Why Does A Moving Bicycle Stay Up?
    By News Staff | April 14th 2011 08:05 PM | 4 comments | Print | E-mail | Track Comments
    You know this already - given sufficient forward speed, a bicycle pushed sideways will not fall over.

    Since the bicycle was invented, scientists have postulated various reasons as to why a bicycle is self stable above a certain speed.  The consensus has been that a bicycle's stability is related to two factors:  First, the rotating wheels of the bicycle provide stability through gyroscopic effects; secondly, that the ‘trail’, the distance by which the contact point of the front wheel trails behind the steering axis, plays an important part. 

    A new study in Science claims to have settled the issue - gyroscopic effects and trail help, says researcher Dr Arend Schwab of the 3mE faculty at TU Delft, but are not necessary above a certain speed .  In a 2007 Proceedings of the Royal Society article  (doi:10.1098/rspa.2007.1857),  a mathematical model with around 25 physical parameters was developed at the time which appeared to predict whether, and at what speeds, a particular design of bicycle would be stable.

    The authors designed and constructed a Two Mass Skate bicycle, with small and counter-rotating wheels, which means there is no gyroscopic effect to speak of, and a small negative trail (in other words, where the point of contact of the front wheel is marginally in front of the steering axis).   Yet the bicycle remained stable when moving.

    Self-stable experimental TMS bicycle rolling and balancing (photo by Sam Rentmeester/FMAX)

    "It was not easy," explains PhD student Jodi Kooijman, who carried out most of the experimental work. "The first prototype did not work, and we had almost given up hope after a number of iteration attempts, when we suddenly found ourselves able to show the stability. But of course everything has to fall into place. You have to deal with the ground surface, for example, which has to have exactly the right roughness and stiffness. In Sporthal II of TU Delft we found all the right conditions."

    The result is that they have shown that mass distribution is also important for stability, especially the location of the center of mass of the bicycle's steering mechanism.  "For a bicycle to be stable, the steering mechanism has to be unstable; if the bike falls, the steering should fall even more quickly," says Schwab.

    Since this is in Science 2.0's applied physics section, does their theoretical insight have any use to bicycle manufacturers?    Perhaps, though, like those chairs with no backs that made you sit on your knees 20 years ago, optimal does not always equal popular.   While modern bicycles are the result of a fairly long evolutionary process, nothing about the basic design of the bicycle has really changed since the end of the nineteenth century so you may not see anything in the Tour de France soon.

    But "manufacturers can use our model to make directed modifications to the stability of their bicycles. That may be of particular interest for unusual designs, such as recumbent bicycles, folding bicycles and cargo bicycles," says Schwab.

    Citation: J.D.G. Kooijman, A. L. Schwab, J.P. Meijaard, J.M. Papadopoulos, A. Ruina, 'A Bicycle Can Be Self-Stable Without Gyroscopic or Caster Effects', Science, April 2011


    I always remember changing from a 28" "policemans" bicycle to a Raleigh Small Wheel (14" with 2" balloon tyres) and finding the latter weaving from side to side as I applied (undue) pressure to the pedals. I had used the RSW for a considerable time before, and done trips of over 100 miles on it but the relative stability of the large wheeled machine had lulled me into a false sense of stability on the small wheels!

    P.S. Since then I have always felt sorry for children having to learn on small wheels and wondered whether some form of flywheel could be incorporated to improve stability on their bicycles?


    The Stand-Up Physicist
    I designed a recumbent bike. No, I didn't weld it together. For books on bike designs, there is Bicycle Science by David Wilson a professor at MIT. He also recommends a great book from the 1890s, Bicycles and Tricycles. At $73 used, I guess it can be skipped. I bought it when the MIT press was making the book at Wilson's request.  The old timer was well worth a read. He calculated how large a rock is needed to do a header on one of those big wheel bikes. Men of old used to get serious injuries by freezing the front tire while traveling down a hill and hitting a rock, then smashing head first into the ground with no helmet. Ouch.
    One thing not mentioned in the blog is the fact that a bike is an inverse pendulum. Galileo knew the frequency of oscillation was related to the inverse of the distance to center of mass. The corrections one needs to make trace out a sinusoidal path. What a professional biker can do is make the amplitude of the waves small, but the frequency cannot be skipped.  Should you ever ride one of those big wheel bikes, it will feel unusually stable. What is going on is the required frequency of correction is lower. Likewise a low to the ground bike requires a higher frequency of correction. In my design, I went for a center of mass about the same height as a standard bike, so the mind would not need to make an adjustment.

    This was a one-off design. I got lucky that the bike is stable at low speeds. That may be the trickiest thing to do.  
    Another thought: Gyroscopic forces resist turning - so the counter-rotating wheels would ADD to the stability of the experimental machine?

    an object in motion will stay in motion unless acted on by an equal and opposite force. thats why a bike stays up. why is this even a question?