OK, dealer did it for $45 (+tax) and I have to take it on a test run tomorrow to see how accurate it is.
Here is what I've found (bear with me, my thought process is very linear):
Simple math:
Circumference = Pi x Diameter, so if I used 31, it would be:
31 x 3.14 = 97.34 and 63660 / 97.34 = 650.9 revs/mile
Little research + simple math:
But we know this is not correct, since the tire is 30.7" tall overall (no load).
30.7 x 3.14 = 96.39 and 63660 / 96.39 = 657.2 revs/mile
Little more research:
Well, the website lists the 31x10.50-15LT A/T TA/KO as 677 revs/mile @ 45mph, but at what pressure and what temperature?
Some real world data:
I decided to chalk test, only I used electrical tape for a smooth, definitive edge to measure from. I verified the cold pressure of 38 psig, and after 30 miles of highway driving it measured just shy of 40 psig (warm). While the tires were still warm, we rolled one complete rotation for a distance of 92.625", being sure to measure everything using the trailing edge of the tape.
63660 / 92.625 = 684.0 revs/mile!
Now, which one is right? Well, none of them.
When I test it tomorrow using the measured distance, I believe there is going to be two variables introduced that haven't been discussed at all in this thread (just hinted at here).
"Growing": As the tire spins faster the effects of centrifugal force move the tire walls outward and the tire grows taller with speed.
...and "Balance": if one side is at 38.0psig and the other is at 38.2psig, our L/S differential is going to "eat" some of that difference as heat, and the tone ring will show an average of the two tire circumferences.
Originally, we posted -5mph differences over a timed stretch and I was using my XCal2 to data-log the runs so the times are very close. We'll see how the actual road test does. I think it will be close enough to work, but there are far more variables in the process than we've covered so far. I need to find a way to get tone ring counts at speed!
I'm sure the 684 rev/mile number that we had flashed int he ABS module is dead on for the wife's tires, when hot and when the vehicle is at or near zero ground speed, on one side!
Anyway, does it matter? I think not. I just don't want the wife to get a ticket with the new tires reading 5mph slow.
Any takers?