Well, as I said it was just for fun. I got interested in the math and kinematics and you can actually calculate the velocity and position of a tire element... wait - as Johngrass1 said - put down the pencil, step away from the paper...
Billyshope - I think I do understand your point, I just didn't agree and was attempting to explain why. And believe me, I would never think of disagreeing with the industry. In fact, thought I was just discussing it with you!
Regardless, I did what all good nerds do when faced with a problem - I Googled it. This is not a new question and people have made careers out of tire mechanics and dynamics. (Check out http://www.mathworks.com/access/help...rive/tire.html
) The net is that "Rolling Circumference" (ie. the distance a loaded tire rolls in one rev) is not the same as the unloaded tire circumference. The difference is due to the tire deflection under load. There are plenty of references and papers on this. Alot of patents, papers on estimating tire pressure by monitoring changes in rolling circumference.
This one from Continental Tire. " Deflation Detection System (DDS). DDC identifies a loss of pressure indirectly, using data from the wheel speed sensors of the electronic braking system – because when a tire loses pressure its rolling circumference decreases."
The clearest answer was from a tire expert answering the same question.
There are a couple of things that complicate the "circumference" of tires.
1) There are "calculators" that will calculate the circumference (diameter) of a tire based on the tire size. Use a search engine with the key words "tire calculator"
2) These "calculators" give you an answer based on the "size", which is different than the actual physical dimensions. Said another way, a P205/65R15 does not
actually have to be 205 mm wide and have an aspect ratio of 65%. There is quite a bit of variability in the market
3) The actual circumference (diameter) of a free hanging (not touching anything) tire is different than the rolling circumference (Rolling diameter) because the tire deflects
under load. Different inflation pressures and different loads will affect the rolling circumference, but as a general rule a properly inflation and properly loaded tire will have a rolling circumference about 97% of the free hanging circumference - a 3% difference.
4) The difference in circumference between tires will have a minor effect compared to other factors. Rolling resistance greatly affects fuel economy, so acceleration is also affected and rolling resistance varies from tire to tire. However, a change in rolling circumference of a tire acts in a similar way as a change in final drive gearing.
Hope this helps.
About Barry Smith
I have over 30 years experience in the design, manufacturing, and testing of tires. I have served as the technical advisor to the "800" number. I have authored or co-authored many publications - usually without credit. I can answer almost any technical question, but please don`t ask me to compare brands. I have prejudices because of my work experience.
Member SAE (Society of Automotive Engineers) Member Tire Society (Tire Technical Organization) SCCA Regional Competiton License holder Authored many training manuals on tires, their care and use.
So, if you really care - you need to adjust unloaded circumference by about 3%. However, now that I know - I don't care anymore!
Thanks for the responses!
Ed aka "Bob Goodyear"