Cornering stiffness for different sizes of the same tire

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tomislavp4
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Joined: 16 Jun 2006, 17:07
Location: Sweden & The Republic of Macedonia

Cornering stiffness for different sizes of the same tire

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Hello guys.

I've been doing some calculations on how the tire size affects the understeer/oversteer behaviour of a vehicle and I've been trying to find information on how the cornering stiffness (or max. lateral force) differs between different tire sizes of the same tire without luck. Does anyone here have any data on this, by chance? I'm mostly interested in road-legal tires but a this point, anything will do. Thanks!

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DiogoBrand
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Re: Cornering stiffness for different sizes of the same tire

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Well, if you're talking about tyre width, as far as I know, it doesn't affect grip, what it does affect is the load that the tyre can bear before getting into plastic deformation and therefore losing grip, and it does that by increasing the contact area and therefore reducing the overall pressure. To get an idea of the load limit, you could get some deformation graphs for the desired rubber compounds and then calculate at which point in lateral acceleration the load on the tyre will overcome elastic deformation, and then apply that to different tyre widths.

But of course, unless someone more educated on the matter confirms what I'm saying, assume it's total BS.

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Tim.Wright
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Joined: 13 Feb 2009, 06:29

Re: Cornering stiffness for different sizes of the same tire

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I will have a look at some of my front/rear tyre models (which are same model different dimensions) this weekend and see if I can extract a trend. Unfortunately, my database isnt that big so you cant draw many hard conclusions.

The major unknown here is obviously whether there is a construction change as well as a dimension change between front/rear. All identically sized tyres are not necessarily of equal construction and this may skew my results.
DiogoBrand wrote:Well, if you're talking about tyre width, as far as I know, it doesn't affect grip,
Tyre width does affect grip - generally with wider/bigger giving more grip (all other things like construction and compound being equal). This is because tyre grip isn't purely produced by dry coulomb friction (which depends only on vertical load) but also a number of adhesive (chemical bonds) and hysteretic sliding frictions which are dependant on contact patch area. Therefore increasing tyre size increases the contact patch area and generally this gives more grip.
Not the engineer at Force India

Greg Locock
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Re: Cornering stiffness for different sizes of the same tire

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Yes it is possible to model the effect of small dimensional changes on cornering stiffness, but I know of no open source tool to do so. A database of thousands of tires tested means we can do that sort of thing with r^2 of 0.8 or better.

Bear in mind if you fit a wide tire on the same rim width the cornering stiffness will often drop.

Tirewidth rim cornering stiffness (mu/deg) peak mu

235mm 8" .232 .969
235mm 9" .242 .979
255mm 8" .224 .947
255mm 9" .235 .958

Now you want might the same SLR, so the AR will drop for a given tirewidth, but you didn't ask that. It'll turn those numbers upside down, sidewall height is crucial.

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tomislavp4
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Re: Cornering stiffness for different sizes of the same tire

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Greg Locock wrote: Tirewidth rim cornering stiffness (mu/deg) peak mu

235mm 8" .232 .969
235mm 9" .242 .979
255mm 8" .224 .947
255mm 9" .235 .958
Thank you for the data! Ok, so this suggests that moving up a size gives an increase in cornering stiffness of 12-ish percent. A bit higher than what I expected. Do you happen to have data on 215s and 195s as well? I assume that the difference of 12% is more or less true for a size jump between 235 and 215 as well as between 215 and 195. Is this assumption correct?
Tim.Wright wrote:I will have a look at some of my front/rear tyre models (which are same model different dimensions) this weekend and see if I can extract a trend. Unfortunately, my database isnt that big so you cant draw many hard conclusions.
Ok, I'm mainly interested in tires between 195 and 255 in width so if you database includes these then great, we can compare your data with Greg's and see if they differ an by how much.

Thanks guys, I appreciate it!

Greg Locock
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Re: Cornering stiffness for different sizes of the same tire

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I'm afraid you have misinterpreted that table.

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tomislavp4
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Re: Cornering stiffness for different sizes of the same tire

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Greg Locock wrote:I'm afraid you have misinterpreted that table.
How so? If the stiffness for the 235 mm tire on a 8'' rim is .232 mu/degree and for the 255 on a 9'' rim .235 mu/deg that is a difference of .003 mu/deg, no?

Greg Locock
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Re: Cornering stiffness for different sizes of the same tire

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Well, ok that is one way of looking at it, but why not go the 235 on a 9" rim?

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tomislavp4
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Re: Cornering stiffness for different sizes of the same tire

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Greg Locock wrote:Well, ok that is one way of looking at it, but why not go the 235 on a 9" rim?
You have a point there. Must've confused 235 for 225 and since 225s are usually mounted on 8'' rims I used that value.

Jersey Tom
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Re: Cornering stiffness for different sizes of the same tire

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I haven't personally acquired and read through this, but perhaps this would provide some insight: http://papers.sae.org/760732/

I'd also be a bit wary of the study or understanding you're trying to undertake. I'll give some insight from my recollection of several years at Goodyear's world headquarters:

Say you're developing a tire line with a matrix of different sizes - bead diameters, widths, overall diameters, whatever. There are only a handful of "development sizes" sprinkled throughout that matrix that get the up front design work. Gets expensive with each mold iteration you cut being $30,000-50,000! You'll have at least one vehicle platform that you track test these on. Maybe multiple if you've got say a 15" and 18" bead diameter tire in the same tire line.

Do all the design work to try and hit your subjective handling targets on each development size, noise, wear, durability, etc. Then the rest of the sizes are more or less "interpolated" from there. So as what trend you get, that may be entirely contingent on the particular tire line, how the development sizes were done, and whatever company policy is as far as interpolating between sizes.

Can also be dependent on the vehicle platform you're using and load range you're in. Just like sometimes adding air pressure will increase cornering stiffness, sometimes decrease it...
Grip is a four letter word. All opinions are my own and not those of current or previous employers.

Greg Locock
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Joined: 30 Jun 2012, 00:48

Re: Cornering stiffness for different sizes of the same tire

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Unfortunately the original question was written in such a way that the results are a muddle. By increasing tire width, on the same size rim, you get two strikes against you, deeper sidewalls, so less stiffness, and, typically, inclined sidewalls, so less stiffness.

In reality if you go up from a 195 55 R16 on 6" rims to a 225 you'd probably go to 7.5 or 8" rims, and you'd drop to a 45 or a 50 AR, or far more likely switch to R17 with a further reduction in AR. These all have significant implications for cornering stiffness and peak mu.

However street tires that are ostensibly the same design may have significant shifts in construction, for example the 20" version of a 17" tire for a production car may have features in the sidewall specifically designed to reduce sidewall stiffness, to reduce impact harshness etc, and this will affect cornering stiffness. Also to be honest we don't want to release a completely different suspension and steering tune for each tire, so ideally all the tires would have similar characteristics. The crucial one for limit handling is the tire load sensitivity, if all the tires in the family have the same trend then their limit handling balance will be similar, so they won't need huge rebalancing in the suspension to make them work.

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