We dont know how a bicycle works Really?

[rcgldr]

The only dissension here is whether gyroscopic reactions help or hurt self-stability (defined as a tendency to return to a vertical orientation).

A better definition of self-stability is "a tendency to return to a vertical orientation, an stay there, not oscillate around it." That is the point of "damping", or the derivative term in control theory: preventing over-correction and oscillation around the optimum.

My concern is that gryoscopic reactions are sometimes described as correcting factors as opposed to dampening factors.

The caster aspect of trail is a dampening factor, and increasing trail can reduce or eliminate speed wobble. In the case of motorcycles, this was done on the Honda CBR900RR (1990's) which increased trail by reducing the triple clamp offset used on the early versions of that bike, initially an aftermarke part before Honda made the same change in later versions. Early radio control motorcycles used a lot of trail (like fork tubes located behind the pivot axis), but the newer ones rely more on gyros and/or active control.

Other dampening methods called steering dampers are used on some motorcycles. These can be friction oriented, small shocks linked to frame and triple clamp, or electronically controlled.

The test bikes made with counter rotating wheels don't seem to have an oscillation problem with self stability, but the test speeds may not have been fast enough to result in speed wobble.

I'd like to see an actual two skate bike gliding on ice to show that gryoscopic reactions are not required for correcting or dampening lean angle.

Speed wobble can also be caused by too much flex in the frame and/or swing arm. I don't know if trail and/or steering dampers can compensate for this.

 

[A.T.]

My concern is that gryoscopic reactions are sometimes described as correcting factors as opposed to dampening factors.

If you think that the two are mutually exclusive, then maybe the term "damping" is misleading here. Its better to see the derivative correction as a predictive correction. It's based not on the current error, but the projected error, based on it's current change.

 

[rcgldr]

My concern is that gryoscopic reactions are sometimes described as correcting factors as opposed to dampening factors.

If you think that the two are mutually exclusive, then maybe the term "damping" is misleading here.

My point is the potential misconception that gyroscopic reactions alone (without any trail or other corrective steering geometry) would result in a self stable (one that tends towards a vertical orientation) bike. In order to correct a lean, the front tire must be steered inwards enough to produce an outwards roll torque, which gyroscopic reaction alone will not do.

However trail without gyroscopic reaction can result in a self stable bike without oscillation if the caster effect related to trail is large enough (within a range of speeds). In the Delft test bike without gyro or trail effects, I'm not sure what prevents oscillation. The front steering assembly has weights attached to the sides, but I'm not sure if this is used to dampen the reaction. Friction in the steering bearing could be sufficient to dampen oscillation.

 

[Wes Tausend]

If you think that the two are mutually exclusive, then maybe the term "damping" is misleading here. Its better to see the derivative correction as a predictive correction. It's based not on the current error, but the projected error, based on it's current change.

I agree, "predictive" is better word. Damping can only slow a process, not correct it.

I also agree with , rcgldr when he said in post #34, "...that the gyroscopic reaction is always opposing the corrective action..." . There are times when the wheel must automatically freely self-turn to drive back under the bike's own center of gravity, and gyroscopic forces could only be detrimental.

I believe David E.H. Jones nailed the primary self-stability principle on page four (mid-right column) of his pdf (given us earlier in post #15 by jedishrfu - thank you).
Jones said:
"Why does steering geometry matter? One obvious effect is seen by wheeling a bicycle along, holding it only by the saddle. It is easy to steer the machine by tilting the frame , when the front wheel automatically steers into the lean. This is not a gyroscope effect, because it occurs even if the bike is stationary. A little study shows that it occurs because the center of gravity of a tilted bicycle can fall if the wheel twists out of line. So here was a new theory of bicycle stability--the steering is so angled that as the bike leans, the front wheel steers into the lean to minimise the machine's gravitational potential energy. To check this theory I had to examine the implications of steering geometry very seriously indeed."

So basically, because of castor (steering-head) angle and subsequent trail, the weight of the bike geometrically seeks to settle to a lower gravitational level which is found by the wheel self-turning (allowing frame falling) whenever the bike tilts. This self-evident observation is consistant with the wheel self-turning whenever we may place a stationary bike on it's side-kickstand, whereby the bike leans onto the stand and the wheel prefers to turn into the lean. This self-turn is also designed to be the correct direction the falling bike must take to cause a corrective, uprighting force when rolling. As the bike then "uprights", the self-steering event tapers to naught and the rotating frame only overshoots if the uprighting momentum is too great. In this case the same self-correction events tip it back upright from an alternate lean. The well designed bike may exhibit a momentary diminishing wobble as it thus oscillates, but soon recovers to a smooth roll.

Intuitively, I think the speed (distance per time) of forward bike motion with which the events unfold successfully with a particular geometry depend on the distance per time of gravity. IOW, the bike-spec ideal speed range would change with gravity or inertia. This entire principle could account for high speed motorbike wobble, sometimes appearing during acceleration or deceleration. Of course the easiest fix is a friction damper or geometry change. But even then, during increased centrifigal forces against a dirt berm or banked track, wobble could still suddenly rear it's ugly head under additonal inertial "gravity".

Since this all involves suspension science, I believe there is another way to look at the situation. The ideal chosen geometry when moving, seems to project a virtual center of gravity significantly higher than the bikes actual stationary center of gravity. Thus the rolling bike acts as though it is guided by a tightrope strung somewhere above it. If the seat were to be removed and a vertical pole mounted in it's place, one could theoretically attach a laser pointer to said pole, aiming straight ahead parallel with the frame. In spite of minor bike directional disturbances, the point of light should continue to subscribe within a limited circle on a building directly ahead of the direction of travel. One might be able to more simply imagine this by observing a riderless bike seemingly attempting to swing from such an invisible overhead guiderope.

Wes
...

 

[DaveC426913]

Point of order : before we beat to death the factors that make a bike work, are we sure.we are all.agreed on what it means for a bike to "work"?

To my mind an empty bike is fundamentally different than an occupied bike. The forces that keep a riderless bike vertical even while it follows an unguided trajectory.to nowhere are almost entirely irrelevant to the forces that keep an occuped bike vertical, stable AND going.in a USEFUL direction.

seems to me that is a critical point of contentin we must resolve BEFORE.deciding we have.proven any point about it.

Please. Convince me that a riderless bike is synonymous with a purposefully driven ridered bike.

 

[Paradox101]

Point of order : before we beat to death the factors that make a bi

ke work, are we sure.we are all.agreed on what it means for a bike to "work"?

To my mind an empty bike is fundamentally different than an occupied bike. The forces that keep a riderless bike vertical even while it follows an unguided trajectory.to nowhere are almost entirely irrelevant to the forces that keep an occuped bike vertical, stable AND going.in a USEFUL direction.

seems to me that is a critical point of contentin we must resolve BEFORE.deciding we have.proven any point about it.

Precisely. If one refers to an empty bike, it can be clearly explained because of the angle of the fork and yes, as everyone said, gyroscopic precession and equalized torques(duh).However, when a rider sits on a bike, we can't try to explain how it works in the very manner we would attempt to explain an empty bike,as there are a lot of factors(weight of biker,center of gravity,horizontal weight distribution,etc).

 

[Wes Tausend]

Point of order : before we beat to death the factors that make a bike work, are we sure.we are all.agreed on what it means for a bike to "work"?

To my mind an empty bike is fundamentally different than an occupied bike. The forces that keep a riderless bike vertical even while it follows an unguided trajectory.to nowhere are almost entirely irrelevant to the forces that keep an occuped bike vertical, stable AND going.in a USEFUL direction.

seems to me that is a critical point of contentin we must resolve BEFORE.deciding we have.proven any point about it.

Please. Convince me that a riderless bike is synonymous with a purposefully driven ridered bike.

Dave,

For what it's worth, I never had a problem with your original point that a bike would tip, with and without a rider, if it's wheels were caught in a streetcar track. I thought it a valid insight. But if the bike can, it will steer itself to remain upright, even without a rider.

The forces that keep a riderless bike vertical even while it follows an unguided trajectory.to nowhere are relevant to the forces that keep an occuped bike vertical, stable. Let me try to explain.

I agree, a riderless bike is not synonymous with a purposefully driven ridered bike, but it acts synonymous to a large degree. The difference is only that a change of direction cannot be normally chosen by a riderless bike. As an example, Jones (in his pdf), allowed a riderless bike to roll after wetting the tires. The tires therefore wrote their path on the pavement (figure 7, bottom). One can see that the rolling riderless bike initially attempts to stably continue in the same direction when undisturbed.

When Jones bumps the handlebar, he steers the bike in a "permanent" new direction as though he is momentarily the controlling rider although he is not aboard as normal. The wobbly bike then automatically seeks to geometrically straighten it's new "permanent" path. In my opinion, the initial wobble is characteristic of an instability that forms from gyroscopic reaction forces to steering input, but the bike geometry still automatically recovers on it's own. Because of castor, rake and trail geometry, the bike literally automatically steers under it's own center of gravity when leaned, aka "when falling". It does this when leaning because the frame can drop to a lower level.

One can more readily imagine the frame dropping when the wheel turns into the lean, by exaggerating the situation. Imagine the bike rake at rest has an extended fork, so extended the fork is closer to horizontal rather than vertical. When the bike is leaned in the least degree, the fork will automatically turn into the lean and the front wheel will nearly lay on its hub as the frame drops. At a lesser rake, the same frame drop occurs more subtly. The frame always naturally seeks the lowest gravity possible automatically. That is the secret, IMO.

In a different perspective, when rolling ahead, the bike geometry behaves as though it's dynamic center of gravity has moved above it, and it "hangs" from this invisible, virtual guidewire. A rider in continuous control can alter the bike path (alter the virtual guidewire) innumerable times, but as long as it rolls within a certain speed range, the bike itself (and load) remains automatically stable, seeks upright and favors the latest straight ahead path nearly regardless of loaded weight.

The Jones "geometry theory" I quoted in post #39 pretty much solves the primary moving stability of a ridered, or riderless bike, IMO.

The stable speed range of a bike appears to be in between too slow to steer-compensate for gravitational "fall", and too fast whereby the steering feedback corrects too fast (overcorrects) and oscillation (headshake) occurs. In addition, this principle seems to be the most likely candidate for the reason that some grocery cart castor wheels shimmy too.

The cart wheels are simply unstable when driven above the speed range afforded by their worn geometry. With a loose axle and/or "kingpin" (head bearing), the "leaning" cart wheel begans to oversteer from center (shimmy). I haven't thought this much about bikes geometry before, but I have long wondered why the cart wheels shimmy. The speeds are too slow for significant gyro forces. Having worked part-time in a grocery store while in college, I know oil didn't help, but rather made it worse.

Wes
...

 

[FactChecker]

We have to be careful here. Just because other designs do not require rider balance, trail, or gyroscopic effect does not mean that the common design does not need it. Also, examples where the tire is on a slippery surface may defeat all those mechanisms, so I don't think it proves anything. There are probably multiple modes that depend on different stability feedbacks. Clearly, a fast moving bicycle is stable for a short time without a rider but not for a long time. Just as clearly, there are situations where a bicycle is so unstable in a short period mode that no rider can keep it up. (I have been on a motorcycle on streetcar tracks that flipped so fast that no one could control it, Same for tank slap.) For the common design, I am confident that rake, trail, rider balance, and gyroscopic forces are all major factors in certain situations.

To answer the original question, I believe that we have the capability to model the equations of motion of a bicycle and know how much force is coming from every possible feature of the design at every speed and condition. If it hasn't been done, it is because no one needed to do it. I bet it has been done for motorcycles. But the stability is probably not so simple that a blanket statement can be made. Nothing is simple.

 

[Dylan Cram]

Hello All, I am new here, and have been an avid cyclist for 12 years (not including the usual stint in childhood that much of us probably share). I have long been interested in this topic, because bicycles are truly fascinating to me.

Anyway, I have an idea about what the root cause of bicycle stability is. There are many factors involved in the operation of a bicycle, but overall, the way they turn into a fall without a rider is the key. Now, the task is to explain WHY they turn into a fall. The reason isn't gyroscopic, or dependent on trail, although those factors affect the performance of a bike. For example: the longer trail of a touring bike has a less twitchy feel than the shorter trail of a track bike. I have both, and a track bike feels like an f-16 compared to a b-52 tourer.

As to the why. I will use an analogy. The reason bicycles self correct is the very same reason that trains stay on their tracks. Trains are not bound to their tracks in any way. They have beveled wheels, such that the outermost part has a smaller diameter than the inner part. So, if a train moves laterally on the tracks (perpendicular to it's direction of motion), on one side the diameter at the contact surface of that wheel will be smaller, and the other side will have an increase in diameter. That asymmetry will cause a corrective turn toward the lower rotational velocity, and the train continuously self-corrects and stays on the tracks.

Now, imagine a bicycle perfectly upright. It's tires have a round cross section. The weight of the bike, or bike plus rider, ensures that the contact area of the tire to the ground is a non-zero area. Across the contact patch, from left to right of the bike, there are different rotational velocities at play. The outer parts of the patch are different than a dead-center abstract point. That's okay~ it's balanced on both sides. If the bike starts to fall over, which it obviously would, the contact patch remains pretty much the same, but is shifted to one side of the tire. When that happens, the side of the patch 'inside' the lean has a slower rotational velocity than the part 'outside' the lean. What we have here analogously, is both wheels of a train contained within the contact area of the bike tire. What will happen, is that the front wheel will turn about it's steering axis toward the lean, because of the higher rotational velocity outside of the lean. The true key to why a bicycle stays upright is a combination of two things: the ability of the front wheel to rotate about a steering axis relative to the rest of the bike, and the cross-sectional shape of the tires. The bike referred to in earlier posts~ with the trail and gyroscopic effects nullified, still had wheels with a rounded cross section. That is the key. I'm actually kind of baffled as to why they didn't see it.

There was a previous poster whom asserted that rider balance is the most important factor. There is no truth to that. If I stop at a traffic light, I can balance pretty good, such that I might not have to put a foot down, but once the bike is stationary, that's all on me, and I have to do a track stand, which has nothing to do with why a bike stays up in motion. Once the bike is moving, there is no effort to balance. You can tell adept bicycle riders from the less skilled by how much of a line they can hold. If a rider can keep their tires inside a white line on the side of the road (a few inches) at high speed, they are good, but it doesn't mean that rider balance plays much of a part, just that fine motor control of the handlebars is good. Good riders know how to work WITH the bike. They just intuitively know how it responds.

A good experimental angle to pursue, is different contact area cross sections.

 

[rcgldr]

The stable speed range of a bike appears to be in between too slow to steer-compensate for gravitational "fall", and too fast whereby the steering feedback corrects too fast (overcorrects) and oscillation (headshake) occurs. In addition, this principle seems to be the most likely candidate for the reason that some grocery cart castor wheels shimmy too.

On most bicycles / motorcycles, if the speed is too fast, the gyroscopic dampening effect (which counters the corrective steering related to trail) is large enough to dominate and the bike doesn't correct (or wobble), but instead holds the current lean angle or falls inwards at an extremely slow rate, called "capsize" mode. Speed wobble on a bike is bike specific, factors include flexing within the frame work, too little trail, ... , and on some bikes, steering dampers were used to solve the issue.

It's tires have a round cross section. ... Across the contact patch, from left to right of the bike, there are different rotational velocities at play.

If this was true then a bike with the front tire locked straight ahead would steer if leaned but this doesn't happen. A pair of cone shaped "wheels", one in front of the other with parallel axis will move in a nearly straight line, with a lot of slippage on the surface of the cones. In the case of a bike in a turn, the cornering forces result in the contact patches being twisted a bit outwards.

 

[Dylan Cram]

If this was true then a bike with the front tire locked straight ahead would steer if leaned but this doesn't happen. A pair of cone shaped "wheels", one in front of the other with parallel axis will move in a nearly straight line, with a lot of slippage on the surface of the cones. In the case of a bike in a turn, the cornering forces result in the contact patches being twisted a bit outwards.

How would a bicycle 'steer' if leaned, if it's ability to steer is removed? A bicycle with a locked headset would not apparently turn if leaned, because there are two wheels involved on the same plane, and the contact area is tiny. You can do it yourself by standing on one side of the frame while coasting. The forward momentum of the bike would easily overcome the varying rotational speeds in the contact patch. Your example of come-shaped wheels is an extreme and thus an inaccurate analogy, yet kind of nullifies your point at the same time? I don't follow you there. The contact patches of a bicycle are very small, especially in the case of my road bike with 25 cm, 100psi tires.

With the train analogy, it is the limited freedom of motion between cars that allows the beveled wheels to do their job. If the entire train was a monolithic body, the train wouldn't be on the tracks for long.

When a bike is cornering, the contact patches move inwards, not outwards.

 

[cosmik debris]

Having read through all this it seems the original poster's suggestion, that no one know how a bicycle works, is true :-)

 

[rcgldr]

A pair of cone shaped "wheels", one in front of the other with parallel axis will move in a nearly straight line, with a lot of slippage on the surface of the cones. In the case of a bike in a turn, the cornering forces result in the contact patches being twisted a bit outwards.

How would a bicycle 'steer' if leaned, if it's ability to steer is removed?

I misunderstood what you were getting at. I thought you meant that the round profile of a tire would generate an inwards force, as opposed to generating a steering torque. What I should have posted is that the contact patch on a bicycle with thin tires is too small to generate a significant steering torque, yet such bicycles are very stable due to trail.

In the case of a bike in a turn, the cornering forces result in the contact patches being twisted a bit outwards.

When a bike is cornering, the contact patches move inwards, not outwards.

The contact patches shift laterally inwards, but twist (rotate) outwards due to the cornering loads. The path of a tire is a bit outwards of the direction of the tire due to this outwards twisting at the contact patches, known as slip angle, although actual slippage is not required to have a slip angle.

 

[Dylan Cram]

Having read through all this it seems the original poster's suggestion, that no one know how a bicycle works, is true :-)

Perhaps, but it seems we are in the end game now.

Hey rcgldr, looks like you edited a post :)

 

[rcgldr]

Hey rcgldr, looks like you edited a post.

I did a strike through, since I worded that badly. That should have been about lateral forces related to a leaned round tire, not a steering reaction.

Having read through all this it seems the original poster's suggestion, that no one know how a bicycle works, is true.

It's well understood that self-stability is related to having a geometry that causes the front tire to steer in the direction of lean sufficiently enough to tend to correct the lean and return to a vertical orientation (the direction of the path will change due to disturbance, but the bike will return to vertical). Depending on the geometry, there is a range of speed for that self stability. The conventional method for self-stability is trail / caster. One alternate method is to locate a weight above and in front of a front wheel with zero caster, so that when leaned, the yaw torque (about the vertical axis) results in a steering reaction by the front tire.

As posted before, although gyroscopic reactions seem like they would help, gyroscopic precession is a reaction to torque, not lean angle. In general, gyroscopic reaction dampens (resists) the self-correcting steering related to geometry.

The contact patches shift laterally inwards, but twist (rotate) outwards due to the cornering loads. The path of a tire is a bit outwards of the direction of the tire due to this outwards twisting at the contact patches, known as slip angle, although actual slippage is not required to have a slip angle.

Complicating matters is the relative slip angle at the front and rear tire (relative camber stiffness), similar to understeer versus oversteer and the effect on steering inputs.

 

[Dylan Cram]

I misunderstood what you were getting at. I thought you meant that the round profile of a tire would generate an inwards force, as opposed to generating a steering torque. What I should have posted is that the contact patch on a bicycle with thin tires is too small to generate a significant steering torque, yet such bicycles are very stable due to trail.
A steering torque is indeed induced by the variation of rotational speeds within the contact patch~ given a bike with a front wheel that is free to rotate on a steering axis, and has a circular cross-section. It really cannot be any other way. That is how these things work. That is how three dimensional rotating objects behave. How significant the force is? That seems to be more a matter of personal intuition at this point than anything else. My bike with thin tires has a very short trail relative to other bike designs. It is essentially a track bike, and the design has a short trail and short wheelbase so that it is very responsive to changes in direction. Trail doesn't keep bicycles upright. That has been shown adequately enough for me. The experimental bike that convinced me, however, still had tiny little wheels with a rounded cross-section at contact with the ground.

 

[rcgldr]

A steering torque is indeed induced by the variation of rotational speeds within the contact patch~ given a bike with a front wheel that is free to rotate on a steering axis, and has a circular cross-section. ... How significant the force is? Trail doesn't keep bicycles upright. That has been shown adequately enough for me. The experimental bike that convinced me, however, still had tiny little wheels with a rounded cross-section at contact with the ground.

That experimental bike is supposed to model a two skate bike, one with infinitely thin circular blades instead of wheels (this is why counter rotating wheels were used, to eliminate gyro effects). In the case of that experimental bike, there is no trail / caster, but instead a weight locate above and in front of the front wheel. When the bike leans the weight generates a torque about the vertical axis of the bike (yaw), that causes the front wheel to steer in the direction of the lean. A two skate bike using conventional trail / caster steering geometry would also be self stable.

How significant the force is?

I'm wondering what happens if a conventional bike with trail is let go rider free to travel on a side banked or crowned road? Does it steer sideways uphill because of the different radius at the tire edge versus the tire center, or does it continue to go mostly straight, or does it steer sideways downhill due to the lateral load? If a road were reversed crowned (lowest at the middle), would a rider free bike tend to steer off road, mostly hold it's current line, or tend to steer toward the middle of the road?

update - I tested on a private road with a central drain, where the road is angled somewhere between 5 and 10 degrees on both sides, with an old Centurion Super Lemans with 700c tires. Pushing the bike by the seat and letting it free for a few seconds, there was no tendency to steer "upwards". Due to the small angle, the contact patch would only be slightly offset, so the amount of steering torque related to the offset contact patch was imperceptible. However, leaning the bike on a level surface at around 5 degrees was enough to result in significant inwards steering.

Where I have noticed a steering effect related to an offset contact patch is when braking while leaned over on a motorcycle, which tends to turn the front tire inwards, requiring more counter steering effort to hold a lean angle. The same effect occurs if braking on a banked section of road (the tire tends to steer up the bank). The amount of counter steering effort involved varies between bikes and probably between tire profiles. However the effect is only noticeable under braking. I don't feel any effect on a banked road when not braking.