: car weight importance explained relative to wheels and rotating mass



haterinc
08-14-09, 09:31 AM
I got some info from Dymag and had a brief convo with KCK about how important rotational mass reduction is. So, I figured I'd pass this along... as a lot of guys are looking at heavier rims for aesthetics, but not really considering how much they're losing. The numbers gained on here can be reversed as well as lost rwhp if you're adding similar weight.

I like the Dymag magalum carbon fiber racing wheels, but the set used in the description including tires is $11k, so they're not cheap.

CTS V rear wheel comparison

Assumptions:
CTS V stock front wheel: 19x9" = 24.0 lbs
CTS V stock rear wheel: 19x9.5" = 26.4 lbs

Most guys when upgrading want to go to a 20" rim for looks, as do I, so I've used a 20" rim in this comparison.

Dymag front wheel: 20x9.5" = 17 lbs
Dymag rear wheel: 20x11" = 19 lbs

Comparing a 19x9.5” V wheel with a Dymag carbon/magnesium 20x11” wheel.
V: 26.4lb x19” M=26.4lb, R=9.5”

Therefore: ˝ x 26.4 x 9.5˛ = 1,191.3 lb/in˛ MOI

Dymag: 19lb x 20” M=19lb, R=10.0”

Therefore: ˝ x 19 x 10˛ = 950.0 lb/in˛ MOI which is 79.7% of the MOI of the V wheel.


Why is this important?

Consider 2 factors of the wheel in use, rotating and steering.

To rotate the wheel, the work energy required is calculated as force of net angular position change = ˝ MOI x angular velocity˛, strictly speaking it is Force net θ = Δ( ˝ MOI ω˛)

Which in English means that the energy consumption goes up as a function of the moment of inertia x the square of the speed, or as you go quicker it takes much more energy! This equation also shows that both acceleration and braking are both effected significantly by a reduction in MOI

Steering changes are even easier to understand. The change in direction is governed by the momentum of the wheel which is calculated as the MOI x angular velocity, so in the above example, the V on the Dymag wheel will use 30% less energy input to steer the car, either driver or power steering input, this is why the car feels “lighter” to drive and more responsive to steering input.

Rule of thumb calculations
Keep in mind, this is a minefield of assumptions!! Two of the old tuning rules of thumb were that 6lb weight saved on a car was equal to 1 bhp and that 1lb of rotating weight was worth 10lb of static weight, so in the V example above, we are saving 28.8 lbs between all 4 wheels, x 10 = 288lb ÷6 = 48.0 bhp we think this is probably excessive as the 10 factor does not take into account the diameter of the rotating part. A carbon fiber driveshaft would not have the same effect for example.

We have been stating that the rotating/static weight factor is about 6:1, this would give a result as above of 44bhp, which is roughly the gain effect that Parr Porsche said about the original tests of the carbon car wheels on the 996 GT3 RS!

Power to weight calculation

So, if you want to go to actual rwhp and you're planning mods, we will use 600 rwhp for the bench mark as a lot of us are shooting for that magical number. I'm going to use an 18% drive train loss for an auto based on 556 sae rated hp and an average (conservative) of 460 rwhp dyno. Now if we take the V wheels, the V weighs 4,300lbs and has 600 rwhp = 731 hp at the crank, which gives it a power to weight ratio of 5.88:1 or, if you lose 5.88 lbs it is equivalent to 1 hp equivalent gained.

So if we take the Dymag 6x factor for the carbon wheels then saving 28.8 lbs total wheel weight x 6, ÷ 5.88 lb/bhp = 29.4 hp an important 4.0% power gain simply by bolting on different wheels. Roughly 24.1 rwhp!

But if we take the sometimes accepted 10x rotating to static weight factor this figure comes to 49.0 hp gained. Roughly 40.2 rwhp! This is probably an over estimation, but I figured I'd include this anyway.

Obviously using this type of formula, the more power to weight ratio, the bigger the wheel effect on performance – not too surprising really!

There are obviously a lot of other mods to do as far as bang for your buck, but once you've reached your engine limit and want to pick up another 4% hp talk to Jonathon at Wheel Boutique and he can get you into a set of these.

I'm sure some of this info is "slightly" disputable based on what assumptions you use, but you're talking to an engineer here... so trust me... this info is pretty accurate.

good luck

CEO

wait4me
08-14-09, 09:59 AM
My oz rims are 17 lbs a piece also. But they are 18s. 17lbs for a 20 inch rim is pretty damn light! Good info!

SlvrBullIT
08-14-09, 08:34 PM
@Jesse: Were your OZ Superleggra III forged center cast outer for $400/per?