There is occasionally considerable discussion about tire sizes and why the rolling distance of a tire is less than the measured circumference. I believe I have a clearer answer to this "apparent" discrepancy.

At 09:45 AM 6/6/05 +0100, Paul Hunt wrote:
"The biggest discrepancy is that my tyre measured 1940mm circumference whether inflated to 24psi, 10psi, laden or unladen. But it only traveled 1885mm at 24psi and 1876mm at 10psi."

The inner plies of the tire, especially for a belted tire, will not stretch or compress much under any circumstances. This means the steel belt remains the same length regardless of air pressure or deformation of the tread. In the measured example above, the actual measured travel distance divided by PI equates to the diameter of the steel belt, which is at about 3/8 inch less radius from the outer tread. The rolling travel distance is therefore very nearly equal to the circumference of the steel belt. A worn out tire will have almost the same rolling distance as a new tire. Surprise!

As the tire tread is deformed to be flat against the ground, the outermost part of the tread is compressed slightly to be shortened to the same length as the steel belt over the length of that flat area. This then accounts for the slightly reduce travel distance relative to the tire circumference, not the length of the flat relative to the initial arc length.

The much smaller variation in rolling distance with the large reduction of air pressure is accounted for by more squirm in the tread as the sidewalls flex considerably. In essence, when you have a gross amount of squirm the tread slips some on the pavement, and the total travel distance is slightly reduced. In the example above the travel difference between 24 PSI and 10 PSI is only 0.5% (representing a lot of squirm on a half flat tire).

"However the rolling radius (which is what is used in speedo calculations) indicated that it should have traveled 1823mm at 24psi and 1615mm at 10psi."

No, that's a small point of confusion. The rolling radius noted is likely to be the distance of the wheel center from the pavement, which changes with air pressure but has not much to do with travel distance. If you look at tire stats you will often find a specification for Revs Per Mile, which is the number needed for speedometer calibration. This would correlate closer with the actual measured travel distance in the example above.