Hi Folks,

Here's an approximate rule of thumb I use for calculating rim width to keep the sidewall neutrally biased, and not bowed inward nor outward at the rim, relative to the tread area:

Wr = Wt*[1-0.42*(AR/100)]+8.4mm

(This should get you within about a half-inch of the correct value.)

Where:
Wr = rim width in mm (measured inside-to-inside)
AR = tire Aspect Ratio (40,50,60,etc.)
Wt = advertised tire section width (245mm, etc.)

Remember that 1" = 25.4mm (exactly.)

Example: I have a 265-50 R15 tire. What rim width should I buy?

Wr = 265mm*[1-0.42*(50/100)]+8.4mm
= 265mm*0.79 +8.4mm
= 209.4mm +8.4mm
= 217.8mm
= 217.8mm*(1"/25.4mm)
= 8.575" > ans.: a rim width of 8.5" or 9" should be viable.

Best,
MAP

On edit: I've changed the AR factor from 0.44 to 0.42, to give better agreement with the data I have. As a sanity check, I also compared the recommended tire and rim sizes posted at the beginning of this thread, and they agree well with predictions from this formula.

On further edit: The prediction you get from this formula probably won't yield a value which corresponds exactly to a stock rim width (as in the example cited here: you can't buy a rim that's 8.575" wide off-the-shelf.) This being the case, do you go wider or narrower than the indicated value? I believe that from a handling perspective, it's generally better to go wider. Here's why: as the car rolls in a turn, the wheel top generally tilts away from the center of the car's direction of turn. As the tire top tilts outward, the centrifugal force simultaneously acting on the wheel causes the rim to be pushed outboard with respect to the center of the tread area in contact with the ground. This lateral displacement between rim and tread causes a distortion of the sidewalls. If the rim is narrower than the tread area, then this lateral displacement causes the outboard sidewall to "want" to assume a more planar shape, while the inner sidewall "wants" to do the opposite and assume a more conical shape. In so doing, the outer sidewall "pushes down" on the contact patch, while the inner sidewall "pulls up" on the contact patch. The net result is a distortion of the tread area where the contact pressure is concentrated on the outboard side of the contact patch: the tire almost literally wants to "roll over" itself in a lateral sense. Such pressure concentration reduces total lateral traction.

If the rim, on the other hand, is wider than the tread area, then the lateral displacement causes the inner sidewall to get more planar, and the outer more conical. In so doing, the inner sidewall "pushes down" in the tread area, while the outer sidewall "pulls up" on the tread area. This is the exact opposite, of course, of the narrow-rim scenario. The net result is that the tread area in contact with the ground is distorted in a way that tends to oppose that created by the outward tilting of the wheel overall. This counterbalancing effect tends to maintain uniform pressure across the contact patch, and so lateral traction is maximized.

Hopefully the crude sketch below conveys what I'm trying to say (shapes, angles, and distortions have been simplified and exaggerated to increase clarity...)

With further consideration given to how much each wheel tilts outward as a function of body roll, one can generally conclude that a solid live axle should probably have a neutrally-biased sidewall, while the front end should be biased toward a wider rim in relation to the tread area, with the difference in width: 1.) growing as the front roll center height decreases (relating to the matter of camber gain,) and 2.) diminishing as the car's roll stiffness increases.



Comments:

1.) Despite the optical illusion effect, both tread widths (and presumed advertised section widths) are equal.
2.) In the accelerated case, we have the angle of wheel roll, theta (which looks like a zero with a horizontal line through its middle,) which is a function of: the magnitude of centripetal acceleration a sub c; the car's roll stiffness; and the camber gain at that particular wheel as a function of suspension deflection at that wheel.
3.) Note that in the static case, the tread centerline is coincident with the rim's centerline.
4.) Note that in the accelerated case, because of centrifugal force, the rim centerline is displaced outboard of the tread centerline by a distance delta (which vaguely resembles a "six."). It is this displacement which fundamentally causes the kind of sidewall distortion shown here (again, simplified for the sake of clarity. Sidewall vertical compliance and its resulting deflection aren't even suggested in this sketch, for instance.)
5.) The displacement delta is roughly proportional to the centripetal acceleration, a sub c.

Very nice explanation MAP!

That explains how you came up with that tire width vs. rim width formula... I was at a loss at first as to how you did that.

Hi SSM,

Thanks! But truth be told, I never did explain how I got that formula, but rather the reasons why one would, or wouldn't, want to go with a higher rim width than what the formula predicts. The formula is only an approximation for the rim width that yields a neutrally-biased sidewall, i.e., one that ignoring the overall convex bulge of the sidewall viewed in cross-section, generally conforms to a plane, rather than to a frustum (frustum = section of a cone, from the Latin.)

If you or anyone else would be interested, I could post the derivation of the formula.

Thanks,
MAP

Yes, I would be interested in seeing that. I thought you might have worked backwards from the geometry above to optimize a ratio between tire and rim width.

Hi SSM,

Here's the derivation of the equation:

Wr = Wt*[1-0.42*(AR/100)]+8.4mm



Thanks,
MAP

MAP's formula probably works well in a lot of cases. However,folks should know that tire and wheel manufacturers design to the standards of the Tire & Rim Association. TRA produces their guidelines with updates every year. So when you look up a tire size on a manufacturer's website, normally they show you the approved rim widths for a given tire. Set of formulas they use for rim width hasn't been published to the public that I have seen, though I do know that there is a series of "if/and" statements and is based largely on aspect ratio.

Hi FM,

I found their website here:

http://www.us-tra.org/traHome.htm

But for non-members, there's very little to see, and I admit that the price of admission is higher than my cost of curiosity.
Anyone have an inside scoop?

Thanks,
MAP

Here is a link I found helpful
Wheel Technical Information
Hope its useful to others as well

I have 275/60/15's on the rear of my 87, no problems with rubbing at all.

Did you see the shiny area on your frame? If not, you will eventually...

Hi Folks,

Since I posted the formula for rim width (see a few posts back with drawing) about one year ago, I thought I'd offer an update.

I've used this formula and compared results with known data over the past year quite extensively; in fact, to a far greater extent than all of the times previous to the posting of said formula.

What I've learned is that the formula is considerably more accurate and general than I first suspected. This surprised me, since some of the presumed values of constants (in particular, that of "k",) were based on eyeball estimates of averages for many tires and many rims.

For the record once again, the equation is:

Wr = Wt*[1-0.42*(AR/100)]+8.4mm

Where:
Wr = rim width for neutral sidewall bias, in mm. (1in = 25.4mm exactly.)
Wt = advertised tire section width, in mm. (e.g., 215,225,235,245,...)
AR = advertised tire aspect ratio. (e.g., 40,45,50,60,65,...)

Best,
MAP

i have a 275/50/15 on the rear of my 85' with no probs.the car is lowered and without tailpipes.im liking this guide and look forward to using it when the time comes.

Never, been that way for over two years now.

Has anyone posted the Z-28/Trans Am/GTA wheel fitment to the Monte? I'm interested in the GTA 16" wheels that look like the GNX wheels and heard you need spacers to fit the rear wheels. also heard you can run front wheels on the rear and rear wheels on the front without any problem? anyone know for sure what needs to be done?
Thanks,
Dave

when they say cross section arent they actuallt saying at the widest part of the bulge and not actually the tread width?
i have 255r70 15s on the rear and 245r60 15s on the front of my 86 cl.the bulge in the 255s is wide but the actual tread width is kinda skinny

Holy mega bump...

But why is it not safe on an 86 wheel but is on an 87-88?

Fronts only on our cars, is what I've heard....Ask SSNinja (Dave)....thats what he's running I believe

Hi Folks,

A thread from 2/09 titled, "Your rim opinion," speaks of rim options for a 275mm-wide tire on an MCSS. Since this tire is about as large as can fitted on these cars, I thought the following post in that thread merits inclusion here:

"Hi Mike D,

About what rims I recommend - use the equation in the sticky. You'll just about always be right within a half-inch of the correct value.

Also, agree about going at least 17" with the rim to maximize performance options with tires. In the first decade of the 21st century, 17" is what 16" used to be in the '90's, and 15" in the 80's.

Next - with a 275 and an 8-1/2" to 9" wide rim, you'll be pushing the envelope to the very edge in terms of what's likely to fit on the car without rubbing. Rim backspacing will need to be exactly on the money, or you'll have problems. You'll also want to make sure the car body is centered on the frame.

If I were you, I would remove all four springs from the car and disconnect both sway bars. Make a tire/rim template that mounts to each hub just the way the actual rim would. The template will have a puck that represents the rim/tire radial cross-section. This puck gets mounted parallel to the hub's axis of rotation. The puck mounts in an adjustable way to the hub-mounting feature of the template, so you can mock-up and adjust backspacing as well as rim diameter. Obviously, you swing the template a full 360 degrees on the axle to sweep-out the full displacement of a real tire/rim. Making such a template is a snap - I made mine in about an hour with some 1/2" plywood and a block or two of simple wood. A C-clamp is used to adjust the puck position relative to the rest of the template, to explore different rim diameter and backspacing possibilties.

Once you get to this point, check for interference over the full range of suspension travel at each corner of the car. In addition, at the front, repeat over the full range of steering input.

Don't be surprised if you find that a 275 doesn't fit no matter what you do with the rim diameter and backspacing - you'll probably find at least one point of interference. At this point, you'll then have to judge the probability and severity of this occurence (I'm talking a DFMEA for you engineering types here,) and determine whether you could tolerate this. If the answer is "no," then your only easy option is a smaller tire - sorry. Or, if you're really, really determined: some serious surgery on the car."

Best,
MAP

I want to run a 24x12 wheel on a 365/15/24 tire in the back what are some good mods to do without hacking up the body.

Mini Tubbing?

Only the car craft 12"brake conversion write up link is functional.

Hi Folks,

After watching questions on this forum about tires and rims for several years, it seems that all conform to just two simple cases.

CASE 1: I've got a RIM of a certain width (Wr) and a certain diameter (Phir). Question: What's the best size of tire to get?

Answer: You'll need at least one additional piece of information before you can proceed.
Scenario A: I'm set on a particular tire aspect ratio (AR).

Then: Tire width = Wt = (Wr-8.4mm)/[1-0.42*(AR/100)]
Tire OD = Phit = Phir + Wt*2*AR/100
Tire ID = Rim OD = Phir

Scenario B: I'm set on a particular tire OD (Phit,) probably because I want to keep speedometer calibration.

Then: AR = [100/(2*Wt)]*(Phit - Phir)
Wt = (Wr-8.4mm)/[1-0.42*(AR/100)]

CASE 2: I've got a TIRE of a certain width (Wt,) a certain aspect ratio (AR,) and a certain ID (Phir.) Question: What's the best size of rim to get?

Answer: Wr = Wt*[1-0.42*(AR/100)]+8.4mm
Tire OD = Phit = Phir + Wt*2*AR/100
Rim OD = Tire ID = Phir

A caution about rims: rim OD (Phir) and width (Wr) are measured at the mounting surface of the tire, and do not equate with the extreme width and diameter you would measure on the rim. A typical 17" x 8" rim would probably have an extreme OD of about 18.5" and an extreme width of about 9.2", for example. As always, use the conversion factor of 1" = 25.4mm (exactly,) since industry standards are persisting to keep units jumbled. You've got to keep units consistent within any given equation to get valid answers. And, the answers you get will rarely correspond exactly to something you can buy off the shelf. For instance, let's try a Case 2 example:

I've got a 245/45/17 tire. What's the best size of rim to get?

Plugging-in:
Wr = 245mm*[1-0.42*(45/100)]+8.4mm = 207.095mm. Round to 207mm. Units conversion: 207mm*(1"/25.4mm) = 8.15"
Tire OD = 17"+(245mm*1"/25.4mm)*2*45/100 = 25.68"
Rim OD = Tire ID = 17"

Interpretation: the math tells us we need a 17" x 8.15" rim. Obviously, unless this is a custom rim, you can't get that width. Plus, the width equations aren't exact, but will almost certainly get you to the nearest half-inch. So what to do? 8" would work, but 8-1/2" would probably work even better, since it's usually better (see discussion previous posts) to go a bit wider than a bit narrower than what the equation would tell you for neutral sidewall bias. This is especially true for the front of the car.

Let's try another Case 2 example, and go back two posts to the person with the 365/15/24 tire. Is his desire to run a 24" x 12" rim a good idea?

Wr = 365mm*[1-0.42(15/100)]+8.4mm = 350mm = 13.8". Conclusion: a 12" rim is way, way off. Btw, even with the right rim, this is far beyond anything that mini-tubbing could afford unless you just let the wheels "hang out" and hope you never hit any big bumps.
Tire OD = 24"+(365mm*1"/25.4mm)*2*15/100 = 28.31".
Rim OD = Tire ID = 24"

Now, let's turn this into a Case 1-a question: I've got a 24" x 12" rim, and want to run a tire with a 15 aspect ratio. What tire do I buy?

Wt = (12"*25.4mm/1"-8.4mm)/[1-0.42*(15/100)] = 316.3mm. Get a 315mm tire.
Tire OD = 24" + (315mm*1"/25.4mm)*2*15/100 = 27.72"
Tire ID = Rim OD = 24"

Answer: I buy a 315/15/24 tire.

Best,
MAP

Hi Folks,

Some further clarification. In case 1-b the equations seem to be largely reciprocal since they involve similar unknowns. They way to approach this is as follows:

1.) Use a first-guess for tire width (Wt) to get aspect ratio.
2.) Plug the resulting aspect ratio (AR) into the second equation to see if the resulting Wt matches the first guess. If yes, then stop. If no, then adjust Wt accordingly and plug back into the first equation. Iterate as many times as necessary to get convergence.

About having the rim to be wider than these equations would indicate, go back to roughly the middle of the thread to the post which shows a picture of how the tire gets distorted in a turn in the case of a rim that's too wide versus one that's too narrow for a full explanation.

Best,
MAP

Hi Folks,

As time has passed and I've tested more and more tires against the equation I first posted, I've noticed that an improvement and refinement are probably called for.

The issue is the presumed nature of convexity in the sidewall bulge. The factor of 0.42 comes from the presumption that the transverse bulge of the sidewall is, on average, about 21% of the exposed sidewall height (see derivation a number of posts back.) But more recent tests have revealed that this fraction declines as we make the sidewall shorter.

That is, instead of k = constant = 0.21, it should probably refined according to:

k = a1 + a2*H, where "a1" and "a2" are two, new constants.

The refinement amounts to presuming that the sidewall bulge is not a linear function of H, but quadratic, and where a2 is negative. Once I have a more comprehensive study finished about this, I'll share.

Best,
MAP

Just picked up a set of 1987 aluminum 15 inch SS rims to put on my 1986 G body last night. Bolt pattern is correct, but this morning I noticed (1) that the SS rim mounting holes are much larger than on the stock steel wheels on my car, and (2) the mounting holes are not chamfered.

Is there a special nut available / required to mount the aluminum rims? Couldn't find this in the FAQs so ...........