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For the moment, I am only talking about steel or kevlar belted radial tires.Mileage will go down with a tire inflated much more than a couple PSI below the door sticker. This is not because the circumference of the tire tread changes. It is because as some of the sidewall makes contact with the road, it has a circumference different than the tread so it therefore is being dragged. The friction causes a loss in mileage. I am only talking about inflating over the door sticker in an attempt to improve mileage, not the difference between a low tire and proper inflation.For those that believe the tire changes in radius and therefore circumference, please explain how steel or kevlar belts stretch. Vehicle manufactures determine based on a particular tire size what air pressure is needed to keep the tread flat to the road for traction and wear. When you put a large tire on a light vehicle such as Explorer, it needs to run a lower pressure to not wear out the center of the tire. The requirements are then sent to tire manufacturers to quote a tire that meets the specs. Ford requested quotes for tires that were capable of running at 26 psi on the Explorer even though side wall pressure is 35. Firestone tried to blame Ford for setting the pressure to 26 even though Firestone had said their tire was capable of running at 26 psi. Once the tires were replaced, the replacements were still run at 26 psi without issue. The same Firestone tires failed on other vehicles, but due to the high sales numbers of the Explorer, those incidents were much more highly publicized. Ford also requested quotes for Excursion tires. The Excursion, due to not being able to pull a fifth wheel, cannot carry the load of an F250. While it can carry a load greater than load range D tires are rated to carry, Firestone said their load range D tires could carry more than the rating and enough for the Excursion. There were actually a higher percentage of Firestone load range D tire failures than the Explorer tires. The lower total vehicles and incidents prevented news coverage. I now have load range E tires and run them at the original tire pressure which is lower than that listed for the F250. I have no degradation issues including the splits in the sidewall like the Firestones had. The only issue I see is the center of the tires are wearing faster than the outside. I believe this is due to the load range E tires flexing less. So I may run the pressure lower to compensate for the stiffer carcass.
As Masterfabr pointed out, if you run wider tires, you need to lower your pressure. A way to find out how much is to wet a strip across the tread then roll over a piece of paper. The mark left should be the entire tread. Too low and the center will cup upward and . Too High and only the center will leave a mark.
Street tires have little to no change in rolling radius at different pressures.