[RedDevil]

Originally Posted by CapriRacer

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Did you use that same tape measure? Didn’t it buckle when you tried to measure the circumference? I would think that would hurt the measurement in the direction of a larger distance, thus lowering the percentage.

I did use the same tape measure for the 'two halves' circumference measurement and the roll test.
I used the alu hook to measure the diameter, but checked its scale to the tape measure and they were, surprise surprise, identical.

As I wrote I wasn't satisfied with my circumference measurement.
I planned to measure it when I swap to summer tires, as then it would be off the ground.
Then it hit me - I don't have to wait for that!

As the wheel drops there's more space above it. I could simply drag the lead around the wheel, then align it perfectly and pull it tight.

Came out like 192.0 cm. 5 mm less than my first measurement, still more than I expected from the diameter check (which read 190.7 cm)
Looking around the wheel I see gaps between the lead and the tread. The bent metal tape fights being bent around so it forms a polygon rather than a circle.
So I pull it with all my might, and it reduces to 191.5 cm. Even then it polygons and there are faint slits between the tread and the nods of the polygon letting light through. But the real circumference must be close to this anyway.

Conclusion: the circumference of my tire can be anything in the range of 190.7 cm to 191.5 cm. I'd take 191.1 with a 5 mm variance.
Thus the rolling distance would be 36 mm less than the circumference, 1.9% difference.
Assuming it was 3% when new the difference got 1.1% (of the circumference) less through wear and use.
Also, metal tape measures really suck at measuring the circumference of objects with a 1 foot radius.

Originally Posted by CapriRacer

A couple of thoughts:
If the belts don’t stretch, then they must bulge out in front of and behind that contact patch in order to make up for the shorter distance through the contact patch. Either that or they shrink a bit (or perhaps both!)
We already know that a steel belted tire expands when it is inflated. You can see that when the tire is first mounted and adding air causes it to expand. So why wouldn’t deflecting the tire under load shrink it back a bit?

I'd think the whole cross-section of the tire pivots at belt level when it bends sharp ahead and behind the contact patch. The thread would be stretched there, the inside of the tire squeezes together. Then at the contact patch it is the other way round.

The force on the belt would be radius times width times pressure.
At a 30 cm radius at 3 Bar and a 175 mm width that would be:
(0.3 meter) * (0.175 meter) * (3 * 100,000 Newton / meter / meter) = 15,750 Newton.
1.55 times a metric tonne. Enough to lift my car and then some.
And it will very likely stretch out some if the pressure gets higher.

Each wheel supports just about 300 kg (2943 Newton), less than a fifth of the force on the belt.
So the force on the belt marginalizes all other forces in the contact patch.
I'd say the belt is all determining.