Effects of Rotational Inertia on Tires and Wheels - Calculated for OEM Wheels

Hey guys,

I recently bought a set 20" OEM foundry wheels and kept reading how people complained of their weight. As I browsed the forums I kept reading posts comparing unsprung weight and sprung weight, and that saving a pound of unsprung weight would result between 6-10 pounds savings of equivalent sprung weight. That seemed kinda of crazy, and I figured if it was true, then car manufacturers were being crazy for not trying to save as much weight as they could on the wheels.

After reading all those posts I wanted to know what the effect of increased weight on the wheels really is and after doing some research I came across a website that had a calculator that could calculate the rotational inertia for wheels and tires and also calculate the sprung weight equivalent for that wheel and tire. I posted the results below for the OEM wheels that I could find the weights on this forum, but I will also include the links at the end in case you want to compare any combination of wheels and tires that you may be looking at.

Also, I have included the Gear Ratio, which is 3.31 on my car with the stock 18" wheels and tires, and how it changes with the different tire combinations. I'm sure there are many more variables to consider but that was beyond the purpose of this calculation.

From the calculations, I noticed the Tires had between and 1.92-1.95 unsprung to sprung weight ratio, meaning a pound on the tire would be equivalent to approximately 2 pounds of unsprung weight. Whereas, the Wheels had a 1.29-1.35 weight ratio, much lower than I would have thought.

Keep in mind that there is a margin of error for these calculations, but I would encourage you to read the website on the link below as it has more detailed explanations on the effects and other calculators for brake rotors and such.

In my case, switching from the OEM 18" to the Foundry 20" would be equivalent to gaining about 60 pounds of sprung weight on the car. For me, the benefit of higher grip on the summer tires was worth the trade-off on a daily driver. But I can see how on a track car it would make a big difference. Also, don't forget to keep track of the gear ratio and try to match the stock tire diameter, see the link below with the gear ratio calculator.

Let me know if you have any questions!

Results:

Base GT 18” Wheels & Tires – Stock Gear Ratio 3.31

Wheel
Weight: 27.5 Pounds
Rotational Inertia: 0.4345 kg/m2
Equivalent mass ratio: 1.29
Equivalent mass: 35.5 Pounds

Tire – 235/50r18
Weight: 27 Pounds
Rotational Inertia: 1.3457 kg/m2
Equivalent mass ratio: 1.92
Equivalent mass: 51.6 Pounds

Total
Rotational Inertia: 1.7802
Total Equivalent mass: 87.1 Pounds


GT PP Front 19” Wheels & Tires – Effective Gear Ratio 3.34 (If placed in back)

Wheel
Weight: 32.6 Pounds
Rotational Inertia: 0.574 kg/m2
Equivalent mass ratio: 1.33
Equivalent mass: 43.3 Pounds

Tire – 255/40r19
Weight: 28 Pounds
Rotational Inertia: 1.4006 kg/m2
Equivalent mass ratio: 1.94
Equivalent mass: 54.2 Pounds

Total
Rotational Inertia: 1.9746
Total Equivalent mass: 97.5 Pounds


GT PP Rear 19” Wheels & Tires – Effective Gear Ratio 3.26

Wheel
Weight: 33.3 Pounds
Rotational Inertia: 0.5863 kg/m2
Equivalent mass ratio: 1.31
Equivalent mass: 43.7 Pounds

Tire – 275/40r19
Weight: 31 Pounds
Rotational Inertia: 1.6197 kg/m2
Equivalent mass ratio: 1.93
Equivalent mass: 64.4 Pounds

Total
Rotational Inertia: 2.206
Total Equivalent mass: 108.1 Pounds


OEM Foundry 20” Wheels & Tires – Effective Gear Ratio 3.30

Wheel
Weight: 35.7 Pounds
Rotational Inertia: 0.6864 kg/m2
Equivalent mass ratio: 1.35
Equivalent mass: 48.1 Pounds

Tire – 265/35r20
Weight: 28 Pounds
Rotational Inertia: 1.448 kg/m2
Equivalent mass ratio: 1.95
Equivalent mass: 54.4 Pounds

Total
Rotational Inertia: 2.1312
Total Equivalent mass: 102.5 Pounds

Links:

Rotational Inertia Calculator - http://hpwizard.com/rotational-inertia.html
Gear Ratio Calculator - https://tiresize.com/gear-ratio-calculator/

I like it, good work

I'll bite.

Eco PP 19” Wheels & Tires (59.6 lb assembly)

Wheel
Weight: 31.6 lbs
Rotational Inertia: 0.63985 kg-m2
Equivalent mass ratio: 1.38
Equivalent weight: 43.6 lbs

Tire – 255/40r19 (Pirelli P Zero)
Weight: 28 lbs
Rotational Inertia: 1.4006 kg-m2
Equivalent mass ratio: 1.94
Equivalent weight: 54.3 lbs

Total
Rotational Inertia: 2.0405 kg-m2
Total Equivalent weight: 97.9 lbs

18x10 Forgestar CF5 and Bridgestone RE11 (54.1 lb assembly)

Wheel
Weight: 23.1 lbs
Rotational Inertia: 0.41980 kg-m2
Equivalent mass ratio: 1.35
Equivalent weight: 31.2 lbs

Tire – 275/40r18 (Bridgestone RE11)
Weight: 31 lbs
Rotational Inertia: 1.5021 kg-m2
Equivalent mass ratio: 1.93
Equivalent weight: 59.83 lbs

Total
Rotational Inertia: 1.9219 kg-m2
Total Equivalent weight: 91.03 lbs

Conclusion
Sprung Weight Saved: 4x(59.6lb - 54.1lb) = 22lbs
Equivalent/Unsprung Weight Saved: 4x(97.9lb - 91.03lb) = 27.48lbs

The "unsprung/sprung" ratio in my case is 27.48/22 = 1.25. This ratio would be higher if I choose lighter tires, like MPSS or Conti DW. Looking at the most basic point-mass rotational inertia equation, I=mr^2, you can see distance from the center plays the biggest factor in determining rotational inerita.

Assuming I found some 275/40 R18 Conti DW's that are 27lbs, and paired them with some heavy 27.1lb whees, my aftermarket setup would still be 54.1lbs, but the total equivalent weight would go down to 88.70lbs. The sprung weight saved would still be 22lbs, but the equivalent/unspring weight saved would be 36.8lbs. Meaning the "unsprung/sprung" ratio would increase to 1.67.

EDIT, I guess I should finish up this thought experiment by pairing the Conti DW with the aftermarket wheels.

18x10 Forgestar CF5 and Conti DW (50.1 lb assembly)

Wheel
Weight: 23.1 lbs
Rotational Inertia: 0.41980 kg-m2
Equivalent mass ratio: 1.35
Equivalent weight: 31.2 lbs

Tire – 275/40r18 (Conti DW)
Weight: 27 lbs
Rotational Inertia: 1.3083 kg-m2
Equivalent mass ratio: 1.93
Equivalent weight: 52.11 lbs

Total
Rotational Inertia: 1.7281 kg-m2
Total Equivalent weight: 83.31 lbs

Conclusion II
Sprung Weight Saved: 4x(59.6lb - 50.1lb) = 38lbs
Equivalent/Unsprung Weight Saved: 4x(97.9lb - 83.31lb) = 58.36lbs

Interestingly enough, the "unsprung/sprung" ratio in this case goes down to 1.54.

Correct, even though you are saving a substantial amount of weight from the wheels, the heavier tires and the higher equivalent mass ratio of the tire is counteracting the overall weight reduction. That why it's important to match the tires/grip with the application.

Check the article below that car and driver did, going from a 225 to 235 wide tire actually produced worse skidpad performance 0.89g vs 0.88g. However, I disagree on their acceleration data since they did not keep the tire diameter equal across the board, thus changing effecting gear ratios.

http://www.caranddriver.com/features/effects-of-upsized-wheels-and-tires-tested

Did they change wheel width as well? The loss of skid pad grip could just be attributed to the increase in sidewall flex

Its not simply an A to B test. They compared a 19x8.5 with 235/35R19 tire to a 225/40R18 tire on a 18x8 wheel.

From the article:
"We asked the folks at Goodyear why that might be, and they postulated that the added width may have given the outside tire more grip, which would increase body roll and could therefore decrease the load on the inside tire enough to lose 0.01 g on the skidpad."

Interesting post. Been wondering about this stuff since I've been researching tires and wheels. Just a heads up, I'm pretty sure the stock 18" wheels Pirellis are actually 30 pounds.

CrazedAntelope said:

Its not simply an A to B test. They compared a 19x8.5 with 235/35R19 tire to a 225/40R18 tire on a 18x8 wheel.

From the article:
"We asked the folks at Goodyear why that might be, and they postulated that the added width may have given the outside tire more grip, which would increase body roll and could therefore decrease the load on the inside tire enough to lose 0.01 g on the skidpad."

Click to expand...

It is key to note, suspension is just as important to update as tires

I am sure I will need to update my suspension once I upgrade my wheels and tires

Definitely an interesting thread. WHY are the pp wheels so heavy, Ford...? Can't wait to swap them out. It's a shame, because I love the way they look. I love the way the 20" foundrys look too.

This is a good thread, 2 thumbs up