Re: sreering

[Ludwik Kowalski <kowalskil@MAIL.MONTCLAIR.EDU>]

On Sunday, Nov 9, 2003, John S. Denker wrote:

> The magic of steering comes in part from quasi-static
> rolling friction, but there's more to the story.  In
> particular, if the "tires" were rolling *freely* like
> the ball in a ball-point pen, there would be plenty
> of quasi-static rolling friction, but no steering.

Later JohnD compared a wheel with a set of many
sticks pushing the car against the road. I think
that this analogy is useful. But is it not true that
it applies to "powered" wheels only? A stick "just
touching" the road does not contribute to pushing.
Why should it then contribute to steering? Likewise,
not powered front wheels do not contribute to
pushing the center of mass.

The front wheels of a traditional car are not powered;
they roll along the direction of minimum resistance.
That direction, chosen by the driver, is defined, at any
given moment, by the plane of the wheel. Before
turning, the planes of all four wheels are parallel; the
back wheels push the center of the car forward.

Now lets us think about turning. The car turns even
when its front wheels are not powered by the engine.
The problem is more transparent when one observes
a simple tricycle. The tricycle turns when child's legs
are not on pedals. Therefore powering is not an
essential component of steering.

The act of steering a wheel changes the orientation
of its plane. Once this happens the direction of minimum
resistance no longer coincides with the direction along
which the center of mass was moving. That seems to
be essential. The center of the car (via bearings, etc.)
turns as if it were "trying to minimize something." That
is how turning can possibly be described. But what
this "something" is?

A railroad car turns because rails turn. This can be
viewed as a kind of steering. Potential energy would
have to increase to derail such car. The car turns to
stay at the bottom of a potential energy well. The same
is true for a ball constrained to roll along a horizontally
curving groove. In these cases friction does not seem
to be an essential part of steering; turning would also
occur if the wheels of the railroad car, or the ball in a
groove, were sliding rather than rolling. The potential
energy is minimized along a path of the object.

This, however, can not be said about steering a car
along a curving flat road. Here friction is essential. But
frictional forces are not associated with a potential. So
what is minimized when a car is being forced to follow
constrains imposed by steering it? The amount of
unrecoverable (thermal) energy? A lot of "heat" would
be generated if the direction of the center of mass did
not change in response to steering. Front wheels, after
being redirected, would start sliding instead of rolling.

A poet would say that "a car is trying" to avoid something
How should a physicist explain steering a tricycle when
both legs are in the air? Or, more specifically, how to
understand that the centripetal force "comes from quasi-
static rolling friction?" In my mind rolling friction is totally
different from static friction.
Ludwik Kowalski