Vehicle Dynamics / General
The center of mass (”COM”) of a vehicle is the average location of all its mass. It’s the point within the body where, if held by an imaginary string, it would be perfectly balanced. It has a height position, and front-to-rear position, and a side-to-side position, although it is typically symmetric to side-to-side.
Lower is Better
The height of the COM should be as low as possible for best performance.
A higher COM creates a longer lever arm to the roll axis of a vehicle, meaning that for the same amount of force (braking, accelerating, cornering), the weight of the vehicle will shift more (greater load transfer).
More load transfer when braking and cornering is bad because it causes less evenly distributed tire loading, and therefore lower overall grip due to tire load sensitivity. Heavier loading onto a tire also causes more tire deflection, resulting in odd tire orientations (camber change, bump steer, etc.).
More load transfer when accelerating in a RWD vehicle has the upside of increasing grip of the rear drive wheels, but might not be worth the diminished performance when braking and cornering.
More load transfer when accelerating in a FWD vehicle is bad because it removes weight from the wheels we’re trying to use to power the car forward.
Of course there are reasons why the COM might be higher than what is possible. For instance, the aerodynamic rake profile may necessitate a higher rear ride height, moving the COM upward. Or, a track's high kerbing or severe bumps might bottom out the vehicle unless it’s ride height is raised.
Front/Rear has Tradeoffs
The front-to-rear position of the COM should be close to centered, but can deviate slightly for various reasons.
If centered, the front and rear axles will have the same amount of weight and the same lever arm to the COM. This maximizes the cornering grip of the vehicle and provides a natural balance; due to tire load sensitivity, maximum overall grip comes from having the weight spread across all tires as evenly as possible.
If the COM is slightly forward, the front wheels will have more grip, but a lower lever arm to the COM. Due to load sensitivity, the front grip will not be high enough to counteract the shorter lever arm, and so the front tires will not be as effective as the rear tires at holding the vehicle in a turn and so the vehicle will tend to understeer. The only way to fix this chronic understeer is to diminish the corning capacity of the rear wheels, either through the vehicle setup (such as by using a stiffer rear anti-roll bar) or in the design phase (via a higher rear roll center). In either case, the maximum theoretical cornering capacity of the vehicle will not be reached.
If the vehicle is FWD, a forward COM could be beneficial in helping keep weight on the front tires when accelerating out of a corner.
If the COM is slightly rearward the same balance and performance tradeoffs occur as the forward case, but mirrored.
On balance, it is usually beneficial for a FWD vehicle's COM to be ~60% frontward and for a RWD vehicle's COM to be ~55% rearward to aid in corner exit traction in both cases. However, some RWD race cars tend toward an even 50/50 split to maximize cornering performance.