I need a physics refresher...

I remember that Sport Compact Car tried to resolve this issue a few years back, and got a very perplexing answer.

It all came down to the fact that the weight is most important at the outer rim and tire, and gets less and less significant closer to the hub. This correlates directly with common sense of course. HOWEVER, the actual math involved is incredible, even with just a solid disk and a ring for a wheel hoop. Let alone the craziness involved with spokes and such.

However, you can establish some rough guidelines to help figure out which wheel will impact performance the most or least:

The outer hoop or "rim" matters the most. A lightweight rolled aluminum rim vs. a part of a 1 piece cast wheel...the weight is less with the thin rolled aluminum.

The number of spokes doesn't matter, but the total mass of course, does. If the spokes taper to a wider form near on the outside of the rim vs. a narrow taper form, then the narrow one will have less inertia to muscle around.

The differences are minor, but they are there. However, when it comes to wheels, I'd choose durability as my primary factor if I'm looking for lightweight. You don't want to go to thin and feathery, since they might fail if you hit something hard enough!
 
so will you get better results goin from an 18 inch wheel to a 17 inch lets say they both weight the same?
 
YES! But the tire will weigh less in a 17" design as well, given a smaller bead circumference (anyone care to verify this with a scale, given two otherwise identical tires except for rim size and matching ratio?)

Keep in mind that a 17" would still need to end up with a tire that matches the height of the 18" did, so the sidewall ratio will need to be a bit higher (example: 215/45-18 to a 215/50-17)...this means the tire will have a little more rubber on the sidewall as well, but the savings in weight would go toward the 17", and so would the savings in inertia!
 
When you start trying to calculate moments of inertia with a non-uniform weight distribution, you start needed to get into a lot of calculus, which I'm just not going to do here.

More weight near the hub = good.
More weight near the outer diameter of the wheel/tire = bad.

For this reason, a lighter rim with a worse weight distribution may not actually provide you any benefits.
 
if you want to go faster around a road circuit instead of just getting better 1/4 mile time, use that money you would've spent on 'lighter' wheels, and get stickier compound or wider tires, a MUCH better approach to go faster!
 
Very interesting subject. There is a very simple way to measure it from an accelaration perspective. Dyno the same tire on diff wheels or even diff wt tire/whl combo's. I spent a fair amount of time on a 350Z forum when I had one recently and the conensus was that the wheels made a bigger difference than you think. I put 20" TSW wheels on the Z with BFG tires and although it stuck like glue, it did not accelerate or stop like a car of this caliber should (had Brembo's). My feeling was the tires/wheels were the cause.

Also look at the highest form of motorsport competition such as F1. No large diameter wheels/tires are used. Look at road course racing same thing. Look at drag racing, same thing. I don't know the formula behind it, but it can be measured.

I don't think many, if any, of the mod's we make on these cars can be cost justified. I don't think anybody is trying to cost justify mod's unless they are getting approval from their wife. Mine wont approve them so I don't ask(drinks) and she can't say no......
 
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