T.Donaldson wrote:Let's think about this logically, we have two cars (one with high CofG and one with low CofG). Let's say that the higher CofG car has the stiffer roll bars adjusted to ensure body-roll is the same for lateral loads in both cars. Now, which car corners faster? [...]
It can be argued that a low CofG is better because I read that "A flatter car, one with a lower CG, handles better and quicker because weight transfer is not so drastic as it is in a high car." and also your point about tyre load sensitivity.
However, you could make an argument for a high CofG too. A higher CofG would shift more weight to the driven axel, thus providing more grip and therefore more speed.
You asked which car could
corner faster, not accelerate off the corner better. Low CG car will have higher mid corner speed. As far as "equations" are concerned.. with tire load sensitivity consider a simple tire model of mu_lateral = mu_lateral_max - c * Fz. You'll have to take my word that this is a pretty decent representation of things under a vast majority of cases. Or alternatively, you can find this as part of the Pacejka Magic Formula equations.
That being the case, peak lateral traction is Fy_max = Fz * (mu_lateral_max - c * Fz). Let's say in your above example the car nominally has 600 lbf on each corner on scales.. is aero neutral, our mu_lateral_max is 1.10, and our c factor is 0.20 / kip.
Say the low CG case has 200 lbf load transfer from inside to outside, so 400 lbf vertical load on inside tire, 800 on outside tire. Using our above tire model, I'll let you work the algebra out yourself, but Fy_max_inside_tire = 408 lbf, Fy_max_outside_tire = 752 lbf, for a sum of
1160 lbf.
We'll double the load transfer in the high CG case to 400 lbf, putting 200 lbf on inside tire and 1000 on outside tire. Fy_max_inside_tire = 212 lbf, Fy_max_outside_tire = 900 lbf, for a sum of
1112 lbf. So we've lost 48 lbf of cornering capacity, which is a solid ~4.1%. No matter what value you pick for mu_lateral_max or the c factor (so long as both are positive)... low CG (low load transfer) case will always have more total capacity. C factor really determines how dramatic it is.
Now you do raise the point that higher CG will be able to dump more load rearwards on the driven tires. That is true. However (a) higher CG case will be exiting the corner at a slower speed so it's already got to make up that deficit compared to the low CG car carrying more speed, (b) by the time you're on the straightaway you'll most likely not be traction limited any more in which case the high CG advantage disappears, and (c) there are drivetrain considerations as well.
To briefly elaborate on point (c) let's say our cars use open differentials. That being the case you'll be limited by how much vertical load is on the inside tire. Typically a car will have a shorter track width than wheelbase.. so more lateral load transfer per G than longitudinal load transfer per G. And I'd say typically cornering acceleration will be greater than longitudinal (driving) acceleration.
So even if a higher CG car can transfer more load back to the driven axle, it will probably not be able to make up for the additional lateral load transfer. In our open diff example, the low CG car would then be able to have higher cornering speed
and probably get off the corner better (again this assumes the limiting factor is the inside driven wheel). This is also why high power RWD cars will typically be set up for mechanical understeer mid corner via front load transfer distribution bias - to keep the vertical load on that inside rear tire.
Ultimately, the vast majority of the time.. racecar engineer or designer will aim to get CG as low as possible because it typically winds up being fastest. As I'm fond of saying, there are few if any universal truths in racing.. but suffice to say low CG is best almost all the time in circuit racing.
Grip is a four letter word. All opinions are my own and not those of current or previous employers.
. But I think it is difficult to talk in general terms.
