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Re: steering



On Thursday, Nov 20, 2003, John S. Denker wrote:

I say again: you have to understand the axle and
bearing in the middle of the wheel.

The thought about the railroad is apt and useful.
The wheel has a flange that is to a first approximation
cone-like ... I'm calling attention to the fact that
the wheel has a smaller diameter zone on the outboard
side and a larger-diameter zone (the flange) on the
inboard side.

| | | |
| | | |
|_ | | _|
R|_| |_|R (R = rail)
R R

The bicycle exploits the same physics, BUT IT HAPPENS
INSIDE THE BEARING, nowhere near the tire/road interface.
The bearings are distinctly conical. It's like the
railroad wheel+rail, all rolled up into a package.

I'd tell you to take one apart but it is a bit of
a bother to get it put back together properly.
Perhaps you could go to the bike shop and ask
Wilbur or Orville to give you a scrap one. Similarly
an auto shop should be able to give you scrap
bearings from a car wheel. They are distinctly
conical.

Here's a picture that shows part of the story.
http://static.howstuffworks.com/gif/bearing-wheel.jpg

To repeat: The bearing can roll freely in one direction
for the same reason a railcar can roll down the rails.
The bearing develops a tremennndous force if you try
to push it in the cross direction, for much the same
reason that the flange on a railcar wheel develops
a force if you push it sideways. The bearing actually
carries the idea to perfection; you can't "derail"
it.

Instead of going to the bicycle shop I can idealize
the bearing. I am thinking about a tricycle whose
front wheel and axle form a rigid body. That body
is supported by two holes (well lubricated bearing)
in the steering fork. But this does not help me to
produce a free-body force diagram (for the tricycle
without pedals). The net force was nearly zero
before turning the fork; after turning the fork the
sidewise net force appears.

The only force I recognize is due to kinetic friction.
That force WOULD be very large if wheels were
locked. But wheels are not locked and the net
force is sidewise. I do not know how an internal
torque applied to the handle bars generates
such net force.

Bob Sciamanda wrote:

Remember how you steered your "belly slam" snow
sled? You simply deformed the runners so that the
leading portion took a new orientation. You can find
adult vehicles which turn without the (apparently
difficult) complication of a wheel/axle, simply by
orienting sliding front skids. I think some snow-mobiles
may do this. Is this the rudder/keel effect adapted to
wheel-less land vehicles?

Perhaps beginning with an analysis of these "steering
skid systems" would give a fresh and easier start to
grasping this "turning physics".

This again shows that the vehicle "is trying to do the
best it can" to minimize a loss of speed. Or, one may
say it "chooses the path of minimum resistance."

Yes, I know that descriptions involving "trying" or
"choosing" are not appropriate. But some kind of a
principle of minimal resistance does seem to be
involved in turning situations (like in turning along
a rail track or along a groove).

It is interesting to note that Bob's vehicle also turns on
a flat road without being "powered" (by gravity, or an
inner engine). The same is true for a tricycle; it does not
have to powered (pushing against the road) in order to
be steered. A poet can also say that the tire "does not
want" to loose too much rubber; it "does not want" to
generate too much thermal energy, it does not want
to waste to much time, etc

The double-headed arrows (see below) represent
two parts of a snow sled moving to the right. I am
using x to show the hole in the sled. The front runner
is mounted on a vertical column which is passing
through that hole in the body of the sled. C is the
center of mass of the entire vehicle.

<---------------C-------> <--x-->

The sled is moving with a nearly constant speed.
The steering column is turned so that the runner
is at an angle (to impose the right turn). A large
frictional force starts acting on the sled. We can
decompose this force into two components. This
indicates that a rapid change of the speed of C is
occurring. In the case of a front wheel, on the other
hand, the speed of the center of mass seems to be
essentially constant during turning. Why is it so?

To slow down rapidly, while skiing, I reorient my
skis and slide along the direction of my initial
velocity. But to turn without loosing too much
speed I reorient the skis and push the snow down
to create a guiding groove. Does a front wheel of a
tricycle create a temporary groove on a road?

In a later message Bob described the "landing wheel"
situation. One spinning wheel lands being oriented along
the direction of the velocity of C and another landing
being oriented at a 45 degrees angle. I think that this
is different from a situation in which the wheel has already
been rolling (along a given straight line, without being
powered) when its orientation was changed. Touching a
stationary floor (by a spinning wheel) is like "powering;"
the wheel pushes the floor backward and can gain speed.

Now you know why the textbook description, "the force
in the radial direction on the car is the force of static
friction," was so hard to comprehend. Static friction is
totally absent when a sled is steered. The textbook is
probably correct about a vehicle on wheels but the
statement is not at all obvious.
Ludwik Kowalski