Center of Gravity

The center of gravity (also referred to as center of mass or CG) is the average location of the weight of the car. The point in space that sums the vehicles mass in a single point. To put it in simple to visualize terms, if we could suspend the car from that point only we would not witness any forces twisting the car into a specific orientation since the mass would be equally distributed in all three dimensions.

Measure the CG

Total Vehicle CG

Measuring the total planar center of gravity is fairly easy with only 4 weight scales, one under each tyre. We say total because we are not making a distinction between non-suspended and suspended mass. Make sure floor is level so that the weight on the scales doesn't get influenced by inclination.

We can start by determining the distance of the CG to the front axle. This is also normally referred to as the distance "a".

$a={\frac {W_{rear}}{W_{total}}}W_{b}$

Where $Wb$ corresponds to the wheelbase of the car (distance between axles), $W_{rear}$ the rear weight (sum of both rear tyre scales) and $W_{front}$the front weight (sum of both front tyre scales). From this we can get the distance normally referred as "b"(from rear axle to CG) just by subtracting from the wheelbase:

$b={\frac {W_{front}}{W_{total}}}W_{b}=W_{b}-a$

You can also apply the same formulas to find lateral location of the center of gravity. For a balanced and best performing car all around it should be in the center longitudinal line of the car but it should be measured to find if this is true for a specific car. We can call this measurement of distance of CG to the side as "c" for example and calculate it as such:

$c={\frac {W_{left}}{W_{total}}}Track$

Once again the advised it for "c" to be half the track of the car. For cars with different front and rear tracks you can still calculate this "c".

Now for determining the height of the center of gravity we need to tilt the car around one of the horizontal axis. This could be with a tilt table or just by raising both the front or the rear wheels (as illustrated on Figure 1).

Figure 1 - Measuring height of the CG

[under construction - Formula missing]

Mass Centroid Axis

The Mass Centroid Axis

The Mass Centroid axis is measured in sections of the car, it's the axis, which isn't necessarily linear, which goes through every 2-d center-of-gravity. It doesn't have to be measured at every point in the car, you can approximate and get a better sense of the roll center moments, which aren't just measured on a parallel c.o.g. axis to the ground.