Very cool papers proving gyro and caster aren't required for bicycle stability are out.
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come to realize since his paper that much of his explanations are not that valid (hopefully this current work will be superseded too in the near future!).
- Their website on the topic: http://bicycle.tudelft.nl/stablebicycle/
- http://www.scientificamerican.com/article.cfm?id=self-stable-bike (Mont is quoted here!)
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.