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





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Published on Apr 15, 2011

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/


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