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Tires Part 3: tire pressure and tire perimeter

First I thought I could capture what I intended to write about tires in one article, but soon I recognized that it is better to split it into 2 parts. And while I was finishing off part 2, I read a few entertaining comments about whether the perimeter of a tire will change with the tire pressure on a 4WD forum… so here is even a third page about tires…

While some of the comments in the thread are at least adventuresome, I think this is still an interesting question that deserves some pondering.

Now, first the perimeter of a tire is calculated by 2 π R, and secondly this perimeter is nearly independent from the pressure!

When I changed my genuine tires to 265/75-R16 tires, the bigger spare didn’t fit anymore in the narrow spare well. I tried to find out whether reducing the pressure would make any difference for the spare wheel, so I started measuring. The outcome was that the difference in diameter and therefore perimeter is nearly independent from the pressure. With the tools available for me, I couldn’t measure any difference wrt the diameter for 0 psi and the diameter for 40 psi!

First I was a little bit surprised, but pondering a while about it I recognized that it has to be like this!

The plies made from steel in the tread are like a metal band, they are not elastic like a rubber band and can’t respond to the increased pressure by longitudinal flexing.

Of course the tire with 0 psi is less stiff than with 40 psi, but it has no impact on the perimeter! … if you don’t believe it measure it, with the spare wheel it is quite easy to do and accurate in order of plus-minus 1 mm: just use a string / fishing line and wind it around the tire and mark the line where the coils met each other. Then measure the length from 1 mark to the other. Do this for 0 psi and 40 psi or for any other pressure.

The impact of the pressure on the perimeter and diameter is negligible compared to e.g. differences in tread depth or differences in diameter for different tire brands. Note that the tire code, e.g. 265/75-R16, doesn't mean that the corresponding tire from every brand has a diameter of exactly

D = 2 R = (2 x [265/0.75] ) + (16 x 25.4) = 803.9 mm

The difference can be in order of 10 mm and more depending on the actual norm diameter and brand! Terracan owners who fitted 265/75-R16 Maxxis tires could do this without the need of removing the front mud flaps; conversely when I fitted the 265/75-R16 Scorpion Pirellis ATR tires I had to remove them as they collided with the tire.

Lets have a look what the impact of 4 mm in diameter - whether it is caused by unequal tread wear of different tire brands - means for the perimeter:

The perimeter is 2 π R or just π D, so for D = 804 mm the perimeter is 2,526 mm - for every complete wheel turn the distance covered is 2,526 mm! For a tire with a D = 800 mm the perimeter is only 2,513 mm - that’s 13 mm less for every turn! … 10 turns and the difference is already 130 mm!!

No wonder that this will stress drive components and will cause tire wear. It is even more impressive respectively scary as a difference of 4 mm in diameter is already caused by 2 mm tread difference!

Just 2 mm difference in tread, e.g. due to unequal wear and tear, on the rear axle and the LSD will cope a tremendous stress. Or it will cause significant wind-up of the transfer case in 4WD mode on bitumen / hard surface if the diameter of the front wheels differ by just 4 mm compared to the rear wheels!

I know why I do a tire rotation every 5,000 km and why I include also the spare in this rotation.

While the physical tire perimeter is virtually independent from the pressure, is there still an impact on the distance covered per axle turn due to different pressures?

Considering the impact on the tire footprint the pressure has, the following seems to be a common argument:

With a lower pressure, the “radius” defined by the distance between axle and ground is smaller - the height difference can be significant; hence the now smaller “radius” would cause the same effect as a physical changed tire perimeter respectively diameter: per axle turn the distance covered for wheels with different tire pressures can differ significantly.

Is this true? … that’s indeed a tricky question… if the physical perimeter of the tire - as stated above - is not changed by the pressure, but would differ wrt the “radius” defined by the lowered height from the axle to the ground, what consequences would it have?

Well, if we assume that the tire is not constantly slipping on the rim thus representing a kind of planetary gear, it is just not possible!

So where is the error in this approach?

The error lies in the assumption that the distance between the axle and the ground would define a new radius respectively could be used for the equation 2 π R to calculate a new perimeter! Obviously the contact surface of the flat spot isn’t a circle, so the equation 2 π R is not valid here.

Looking at the sketch it hopefully becomes clearer: without slipping of the tire on the rim (!), every point on the perimeter of the tire corresponds with a point on the perimeter of the axle, so one full turn of the axle means consequently one full turn of the tire covering the whole tire perimeter! … it doesn’t matter what shape the tire has and that the axle doesn’t sit in the centre of a circle!

So no wind-up due to changed diameter or perimeter, however unequal pressure in the tires should be avoided: as outlined in part 1 different pressures will cause a different rolling resistance for each tire due to the different amount of work required for flexing. The different rolling resistance can put stress on LSDs, will impact the steering and will causes unequal tire wear.

The tire pressure has of course also an impact on fuel consumption, but again not because of changing diameters respectively perimeters, but mainly because of the different deformation work required for flexing… I guess this is sufficient covered by part 1…

Still in doubt about all this mumbo-jumbo? ... have a look at this You Tube clip here:

Interesting stuff those tires … and I thought I get away with 1 page… yep, it’s opening a can of worms every time…

Update 20-02-13:

I recognised that this article is cited on different forums, e.g. here, and comments are made that car manufacturer would link TPMS with ABS, because a different perimeter due to different tire pressure would compromise the ABS performance. Of course tire pressure will affect braking! ... as it affects traction!...that’s why we let pressure down for more traction, but the same tire with different pressures will still cover - nearly - the same distance per turn!

The reason to implement TPMS is safety... it is as simple as that, no hocus pocus or mumbo jumbo. Under inflated tires cause a risk, also tires with a pressure difference as this will result in a different rolling resistance - which of course would compromise braking performance. Wikipedia explains it in a simple way, see “Benefits of TPMS”...yes, the article says that

quote: …First generation iTPMS systems utilize the effect that an under-inflated tire has a slightly smaller diameter (and hence lower tangential velocity) than a correctly inflated one…

…but that “slightly” smaller diameter (0.5 …1 mm ??) is only measurable for advanced ABS - or other sophisticated measurement systems - and as showed in this article negligible compared to other parameters like unequal tire tread, which can have a much bigger impact.

This article here was meant to show, that reducing the tire pressure in a magnitude that the car respectively axle will sit 20 mm … 30 mm … lower won’t have a significant impact on perimeter, thus won’t cause wind-up as the - incorrect - use of the equation 2 π R would implicate. The sketch shows why this equation can’t be used. If the new height for a lowered pressure would really be used as radius for this equation, the difference in perimeter, e.g. for a 20 mm drop, would be 126 mm!! …the You Tube clip shows that this is not the case and compared to this wrongly implicated magnitude the real impact of the pressure on tire diameter, which is only measurable with sophisticated equipment, seems to be negligible.

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p. issued: 19-01-2013 - last update: 22-02-2013

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