TMS Bicycle, stable without gyros or trail (TMS=two-mass-skate)

Long known, but still amazing, is that a moving bicycle can balance itself. Most people think this balance follows from a gyroscopic effect. That's what Felix Klein (of the Klein bottle), Arnold Sommerfeld (nominated for the Nobel prize 81 times) and Fritz Noether (Emmy's brother) thought. On the other hand a famous paper by David Jones (published twice in Physics.Today) claims bicycle stability is also because of something called trail". Trail is the distance the front wheel trails behind the steer axis. The front wheel of a shopping cart castor trails behind its support bearing and so must a bicycle front wheel, Jones reasoned. Jones insisted that trail was a necessary part of bicycle stability.

We suspected that such simple images (above) were missing at least part of the picture.

To find the essence of bicycle self balance we looked at simpler and simpler dynamical models until we found a minimal two-mass-skate (TMS) bicycle that theory told us should be self-stable. This bicycle has no gyroscopic effect and no trail. We built a bicycle (of sorts) based on the theory to prove the point.

This bicycle proves that self-stability cannot be explained in any simple words. Bicycles are not stable because of gyros, because you can make a self stable bicycle without gyros. We did that. And they are not stable because of trail, you can take that away too. And we did that. More positively, we have shown that the distribution of mass, especially the location of the center of mass of the front assembly, has as strong an influence on bicycle stability as do gyros and trail.

Why can a bicycle balance itself? One necessary condition for bicycle self stability is (once we define the words carefully) that such a bicycle turns into a fall.

The paper and supplementary material describe the problem and our solution in more detail, available at: http://bicycle.tudelft.nl/stablebicycle/

This research was started by Jim Papadopoulos, working with Andy Ruina and Scott Hand at Cornell in 1985. The basic theoretical result was in-hand then. In some sense, the recent Proceedings of the Royal Society paper on bicycle stability was written to support the present paper. We couldn't publish this gyro-free-no-trail result without that foundation being in the literature. The experimental two-mass-skate (TMS) bicycle, and the fleshing out of the theory, were carried out by Jodi Kooijman and Arend Schwab at Delft University of Technology, starting in 2008. Jaap Meijaard found the key errors in Klein & Sommerfeld and in Whipple.

More details at: http://bicycle.tudelft.nl/stablebicycle/

Category:

Science & Technology

Tags:

• bicycle
• dynamics
• stability
• gyro
• trail
• rake
• caster
• castor

[herpolhode]

Excellent video, great introduction to mechanical physics. Outstanding!

[TheLiberalSoup]

hm, that is a good explanation. I would think at least some of it has to do with inertia of the bicycle and not being able to topple it over as easily, but I dont even know if that makes sense. I dont know, just a thought. If anyone can tell me if this is wrong please respond.

[rvocke]

for those interested (or confused) you can check out the full paper (linked to in the info). It explains everything out quite plainly.

[Grrrrrene]

If you hold an ordinary bike sideways, so as if it would fall, the wheel "falls" in the correct direction. Judging by the drawings in your paper the majority of the mass of the steering part is ahead of the steer axis, so it would behave the same. I wonder what would happen if you had no trail _and_ a steering system that has it's center of gravity exactly aligned with or even behind the steering axis.

[Grrrrrene]

Hmm, shouldn't the counter rotating gyros be on the same axis if they are to truly cancel each other out?

By the way: it is very difficult to get a feeling for this "counter rotating gyro" effect :D

[rvocke]

@SquirrelFromGradLife Its not at all like counter rotating propellers in this case. The counter rotation he refers to here is a fairly basic dynamical concept that ties in angular momentum with applied moment (w x L = M). If one were to hold two bicycle wheels is in your example, one spinning in the opposite direction of the other, there would be no net moment induced in the chair.

[Proemeteues01]

@SquirrelFromGradLife Sorry, it is hard to explain, also in order to the limitation of the post's length and maybe my limted english vocabulary knowledge.

I just can ask you to trust me: Both axis try to "escape", but in opposed directions, and that's what eliminates the gyroscopic effect.

[SquirrelFromGradLife]

@Proemeteues01 I don't understand a word you're saying... not a single one

[Proemeteues01]

@SquirrelFromGradLife Though I also had to think some time, I found out that the gyroscopic effect is actually eliminated. Why? This effect means basically, that the axis wants to hold it's position in space.

As you mentioned, it can be shown easily by for instance holding a rotating wheel and just trying to tilt it. The wheels will react just like on a bicycle.

Once you turn the wheel into the other direction, the reaction will also be the other way round, and that's why it works. :)

[SDSMJ]

@SquirrelFromGradLife : the Gyro effect is real and adds to the stability of the bike, but it doesn't correct steering in a fall. To prove this, lock the handle bars into a straight line, or try to push the bike backwards.