the direction of motion so it lines up the wheel with the direction of travel.

 

[sophiecentaur]

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]

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:
http://home.tudelft.nl/fileadmin/UD/MenC/Support/Internet/TU_Website/TU_Delft_portal/Onderzoek/Wetenschapsprojecten/Bicycle_Research/Dynamics_and_Stability/doc/Koo06.pdf

 

[rcgldr]

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:

http://home.tudelft.nl/fileadmin/UD/MenC/Support/Internet/TU_Website/TU_Delft_portal/Onderzoek/Wetenschapsprojecten/Bicycle_Research/Dynamics_and_Stability/doc/Koo06.pdf

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

 

[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

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. :-)

 

[rcgldr]

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.

 

[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]

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.

 

[AndyRuina]

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.

 

[Gnosis]

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]

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]

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).

links to articles:
http://home.tudelft.nl/index.php?id=13322&L=1

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:
http://home.tudelft.nl/fileadmin/UD/MenC/Support/Internet/TU_Website/TU_Delft_portal/Onderzoek/Wetenschapsprojecten/Bicycle_Research/Dynamics_and_Stability/doc/Koo06.pdf

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

 

[arendschwab]

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]

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]

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.

 

[danmay]

I think the bicycle stability article (Physics Today 1970) by David E.H. Jones has summed up most of this issue. It was posted by another user earlier in this thread, but I can't seem to find it now going back. So here are the links to the same article:

http://www.phys.lsu.edu/faculty/gonzalez/Teaching/Phys7221/vol59no9p51_56.pdf and http://socrates.berkeley.edu/~fajans/Teaching/MoreBikeFiles/JonesBikeBW.pdf.