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What a physics graduate student who was at the FSAE club told me was that as the tire deforms and meets the road, the effective diameter is never quite the same as the actual tire diameter. He said to think of it as thousands of tiny little feet scuffling across the road, rather than a smooth surface that follows the road.
If you're running really low pressure, the increased tire deformation probably slightly reduces the rolling circumference. That's my guess.
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