Reducing Rotating Mass: Ditching Dead Weight

[KILLR B]

I have gone from SSR Integral 18's w/ SO3's to SSR Comps 17's w/ Michellin Rcomp. My mechanic said the total weight difference between these setups is about 48 pounds.

I have heard for each pound of rotating mass that is eliminated equates to removing 7 pounds from the vehicle. True?? If so, I have effectively shed about 336 pounds!!

[dave is cool]

Another good thing to get would be a LTW flywheel to complement those awesome wheels!!

I'm not sure about the 7 pound thing though.

[b0rf]

...Can you feel a difference?

[M3formeM3foryou]

a lot of mechanical engineers who study here are car buffs, so this potential argument always comes up. one particular dynamics professor lays the issue to rest during lecture. the mechanic is right in that the polar moment of inertia will be decreased significantly by the change. so, say if your rear tires were jacked up off the ground, and you were seeing how quickly you could accelerate each set of wheels, the lighter ones would have a marked advantage. but, since you are still accelerating about 3000 pounds of car that is attached to the wheels, the wheels could even weigh nothing and the difference in acceleration given a constant force (ie-same engine) would be tiny.

this is very similar to the big debate over light flywheels. the big difference is that flywheels get accelerated to much higher speeds in far shorter periods of time. in this case, the weight loss is far, far more perceptible, and even then, when you get into 4th or 5th, the engine speed isn't changing fast enough for one to notice a big difference over stock.

[M3formeM3foryou]

there are plenty more things that i left out, but one thing is if you decreased the overall diameter of your wheels, given the same torque to your wheels (same engine, once again), you will have more force transmitted to the ground, which equals increased acceleration.

this stuff is confusing, but the best way i can think to sum it up is that by minimizing rotational inertia, you are reducing the power you put into giving your wheels angular momentum (not turning slower--just reduced weight) and putting it toward the linear momentum of your car. but cars are so heavy and wheels so light in comparison that this won't do much.

[EvanL]

You're also forgetting the advantages that lighter wheels have for your suspension. The lower unsprung rate will translate into less linear momentum in the y-plane, and thus allow your suspension to respond much quicker.

[M3formeM3foryou]

of course. but the 7 pounds thing in terms of acceleration or handling doesn't make sense.

[EvanL]

Well, not really, no...but I just thought it was necessary to point out that suspension is pretty much the only reason to buy lighter wheels.

I love my SSR Comps on the track...I believe they're part of the reason that my car seems to be set up so well.

[frayed]

Originally posted by EvanL
Well, not really, no...but I just thought it was necessary to point out that suspension is pretty much the only reason to buy lighter wheels.

So, two things at play: reduction in polar moment of inertia helps acceleration, braking, turning. I think the delta in acceleration is not really that noticable, but braking and turning can be.

The second is reduction in unsprung weight and its benefits on suspension action. I haven't been able to discern any differences in how my car hooks up due to better suspension action.

[KILLR B]

Do not understand "y planes", "polar moment of inertia" and "the delta in acceleration". All I know is the '99 M Coupe last night had no chance from 55 mph roll even with my SSR Integrals and SO3's. I have taken about 400 pounds out of the car which allows the car to accelerate, brake and dance infinitely better than it did!! :

[frayed]

Originally posted by KILLR B
Do not understand "y planes", "polar moment of inertia" and "the delta in acceleration". All I know is the '99 M Coupe last night had no chance from 55 mph roll even with my SSR Integrals and SO3's. I have taken about 400 pounds out of the car which allows the car to accelerate, brake and dance infinitely better than it did!! :

LOL. Well, shit, that's what counts in the end! Good for you.

[Def]

Originally posted by M3formeM3foryou
a lot of mechanical engineers who study here are car buffs, so this potential argument always comes up. one particular dynamics professor lays the issue to rest during lecture. the mechanic is right in that the polar moment of inertia will be decreased significantly by the change. so, say if your rear tires were jacked up off the ground, and you were seeing how quickly you could accelerate each set of wheels, the lighter ones would have a marked advantage. but, since you are still accelerating about 3000 pounds of car that is attached to the wheels, the wheels could even weigh nothing and the difference in acceleration given a constant force (ie-same engine) would be tiny.

this is very similar to the big debate over light flywheels. the big difference is that flywheels get accelerated to much higher speeds in far shorter periods of time. in this case, the weight loss is far, far more perceptible, and even then, when you get into 4th or 5th, the engine speed isn't changing fast enough for one to notice a big difference over stock.

I agree to a certain extent. Don't buy lightweight wheels expecting to now run 1 second faster in the quarter mile, but if you add up enough mole hills - you will eventually get a mountain.

An even BIGGER difference in getting lighter wheels is getting lighter tires. Really stiff tires like S03's are proverbial bricks compared to most other street tires. Losing 3-5lbs on the VERY outside edge of your tire will make more of a difference than probably losing 6-8lbs on your rim lip. Even then, most lightweight rims save it around the hub area, so the inertia of the body is usually very close to a seemingly much heavier wheel. So don't overlook those tire weights guys! Manufacturers like to hide them, but you can dig around and usually find pretty reasonable values.


I also doubt lighter weight wheels will cause any discernable benefit in suspension reaction. I mean - you're dealing with LARGE forces with performance oriented springs and dampers, is a 40lb wheel assembly moving at a few inches per second(MAX) really going to be anything more than basically negligible when tossing around a 3000lb car?

[Matthew C Smith]

not sure if this will really help anybody who's a little confused about this but you want the moment of inertia (I) to be as low as possible (it'll take less energy to spin it). Moment of inertia (I) is proportional to the mass of the object spinning times the distance from the point it is spinning squared. So removing weight from the farthest point away from the center (ie. the tire) will show the best gains.

[Hellrot Sachin]

this post really couldn't have come at a better time. I'm pretty convinced that my having gone to lighter tires made a dicernable different in acceleration and such, but now I'm consider bailing out on 18" RKs (don't remember their exact weight) and possibly going to 17" contours. The new rims will be considerably heavier but my main reason for holding back is my perception of acceleration. I really don't want the car to feel much slower, but if the increased weight is that focused around the center of rotation and not all that significant considering the weight of the car, no biggie.. Maybe I won't feel a difference in performance with this.

[lkstaack]

The details of this thread is way above my current level of understanding. My perception is that (all things being equal) a 17" wheel will accelerate and handle better than a heavier 18" wheel. If this is true, will a 16" wheel perform better than a heavier 17" wheel? Why or why not?

[nsk223]

The '7 pound' rule sounds about right to me. Some people have argued that reducing the weight of wheels and tires by say 40 lbs is the equivalent of reducing the overall weight of the car by 40 lbs. Not true: While the the car would clearly be 40 lbs lighter, the fact that this weight came from the rotational mass of the the wheels means it has effectivley reduced the force necesary to accelerate the given car at a given rate. In other words, given two identical cars with one with 40 lbs removed from the actual car of one and 40 lbs removed from the wheels of the other, the car with lighter wheels will be faster. This car could, concievabley, be the equivant of 280 lbs lighter (7x40 lbs wheel weight). Another component of this thread which I would like to clarify is the term 'polar moment of intertia.' Automotively speaking, this term describes the relative willingess of a certain car to change directions. A car with all the mass centered around the center of the car will be much more responsive that a car with the same amount of mass spread out around the car. This is why many/most purpose built race cars are mid-engined. The aforemtionted '7 pound,' regardless of whether or not 7 is the actual number, relates to much more than a cars ability to accelerate. I'm sure that most of you are familiar with the concept of 'unsprung weight' and it should be stressed that increases in handling performance with lighter wheels and tires will be much more signigicant than increases in acceleration.

[SI///M3]

Originally posted by Hellrot Sachin
this post really couldn't have come at a better time. I'm pretty convinced that my having gone to lighter tires made a dicernable different in acceleration and such, but now I'm consider bailing out on 18" RKs (don't remember their exact weight) and possibly going to 17" contours. The new rims will be considerably heavier but my main reason for holding back is my perception of acceleration. I really don't want the car to feel much slower, but if the increased weight is that focused around the center of rotation and not all that significant considering the weight of the car, no biggie.. Maybe I won't feel a difference in performance with this.

I don't remember the exact weight of RKs but if they're anywhere close to the weight of my RCs it shouldn't be TOO much of a difference. When I got my RCs I did some basic calculations (not the most accurate since I made quite a few assumptions, I know), but the moment of the contours was almost exactly the same as my RCs (23lbs for the contours, 18.7lbs for the RC). Of course I just did the wheels since I had no ideas how much my tires weighed, but it wasn't a huge difference really. With tires I bet the contours are actually ahead (lower moment) of the RCs. Weight is very important in looking at wheels, but diameter is alot more since it the moment goes up by distance^2.

[SI///M3]

Originally posted by lkstaack
The details of this thread is way above my current level of understanding. My perception is that (all things being equal) a 17" wheel will accelerate and handle better than a heavier 18" wheel. If this is true, will a 16" wheel perform better than a heavier 17" wheel? Why or why not?

Yep a 16" wheel is better in terms of how big the moment is. Smaller is better when looking at that. Thing is with 16s that most rims won't clear M3 brakes, and even though your moment is smaller sidewall flex and such starts to work against you. I remember a magazine article a long time ago comparing the best size for performance, 17 was it. Any bigger and the moment starts to kill your power, any smaller and tirewall flex starts to kill your handling.

[scottycs]

I went from 26 pound wheels, to 16.5 wheels. There was NO difference to be felt in acceleration. Don't hope to feel anything different. The 7 pound rule is WAY off, it is no where near the equivalent of 280 pounds lighter. Don't follow the hype.

[Bernman]

I went from a 40 pound wheel and tire combo to a 47 pound one. The acceleration difference is *definately* noticeable.

It is not hype, though the 1:7 pound rule of thumb may not quite apply.

Acceleration is not everything (but it sure is nice) and I am very pleased with the handling and looks of this combination.

[scottycs]

Mine was noticable, but it was all psychological.

[nsk223]

You can't really argue with physics here, if your wheels are lighter they will have less inertia and the car will accelerate better as a result. It should be stressed, though, that improvements in handling resulting from lower unsprung weight will be much more significant than improvements in acceleration. With respect the wheel diameter and its respective level of inertia, diamater is very important, but equally important is the height of the tire sidewall and the weight of the tire. For example, assume an overall wheel/tire diameter of 20 inches, not all cars with a 20 inch overall diameter will have the same level of rotational intertia: what matters is where the mass is concentrated on the this diameter-if the wheel weighs very little and the tire weighs a lot or the other way around.

[stevegee]

Ok, lets do some math here. Hopefully one of the Mech. Eng's will check my math since it isn't so good.

If you just want to trust my calculations, jump to the end...


Assumptions:
1. M3 Curb Weight (except wheels): 2950 lbs

2. M3 Peak Wheel Force in 1st Gear: 2830 lbs (actually doesn't really matter, but just to make realistic numbers. I'm assuming stock wheel sizes and gearing, and 200 lb/ft pk torque after drivetrain losses)

3. All wheels same size, running 225/45-17" tires. Wheel+tire radius R=1.04ft.

4. No friction forces (wheel bearings, etc)

5. No wheel slip

6. Wheels+tires have evenly distributed mass (uniform disc).


Math:
Angular acceleration of wheel = aa.
Car acceleration = A = aa*R

F (tire-to-ground) = mass(M3) * A + I(wheels)*aa
= mass(M3) * A + I(wheels)*(A/R)
= (mass(M3) + I(wheels)/R) * A

Or otherwise

A = F / (mass(M3) + I(wheels)/R)


Moment of Inertia of 16lb wheel + 20 lb tire:
I = mr^2 = (36/3.215)*(1.04ft^2) = 12.111

Moment of Inertia of 24lb wheel + 25 lb tire:
I = mr^2 = (49/3.215)*(1.04ft^2) = 16.484

Mass of M3 = (curb weight) / G
With 16lb wheel combo: = (2950+ (36*4)) / 3.215 = 962.36
With 24lb wheel combo: = (2950+ (49*4)) / 3.215 = 978.54


Results:

Acceleration with 16lb wheel+20 lb tire combo
= 2830/(962.36 + 4*(12.111)/1.04)
= 2.804 ft/sec^2 = 0.872g

Acceleration with 24lb wheel+25 lb tire combo
= 2830/(978.54 + 4*(16.484)/1.04)
= 2.716 ft/sec^2 = 0.845g


Conclusions:

With the assumptions used, lighter wheel+tire combo gives 3.1% acceleration improvement. Equivalent to dropping a 6.2s 0-60 to 6.0s.

If stock M3 is then 3146 lbs (24lb wheel+25 lb tire combo) then 3.1% weight reduction is 97.53 lbs. Actual weight reduction was 52 lbs. So in this case, 1lb of removed rotational weight is equivalent to removing 1.87 lbs from the body. That's not even close to the 7lb number tossed around. Though the assumption of even distribution of wheel mass does skew this number down some.

[M3formeM3foryou]

*dusts off the ol' dynamics book*

one little problem Steve... the moment of inertia you used is for a uniform hollow cylindrical shell. for a solid cylinder, it's mr^2/2.

i didn't verify your calculations at all or recalculate the results, but let's all think about this. rather than losing 13 pounds off of the outer most radius, the weight lost is distributed evenly across the wheel. in terms of the calculations, the difference between the before and after moment of inertias will be smaller, and thus, so will the change in acceleration.

i'm not saying that using a solid cylinder is a more accurate approximation of the actual moment of inertia; the hollow cylindrical shell approximation might actually be better. it may even be better to try using mr^2 for the tire and adding mr^2/2 for the wheel... you can simply add the two since they're spinning about the same axis.

number junk aside, this is an awesome thread. thanks for everyone's input.

----------------------

At a divorce hearing for Mickey and Minnie Mouse, the judge asks Mickey, "So you’re saying your wife is crazy?" Mickey responded "No, I said she is fucking Goofy."

[Nimble]

Originally posted by scottycs
I went from 26 pound wheels, to 16.5 wheels. There was NO difference to be felt in acceleration. Don't hope to feel anything different. The 7 pound rule is WAY off, it is no where near the equivalent of 280 pounds lighter. Don't follow the hype.

I do agree the 7lb rule is way off...closer to 4 in my opinion.....but you have to realize one other thing.....our perseption of the accelerative difference of adding/removing weight from wheels/tires is easier to tell when going to a heavier wheel.

So in your case, Scotty, if you were to put on those heavy 26lb wheels after being used to the lightweight RC's you WOULD feel a difference in acceleration. I mean a 10 lb PER corner weight difference is huge. It is a possibility, however, that the RC's you put on your car had heavier tires than did the 26lb wheels, thus negating the positive benefits of the lightweight RC's....just a thought.