Unsprung Weight and Rotational Inertia Info - BMW Forum - BimmerWerkz.com
3-Series (E36) Chat relating to the BMW 3-Series from 1992-1999. Autodoodad Specific models include: BMW 316i, BMW 318i, BMW 318iS/ti, BMW 320, BMW 323, BMW 320, BMW 324, BMW 325, BMW 328.

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#1 (permalink) Old 08-16-2004, 12:15 AM
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Check out this excellent article on how your vehicle's Unsprung Weight and Rotational Inertia affect the handling and ride quality of your ride:

http://www.nissanperformancemag.com/february02/oz.shtml

Suddenly, my oh so stock 15 inch OEM wheels and tires don't suck as bad as I thought... :P

(yeah, I know, they still suck hind teat!)


For years, I have been looking at those big ass trucks from Dodge and others with those fat ass wheels and knobby tires that must take gobs of torque to turn!

Just image a lowly, torque anemic v-tech engine busting a nut trying to turn 18, 19 or 20 inch wheels, even if they are light weight designs...

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#2 (permalink) Old 08-16-2004, 12:35 AM
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very good information, we might want to post this again the in BMW Motorsports forum area as well because it does apply to all cars. Nice find Doc
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#3 (permalink) Old 08-16-2004, 03:12 AM
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#4 (permalink) Old 08-16-2004, 06:40 AM
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that wheel has a removable lip so you can polish it without taking the wheel off, man i would like to have the supperleggra but i don't think it looks good on e36's i saw some on a mercedes and they looked amazing then i saw some on a e36 m3, and they looked pretty nasty,


good info, now i know what unsprung weight is

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#5 (permalink) Old 08-16-2004, 01:13 PM
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I wish some car mag would deal with the loss of advertisement it would suffer by printing an article like this: show how a wider than stock +0 setup, then bigger +1, +2, +3, etc. wheels and tires sometimes negatively affect some aspects of vehicle performance.

A Mag could do 0-60, 1/4 mile, lane change, lateral acceleration, braking from 60 and 80, and maybe even friction circle results with stock wheels and tires to set a baseline. They could go +1, with a popular wheel and tire set and redo all the tests, then with +2, and +3, etc. and then tally the results up.

My '92 325i is a perfect example of light(er) OEM wheels and tires and they still weigh 40 lbs each! Imagine going to a +4 setup on my car with all the weight on the outside of the wheels! A stock 318i would beat me probably!

I expect that a +0 and +1 setup would have higher than stock lane change, and lateral acceleration numbers, reduced 0-60, and 1/4 mile times, with shorter braking distances. At this level the increased traction rules.

As you go +2, +3 or higher, the increased Unsprung Weight and Rotational Inertia will show themselves more and more as acceleration times, lane change, and lateral acceleration times slow down. Braking will take longer distances, and if they test, friction circle results will also decrease as the circle get smaller, not larger; showing reduced performance. n

If a magazine did this, bucking the (to me silly) Bling Bling over Performance trend, it could easily cost them advertising revenue. Maybe it will only happen on the Internet, where advertising tends to be more general then in car mags.

Other driving factors that are affected by larger wheels and tires include the quality of ride over bumps, pot holes, rumble strips, expansion joints, etc. When you go to 45, 40, 35, etc. series tires, you give up ride quality for the benefits of those stiffer sidewalls.


Wouldn't you like to know how a larger set of wheels and tires positively or negatively affects the performance and quality of your ride?
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#6 (permalink) Old 08-16-2004, 02:32 PM
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Wow good article, now i'm wondering if my decision of putting the E36 328 sport rims on my stock 318 was a good idea... I went from 15' to 16' and I think that the rims may be slightly heavier but I'm not sure...hope my engine won't be struggling all the time when driving in town.
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#7 (permalink) Old 08-16-2004, 03:05 PM
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You don't notice power loss unless you go from 15s to 20s. 15 to 16 would reduce the speed marginally, at best.

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#8 (permalink) Old 08-16-2004, 05:59 PM
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Ok.. So you hit a sore spot.... physics... Open your minds brothers...

I read that whole article... and yes.. it is all very very true. But only one underlying factor.... no calculations for you to see exactly how much force changes when you actually increase or desrease the weight and or size of the wheel.... I'll show you...

Moment of Inertia - The property of an object associated with its resistance to rotation. It depends on the objects mass and the distribution of mass with respect to the axis of rotation.


Basic Rotational Inertia formula. I= ˝ MR2 (2 = squared)
I= Moment of Inertia... M = mass and R = radius of the wheel.

So... lets take a 20 pound wheel... 17 inch.. (I'll work in SI units)

I= .5x(9.0718474)x(0.4318/2)>2 (>2 means squared)
I= .959040098 kg/m>2

The same equation for a 15 pound wheel that is 17inches...

I=.5x(6.8038856)x(.4318/2)>2
I= .539460063 kg/m>2

Just for clarity.. the next exp. is the same two wheels being pushed by 200 HP. ( Its not exactly right because I'm not taking in acount for the weight of the car.. but this should demostrate how much the weight of the wheel actually plays in acceleration of the car..)

Ok.. still speaking of a 17 in. wheel here...
Equation for torque being applied to both wheels is: Force times the Radius:
BTW 200HP is equal to 529559102.065818 Newtons

t = Fr = (529559102.065818N) x (.4318/2)= 114331810.1
This torque value is a constant... because it is just showing how much force is applied.

AND finally... when you take the Torque.. or Force being applied to each wheel.. and DIVIDE it by the moment of inertia.. which I remind you is the resistance to rotation. You get.....

20lb Wheel : I/t = (114331810.1)/(114331810.1) = 119214838.2 rad/sec>2
15lb Wheel : I/t = (.539460063)/(114331810.1 ) = 562500008.2 rad/sec>2

Ok... So.. now your wondering what the hell I've found with these numbers... well after another converstion from radians per second squared.. to RPMs... I get..

20lb Wheel : 5270.45301489 RPMs
15lb Wheel : 24867.9603047 RPMs

Both of those nubers clearly demonstrat... that with less weight you can speed that wheel up faster... an almost 2000 RPM increase due to 5 lbs of weight.

So... in short... lol... it takes

This is how much HP it takes to move each wheel....

20lb = 0.13039 horsepower
15lb = 0.07335 horsepower

As you can see... the 15lb wheel... takes less horse power to move..

All in all.. this is a sick conclusion.. to... who cares about 5 pounds.. when it comes to a cylindrical object being pushed by your engine... unless you want to gain... 0.5704 HP. Your choice...


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#9 (permalink) Old 08-16-2004, 06:31 PM
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I will work the numbers if you guys want to see the differences in the size of the wheels.... not just the weight... I didnt want to complicate things any more than I already did... ghead


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#10 (permalink) Old 08-16-2004, 06:32 PM
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.5704 hp is actually .339 percent of my 168 hp. I would surely like to keep that massive power...

as a matter of fact I think I'll upgrade to lightweight 11 inch wheels to gain my .5 hp.

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#11 (permalink) Old 08-16-2004, 06:44 PM
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go physics!

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#12 (permalink) Old 08-16-2004, 07:31 PM
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97alpineM3's calculations assume the wheel+tire's weight is even across the diamater of the wheel & tire. More weight is on the wheel towards the outisde, this affects the rotational inertia a good deal. 97alpineM3's calculations may be off by maybe half a horsepower... Still, So what.
Rotational velocity isn't too much of a worry, but the weight of the actual unsprung weight... the article talks about the suspinsion system's ability to keep the wheel on the ground - This is probably one of the most important factors.

The heaver the suspinsion, the harder it's going to hit bumps in the road & more time it's going to spend in the air as a result of the bounceback, which translates to less traction.


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#13 (permalink) Old 08-16-2004, 07:53 PM
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Yes that is very true.... bitcore.... bravo... it is rather difficult to calculate the actuall effects of the off balanced wheel math matically... but I do think it would change the numbers slightly... There are other factors... I was just concentrating on the weight of the wheel towards acceleration... that is all.


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#14 (permalink) Old 08-16-2004, 10:08 PM
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Dude that would be nuts to try to calculate all that shit. lol

Yah, it'd change your numbers like...... barly. We go tthe idea

G/J and stuff...


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#15 (permalink) Old 08-16-2004, 11:53 PM
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Nice additions to the thread guys!

Closet Physics Geeks Unite!!!

Rotational Inertial on a given sized wheel and tire depends on the total weight, and where that weight is; towards the inside (good), or outside (bad) of the wheel and tire combo.

If you have a lightweight wheel, but a heavy tire, it will take more energy to turn them then if you have a heavy wheel and a light tire or the same total weight.

Imagine a metal top with most of the mass near the center of the top. It will be easy to get it to spin at a high rpm by twisting it by hand. Another metal top with the same weight, but with most of its mass near the outside edge of the top will not spin as fast with the same amount of twisting force (aka torque) applied.

Indirectly, this is why Dinan, AC S. and others use lightweight flywheels to reduce rotational mass on their motors so they are more responsive and rev faster.

Tire Rack likes to send me e-mails with test reports, but I doubt they would do a test like the one I mentioned in my opening post...
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