Front and Rear roll stiffnesses

[The_Man]

I was reading through the forum and I saw mentioned at many places that you can control your under steer and over steer characteristics but changing the relative front and rear cornering stiffness of your car. How does this happen? As in mathematically. I tried to make a quick FBD and jot down a few equations and couldn't find a direct relation. I am assuming a rigid chassis and the fact that the difference in load transfer in front and rear is causing the change steer characteristics.

[Jersey Tom]

Roll stiffness != cornering stiffness. But they do both have an impact on vehicle sideslip and/or understeer rates.

For example with cornering stiffness... for grins let's assume we have a bicycle model with 50kg F/50kg R static split. Heavy bicycle...

To corner at 1m/s/s, the front and rear must be generating 50N each of side force.

Case 1 - Neutral car.. where front and rear cornering stiffness (or really cornering coefficient) are equal, at say 50N/deg. To generate 50N each, the front and rear tires both would be operating at 1deg slip angle. Classically if we define understeer as (front slip - rear slip), the difference is 0 and at that lateral acceleration the car is neutral.

Case 2 - Understeer car. If we keep the same front tire, but now our rear tire has 100N/deg cornering stiffness... in our 1m/s/s corner the front will operate at 1 deg slip, the rear at 0.5 deg. Understeer = 0.5 deg.

Case 3 - Oversteer car. Front tire again stays at 50N/deg cornering stiffness, rear now at 25N/deg. For our 1m/s/s corner the front operates at 1 deg slip, the rear at 2 deg. Understeer = -1.0 deg (or 1 deg oversteer).

Make sense?

That works to describe vehicle yaw attitude. Limit balance will be dominated by roll stiffness distribution (among other things). Let's picture a 4-wheel vehicle now, cornering so fast that we're pretty much unloading the inside tires and the handling is dominated by the outside tires.

If you have a heap of front roll stiffness (relative to the rear) you will be dumping lots of load on the outside front tire. More load on a tire, it operates less efficiently, and it will use up all its grip faster than the rear -> limit plow.

If you have a heap of rear roll stiffness relative to the front, you dump lots of load on the outside rear tire. This time the rear is overworked and uses all its grip up faster than the front -> limit spin.

[donskar]

JerseyTom, am I correct in believing (in general) that increasing rear roll stiffness will decrease understeer? Further, the reasoning is that stiffening the rear will decrease rear grip, increasing what we might call "neutrality"? I know it works like a charm for my 200SX -- I'd just like to understand better WHY it works! Does stiffening the rear cause the front to grip better, or the rear to grip less?

[Jersey Tom]

Correct. In general, adding spring or bar on the rear end will shift the balance to "less understeer" or "more oversteer."

In one sense, you're both making the rear grip worse AND the front grip better. Roll stiffness distribution is really about percentage. So if for example your front roll stiffness was "20" and your rear stiffness was "20" the split would be 50/50. The 50/50 is the important bit.

If you now bump the rear up to "40" without changing the front, the split is 33/67 so you've both in effect increased the rear and decreased the front in terms of how much load transfer they get.

Though it's also worth nothing by increasing rear stiffness you are decreasing it's mechanical compliance with the track which further decreases its grip, and would manifest itself as a "snap" oversteer going over bumps... for example maybe into and out of the front straight at Sebring, or T1 at VIR's got a bit of a bump I think.

Also, you may have the case where a car is fairly undersprung and likes to "wallow around" and snap to oversteer while changing directions quickly. In that case stiffening the rear would "free" the car up through the center of the corners, yet make the car more "settled" in dynamic maneuvers.

[The_Man]

OK I'm looking at a model where I use the bicycle model such that I reduce the Front to tyres to an effective axil system, ie I have a effective axil slip angle and a effective axil cornering stiffness.
I read that the effective cornering stiffness can be varied by messing with the roll stiffnesses of the vehicle.
So is this the right way to look at it then:

If M is the moment due to centrifugal force @ CG.
Kf & Kr are the roll stiffness(front and back)
θ is the Roll angle.
Assume rigid chassis.
Therefore,

Analogy to the a rod with two torsional springs at its ends.
M=(Kf+Kr)θ

Front Load transfer = Kfθ / (T/2)
where T is the front track width.

Now if Kf > Kr
Then there is more load transfer in the front the front load transfer is going to be more(assuming equal track width) and hence the effective cornering stiffness at the front will become less than the rear so there will be more understeer.

Am I understanding this effect right?

[Jersey Tom]

Eh.. for the most part.

Just keep in mind that using cornering stiffness to evaluate understeer is a linear range thing. Limit understeer/oversteer is a function of using up all the tire's grip and if that happens first at the front or rear.

[The_Man]

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[The_Man]

Just keep in mind that using cornering stiffness to evaluate understeer is a linear range thing. Limit understeer/oversteer is a function of using up all the tire's grip and if that happens first at the front or rear.

Sorry about that!

Can you explain this in more detail?

if I do use effective cornering stiffness and the bicycle model the understeer and oversteer effect will be determined by the effective cornering stiffness right?
Or are you considering a tyre friction circle and hence the max slip angles would depend on the slip ratio also.

In that case wouldn't the front and rear slip ratios be similar simply just scaling down this cornering stiffness of the tyre?

[Jersey Tom]

Nothing to do with slip ratio yet.

I'm saying there's a difference between balance AT the limit, and BEFORE the limit.

BEFORE the limit, and close to the linear range, cornering stiffness works.

AT the limit, whether the car spins or plows is a matter of which tire has more peak grip.

Though they probably both tend to follow each other.

[Birel99]

Jersey Tom,

Can you please explain why under braking, when the load goes to the front tyres, we have an oversteering car? And why when we add dynamic load to the rear, we get understeer?

Regards, Birel

[Jersey Tom]

I answered your question earlier. See below:

viewtopic.php?f=6&t=6373&p=96226#p96226

Or did it not make sense?

[Birel99]

Thanks Jersey Tom,

I had weight Vs. Load transfer confused.

But what about aero vs vertical load?

Previously I read that (in most cases) lateral load transfer is undesirable, but doesnt aero load do the same thing (up to a point)?

Is it because aero load effects the left and right side tyres the same (for the most part) and lateral load effects one side more than the other?

Regards,

[Jersey Tom]

Correct. Lateral load transfer is undesirable (for the most part) since you're just moving load around, and the efficiency you lose on the outside tire isn't made up for by the efficiency you gain on the inside tire.

Aero downforce DOES add load and decreases grip [/i]coefficient[i]. HOWEVER, since you are loading ALL tires more you ARE getting more grip, but your mass is staying the same.. so the end effect is a hell of a lot more cornering power.

[Birel99]

Thanks again Jersey Tom,

Lets say that we are going around the carousel at Road America, and we apply some throttle. How would this give rear grip? It is primarily loading the outside rear.

Thank you, Birel

[Jersey Tom]

The cornering loads the outside tires, yes. As you start to get on the throttle, load transfers from both fronts to both rears. This gives the rears a little extra stick so the car will begin to feel tight.

When you put in sufficient throttle you'll break the cornering traction and start spinning one of the tires. On a RWD car, the rear would then step out (limit oversteer), on a FWD car the front end would lose grip and you'd plow off the track.