Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-l] Another tire question





-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Brian Whatcott
Sent: Friday, November 09, 2007 1:02 PM
To: Forum for Physics Educators
Subject: Re: [Phys-l] Another tire question

At 09:22 AM 11/9/2007, Jeffrey Schnick, you wrote:

Brian W. said...

Sophisticated (in this context) means you can understand
a pneumatic tire can be contrived with NO contribution
from its upper half, and that this can be made to
function on a spoked wheel assembly.

I guess I am not sophisticated because I cannot understand that
unless
the tire is internally sectioned.

The spoked bicycle wheel/tire is no different than the auto
wheel/tire.
The axle "hangs" from the top rim via the top spokes. The rim
"hangs"
from the top sidewall of the tire.

No. The bead hangs from the top sidewall. The rim is supported from
below by the bead.


Well, well, well, Jeffrey. You didn't start out as a physicist, did
you?
:-)

You might enjoy responding to the design issue of showing the
ice/snow loading capacity of a blown diaphragm roof on a circular
"pill-box" arena.
These tension roof skins can be held down by a rim, despite the air
pressure differential applied across them. The side walls pull down
on the rim to keep the roof in place, unless the snow load gets too
great!

Wait: isn't that a bit like a tubeless tire? Oh yes!


There are similarities between the arena and the system we have been
discussing but there are important differences. The loading in the case
of the arena is the snow pushing downward on the roof. The question,
analogous to the one being asked about tires is: What is the upward
force on the roof that keeps the roof from accelerating downward once
the load is applied? The answer in the case of the roof is the pressure
of the air upward on the roof integrated over the area of the roof.
This force was always there but prior to the loading it was
counterbalanced by the net downward component of the tension force
exerted by the rim on the roof. That tension force automatically
adjusts to whatever it has to be to keep the roof from accelerating
upward. It decreases as you add snow to the roof.

In the case of the car wheel, the loading is the axel of the car
pressing downward on the central regions of the hub. The (hub + bead)
for this system, plays a role similar to the role played by the roof in
the arena. The question here is: "What keeps the (hub + bead) from
accelerating downward once the load is applied?" The answer in this
case can't be the pressure of the air on the hub integrated over the
surface of the hub in contact with the high pressure air, because that
adds up to zero. The only other thing in contact with the (hub + bead)
is the sidewall of the tire. The sidewall of the tire is everywhere in
tension so wherever it is touching the bead it is pulling on the bead.
To be providing a net upward force on the (bead + wheel) the upper
sidewall must be pulling upward on the upper half of the bead harder
than it is pulling downward on the lower half of the bead. This has
been explained well in this thread by others who have stated that even
though the tension in the sidewall is pretty much the same at all points
where it is pulling on the bead, the sidewall makes a greater angle with
the plane of the bead at points below the hub than it does at points
above the hub.

My inspection of the wheels on several vehicles in the parking lot
outside my office confirmed this point about the greater angle with the
plane of the bead, to my own satisfaction. One owner was kind enough to
have an underinflated tire in which the angle difference above and below
the rim, right up to where the tire came in contact with the rim, was
obvious.

Did you read my first post on this topic? It made it into the Phys-L
archives, see:
https://carnot.physics.buffalo.edu/archives/2007/11_2007/msg00071.html
but it didn't draw any comments. In it, I made the point that where the
tire makes contact with the rim, the tire only pushes on the rim. I
thought that was your position. (In my case however, it is because the
only part of the tire that is touching the rim is the bead.)

I don't think your idea of pneumatic stiffening is wrong in all cases:
If I put one edge of my mouse pad on the floor up against the wall and
push on the opposite edge with a clipboard, the mouse pad buckles with
very little force. But if I put another clipboard on top of the mouse
pad, to simulate the pneumatic stiffening of which you wrote, I can
apply a much larger force to the edge of the mouse pad. The thing is,
when I do that, the mouse pad is clearly in compression. It becomes a
little bit shorter as measured along a line collinear with the applied
force. My observations on tires are that when you fill them up with air
they stretch a little bit. They appear to me to get a little bit
bigger. The way the car tire bulges below the hub when the car is
standing on the pavement makes it look like the material making up the
sidewall is stretched rather than compressed. A sheet of rubber that is
in tension is pulling on whatever it is attached to its edges, not
pulling. This supports the idea that the sidewalls are only pulling on
the beads.



Brian Whatcott Altus OK Eureka!

_______________________________________________
Forum for Physics Educators
Phys-l@carnot.physics.buffalo.edu
https://carnot.physics.buffalo.edu/mailman/listinfo/phys-l