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Hi there,

I'm new to the forum so please don't scald me if I have posted this in the wrong forum thread

I am a student doing some research into how CofG & Roll Stiffness effects an open-wheel racing car in two scenarios, and need a little guidance:

1) Acceleration from rest

It is my understanding that a car with a lower CofG would accelerate faster than a car with a higher CofG from rest because smaller rolling and pitching moments would be present in reaction to the track inertial forces ... and that essentially means more downforce, and more grip. I'm not entirely sure roll stiffness would come into play in this scenario? Sure it would effect the car ... but acceleration from rest - wouldn't CofG be the over-riding factor?

2) Cornering speed

If we have two cars (one with a higher CofG and stiffer roll bars and one with a lower CofG and less-stiff roll bars), I think the second one would have the higher cornering speed. A lower CofG means more downforce which would obviously help - but I have no idea how roll bar stiffness would effect things. If I had to guess, the less-stiff roll bars would be better because it would allow the car to lean or roll into the corner, thus improving the aero effect. Although not so un-stiff that the car becomes crazily unbalanced ..

Just looking for some general guidance on what I have said really, is my reasoning correct - or do I have flawed understanding?

Thanks in advance.

T.Donaldson wrote:It is my understanding that a car with a lower CofG would accelerate faster than a car with a higher CofG from rest because smaller rolling and pitching moments would be present in reaction to the track inertial forces ... and that essentially means more downforce, and more grip. I'm not entirely sure roll stiffness would come into play in this scenario? Sure it would effect the car ... but acceleration from rest - wouldn't CofG be the over-riding factor?

Roll stiffness doesn't come into play if you have no roll moments.

What you have said may be true for a front wheel drive or 4 wheel drive car, but what about for a rear wheel drive car that is traction limited (ie. has more power than it can put down) at launch? Why would smaller pitching moments mean more downforce and more grip? If you're accelerating from rest, does downforce even matter at the beginning? How long before it comes into effect?

T.Donaldson wrote:If we have two cars (one with a higher CofG and stiffer roll bars and one with a lower CofG and less-stiff roll bars), I think the second one would have the higher cornering speed. A lower CofG means more downforce which would obviously help - but I have no idea how roll bar stiffness would effect things. If I had to guess, the less-stiff roll bars would be better because it would allow the car to lean or roll into the corner, thus improving the aero effect. Although not so un-stiff that the car becomes crazily unbalanced ..

again, why does lower CoG mean more downforce? why would rolling into the corner improve aerodynamics? how does absolute stiffness effect balance?

Perhaps you should brush up on your understanding of vehicle dynamics. Start with Carroll Smith's Tune to Win or, if you'd like to jump straight into the deep end, Racecar Vehicle Dynamics.

T.Donaldson wrote: 1) Acceleration from rest

It is my understanding that a car with a lower CofG would accelerate faster than a car with a higher CofG from rest because smaller rolling and pitching moments would be present in reaction to the track inertial forces ... and that essentially means more downforce, and more grip. I'm not entirely sure roll stiffness would come into play in this scenario? Sure it would effect the car ... but acceleration from rest - wouldn't CofG be the over-riding factor?

Hi, T.Donaldson. Sometimes downforce increases with pitch if front ride height is relatively small and sometimes increases with roll angle. This information provides you the aeromap.

Roll stiffness doesn't matter. It is another mode of vibration.

T.Donaldson wrote: 2) Cornering speed

If we have two cars (one with a higher CofG and stiffer roll bars and one with a lower CofG and less-stiff roll bars), I think the second one would have the higher cornering speed. A lower CofG means more downforce which would obviously help - but I have no idea how roll bar stiffness would effect things. If I had to guess, the less-stiff roll bars would be better because it would allow the car to lean or roll into the corner, thus improving the aero effect. Although not so un-stiff that the car becomes crazily unbalanced ..

Lower CofG allows softer springs so you will have more grip . But I think it is difficult to talk in general terms.

Downforce does not depend on the CofG. CofG is a mass-geometry parameter although a lower aero car, well used, will create more downforce. More depression under the car.

I think you must look at the relationship between the mass transfer and tyre dynamics. I think that is what you are looking for.

Regards

You need to forget about aero for a minute and look into tyre load sensitivity (and tyres in general). This is where the main effects of CG location (longitudinal location not just height!) and roll stiffness come from.

CGh has very little to do with aero. A high CG jut means you need stiffer springs to maintain the same body control.

For your longitudinal situation, think about if the car is front or rear drive and what the longitudinal load transfer is doing to your driven axle. You will see that for a RWD, a high CG is actually an advantage.

Actually all of these effects are a bit of an unending rabbit hole starting with the tyres.

Enjoy...

Just as a reference point, in theory a CoG at the same level as the tire contact patches would induce no inertia weight transfer since there would be no force couple. On the other hand with a force couple, increased roll or pitch stiffness would not affect weight transfer for a given CoG and track/wheelbase, but will only reallocate the weight transfer side to side or end to end.

Higher CoG would make the car "squat" more under acceleration, transferring more weight on the rear tires and giving them more grip.
You should not worry about aerodynamics because:
1. Aero requires speed to have any effect and your start is from 0 speed.
2. When the car accelerated enough for aerodynamics to have effect, the acceleration will be much smaller and would cause less "squatting".
3. You need more information to determine whether squatting would increase or decrease the downforce at the rear.

For your second question - CoG has nothing to do with downforce by itself. However I would guess that the bottom of the car would produce more downforce if it's more paralel to the ground.

You can also look at 3rd springs. Similar to how rollbars affect the suspension only when the car rolls, the 3rd springs are compressed only when both left and right side of the suspension are compressed - meaning they would stiffen the rear suspension when squatting. They would also stiffen the suspension when all 4 corners are loaded by downforce.

Hmmm, taking into account everything you guys have said - and some additional research - I have come to a new conclusion for acceleration from rest. The car with higher CofG would accelerate faster because Fh (longitudinal moment) would be higher. I am pretty sure this is right, thoughts?

I am very stuck on the cornering speed scenario however, need a bit more guidance if possible. Obviously downforce is the key to this question .. but I'm not sure how to logically come up with an answer

Why would lower CoG result in higher longitudinal moment?

Why don't you forget downforce then? assume it's a road car with negligible downforce, or a car cornering at low speed. Once you have that figured out, add downforce and see how it changes.

Whoops, that should have said higher not lower. Reason is the same, higher Fh.

Ok. What about a front wheel drive car? a 4WD car with front static weight bias? 4WD with rear static weight bias?

T.Donaldson wrote:Hmmm, taking into account everything you guys have said - and some additional research - I have come to a new conclusion for acceleration from rest. The car with higher CofG would accelerate faster because Fh (longitudinal moment) would be higher. I am pretty sure this is right, thoughts?

Basically, for acceleration on a RWD car, a higher CG is better better since it transfers more load onto the driven wheels.

For braking though, the opposite is true - mainly because al four wheels are braked and again tyre load sensitivity comes into play.

T.Donaldson wrote:I am very stuck on the cornering speed scenario however, need a bit more guidance if possible. Obviously downforce is the key to this question .. but I'm not sure how to logically come up with an answer

If you don't take my recommendation about reading up on tyre load sensitivity, you will never understand the reasons behind why the CGh and roll distribution changes the car's behaviour. For cornering, a low CG is better, and tyre load sensitivity is the reason why.

Lycoming wrote:Ok. What about a front wheel drive car? a 4WD car with front static weight bias? 4WD with rear static weight bias?

I'm only looking into RWD cars for the moment, let's not open up that can of worms just yet

Tim.Wright wrote:If you don't take my recommendation about reading up on tyre load sensitivity, you will never understand the reasons behind why the CGh and roll distribution changes the car's behaviour. For cornering, a low CG is better, and tyre load sensitivity is the reason why.

I am doing research, however I've seen some people make valid arguments for both so I am a bit unsure.

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? Note: One thing I haven't taken into consideration is if the corner is high-speed or low-speed, correct me if I am wrong, but I don't think that's relevant to the answer.

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.

This is an interesting debate, but I am clearly very confused

Perhaps some explanations in terms of equations might help here.

Here's the difference between your two senarios (RWD only):

Acceleration: the forces in the tire patch are all parallel to the direction of travel, meaning that the additional force being implemented on the tires is solely from above, which helps the tires find more grip. The contact patch cannot change because the wheel is round in that direction.

Cornering: no static difference. Here you have a force in the forward movement and an additional force perpendicular to the tire (parallel to the axle). This perpendicular force causes the car to roll, which also moves the CoG outward. Now your tire's contact patches are subjected to forces in two directions. The perpendicular force also changes the geometry of the contact patches, causing the outer tires to carry more load, and moving them toward the friction limit.



By increasing the height of your CoG you increase the leverage on the shoulders of the outside tires, until you reach the tipping point. If the friction force in the tire patches is not exceeded by the centrifical force on the car and the tipping point is not reached, there is no major difference in the higher or lower CoG, since the increased pressure on the outside tires is offset by the decrease on the inside tires (torsion bars help against this problem, different subject though). It doesn't feel very comfortable for the driver when the car rolls excessively however, and this roll can cause dynamic problems (i.e. reaching the tipping point earlier).

I hope I managed to be somewhat clear, otherwise I'll try to translate it again.

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.

CBeck113 wrote: The contact patch cannot change because the wheel is round in that direction.

That's wrong. The contact patch is proportional to the tire load. Contact patch area=load/tire pressure.