I have re-read the posts in this thread, and I think I know why there seems to be a paradoxical loggerhead here. That is, why the "height" crowd seems to be right and why the "diameter" crowd also seems to be right. Here's my take... We need to look at the geometric relationships involved.

As we all know, in a circle, the radius (1/2 the diameter) of a circle has a certain relationship to the circumference of a circle. Simply put, the circumference is equal to Pi diameters.

But here's the problem in this threaad --- once a tire is installed on a car, in almost all instances it is NO LONGER a true circle. That is, it's flat on the bottom. Deflate the tire a little, and the distortion is even worse!

Since the tire is no longer a true circle when mounted. the geometric relationship between diameter (or radius) and circumference ceases to exist!

So, some of you are correct -- regardless of the inflation pressure of the tire (within resonable limits), the circumference of the tire will not change. Therefore the distance the car travels per revolution of the tire does not change, despite the fact that the distance from the center of the hub to the ground has changed.

On the other hand, some others of you are also correct in stating that the effective "gear ratio" of a vehicle with deflated tires changes as the tire is deflated. Since the tires are no longer perfect circles, we can no longer use the diameter or radius of the tire when computing effective gear ratio. We must use the distnce from the center of the hub to the ground, which I'll call the "inflated height distance."

Think of it this way... torque generated by the engine is multiplied (unless in a straght gear or overdrive gear)by the transmission, and then multiplied by the rear axle ring and pinion gears. The differential applies the resultant torque to the axle shaft. The axle shaft applies that torque to the hub, and to the wheel and the tire. If I install a smaller size tire, I will have greater leverage to rotate the tire. So I have more grunt with a 31" tire than I do with a 44" tire. The same increase in grunt (change in effective gear ratio) occurs when I keep the same tire on, but just deflate the tire womewhat. By reducing the "inflated hieght distance", I decrease the length of the lever arm in the Third Class lever that the axle/tire represents.

The upshot of all this is:

(1) The deflation of a tire will increase the effective gear ratio (making it act like a numerically-higher gear ration).

(2) However, the deflation of the tire will not change the circumference of the tire, therefore the distance traveled per revolution of the tire will remain essentially the same.