Re: [Phys-l] Another tire question

[John Denker <jsd@av8n.com>]

On 11/06/2007 05:34 PM, Edmiston, Mike wrote:
> I think I disagree with John that the sidewalls pushing up from below or
> pulling up from above amount to the same thing.  I have a drawing and
> some explanation posted at the reference below.  Please check this out
> and see if it makes sense.
>
> www.bluffton.edu/~edmistonm/Car.Tires.pdf


There's one detail that you may or may not consider important:
The rim of the wheel is shown grasping the bead, much as 
parentheses grasp the o here:
  (o     o)

But I've never seen any such structure in a real rim.  What
I see is more like this:
  \o     o/

And here is some real-world data that makes the same point
in more detail:

  http://www.alloywheelsindia.com/images/crosssection.jpg

I'm not opposed to saying that in some sense the car hangs
from the bead, but AFAICT it is cradled by the bottom bead
rather than dangling from the top bead.

This connects to my model that says the bead in such tires is
in constant tension, and the sidewall forces merely increase
or decrease the tension.  Hence my previous remark about the
particle in a square well was not 100% apt.  What we really
have is a shift in reference-line for the tension.  We can
either measure the absolute tension in the bead, or we
can measure it relative to the amount of "baseline" tension 
i.e. the amount of tension when the tire is fully inflated
but not under load, e.g. when the car is on the lift.


In my analysis, I instinctively dropped out the baseline
tension since by symmetry it doesn't contribute to the
final answer.  But if you want to emphasize it that's not
wrong, it's just a shift of emphasis.