View Full Version : Centre of Gravity of Race Car

01-01-2007, 03:22 PM
Hi Everyone,

Out of interest, has anyone ever come across any equations (that include unsprung mass, unequal track width, different wheel diameter) used to calculate centre of gravity of a race car. There must be something out there on this. So far all the equations I have found are based on simple models for a "rigid" car.

I would like to put together a little excel sheet where I can punch in a few things like vehicle weight measured at individual corners, (=total weight), tilt angle of car, wheelbase, track width, mass of unsprung weight per corner, wheel dimensions etc and have it calculate the Centre of Gravity.

Any help on this topic?

Norm Peterson
01-02-2007, 04:53 AM
I haven't seen any equations other than the simple "rigid body" ones either. My initial thoughts are that it's a slightly bigger can of worms, since as soon as you separate sprung mass from unsprung mass and then tilt the whole business, suspension wheel rates and tire spring rates creep into the picture (acting at different angles). The actual sprung mass CG ends up being not quite where the difference in elevation and wheelbase*cosine predicts, even after assuming that the unsprung masses do not move in the vertical (Z) direction (which is valid as long as tire deflection changes are small enough such that they can be ignored).

Maybe somebody with Formula SAE experience can help out.


01-02-2007, 02:58 PM
Yes indeed! It is a "bigger can of worms" than I initially thought as well. Not only does the k rates of tyres and springs affect calculated tilted CG position but other aspects have to be taken into consideration like chassis stiffness, fluid levels (measure with full or empty fuel tank?), driver seated in car etc.

Thanks for the reply...

David Pozzi
01-03-2007, 09:35 PM
Here is an interesting page: http://home.earthlink.net/~whshope/
Scroll to the bottom for a different way to measure RCH. I have no idea if this will work.

02-13-2007, 04:04 PM
determining front to back and left to right isn't too hard, you just need a way to weigh the car independently.
once you do that the ratio of weight f/r or r/l is the ratio of distance of center of gravity from the respective positions, but that's pretty simple so you probably know that. I was thinking about going to a local dump where they weigh your car before and after, sweet talking the operator and get creative with the scale. the height is a lot harder to measure. but as a reference i posted a paper on here that included a ton of parameters for production cars including cog positions, moments of inertia, etc, you might be able to extrapolate something from it. here's the link to the post

David Pozzi
02-14-2007, 02:00 PM
I took a floor jack to the local truck scale. First weighed the whole car, then drove the rear wheels off the scale and took a weight, then jacked it up as high as the jack would go, and took a weight.

This get's you close, but I have read over and over that you need to lock up vertical suspension travel and increase tire pressures when you measure, or you won't get accurate readings.

02-15-2007, 10:09 AM
I have a 4 pad scale that will give individual readouts if anyone in the New England area wishes to weigh their car. They're located in Milford MA. Just PM me.

05-19-2007, 08:50 AM
Here is an interesting page: http://home.earthlink.net/~whshope/ (http://home.earthlink.net/%7Ewhshope/)
Scroll to the bottom for a different way to measure RCH. I have no idea if this will work.

I have an article in the June issue of "Racecar Engineering" in which I go into more detail and present an example.

Of course, this is only indirectly related to the subject of this thread. When it comes to finding the CG height, I'm rather partial to the tabular method. This is where you simply tabulate the height of known masses and then lump the remainder at the best guess. This works quite well on a competition car with a tube frame, but is of questionable value with a production car or competition car with monocoque construction.