Re: [Phys-l] Bicycle question

[John Denker <jsd@av8n.com>]

Savinainen Antti wrote:

> It is easier to stay on a bicycle when it is moving with 
> some velocity whereas it is quite hard to stay up when 
> the bicycle is just barely moving.
>
> I thought about this for a while and said that it's 
> a good question! 

It is indeed a good question.

The answer is reasonably complex.  There are always a pair of
issues -- stability /and/ controllability -- that are, in general,
impossible to separate.

The zeroth-order contributions are:

  1) The non-moving bike is obviously unstable.  Top-heavy.

  2) The moving bicycle can generate centrifugal forces.

   I've taught a lot of kids how to ride.  One of the fundamental
   things I tell them is:  If you find yourself leaning to
   one side, all you have to do is turn toward that side, and
   that will create a centrifugal force that will push you back
   toward vertical.

   The force is proportional to the tightness of the turn and to the
   *square* of the speed.  At low speeds the control response is mushy,
   and at high speeds it gets very twitchy.

   This is part of a cybernetic control system, with you (the rider)
   as one element in the feedback loop.

  3) FWIW, standard procedure if you _want_ to turn is to anticipate
   the turn by leaning toward the inside... then you can steer toward
   the inside in accordance with item (2) above.

   Try it sometime:  try turning on the spur of the moment, with no
   anticipation.  It's tricky.  This is a new skill you need for
   mountain biking that you generally don't need for street biking.

If you look closer, you will discover lots more detail.

A classic paper is
  David Jones, "The Stability of the Bicycle", Physics Today 23 (1970).

A simple introduction that mentions the main stability and control-feel
issues (such as fork trail) is:
  http://www.velonews.com/media/Block40.pdf