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Re: [Phys-l] Another tire question



Brian,

To me, what is still in question is just how is the force that acts upwards
ON THE WHEEL applied by the tire bead--which is the only part of the tire in
contact. I hope all agree that there is no force contribution ON THE WHEEL
from the air pressure.

I'll add a couple recent thoughts. One--we need to remember that there are
two beads and two sidewalls per tire--therefore we can halve the needed
force from each bead--to 250-500 lbs, depending on size of car. Two, I
think I now am reverting back to part of the TPT article explanation (don't
have it here at home) in that when the tire sits off the ground but
inflated, the forces on the bead from the sidewalls should be pretty much
the same all around and is a tension force. However, when the car is placed
on the ground, the weight of the car is now pushing downwards on the lower
half of the bead and the ground is pushing up on the bottom of the tire.
Doesn't this produce a compressive force in the sidewalls that will lower
the tension in the lower half of the tire. This part is independent of the
'bulging' of the tires but in fact helps create some of the bulging which
then lowers the vertical component of the tension even more. Are these then
the two components in the TPT article.

All of that above agrees with Michael and Jeffrey (I think) at least in the
fact that the vertical tension in the upper sidewall is greater than in the
lower sidewall--by the amount of the weight to be supported by the wheel.
But we come back to the problem that if the bead is not trapped--doesn't
seem like it is in a car wheel/tire from pictures that have been
offered--then the bead can't be pulling the tire up from below. The force
on the wheel must be from the bead below. Could it be that in effect the
tension above is pulling the bead away from the wheel (but not enough to
break the air seal) while the compressive component of the forces on the
lower part of the tire are maintaining a firm hold of the bead on the lower
part? This would give us a differential force of the lower bead upwards on
the wheel but still agree with the tension forces being greater in the upper
half.

BTW--tire material tensile strengths seem to be on the order of 4000 MPa.

Rick

----- Original Message ----- From: "Brian Whatcott" <betwys1@sbcglobal.net>

I will admit, I was hoping for more from you.

Here we go. Tension structures have mechanical properties
that you might not expect from floppy rubber, fabric and
steel bands.
They can react tension, and they can react compression.
The tension structure we know and love as the pneumatic tire
has two ways of reacting ground forces at the hub.

Where the hub makes a strong connection to the tire case,
the two dimensional stress field of the surface of the inflated
tire has a particular pattern when reacting the ground force:
it is an enhanced tension region around roughly the top half
of its area, and a compression region in the lower half.

For a tire case not strongly connected to the wheel hub, the field
of compression is largely confined to the lower half of the case.
It is not overwhelmingly necessary that the tire's case deflect
in some particular way at the hub. The structure has stiffness
due to inflation.

The tire's footprint area transmits internal air pressure,
as does the belt bending force and the sidewall bending force.
A decent reading of the product of footprint area and
internal air pressure should provide a large fraction of the
total ground reaction force, in non-pathological cases.

Disappointing, but that's all there is.


Brian Whatcott Altus OK Eureka!