Originally Posted by swamp2
Fair enough. I will respectfully disagree back, but this time with a wealth of evidence to make my case.
Have a look at the table below. I have made a nice spreadsheet (and even attached it for the real nerds) to calculate wheel moment of inertia (among other things). As you can see in your particular cases colums D vs. E and F vs. G the larger wheel (despite not
being quite apples to apples in terms of widths) uniformly have MUCH larger moments of inertia. The moments are larger because of the effect of the wheel, not the tire. The larger wheels have a much higher concentration of mass at a large distance away from the center of rotation. I can't quite follow/decipher your "reasoning" above but it is not correct and does not arrive at realistic numbers, trends nor conclusions. Your insight here is simply flawed.
I should add some key assumptions in my calculations (again for all the real nerds that may scrutinize the details):
1. I assumed the cross section of the wheel is a squared "U" on its side, i.e. with no spokes but solid. This is a fair assumption as you can make that section of a uniform thickness that approximates tapered spokes as are present in most real wheels.
2. I also assumed that a tire is a squared U (rotated 90 degrees clockwise to mate with the wheel).
3. I used the "thin shell" volume approximation for the barrel parts of the wheel and tire for volume calculations.
4. The thicknesses of the various sections are reasonable educated guesses, but as you can see they give very reasonable values of component weights, in many places properly predicting which wheel/tire is heavier/lighter compared to your data. As well you can tweak these values around quite a bit and the overall conclusion about I total will not change.
5. Don't worry about the weight prediction being spot on - it really does not matter much. The moment of inertia is the key parameter here and it depends much more on simply predicting where the wheel is in space and where the tire is in space and having those densities close.
6. I used a reasonable value of .02 lb/in^3 density for a tire (note almost 5 times less than aluminum as per my original point!). This value was determined by computing the volume of my simplified U shaped tire and dividing a known tire weight by this.
As far as my second point in my previous post, I'll disagree again. Your counter example doesn't prove what is or is not good for the M3. See comments from footie above. It isn't that you can't make a car work with less sidewall than the very particular M3 18" tire. It just takes engineering the entire suspension and suspension mounting elastomers and other minutia AROUND the particular choice of tire. And, as I said, for the M3 the 18 is ideal.
Once again (for the E9X M3)....
18s for performance
20s for looks
19s for a decent compromise
And of course the driver will be an even bigger factor than these differences.
There are couple of points I would like to make, first about your chart:-
I see a problem in your chart and that is when you go up in rim size to 20" the series size of the tyre drops by 5. 19" wheels with 265/30/19 rears change to 285/25/20. You seem to have used the wrong wheel sizes, 265/30/19 are the right size on a M3 not 265/35/19 as in your chart and the fronts are 245/35/19. In most cases the overall wheel diameter of the tyre does not change and in fact if you went to 275/25/20 the wheel diameter would be smaller than the 265/30/19 but the 20" wheel would be wider. Taking into fact that you could also attain a weight reduction with a 20" combination your chart needs to be recalculated. Your chart simply widens the wheel size & width but not the series size and your start point is wrong. The other fact is that a Michellin tyre is actually 5mm wider than its actual size and your will find that with quite a few tyre companies tyres. I could not see anyone running a 295/30/19, you would run a 295/25/19 to keep the rolling diameter the same. The difference between a 265/30/19 (79.5 side wall) and a 295/25/20 (73.75 side wall) is only around 5.5mm and with tyres not being exact widths as stated that maybe only 2-3mm side wall difference.
Further, is straight line drag from 0-100mph the 20" M3 because of more rubber on the ground would be quicker with LC off or on because it could lay more of its power down because there is more power in the M3 than the 18" tyres can handle.
As far as I can see by your chart your are telling me there is a difference between 19" & 20" wheels when in fact you could be presented with a 20" wheel that maybe only 5mm wider, have smaller rolling diameter and be lighter.
I do take onboard your statement that the M3 was (1) setup for 18" & (2) test results were with 18" but thats now the car was tested. I do not see any evidence that was how the car is sold to us. I do not see BMW tunning the car to 18" and then selling an option of 19", nearly all the M3 coming to Australia have 19". I believe the M3 is setup to run both on 18" & 19", the tyre choice of 18" is more to do with the condition of roads in some countries and the 18" being softer tyre to ride on & helps with rim damage. Oh yes don't forget snow chains? hey can you put snow chains on a M3?
I do agree that there is a fair bit of difference between a 18" & 20" wheels, but I believe the HP of the car plays a great part. Here we have a V8 with a e-diff running the same tyres as the e46 M3, the other point is that the DTC 7 speed is quicker than the 6MT.
Now if the M3 has power to spare then 19" would be a benefit. The DTC M3 is faster than a 6MT M3, 3rd gear is less of a problem with the 7 speed DTC, I bet it runs better on 19" than 18".
Your point rests with the fact that you state the M3 was designed around 18" wheels and tested around 18" wheels thats fine, but I say its not sold to us in that format, its been compromised, its been sold to us to run both 18" & 19", its also de-turned for different countries, due to both fuel quality & sub-tropical climates. I don'e see anywhere in the manual that the car performs better on 18" then 19' and I do not see any warnings that the handling will be compromised if you put 19" on. I also don't see anywhere where it says for best track times use 18". If anything the suspension has been beefed up to handle 19" not vice versa.
My principal is give me more power then give me more rubber, I don't drive on a track I drive on a road and I probably apply the brakes more than the accelerator anyway.
Anyway bring it on, I'm waiting?
PS. On M3 test track days I asked why they were running on 18", I was told because the car was more forgiving for the average driver, the tyres were promotional from the tyre company and if they used more than they had they were cheaper than the 19" to buy, they also had less damaged rims.