Rolling diameter/circumference clarification - understanding

[Tbonem3]

In re "up sizing" wheels and tires, the e46 m3, from factory, with 18"s, has a circumference of 81.6 F & 81.7 R iirc.

Our wheels, usually, are staggared, and for us to maintain that even diameter or circumference requires that we go down a profile (45 to 40, for example) when going 30mm wider (225/45 to 255/40).

Here's my question:

Why does a wider tire with same (18") wheel diameter spec and same profile have a different rolling circumference?

I can understand it when you've put that wider tire on the same size rim - the wider tire will be squeezed, and I assume, become a bit taller. But if you extend the wheel width by the same amount of tire width, why would that wider tire be taller?

Wouldn't it fit the tire just as well as the narrower tire would fit the narrower wheel?

When you look at Tire Rack ,for example, and you see they're measurement for diameter and revs per mile (225/45/18 is 25.9" / 802rpm), do we trust that's true no matter what wheel the tire is installed on?

And if so, what is it exactly then, that makes a wider tire taller? Same diameter of wheel (18"), same profile (45) just wider to fit the wider wheel, so smae amount of stretch. Why would a 255/45/18 be taller than a 225/45/18, if installed on wider wheel (9" versus front 8")?

Thanks

[Tbonem3]

Here's an example:



Stock is 225/45/18 & 255/40/18, but I've put in 45 for argument's sake.

So this is saying the sidewall is taller (half inch) - does that mean that the profile # "45" isn't just a measure of side wall to diameter, but width, too, is included in the formula?

All things being equal, a wider tire shouldn't be taller, just wider. But maybe the wider tire is also taller, but that begs the question - why?

Wouldn't it be a lot easier if all tires (of the same wheel diameter and profile #) were the same? Then you'd just pick the appropriate width for you particular wheel width.

[D-O]

245/40R18

Height of sidewall is 40% of 245mm (98 mm, or 3.86 inches)

Diameter = 18 (wheel diameter) + 7.72" (sidewall height *2), for a total of 25.72 inches


255/40R18

Height of sidewall is 40% of 255mm (102 mm, or 4.02 inches)

Diameter = 18 + 8.04, for a total of 26.04 inches.

Circumference = Pi * Diameter, so the slightly larger diameter of the wider tire results in a larger circumference.

As long as the aspect ratio/profile stays the same (40 in this case), then if width increases so does diameter and circumference.

*must have been working on your second post while I worked on this one -

"does that mean that the profile # "45" isn't just a measure of side wall to diameter, but width, too, is included in the formula?"

The profile/aspect ratio is really a measure of the height of the sidewall as a percentage of width. Sidewall height is the product of profile and width.

[Obioban]

Unclear if you grok this, so if I'm saying something you already realize then ignore me...

The middle number/aspect ratio is a percent of the tire width-- not of the diameter.

In your example, the aspect ratio is 45, meaning the sidewall is 45 percent as high as the tire is wide (225mm). So, as the tire gets wider at the same aspect ratio, the sidewall gets taller.

It's a stupid system, but it's the system we have.

... D-O replied while I was typing

[heinzboehmer]

Hmm, I think there two separate questions here. One about rolling circumference vs tire diameter and another about how aspect ratio relates to sidewall height.

The answer to the rolling circumference question is basically that tires are squishy. Because of this, the tire will not be perfectly circular with the vehicle weight on it. This means that the distance a tire travels in one revolution (rolling circumference) is not exactly directly proportional to the tire's (ideal) diameter. If the tire were perfectly rigid and did not deform, then rolling circumference would equal tire_diameter * pi. Tires are not perfectly rigid though, so rolling circumference is actually the aforementioned value plus some factor that is dependent on a bunch of stuff (tire wear, tire material, sidewall stiffness, tire pressure, surface geometry, etc.).

The answer to the other question comes from what the aspect ratio is. The aspect ratio is a multiplicative factor used to calculate the sidewall height based on the tire width. For example, the "45" in 225/45/R18 means that the sidewall will be 45% as tall as the tire is wide. In other words, the sidewall will be 225 * 0.45 = 101.25 mm tall. On a 255/45/R18, the sidewall will be 255 * 0.45 = 114.75 mm tall. So the aspect ratio isn't directly telling you how tall the sidewall is, but rather how it relates to the tire width, hence why a wider tire with the same aspect ratio is taller.

[Tbonem3]

Thanks guys. I was unaware of width playing a role in profile.

Picking tires for a non standard wheel size for e46 can be tricky, especially when manufacturers don't all adhere to specific standards.

I'm focusing on tread width, sect width and revs per mile, but still having trouble settling on a staggered set. Yoko a052 in one size is way wider than a ps4s, yet is the same circumference.

It's hard to match close to factory circumference, but also pick a tire that has the right amount of stretch or fitment on the wheel.

[Obioban]

I'd focus on getting the same revs/mile front/rear over keeping them the same as stock. DSC is a PITA when those start to get different front rear.

[Tbonem3]

No, I'm not too concerned sticking to stock values, I've had and prefer 235/265 and 245/275. Though, for the driving I do, dsc is off, but I still prefer to match front to rear as well as I can.

[maw1124]

Yoko a052 in one size is way wider than a ps4s...

Really?? How is this possible, (unless they measured it on a different width wheel)?

I've run into this, where one size was measured on a 8.5" wheel and the wider size was measured on a 9" wheel. Yes, I too have spent too much time looking at the tirerack.com spec sheets to determine non-OEM fitments.

Sorry, I just re-read your original question. That "measured wheel width" spec they use may hold the key to your answer.

maw

[Tbonem3]

I like that Tire rack does that, and you would assume it's consistent, but i've read that, the A052 again for example, runs even wider than what tire rack says. I've seen one person say a052 is 1/2" wider than equivalent ps4s, but I've also seen someone say 20mm.

I'm leaning towards 235/40 & 265/35 for 9"/10" but even that seems almost buldgy knowing how wide A052 run, but height-wise, they're quite a bit shorter than stock 26" at 25.5/25.4. I'm fine with that, but I'd love to see them mounted to see how buldgy, perfect or stretched they are.

If i go to 9.5" front wheel, then it gets worse, do I run 265 square, but then that front is pretty wide for a 9.5" even though other brands' 265 is perfect for 9.5" wheel. Or do I go with 255/35/18 front 7 265/35/18 rear. 255/35 is kind of a no-no on this car, it should be 255/40 (stock), but because of how wide the a052 is, even the 255/35 has a diameter of 25.1 (versus tock of 26). that's still quite a bit shorter, but the tread width of 255 a052 is wide at 9.5" and would fit squarely on 9.5" rim. Or I could do 245/40 (9" tread width - perfect for 9.5" wheel) and it's 25.8, but that's quite a bit more than the 265/35 at 25.4. Not too bad I guess.

This is when keeping it factory is nice

[maw1124]

I like that Tire rack does that, and you would assume it's consistent, but… This is when keeping it factory is nice

Yeah that part… I think that’s why I’ve always kept my non factory changes to within the same measured wheel width. When tirerack suggests (or starts measuring a wider tire on) a wider wheel, that’s where I stop. That’s usually one size wider, keeping the rolling circumference in check. I just don’t have time for the headache. Now, a wider tire that keeps the same circumference seems like a good thing, but I tend to stick with Conti or Michelin on these heavier sporty German cars. I once put Yoka and Kumho on my Allroad 4.2 and that didn’t work out. I think these cars load tires more aggressively (think Zion Williamson’s Nike adventures), but that’s not something I’m concerned with proving. I’m actually concerned with not proving it.

maw

[RazorM]

No, I'm not too concerned sticking to stock values, I've had and prefer 235/265 and 245/275. Though, for the driving I do, dsc is off, but I still prefer to match front to rear as well as I can.

Are you planing to go squared? Or what are your intentions When trying to change currently 245/275 9/10j setup?

[Tbonem3]

Ya so I really like having a 10" rear visually, and since I do have a decent more power than stock, but I really don't want a 10" up front. I thought 9/10 was gonna be the shit, but due to my 996 calipers, I still need a spacer up front. Part of my goals was no spacers. So I'm thinking 9.5et22 up front will do the trick (and I don't mind having to keep my hands on the wheel more), but then the tires are an issue a bit. I'll probably end up with 265/275 or even 255/265 on bigger tires like cr-s and a052.

[bigjae46]

You might be thinking about race tire sizing - 275/640R18 - the 640 is the overall diameter, not a ratio to the width.

You want to stay + 1/4" or -1" in outer diameter from stock. Stock is about 26" so 25" to 26.25" is fine. Your speedo will be off and DSC might not be optimal. And if you have the TPMS function that might not work properly when you get closer to 25".

A smaller OD tire will have more RPMs so it will shorten the gearing a little and generate more heat at a given speed. A smaller OD tire will wear faster. On the track if you get below 25" then you'll start overheating the tire much faster. Some things to consider...

[Nate047]

Here's a good link, the author is a very successful time attack and race driver.

https://motoiq.com/how-to-properly-select-and-size-tires-for-performance/

Basically if you're doing a setup for street, it really is best to just stick with PS4s or similar and the 225/255 or 235/265 split. You do not need wider than that on a 9" / 10" wheel setup and you'll be losing performance.

A052s are way overkill for a street tire. But if you really want what is in reality, a track day tire, then do yourself a favor and do not get 245/275s. They will be way too wide.

Lifespan is also trash on the A052 lol. I would take a look at the AD09 which is supposed to have almost the same grip level but with much improved lifespan.