Thoughts on tire pressure vs. tire diameter

[mechman600]

...or more specifically, tire pressure vs. under axle radius.

My '07 Matrix has the last of the ABS based TPMS, before the EPA mandated pressure sensors. If it sees one wheel spinning slightly faster than the others, it triggers the low pressure warning. The tire pressure is supposed to be 30 psi all around, and the TPMS is sensitive enough to catch a tire that is only 2 psi below the other tires.

Lately I have been running at 42 psi all around. Max is 44 psi for these tires. I have one leaker and it can drop well below 35 without the light ever coming on. This tells me that as tire pressure increases, the lower radius increases to a point and then stops increasing.

Just something I have noticed, that's all.

[serialk11r]

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.

[gone-ot]

...when you compare calculated tire diameter (Dc) versus actual tire diameter (Da), using various tire manufacturer's published Revolutions-per-Mile (rpm), you'll find that 0.97 -- or 3% deformation -- seems to be a typical / common value seemingly regardless of actual tire size, make or manufacturer.

Here's the basic formula to use which assumes NO deformation:

MPH = [ 60 / (G × A) ]×[ RPM / rpm ]

...where:
MPG = vehicle speed, miles-per-hour
RPM = engine speed, revolutions-per-minute
rpm = tire speed, revolutions-per-mile.
60 = conversion constant, minutes-per-hour
G = transmission gear ratio (usually highest gear)
A = axle ratio

[CapriRacer]

First, I think you'll find that the indirect TPMS only needed to trigger an alert at 25% underinflated. In the case of 30 psi, 25% under would be 23 psi.

I think you'll also find that increasing inflation pressure increases the diameter - and that the effect diminishes as the pressure goes up.

Put another way, the difference in diameter between 30 psi and 23 psi (7 psi) is greater than the difference between 42 and 35 psi (also 7 psi).