Center of gravity highth

Bubstr · Post by **Bubstr** » Wed Oct 25, 2006 12:51 pm

I used to have a formula to find the center of gravity hight, but cannot find or remember it. I do remember that you scaled front and rear, then added fron up and rear up. Then raised fron a specified amout depending on the wheelbase and rescaled at the higher level. I seem to remember you found the center of gravity length for both and triangulated both to find the highth. Any help on this would be appreciated.

BillyShope · Post by **BillyShope** » Wed Oct 25, 2006 5:59 pm

You only have to lift one end. If you lift the rear end:

The CG height = L(nsubr-Nsubr)/(WT) + r

where "L" is the wheelbase, "nsubr" is the weight on the rear wheels before lifting, "Nsubr" is the weight after lifting, "W" is the total car weight, "r" is the tire radius, and "T" is determined by:

T = R/ (square root of (1- Rsquared))

Where "R" is the ratio of the height you lifted the centerline of the rear axle to the wheelbase.

Suppose, for instance, that you lifted the rear of a 3500 pound car by 24 inches. The rear wheel weight, before lifting, is 1680 pounds and is 1638 pounds at the elevated height. The wheelbase is 112 inches and the tire radius is 12 inches. "T" works out to 0.2194 and the CG height comes out at about 18 inches. Note that the weight difference is only 24 pounds. This means you have to be very accurate in all your measurements if your answer is to be accurate.

MadBill · Post by **MadBill** » Wed Oct 25, 2006 6:09 pm

To really get it accurate, you also need to include the driver, lock the suspension heights, account for changing tire deflection, eliminate and/or account for all liquids re sloshing, etc., etc.

Bubstr · Post by **Bubstr** » Thu Oct 26, 2006 12:50 am

Thanks for the formula. Is there anyway this could be used by elevating the front of the car , as that would put the liquids in a place an active car would have them?

BillyShope · Post by **BillyShope** » Thu Oct 26, 2006 7:10 am

That was supposed to be a difference of 42 pounds, not 24. (A bit of dyslexia, I guess.)

Anyway, as I said, you can lift either end. The equation is still valid.

I think Bill was just giving us a hard time. Don't worry about the liquids, as your scales aren't precise enough to detect any differences. Same with suspension spring deflections. And, tire deflection rates being as high as they are, you don't need to worry about that, either. Your concerns will be with the use of the tape measure and recording of the scale readings.

MadBill · Post by **MadBill** » Sat Oct 28, 2006 3:17 pm

I guess for drag race purposes my comments were mostly irrelevant, but for a serious road race or circle track car, all that and much more is very important. A good friend of mine makes his living as a hired gun for race teams, e.g. Champ Car, NASCAR, etc. http://www.rowleyrace.com/ and he spends a ton of time getting such stuff measured before any on-track testing.

BillyShope · Post by **BillyShope** » Sat Oct 28, 2006 5:02 pm

Yes, Bill, you can be a bit off on CG height and it's not going to make that much difference in adjustment of link angles and such.

Your friend sounds like a good candidate for use of Page 1 at my blog:

http://home.earthlink.net/~whshope

wherein the front and rear roll center heights and roll stiffness distribution can be measured directly with little more than a set of wheel scales.

MadBill · Post by **MadBill** » Sat Oct 28, 2006 9:24 pm

Wow! Sure is simple by comparison. I'll pass it on to Warrren. He's been really sick and unable to work, but maybe this will keep him amused until he (hopefully) recovers..