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Old 10-26-2006, 10:04 AM
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Well, I agree the best way is to do it on the road while rolling. Once I get the transmission back in the car, I'll do that for these tires and see what I get. I also agree that if you are changing tire sizes and want to know the effect on your speedo - comparing undeformed circumferences is fine. The only time it may matter is when you are doing something from scratch and trying to calcluate what speedometer gears to put in your transmission - and even then we're only talking 3-5%.
But, since we are having fun and debating angels on pins...
The tangential velocity of any point about a center of rotation is the product of the distance from the center and the angular velocity. That is the radius x rotation rate in rad/sec. The tangential acceleration is radius x angular accel in rad^2/sec. The radial accel, that is the acceleration required to keep it moving in a circle is radius x angular accel squared. (This is the term which results in drag tires ballooning out when spinning fast.

When a tire is deflected by load the perimeter length of the tire does decrease from the undeflected perfect circle. The rubber deforms as it goes through the contact patch. The tangential velocity of a tread block going around the undeflected part is actually a little faster than it's speed when it's directly underneath the axle. The reason is the distance from where the tire touches the pavement at the front straight back to where it leaves the pavement is a little shorter than arc of an undeflected tire (draw an arc and connect ends with straight line - the straight line is shorter than the arc). All this deformation takes energy and it ends up as heat. Which I understand is why under-inflated tires degrade gas mileage. I've also heard that this generated heat is one of the reasons tires can fail at very high speeds as the tire construction can't disapate the heat and it weakens. I assume radial acceleration forces also play a part in that.

I'm sure more than any of you wanted - but long story short. It looks like the tire deformation does matter a litte and I assume that this is why tire manuf. spec both a circumference and a revs/mile - and they don't match doing straight math.
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