Tire pressure, load, and contact patch math

I just put new AT tires on Snoball the ZJ and I've been thinking about pressures, contact patch, and psi.  Tell me if it works this way.

Let's talk in terms of basic tire safety. Not performance, driving feel, or wear.

Tires are rated for a certain weight at a specified pressure. At that weight and pressure the tire will deform a specific amount to provide a specific contact patch. I assume (!!) this means the tire is safe to run at reasonable speeds with that amount of deformation. 

So, to get the same contact patch (and therefore same safe level of deformation) at a lower weight, can I calculate a safe lower psi based on the max rating?

Example with round numbers:

Tire is rated for 2400lbs at 44psi.  2400/44 gives a contact patch of 54.5454 sq in.  

Loaded at 1200lbs, you should get a 54.5454 sq in contact patch at 1200/54.5454 = 22psi

Should those be an equivalent level of safety? 

I have some reservations about impact loading but let's start the discussion there.

On A Street Tire Part of that is to Keep the Sidewalls 'Erect' (Likely not the correct Term) An Under Inflated Tire Will Heat up the Side walls to a Point they will Get Soft and Blow out. 22 PSI Might be a bit low , I think I would stay above 30-32 to keep this from Happening.

If you remember Back when Ford Explorer's Had a Problem with Tire Blowing out It was the Tire Makers that got Sued but the Problem was The Aluminum Rims were Leaking Air out and the Side walls Blew.

GTXVette said:

On A Street Tire Part of that is to Keep the Sidewalls 'Erect' (Likely not the correct Term) An Under Inflated Tire Will Heat up the Side walls to a Point they will Get Soft and Blow out. 22 PSI Might be a bit low , I think I would stay above 30-32 to keep this from Happening.

But thsts exactly my point. Equal contact patch has to give equal sidewall shape by simple geometry. Sidewall collapse has to be the same at the recommended 2400lbs/44psi as 1200lbs/22psi.

If I'm wrong and it's not, why?

This isn't a Scientific answer but ...... The Additional weight May not Spread the Width but will Increase the Patch Front to rear instead of Side to side......?  Making a Longer Patch Instead of a Wide Patch.  You of Course are asking for a reversal of this, but I would say it's better to Stay Stiff Than Limp.   Not Gonna Post the obvious 'She Said'.  Oh wait I just Did.

Ignore the sidewall (as long as you're under the max), run the recommended pressure on your door jamb. Your tire doesn't know what car it's on...

Roughly speaking, your math is correct for TIRE safety, but not vehicle safety.

You can’t ignore the sidewall. It has significant structure inside.  I’ve actually done contact patch vs pressure testing, there’s less variation than you think. 

Pressure vs load isn't necessarily a linear relationship.  There are load / inflation tables out there to give you the minimum pressure required to safely support a given weight for a size / load range of tire.  

In your case, for figuring out ideal pressure for your ZJ, what size tires, what load rating and what's the max psi?  

A friend ran his front tires at very low psi for street use and low rear, upping them for track use.  This was way below the sidewall number but only slightly lower that the door card.  On a Lotus Exige and it was for ride quality, I want to say the pressures were in the low teens.

Use the door sticker as long as it doesnt exceed the tire max psi. Usually only an issue on 3/4 ton and larger trucks with cheap tires.

Yeah on light cars such Locosts and my Midlana, tire pressure is typically mid to high teens. Anything higher and the tire balloons, wearing the center. Below that and the tire becomes squirmy. A side benefit of low pressure is a smoother ride.

Speaking of sidewalls, with such low pressure, the sidewalls end up supporting a significant fraction of the total weight and it can sometimes be hard to tell of there's even air in the tire. This is especially true with low-profile tires with their stiff sidewalls.

This started as thinking about the right pressure for the Jeep, but that's easy enough. It sort of progressed into a purely theoretical exercise.

Keith Tanner said:

You can’t ignore the sidewall. It has significant structure inside.  I’ve actually done contact patch vs pressure testing, there’s less variation than you think. 

What I mean is that the max pressure on the sidewall can be wildly different than the pressure you should run or need. My Xterra needed 30psi but the max pressure was 80psi (!) for the E-load rated tire it was on.

What did you find from testing?

First, assume a spherical cow...

I feel like this is pretty well answered, but the central explicit notion is that there's a lot of structure and shape to a tire, so you're not getting any kind of direct relationship between pressure, contact patch, and deformation.

It made me think of the Spherical Cow thing...

ultraclyde said:

Tire is rated for 2400lbs at 44psi.  2400/44 gives a contact patch of 54.5454 sq in.  

Loaded at 1200lbs, you should get a 54.5454 sq in contact patch at 1200/54.5454 = 22psi

Should those be an equivalent level of safety? 

I'm not going to make any guesses as to which is more or less safe than the other, but logically speaking I'm going to say that they are NOT an equivalent level of safety. 

First of all, 54.5454 is not your actual "contact patch".  This would only be true with a nearly structureless balloon.  Due to the way tires are shaped and constructed to hold weight, the math simply cannot be this simple.

Secondly, You're using the same calculation in two opposing ways. Once for the 'maximum safe' number, the other for the 'minimum safe' number.  They cannot logically be equated like that.  As I see it, if 54.5454 is your maximum safe 'theoretical contact patch', this would actually seem to imply that 22psi is the maximum that should be used with 1200 lb load.

Here, check this out:

Toyo Tire - Application of Load Inflation Tables.

I have always used the sticker pressure with no problems.    Trying to out think the tire and vehicle engineers only results in frustration.

I fell for the “pressure in the teens because light car” thing on my 1200 lb Locost for a while, but then discovered that every time I added pressure my lap times went down. It worked best when it had pressures similar to the same tire on a Spec Miata. So now I pay more attention to where the tire works best. 

What did I find when measuring pressure vs contact patch? The sidewall is key. You can drop significant pressure without much change in contact patch. 

My Tundra ran 70 psi, even though the suggested numbers were a lot less. Better tire wear, better economy, better handling. On cartrucks like Toyotas and Xterras, the recommended pressures are low for comfort. You also don’t need an E tire for that application. 

Keith Tanner said:

I fell for the “pressure in the teens because light car” thing on my 1200 lb Locost for a while, but then discovered that every time I added pressure my lap times went down. It worked best when it had pressures similar to the same tire on a Spec Miata. So now I pay more attention to where the tire works best. 

What did I find when measuring pressure vs contact patch? The sidewall is key. You can drop significant pressure without much change in contact patch. 

My Tundra ran 70 psi, even though the suggested numbers were a lot less. Better tire wear, better economy, better handling. On cartrucks like Toyotas and Xterras, the recommended pressures are low for comfort. You also don’t need an E tire for that application. 

Yeah, the X had brand new E tires on it, wasn't about to throw them away. They still had plenty of life left on them when I sold the car 50k later!

I think we are misunderstanding each other - what do you mean by the sidewall being key? I was referring to the max allowable pressure that's printed on the sidewall.

I'm interested in whether you did in depth-testing of what the contact patch looks like based on pressure. For example, my Miata on Pirelli snow tires handles TONS better at 40psi than 26, but I haven't done A/B testing in the snow with it.

Driven5 said:

Here, check this out:

Toyo Tire - Application of Load Inflation Tables.

This is a good reference. The industry has standards for load capacity at a given inflation pressure. The door jamb placard is the best place to be. Lower pressures have lower load capacities.

Air pressure is what allows the tire carcass to work - otherwise it's just a floppy weave of rubber and strings.

Driven5 said:

First of all, 54.5454 is not your actual "contact patch".  This would only be true with a nearly structureless balloon.  Due to the way tires are shaped and constructed to hold weight, the math simply cannot be this simple.

Secondly, You're using the same calculation in two opposing ways. Once for the 'maximum safe' number, the other for the 'minimum safe' number.  They cannot logically be equated like that.  As I see it, if 54.5454 is your maximum safe 'theoretical contact patch', this would actually seem to imply that 22psi is the maximum that should be used with 1200 lb load.

To your first point, although you are correct, since we're comparing load deformity at different pressures in the same structure it should be valid as a comparison even if the calculated value isn't accurate. (Which of course it isn't)

Now you're second point, you're absolutely correct. I hadn't thought about it that way.

Now, as for real world numbers in my real world, 4800 lb (loaded, apprx) Jeep ZJ, I would never run 22psi on the road. The door tag lists 36psi on 235/70r16 tires. According to the Toyo chart you linked that puts the per-tire load capacity at about 2000lbs. I'm running 255/70r16s with a 111T load rating, and the Toyo chart puts that size at 2072lbs at 29psi.   I'm currently at 32psi on all four and it rides and drives nicely, but I think I'll be adding a little back to the fronts. It's got a little too much bulge for my taste. OTOH, This also means if I'm exploring the forest roads around here I'll probably air down to the mid 20s and keep it under 40mph. If it gets really muddy I'd feel safe as low as 20.

Cooper doesn't publish load/inflation charts but I did find some info from their Australian market that suggests some off road pressures in those ranges.

In reply to ultraclyde :

FWIW, Jeep's stock pressures are a bit off IMO.  And I've found different tires need different amounts of front / rear pressure stagger to feel happy and wear well, even in the same size.  

For my 235/70R16 snows (106R) on 16x7 wheels, the fronts are best around 36 - 38psi, rears around 30  (assuming 1 - 2 people and no cargo in the Jeep).  And even 30 wears slightly to the center on the rears.  For my 255/60R17 summers (106V) on 17x8 wheels, the fronts get 40 - 42 psi, rears get around 35 to feel good and wear well IIRC.  For some reason, the snows hate higher pressure.  They feel fine (and less mushy in the rear) with more air but they wear horribly to the center.  

When I ran a set of 245/70R16s on the stock 16x7s, there was bulge no matter what.  Running them up to the 44psi sidewall max still didn't kill the bulge.  It's just the nature of a P rated tire with tall sidewalls, especially on narrower wheels.  My 225/75R16 (LT, load range E) mudders on 16x7s bulge less at 38 front / 32 rear when I've rallycrossed on them than the 245s did at sidewall max.  

Blaise said:

Keith Tanner said:

I fell for the “pressure in the teens because light car” thing on my 1200 lb Locost for a while, but then discovered that every time I added pressure my lap times went down. It worked best when it had pressures similar to the same tire on a Spec Miata. So now I pay more attention to where the tire works best. 

What did I find when measuring pressure vs contact patch? The sidewall is key. You can drop significant pressure without much change in contact patch. 

My Tundra ran 70 psi, even though the suggested numbers were a lot less. Better tire wear, better economy, better handling. On cartrucks like Toyotas and Xterras, the recommended pressures are low for comfort. You also don’t need an E tire for that application. 

Yeah, the X had brand new E tires on it, wasn't about to throw them away. They still had plenty of life left on them when I sold the car 50k later!

I think we are misunderstanding each other - what do you mean by the sidewall being key? I was referring to the max allowable pressure that's printed on the sidewall.

I'm interested in whether you did in depth-testing of what the contact patch looks like based on pressure. For example, my Miata on Pirelli snow tires handles TONS better at 40psi than 26, but I haven't done A/B testing in the snow with it.

I'm still talking about contact patch vs tire pressure, like your original post. It is not a 1:1 ratio unless you're running a tire with the literal structural integrity of an inner tube. The strength of the sidewall is a major factor in your contact patch as it provides a lot of support. In extreme cases, it will support almost the entire load. My BMW has a slow leak in one tire, and I can't tell that it's low until it's down to about 50% of running pressure because it has high performance low profile tires with a lot of sidewall strength. Running an E tire on a light truck like an Xterra, you won't see much sidewall deformation. Run a mall-terrain rated street tire on the same car and you'll see much bigger changes with pressure.

My testing was simple. I took a print of the contact part of a given tire on a given car (guess what the car was?) at different pressures. This was done like taking fingerprints - a bit of ink on the treads and drop the car on top of a piece of paper. The increase in contact patch was minimal with pressure changes. I was not looking at handling or noise or ride comfort, I was curious as to just how much the contact patch changed with pressure so that's exactly what I measured.

ultraclyde said:

To your first point, although you are correct, since we're comparing load deformity at different pressures in the same structure it should be valid as a comparison even if the calculated value isn't accurate. (Which of course it isn't)

As noted by Keith, the shape and construction of a tire prevents it from deforming with a simple linear relationship to pressure.  So without knowing what the exact nature of that relationship actually is, it cannot be directly compared as such.

okay, I get what you're saying. The sidewall structure itself results in a non-linear change in contact patch / sidewall bulge with pressure variation.

So back to more real world questions - what's the hive's favorite method for optimizing pressure for tread wear? Chalk test? Temp variation across the tread? Run it a while and measure tread depth?

Chalk test should get you close.  I usually go based on how the tire looks against the ground from the side (squish) and adjust a little based on feel and how things appear to wear.