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Old 10-08-2007, 08:39 PM   #1
Yoo Shin
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Default Calculating the effects of larger wheels and tires, and loss in performance

I was wonder if there's a good formula out online that calculates the effects of increased wheel/tire mass, diameter and rolling resistance, in relation to performance, mainly acceleration.

I remember once stumbling across an Excel spreadsheet that someone had put together in an autocross forum that was pretty good at calculating values that were easy to assess power/performance loss.

On my 06 WRX, going from stock 215/45s (24lbs IIRC) on the stock 17 wheels (aprx 21lbs IIRC), to a 245/40 on 17x8s (weighing 27 and 21 lbs respectively) with only a .10" increase in diameter and I noticed quite a noticeable degradation in acceleration and braking.

My next tire upgrade was to a 225/45 (25lbs) on the same wheels and I was expecting a wash or even better performance, since the tire was only .25" taller but 2lbs lighter and (according to the tire manufacturer) .3" narrower. This set up felt even "heavier" and again,I felt the loss in acceleration.

I understand that the "butt dyno" theories are all circumstantial and completely subjective but I do a fair bit of driving in various conditions and consider myself pretty attuned to my car's behavior, so I do actually feel the differences in performance.

I bring all of this up mainly because I plan on switching to a 18x8 wheel with a 235/40, which will again add a 1lb or two plus an increase in diameter, and I plan on going from Stage II to a Protuned VF39. What I don't want is a only a partial net increase in performance with the turbo upgrade, due to the wheel/tire change.
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Old 10-08-2007, 08:56 PM   #2
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calculating for the weight effect of the tire is going to be nearly impossible without the right test equipment... a heavier wheel isn't always bad for acceleration, what matters more is where the weight is. an ounce of extra weight at the very edge of the tire will have more effect then a pound in the very center.
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Old 10-08-2007, 08:59 PM   #3
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wow 21 pound 17x8s. Where are you shopping?
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Old 10-08-2007, 09:05 PM   #4
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This article discusses this and has some links to spreadsheets like you are talking about:

http://www.mazda6tech.com/index.php?...d=16&Itemid=32
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Old 10-08-2007, 09:08 PM   #5
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Tire size calculator

not sure if it's what you're lookin for or not...
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Old 10-08-2007, 09:42 PM   #6
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Double post

Last edited by KingOfSiam; 10-08-2007 at 09:45 PM. Reason: Double post
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Old 10-08-2007, 09:44 PM   #7
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Just get some lightweight wheels, 18" or less and you should be fine. As long as you have 225+mm tire width the performance in the turns will strongly outweigh any effects with acceleration. ESPECIALLY when replacing the RE92's.
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Old 10-08-2007, 09:57 PM   #8
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Quote:
Originally Posted by waktasz View Post
wow 21 pound 17x8s. Where are you shopping?
That's what the STI Limited wheels weigh.
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Old 10-08-2007, 09:58 PM   #9
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This is very simple; a lighter wheel and tire make a BIG difference in drag racing [also road and circle track; I have experence in all 3]. I asume you understand the concept of unsprung weight[ tire[tube], wheel, brake rotor[drum], axle, driveline, etc.
A simple, proven, repeatable example everyone can understand:
I raced in NHRA, divison6, super/ street class; the object in this class is to run a 10.90 each time with a perfect light on a pro tree and cross the line befor the other car without breaking out[ going faster 10.89 ]sounds easy but a very competitive class[ also the lowest class in nhra racing]
each winter you go thru your car and make changes to be more competitive;
one time a life long drag racer asked me why I was running tube type slicks[13 inch]I said I really did not know: he said I would 60 foot faster with out tubes???how could 2 tubes make a difference to a 590 hp./ 445 tq./ 2800lb. car with driver]
But he was right; faster 60', mph/ this in a car where every run 7-10 stat's are kept. I then went to lighter wheels and brakes[ big difference but big $'s]I think in a wrx because of the low hp/ weight ratio that light tires and wheels make a HUGE difference.
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Old 10-09-2007, 07:49 AM   #10
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If the stock 17" wheels on our Subarus weigh about 21 lbs, I just don't get why people pay big bucks for wheels that weigh just a couple pounds less...moving to a wider wheel so you can run wider tires I can see though, but to buy expensive wheels to save a pound or two is just crazy.

IMO, an aftermarket wheel would have to weigh at least 5 lbs less each for me to even consider it. For the money I think the Enkei RS-M 17" x 8" 5-100, 45mm offset at $260 and 15.5 lbs each is the best wheel out there for the money on a WRX.

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Old 10-09-2007, 08:38 AM   #11
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Old 10-09-2007, 01:10 PM   #12
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Quote:
Originally Posted by bnt0726 View Post
This article discusses this and has some links to spreadsheets like you are talking about:

http://www.mazda6tech.com/index.php?...d=16&Itemid=32
That's excellent, thanks. That first spread sheet was the one I was talking about.

Quote:
Originally Posted by waktasz View Post
wow 21 pound 17x8s. Where are you shopping?
21lbs = about any stock WRX or STI rim and 17x8 Rota. I have 17x8 Rotas.

Quote:
Originally Posted by 05wrxmatt View Post
That's what the STI Limited wheels weigh.
Bingo

Quote:
Originally Posted by silver-duck View Post
This is very simple; a lighter wheel and tire make a BIG difference in drag racing [also road and circle track; I have experence in all 3]. I asume you understand the concept of unsprung weight[ tire[tube], wheel, brake rotor[drum], axle, driveline, etc.
A simple, proven, repeatable example everyone can understand:
I raced in NHRA, divison6, super/ street class; the object in this class is to run a 10.90 each time with a perfect light on a pro tree and cross the line befor the other car without breaking out[ going faster 10.89 ]sounds easy but a very competitive class[ also the lowest class in nhra racing]
each winter you go thru your car and make changes to be more competitive;
one time a life long drag racer asked me why I was running tube type slicks[13 inch]I said I really did not know: he said I would 60 foot faster with out tubes???how could 2 tubes make a difference to a 590 hp./ 445 tq./ 2800lb. car with driver]
But he was right; faster 60', mph/ this in a car where every run 7-10 stat's are kept. I then went to lighter wheels and brakes[ big difference but big $'s]I think in a wrx because of the low hp/ weight ratio that light tires and wheels make a HUGE difference.
Exactly. Those who say they can't feel the difference going from a stock wheel/tire to one that is 1" wider, .5 " taller and 2-3lbs heavier, are not in tune with how their car feels.

Quote:
Originally Posted by WRXLTD View Post
If the stock 17" wheels on our Subarus weigh about 21 lbs, I just don't get why people pay big bucks for wheels that weigh just a couple pounds less...moving to a wider wheel so you can run wider tires I can see though, but to buy expensive wheels to save a pound or two is just crazy.

IMO, an aftermarket wheel would have to weigh at least 5 lbs less each for me to even consider it. For the money I think the Enkei RS-M 17" x 8" 5-100, 45mm offset at $260 and 15.5 lbs each is the best wheel out there for the money on a WRX.

Exactly. I can't see myself paying $600-700 for a wheel that is 2-3lbs lighter when i can easily counter that with a simple tune and add a little more power. Enkie RPs would be a nice option as well, as they're just a bit more then a Rota and weigh a bit less, 2-3lbs IIRC.
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Old 10-09-2007, 02:06 PM   #13
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I don't think there is a calculator that can do what YooShin wants... because there is a critical piece of data that is NOT given by the manufacturers and most people don't have the equipment to measure it: inertia.

An "18 lb wheel" will not have the same inertia as another "18 lbs wheel", and it's the inertia that matters. Either you measure inertia (no one has the equipment) or you must know that radius of the CG "hoop" (ie the "moment" of the wheel. We have only to go on anecdotal data.

I'm going to use the term "sluggish" to refer to rotational acceleration of the wheel/tire, as opposed to static weight, because I believe that takes into account the inertia. (And since I can't measure inertia)

In my case, I had:

(A) 23 lb 17x7 2006 OEM WRX wheels + 25 215/45/17 RE92

(B) 14 lb 17x7 Kosei K1TS wheels + 215/45/17 F1GSD3

It was obviously plain as day A more sluggish than B.

Then I got:

(C) 18 lb 2004 17x7.5 STi BBS wheels + 225/45/17 F1GSD3

C was noticeably more sluggish (and grippier) than B, but not as much as A.

But I was considering:

(D) 16 2001 16x7 RS wheels + 205/55/16 BFG traction T/A's.

Static weight of D is more than B, BUT I theorize that inertia of D might actually be closer to B than I'd expect because of the radial difference of the wheels. I'm guessing that the radius of the moment of the 16" wheel and tire are smaller than the 17" ones.

Anyone have data to prove this?

(Note: it appears summer tires generally tend to be lighter than all-season/winter/offroads)

Last edited by chimchimm5; 10-09-2007 at 03:33 PM.
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Old 10-09-2007, 02:09 PM   #14
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sounds like you'd need a physics degree to accurately figure it out. Rotating mass and balancing is a real science.
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Old 10-09-2007, 02:17 PM   #15
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Quote:
Originally Posted by CF-Ninja View Post
sounds like you'd need a physics degree to accurately figure it out. Rotating mass and balancing is a real science.
You don't need a degree. Just basic physics. From wikipedia:

Quote:
The (scalar) moment of inertia of a point mass rotating about a known axis is defined by
where
m is the mass,and r is the (perpendicular) distance of the point mass to the axis of rotation. The moment of inertia is additive. Thus, for a rigid body consisting of N point masses mi with distances ri to the rotation axis, the total moment of inertia equals the sum of the point-mass moments of inertia:
For a solid body described by a continuous mass density function ρ(x,y,z), the moment of inertia about a known axis can be calculated by integrating the square of the distance (weighted by the mass density) from a point in the body to the rotation axis :
where
V is the volume occupied by the object. (While the triple integral may be taken over all space, only the region where ρ(x,y,z) ≠ 0 will contribute).ρ is the spatial density function of the object, andx, y, z are cartesian coordinates of a point inside the body.
Diagram for the calculation of a disk's moment of inertia. Here k is 1/2 and r is the radius used in determining the moment.


The moment of inertia for many non-point objects can also be found or approximated as the product of three terms:
where
k is the inertial constant,M is the mass, andR is the radius of the object from the center of mass (in some cases, the length of the object is used instead.)
So, in the last equation:
This is the approximation CG "hoop" (moment) that I was talking about.

We know M as the static weight but we don't know R. I/k is combined for use in acceleration calculations. So, the only way to find out, is to measure I (and who has a machine that can do that?) or get R from the manufacturer. AND THEY WILL NEVER GIVE YOU R.
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Old 10-09-2007, 02:25 PM   #16
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Quote:
Originally Posted by WRXLTD View Post
If the stock 17" wheels on our Subarus weigh about 21 lbs, I just don't get why people pay big bucks for wheels that weigh just a couple pounds less...moving to a wider wheel so you can run wider tires I can see though, but to buy expensive wheels to save a pound or two is just crazy.
How much unsprung weight do you think a car has? Removing 8-10lbs of unsprung weight is a good and noticeable amount. Case in point, the OPs car feels way slower since adding unsprung weight.
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Old 10-09-2007, 02:35 PM   #17
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Quote:
Originally Posted by chimchimm5 View Post
You don't need a degree. Just basic physics. From wikipedia:



So, in the last equation:
This is the approximation CG "hoop" (moment) that I was talking about.

We know M as the static weight but we don't know R. I/k is combined for use in acceleration calculations. So, the only way to find out, is to measure I (and who has a machine that can do that?) or get R from the manufacturer. AND THEY WILL NEVER GIVE YOU R.
Damn it, see that's the key is R and I want a way around R.

This has been good help though guys. I have a feeling I'm going to end up doing some elaborate experiement that'll be non value added and pointless but maybe fun.
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Old 10-09-2007, 02:44 PM   #18
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^^^I want in on said experiment Beers !
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Old 10-09-2007, 02:49 PM   #19
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I've read that "most" of the wheels weight is at the outer rim. So if we rough estimate the moment radius to be the rim radius, then for comparison sake I did this rough calc:

Code:
WHEEL			DIAM	ST WT	I	%
2006 OEM WRX wheel	17	23	1661	0%
Kosei 17x7		17	14	1011	-64% savings
2001 RS 16x7		16	16	1024	-62% savings
2004 Sti BBS 17x7.5	17	18	1300	-28% savings
18's			18	25	2025	18% penalty
DUB-buhdub bling blang	19	33	2978	44% penalty
Interesting... it says I should go get some 16" RS's.... or 16" Enkei RPF1's or something 16" with a weight about 16 or less

Last edited by chimchimm5; 10-09-2007 at 02:55 PM.
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Old 10-09-2007, 02:52 PM   #20
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Quote:
Originally Posted by Yoo Shin View Post
Damn it, see that's the key is R and I want a way around R.

This has been good help though guys. I have a feeling I'm going to end up doing some elaborate experiement that'll be non value added and pointless but maybe fun.
ALSO NOTE HOW "R" IS SQUARED, WHILE M IS NOT.

That shows how significant the R is.

Oh... and multiply the saving/penalty by 4 because there are 4 wheels on the car

Last edited by chimchimm5; 10-09-2007 at 02:59 PM.
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Old 10-09-2007, 03:04 PM   #21
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One thing is that if the overall tire diameter stays the same, you still can reduce the polar moment of inertia by picking a smaller wheel. Since more mass will be closers to the centroid(center axis), this is due to the fact that inertia increase substantially with increasing distance from the centroid.

For example the polar moment of inertia of a disk is I = ( pi * radius^4 )/2. A small change in radius can effect the overall inertia substantially.

IF you want I can try to simplify calculating the polar moment of inertia of a wheel + tire. It would just take a while.
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Old 10-09-2007, 03:05 PM   #22
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can we say 17x8 Enkei RPF1's??? 15.5lbs...wider(check)+lighter(check)

I would hazard a guess this a great reason why people like the RPF1's. I for one will be getting a set of them for this reason.

I can say from personal experience that wheels in the 15-16.5lb range make a noticeable difference.
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Old 10-09-2007, 03:07 PM   #23
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according to some, the 17x7.5 bbs wheel weighs anywhere from 15-17lbs. the 17x8 for the 05+ are 19lbs.
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Old 10-09-2007, 03:23 PM   #24
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Quote:
Originally Posted by chimchimm5 View Post
I've read that "most" of the wheels weight is at the outer rim. So if we rough estimate the moment radius to be the rim radius, then for comparison sake I did this rough calc:

Code:
WHEEL			DIAM	ST WT	I	%
2006 OEM WRX wheel	17	23	1661	0%
Kosei 17x7		17	14	1011	-64% savings
2001 RS 16x7		16	16	1024	-62% savings
2004 Sti BBS 17x7.5	17	18	1300	-28% savings
18's			18	25	2025	18% penalty
DUB-buhdub bling blang	19	33	2978	44% penalty
Interesting... it says I should go get some 16" RS's.... or 16" Enkei RPF1's or something 16" with a weight about 16 or less
Factor in the tire though which could and probably will be heavier and will probably expand more then the 17" tire will as speed increases.
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Old 10-10-2007, 09:15 AM   #25
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The tire is farther from the center axis so it has a bigger percent of effect on performance.why do some bicycle wheels cost 2000; when working with .5-.7 hp. wheel / tire weight are huge.
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