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Re: steering



On Thursday, Nov 20, 2003, at 20:59 US/Pacific, Brian Whatcott wrote:

At 12:34 AM 11/21/2003, Ludwik, you wrote:
//
The front wheels of a traditional car are not powered;
they roll along the direction of minimum resistance.

//

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?

///

This seems like an awful lot of hand-wringing about
turning a car. I am happy to visualize the steered wheels
(and the driven wheels too) providing a brute force
sideward push, at the cost of scrubbing more or less
rubber off the tread. I find no need for a minimization
model. Am I missing something?

I was certainly missing something. Let me try again.
A single large and heavy tire is cut to make a vertical
groove. It is wide enough for me sit in it, at the bottom.
The tire is at rest on an icy road supporting it; that road
is only slightly wider that the tire. The snow around the
road allows me to use ski poles, when I want.

1) What should I do to reorient the tire left-wise
without moving our center of mass? I push backward
with my left pole and I push, with the same force,
forward with my right pole. A frictionless tire on a
frictionless road would start spinning around the
vertical axis. My work resulted in an increase of
rotational kinetic energy.

2) Suppose I did the same thing on a snowy road.
My work resulted in reorienting the wheel and in
generation of heat. The wheel ends up being at rest.
But it was powered (by me); heat was produced by
kinetic friction between the rubber and snow (or
asphalt if you prefer).

3) After all this I take a real car wheel with a tire
and let it roll along an asphalt road to observe
rolling friction. The contact between the tire
and the road is a rectangular area, for example,
20 cm long and 5 cm wide, depending on the
weight of the tire; it is never a perfect line. A
different segment of rubber is compressed
and decompressed in sequential time intervals.
Pressing and decompressing segments of
rubber is like bending and unbending a wire.
The wheel slows down "because" its kinetic
energy is used to produce thermal energy
via internal friction. (A tire inflated to a higher
pressure would be loosing kinetic energy at
a slightly slower rate, as most drivers know.)

4) Siting on my tricycle without pedals I ask
somebody to push me. I am riding along a
straight line at a nearly constant speed. Then
I rotate the fork and the tricycle turns left. Why
does this happen? Because the right back
wheel is pushing the road backward, like if
it were the end of my ski pole. I am applying
this force by reorienting the front wheel. At the
same the left back wheel is pushing the road
forward, as if it were a ski pole. Reorienting
the front wheel (working against kinetic friction)
is like working through ski poles. In this situation,
however, the vehicle has three wheels and it
rotates around the vertical axis passing through
its center of mass.

5) What role does the static friction force play
in this scenario? It is responsible for a delay
between the moment I start turning the hands
bar and the moment the front wheel stars
changing its orientation. It also prevents the
back wheels from skidding. In writing the

0.5*m*v^2 < mu_s*mg

we can calculate the maximum speed to avoid
skidding. This, however, is not a satisfactory
description of what happens in steering a car.
Is my qualitative explanation acceptable to you?
If not then why not? Please give an acceptable
explanation, if you have time. Focus on #4.
Ludwik Kowalski