[CapriRacer]

A couple of thoughts about rolling diameter (circumference):

If you measure the freestanding circumference (not loaded, hanging in the air), you will find that it is larger than the distance traveled in one revolution by a tire at its rated load and pressure by about 3%.

If you do the math, the rolling diameter is NOT the static loaded radius times 2 (The static loaded radius is the distance from the ground to the hub when the tire is loaded.)

- BUT –

The rolling diameter is about the same diameter as the steel belt (on a radial tire) – which sort of means that if you think the steel belt as a tank track (like RedDevil’s image above) you’ll be pretty close.

- AND –

The distance traveled in one revolution by a loaded tire varies with load/inflation (those 2 things are linked), so varying the pressure without changing the load, will result in a different answer (which is what I did some time back to prove that point)

Why? Because the steel belt pantographs – changes angle - as the belt rolls through the footprint. It gets shorter (and wider).

Further, the tire will have a different freestanding circumference between inflated and not inflated.

Is there a formula? Probably, but I don’t know what it is.

But what does a difference in tread depth do? According to the tank track theory, nothing, but I don’t think that is 100% accurate – meaning the theory is wrong, but close.

And I am nearly 100% sure that the difference in tread depth doesn't account for the difference in rolling resistance from new to worn. I am sure of that because I've tested a lot of tires for rolling resistance and the amount of tread (volume) is one of the determining values. We used to design tires to get good RR values by reducing the width of the tread and/or by having wider grooves.