Rotational Mass & Acceleration - A Case Study

I know a lot of you like lightweight wheels, and for a good reason -- shaving weight at the wheels improves acceleration. But how much? I'll answer that.

I've done the research once before with my Hyundai, and it's nice to know what to expect.

Based on Driver72's thread here the stock 17" wheels on the LGT weigh in at 19.8 pounds and the tires are 23 pounds.

So that would mean that if I got the following I'd be saving a lot of weight:

17x7.5" SSR Competition - 12.8 pounds

225/45-17 Toyo T1-S - 20.9 pounds

Total - 33.7 pounds

That's about 7 pounds lighter at the wheels and 2.1 pounds lighter at the tires.

Based on the rule of thumb that adding 1 pound at each wheel is like adding 6 pounds of total static weight to your car, and adding 1 pound at each tire is like adding 8 pounds to the car, here's how much effective weight will be removed:

(7 lbs x 6) + (2.1 lbs x 8) = 58.8 pounds lighter

Now I use my acceleration calculator to perform a before & after comparison.

Stock:

3300 pounds

0-60 mph in 5.55 seconds

New Wheels:

3241.2 pounds (static weight equivalent)

0-60 mph in 5.47 seconds

Independent of traction differences, this upgrade would be shaving about 0.08 seconds off the 0-60 time.

In order to be dead-accurate, yes. But I don't have that kind of time.

To truly compare rotational mass between 2 sets of wheels/tires you'd need to calculate 'I' for each to use in the rotational mass formula. Unfortunately weight distribution variables are not published and would require some testing to determine yourself. This is just completely unreasonable for the average Joe (especially if you don't have access to the wheels you want to compare). The calculations I posted above are more estimations than anything, but I think they're good estimations. And it's a test that's repeatable for any car with any wheels.

It's a respectable number and simplified calculation (but well rounded off and it's just to demonstrate that there is a difference). It doesnt take a physics genius to know that it takes a lot more power to swing a big heavy axe than a small and shorter lighter axe.

Here's a simplier idea.. just drive the car with four 200 lbs adults vs. four 100 lbs children.. still people (still wheels) but the weight will be felt.. the spinning of the wheels just amplifies the weight differences due to forces.

The simpliest way to understand in terms of math/physics is really Force=Mass*Acceleration, and we all know that Force can be expressed in weight. Mass, well, that's easy enough since we weigh tires and rims in a static state of it's own mass at 1G (Earth's gravitational pull). Imagine what the Force is when you start increasing the Acceleration of the wheel.

Keefe

Just to explain further... one of the things that's weird about the estimations is the whole 'effective weight' concept. But the idea is to compare the effects of rotational mass to static weight in terms of how acceleration will be affected. That's where the 'rule of thumb' comes from in that SCC article.

Once you have the static weight equivalent (what I called effective weight), you can estimate acceleration based on the power/weight ratio. That's what the acceleration calculator does.

and what is the center acceleration for your rule of thumb? the results mean nothing without knowing this. It might make some sense if your rule of thumb were to have a coefficent of acceleration

It's not my rule of thumb, it's Dave Coleman's from Sport Compact Car Magazine. I don't know if you read the article, but here's the key paragraph.

The answer, it turns out, depends on how the weight is distributed on the wheel. An extra pound on the tread of a rolling tire has as much kinetic energy as 2 lbs on the floor of the car. As you move toward the center of the wheel, the rotational effect drops until, at the center, a pound is just a pound. The formula I derived to determine the exact relationship between weight on a wheel and weight in the car isn't worth repeating here for one simple reason. It requires that you know the moment of inertia of the wheel, and measuring that is virtually impossible. What you need to know is that changing to tires that are 1 lb heavier will effectively add 8 lbs to the car (four tires, remember) and that adding a pound to the wheels will effectively add somewhere around 6 lbs to the car.

I just realized I made a stupid mistake, I multiplied by 4 thinking that the rule applied to each wheel when it actually applies to all 4 wheels together. So the improvement is much less impressive than I was thinking. I edited my first post accordingly.

It's not my rule of thumb, it's Dave Coleman's from Sport Compact Car Magazine. I don't know if you read the article, but here's the key paragraph.

 

I just realized I made a stupid mistake, I multiplied by 4 thinking that the rule applied to each wheel when it actually applies to all 4 wheels together. So the improvement is much less impressive than I was thinking. I edited my first post accordingly.

Phew, and I was about to amputate my left leg, 5EAT, to save that weight!!!!!

50 schmifty...if it don't got that bling it aint gonna sing.

still waiting for my bling

Its inaccurate to use a 'rule of thumb' because there isn't any. Shaving one lb off a tire on a 12in wheel is way different from shaving one lb off a tire on a 22in dub. Its easy to see it can't be '8 lbs' in both cases.

True, but the idea is to compare tires with about the same overall diameter. And we're not typically comparing wheels that different in size. The reason the 'rule of thumb' is used is because it's very difficult when size & weight distribution comes into play.

Consider the formula I = 1/2 MR^2

http://library.thinkquest.org/16600/advanced/rotationalinertia.shtml

Where I = rotational inertia, M = mass, R = radius.

I = 1/2 (10 kg)(.5 meters)^2 = 1.25 kg-m^2

I = 1/2 (5 kg)(.5 meters)^2 = 0.625 kg-m^2

I = 1/2 (2.5 kg)(.5 meters)^2 = 0.3125 kg-m^2

Everytime I cut the mass in half the rotational inertia is also cut in half, so the equation is linear in relation to mass, but exponential in relation to distance. So increasing a wheel's diameter will increase rotational inertia exponentially, but then you also have to consider the lower profile tire and how that affects rotational inertia. It's just a painfully difficult thing to calculate accurately so that's why I used estimations and a rule of thumb instead.

But if you're not happy with my method, feel free to try & come up with something more accurate. I'd be interested to see the results although I know there will still be plenty of unknowns when you don't know the weight distribution characteristics of the wheels or tires.

the concept of going light has plenty of positives. It's the comparison and applications that will we continue to argue too much about since that in itself has too many variables to demonstrate a correct and accurate answer that we are all looking for that are protesting to this thread.

To make it short: going light has its benefits.

Keefe

I actually have done some calculations (ask Keefe about the old version I sent him) that are more realistic than the simple rule of thumb above. It assumes a single density in the wheel, and one in the tire, and does rudimentary cross-section calculations to come up with the radius of the "center of mass" for the rim, and then assumes one for the tire based on sidewall stiffness and profile height...

Given more data, it could be more complete, but it can quickly show advantages and disadvantages. Going to a lighter 19" wheel and tire combo does not by any means have a 1 lb rule of thumb. The change in the moment arm makes a major difference...

Ted

I actually have done some calculations (ask Keefe about the old version I sent him) that are more realistic than the simple rule of thumb above. It assumes a single density in the wheel, and one in the tire, and does rudimentary cross-section calculations to come up with the radius of the "center of mass" for the rim, and then assumes one for the tire based on sidewall stiffness and profile height...

 

Given more data, it could be more complete, but it can quickly show advantages and disadvantages. Going to a lighter 19" wheel and tire combo does not by any means have a 1 lb rule of thumb. The change in the moment arm makes a major difference...

 

Ted

^ Agreed!

Keefe

And actually, after fixing a few bugs in my spreadsheet from before, the tire makes the most difference in most circumstances. Think of it from the equation above. Say we have the exact same rim (17x7), one is 15 lbs and the other is 20 lbs. (same profile, weight distribution, everything...) With equal tire weights, 25 lbs, the rotational inertia for the heavy wheel is 11.94 lb*ft^2 and the light rim's rotational inertia is 11.45 lb*ft^2, a difference of roughly 0.5 lb*ft^2. Now take the 20 lb rim and put on a 20 lb tire. (the center of mass for the tire will actually move out just slightly because we are assuming part of the decrease in mass is due to a thinner sidewall) The new rotational inertia for this heavy rim/light tire combo is 10.02 lb*ft^2. The exact same difference in mass creates almost 2 lb*ft^2 of difference when that mass is taken out of the tire…

Ted

Cliff Notes: Tire weight has a much greater effect than rim weight…

Oh yeah, if you want a copy of the spreadsheet, pm me your e-mail...

Ted

Keefe, this one is quite a bit better (and more accurate) than the last one I gave you...

All right, after more R&D I might just have some cool numbers that are backed up by more than smoke and mirrors(that was a jab at SCC for making a rule of thumb that very rarely applies)...

Stock Car (19.8/23), 3300 lbs

Effective weight, 3430 lbs

0-60 = 6 sec (repeatable without torching the clutch)

Stock Car light Tires (19.8/20.5), 3290 lbs

Effective weight, 3410

0-60 = 5.97 sec

Stock Car 17” SSR Light Tires (12.8/20.9), 3264 lbs

Effective weight, 3373

0-60 = 5.9 sec

Stock Car 19” Rims (20.5/23), 3303 lbs

Effective weight, 3442

0-60 = 6.02 sec

Now, one other thing that should help in acceleration is that the lighter tire will reduce drivetrain losses, so the difference between crank hp and wheel hp will be less…

Ted

Oh yeah, my acceleration numbers are slightly different than Steve’s, but most of the deltas are the same…

I know a lot of you like lightweight wheels, and for a good reason -- shaving weight at the wheels improves acceleration. But how much? I'll answer that.

 

I've done the research once before with my Hyundai, and it's nice to know what to expect.

 

Based on Driver72's thread here the stock 17" wheels on the LGT weigh in at 19.8 pounds and the tires are 23 pounds.

 

So that would mean that if I got the following I'd be saving a lot of weight:

17x7.5" SSR Competition - 12.8 pounds

225/45-17 Toyo T1-S - 20.9 pounds

Total - 33.7 pounds

 

That's about 7 pounds lighter at the wheels and 2.1 pounds lighter at the tires.

 

Based on the rule of thumb that adding 1 pound at the wheels is like adding 6 pounds of static weight to your car, and adding 1 pound at the tires is like adding 8 pounds to the car, here's how much effective weight will be removed:

 

(7 lbs x 6) + (2.1 lbs x 8) = 58.8 pounds lighter

 

Now I use my acceleration calculator to perform a before & after comparison.

 

Stock:

3300 pounds

0-60 mph in 5.55 seconds

 

New Wheels:

3241.2 pounds (static weight equivalent)

0-60 mph in 5.47 seconds

 

Independent of traction differences, this upgrade would be shaving about 0.08 seconds off the 0-60 time.

Well, I gotta say, I don't know where this "rule of thumb" of 1 pound

rotational weight is equal to 6 pounds static.

But rest assured, I'm sure if you lost 7 pounds rotational mass on EACH wheel/tire combo you'd do a lot better than dropping just .08 seconds

off your 0-60 time. I'd think it was more like .1 to .12 seconds.

I wish someone who had the time and access to a dyno and different

kinds of wheels/tires (hello Tirerack how are you guys?) would

conduct a test on a "normal" car with "normal" naturally aspirated power, to

see what the effect of different weight wheel/tires have on dyno results!

Guess I could of read the other posts first.

Someone already noted that a "rule of thumb" doesn't really work.

But in any case, as stated, lighter tires makes more of a difference than

lighter wheels.

I was going to dyno my car with the stock wheels then swap to my

Enkei's and Pirelli's and dyno again to see the difference.

Wish I would of.

I could of at least had SOME scientific results on wheel/tire weight on our LGT's.

Well, I gotta say, I don't know where this "rule of thumb" of 1 pound rotational weight is equal to 6 pounds static.

Actually... that's where I was trying to be clear but I probably still didn't word it right. The rule of thumb is that installing 4 wheels that are each 1 pound heavier would be equal to about 6 pounds of static weight total. In this case the result was pretty close. But there are plenty of flaws in this 'rule of thumb' technique when considering wheels & tires of different dimensions.

Anyway, praedet made a really cool spreadsheet which is much more advanced & accurate than my estimations. He's an engineer & I'm not, haha. We exchanged a few emails today and with what I've learned from him already I think I'm gonna take a stab at building an online calculator that you guys can use to calculate this stuff yourself. Thanks praedet for all the help!

I was going to dyno my car with the stock wheels then swap to my

Enkei's and Pirelli's and dyno again to see the difference.

Wish I would of.

I could of at least had SOME scientific results on wheel/tire weight on our LGT's.

That wouldn't show as much as you think. The improvement from lighter wheel/tires will be downplayed at an inertia dyno due to the heavy non-standardized rollers from dyno to dyno. And you'll barely see any improvement on a steady-state dyno. The better test would be doing an actual 1/4 mile run or maybe a rolling start 5-60 mph run. You might be able to get some pretty good real-world results that way.

But there will still be plenty of variables (engine temp, intake temp, humidity, tire grip, etc) from run to run which would throw off the results. So calculating it still has its advantages.