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Re: [Phys-l] Another tire question






----- Original Message ----- From: "Jeffrey Schnick" <JSchnick@Anselm.Edu>


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.

Somehow I have the impression (maybe mistaken) that you have shifted from a push up from below. I keep following everything to the point where you are at above, but then how does the bead transfer the net upwards force to the wheel. It is NOT trapped (as in some bike wheels) so it can't pull up on the wheel, AFAICT. But that leave pushing up from below, but I accept that it makes sense that the tension in the sidewalls is pulling harder on the top half of the bead. This is where I'm still confused.

Also, though at least one person has referred to it, what about my estimates of the needed tension. For a 10 degree bulge, I got 40,000 lbs of tension! What's reasonable here.

Rick