Talk:Bicycle and motorcycle dynamics/Archive 1

Bicycle physics in German
If anyone speaks German, de:Fahrradfahren seems to be about bicycle physics. --Christopherlin 03:25, 3 April 2006 (UTC)
 * I don't speak German, but the existing links cover the topic quite well. Perhaps you would be interested in modifying the section with thinks such as these:


 * Effect of steering-column angle on trail and stability
 * - Finally covered, but out of Whitt and Wilson. -AndrewDressel 16:32, 8 August 2006 (UTC)


 * Give typical values of trail and explain the pros/cons of different values
 * - Partially covered, but out of Whitt and Wilson. -AndrewDressel 16:32, 8 August 2006 (UTC)


 * Flense the speculation about shimmy
 * - Don't know if there is any left. -AndrewDressel 16:32, 8 August 2006 (UTC)
 * JethroElfman 22:02, 3 April 2006 (UTC)
 * Which 'existing links' do you mean? The steering and trail discussion could use some expansion. Another one of those things I'll do when I get a round tuit... :-> --Christopherlin 00:50, 4 April 2006 (UTC)

Bicycle physics
Copied from the article:

"A rider stays upright on a bicycle by steering the bicycle so that the point where the wheels touch the ground stays underneath the center of gravity. Once underway, this effort is largely replaced by physical forces generated by the rotation of the wheels which produce a remarkable "self-steering" effect. The angular momentum of the wheels and the torque applied to them by the ground generates a phenomenon called precession, by which the wheel turns, or trails, toward whichever side the bicycle tilts. Like the rider's steering adjustments, this motion automatically returns the contact point of the wheel directly under the center of gravity. These forces, perhaps aided at very high speeds by the gyroscopic effect of the spinning wheels,4 are sufficiently strong that a riderless bicycle going down a slope will stay upright by itself."

The effect described in sentences 2, 3, and 4 above IS the gyroscopic effect, so to say in sentence 5 that it is perhaps aided by the gyroscopic effect is confusing. The more important effect, according to Jones and others, is that of trail, described in the third paragraph of the 'Bicycle physics' section. Rracecarr 18:54, 11 May 2006 (UTC)


 * I agree. In fact, 2, 3, and 4 are far too vague. They are only valid for a particular range of forward speeds and only for bikes that have the necessary geometry and mass distribution. "The wheel" should be identified as "the front wheel". Using "trail" to describe this phenomenon begs confusion with "trail" described below.


 * Also, Andy Townsend's article (note #4) gives a poor analysis of the mechanics involved. There is no 'gyroscopic "resistance" to change in lean angle' no mater how fast the wheels are turning.


 * Again, "are sufficiently strong that a riderless bicycle going down a slope will stay upright by itself" is only true within a certain speed range and for bikes with the necessary geometry and mass distribution.


 * Finally, in the second paragraph, the last sentence shows that the gyroscopic effects are "unnecessary to ride a bicycle", not necessarily "unimportant". AndrewDressel 21:34, 14 May 2006 (UTC)

All of these issues were corrected by me back in February. On May 5 someone reverted the entire article back a few months. Even the first sentence here is poor. The goal isn't just to keep the centre of gravity over the line between the wheels -- the rider also wishes to drive the bike where he wants it to go. While turning, the centre of gravity must lean into the turn (not stay over the wheels) or the bike will tip over. - JethroElfman 16:26, 15 May 2006 (UTC) Okay, I restored the section. Perhaps someone would like to restore the entire article. The physics section could be tinkered with further. For instance, the "geometry of the front forks" has two components. One is how the contact of the tire to the road trails where the steering axis intersects the road. The second is the angle of attack of the steering axis. The exaggerated angle of a chopper is less stable, yet it is presumably advantageous to have the slight angle of a regular bike. I don't understand why it isn't perpendicular like a furniture caster. The length of trail is 1.5" for standard use, and up to 2.5" for racing duty. Increased distance adds stability for hands-free or aero bar operation, but makes cornering stiff. The speed-wobble section could be reworded. I don't think the comparison to a shopping-cart wheel is entirely accurate in this case. JethroElfman 16:43, 15 May 2006 (UTC)


 * It's definitely better than it was. I don't know enough to add anything myself, but I would like to see a discussion of rake angle included in this section. Rracecarr 17:56, 15 May 2006 (UTC)


 * Much better. I'll look for a better reference than Townsend AndrewDressel 18:00, 15 May 2006 (UTC)


 * I've gone ahead and made some major changes. I clarified self-stability vs rider control and what role gyroscopic effects play. I added a diagram to clarify head angle, rake, and trail. I added a paragraph about the effect of the steering assembly center of mass. I added a link to a video demonstration of self-stability. I probably violated some protocols, but I'll happily fix them when pointed out. AndrewDressel 04:28, 16 May 2006 (UTC)

I think you are putting too much emphasis on precession. I thought that the Jones article settled that precession isn't such a big deal for bicycles.


 * My reading is that he established that is isn't necessary. I don't mean to emphasize it. I could put it last. It is still significant because it varies with speed and so contributes to the low and high speed instabilities that usually bracket the self-stable range. AndrewDressel 18:18, 16 May 2006 (UTC)

For motorcycles it is, so it's good to explain the principles involved.


 * Its role there is arguable. AndrewDressel 18:18, 16 May 2006 (UTC)

In that regard, the rear wheel is restrained from precessing because it is rigidly attached to the frame, whereas the front wheel can turn the head axis.


 * And the frame is constrained because it is attached to two wheels that touch the ground. I just mention the friction of the wheels with the ground, but could add text to include the frame necessary to transmit the force to the rear wheel. AndrewDressel 18:18, 16 May 2006 (UTC)

Even so, as the bike turns through the corner, the rear wheel is thereby allowed to precess and thus aid in turning the mass of the bike.


 * Nope. Still constrained by the frame, wheels, and friction with the ground, as above. AndrewDressel 18:18, 16 May 2006 (UTC)

The first paragraph offends my memories of grade 10 physics class. Inertia is not a force. Its effects are applied to the bike through the tire contact to the road.


 * Depends on the reference frame used, as I mention. See Centrifugal force. AndrewDressel 18:18, 16 May 2006 (UTC)

I think your descriptions of trail and head angle are still too intertwined. Trail turns the wheel by gravity when the bike is leaning. Head angle generates a gravitational force to turn the wheel when the wheel is turned off centre, even if the bike is perfectly vertical.


 * Sorry, but I don't follow you here at all. I specifically do not understand what you mean by "Trail turns the wheel by gravity" and "Head angle generates a gravitational force". Could you clarify? AndrewDressel 02:15, 17 May 2006 (UTC)

If trail is kept to zero, a leaning bike's wheel won't turn regardless of the head angle (you have to extend the curvature of the forks forward to do this).


 * Not true. With zero trail, it won't turn due to the ground reaction force, but if the CG of the entire steering mechanism, including front wheel, fork, stem, handlebars, brake levers, shifters, basket, rack, etc., is forward of the steering axis, as is common, then it will turn into the lean. If it is behind, then it will turn away from the lean. Either case effects self-stability, of course. AndrewDressel 02:15, 17 May 2006 (UTC)

Oh, and Jones claims that negative trail makes a bike entirely unrideable, so what's your reference that says it's rideable but difficult?


 * I'll have to reread. It may be a matter of degree. Rear steering with negative trail is very unstable, but people do learn to ride fixed-gear bikes backwards as a trick. AndrewDressel 18:18, 16 May 2006 (UTC)


 * The exact quote, from the second to last paragraph of the article, is "I made URB IV by moving the front wheel of my bicycle just four inches ahead of its normal position [giving it negative trail, as seen in FIG. 1 of the article], setting the system well into the unstable region. It was indeed very dodgy to ride, though not as impossible as I had hoped" AndrewDressel 01:27, 17 May 2006 (UTC)

What's your reference for the note about long-wheel-based recumbents. It sounds interesting and I'd like to read that one.


 * I just performed the physical experiment described by Zinn on such a bike. I'll see if I can find someone else who has and wrote about it. AndrewDressel 18:18, 16 May 2006 (UTC)

I still don't understand why head angle isn't just 90 degrees. Is it to keep the rider from going over the handlebars when braking perhaps?


 * It negligibly reduces that tipping tendency. I think is mostly for trail. I remember reading that the historical origin is lost, but it works well and so is continued. I'll look for that reference. AndrewDressel 18:18, 16 May 2006 (UTC)


 * It increases the steering effect of the steering mechanism's forward CG. AndrewDressel 01:27, 17 May 2006 (UTC)

Your internal links are done with html references rather than the simple square-bracket approach. Why is that? - JethroElfman 16:40, 16 May 2006 (UTC)


 * User error. Will fix. AndrewDressel 18:18, 16 May 2006 (UTC)

In the new diagram, things are labeled differently from how I learned them. I thought rake was the angle of the steering axis from vertical, which in the diagram is labeled "head angle" (well, 90 degrees minus what I thought was rake is so labeled). Someone on wikipediea appears to agree with me: rake and trail. Here is another random example: www.performanceoiltechnology.com/rake_and_trail.htm However, I also found a reference agreeing with AndrewDressel: www.sheldonbrown.com/gloss_ra-e.html ???? Rracecarr 19:10, 16 May 2006 (UTC)


 * Perhaps things are different in the motor cycle world, but go to any bicycle manufacterer's web site (LeMond, for example), head angle is given in degrees from the horizontal (73°, for example), and rake is give as the offset in milimeters of the front hub from the steering axis (45mm, for example). These two parameters, along with wheel radius, define trail. That's how Zinn defines them, too. AndrewDressel 21:39, 16 May 2006 (UTC)


 * Sure enough, all the motorcycle manufactures specs I found use 'rake' for head angle. At the same time, bicycle fork manufacturers seem to use either offset or rake. Meanwhile, the Wikipedia rake and trail article was actually "nominated for deletion on 2 April 2006" and the WIkipedia [Bicycle fork] article mentions neither rake nor offset.AndrewDressel 02:01, 17 May 2006 (UTC)


 * Okay, I did some sketches and see what you mean about the recumbent. If the wheel rather than projecting forward of the forks, is mounted rearwards, the centre-of-mass makes it steer the opposite way.


 * Actually, the one I used has a normal fork, but a long boom to bring the handlebars back to the rider. I've actually flipped the fork around to increase trail, and it goes a long way toward counteracting the adverse effects of the CG being so far behind the steering axis. Still need to find a reference, though. AndrewDressel 23:44, 16 May 2006 (UTC)


 * The rake and trail article is terrific. I didn't know it existed.  It needs linked, and perhaps the caster-angle article as well.


 * I thought it was, if I can't find it, I'll add it. AndrewDressel 23:44, 16 May 2006 (UTC)


 * What I meant about precession is that you put an awful lot of verbage covering it, when everything I've read, including the rake-and-trail and caster-angle articles says that it's trail that makes the bike stable. Angle provides damping in respect to trail.  The one motorcycle reference though, says that precession makes a motorcycle corner.  How about moving precession farther down and abbreviating it a whole bunch?  - JethroElfman 22:22, 16 May 2006 (UTC)

I've changed the links I can from html references to the simple square-bracket approach. I've found and moved the Zinn reference to come at the end of the trail paragraph. I've moved gyroscopic effects to last, but left it verbose because it is the one effect that varies with speed. I've added a reference for the low and high speed instabilities I mention. I've added information about making turns. AndrewDressel 01:27, 17 May 2006 (UTC)


 * Fixed some typos AndrewDressel 03:56, 18 May 2006 (UTC)


 * I think the paragraphs on countersteering are too absolute concerning it. The very fact that you can ride and negotiate a corner with no hands makes it look to me like you don't necessarily have to employ the technique.


 * Just because you don't have your hands on the handlebars, doesn't mean you don't countersteer. You do steer in the direction of a turn as necessary, right? If the bike starts to lean, you do steer the wheels back under the center of gravity, right? I get that one can have quite a lot of control over the steering of a bike without the use of hands. The issue is lean angle, however. AndrewDressel 03:56, 18 May 2006 (UTC)


 * On a motorcycle sure, since the bike outweighs the rider. On a bicycle, since the rider is so much heavier (and manoevreable compared to being on a motorcycle seat) the rider can shift his weight to produce lean.


 * Ah, but leaning the bicycle does not move the combined center of gravity of the bicycle and rider to the side. It just lowers it in most cases. If the combined center of gravity is not leaned into the turn, the bicycle and rider will fall over as soon as the turn is initiated due to centrifigul force, or, if you prefer, because they continue straight as the wheels begin to accelerate around the center of the turn. There simply is no other way to initiate a lean, short of some external influence. AndrewDressel 03:56, 18 May 2006 (UTC)


 * Here is a fascinating page about steering motorcycles: No B.S. Machine. Perhaps the Countersteering article should reference it. I'll reference it here for now. AndrewDressel 03:56, 18 May 2006 (UTC)


 * It won't be as efficient, and might not be the norm, but isn't it at least possible?


 * Nope. No more so than accelerating in space without expelling mass. AndrewDressel 03:56, 18 May 2006 (UTC)


 * If the rider tightly grips the handlebars to rigidly keep the wheel straight, the bike will lean just by gravity.


 * Well, yes, you could continue riding in a straight line until an inevitable purturbation tips you in the desired direction. Then, override the natural righting tendency inherent in the bicycle design until the necessary lean angle is achieved. However, if you want to turn when you want to turn, your only alternative is countersteering. AndrewDressel 03:56, 18 May 2006 (UTC)


 * To feel the effect of shifting weight, try riding by standing with your left foot on the right pedal. The bike leans greatly left, and you must torque the handlebars right to go in a straight line.


 * True, due mostly to trail, and not related to the issue except as an extreme example of moving the combined center of gravity far from the vertical axis of the bike. If you let the bike steer to the left, you'd better have leaned the combined center of mass appropriately. AndrewDressel 03:56, 18 May 2006 (UTC)


 * Likewise, I still dispute the precession contribution of the rear wheel. If the frame is constraining the wheel to not precess, the wheel is conversely applying the same rotational moment back onto the frame in the direction of the turn.  Hence the spinning rear wheel is applying a yaw torque to aid the yaw torque coming from the friction of the road on the front wheel.  Will you say naw to that?


 * The problem is that unless the precession induced in the rear wheel by leaning the bike has enough torque to skid the front wheel (say 100ft-lbs or more for an adult rider on an average bike with rubber tires on pavement), then it has no effect on the yaw of the bike. The front wheel of a bicycle does not skid in the direction of the turn, and so applies a torque through the frame on the rear wheel about the vertical axis. If you follow the right-hand rule, you find that this torque induces a precession in the rear wheel about the longitudinal axis of the bike causing it to lean in the same direction as the bike is leaning. You can verify this with much more rigor by applying Euler's Equations for 3D rigid body motion. You can also demonstrate it with a toy gyroscope. AndrewDressel 03:56, 18 May 2006 (UTC)


 * With my link to the Rake and trail article it is unfortunate that they define rake as equivalent to caster angle.
 * - JethroElfman 02:24, 18 May 2006 (UTC)


 * Yeah, that one needs attention, too. AndrewDressel 03:56, 18 May 2006 (UTC)

Bicycle braking
Added quick analysis of braking forces, but forgot to login first AndrewDressel 12:42, 7 June 2006 (UTC)

Generalization needed
All of the topics mentioned in the article apply equally to motorcycles as well. Moreso in fact due to their larger mass. --Hooperbloob 13:56, 7 June 2006 (UTC)


 * I'd agree, but I dread the controversy. Many of the references are different. Much of the motorcycle research includes front and rear suspension which does effect the dynamics. I don't know of any single source that explicitely covers both vehicles. AndrewDressel 19:43, 7 June 2006 (UTC)

Kudos on the bicycle->bike revision, it does the job perfectly. --Hooperbloob 15:17, 20 June 2006 (UTC)


 * I guess all I have to do then is incorporate the main section on stability from the motorcycle article (different due to full suspension, tires size, mass, etc.) and then we can have just one article, not two. AndrewDressel 01:32, 21 June 2006 (UTC)

Then the last step would involve renaming the article itself to "Bicycle & motorcycle physics" ? --Hooperbloob 02:11, 21 June 2006 (UTC)


 * Done, without too many errors, I hope. AndrewDressel 12:40, 22 June 2006 (UTC)

Racing physics
I notice on my bicycle that I shift my body away from the direction of a turn. That is, on left-hand turn lean the bike left, but keep a body position almost vertical. This is to counteract the way the front-wheel trail wants to straighten the bike back up. In motorcycle racing however, they lean way into the turn (with a knee stuck out). Is this because the gyroscopic effect of the wheels is trying to stand the bike up, and needs counterbalanced? JethroElfman 16:02, 30 May 2006 (UTC)
 * I cannot say for sure why you lean away from the direction of a turn on your bicycle. It is not commonly practiced in racing. Check out pictures on http://www.freewheel.com/mvw/pooleyphotos.htm
 * In motorcycle racing, I just read recently, but can't yet find the link, that riders lean into the turn in order to lean the combined bike/rider center of gravity farther than would otherwise be possible due to interference between the bike and the ground. The lean of the combined CG is exactly dictated by the radius of the turn and the forward speed.AndrewDressel 01:27, 31 May 2006 (UTC)
 * Here are more details from http://www.superbikeschool.com
 * "Hanging off certainly moves YOUR CG to the inside of the corner (but moves the bikes out a little...) and the COMBINED CG stays at the same height."
 * "One would want to pick the bike up off the edge of the tire while coming out for a couple reasons... One, you want to save the edge to maximise mid-corner speed through the race. Two, you can put more power down when the tire isn't right on the edge. Three... (this ones a little tough to follow for some) the tire is smaller the closer you get to the edge... This means that when you roll over to the edge, if you keep the same speed, your RPM's will rise... You can use that extra HP WHILE picking the bike up to help add drive out of the turn... If you're in an endurance race you MAY be able to save a bit of fuel by hanging way off and using the larger portion of the tire. That is... if the extra wind resistance isn't offsetting the fuel savings..."
 * "Each tire will have a lean angle where it will generate the most grip. You want to use THAT lean angle mid-turn"
 * AndrewDressel 03:23, 31 May 2006 (UTC)


 * From my recollection of a brief involvement in seventies production motorcycle racing, "hanging off" was a tactic used to offset poor ground clearance. Seasalt 01:42, 15 October 2006 (UTC)

Steering section
Having read through the steering section, I've noticed that the description of a number of items (particularly in the 'counter-steering' portions) don't square with my own experience riding. In particular, there are two items I feel might warrant changes: 1. The process of counter-steering a motorcycle through a turn does not, at least in my riding experience, involve a discernable deflection in the actual path of the motorcycle. It's possible that there is some small path change, but in my experience (at street speeds) it's not a significant (or even noticable) effect.


 * Even if you don't discern it, there isn't another way to lean the combined center of gravity of a bike and rider, short of waiting for it to tip in the desired direction due to random perturbations, and then letting it continue to lean without correction. At street speeds, it doesn't take much countersteering to create the necessary lean. At 15mph a 1° deflection of the front wheel will move the wheels nearly 5 inches in that direction in just 1 second, 5° will get you nearly 2 feet. AndrewDressel 04:25, 14 June 2006 (UTC)


 * Perhaps I'm not steering very aggressively, but at speeds over around 15 mph I don't notice the wheel deflecting much at all when I'm steering - perhaps that's why I don't see a path change when I steer? Saturn V 16:39, 14 June 2006 (UTC)


 * Right. It doesn't take much. -AndrewDressel 12:14, 8 August 2006 (UTC)

2. There is a statement to the effect that 'all turning on a motorcycle uses counter-steering' which is not strictly true, I don't believe. While it is probably the case that basically all steering on a motorcycle involves deflection of the front wheel, the cause of that deflection is not necessarily counter-steering. The shifting of body weight on the motorcycle (without input to the handlebars) can cause the motorcycle to steer (although it is markedly less efficient than the use of the bars), and any wheel deflection involved is due to frame geometry effects as opposed to active counter-steering.


 * Well, the first sentence defines countersteering as the turning of the front wheel and does concede "usually via the handlebars". You as a rider are welcome to use whatever technique you prefer, but the handlebars are certainly the most direct and efficient. AndrewDressel 04:25, 14 June 2006 (UTC)


 * I certainly agree that using the handlebars is indeed the most efficient way of controlling the bike - I think it is important, however, to at least mention that it's not the only way in which you can affect the path of the bike. Saturn V 16:39, 14 June 2006 (UTC)


 * Done. No-hands riding has its own section immediately following countersteering.-AndrewDressel 12:14, 8 August 2006 (UTC)

I think perhaps a wording change is in order there (and the citation of the 'no-bs' bike isn't without the potential for controversy).


 * The No B.S. Bike meerly provides a vehicle for riders to discover this for themselves. By all means, cite other examples of physical experiment. I submit, however, that an individual rider's own perception of what they do during a turn is not exactly objective. AndrewDressel 04:25, 14 June 2006 (UTC)


 * Another neat experiment was performed by Dr. Richard Klein at University of Illinois. "The Rocket Bike" had a small rocket attached to the handlebars and fired momentarily while the bike was rolling without a rider (demonstrating self-stability). When the rocket fired, it applied a torque to the steering. Counter-intuitively, the bike turned in the opposite direction. -AndrewDressel 12:14, 8 August 2006 (UTC)

Would anyone else like to chime in here before I go and edit this section? [The above entry is by user Saturn_V timestamped 15:39 13 June 2006]


 * Have at it. There is still too much of a "rider school lecture" flavor to it for my taste. AndrewDressel 04:25, 14 June 2006 (UTC)


 * I thought that the no-bs article was wonderful and I don't know in what way it can be considered controversial. Any other literature I have seen agrees that you must countersteer.  I can see there being an argument if you are talking about a bicycle, because the rider's mass is so much greater than the bike's.  Even in that case, if you ride with no hands, the bike will countersteer for you.  When you shift body weight to the right, the bike responds by leaning to the left.  Front-wheel trail will make the forks turn into the direction of the lean.  Hence, when you lean right, the bike naturally countersteers left, and you end up going right. - JethroElfman 04:21, 14 June 2006 (UTC)


 * The primary issue I've seen come up in the discussions of the no-bs bike is that it is sometimes used to argue that weight transfers (without active pressure on the handlebars) on the bike have no effect on the path of the bike. That's the only issue I take with it...  Saturn V 16:39, 14 June 2006 (UTC)


 * Code concedes "The best result was one of my riding coaches. He got into a full hang-off position and was able to persuade the bike, by jerking on it, to start on a wide, wide arc in the paddock at Laguna Seca" so the assertion of 'no effect' is perhaps a misread. AndrewDressel 20:25, 14 June 2006 (UTC)

Regarding: Only One Way to Lean a Bike
"there isn't another way [other than counter steering]      to lean the combined center of gravity of a bike and rider,"

How do people fall off bikes? The model of a rider/bicycle system as the rider is but a 160 lbs. seat is flawed. Humans have the ability to become off balance first, and use the regaining of balance as the mechanism of turning.

A process I see like this:


 * 1) Rider instigates loss of balance without counter steering as if falling off to left or right
 * 2) Rider brings bike along without counter steering, i.e. leans bicycle into turn
 * 3) Rider modulates steering angle to balance centripetal force with static friction force

The key points:


 * 1) Fallacy: Unbalancing the bicycle-rider system can only be accomplished by counter steering.
 * 2) Counter steering creates an unbalanced system by moving the bike
 * 3) Intuitive steering creates an unbalanced system by moving the human

What matters is that in counter steering the rider is a reacting agent and in intuitive steering the rider is an active agent.

I guess I'm asserting that the article needs to reflect this.

Earth to McFly (talk) 22:22, 24 November 2007 (UTC)


 * We would love to read a reference that explains this. That is the only way that this article could reflect it. -AndrewDressel (talk) 02:37, 25 November 2007 (UTC)


 * Regarding References
 * Here is a reference for changing the language to show that countersteering is only one method, not the only method, of performing a turn. These are the first lines of the first two paragraphs from Fajans, Joel (July 2000), "Steering in bicycles and motorcycles", American Journal of Physics 68 (7): 654–659., emphasis added.


 * "Centrifugal forces will throw your bike over on its side if you steer the handlebars in the direction of a desired turn without first leaning the bike into the turn."
 * "One method of establishing the proper lean is countersteering..."


 * Compare that language with the Wiki article's language which cites the same article as reference, emphasis added.


 * "In order to initiate a turn, a bike must momentarily steer in the opposite direction. "
 * "countersteering happens in every turn."


 * Earth to McFly (talk) 16:41, 25 November 2007 (UTC)


 * Interesting mention of centrifugal forces. Never-the-less, the countersteering article explains "It is important to distinguish between countersteering as a physical phenomenon and countersteering as a rider technique for initiating a turn (the usual interpretation of the term). The physical phenomenon always occurs, because there is no other way to cause the bike and rider to lean short of some outside influence such as an opportune side wind, although at low speeds it can be lost or hidden in the minute corrections made to maintain balance."
 * A reference merely stating that "One method of establishing the proper lean is countersteering..." does not show how "in counter steering the rider is a reacting agent and in intuitive steering the rider is an active agent."


 * At the same time, David Gordon Wilson and Jim Papadopoulos in Bicycling Science do state "and the only way to cause that lean (of the combined center of mass of bike and rider) is to move the support points in the opposite direction first."


 * -AndrewDressel (talk) 01:58, 26 November 2007 (UTC)


 * "there is no other way to cause the bike and rider to lean" How does a bike that can't steer at all fall over, i.e. lean?
 * If a bike is incapable of steering left, can it turn or lean right?
 * "without first leaning the bike into the turn." is not the reason/reference that the rider is a reacting agent in counter steering. Is not that much of the point in countersteering, that the bike moves first, then the rider, so the rider does not fall off high side?
 * Earth to McFly (talk) 04:22, 27 November 2007 (UTC)
 * A bike that cannot steer falls over randomly. The rider has no control over the direction or rate.
 * A rider cannot make a bike lean to the right if it is incapable of steering left, short of waiting for a random purturbation to cause the lean.
 * I do not know what you mean by "a reacting agent". The point of countersteering is definitely not that the bike moves first, then the rider. The point of countersteering is that the only way to cause the combined (bike and rider) center of mass to lean one way is to move the wheels the other way. If just the rider leans relative to the bike, the bike must lean the other way to conserve angular momentum, and the combined center of mass does not lean at all, it just moves closer to the ground. There is no way for the rider to lean one way and then pull the bike with him because he has nothing to pull against. -AndrewDressel (talk) 14:39, 27 November 2007 (UTC)


 * 2. "A rider cannot make a bike lean to the right if it is incapable of steering left, short of waiting for a random purturbation to cause the lean."
 * That assumes a rigid body model.
 * The rider can use tire/ground friction to work the system equilibrium point.
 * The rider is not a collection of momentum conserving levers. A human can turn and otherwise reorient the body without a corresponding counter motion: divers, freestyle ski jumpers, gymnasts, trials riders are some of the more overt examples of models of human function more  everyday and real world than the 160lbs.-seat model.  The millions of muscles/muscle fibers in the body are quite adept at creating, transmitting, absorbing, dampening, isolating, and modulating motion, and at great speed.


 * Has anyone made the left-turn-only bike, the Lefty?
 * Earth to McFly (talk) 00:58, 28 November 2007 (UTC)


 * I do not see that a rigid-body model is necessary.
 * I do not know what you mean by "work the system equilibrium point". Are you refering to the slight displacement of the center of mass you can get by steering a stationary bike due to non-zero trail?
 * Divers, freestyle ski jumpers, gymnasts, and trials riders are all excellent examples of systems that strictly conserve angular momentum. Once they leave the board, jump, or mat, they can neither create nor destroy (except through air drag) angular momentum. The most common trick is to change their angular rate by changing their moment of inertia. I do not see how that would help lean a bike. Humans tend not to have the spinal flexibility necessary to roll the way cats and alligators do, but I don't see how that would help lean a bike either. Especially in the usual case of straddling the seat and holding on to the handle bars with both hands. Maybe if the rider where standing on the seat and not holding on...
 * I haven't heard of a left-turn-only bike, but I would argue that it would be nearly as unridable as the no-steer bike. -AndrewDressel (talk) 02:56, 28 November 2007 (UTC)

I studied this as part of my engineering degree on control theory. It's unfortunately too long ago for me to remember off the top of my head the maths or the details, but the conclusion is interesting. Bicycles are examples of positive pole systems. This explains the counter steering needed, and also other features of the dynamics such as how easy it is to make it unstable. If you put too much gain in and try to counter steer too much you go over, so there's only a limited range of gain you can use in your control system (the rider). This sounds a similar analysis to the Eigenvalues but using a different technique and a different way of interpreting the results. —Preceding unsigned comment added by 213.146.159.254 (talk) 12:07, 30 January 2008 (UTC)


 * Yes, the eigenvalues are the same as the poles of the transfer function. -AndrewDressel (talk) 15:04, 30 January 2008 (UTC)

New topics
Unicycle physics and Physics of a rolling coin Wow! Anyone know who is 80.168.225.36? The "fmt hdrs as per manual of sty" looks good. AndrewDressel 13:56, 23 June 2006 (UTC)

Misconceptions
The_Anome "rm unnecessary cite: all this can be confirmed from the other cites given below" at 22:49 on 23 June 2006, but I think he misunderstood why I included the link. Instead of just restoring it, I made a new section and listed a handfull of other examples. It may not be appropriate for this article, but it gives me a chuckle. AndrewDressel 01:23, 24 June 2006 (UTC)

Name Change?
After reading the FA requirements, especially for lead section, I'm thinking of changing the title to "Bicycle and motorcycle dynamics". Dynamics is a much better fit than physics. Otherwise, in order to be complete, the article would need to be expanded to include performance, efficiency, etc. Given the very different power plants and speed ranges of bicycle and motorcycles, I believe this would be impractical. Comments? AndrewDressel 14:32, 26 June 2006 (UTC)
 * Done AndrewDressel 14:28, 27 June 2006 (UTC)

Peer Review
I probably won't be able to go through this article in the detail I'd like until this weekend, but I'll try and put the things I find that I haven't had the time to correct yet and maybe some other folks can help? Some of these are more questions of style than actual problems...


 * Do we really want a 'Examples of misconception' section? It seems odd to point to information that is known to be incorrect.  In my mind, it is sufficient to have correct and verified information in this article.


 * -My concern is that the misconception is so prevalent that if the article doesn't address it, it becomes a glaring omission. The Coriolis effect article addresses the "popular misconception...that the Coriolis effect determines the direction in which bathtubs or toilets drain". Perhaps that is not the gold standard. AndrewDressel 01:44, 30 June 2006 (UTC)


 * I wonder if it'd be better to address common misconceptions in the main portion of the article (perhaps with references to sites which have an incorrect explanation), rather than a section which has only links to external sites that are 'incorrect,' but without reference to what at those sites is incorrect? Saturn V 17:36, 30 June 2006 (UTC)


 * Took a step in that direction. AndrewDressel 01:21, 2 July 2006 (UTC)


 * The braking section is almost entirely bicycle-centric (if that's a valid term). For example, flipping the rider over with the front brake is less of a concern (to my mind) for motorcycling than locking the front wheel.  I don't know whether the dynamics of high-side crashes on motorcycles are appropriate for this article, but to my (purely annocdotal) knowledge, a front tire locking is the most common cause of such events...


 * -It may be more prevalent with bicycles, but just do a quick Google image search on "stoppy" to see how 'popular' it is with motorcycles. Perhaps I can list cruiser style motorcycles as another example along with recumbents. AndrewDressel 01:44, 30 June 2006 (UTC)


 * Stoppies are often discussed in reference to motorcycle stunting, and most modern sportbikes and standards have powerful enough front brakes to allow for such behavior (although it's not really recommended as a panic stopping technique), but I think that in everyday motorcycle usage, locking the front wheel is a much larger concern. That's not to say that the physics presented on the amount of brake force required shouldn't be included - it should.  My wish is that I'll be able to find something with reasonable physics content on high-side dynamics to accompany this portion of the article. Saturn V 17:36, 30 June 2006 (UTC)


 * High-side physics will be tricky. It all depends on an increase in friction: either from hitting a solid object such as a curb or sliding through a low friction patch such as oil or sand. AndrewDressel 01:21, 2 July 2006 (UTC)


 * 'Mass distribution' contains no mention of rider positioning, which again may be primarily a motorcycling concern.


 * -Actually, given the ratios of rider mass to machine mass, it is a bigger factor in bicycling. What mention do you suggest? AndrewDressel 01:44, 30 June 2006 (UTC)


 * I was thinking of including it in the last sentence - I'll try and wordsmith it this weekend...Saturn V 17:36, 30 June 2006 (UTC)


 * Question for the physics savvy out there: Does tire profile play any role in the dynamics of motorcycles (or bicycles) beyond providing a surface for traction?  Are there differences in the amount of deflection of tire required to initiate the lean based on tire profile, or even width?


 * -Yes, tire profile does play a role. Tires are mentioned in the second paragraph of the "Balance" section and again in the "Stability with full suspension" section. Perhaps there should be more. AndrewDressel 01:44, 30 June 2006 (UTC)


 * Another question for the physicists: The article states that '(vehicles) with more trail feel harder to steer.'  I assume that this is because they are harder to steer (in other words, it takes greater force to deflect the tire while moving) - which means that we probably ought to include something on why that is.


 * -If we can find someone who "published" an explanation, right? AndrewDressel 01:44, 30 June 2006 (UTC)


 * Yes - I'll go looking for an explanation that I remember reading about in an article in one of the online motorcycle magazines on motorcycle dynamics, since I think that's where I remember reading something about why trail has this effect. I'll try and vet the actual physics of the article when I find it.  Saturn V 17:36, 30 June 2006 (UTC)


 * Should there perhaps be at least a mention of wheelbase and the effects of that variable, since it's in the figure for this document?


 * -Same as above. I believe that the effects are secondary or tertiary. I'll see what I can find. AndrewDressel 01:44, 30 June 2006 (UTC)


 * Although wheelbase is generally a secondary variable, for things like turning, the wheelbase has a significant determinative value (imagine, in a completely silly example, a motorcycle with a 100m wheelbase - the turning radius is unlikely to be that of a motorcycle with a 1m wheelbase, regardless of lean angles involved) in some aspects of the dynamics of the bike. Saturn V 17:36, 30 June 2006 (UTC)


 * All true, but not necessarily a 'dynamics' issue. AndrewDressel 01:21, 2 July 2006 (UTC)


 * I disagree with the statement (in 'Stability with a full suspension') that high frequency front wheel oscillations are "relatively harmless" - in the case of motorcycles, the oscillation (also referred to as a 'tank-slapper' when it gets bad) can occur with enough force to injure the riders arms and hands, and uncorrected can cause loss of control of the bike. I've also read that slowing down (well, actually, more specifically braking) may not be the best way to correct the issue - braking will transfer weight to the front wheel, which if I'm understanding it correctly, can lead to more forceful oscillations.

I'll update this list as I find more (or fix things). Saturn V 16:58, 29 June 2006 (UTC)

Automated peer review suggestions

 * by Andy t


 * See if possible if there is a free use image that can go on the top right corner of this article.
 * - is it possible to have lead image next to table of contents for better use of space? AndrewDressel 02:03, 28 June 2006 (UTC)


 * Per WP:WIAFA, Images should have concise captions.
 * - added caption to last image AndrewDressel 02:03, 28 June 2006 (UTC)


 * There may be an applicable infobox for this article. (Note that there might not be an applicable infobox; remember that these suggestions are not generated manually)
 * -Don't know of one that would apply. AndrewDressel 02:03, 28 June 2006 (UTC)


 * Per WP:MOSNUM, there should be a non-breaking space -  between a number and the unit of measurement. For example, instead of 18mm, use 18 mm, which when you are editing the page, should look like: 18&amp;nbsp;mm.
 * -Done. AndrewDressel 13:47, 28 June 2006 (UTC)


 * Per WP:MOSNUM, when doing conversions, please use standard abbreviations: for example, miles -> mi, kilometers squared -> km2, and pounds -> lb.
 * -Done. AndrewDressel 13:47, 28 June 2006 (UTC)


 * Per WP:MOS, headings generally do not start with the word "The". For example,  ==The Biography==  would be changed to  ==Biography== .
 * - None do. AndrewDressel 02:03, 28 June 2006 (UTC)


 * Please alphabetize the categories and/or interlanguage links.
 * - Done. AndrewDressel 02:03, 28 June 2006 (UTC)


 * There are a few occurrences of weasel words in this article- please observe WP:AWT. Certain phrases should specify exactly who supports, considers, believes, etc., such a view.
 * Watch for redundancies that make the article too wordy instead of being crisp and concise. (You may wish to try Tony1's redundancy exercises.)
 * While additive terms like “also”, “in addition”, “additionally”, “moreover”, and “furthermore” may sometimes be useful, overusing them when they aren't necessary can instead detract from the brilliancy of the article. This article has 10 additive terms, a bit too much.
 * Vague terms of size often are unnecessary and redundant - “some”, “a variety/number/majority of”, “several”, “a few”, “many”, “any”, and “all”. For example, “ All pigs are pink, so we thought of a number of ways to turn them green.”


 * The article will need references. See WP:CITE and WP:V for more information.
 * - It now has a references section.


 * Please ensure that the article has gone through a thorough copyediting so that the it exemplifies some of Wikipedia's best work. See also User:Tony1/How to satisfy Criterion 2a.

What still needs to be done?

 * Clean up notes and references. There seems to be a few different styles in use.
 * -Worked on, perhaps done.
 * Does the section on braking belong? It is certainly a part of bike physics, but it is not mentioned in the intro, and I can't think of a good way to add it.
 * -Now mentioned in lead section
 * Is the section on misconceptions appropriate?
 * -See discussion below...
 * A picture showing the relevant forces (gravitational, inertial if in a turn, aerodynamic, and ground reaction) would be nice.
 * -Added in turning section
 * Turning and braking could also use an illustration, but I can't think of what they would be, yet.
 * Should 'Turning' and 'Braking' come before 'Wobble and Shimmy' and 'Stability with full suspension'? They seem to be more basic.
 * -Well, wobble, shimmy, and stability all relate to balance, so leave them there.

AndrewDressel 01:33, 24 June 2006 (UTC)

Suggestions
1. This article is awfully light on non-science explanations - it would be nice if instead of "Bicycle and motorcycle dynamics is the science of the motions and forces of bicycles and motorcycles. It includes how they balance, steer, and brake." and so on that it was a bit simplified for the casual reader. For example, something like "Bicycle and motorcycle dynamics is the science of the steering, balancing, and breaking of bicycles and motorcycles." or something (I imagine that is incorrect but hopefully helps someone).


 * -Thanks for the suggestion on the lead paragraph. I tried to model it after other science articles, and it was a mess. AndrewDressel 01:24, 30 June 2006 (UTC)

2. "Examples of misconception" scares me - if it were me I'd nuke it - it seems pointless and something the reader should decide. Ditto for the mention of "incorrect" online examples (which, BTW, in these articles one really needs to be more specific then just "online").


 * -The problem is that with the prevalence of these misconceptions, it could seem that the article is incomplete without at least addressing them. AndrewDressel 01:24, 30 June 2006 (UTC)

3. "careful" in the lead is really redundant and speculative without attribution - "in fact", again, makes me think that the article is trying to prove some sort of point.


 * -Again, there are sites that refer to holding a spinning bicycle wheel to see how the gyroscopic effect keeps a bike upright. However, this is not correct. AndrewDressel 01:24, 30 June 2006 (UTC)

4. The lead should really have less stubby "paragraphs" 5. Referencing is a bit odd, I'd recommend some sort of script to convert those links to some other more accessable reference style.


 * -Isn't this "Embedded HTML links" as desicribed in Citing sources?AndrewDressel 01:24, 30 June 2006 (UTC)

6. "The design charactersics of a bike can affect the stability in the following ways"
 * a. "caractersics" is misspelled :) -Ouch AndrewDressel 01:24, 30 June 2006 (UTC)
 * b. This list should really be turned into prose

7. "A bike is a nonholonomic system because its outcome is path-dependent" and now the writer has lost me :(. This makes it difficult to evaluate the article... RN 08:03, 29 June 2006 (UTC)
 * Good job on improving the article!! I'm still uncomfortable with the misconception section, but even that is quite a bit better. Hopefully you'll get some comments from someone else! RN 06:54, 3 July 2006 (UTC)

Removed uncited claim
Would love to find a reference for:
 * "Nonstandard bike configurations, such as long-wheel-base recumbents that have a long steering boom, may have the steering mechanism center of gravity so far behind the steering axis, that in a lean, this factor over-powers all others, the front wheel actually steers away from the lean, and they do not exhibit self-stability at any forward speed."

Until one is found, it can stay here. -AndrewDressel 00:50, 4 August 2006 (UTC)

Lean angle calculations
I cannot believe that stayed incorrect as long as it did. Maybe someone tweaked it and I didn't notice. More likely, I just goofed. The equation that was there was for lean away from vertical, but the drawing of course shows lean up from horizontal. Anyway, great thanks to 128.227.67.147 (in their first and only edit so far) for noticing it and fixing it. -AndrewDressel 03:14, 8 February 2007 (UTC)

Physics article assessment
While I may be biased, because of the work I have done on this article, I gave it an "A" because I believe it meets these criteria:
 * Provides a well-written, reasonably clear and complete description of the topic
 * -Check


 * It should be of a length suitable for the subject, with
 * a well-written introduction and
 * -Check
 * an appropriate series of headings to break up the content.
 * -Check


 * It should have sufficient external literature references, preferably from "hard" (peer-reviewed where appropriate) literature rather than websites.
 * -Check


 * Should be well illustrated, with no copyright problems.
 * -Check


 * Very useful to readers.
 * A non-expert in the subject matter would typically find nothing wanting.
 * -Check


 * May miss a few relevant points.
 * -Probably true


 * Minor edits and adjustments would improve the article, particularly if brought to bear by a subject-matter expert. In particular, issues of breadth, completeness, and balance may need work.
 * -Probably true


 * Peer-review would be helpful at this stage.
 * -Done, but only 2 editors participated, and one was automated.


 * At the stage where it could at least be considered for featured article status, corresponds to the "Wikipedia 1.0" standard.
 * -Nominated by The Anome 22:47, 23 June 2006 (UTC), but failed.

If anyone disagrees, I'd love to hear about it. -AndrewDressel 18:40, 1 March 2007 (UTC)

Redundancy and potential original research
"These roles of gyroscopic effect and precession are often given as the prime reasons that bicycles and motorcycles are inherently stable."


 * This is covered later in the article in the "Other hypotheses" section in a way that has so far avoided POV objections.

"While they have an effect at significant speeds, the role of caster angle, and the rider's steering action, actually provide the bulk of a bike's inherent stability at lower, nominal speeds."


 * The liturature already cited in this article indicates "trail" to be primary parameter. Also, it seems contradictory to attribute "inherent stability" to "the rider's steering action".

"This is easily proven. As a first example, a bicycle rider at even the slowest speed of 1 or 2 MPH can easily keep the bike stable. The contribution of gyroscopic and precession effects are absolutely negligible at such a speed (only the rider's steering and body movements influence stability at such speeds)."


 * Without a reference, this assertion about negligible gyroscopic effects is OR.

"Moreover, consider an ice skater on one skate, or a pogo stick rider, neither of which has any gyroscopic or precession effects in action: the skater or pogo stick are stabilized by "driving" the vehicle in question manually. This means simply riding -- keeping the surface that contacts the ground, on average, under the center of mass."


 * This may be better placed in the "Balance" section.

"As another test, one can try locking the steering of a bicycle or motorcycle, and then giving it a push - it will fall over just as quickly as leaving it stationary and letting go."


 * This is already stated in the "Balance" section.

"A bike with a free steering mechanism can be given a push at a relatively slow speed, and due to caster effect, will move smoothly with stability -- there is no rider, and there are no significant gyroscopic effects whatsoever."


 * This is already described in the "Self stability" section and quantified in the "Eigenvalues" section.


 * -AndrewDressel 02:28, 7 April 2007 (UTC)

GA nominee
Let's see how far the reviewers like the article now that most things seem to have been cleaned up. I went through it once and didn't see anything *obvious*. Nominated as a GA. SeveroTC 23:25, 17 May 2007 (UTC)

GA review comments

 * What is the link between the topic and the image in the lead section. I am not able to correlate. Can you please consider adding additional notes to the image to make it clear. Suggestion: I think an animation file explaining a simple concept would be really helpful to get a FA vote. it is not an issue at GA.
 * I've added some info&mdash;does this make sense now, or does it need explaining in a different way? SeveroTC 22:48, 2 June 2007 (UTC)


 * "Bicycle and motorcycle dynamics is the science of the motion of bicycles and motorcycles. It is concerned with the motions of bikes, their parts, and the forces acting on them. Specific subjects include balancing, steering, braking, and suspension." - lot of redundancy in the sentences. my try to make it concise would be "Bicycle and motorcycle dynamics is the science of the motion of bicycles and motorcycles, in entirety or its parts, due to the forces acting on them during balancing, steering, braking and suspension."
 * ✅ Done &mdash; your suggestion sounded good so has gone straight in. SeveroTC 22:43, 2 June 2007 (UTC)


 * combine all four paras into one long lead para. please ensure that a para contains atleast four if not more sentences
 * ✅ Done &mdash; SeveroTC 22:43, 2 June 2007 (UTC)


 * MAJOR Concern: A non-physics grad will have difficulty in understading this article (at its basic level). I suggest you add a section that provides details on the various forces that are at work and what their impact would be. Eg: Centrifugal force - how does it affect a bike in motion?
 * Please respond to this comment. This pertains to the section "Forces". How does each of the force affect the bicyle individually. This is the biggest concern i had. --Kalyan 14:39, 13 June 2007 (UTC)
 * Although I started the section on forces, I do not think it will be worth while to expand it much beyond simply enumerating them. They interact in complicated ways, and I can't think of a way to get started at explaining how each of them affects the bicycle individually. None of the references cited use this approach either, as far as I know, so it would also most likely come across as a lot of original research. Instead, what all the authors that I have read try to do is describe the important parameters of a bike and what role they play, and then describe the different motions that a bike can go through.


 * If you have a specific question that the article does not already answer, perhaps I can add that. -AndrewDressel 19:39, 14 June 2007 (UTC)


 * Fair enough. If that is the case, can you revisit the "Forces" section and maybe considering listing the various forces or types of forces so that it is easier for understanding. Even that is just a suggestion. --Kalyan 09:45, 19 June 2007 (UTC)


 * "Forward speed: The faster a bike is moving forward, the smaller the steering inputs ..." - this needs to be explained
 * Rewritten&mdash;does this make sense now? SeveroTC 23:02, 2 June 2007 (UTC)


 * can you add Rw, Ah to the figure for better understanding
 * Not without an image editor that handle svg images. -AndrewDressel 19:15, 4 June 2007 (UTC)
 * Fair enough. re-categorise to "suggestion". --Kalyan 14:39, 13 June 2007 (UTC)


 * "distance by which the front wheel ground contact point trails behind the point where a line through the steering axis intersects .." - what is steering axis? where is it defined prior to this point?
 * It is defined, along with several other terms in the Bicycle and motorcycle geometry article linked to at the first use of the word "trail" in the text. -AndrewDressel 19:15, 4 June 2007 (UTC)
 * I've used the one sentence definition from Bicycle and motorcycle geometry and provided a link to that article at that point as well. SeveroTC 10:47, 6 June 2007 (UTC)


 * " This can occur very slowly if the bike is moving forward quickly." - what does this sentence mean?
 * Reworded, although not much. Is this enough? SeveroTC 23:59, 2 June 2007 (UTC)


 * The article needs copyedit as it is not easy to understand even the non-physics, non-formula portion
 * Still believe that the article needs copyedit before it gets to FAC. --Kalyan 14:39, 13 June 2007 (UTC)

It is getting pretty late and i shall come back with more feedback as i see that i have already given enough to work/chew on. --Kalyan 20:30, 2 June 2007 (UTC)

Balance of forces
"This is necessary in order to balance the sideways friction against the road which is the centripetal force due to the turn, with gravitational forces due to the lean."


 * Since frictional forces against the road and gravitational forces are perpendicular to each other(in the ideal case), I don't see how it can be said that these balance each other. Centrifugal force is a perfectly valid explanation from the point of view of a bike and rider, and it matches better with a person's experience of the world. A rider in a vehicle in a turn can definitely feel centrifugal force pulling or pushing them towards the outside of the turn.

"a bike and their components"


 * "its" is correct here.

"Friction"


 * The main frictional force, at the tire contact patches, is already included in ground reaction "with both horizontal and vertical components". If it is listed, a little detail about where it acts is necessary.

"These forces make bicycle accelerate forwards or sideways (if moving in a circle at constant speed)."


 * This is certainly not all they do (increase or decrease lean, for example). If we're going to open this can of worms, it will require a lot more detail than this.

-AndrewDressel 16:03, 15 June 2007 (UTC)

lean angle and wheelbase
I removed the mention of wheelbase as a factor in the lean angle in the introduction by LarRan. This would need a reference and should be included in the section on turning, especially the equation used to calculate lean angle from turn radius and forward speed. -AndrewDressel 15:50, 27 August 2007 (UTC)
 * It is a "well-known fact" among motorcyclists (such as myself) that the longer the wheelbase, the more lean is required for the same turn at the same speed. There must be scientific evidence for this somewhere. Or is this a myth, such as the gyroscopic effect of the wheels keeping a bike upright? LarRan 11:15, 31 August 2007 (UTC)
 * I can find no mention of wheelbase being a factor in the lean angle of bikes in either "Bicycling Science, Third Edition" by Wilson or "Motorcycle Dynamics, Second Edition" by Cossalter. I imagine, that in the extreme case, when wheelbase is a significant fraction of the turn radius, then the necessary lean angle would be different than the stock calculation predicts because the center of mass would be on a significantly different trajectory than the wheels. However, I can find no reference for this. -AndrewDressel 15:39, 4 September 2007 (UTC)

Recent unsourced additions
I've moved some recent addtions to here:


 * - for the case of bicycles at low speeds


 * -, though it has less of a tendency to balance itself


 * - Most motorcycles are self-stable at highway speeds, and will remain upright with no rider input.

At this point, after the good article review, these all would need a reputable (on the order of "Bicycling Science" by Wilson, "Motorcycle Dynamics" by Cossalter, or a published paper) to be included. -AndrewDressel 01:37, 19 September 2007 (UTC)

Additions to braking
I believe this material is better suited to the Bicycle brake systems article, partly because it is only about bicycle braking, but also because it is more about the mechanics of braking than the dynamics of bikes. However, before I insert it there, it needs a clean up:


 * - There are several sentences that do not seem to be complete: "The limiting braking is the lesser of ..."


 * - There are several instances of non-encyclopedic language: "... majority of (low quality) cyclists", "Off-road things get more gnarly...", and "Use only minimal braking, turning, acceleration lest LF is exceeded."


 * - Bicycle brake systems, as does Bicycle and motorcycle dynamics, uses American English spelling, and so 'tyres' should be 'tires', etc., per Manual of Style. -AndrewDressel 21:39, 14 October 2007 (UTC)


 * ===Front wheel braking===


 * The limiting braking is the lesser of:
 * Limiting friction of tyre/ground,
 * Pitching over front wheel
 * brake pad to rim/disk.


 * For a bicycle on good ground with excellent brakes pitching will apply: CofG on a typical diamond frame will be about 600 mm back from the front wheel contact patch and 1200 mm above, giving 0.5 g (4.9 m/s² or 16 ft/s²)deceleration. However if the rider modulates the brakes there is no problem. If the rider moves his weight back and down he can get even bigger decelerations.


 * Most front brakes aren no strong enough so on the road they are the limiting factor. Cheap cantilever brakes, especially with "power modulators", severely restrict the stopping power. So do Raleigh style side-pull brakes. In the wet they are even less effective.


 * Off-road things get more gnarly so front-wheel slides are more common.


 * ===Rear wheel braking===


 * Fine for gentle speed control but can only give about 0.1 g at best.
 * Note that this is contrary to the received wisdom of the majority of (low quality) cyclists.


 * ===Wet weather stopping===


 * Water and mud act as a lubricant between tyre and ground as well as between pad and rim. As braking starts the water and mud get driven off the pad and rim so the available friction will increase. With good disks they dry out quickly so the limiting factor is the friction between tyre and ground. With good compounds wet stopping can approach dry stopping.


 * Most bicycles have rim brakes that get continually wetted and so do not provide such good stopping in the wet. Cheap or badly maintained bikes cannot provide enough pad force to push through the water and mud film on the rim, so they do not stop in the wet.


 * ===Icy weather stopping===


 * The limiting friction will be between the tyre and ground, and will be small and variable. Use only minimal braking, turning, acceleration lest LF is exceeded. Use only very gentle braking and mostly the rear to stop front-wheel slides.

It all came back again, even the typos ("aren no"), so to avoid some kind of revert battle I tried to clean it up. It still overlaps longitudinal stability some. However, the sections on wet weather and icy weather really have nothing to do with Bike Dynamics. They belong in the Bicycle brake systems article if anywhere. Even there, the icy weather section is more of a "how to" than wikipedia wants. -AndrewDressel 21:21, 15 October 2007 (UTC)

The examples of braking, whether front,rear, wet or icy, were for bicycles. However the physics apply to both bicycles and motorcycles. Wet and icy conditions do affect the braking and steering of a bike, that's why they were inserted.


 * True, but this is an article about dynamics, not physics. A discussion of the effect of lubricants on the friction between brake pads and rims belongs in the bicycle brake system article. -AndrewDressel 13:15, 20 October 2007 (UTC)
 * Dynamics is a subset of physics. However I would admit that rim braked bicycles are more affected in the wet than motorcycles that have drum or disk brakes. In the the general case most brakes need drying/cleaning before they start to work. This is why you are supposed to drag your brakes after fording to get rid of the water, especially from drums. Rim brakes do take a relatively long time for the water and mud to be removed. Disk brakes still need some cleaning/drying. For the brake to work the lubricant film must be broken, this is why I used the term "pressure". Verity1234 06:48, 21 October 2007 (UTC)
 * It can be argued that every physical science is a subset of physics. In any case, as you point out, this article is about the clearly defined subset of physics called dynamics. The intricacies of brake opperation and tire adhesion on different surfaces are not in that subset. -AndrewDressel 16:03, 21 October 2007 (UTC)

Your edits to do with braking friction reduce the clarity. Limiting and sliding friction are different and should be written as such. Read Wilson (Bicycling Science). Verity1234 08:08, 20 October 2007 (UTC)


 * I have read Wilson, and I cannot find the expression "limiting friction" there just "limiting value". Beer and Johnston do not use it in their "Vector Mechanics for Engineers". Meriam and Kraige mention "limiting or maximum value of static friction" in their "Engineer Mechanics". Hibbeler goes so far as to mention "limiting static friction" in his "Engineering Mechanics". Perhaps limiting friction is a British English term. It does not appear to be in common usage here in the US. It certainly did not make the article clear to me. The sentence fragments did not help. -AndrewDressel 13:15, 20 October 2007 (UTC)


 * http://en.wikipedia.org/wiki/Friction Verity1234 06:48, 21 October 2007 (UTC)


 * Sadly, the definition of that term is not referenced in that article, and one Wikipedia article is a poor reference for another Wikipedia article. -AndrewDressel 16:03, 21 October 2007 (UTC)


 * In fact I've gone ahead and updated the friction article to reflect the reality that while at least one source does use the term, plenty of others do not. It is not used universally and so would be confusing to use here without explanation. -AndrewDressel 12:17, 22 October 2007 (UTC)


 * Anyone with A-level maths or better would call it limiting friction. It is actually an aggregate term in that it covers a number of small scale physical effects, it is called LF because the exact physics isn't important, just that it starts to slip at a particular force. Again sliding friction is caused by may bits of physics but on a real road/trail it is hard to do the detail, just work out the lump sum. So for most purposes coefficient of friction is a magic number used to do the calculations. Verity1234 10:43, 12 November 2007 (UTC)


 * That may be true where ever the expression A-level maths is used, but not universally, hence the current wording. In fact, my spell checker flags maths as a misspelling. -AndrewDressel 14:19, 12 November 2007 (UTC)

Forces – Centrifugal and Free Body Diagram
Since centrifugal forces do not exists they should not be referred to in a physics article. They could be identified as a colloquialism and the misconception could then be addressed.

A free body diagram within the section is a must as it represents how physicists assess such things. And on such a diagram "centrifugal" would not be found.

People often believe a force is necessary to keep something going as a apposed to necessary for changing its motion. Referring to a centrifugal force is similar. Nothing is pushing the rider outward, something is pushing the rider inward. This is neither nuance nor a small matter.

Earth to McFly (talk) 22:16, 24 November 2007 (UTC)


 * According to the Centrifugal force article,
 * "centrifugal force appears when a rotating reference frame is used for analysis."
 * "In the reference frame that is rotating together with the [vehicle] (a model which those inside the [vehicle] will often find natural),"
 * "A number of physicists treat it much as if it were a real force, as they find that it makes calculations simpler and gives correct results."
 * That is how centrifugal force is used in this article. -AndrewDressel (talk) 02:50, 25 November 2007 (UTC)

Light rear wheel braking: "dragging"
This claim remains unsourced since October 2007, so I've moved it here. -AndrewDressel (talk) 16:55, 14 February 2008 (UTC)
 * On motorcycles, light rear-wheel braking, sometimes referred to as dragging, can be a useful aid to stability when turning at low speed.

Delisted from GA
In order to uphold the quality of Good articles, all articles listed as Good articles are being reviewed against the GA criteria as part of the GA project quality task force. While all the hard work that has gone into this article is appreciated, unfortunately, as of February 13, 2008, this article fails to satisfy the criteria, as detailed below. For that reason, the article has been delisted from WP:GA. However, if improvements are made bringing the article up to standards, the article may be nominated at WP:GAN. If you feel this decision has been made in error, you may seek remediation at WP:GAR. GA review – see WP:WIAGA for criteria


 * 1) Is it reasonably well written?
 * A. Prose quality:
 * B. MoS compliance:
 * 1) Is it factually accurate and verifiable?
 * A. References to sources:
 * B. Citation of reliable sources where necessary:
 * C. No original research:
 * 1) Is it broad in its coverage?
 * A. Major aspects:
 * B. Focused:
 * 1) Is it neutral?
 * Fair representation without bias:
 * 1) Is it stable?
 * No edit wars, etc:
 * 1) Does it contain images to illustrate the topic?
 * A. Images are copyright tagged, and non-free images have fair use rationales:
 * B. Images are provided where possible and appropriate, with suitable captions:
 * 1) Overall:
 * Pass or Fail:
 * 1) Is it stable?
 * No edit wars, etc:
 * 1) Does it contain images to illustrate the topic?
 * A. Images are copyright tagged, and non-free images have fair use rationales:
 * B. Images are provided where possible and appropriate, with suitable captions:
 * 1) Overall:
 * Pass or Fail:
 * B. Images are provided where possible and appropriate, with suitable captions:
 * 1) Overall:
 * Pass or Fail:
 * Pass or Fail:

Detailed comments
 * The forces section is a list disguised as prose, with meandering parentheticals. This whole section shoud be dissolved into the rest of the article or expanded.
 * This is arbitrary as the section was added during the GA nomination process to explain and link to the forces early on. How can the concerns of the original GA reviewer be met without the section? SeveroTC 01:52, 13 February 2008 (UTC)
 * There are two aspects to this comment, one pertaining to the forces section and the other to the GA process. Regarding the forces section, as I understand the original GA section above, the original reviewer asked for it to be expanded to list "the various forces or types of forces so that it is easier for understanding".  This has been done, which is great.  My concern is that the section only consists of a single long sentence listing all of the forces and giving details of them in parenthesis after each.  It reads like a bulleted list without the bullets).  To meet with the wp:manual of style, the paragraph should be changed so that each force has its own sentence which names it and includes the information currently in brackets.  There's an example of this at Embedded list.
 * In reference to having GA reviewers with deferring opinions, I completely agree that this is an issue with the GA process. It's solved in the featured article process by requiring consensus from any number of reviews—the cost of the good article process being simpler is that different articles will inevitably be held to different standards.  One way the good article project is trying to mitigate this problem is by having all existing good articles checked by vetted reviewers at Good articles project quality task force.--jwandersTalk 02:29, 13 February 2008 (UTC)


 * Rewritten with just one remaining parenthetical (detailing what is meant by steering mechanism) and no single-sentence paragraphs. -AndrewDressel (talk) 15:31, 13 February 2008 (UTC)


 * Example of chunky writing: "Speed changes, making the bike stiffer or lighter, or increasing the stiffness of the steering (of which the rider is the main component) can change the oscillation frequency, though only speed change is applicable in the situation."


 * Dechunked to "The oscillation frequency can be changed by changing the forward speed, making the bike stiffer or lighter, or increasing the stiffness of the steering, of which the rider is a main component." -AndrewDressel (talk) 20:56, 13 February 2008 (UTC)


 * Paragraph out of place in "Balance" section: "If the steering of a bike is locked, it becomes virtually impossible to ride. Instead, if just the gyroscopic effect of rotating bike wheels is cancelled by adding counter-rotating wheels, it can still be easily ridden."


 * It does belong there. Clarified by specifying "balance while riding". -AndrewDressel (talk) 01:04, 13 February 2008 (UTC)


 * Run-on sentence: "A factor that influences how easy or hard a bike will be to ride is trail, the distance by which the front wheel ground contact point trails behind the point where a line through the steering axis, the axis about which the steering mechanism (fork, handlebars, front wheel, etc.) pivots, intersects the ground."


 * Split into "A factor that influences how easy or hard a bike will be to ride is trail, the distance by which the front wheel ground contact point trails behind the steering axis ground contact point." and "The steering axis is the axis about which the entire steering mechanism (fork, handlebars, front wheel, etc.) pivots." -AndrewDressel (talk) 01:09, 13 February 2008 (UTC)


 * Manual of Style problem: Many single sentence paragraphs, even single sentence sections, see Guide_to_layout.


 * No remaining single-sentence sections. -AndrewDressel (talk) 21:50, 13 February 2008 (UTC)
 * No remaining single-sentence paragraphs, except perhaps paragraphs with several equations that are difficult to categorize. -AndrewDressel (talk) 17:15, 14 February 2008 (UTC)

--jwandersTalk 00:05, 13 February 2008 (UTC)


 * I believe all the deficiencies itemized above have been addressed. Any chance that means the article can simply regain its GA status? -AndrewDressel (talk) 17:21, 14 February 2008 (UTC)

Yup, I'm happy to simply re-instate this. Thanks for all your prompt hard work; first time an article that I've had to delist has received any sort of reply. Kudos! --jwandersTalk 19:39, 14 February 2008 (UTC)

Dynamic instability
There is something fundamentally wrong here. As anyone learning to ride a bicycle knows, you can have the easiest, most self-steering bicycle in existence and you will still fall off. After a painful learning process you discover the knack of making small adjustments, and once that becomes a reflex, the experience of riding is just the same as if the bike stays upright on its own.

The way a bike stays upright is by making constant small corrections. I'm not a physicist but dynamic instability is the term that comes to mind - possibly dynamic equilibrium (neither has a Wiki entry that is remotely relevant here). It is highly misleading to suggest that some bikes are self stabilising. Until you get into the realms of powered computer-controlled systems, e.g. Segway, this is simply not true. Yes, a lot of rake increases stability but it does not eliminate the need for corrections.

There is an interesting essay on the subject, here How two bike mechanics taught the human race to fly ProfDEH (talk) 07:33, 8 May 2008 (UTC)


 * Although people may find it tricky to lean how to ride a bike, the fact remains that many bikes are self-stable at forward speeds in a specific range. This is extensively documented, and there is even a video demonstration linked to by the article. Perhaps the difficulty is that many beginning riders move too slowly and so do not reach the speed necessary for self-stability (12-18 mph in the example given in the article), or they simply apply their own control algorithm that negates the inherent self-stability of their bike. Another possibility is that the particular bikes that are often used by learners, small kids' bikes, do not possess self-stability at any speed. All this is pure speculation on my part, as I have not read any studies on the matter. Never-the-less, as the video shows, the right bike at the right speed is perfectly capable of generating its own steering corrections, even rejecting a strenuous push to the side.
 * Both Wilson in Bicycling Science and Cossalter in Motorcycle Dynamics refer simply to 'stable' and 'unstable' or 'stability' and 'instability'. Perhaps 'dynamic' is assumed. In any case, I believe stability is usually defined in reference to 'equilibrium' so that part is covered too. One interesting thing about the Wright Flyer is that they managed to be so successful with such an unstable machine with its negative dihedral, extreme aft position of the center of gravity, and canard horizontal stabilizer. It certainly was not an easy plane on which to learn, as recent attempts to fly reconstructions attest. -AndrewDressel (talk) 14:08, 8 May 2008 (UTC)
 * The movie is currently missing. ProfDEH (talk) 21:37, 8 May 2008 (UTC)
 * Hmmm. I watched it just this morning and again just now. It's a 3.7mg mpeg. Here's a link to another, slightly longer copy: . Both are on the same server and take a while to load, during which time my browser gives no indication that anything is happening. -AndrewDressel (talk) 21:58, 8 May 2008 (UTC)
 * I've redirected the link there. It certainly convinced me the bike is stable on its own. Bike and rider together is more complicated. ProfDEH (talk) 06:46, 9 May 2008 (UTC)

Karl von Drais
I've been taking a look at this article with the idea of doing some copy-editing, and I can tell immediately that this will be a real challenge&mdash;the article is basically in terrific shape right now. I'll keep looking, though. And perhaps another role I can play here is Sample Layperson. When reading the History section it jumped out at me that it was "Karl von Drais himself" (emphasis is mine). I had to follow the wikilink to find out who he was. Could we add a small phrase, within commas or parentheses, about this notable person (notable not just to science, but to the article at hand as well). I'm not the best person to word this, but it would be something like: "In the early 1800s Karl von Drais, inventor of the velocipede (a bicycle prototype) showed that a rider..." This might be appreciated by your lay readers. --AnnaFrance (talk) 18:44, 27 May 2008 (UTC)
 * Good idea. I've given it a try. -AndrewDressel (talk) 03:02, 28 May 2008 (UTC)

Center of mass location
In speaking of a bike as an inverted pendulum, the point is made that balancing is easier with a higher center of mass, but that a lower center of mass actually seems easier to the rider when stationary. I gather from this section that balance actually is easier with a lower center of mass when stationary. But then the last sentence says that touring cyclists are advised to carry loads low, i.e., maintain a low center of mass. This confuses me. They would be in motion more of the time, so wouldn't they want to maintain the higher center of mass? Extra note: Isn't it about time to archive this talk page? --AnnaFrance (talk) 14:54, 29 May 2008 (UTC)


 * That should be 'hold upright' when stationary, as at a traffic light, not 'ride'. I don't have a reference that address the entire issue, just the two separate cases: 1) balance while riding is easier with a higher center of mass, and 2) tourists are advised to pack their gear low. I've tried to synthesise a bridge between them without injecting original research. The first point is illustrated by an inverted pendulum. The second point could be illustrated by second-class levers (A bike can be thought of as a vertical second-class lever. A small force at the end of the lever, the seat or handlebars at the top of the bike, more easily moves a large mass if the mass is closer to the fulcrum, which is located where the tires touch the ground). -AndrewDressel (talk) 15:08, 29 May 2008 (UTC)


 * That makes perfect sense. I wish your explanation could be worked into the text, but I understand your point about not introducing original research. Thank you for the explanation, though. It really helped. --AnnaFrance (talk) 23:04, 29 May 2008 (UTC)


 * I've given it a try. I don't think it is any more OR than before. The second-class lever analogy can be confirmed in the lever article. -AndrewDressel (talk) 00:42, 30 May 2008 (UTC)


 * Sure to the archive. What are the rules? Does it have to go by date? Some of the stuff is just conversation that only needs to be kept for archival purposes, I guess, but some stuff is meaty discussion that might help skeptics. -AndrewDressel (talk) 00:42, 30 May 2008 (UTC)

Instability lead section
Do you think it would improve this opening section to take the second paragraph and insert it between the 1st and 2nd sentences of the first? Then you would be introducing the idea of instability, defining the terms stability and instability, and finally introducing the types of instability. Also, I wish something more could be done with the Modes section. It's a section that consists of one line, and much of that is redundant. But it is needed to balance out the Design Criteria section. If you have any free time, you might want to see if there's any way the Modes opening section could be expanded.

Old Business: I like the way you included the second-class lever explanation in the Center of Mass Location section. I think it helps.

Archiving talk page: I've studied up on archiving talk pages, and I think I understand. Let me try it late tonight. That way the activity should be done for the day here, and we can label the archive as being Apr 06 - May 08, starting fresh tomorrow with June 1. --AnnaFrance (talk) 19:46, 31 May 2008 (UTC)

Assessment comment
Substituted at 14:21, 1 May 2016 (UTC)

Talk Page Archive
Archive 1 has been created with a link at right. Archive 2, when needed in the future, should be a new subpage (same as creating an article) titled "Talk:Bicycle and motorcycle dynamics/Archive 2" and the link added to the template on this page's code. For further information on archiving see How to archive a talk page. --AnnaFrance (talk) 04:24, 1 June 2008 (UTC)

Wobble or shimmy
In reference to a change I just made in the sentence:


 * While wobble or shimmy can be easily remedied by adjusting speed, position, or grip on the handlebar, it can be fatal if left uncontrolled.

The "it can be fatal" was originally "they can be fatal". When I made that change, I was assuming that "wobble or shimmy" was referring to 2 words for the same (one, singular) thing. The longer I stare at the sentence, though, the less sure I am that this is what was meant here. Did you mean them to be one thing in this particular sentence, or two?


 * As far as I can tell, authors use either or both of those words to mean the same, single phenomenon. Perhaps after the lead sentence of that paragraph/section, only one term should be used, though I don't know which would be best. -AndrewDressel (talk) 14:26, 3 June 2008 (UTC)


 * I think the paragraph is perfectly clear as it is. My only concern was that the sentence might have been intended to separate the terms, and I wanted to make sure I wasn't changing the meaning. --AnnaFrance (talk) 00:40, 4 June 2008 (UTC)

Old business: I think the opening paragraph of the Instability section works better now (and you eliminated the repetitions). --AnnaFrance (talk) 15:56, 2 June 2008 (UTC)

A few small copy-edit issues

 * Could you check all occurrences of handlebar(s) to make sure they are correctly singular or plural?
 * Hmmm. Probably should all be the same, right? Unfortunately, I don't know which, and the bicycle handlebar article doesn't help. -AndrewDressel (talk) 22:14, 5 June 2008 (UTC)


 * I did a quick check, but couldn't find a policy on whether the initial occurrence of section titles should be bolded. Article titles definitely. But section titles? I'm not sure. Do you know? If not, I'll investigate. Right now we've got some sections that do, some that don't. We need to find out what's correct.
 * I do not know. -AndrewDressel (talk) 22:14, 5 June 2008 (UTC)


 * In Two-wheel steering this sentence doesn't work:


 * One working prototype by Ian Drysdale in Australia is reported "by all accounts it seems to work very well."


 * Could we say something like:


 * One working prototype by Ian Drysdale in Australia is reported to "work very well".

--AnnaFrance (talk) 18:33, 5 June 2008 (UTC)
 * Looks good to me. -AndrewDressel (talk) 22:14, 5 June 2008 (UTC)

The handlebars issue is a minor one. I've changed the sentenced discussed above. About the bolding: I hear that WP generally discourages bolding outside of titles. Since there are so many sections in this article, it seemed to me that any extra bolding might be seen as screen clutter, so I've taken it all out. --AnnaFrance (talk) 19:40, 6 June 2008 (UTC)

Turn normal to the plane
In the first paragraph of the Tires section, could we get a brief definition of the term "normal" in parentheses? I think the lay reader can infer the gist of most of the technical terms in this article (contact patch, side slip, etc.), but this one may be a little advanced. --AnnaFrance (talk) 20:20, 7 June 2008 (UTC)
 * Tried to make clearer without just defining normal in parentheses. That's what the wikilink is for, right? -AndrewDressel (talk) 15:41, 9 June 2008 (UTC)
 * It does seem more understandable now (it's a little difficult to imagine reading it for the first time now). About the wikilinks, as I understand from the WP guidelines, we should try to reserve them for further reading or more in-depth reading. The article, though, should be intelligible to a lay person in itself. That's the ideal, which becomes less attainable, surely, the more technical the article's subject becomes. This particular article is in a rather gray area: most is within the average person's grasp, but some material is necessarily more advanced. I think it does a remarkable job of making technical information understandable. --AnnaFrance (talk) 17:45, 9 June 2008 (UTC)

Opening definition
I'm going to go back through the article now with an extensive list of WP:MOS guidelines, to try to find any small points missed before. (If anyone would rather that I stop with the nitpicking, please just say so.) One small item that I think would be worth some real effort to get perfect is the opening definition of the article's subject. As a grammatical sentence, I don't think it works all that well: "Bicycle and motorcycle dynamics is the science of the motion of bicycles and motorcycles, in entirety or in parts, due to the forces acting on them during balancing, steering, braking, and suspension." The part that's bothering me is "the forces acting on them during...suspension". That doesn't sound right. Grammatically, it would certainly be best to have a fourth -ing, but "suspending" obviously is ridiculous. Is there a way of referring to all four elements that would be appropriate to all of them? Or am I not interpreting this correctly? --AnnaFrance (talk) 17:59, 9 June 2008 (UTC)
 * You're reading it right. It is non-parallel. I don't like the science of the motion of either. -AndrewDressel (talk) 19:48, 9 June 2008 (UTC)

Images
While I finish up the final run-through on the text, I'm going to ask my husband, Sfbart (talk) (who was a professional web developer), to take a look at the image placement. According to the Wikipedia Manual of Style, they prefer the first image to be on the right, then alternate down the page, if possible, to avoid what they call "stackups". We do have a bit of a stackup at one point on the page. I'll ask him to see if he can untangle the stack and alternate sides at least occasionally, without moving any image out of its basic position within the article. --AnnaFrance (talk) 22:13, 16 June 2008 (UTC)


 * Well I'm not sure what when wrong, but the changes by Sfbart (talk) caused the images to appear behind the text in my copy of IE7. Anyway, WP suggests not using tables to format images. Plus, the images look fine in the article now. I do not see any "stackups" no matter how much I shrink or expand the window. Three images do appear in a row, but I put them there that way specifically to avoid formating issues. At some point in the future, there may be enough images to cause a problem, but that does not appear to be the case at this time. -AndrewDressel (talk) 03:32, 17 June 2008 (UTC)


 * Odd and odder. The pictures look the same now as they did before to me. No improvement with the disarrangement of the sections. Still, this article isn't going to rest on its images. But even if we can't get the images repositioned, I sure wish we could get the opening sentence/definition rewritten. --AnnaFrance (talk) 05:17, 17 June 2008 (UTC)


 * Well, I gave it one tweek (and forgot to include an edit summary). Sounds better, more straight forward, to me. The list of motions is now clearly not comprehensive. Oh, and wikilinked motion. -AndrewDressel (talk) 02:17, 18 June 2008 (UTC)


 * I think that reads much better. -- AnnaFrance  (talk)  13:26, 19 June 2008 (UTC)

Equations of motion
In the beginning of this section, one of the features of an idealized bike is:


 * operating at or near the upright and straight ahead unstable equilibrium

Could this be changed to:


 * operating at or near the upright and straight-ahead, unstable equilibrium

-- AnnaFrance  (talk)  15:20, 19 June 2008 (UTC)


 * Yes, that probably would be better. -AndrewDressel (talk) 01:00, 20 June 2008 (UTC)

Copyedit done
What's next for this article? Try to get a peer review? -- AnnaFrance  (talk)  16:27, 20 June 2008 (UTC)


 * Perhaps. The article is a little off the beaten path, and so hasn't attracted many reviewers on previous attempts. That's why I invited you right away when I read you specialty. Thanks for all your hard work. -AndrewDressel (talk) 12:28, 21 June 2008 (UTC)


 * I've noticed that scientific articles don't get much attention in peer reviews. I'll keep this page on my watchlist in case it does get reivewed for peer reviews or promotion, so that I can help with any extra cleanup. I can recite some parts of this article from memory. -- AnnaFrance   (talk)  12:42, 21 June 2008 (UTC)

Inertia
This discussion (centrifugal force vs inertia) has appeared here before, and has since been archived. As the article on that subject currently states: "Despite the name, fictitious forces are experienced as very real to those actually in a non-inertial frame. Fictitious forces also provide a convenient way to discuss dynamics within rotating environments, and can simplify explanations and mathematics." Centrifugal force provides a simple way to explain leaning in a turn, a convenient way to calculate the lean angle necessary, and so is used in this article.

The current wording; "the external forces are due to gravity, inertia, contact with the ground, and contact with the atmosphere"; does not actually call inertia a force any more than it calls gravity a force. More detail about reference frames is provided just three paragraphs later.-AndrewDressel (talk) 14:25, 26 June 2008 (UTC)

Eigenvalues
It appears to me that the capsize speed and the weave speed are reversed, both in the text, in the eigenvalue plot and in the PDF reference [17] by Meijaard, et al. My own experience is that at low speed a bicycle will "capsize" (fall over without any weaves), while at high speed on a poorly designed bicycle the weaves can increase in amplitude until "failure". I'm not an expert, nor a prior contributer to Wikipedia, so I hesitate to make any changes. Comments? —Preceding unsigned comment added by 70.19.235.105 (talk) 16:41, 13 July 2008 (UTC)
 * The text currently glosses over a mode that perhaps matches what you describe. Before the two most positive eigenvalues coalesce into a complex conjugate pair, which indicates oscillation, they indicate simply falling instead, as an inverted pendulum. It is only when the complex components show up, at about 1 m/s, that the weave oscillation begins. Perhaps that better matches your experience. You or I should add that detail. -AndrewDressel (talk) 23:37, 13 July 2008 (UTC)
 * In the Eigenvalues section I suggest the following. "The plot indicates that the bicycle is stable between 5.3 and 8.0 m/s. The upper limit, 8.0 m/s, is the capsize speed: at higher speeds the bicycle experiences increasingly rapid and extreme steer and lean, until it falls over.  The lower limit, 5.3 m/s, is the weave speed: at lower speeds the bicycle weaves through increasing angles and wider, slower arcs, until it falls over (in the weave mode there is a slight delay in the steer relative to the lean).  Below 1.0 m/s, where none of the eigenvalues have an imaginary component, the bicycle falls to one side without making a single oscillation." —Preceding unsigned comment added by 70.19.235.105 (talk) 16:41, 14 July 2008 (UTC)
 * I've posted a change this morning. After rereading the source material, and reading what related articles already exist in Wikipedia, I opted not to use the text you provided. I hope you don't mind. Please let me know if what I wrote is clear and addresses your concerns. I look forward to any other suggestions you may have. -AndrewDressel (talk) 23:37, 14 July 2008 (UTC)
 * I guess the bicycle's behavior would only become clear to most people if they could view an animation for each mode. In particular, I am still a little unclear about the behavior above the capsize speed:  is it correct that possible initial oscillations are damped out, as in the stable region, but with a residual, non-zero lean that then increases until the bike falls; or, is the bike forbidden to make any oscillations at all in this region, regardless of initial conditions? —Preceding unsigned comment added by 70.19.235.105 (talk) 16:41, 15 July 2008 (UTC)
 * I know what you mean about the animations, but they are big, don't easily show the details, are subject to disbelief ("Oh, that's just a video game animation"), and I hesitate to add another one to wikipedia. Instead, perhaps a graph of lean angle and steer angle over time would do the trick. They take up much less room, you don't have to watch them over and over again to see the detail you want, I can exaggerate and label the scale as necessary, and I can generate them from the exact equations published in the Proceedings of the Royal Society for the sake of credibility.
 * Finally done. Sorry for the delay. -AndrewDressel (talk) 16:02, 18 October 2008 (UTC)


 * Yes, above the weave speed, oscillations do die out. The higher the speed above the weave speed, the faster they die out. Even better, in the pure model, with no friction or other dissipation, the energy added by a sideways impulse ends up as increased forward speed. -AndrewDressel (talk) 14:28, 15 July 2008 (UTC)


 * The eigenvalue stuff appears to be ignoring gyroscopic effects on a two wheeled vehicle. As speed increases, gyroscopic effects tend to create lean stability, the tendency for a bicycle or motorcyle to hold it's current lean angle. Steering geometry tends to create vertical stability, the tendency for a bicycle to remain or return to an upright position, once above a minimal speed. As speed increases, the gyroscopic effects become more significant, and at around 100mph on a motorcycle, gyroscopic effects are dominant, and the motorcyle just tends to hold a lean angle. At these speeds or faster, body leaning no longer works, and the amount of (inwards) counter steering effort it takes to "unlean" a motorcycle feels the same as the amount of (outwards) counter steering effort it takes to lean, and the effort is more of one of force with little perceptible movement of the handlebars. Jeffareid (talk) 18:04, 17 October 2008 (UTC)


 * 1. The current eigenvalue plot is for a utility bicycle. You can see the need for motorcycle eigenvalues in the to-do list at the top of this page. I have not yet found a good source for these. Cossalter only presents a plot based on Sharp's motorcycle model that looks hand-drawn. I'd prefer to use a graph of calculated numbers, but it does show the weave and capsize modes crossing the real axis in about the same way as in the current plot.
 * 2. The current eigenvalue plot does completely incorporate gyroscopic effects. One interpretation, as given in this section, is that
 * at low speeds, gyroscopic precession is too quick, so the bike oversteers and experiences weave instability;
 * at just the right speed, gyroscopic precession is just right, and so the bike is self-stable; and
 * at high speeds, gyroscopic precession is too slow, so the bike understeers and experiences capsize instability.
 * If you have a source that contradicts the main sources used for the current article (Wilson and Papadopoulos; Klein; Meijaard, Papadopoulos, Ruina, and Schwab; Cossalter; or Sharp), I'd love to know about it. -AndrewDressel (talk) 18:32, 17 October 2008 (UTC)
 * Under gyroscope effects, the article mentions that the rate of gyroscopic precession is less than the rate of steering reponse required for vertical stability at higher speeds. Not mentioned in the article is the tendency for gyroscopic effect to resist any change in lean angle at high speeds, so although a motorcycle is technically in capsize mode, there is enough resistance along the roll axis to give the impression of lean stability. Jeffareid (talk) 00:57, 18 October 2008 (UTC)


 * There is no "tendency for gyroscopic effect to resist any change in lean angle at high speeds". At high speeds, gyroscopic precession is slower than at low speeds. That is all. If a rotating body, such as the rear wheel or the rotating parts of the engine and drive train of a bike, is prevented from precessing by an appropriate torque such as that generated by friction between the wheels and the ground, then it responds to the combination of that torque and some other input torque, due to gravity acting on a leaning bike for example, exactly as a non-rotating body would. This can be shown with Euler's equations (rigid body dynamics) be setting the appropriate angular rates and angular accelerations to zero and thereby eliminating precession as an option. -AndrewDressel (talk) 16:02, 18 October 2008 (UTC)


 * capsize speed - Assuming this means speed wobble, it's rare, and perhaps gyroscopic effects again play a role in eliminating this in real world situtations. At least the stated speed (18mph) seems slow. There have been a few incidents where bicycles have been sent down long hills, that resulted in fast speeds and yet the bicycles remained stable. Jeffareid (talk) 18:14, 17 October 2008 (UTC)


 * No. The capsize mode is definitely not speed wobble. The capsize mode eigenvalues have no imaginary part, so the mode is not oscillatory. In the eigenvalue plot Cossalter provides, based on Sharp's model, capsize is the only unstable mode at speeds higher than 10 m/s, similar to the bicycle eigenvalues shown in the current article.


 * The capsize mode can be very slow, however. The eigenvalues are positive, but small. Perhaps the down-hill tests just were not long enough for the instability to manifest itself, or the particular bikes used had very high capsize speeds. -AndrewDressel (talk) 18:38, 17 October 2008 (UTC)\


 * Mabye the issue is that bicycle usually crashes into something before a capsize takes place. There have been a few instances of riders falling off racing motorcycles at high speeds, and the bikes continue on in a very stable fashion, until they crash into something. Jeffareid (talk) 00:40, 18 October 2008 (UTC)


 * That is a definite possibility. -AndrewDressel (talk) 16:02, 18 October 2008 (UTC)

trail and self stability
Maybe I missed it in the article, but the main reason for self stability is trail. When the front wheel is leaned, the pavement pushes up (opposing gravity) at the contact patch, and since the contact patch is "behind" the pivot axis (trail), the result is an inwards yaw torque on the front wheel, causing it to steer inwards. Once above some minimum speed, the inwards torque generates enough steering input to result in vertical stability. Note that gyroscopic effects can be eliminated, for example using skates on ice or skis on snow, and "trail effect" would still result in vertical stability. Trail also creates caster effect, which dampens overcorrection due to momentum. Jeffareid (talk) 01:26, 18 October 2008 (UTC)


 * Trail is discussed in this section. It is by no means exhaustive. However, it isn't clear in the source material that trail is the main reason for self-stability. I haven't seen a reputable source that claims any of the physical examples you cite are self-stable, that is stable without a rider. Instead, they all have a 'rider' providing an active feedback control system. -AndrewDressel (talk) 13:27, 18 October 2008 (UTC)


 * The trail of a bicycle makes it easier to ride because it links the lean angle of the frame with the turning angle of the fork. trail Jeffareid (talk) 01:57, 18 October 2008 (UTC)


 * I don't see a mention of self stability in Karl Anderson's article. -AndrewDressel (talk) 13:27, 18 October 2008 (UTC)


 * The article linked to above mentions that the trail causes the front tire to steer inwards to the point that lowers the center of mass of the bicycle or motorcycle. Another way of stating this is to note that the contact patch moves "forwards" as the front wheel is steered inwards, and the inwards steering (yaw) torque diminishes to zero as the contact patch moves forward to line up with the pivot axis. The pivot axis angle, amount of trail, and effective tire radius affect the lean versus steer response. Jeffareid (talk) 06:26, 18 October 2008 (UTC)


 * All true, but no guarantee of self-stability. -AndrewDressel (talk) 13:27, 18 October 2008 (UTC)


 * I didn't see any reference to trail in the equations of motion or the eigenvalues. Jeffareid (talk) 02:43, 18 October 2008 (UTC)


 * It is hard to see anything in the equations of motion. That is one of the reasons the canonical equations with two independent verifications and an exhaustive literature review were only published last year. The expressions for the coefficients of the linearized equations show that the term (trail/wheelbase)*cos(headangle) can be found in the M, C, and K matrices. -AndrewDressel (talk) 13:27, 18 October 2008 (UTC)


 * Are we just using different definitions of "self-stable"? I am using it to mean that a riderless bike will not fall down, and will even reject disturbance. -AndrewDressel (talk) 13:27, 18 October 2008 (UTC)


 * No, trail is the main factor for self stability, links:


 * Jones may have been the first person to show the connection between front fork geometry, namely trail, and the inherent stability of the bicycle in an article suited to the layman ... negative trail experiment: This bicycle had negative trail. It was rideable, although difficult, and fell instantly when released riderless. These three bicycles experimentally verified Jones' self stability index. bicycle handling


 * Many bicycle analyses aimed at understanding rider control are based on qualitative dynamics discussions that are too reduced to capture the ability of an uncontrolled moving bicycle to balance itself. The Physics Today paper by David E. H. Jones (1970) is the best-known of these. - Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review By J. P. Meijaard, Jim M. Papadopoulos, Andy Ruina and A. L. Schwab, Proc. R. Soc. A. 463, 2007 -AndrewDressel (talk) 17:51, 18 October 2008 (UTC)


 * the way to increase the stability of a bicycle is to increase T (fork trail). frame geometry and bike stability


 * Stability does not mean self-stability. The actual analysis appears to be based mostly on the work of Jones. See comments about Jones' work above. -AndrewDressel (talk) 17:51, 18 October 2008 (UTC)


 * Trail is the most important determinant of stability. bicycle geometry


 * Stability does not mean self-stability. No analysis give nor sources cited. -AndrewDressel (talk) 17:51, 18 October 2008 (UTC)


 * We show that a bicycle is almost, though not quite, self-stable; the most important parameter governing the stability is the “castor” of the front wheel.stability of bicycle


 * Cool, I haven't seen this one before. However the model of the bicycle discussed in this paper is not as accurate as it should be in order to precisely explain the stability of a real bicycle. stability of bicycle


 * None of their plots actually show asymptotic stability, as the ones I added to the article today do. It appears that they didn't examine the eigenvalues of their model to identify the forward speeds at which it would be self-stable. They don't provide the bike parameters that they used, so I can't calculate them either. Perhaps they never examined a speed inside the stable range. -AndrewDressel (talk) 17:51, 18 October 2008 (UTC)


 * The article clearly mentions self-stability as it's included in the chapter titles. Jeffareid (talk) 19:00, 18 October 2008 (UTC)


 * From this article: In traditional bike designs, with a steering axis tilted back from the vertical, trail causes the front wheel to steer into the direction of a lean, independent of forward speed Bicycle and motorcycle dynamics
 * Jeffareid (talk) 17:32, 18 October 2008 (UTC)


 * While certainly true, this by itself does not mean self-stability. -AndrewDressel (talk) 17:51, 18 October 2008 (UTC)


 * Yet another link greater fork trail means greater self-stability of the bike. reference to Zinn's cycling primer

To me, terms like stability and riderless bicycles are synonomous with self stability. Note that the Jones article involved real testing of bicycles, not just a paper exercise. Riderless bicycles with negative fork trail fell over almost immediately, riderless bicycles with normal amounts of fork trail were self stable above a minimum speed, riderless bicycles with large amounts of fork trail slowed to a near stop before falling over. I'd call that evidence of a relationship between trail and self-stability.

I'm not claiming that trail is the only source of self-stability, just that it's the main source. Every web article I've found defines a strong correlation between stability and trail, some specifically using the term "self-stability". The fact that trail tends to steer the front tire towards the direction of lean is mentioned in this article. To me, it's this inwards steering reaction that results in self stability. Are you stating that trail has no effect on self stability, in spite of real world experiments that appear to establish a relationship between the amount of trail and the amount of self-stability? Is there some hidden factor I'm missing here? Jeffareid (talk) 19:35, 18 October 2008 (UTC)


 * I am sure stability and self-stability are not carefully distinguished by many authors. However, in this article, I am doing my best to make that distinction clear. I also am trying to use the best original sources I can find and minimize the use of self-published web pages as much as possible. Jones' article involves real testing of four bicycles, and a paper exercise that has since been shown to be too simplistic for the conclusions he drew. The fact that gyroscopic forces and steering mechanism mass distributions also tend to steer the front tire towards the direction of lean is mentioned in this article. All these factors contribute to self-stability to varying degrees. I am certainly not stating that trail has no effect on self stability. At least I certainly do not mean to. I am merely stating that I have not seen a source of comparable quality to Wilson and Papadopoulos; Klein; Meijaard, Papadopoulos, Ruina, and Schwab; Cossalter; or Sharp that does. -AndrewDressel (talk) 19:40, 18 October 2008 (UTC)


 * OK. Based on my own experience, at speeds below 80mph, constant counter steering torque has to be applied to the handlebars to maintain a lean. At around 100mph, the handling goes neutral; the bike holds a lean angle without any control inputs. I've read that the neutral handling remains that way at even faster speeds, at least at speeds up to 200mph (Ilse of Mann is one of the few tracks that involves very high speed turns). (Note that no one hangs off a motorcyle while doing 150mph to 200mph turns, it's all steering inputs). I've never read that a bike tends to fall inwards at high speeds, only at very low speeds. The explanation usually given for neutral handling was gyroscopic effects at high speeds. As mentioned at mroe common speeds, I've read that trail is the biggest factor in vertical stability, and I recall several cases other than Jones where trail has been adjusted, such as turning the front forks backwards, with a resultant change in self-stablity. On a side note, the amount of force required to change lean angle incrases as speeds increase, but this true at speeds from about 40mph and up, independent of the neutral handling situation.


 * Regarding capsize speed, in the case of motorcycles, apparently the gyroscopic resistance to any change along the roll axis is so strong that any long term instability issue is imperceptible by the riders over period of a few seconds. In the case of bicycles, 18mph just seems too slow, but I don't know about utility bicycles. I recall some story about experiments where 10 speed type bicycles were launched at speeds up to 50mph, with the main issue being speed wobble. Again, it could be that the bicycles simply ran out of room and crashed into the barriers used in these experiements before the instability became noticable. I do recall hand handlebar momentum was an issue involving overcorrection oscillations, and the handlebars were removed in those experiements in the story I read. Jeffareid (talk) 22:10, 18 October 2008 (UTC)


 * I'm not a phsycist, but I did my best to read through references to capsize mode in this article: Experimental Validation of a Model for the Motion of an Uncontrolled Bicycle and it seems that one issue with the actual measurments was that the high speed capsize mode wasn't causing sufficient dynamic reactions (apparently weave mode was dominant), and that the high speed testing was limited (why didn't they test in a larger area?). Is capsize mode similar to what I call netural stability mode (holding the lean angle instead of correcting it)? As mentioned before, no motorcycle article has ever mentioned a tendency to fall inwards at very high speeds, but the larger rear tire could be a factor here. Jeffareid (talk) 23:01, 18 October 2008 (UTC)


 * Thanks for reminding me about that article. I added a short paragraph to the eigenvalue discussion about experimental validation with that as a reference.
 * As for capsize in motorcycles, Cossalter devotes 11 pages to it in his Motorcycle Dynamics book. He concludes with a list of parameters that improve or worsen capsize stability. It can be improved by decreasing (ordered by decreasing influence) caster angle, front tire cross section radius, center of mass height, front wheel spin inertia, front tire trail (I think he means pneumatic trail) or by increasing (again ordered by decreasing influence) twisting torque of front tire, front wheel radius, mechanical trail, rear wheel to center of mass distance, rear tire cross section radius. -AndrewDressel (talk) 16:02, 19 October 2008 (UTC)


 * I found some videos testing stability on a treadmill from the Delft bicycle research page. The fastest test is at 30km/h = 18.64 mph, or 8.33 m/sec, (slightly above the stated capsize speed), the bike is very stable. treadmill measurements. Jeffareid (talk) 23:18, 18 October 2008 (UTC)


 * Since that page you link to doesn't state a capsize speed, I'm guessing you are refering to the capsize speed stated in this wikipedia article. That value is merely an example calculated for one particular idealized bicycle. I've added some words that I hope make it clearer that the plot of eigenvalues is for one particular bike. -AndrewDressel (talk) 14:27, 19 October 2008 (UTC)


 * The capsize speed is shown in a graph on another article from Delft, and it appears to be the same bicycle: Koo06.pdf
 * The graphs shows capsize speed at below 8m/s, but the tread mill runs shows and states that the bicycle is very stable at 30km/s == 8.64 m /s. I'm waiting for feedback from someone at Delft, but my guess is that tire width is an issue. When leaned over, the contact patch is on the side of the tire, and this offset creates an outwards torque on the roll axis. Tire width and a rear tire much larger than the front tire may explain why the capsize "rate" is imperceptible on motorcycles at high speed. Jeffareid (talk) 22:52, 19 October 2008 (UTC)


 * I see you mentioned tire cross section radius as a factor, specifically front tire cross section radius, with rear tire effects much less. I wonder about the effect of having a larger rear tire with more momentum, and due to a larger rear tire cross sectional radius, the slight yaw and pitch effect it has on a motorcycle while leaned. Jeffareid (talk) 23:05, 19 October 2008 (UTC)