Gee, I wish I had time to think about this carefully, but I'm awfully
busy right now.
I like Leigh's analysis. It coincides with my own experience, and
seems to be quite an improvement upone what I've read before. Several
years ago I tried to study up on this subject. The book Bicycling
Science, by Whitt and Wilson (MIT press, 1982) is generally excellent.
The chapter on balancing and steering summarizes the Jones article
from Physics Today, but as I recollect, both are rather misleading
about the effect of fork rake (or "trail" of the contact point of
the front wheel behind the imaginary intersection of a line through
the steering column with the ground). Jones says that a bike with
an extreme fork rake and hence negative trail is unstable and un
ridable, yet bicycle manufacturer will tell you that the larger
the fork rake and the smaller the trail, the *more* stable the
bicycle feels. (Some mountain bikes that are meant to be less
stable and more maneuverable have no fork rake at all.) I once
repeated the Jones experiment of adding some extensions to the fork
to put the wheel several inches farther forward, and found that
the bike was quite ridable, though hard to turn. There's a CENCO
poster that discusses balancing a bicycle and repeats the "myth"
about negative trail with more emphatic language, saying that such
a bike would be "virtually impossible to ride"; again, that wasn't
my experience.
The reason why trail is important is interesting, but I won't try
to explain it here in a hurry without pictures. I'm not sure I
understand it myself anyway.
Leigh, do you have some good references on the turning mechanism
that you described?