The "math and science" of unsprung weight

[pixelcodex]

Ok, so now I got your attention. I have always read on forums about how switching to bigger/heavier rims and tires on a Jeep (or any vehicle by the same token) is about the worst you can do for performance/economy due to the increase in unsprung weight. Now, can anybody elaborate on the actual physics of it? What kind of calculations can I make to get an idea about the loss of HP/TQ I should expect per added pound? I own a Grand Cherokee CRD which is my daily driver, and I am conscientious about fuel consumption/performance. Well, I am trying to learn more to see if I should give up on the idea or I can live with the losses it would entail.

Any advice/enlightenment on the subject is greatly appreciated.

[Jim K in PA]

If by "performance/economy" you mean acceleration, braking, and fuel economy (A/B/FE), it is not the unsprung weight, but the rotational inertia (mass) that hurts all of the above. A tire/wheel combination that weighs 70# and is 35" tall is going to have a more substantial impact on A/B/FE than a 70# wheel and tire that is only 25" tall. Loss of torque can be calculated based on the diameter of the larger wheel tire, as that is a linear relationship. The effect of the higher rotational mass is dependent on where the mass is located, which is not easy to estimate or measure. More important, driving style (rate of acceleration) will have as great an impact on fuel economy as rotational mass. There is no "holy grail" formula that you can use that will determine the overall effects of larger/heavier wheel and tire combinations on A/B/FE. However, you can expect a detrimental effect on all three when increasing rotational mass and the radius of the tire.

Keep in mind that more unsprung weight can be an advantage when traversing highly uneven terrain where there is substantial transfer of sprung weight from one side of the axle to the other.

[cnynrat]

I think you may be mixing a couple different issues together here. Heavier tires/wheels will do two things: 1) Increase unsprung weight, and 2) Increase rotational mass. The increase in unsprung weight will generally degrade handling, while the increase in rotational mass will degrade acceleration and/or fuel economy.

The weight of your tires/wheels must be accelerated to accelerate the vehicle. Without getting into the physics involved I'd imagine it's pretty intuititive that heavier wheels/tires will require more torque to spin them up to speed. You could try a simple experiment by comparing the effort required to spin up a relatively heavier mountain bike wheel/tire compared to a high performance road bike with a very light wheel/tire combo. Even across this fairly small weight variation the difference in effort required to bring them up to speed will be very noticable.

Unsprung weight is a term that refers to weight that is not riding on the suspension of a vehicle, or you could think of it as weight that is not "suspended". In cars that would typically include not only the wheels/tires, but braking components, suspension members, and the shocks. Lots of unsprung weight is generally a bad thing for handling, but not usually a big factor in the typical 4x4 truck. Designers of sports and racing cars pay more attention to unsprung weight. The reason it's not a good thing has to do with the fact that as the unsprung weight increases it's more difficult to control the motion of these components in response to cornering loads and terrain variations.

[wardrow]

Pixelcodex,

I think what you are talking about has more to do with Tractive effort also called motive force or motive power. These are engineering term to describe the amount of thrust that the engine and drive train can generate at the road surface. This is how much torque is generated by the engine, drivetrain and how much torque is reduced by tire size of the drive wheels. The formula for actual tractive effort is

TF= Tractive force in pounds
Te= engine torque in foot pound
Rt= gear ratio of transmission
Ra= gear ratio of axles
r= effective loaded radius of drive wheel in feet

Te X Rt X Ra
TF=---------------
r


Hope this helps.

[Hill, Bill E.]

... More important, driving style (rate of acceleration) will have as great an impact on fuel economy as rotational mass. There is no "holy grail" formula that you can use that will determine the overall effects of larger/heavier wheel and tire combinations on A/B/FE. However, you can expect a detrimental effect on all three when increasing rotational mass and the radius of the tire.

Keep in mind that more unsprung weight can be an advantage when traversing highly uneven terrain where there is substantial transfer of sprung weight from one side of the axle to the other.

I can add this bit. The difference between steel wheels and alloy, while may seem significant, is not noticeable on something like a Jeep.

At least I sure cant tell the difference. I have run both on my XJ, and on my TJ. There was no noticeable drop in performance, nor noticeable gain in fuel economy.

However, when it comes to diameter, you will feel the difference. (rotational mass) If you go from even a 33x12.5 tire, to a 35x12.5 tire, you will feel the difference, in both acceleration and braking.

Even with a 33" tire, you should look at regearing the axles in order to maintain decent performance and mileage.

[scootr29]

Hey check out my build thread.....I have a CRD as well and I was concerned with added unsprung weight. I ended up going with the GY Duratrac 265/70/17C and the AEV Pintler....

Stock tire wheel = 59 pounds

Duratrac and pintler = 67 pounds

That is an additional 8 pounds or 32 total pounds.....

http://www.expeditionportal.com/foru...ad.php?t=72495

[pixelcodex]

Hey Scott, yeah I have seen yours. Looks good, but I was thinking about something more "eccentric" for mine. I wanted beadlock steel wheels and they are about 46 pounds per wheel. I can leave with a little loss for those but if it is really drastic, then I might reconsider. I have to see which tires I decide to get, add it all up and make a decision.
I know WKs are less common on Expo, but I would love to hear from people in the same situation as us, and even specifically like you with the CRD. Thanks all for the replies so far. Keep them coming.

[scootr29]

Cool I would highly recommend the GDE tune for added HP/Torque and improved fuel economy. That will help with the added weight.