Lets say I had 4 wheel scales and I wanted to find the center of gravity of my car from a top view. How would I go about doing this based on the weight on each corner of the car?

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trying to remember the math - but the numbers needed are
the weight at each wheel
and the distance between all the wheels

hm Im thinking take the weight of the front and then weight of the rear and find the distribution. Multiply the distribution by the wheel base and you get the front/rear center. Then do the same procedure for the left and right but use the track width. Then you have the intersection of the two lines and thats your center?

yup
extrapolation
and, diagonal too
then average the intersections

Here's an example:

Let's say your car's weights in lbs are as follows: FRH = 602; FLH = 590; RRH = 821; RLH = 761
The wheelbase of the Fiero is WB = 93.4"
The front track width is FTW = 57.8"
The rear track width is RTW = 58.7"

To figure out how far forward from the rear axle your center of gravity lies along the length of the car, here's the formula you need:

Dist of Longitudinal CofG from rear axle = [(FRH + FLH) / (FRH + FLH + RRH + RLH)] x WB
= [(602 + 590) / (602 + 590 + 821 + 761)] x 93.4"
= [1192 lbs / 2774 lbs] x 93.4"
= 0.43 x 93.4"
= 40.16"

So imagine a line drawn across the width of the car that's 40.16" ahead of the rear wheels. This gives you the location of the center of gravity along the length of the car. So next, you need to figure out where along the width of that line the CofG lies. Here's the rather complex equation needed to account for the difference in track width from front to rear:

Transverse CofG along longitudinal CofG as measured from RH side =
= [(FLH + RLH) / (FRH + FLH + RRH + RLH)] x [RTW + (Longitudinal CofG / WB) x (RTW - FTW)]
= [(590 + 761) / (602 + 590 + 821 + 761)] x [58.7" + (40.16" / 93.4") x (58.7" - 57.8")]
= [1351 / 2774] x [58.7" + (0.43 x 0.9")]
= [0.487 x 59.08"]
= 28.77"

So, how do you use this info? If you were to draw a straight line on the floor across the car at exactly 40.16" ahead of the center of the rear axle, and then second line between the centers of the front and rear tire patches on the RH side of the car (MUST use RH side), then measured exactly 28.77" towards the center of the car along the first line, starting from where the two lines meet, you would have your center of gravity (in two planes). You'll notice that 28.77" is NOT at the center of the car. That's because the engine is mounted slightly more to one side than the other and biases the weight to the RH side. Again, remember that this is only an example of how to do the calculation. Of course the true center of gravity is measured in three planes (vertical) but the information needed to calculate the height of the the CofG isn't easily found. You'd need the CofG of every component in the car to calculate it, or, if you had a large enough 3D gyroscope you could spin the car on three axis and calculate it too. If you ever run across one, let me know.

Maybe I'm overlooking something here, but I don't see how one can calculate a Fiero's center of gravity based on the use of 4-wheel scales.

For example, suppose one for whatever reason jacks up a Fiero 5 feet. That Fiero now is much more prone to tipping over during an abrupt turning maneuver, because its center of gravity now is much higher than it was previously, is it not?

How would 4-wheel scales detect that difference?

You won't be able to calculate the third dimension based on that data, but you will be able to determine the center of gravity in two dimensions (i.e. along the horizontal plane). I'm not sure how useful that would be, though. After all, you can just look at the weights and tell which corners need more or less weight.

We are in the middle of learning this at school right now. So far we have the weight sitting level, then the weight on the front tires with the rear tires a foot off the ground.

Unfortunately, we haven't learned the necessary math yet.

You're absolutely right there project34. You can only determine the CofG in two of the three dimensions (lateral and longitudinal planes) using scales. You'd need a special spin test rig to determine where the CofG lies in the vertical plane. But even without the vertical plane measurement, you can still glean useful info from the two-plane method, especially if you're upgrading your engine and tranny and have the opportunity (and space) to shift them on the cradle an inch or two one way or the other. Obviously the more evenly the weight is carried front to rear and side to side, the more neutral your handling will be.

Now once you've calculated the centers of gravity, the next project will be front roll center, rear roll center, and overall roll center! Let the fun begin! After that comes weight jacking, by movin' stuff around, then fine tuning w/spring weights, and
"loading" your roll bars.

There's a book (somewhat dated) that has all the formulas one could want, plus descriptions of the hows and whys.
The title is 'How to make your car handle', I forgot the author; Google is your friend.

Norm

First, on level ground, calculate the left/right & front/rear location of the CG, as has been explained already.

Lift one end of the car as high as is practical - the greater the tilt angle, the more accurate your measurement.

With the car tilted, still resting on 4 scales, say 15 degrees, record the weight seen on each scale. The tilt angle must also be known.

You now have enough information to calculate the height of the CG.

[This message has been edited by pmbrunelle (edited 10-07-2009).]

Yep, that is correct. As pmbrunelle mentioned, you can calculate the height of the CoG too.

The fancy electronic race scales will actually do the calculation for you, and tell you the actual 3D position of the CoG after you follow the procedure in the manual.

I'm getting the sense that that the CofG calculation in 3 dimensions (i.e., one including the height of the CofG) is much more complicated than people are letting on:

quote Originally posted by pmbrunelle: You now have enough information to calculate the height of the CG.

quote Originally posted by Steven Snyder: Yep, that is correct. As pmbrunelle mentioned, you can calculate the height of the CoG too.

Yes, that sounds encouraging, but one wonders what --- specifically --- is the formula for this calculation (or dare I ask)?

So far, the comments I've seen here on this subject remind me very much of professors' comments, years ago, who recognized that...

...They deemed it essential for us students to be able to "prove" that a mathematical relationship was true, and...

...They then avoided revealing that proof, dismissively saying only that the mathematical proof "is intuitively obvious to even the most casual observer."

Perhaps the more relevant question here is: "What are you actually going to do with any CofG calculations, doublec4, that you couldn't already do with what Blacktree has suggested":

quote Originally posted by Blacktree: After all, you can just look at the weights and tell which corners need more or less weight.

In any case, doublec4, I'm guessing that if you added more specificity to your inquiry regarding its purpose, fellow PFF members then would be better able to help you accomplish that purpose.

quote Originally posted by project34: I'm getting the sense that that the CofG calculation in 3 dimensions (i.e., one including the height of the CofG) is much more complicated than people are letting on: Yes, that sounds encouraging, but one wonders what --- specifically --- is the formula for this calculation (or dare I ask)?

I don't know the formula to calculate it by heart.

I could derive the calculation if I wanted to, but unless the OP is incapable of doing it himself, I'm not about to spend 15 minutes with a pen and paper lol.

Isn't that the joy of the auto modification hobby? Doing stuff yourself?

This was more of a curiosity type of question. In school we're studying vehicle dynamics and it got me thinking about some things. Not really sure how I would put it to use right now. Thanks for the input though!

quote Originally posted by doublec4: This was more of a curiosity type of question. In school we're studying vehicle dynamics and it got me thinking about some things. Not really sure how I would put it to use right now. Thanks for the input though!

Hey we are studying vehicle dynamics too. We just learned how to find the height of the center of gravity and the distance front to back. Don't think side to side is that important because we didn't learn it. But if you are taking a vehicle dynamics class you will have to learn CoG, or else the lass is pointless.

Yep we're touching on a bit of everything, I googled some stuff and found some info on the height of CofG. Interesting math.

The height of the CG can be determined if you have the ability to drive up on scales that are at a different height. Because the CG will not be exactly between the higher and lower scale, the angle of the vehicle will cause the CG to be shifted horizontally from the horizontal CL of the scales. This number will be determined by the weight difference between the two sides (in addition to whatever your lateral difference in CG was). Given the angle of rotation of the car theta, the height from the "ground" of the CG is given by Z = x / sin (theta).

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