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Very cool papers proving gyro and caster aren't required for bicycle stability are out.

by Jason Moore — last modified Apr 18, 2011 12:40 PM

Jodi Kooijman et al just published a paper about a neat little "bicycle" they built that is stable even though the angular momentum of the wheels is negligible and the trail is slightly negative.

The paper and supplementary material can mostly be found with this doi: 10.1126/science.1201959

When I arrived at Delft in August 2008, Jodi was putting the finishing touches on this bicycle design. He hadn't yet been successful in getting it to be stable. During the year we experimented with it extensively. Jodi changed the roller blade wheels to aluminum and we tried several different floor surfaces: two different rubber gym floors, a linoleum tiled floor, and a wooden slat gym floor. The aluminum wheels offered very little lateral traction on the slick floors (unlike the Whipple model which provides as much traction as needed for no slip) and any imperfection in the floor would send the bicycle toppling, so the rubber gym floors were the only floors that seemed to hold any promise. These were a bit odd though because the aluminum wheels left about one inch long impressions in the rubber material, which seemed to give interesting dynamics. A high frequency oscillation of the front wheel occurred when rolling on the rubber floor, something that the linear Whipple model does not predict. But regardless the bicycle did exhibit stability (although it was probably 1 out of 30 runs or so). We had to tinker with adding weights at various points on the frame to counter any anti-symmetries that were inherent to the frame construction and this seemed to help, otherwise the bike would not tend to stay upright but would quickly capsize.

All in all it is a great demonstration of what we "bicycle stability scientists" basically understand (i.e. that stability of a bicycle is dependent on a complex interaction of the bicycle's physical features and no single parameter governs stability of the bicycle). I'm also happy to see that they've posted much of their work and data on the website and that the work is getting good press. Hopefully, the famous 1970 Jones paper will no longer be cited as the de facto explanation of bicycle stability, because we've come to realize since his paper that much of his explanations are not that valid (hopefully this current work will be superseded too in the near future!).

Other links:


I've also decided to publish my informal review of the paper (requires software that can read pdf comments correctly). This is an earlier version of the article, not the final journal publication. I'm starting to think that reviews should not be hidden behind closed doors as they are part of the scientific process. Also, reviewers do a lot of work and should thus be recognized. For more info on these ideas the Wikipedia page on Open Peer Review is a good start. So in the name of opening up our science, here are my comments. Some of the main points follow:

Update 4/20/2011 - I've been asked by the authors of the paper to remove my review as it also exposes an earlier version of the paper and I'm not really sure how to post the review without the paper as it would be a bit meaningless with nothing to reference to.

Why use trail?

And why use wheelbase and head tube angle as parameters for the model? There are two main reasons I think folks typically use these parameter sets to describe the geometry of an ideal bicycle (i.e. the Whipple type): 1) that is what has been used historically (e.g trail is used in caster dynamics) and 2) it can make sense when you talk about the bicycle equations that are linearized about an upright configuration. But trail, wheelbase, and head tube angle (as typically defined) are not constants in the non-linear sense. They all are functions of the steer and roll angle of the bicycle, which are functions of time. There are geometric parameter sets that are constants in the non-linear sense. One nice example is the front and rear offsets of the wheels relative to the steer axis and the distance between two planes that are perpendicular to the steer axis and that go through each wheel center respectively. Psiaki used these coordinates (among others) and Luke and I prefer them. Jim Papadapoulus presents "mechanical trail", which is also a function of time but actually has the deeper meaning that people typically think that "trail" has (i.e. that the contact force at the wheel generates a torque through this moment arm). I personally think it is time to move on from these historically traditional parameters for bicycle description. I'm sure that the motorcycle dynamics community has to some degree being that they work with non-linear models much more often.

Wheel to floor interaction dynamics

The bicycle often is modeled with pure rolling no slip wheel contacts (e.g. Whipple model). There is little evidence to show that this kind of constraint applies to a real bicycle tire (one example is Kooijman2007), but we use the model. This bicycle was constructed with wheels that would hopefully uphold that type of constraint, but the aluminum wheels where not able to generate enough tractions for the no-slip condition to hold on hard surface floors and the bicycle would inevitably fall before any stability could be detected. But when placed on a rubber gym floor where the aluminum wheels left about a 3cm long depression in the floor due to the weight of the bicycle the bicycle now had enough side force generation capabilities to stay upright. But this introduced a new mode of motion to the bicycle. The front steer would oscillate as the bicycle was brought up to speed at a abnormally high frequency. The frequency was more akin to the frequency observed in shimmy. I believe that the oscillation was related to the aluminum/rubber interaction the long contact patch in the rubber floor. I don't recall observing the oscillation on any floor but the rubber floor. The authors explain the phenomena as shimmy (shimmy doesn't show up in the Whipple model until you add extra degrees of freedom) and that it doesn't affect the other modes of motion. We were able to demonstrate stability of the bicycle even with the shimmy (actually, only with the shimmy!). But I'm curious what the true trail of the bicycle is when the tire is so depressed into the rubber floor. 4mm of negative trail is a small percentage of the 3cm contact patch. The trail would seem to actually decrease (more negative) with a positive steer axis tilt, but that depends on what you choose as the contact point. The contact point could be in various places along the contact patch.

Claims about torque in a steady turn

The authors claim that "A necessary condition for self-stability: in a steady left turn the torque on the handlebars is to the right". I think this is true for the linear equations about an upright configuration, but may not be true for the non-linear model or linear models linearized about other equilibrium points. Luke has some unpublished (or partially published) work on stability in steady turns, that seems to refute this. Hopefully he will get this out to the world soon, as it is very interesting data.


The authors use the term "self-stability" to described what mathematicians and control engineers use the word "stability" for. I'm not real clear from the paper what the addition of "self" adds to help people understand its meaning. It seems to me that "stability" has a clear definition in terms of differential equations and that "stability" is more generally used in many ways to describe an the ability of a system to resist deviations from an equilibrium.

Musings on open science and this project

This was the first project that I have been involved in (in academia) that was very closed and secret. I went to TU Delft on a Fulbright for the 2008-2009 school year and worked with Arend and Jodi on bicycle research. Some of my duties were helping with the project that was in this paper. The first thing I found odd was that I was immediately told not to tell anyone about this particularly interesting bicycle that Jodi was constructing because they were going to get a Nature or Science article out of it. Regardless, I helped run the experiments, did a lot of the video taping, helped come up with the way to measure trail and helped in discussions about getting the bicycle to work. I had a great time helping and appreciate them letting me be part of this really cool myth busting bicycle, but my interest in the project wasn't that great both because it was Jodi's baby so I didn't want to try to get too involved and it was "top secret" which was a bit of a turn off because I couldn't discuss it with anyone.

This top secret science really seems detrimental to me. Science can only progress if we share it with people and I believe that the sooner we share what we are doing the faster and better all of our science will be. This particular project happened over the course about 4 years (but even more if you roll back to the 80s when Jim, Andy and Scott were working on this stuff) but very few people were involved. I don't care how smart you are, there is always someone else that can see something you don't when solving a problem. Maybe the whole thing could have been figured out in half a year if there were a lot more minds thinking about it and we could have moved on to new things by now (check out the Polymath project for a great example of how science collaboration could work). But the prestige and reputation gained from publishing in particular high ranking journals causes scientists to work in secret, which I believe actually slows the progress of science. And because of this we need to move beyond the traditional competitive journal publication method, it just can't keep up with science and will continue to be detrimental until we change it.

In October 2010, Arend and Jodi hosted the best conference I've been to in my academic career. It was super specialized and brought together the motorcycle and bicycle dynamics community who had practically never met each other. There may have never been a meeting like this in history. There wasn't much of the normal big conference "fluff" and we just got down to the meat of things: the science. We had most of the best brains thinking about motorcycle and bicycle dynamics all in the same room for several days and the group involved in the no-gyro, negative trail bicycle never said a public word about the project. It was the perfect opportunity to share the work and get invaluable feedback on the project. When I arrived to the conference, I was sure that was what they were going to do. But to my amazement, not a word was spoken about this fantastic project. And as far as I can tell it was kept secret for the prestige and publicity gained by publishing in Science. This all seems very unfortunate to me.

I'm sure humans are driven by the many types of rewards provided by our society (i.e. money, publicity, recognition, etc), but I hope that we can start to realize the that openness and collaboration in public science will reap much greater rewards to society as a whole than they do when we let competition slow the progress of scientific discoveries.

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Avatar Posted by Jason Moore at Apr 20, 2011 08:27 PM
Jason: April 20, 2011

  I am probably the most to blame about the secrecy thing. And, after me, maybe the journals. Some comments.

First, there was nothing secret about this project for its first 20 years or so. Only at the very tail end did it get secret. So your
comments only apply to that tail end. That is, to 20% of the project or less.

Second, I have so many experiences of things getting diluted by discussion. If you disseminate an idea too widely before you write it up,
and there is, in the minds of the world out there, nothing for you to write up. They know it all already. Rather, the accepted means of conversation
is though publication. In that view, the publication is the unit of conversation.

Third, in this case we had the goal of trying to put out a paper to in some sense replace Jones. We wanted to set the record straight.
To do that we needed a high-visibility publication. To get that we had to a) follow the rules, b) be good at the game of publishing
in such a journal. If our ideas were too-widely disseminated before we submitted we would have a worse shot at getting enthusiastic

Fourth, I can't stand secrecy. I have a pet peeve about it. And I don't think any of the co-authors are in love with it either.
Hence, in the same era you are complaining about, we have talked clearly and openly about all of this research to many people.
But in each case it was with the proviso that there be no public discussion or general dissemination. We might have brought
it up at the bike meeting. But it would have been a gamble. And since the stakes were so high (such big investment of effort
over so many years) we chose not to take the gamble. Did we lose out from that? Some, I am sure. Especially the fun of the
possible discussions.

In summary, I am sympathetic to your emotional response. And you won't find many people more in favor of openness, and in general
a practitioner of same, than me. As your main enemy in this last part of the essay, I think you will find that in practice I
am closer to you than 99% of the people you will encounter in your life.

-- Andy Ruina

reply to secrecy

Avatar Posted by Jason Moore at Apr 20, 2011 10:14 PM
Thanks for the comments on the openness. First of all...I had a bug in the comment feature of our blog and your name is not properly displayed and I'm not sure that it even was saved. It says Jodi at the top but I'm not sure if who wrote this. Please let me know I'll try to fix the name on the comment.

I totally understand your points. Here are comments to each one:

1) Totally, you guys have posted tons of material from the past including non-published material that has been unbelievably valuable to other researchers, including me. In fact, the early released conference papers (~2005) that "gave away" what was published in the Meijaard 2007 Royal Society Paper were so helpful for me. I may not have correctly derived the equations of motion of the bicycle back in 2006 without the details in those conference papers. My comments do only apply to the end of the project, when I wandered into the scene.

2) We certainty have to play the game for things to work out as we intend. But it usually takes a large amount of people to not play the game by the rules for the rules to be changed. One thing that we can start to upset in the game is this accepted unit of conversation, (i.e. the journal publication). The journal was the only way to transmit scientific knowledge and be properly recognize for your efforts, but it will (hopefully soon) morph into a more modern communication method. Internet technology is ripe with new methods of communication of scientific ideas that don't have the limitations that traditional journals require. PLOSOne is one good example of a journal embracing some of these new methods.

I'm not sure why you think that conversation dilutes the reasons to write things up. Writing up a conversation, whether verbal or text, is the only way to bring it into a more readable and understandable form. A paper like you all just published in Science, is basically putting thousands of conversations you all have had over the past 30 years about this topic into a concise complete form. I think there will always room to write up dilute conversations so that it is new and understandable to a new group of people.

3) Similar comment as 1. But I agree, this was the best route to replace Jones and get high publicity. You most likely had to play the game for that outcome. I'm not sure if doing it another way would really overwrite the Jones publication. There is still no guarantee that it will...we will have to wait and see.

4) Great to hear. We should talk more about how we can change the norm in the scientific community (especially engineering!). My essay, wasn't to point out an enemy but to simply start a conversation about how science seems to work and what if it could work differently. I've been thinking about it an awful lot lately and am now heavily involved in an Open Science group here at Davis and we are doing our darndest to educate our fellow scientists about these topics.


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