Topic: "Bigger wheels will cost you performance" they say but why and how much???

[Gentleman Jack]

What's that piece o junk in the picture?  A kit car?
HAHAHAHAHAHAHAHAHAHA!  Just kidding.  A Q1 near me in Bright Orange.  Fantastik car.  A bit quicker than my Solstice (pre tune anyway, haven't seen him since yesterday when the tune went in... should be a bit closer.  )

GJ

[DeepBlueGXP]

Nice looking wheels Parkcaka, can't wait to see a photo of your Opel GT with them on.

[Treeman]

OK.  I have been thinking about this a bit and will finally throw in my  .  Ben's right - I am a scientist, but I am a biologist, so my physics and math is probably as rusty as many of yours.  But, I can bring some scientific thinking to this, so that is what I will try to do here.  IAlso, I am working this out as I write, so corrections are welcome.  It also means that this is an adventure to me, since as I start this, I don't know what the result will be!

Let us keep things simple for the moment with some assumptions.  A scientist starts by simplifying things and then adding back any complicating issues.  I will take at face value the statements that a pound on the wheels is equivalent to 5 pounds on the car (since I don't know) and that the moment of inertia increases exponentially with diameter (if you think of pi r², that makes sense).  Let's pretend that the 19"  wheels weigh the same 26 pounds as the 18" wheels. 

Also, if you remember back to algebra, you can scratch out things in common in a comparison (2x/4x = 2/4 = 1/2).  Since we are comparing moments of inertia for 2 wheels, I am going to make the bold assumption we can scratch out all the rest of the moment of inertia equation and use the part that changes, the radius of the wheel.

First, you will be moving weight out, but only by 1 inch, not two.  The 19" is the diameter of the wheel rim.  Not knowing the equations, but assuming it has to do with r² by rim weight, let's look at the percent change for 1 pound (1 pound keeps it simple).  For the 18" wheel, r=9, so  9²*1 = 81 (I am not assigning units because I am treating this as an index, not something real since I don't know how to calculate that).  For a 19" wheel, that is 9.5²*1 = 90.25. 

That's an 11% difference between 81 and 90.25. 

Second, you will not be moving the weight of the tire out because of the lower profile keeping the total tire diameter the same (in reality, considering you are trimming some from the inside of the tire due to the increased wheel diameter, the tire actually might weigh a little less, but let's say they weigh the same to keep it simple).   Not all of that 26 pounds is at the rim - I am guessing it is 50% rim, 50% hub and spoke.  So, you are moving 13 pounds out half an inch from the center of the wheel.  So 13 lbs * 0.11 (the 11% difference) = 1.43 lbs change in effective weight.

Now, let's say Ben has it right that a pound on the wheel = 5 on the car, and that my figuring is correct that our wheel's effective weight.  So 1.43 lbs * 4 wheels * 5 (the Ben factor) = 28.6 lbs.  So, if this is anywhere near correct, there is about a 30 lb effective difference car weight. 

A stock GXP weighs about 3,000 lbs.  The 30 lb effective difference in weight is about 1%.  Ignoring gearing, various frictions and resistance, and probably a bunch of other stuff, I go back to the formula for acceleration  - a=F/m (acceleration = force divided by mass).  So, acceleration is linear (negatively) with mass and we have about a 1% change in effective mass.  So, we should see acceleration times decrease (again being simplistic) by 1% which for a stock GXP takes us from 5.5 seconds 0-60 to 5.55 seconds 0-60.  I would care about that if I am trying to win a drag race but seriously doubt I would notice that on the street.

All of this assumes the wheels are of equal weight.  But, they are looking at lighter wheels, so there should be that much less of an impact, if in fact they are not making things better over stock.

The other thing, as U-238 points out, is unsprung weight.  That would not be affected by wheel diameter.  Since they are going lighter, this is also positive.

So, unless you are seriously racing (where every ounce is meaningful), I doubt these wheels will have any impact other than on the looks of the car.

[parkcaka]

Treeman thank you very very much:)

Now I can sleep better because I want 19"s sooo much hehe

I think you are correct. I will have no difference in performance between stock and 19" wheels.

I also understand other people's perspectives. People say I will get better performance with 18" wheels because by going that way (new lighter 18" wheels) I will even shave more weight from the stock weight.

So in your example if my 0-60 goes from 5.50 to 5.55 with lighter 19" wheels and tires, then if I choose even lighter 18" wheels the difference will be like going from stock 5.50 to 5.35 (guessing).

so the difference is infact 5.35 seconds to 5.55 seconds.

what people talk about is the opportunity cost of going 19" to be higher.

I understand the argument and I believe I will choose to go with 19"s

[2kwk4u]

So I was combing the interwebs to find a good link about wheel size and I came across this gem:

http://www.nerocam.com/SCC_TAP.asp

It goes a little more into weight reduction in general... and pretty much doesn't apply AT ALL to the thread at hand, but it's entertaining nonetheless.  I'll throw it up here b/c it looks like our O.P. has made his decision anyway...

[Treeman]

Actually, with the size and weight difference they have in that article, it makes me feel like my figurings may be about right.  46 lbs of wheel!

[Gentleman Jack]

Actually, with the size and weight difference they have in that article, it makes me feel like my figurings may be about right.  46 lbs of wheel!

Treeman,

You were looking for corrections - all I see is you say in the beginning that the weight will move out 1 inch, which is incorrect, but later correct yourself to say that it will only move out 0.5 inch.  So really, you caught yourself and your calcs were good based on the assumptions.

The only way to accurately calculate the MoI of each wheel is to separate the wheel/tire in to two parts.  First is the outer section of the wheel combined with the tire as if they were one piece.  This will not be perfect as there is air in there, but will be 99%+ .  The second portion will be the "spokes" of the wheels.  This will be easy for the stock 5 spoke rims as each of the 5 spokes are essentially identical.  For the beautiful rims you are looking at, the math is not so easy, but doable.  You would need to know the total weight of the center section of your rim.  It looks like it could be divided by 8 and be evenly weighted.  Here is the formula for each section:

A) Outer rim section and tire combined:

I=M*r^2 as discussed in prior thread (used for wheels, hoops, etc with open ends)

Thin cylindrical shell with open ends, of radius r and mass m





B) Inner rim section (spokes - calculated as rods of equal length and weight- 5 on stock rim, 8 on your new rim):

Rod of length L and mass m
(Axis of rotation at the end of the rod)







OK, all that being said, I don't know how much each piece of each set up weights.  If anyone has that info, I will gladly calculate all of this out for a real world example.  The math is not that difficult if you have all the info. As you can see from the first formula, width of rim has no impact on MoI, but will have an impact aerodynamically, but that is a whole different discussion.

Ok, if you are still with me here, you are a die hard.  I can calculate the MoI difference of an 18 inch tire and a 19 inch tire, since that info I can find.  Here goes:

18 inch tire: 245-45-18 Goodyear Eagle F1-GS-D3  weight 29 pounds (tire rack) outer r=27"
19 inch tire: 255-40-19 Goodyear Eagle F1-GS-D3  weight 29 pounds (tire rack) outer r=27"

THEY ARE THE SAME MoI!  Those are the two sizes of tire that maintain the same outer diameter while changing rim size from 18 to 19.  There was a close 19 inch - 245-40-19 that reduced the outer r to 26.7, which is probably close enough to keep most factory setting within acceptable range, but would certainly effect MoI (smaller r and less weight, they were 25 pounds as opposed to 29)

I'm tired.

Hope this helps some.  I realize some will just pass over this post, but if you do you will miss the hidden pictures of Jessica Alba....

Just kidding.

GJ

[Gentleman Jack]

I just reread my post and think I have found a flaw that I am working on figureing out.  Here is my thought - the 18 vs 19 inch tire comparison is flawed.  It does not take in to account the thickness of the sidewall and how that impacts the distribution of the weight in respect to the distance from the axis.  What I am unsure of it every place I check, that is a non factor.  None of the formulas for Moment of Inertia provide a variable for the thickness of the hoop/ wheel.  I wonder then if you would take the center of mass and use that a your Radius?  Would there be a difference in center of mass between the two specified tires as it pertains to distance from rotational axis?

Help?

GJ

[Gentleman Jack]

Found it!




Ok, this will work for EVERYBODY when it come to tires ONLY, wheels still need to be broken in two parts.  Check this website for an easy MoI calculator:

http://hyperphysics.phy-astr.gsu.edu/HBASE/ihoop.html#ihoop2

GJ

Here is the math (converted to kg and cm for the calculator-


18 inch tire-


 For mass M = 12.246993989999998 kg,
internal radius a = 45.72cm
and external radius b = 68.58cm,
the moment of inertia I = 4.160018993322792kg m2

19 inch tire-

For mass M = 12.246993989999998 kg,
internal radius a = 48.26cm
and external radius b = 68.58cm,
the moment of inertia I = 4.306192500210677kg m2

So there it is.  There is a difference between the two tires, an increase in MoI of .1461 kg m2
to go up to the 19's.  That will have to be offset by the new wheels being lighter than the stock rims as well as haveing more weight closer to the center of rotation.  It is possible for a Larger rim to have a lower MoI if the weight is distributed differently.  So please, take a rim off of that Rossion and cut it into two pieces, weght them and send me the info.  I really want to know the answer to this now....

GJ

too much time on my hands?

[parkcaka]

thanks GJ.

great posts.

[Critterman]

headache need asprin

[Treeman]

I tip my calculator to you.  Go for it! 

So much for simplifying things!  But I will be interested to see how close we come in the end.

[Gentleman Jack]

I tip my calculator to you.  Go for it! 

So much for simplifying things!  But I will be interested to see how close we come in the end.

Just need the two weights of the wheel:  hoop and spokes of each of the two wheels... then the real results show up. 

GJ