Wheel Weight vs Contact Patch

[Carguy]

I have 2 sets of wheels. The first is the lightweight 16x7 Rota Circuit 10 (Mugen MF 10 knockoffs) I ran on this season. I currently have 225/50-16 Toyo RA1 on these rims. The second set is the heavier 16x8 CSA shod with 225/50-16 Kuhmo V700 I picked recently and tried on the MCO October 2nd lapping day.

The weight of one Rota wheel/tire combo is 38lbs and the weight of one CSA wheel/tire combo is 48lbs. I measured the tire width of the Toyo tire at 220mm and the width of the Kuhmo tire at just under 230mm.

My first impression of the CSA/Kuhmo tire combination is great grip, stiffer sidewalls and at times less forgiving than the Toyos. I also found them surprisingly grippy in the rain with only a bit of tread remaining - it poured buckets in the afternoon. But I can't tell if I was faster on them or not in the dry since I had a passenger in the car for all my laps.

So the question is can a better tire/contact patch overcome the 10lbs/corner weight penalty?

[ScotcH]

My guess is no. I think the unsprung weight diff in this case is significant enough that the bigger contact patch will not overcome it.

There is a very lively discussion on bimmerforums regarding tire width, and how it actually affects grip. Apparently, there are a few engineers who claim that the width (contact patch surface area) of a tire has NOTHING to do with the grip ... in fact, given identical conditions, the grip of a tire remains the same, regardless of the surface area. Of course, other actors like heat, deflection, etc. will affect this, but I don't think you're liely to overheat the 220 mm tire to the point where the 230 mm will make a diff. Id's say just slap the V700s on the rotas, and you're good to go!

[Carguy]

Hmmm... Then making the car 40lbs lighter than it is currently with the Rotas should have the same effect (or reverse depending on your pov). Without having read the bimmer post and rifling through my grade 11 physics "memories" the grip you are referring to should mean coefficient of friction. If that's the case then I understand statement "that the width (contact patch surface area) of a tire has NOTHING to do with the grip". I would argue though that the greater the contact patch, the less tire deflection there is and therefore more grip. How else would you explain that skinny tires don't grip as much as wider tires? So, if I opt for the Kuhmos on the Rota rims what is the effect on a greater side wall angle on tire deflection?

[njansenv]

I've considered this for a LONG time. I remember a high school debate in which our teacher maintained that tire width had nothing to do with grip. (learning about friction that day...) I maintained that 'it must, because everyone adds width/height to a tire to increase grip'. (bad logic...I know) Thing is, there's more going on than just the law of friction. (I realized much later) Say that you have x-grip with a rubber compound. You spin the tires, and it leaves rubber on the ground. That means that f-friction>the allowable shear 'in the rubber'. Increasing contact area decreases the shear stress in the tire.

That said, contact area doesn't change with tire width.:D (all else equal) Anyone want to guess why? I'll give you a hint: it's related to tire pressure. :cool:

My final answer? Too many variables to say definitively which will be faster. (a cop out....:D) Unsprung weight may be less important on a smooth course with a decent powered car. The allowable camber on the car will have an impact on how well you use that extra tire width. etc. etc. etc. Only way to tell 'for sure' is to do a back-to-back comparo, I guess.;)
Nathan

[ScotcH]

Originally posted by Carguy
Hmmm... Then making the car 40lbs lighter than it is currently with the Rotas should have the same effect (or reverse depending on your pov). Without having read the bimmer post and rifling through my grade 11 physics "memories" the grip you are referring to should mean coefficient of friction. If that's the case then I understand statement "that the width (contact patch surface area) of a tire has NOTHING to do with the grip". I would argue though that the greater the contact patch, the less tire deflection there is and therefore more grip. How else would you explain that skinny tires don't grip as much as wider tires? So, if I opt for the Kuhmos on the Rota rims what is the effect on a greater side wall angle on tire deflection?

Agreed ... based on many racer's experiences, wider is better ... to a point, where weight and lack of heat would make the bigger tire slower. Where that point is however, is the big question. In your case, I think the weight would be more of a detriment. Remember that unsprung weight counts for roughly 4x, so your 40lbs is actually like 160lbs of weight in the car itself (or like lugging your son around the track with you ;) ). This is of course also read on the internet, so take it with a grain of salt :)

[Carguy]

Thanks for the feedback guys!

Nathan, can you be more specific about contact patch size and tire pressure?

The way I understand it more-wider rubber = bigger contact patch (area). Consider the following. A tire width of 175mm has a width of 175mm plus a length of Lmm given the weight of the corner and tire pressure. So the static contact patch is 175mm wide X Lmm length = 175L. If you widen the tire to 205mm then the static contact patch becomes 205L and is greater than 175L. Now I understand that we are talking dynamic contact patch so tire deflection, camber, side wall rigidity, vehicle weight, weight distribution, coefficient of friction, center of gravity, body roll, tire angle, amount of heat, and even rubber shear are all factors to consider. Having said that as racers we all aim for maximum tire patch during cornering for maximum grip so while the static measurement will likely over estimate that actual contact patch, it would still be bigger if a wider tire is used with all other factors remaining equal.

"Unsprung weight may be less important on a smooth course with a decent powered car."

I agree. I'm dealing with 2700lbs curb weight, 160hp and 141 lbs-ft of torque so I don't think I'll want to use the heavy wheels at Mosport, or even a flat course for that matter. :p

"In your case, I think the weight would be more of a detriment. Remember that unsprung weight counts for roughly 4x, so your 40lbs is actually like 160lbs of weight in the car itself (or like lugging your son around the track with you :) ). "

Scotch, I concur with your conclusion but the 4x unsprung weight penalty is interesting... Where does that piece of wisdom come from? I'm not being facetious here Arek, just want to know. :cool:

Cheers!

[njansenv]

Well, the '4x wisdom' is trying to take into account rotational inertia. Thing is, a heavier wheel doesn't NECESSARILY have that much more inertia, depending on where the extra weight is. (at the hub, the increased weight has less impact, while at the rim, more impact.....think flywheel effect)

As for contact patches. For a given air pressure in the tire, the contact patch will be the same. If you have 600lbs on a tire (say a 50:50 weight balance on a 2400lb car) , and 30psi in the tire, then the contact patch will be 600/30 inches=20sq inches per tire. More pressure=smaller contact patch. A wider tire will give you a wider, but shorter (along the length of the car) contact patch. A taller, narrower tire will give a longer, narrower contact patch.

Nathan

[ScotcH]

The 4:1 ratio came from a discussion at some point in the past ... of course I don't remember where. Here are a couple of links I came up with which kinda talk about it, but also are quick to say that there is no hard rule:

http://www.hotrodders.com/t46496.html
http://forums.corner-carvers.com/archive/index.php/t-429.html

This one completely contradics the ratio, but does mention that lower wheel mass affects acceleration (makes sense, of course):

http://victorylibrary.com/mopar/sprung-c.htm

[Carguy]

Thanks for the info Nathan.

You've convinced me that the overall gripping surface remains the same for a given corner weight and tire pressure. Math never lies, only the interpreter or the statistician can do that... :) In conclusion the force of the vehicle weight is applied downward (by body roll) and across the width of the tire (sideways g's) during cornering. By modifying the contact patch to a wider width but narrower length you are actually decreasing the shear stress along the tire width axis (as opposed to the tire direction axis) thus increasing grip. Cool.

As for rotational inertia I understand the nearer/farther from the hub idea, but I'd still like to know why the factor is 4x? For vehicle inertia the extra 40 lbs comes into play during acceleration - especially going uphill. Check.

So then what about sidewall angle? I've heard from other racers that for a given tire width a wider rim is better if it corrects the sidewall angle to 90 degrees or thereabouts. This increases tire contact patch (or reduces tire deflection - take your pick). With my 7 inch rims there is a positive angle at the outside edge (negative at the inside edge) while the 8 inch rims provide a more square sidewall both inside and outside.

Cheers - again! ;)

[Carguy]

Thanks for the links Scotch, you posted during my non-cyberslacking time... :)

[GR8 Ride]

Originally posted by njansenv
Well, the '4x wisdom' is trying to take into account rotational inertia. Thing is, a heavier wheel doesn't NECESSARILY have that much more inertia, depending on where the extra weight is. (at the hub, the increased weight has less impact, while at the rim, more impact.....think flywheel effect)

As for contact patches. For a given air pressure in the tire, the contact patch will be the same. If you have 600lbs on a tire (say a 50:50 weight balance on a 2400lb car) , and 30psi in the tire, then the contact patch will be 600/30 inches=20sq inches per tire. More pressure=smaller contact patch. A wider tire will give you a wider, but shorter (along the length of the car) contact patch. A taller, narrower tire will give a longer, narrower contact patch.

Nathan


While the tire pressure / square area relationship is valid, it's not entirely true.

Weight divided by tire pressure is perfectly valid, IF you assume the sidewall strength to be absolutely zero, and the shoulder design of the tire to be completely identical across brands (unlikely).

Take a run-flat tire, for example. Should you pick up a nail, you will maintain a relatively similar contact patch, despite having 'zero' pressure in the tire (zero PSI above atmospheric, that is).

Like anything, it's a case of tradeoffs. Generally, a wider tire in road racing is better, up to a certain point. Eventually you will get to the point where returns aren't greater (or even equal) to the cost involved (in terms of $$$, in terms of performance, etc, etc).



Pat

[Dave Barker]

Pierre, this isn't Solo 2 so go with the wider wheel. You might find that the Toyo mounted on the 8 " rim would be closer to the width of the Kumho anyway. BTW you didn't mention what the offset was. If the wider rim also widens your track this is definitely worthwhile ( and likely at least some of the extra inch of width will be on the outboard side)

BTW I am checking into relative sizes of Kumho Victoracers vs Toyo RA-1s and in my size (275/40-17) on a 9.5"rim the Kumho is apparently 5 mm wider.

[Rob McAuley]

The Physics of Racing (http://www.miata.net/sport/Physics/)

Too much fun for all you nerds!

[Carguy]

Originally posted by GR8 Ride
While the tire pressure / square area relationship is valid, it's not entirely true.

Weight divided by tire pressure is perfectly valid, IF you assume the sidewall strength to be absolutely zero, and the shoulder design of the tire to be completely identical across brands (unlikely).

Take a run-flat tire, for example. Should you pick up a nail, you will maintain a relatively similar contact patch, despite having 'zero' pressure in the tire (zero PSI above atmospheric, that is).

Like anything, it's a case of tradeoffs. Generally, a wider tire in road racing is better, up to a certain point. Eventually you will get to the point where returns aren't greater (or even equal) to the cost involved (in terms of $$$, in terms of performance, etc, etc).



Pat

Good point Pat, thanks for chiming in. Back to physics class... :rolleyes:

[Carguy]

Originally posted by Dave Barker
Pierre, this isn't Solo 2 so go with the wider wheel. You might find that the Toyo mounted on the 8 " rim would be closer to the width of the Kumho anyway. BTW you didn't mention what the offset was. If the wider rim also widens your track this is definitely worthwhile ( and likely at least some of the extra inch of width will be on the outboard side)

BTW I am checking into relative sizes of Kumho Victoracers vs Toyo RA-1s and in my size (275/40-17) on a 9.5"rim the Kumho is apparently 5 mm wider.

Dave, the offset or back spacing is actually 7mm shorter (35mm CSA vs 42mm Rota) so by my calculation the CSA/Kuhmo wheel pushes the griping surface by out by 7mm (diffrence in offset) + 10mm/2 (tire width difference) = 12mm. I did not count the rim width difference since the tire width overlaps the rims and would be counted twice. A bonus is that the tire does not extend past the front or rear fender edges - zero points.

BTW the splice/seam you mentionned in an earlier post has occured on one of my tires after the lapping day. There is also a middle seam the shows on another one. I'm guessing it may have something to do with sudden change in heat during a heat cycle as we got rained on during the event.

[Carguy]

Originally posted by Rob McAuley
The Physics of Racing (http://www.miata.net/sport/Physics/)

Great link Rob! Thanks!

Originally posted by Rob McAuley
Too much fun for all you nerds!


Hey! I resemble that statement... :o :( Come to think of it, so do you Rob! :D

[Rob McAuley]

Originally posted by Rob McAuley
Too much fun for all you nerds!

Okay.

Too much fun for all US nerds!

I loved that site. Somewhere in there is a link to a track simulator, where you can run a Java race simulation program. Pick your track and the number of cars, and off you go!

[Carguy]

Hey Rob,

Lots of great stuff in that series, unfortunately much of the math and explanations are beyond my attention span... :p

I also haven't been able to find the Java-based simulation only the Unix/Linux version. Do you have a link for the Java version?