## Bicycle Stability – Everything Works Together

New theoretical research in bicycle stability shows that many parameters interact to make a bicycle stable. No single parameter (e.g.: trail, head angle, wheel size, weight distribution) determines whether a bicycle is stable or not. When one parameter is altered, then the other parameters may need to be changed to arrive at a stable bicycle again. This matches our on-the-road experience of having to adjust a bike’s geometry for different wheel sizes, load placements, etc.

For more than a century, scientists have tried to resolve why bicycles are self-stable, that is, why they tend to stay upright even without rider input. When a bicycle starts falling over, it automatically steers into the lean, thus righting itself (see video below). In the past, it has been assumed that either the gyroscopic forces of the front wheel cause the wheel to steer into the lean, or that geometric trail and related forces re-align the front wheel.

Bicycle Quarterly contributor Jim Papadopoulos was part of a team of researchers from the Technical University in Delft (Netherlands) and Cornell University who examined the stability of bicycles. Their paper was published in the prestigious journal Science this month, so we now can share their findings and discuss the implications.

Based on theoretical calculations, they discovered that neither trail nor gyroscopic forces are required to make a bicycle stable. To test this, they built a bicycle with negative trail and a second set of wheels that spin in the opposite direction and cancel the gyroscopic forces of the wheels (see photo on top of this post).

As predicted by their calculations, this bicycle was able to roll without falling over, as long as it remained above a certain speed. Even if it was pushed sharply sideways (see the researcher push the bike in the movie below), it would right itself and continue to roll. The authors concluded that the bike steered into the lean because the mass distribution makes the front fork fall faster than the rear frame when the bike starts to lean. If the bike falls to the left, the front wheel turns to the left. Moving the front wheel to the left steers both wheels underneath the center of gravity. The bike is upright again and goes straight.

The “no trail/no gyro” test bike was a final validation of the bicycle stability calculations. The researchers found that no single number could predict whether a bike was stable. There are many possible designs with and without trail, and with and without gyroscopic forces, that are unstable. Many factors are interrelated, and together, they determine the self-stability of a bicycle.

Does this mean that trail and gyroscopic forces are unimportant in determining a bicycle’s handling? Not at all. However, the research confirms that these factors should not be taken in isolation. All factors are interdependent, and if you change one, you need to change the others to retain the desired handling characteristics of your bicycle. That means that to offer similar handling, a bike with a handlebar bag should have a different geometry from a bike carrying a saddlebag. A geometry optimized for single bike will not work the same on a tandem. Simple statements like “xx mm of trail offers neutral handling” only make sense in very narrow applications (for example, racing bikes with 23 mm tires), if at all.

I hope this research will lead to a confluence of theory and practice of bicycle handling. In the past, bicycles have been designed by trial-and-error. Similarly, Bicycle Quarterly’s articles on bicycle handling came from riding different bicycles, and making observations about them, rather than trying to solve the problem of bicycle handling mathematically. Theoretical studies still have a long way to go, since they do not yet include rider inputs. That said, a better understanding of the physics of bicycle stability can only help with our understanding of these fascinating machines.

## About Jan Heine, Editor, Bicycle Quarterly

I love cycling and bicycles, especially those that take us off the beaten path. I edit Bicycle Quarterly magazine, and occasionally write for other publications. One of our companies, Bicycle Quarterly Press publishes cycling books, while Compass Bicycles Ltd. makes and distributes high-quality bicycle components for real-world riders.
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### 12 Responses to Bicycle Stability – Everything Works Together

Hello Jan, that is a very nice writeup on our research. Unlike many brief reports, it doesn’t seem to have any errors, so I commend your care in presenting it.

I would like to supplement your report with some additional points. What you are able to explain and show is just the tip of the iceberg of our research. For example, the equations for a riderless bicycle were described and validated experimentally in previous publications (found on Arend’s or Andy’s websites, which are http://bicycle.tudelft.nl/schwab/Bicycle/index.htm http://ruina.tam.cornell.edu/research/topics/bicycle_mechanics/papers.php or linked from the research website)
Also the research website contains not only the author-generated preprint of the SCIENCE paper, but the 50-page appendix with much additional information and surprisingly-stable oddball bicycle designs, and a writeup of the history of bicycle stability understanding including a critique of the article written by Jones in 1970.

Lastly I would like to summarize some other ‘big ideas’ that we feel arise from the work:

1.We have shown that simply having negative trail is nothing to be frightened of, in itself. It could possibly be part of a good design.

2.We have shown that the two main arguments used to justify trail are incomplete at best:
A.The first is that trail supposedly encourages the steering to turn into a lean, and this is often demonstrated by holding a bicycle at a lean angle and noting that the steering responds as desired. But this is a flawed argument and demonstration. If the bicycle (at rest) is released to FALL, especially if there is a proper mass distribution representing the rider, the steering might turn TOWARD, might turn AWAY, or might NOT TURN. It all depends on mass distribution.

B.The second is the idea that caster (trail) governs the flipping around of the front wheel, just as it does for a shopping cart. We have seen no evidence of that, so we have surmised that casters operate very differently in leaning systems.

3.Lastly this research has strengthened our confidence in the JBike6 software, at least for riderless bikes. We hope that technically inclined users will download it, try it out, and become part of the slow process of improving it for wider utility. It is a free download from Arend’s web page, but unfortunately you need the MATLAB software to run it.

I’m looking forward to people’s reactions to our research. We think it is solid, but there could be flaws, or more likely aspects that are not explained clearly enough. Thanks, Jan, for highlighting it here!

After making my long comment above, I realized that I may not have emphasized one key point. I feel, and I’m sure my co-authors agree, that self-stability is not the same as nice handling qualities. Just because we found something a little surprising about self-stability doesn’t mean that we advocate changing bikes to look like ours, or that we think all bikes should have the same self-stability. We haven’t offered any magical formulas for making bikes better. Rather, we untangled some reasoning about self-stability and showed that it can be achieved in occasionally surprising ways, that might open up how people design bikes. But if a different self-stable design was not very nice to ride, of course we would not advocate adopting it! Nice handling is a topic I hope we can explore in future (it is currently being research at UC Davis, and supporting work on tire properties is under way at UW-Milwaukee and at Delft).

3. djconnel says:

I was initially shocked when, on my tour backwards through Bicycle Quarterly, I came across a ride report that a zero-trail, vertical head tube Boneshaker was “easy to ride”. The religion of trail suggests it should be virtually impossible to ride, requiring skills comparable to a track stand even when moving. The obvious conclusion was the gyroscopic stability of the large, heavy wheels is what helps keeps the stability, as well as the lack of a destabilizing steering moment from the force transmitted through the front fork, due to the 90 degree head tube (zero wheel flop guaranteed).

But perhaps there’s still more to it than that.

• We once rode a 1947 Alex Singer that had about 5-11 mm trail (depending on which head tube measurement you believe, we once got 74° and once 74.5°). It was perfectly stable, and the fork had no tendency to “flip around” as many would predict for a bike with almost zero trail.

4. Jim G says:

In the “TMS” bicycle shown in the above video, is the weight suspended forward and above the front wheel via the black boom supposed to represent the mass of a rider? If so, how does this experimental bike behave when that mass is removed? The older video depicting the yellow bike does not have any similar added mass. Just wondering/curious…?

“is the weight suspended forward and above the front wheel via the black boom supposed to represent the mass of a rider?”

Sort of! Actually, I don’t want to say it exactly represents the RIDER, because this was a purely abstract kind of design, based on point masses. No rider is a point mass. It was just the easiest way to demonstrate clearly that negative trail could work fine, both theoretically and experimentally. (We have another similar design where that mass is in the ‘normal’ position, but then the head angle is reversed — slopes away from rider not towards.)

“If so, how does this experimental bike behave when that mass is removed?”

We wouldn’t dare! The math called for it, and the trials of getting it to work as predicted took many weeks. We do show much-more conventional designs that are self-stable with negative trail, for example on page 25 of http://ruina.tam.cornell.edu/research/topics/bicycle_mechanics/stablebicycle/1201959SOMtext.pdf

If you can get hold of MATLAB software, you can try your own design ideas.

“The older video depicting the yellow bike does not have any similar added mass. Just wondering/curious…?”

That bike was an old damaged beater with regular trail and a forward spinning wheel. Except for lacking a rider, it sort-of represents normal bikes. Those designs are typically self-stable without any extreme additions.

5. Jim G says:

Got it, thanks for clarifying!

6. Jimmy Livengood says:

I read on one of those sites that you changed from inline skate wheels to the metal wheels with 2mm crown radius. Was that a key change? I’ve read about “pneumatic trail” and I wonder how the radius of the tire/wheel as it leans and interacts with the ground matters.

Great catch! We too are actively wondering or even worrying about pneumatic trail. Thank goodness, people are actively pursuing investigations which should provide credible numbers for spin torque, pneumatic trail, and camber thrust.

The best answer to your question is to say we were trying to mimic our math model. That model involves a knife-edge rigid wheel with contact only at a point. Using elastomers with a spread-out contact, or having a wheel TOO sharp so it would dig into the floor, seemingly added too much turning resistance.

By the way, the issue isn’t just the radius of the wheel at the floor — we added that to one version of the equations long ago and it didn’t make much difference. The main problem is that a wheel with spread-out or digging-in contact doesn’t spin very freely. (And of course, this very likely is directly relevant to a real bicycle.)

Of course, thinking logically you will probably see where this is headed: once we have good tire models for a bike with a heavy rider, we may have to update our equations, check predictions, and then see if there can still be stability with negative trail. One step at a time….

Regards

7. djconnel says:

By the way, the issue isn’t just the radius of the wheel at the floor — we added that to one version of the equations long ago and it didn’t make much difference.

Good to know. I’ve wondered about this for a long time, and it was well beyond the scope of my intuition. Given two bikes with the same trail and wheels of the same moment of inertia, will a rigid tire of a larger minor radius have different stability than a rigid tire of smaller minor radius (rolling radius the same)? I guess not really.

8. Kris Wehage says:

Hi Jim, have you considered to make your software available for Octave or Scilab? I would love to try it out but unfortunately do not currently have access to Matlab. Also, do you know which department/faculty at UC Davis are involved in this research? I am starting school there in the Fall. Cheers, Kris

“Hi Jim, have you considered to make your software available for Octave or Scilab? I would love to try it out but unfortunately do not currently have access to Matlab. Also, do you know which department/faculty at UC Davis are involved in this research? I am starting school there in the Fall. Cheers, Kris”

Kris: It’s in Mont Hubbard’s Sports Biomechanics Lab.

If you look around on the web there is a ton of stuff by Jason Moore, who has studying, building, and photographing cool bikes. He is part of the group. Earlier he was at Delft, and you can see a lot of his treadmill work on Arend’s web page. Also look for Dale Peterson, who is busily making open-source bicycle software.

I am not the matlab programmer, so I would not be able to create a scilab or octave version. But you could feel free, the equations are pretty simple and it’s all well documented! Or I think as a student you could probably get a Matlab license pretty inexpensively? (I sympathise, in other words, but am not in a position to do anything about your request.)

http://news.engineering.ucdavis.edu/coe/index.html?display_article=694

http://biosport.ucdavis.edu/

http://biosport.ucdavis.edu/lab-members/jason-moore

http://biosport.ucdavis.edu/lab-members/dale-peterson/dale-peterson

Good luck, the group there is doing high level work so if you could get involved, you would learn a lot (and maybe contribute a lot too!)