Re: counter-steering, with numbers

[palmer@sfu.ca (Leigh Palmer)]

> Leigh Palmer says:
> > In the case of riding no hands the turn is initiated by waiting until the
> > lean and the wheel direction are fortuitously in the correct directions,
> > and then pedaling the bicycle so as to stabilize that condition. If you
> > would like an exercise to demonstrate this, just try riding a bicycle
> > slowly, no hands and without pedalling, through prescribed turns.
>
> Surely you are not suggesting that (while moving straight forward) the
> bicycle is just wobbling about vertical by itself; as you point out, it is
> not stable.

I'm suggesting something a bit like that. As the bicyle falls over
a bit to one side the front wheel naturally steers to that same side.
As the angle of lean increases the bicycle-rider system would come to
a stable orbit if the rider were rigid and no dissipation were
present. If you would like to observe this condition simply ride a
bicycle at moderate speed an a playground or parking lot and get off
while it is moving in more or less a straight line. The bike will
find an equilibrium curved path and execute a long death spiral (when
I was a kid we used to compete to see how far we could get our bikes
to go this way). When you are riding in a straight line with no hands
you are constantly torquing the bike away from the direction it is
currently falling.

What I say in the selection above is that once you are into a turn
with no hands the balancing is much easier, and that is so precisely
because the turn is a stable condition, so adjustments can be made
more easily. I can't roll a polhode on a herpolhode for you, but the
effect is kinesthetically dramatic. When riding no hands in a straight
line one remains tense; when a turn starts one relaxes appreciably.
Kinesthesia is a great measuring instrument.

Bottom line: a bicycle moving in a circle is stable. A straight line
is not a circle, and the degree of stability increases monotonically
with the degree of path curvature.

> Stability is achieved by action of the rider through feedback,
> and when riding no hands, I do not see what action the rider can take
> except to shift their weight.  And any action the rider can take to
> stabilize the bike can also be used to initiate a turn.

The rider can exert torques on the bicycle. These are applied both
through the cranks and via the saddle. The bicycle exerts equal and
opposite reaction torques on the rider of course.

> Let me say that I certainly agree that balancing a bike no-hands with the
> steering column locked would be extremely difficult.  However I think the
> reason is that when you shift the weight and the bicycle leans, the front
> wheel also responds by turning.  This effect seems to assist in
> stabilization.  Note that this is from experience; I don't yet have a
> physics line of reasoning for it.

That's entirely correct, and the physics of that is well understood.
It is well covered in a book more than 100 years old, "Bicycles and
Tricycles: An Elementary Treatise on Their Design and Construction"
by Archibald Sharp, reprinted by MIT Press. I have a copy in my
office. Chapters XVII and XVIII are devoted to stability and
steering.

Leigh