F and R roll center height relationships

Inspired by a couple of comments on Loosecannon's E Mod V12 (now V8) MG build thread... And yes, I will also go look this up in the half dozen books I have that should mention it, but for now...

So it was mentioned that it's preferable to have the rear roll center a bit above the front roll center if there's going to be a difference.

I find this counterintuitive, if for no other reason than roll center height effectively adds geometric roll stiffness, and having greater geometric roll resistance at the rear essentially means increasing rear roll stiffness relative to front roll stiffness as the cornering forces increase.

Unless I've blown a summary somewhere, that effectively makes the car tend more and more towards oversteer as it corners harder.

So, if I'm wrong about the effects, where did I foul up?

And if I'm not wrong about the effects, what's the rationale for a higher rear roll center being preferable (up to a point)?

'It just works out better in real life'

One of my friend who does a lot of chassis design mentioned that the incline does feel better to the driver...

Not much help, technically though.

I'd say driver feel is definitely something to consider. There's no sense having something that corners amazing on paper, but spins if it hits 100.1% of available traction. A driver's got to be able to drive the car at its limit consistently.

Hrm...

I'm even more curious now...

I wonder what the relationship is between the increasing rear roll stiffness (relative to front) as the car corners harder, and how that might relate to the bell curve of peak traction...

It seems to me that it's probably a red herring, as the difference between max cornering force and riding the downward slope of too much slip angle is perhaps a subtler change in force than anything that would have a noticeable effect on roll stiffness via the aforementioned mechanism, but...

If you're pushing hard, the same relationship that makes the car tend towards oversteer more and more as the car corners harder would also cause it to recede from oversteer as traction declines with too much slip angle. So as you push too far, it becomes more benign?

If I had to guess, I'm making things more complicated than they actually are, but I'm really, really curious about why this arrangement should feel "right" to the driver...

It's one of many things that affect handling. As a general rule, if the roll axis tilts down toward the front, the car will tend to understeer at the limit. I say 'as a general rule' because there are many other things which go into this, not the least of which is whether the roll centers move up/down as the body moves in relation to the axle or suspension control arms. The rear suspension geometry arrangement has a lot to do with it too, the length, angle and placement of the arms will control whether the rear axle steers with or against the front. The axis is also affected by more than just geometry, non-yielding suspension bushings are a prime example. Those last two things are why some cars start out plowing like a John Deere then suddenly go into snap oversteer.

I'm thinking this is why the understeer biased car 'feels' better, you have to provoke it into oversteer. I know I like oversteer (it's fun, among other things) but only when I want it to happen!

It's possible to start out with a roll axis which tilts down at the front, which biases the car toward understeer, then tune that in/out as needed by changing spring rates etc. Or it can be done the other way with the roll axis tilted up (higher at the front), the chassis starts out as oversteer biased then again you tune it with springs etc.

I wonder what's lodged sideways in my head, or what I'm just failing to grasp...

The fact that there are other influences is clear, and perhaps there's something geometric that comes as part of the package with roll center height that I'm not getting.

But the fundamental notion that a lower front and higher rear roll center creates a basic bias towards understeer seems backwards, based on the theoretical effects on roll stiffness.

Thanks for the insight; I need to follow through on my assertion that I was going to read up on this...

Roll stiffness does not affect the roll center directly, The rear roll center should be higher so that a greater proportion of weight transfer is taken at the front end in a turn, Roll couple also comes into play here.

In reply to iceracer:

Now I'm confused about what part of what I'm confused about you're confused about

I say this because you've got causality backwards from what I'm suggesting (however confused I may be): Roll stiffness doesn't affect roll center, but the roll center does affect roll stiffness.

If the roll centers were at CG height, you could run no sway bars and a monoshock at each end so that there is no sprung roll stiffness, but the car could have 100% lateral weight transfer to the outside tires without rolling. The lower the roll center goes, the more you have to use springs/sways to counter roll.

Your statement about weight transfer, as a result, sounds backwards to me: I would expect that if we imagined all else in terms of springs and sways to be equal front and rear, I would expect the end with the higher roll center to have more weight transferred from the inside to outside tire than the end with the lower roll center.

All that being said, it sounds like the real-world also has it backwards And I'd rather be on the same page as the real world than be right on paper, but fundamentally I still want to understand why the actual outcome seems backward from the (er, "my") theoretical outcome.

Curmudgeon's summary is spot on.

The human factors of lower front roll center design feature goes like this....Most drivers are thinly disguised passengers. They drive into a corner too fast due to poor traction, inattention, etc. When they turn the steering wheel, the chassis transfers more weight (Relatively) at the front due to the lower roll center. If they are at the limits of traction, the car understeers and the driver intuitively lifts off the gas. Lifting off the gas loosens the rear wheels (and allows the front wheels to grip), and the car can then turn to follow the corner....

The fact that people on this forum are not "Most drivers" and are not intimidated by oversteer is a good thing....

One of Stirling Moss's best lines from the Corvair liability trials went like this...."When a vehicle is oversteering, the passenger is terrified. When a vehicle is understeering, the driver is terrified....."

Rog

There's something about the way a car moves as you turn in to a corner that just feels better if the roll axis slopes down to the front.

It also means that, generally, you can use heavier springing in the front than the rear, which helps traction when you're accelerating out of the corner.

Neat thing about having adjustable roll center heights and easily changed spring rates: There's all SORTS of ways you can get things wrong! And then you invariably find out that what works best is what is normal practice.

One thing that always has bugged me, and I never got a clear answer on: When figuring roll couple, do you figure the car's total CG height, or just the unsprung weight's CG height? Logic says unsprung, but I've seen it in many books where they use total.

From Neil Roberts' book, "Think Fast" (pg112):

It is quite common for the rear roll center to be higher than the front and significantly above the ground plane. That is a consequence of the fact that velocity is a factor in the automotive stability equation, so the slower you go, the more understeer you will have. It's a big problem, so it takes a combination of several design and tuning features and this geometry compromise to combat it. A rear roll center that is higher than the front roll center exaggerates the weight transfer across the rear tires, which helps reduce understeer. It does produce jacking, scrub, and a variation of cornering balance with lateral acceleration, so it's a compromise to help balance the car, and it has some negative side effects. In this case, a higher rear roll center makes the car better balanced at low speed and therefore faster, but harder to drive. It is worth tolerating this handling interaction because going faster is the goal.

Huh. This gives a compelling argument for the rear roll center being higher, but is, if anything, contrary to the "feels better" argument. Or not, depending on how much time you spend being frustrated by understeer...

Most people, when faced with a situation developing, instinctively tend to try to scrub speed off quickly. If the car is oversteering, lifting the throttle can turn this into a full fledged spin. This means now the driver has to turn into the skid in order to bring things back under control. That's multiple inputs: throttle, steering, brake which (let's face it) most people are not trained to do. OTOH, if the car is understeering, lifting the throttle will cause the front tires to grab again. That's all the driver needs to do and it's instinctive. So the mfgs bias their cars toward understeer for the 95% and the 5% just have to suffer. Or do suspension mods.

In reply to Curmudgeon:

??

All true, but if anything, it would suggest that cars leaving the factory would have their roll centers lower at the rear in an attempt to foster understeer at the limit, and in general reinforces the idea that the less-understeer/more-oversteer affect of a higher rear roll center may make the car more of a handful.

I'm under the impression that most of what we've been discussion is setting cars up with a higher roll center at the rear when we have a free hand to do so, and that this is for some as yet poorly-defined aspect of driver feel.

Roberts seems to think it's a relatively-necessary evil that actually makes the car harder to drive (while he does talk about production based cars quite a bit, much of the book seems biased towards open-wheel cars, and I'm not sure whether that's affecting this section), and that seems if anything to run counter to the driver feel thing, at least assuming he's correct about this making the car harder to drive. I guess if the driver prefers oversteer, it will feel better, but I've got more reading to do, I'm sure...

The den is becoming the dining room with the library moving to the living room, and a lot of books are in stacks on the floor, so I haven't located Tune To Win yet...

The lower end of the axis is the one which dictates (I hate to use that word but it's as close as I can get) which end loses traction first. The reason I hate to use that word is because small roll axis angles don't really affect much at all. The rest of the suspension geometry and the tires etc will have a much bigger part to play. Still, the bias toward understeer by having the axis tilted down toward the front combined with other things such as a larger front sway bar will tend to make that end of the car 'loose'. JG covered that subject very well in the series he did on the Fox body Mustang project car a few years ago.

In the vast majority of cases (and the V12/8 MGB GT is one of them) going all out to make the roll centers equal front/rear (a level axis) won't be nearly as important as the layout of the rear control arms to provide rear under or over steer. That's particularly true if the car is sprung so stiffly that it doesn't roll much in a corner since there won't be much RC change. Now in the case of, say, a 250MPH F1 car where you are scrabbling for any tiny edge at warp speeds, then as near to 100% as possible neutral handling at all times is the ultimate goal. In that case I can see putting all the effort into having the axis level (or as near as is humanly possible) at all combinations of vehicle position. But man that ain't easy.

If the car has soggy suspension (allowing a lot of body roll) and a high CG (like a typical SUV or pickup truck), then yeah big roll axis angles are going to rear their ugly heads- to a point. In the case of an unloaded pickup, the roll axis won't have much to say about the whole thing since the rear of the truck is so much lighter than the front. We are back to that 'there are much bigger fish to fry' thing again, the weight distribution is going to have a much bigger effect on vehicle handling than the roll axis. That doesn't mean it should be ignored entirely, though.

Curmudgeon wrote: Still, the bias toward understeer by having the axis tilted down toward the front combined with other things such as a larger front sway bar will tend to make that end of the car 'loose'.

Neil Roberts said: A rear roll center that is higher than the front roll center exaggerates the weight transfer across the rear tires, which helps reduce understeer.

Do you see what I'm driving at? There are some significant inconsistencies in the data I've gathered...

My understanding is the same as Roberts': A higher roll center causes a jacking/anti-roll effect, so that cornering force causes the end of the vehicle with a higher roll center to have a greater geometric roll stiffness (of course this will be affected by the amount of weight and grip at each end; the forces fed into the suspension are proportional to those things, while the effect on roll is only proportional to the net roll torque on the unsprung weight, thus if the end with the higher roll center were lighter and/or had less grip, it could still provide less total anti-roll torque than the end with the lower roll center).

As I understand...

Tires require some load to produce lateral forces (gotta push it into the ground). The relationship between load and lateral forces produced by a tire are not linear. Adding 100lbs gains you less cornering force weight then dropping 100lbs looses you. This means that shifting weight from one side to the other results in an overall loss in max lateral forces produced by the pair of tires.

Two main ways weight can be transferred from one wheel to another.
As the car rolls about its roll centers weight is transfered... however it is transferred slowly as the spring compresses. But weight is not only transferred through suspension. Even with no suspension weight will transfer. Like pushing on a chair, even side force will transfer all weight to one side as it tips. This weight transfer is immediate, and directly responds to applied forces from forcing the car around the corner.

While cornering The CG acts at its height from the roll axis (line between roll centers) to roll the body. The height from CG to the roll center front and rear will not only determine the strength of this couple, but the rate of weight transfer. With CG and Roll center combined there is no moment to roll the body, and weight transfer is immediate. With CG heigh above roll center the body tips on the spring and load slowly shifts from one tire to the other... And everywhere in between.

Having a higher rear roll center accomplishes two things. Weight transfer in the rear occurs quicker, as the CG's moment about the roll center is lower and more weight is transferred with out roll directly through the linkages. This means transitionally the front maintains grip and the car will assume a nose in attitude to aid turn in. In steady state cornering the roll couple is greater for the front end, so the front end rolls towards the outside of the turn, producing a yawing moment that attempts to stabilize the car.

Conversely, a car with a lower rear roll center will want to under steer into the corner as the front end loses grip. As the car enters stead state cornering the rear will roll more, pointing the front end further into the corner... increasing the roll moment, pointing further into the corner... piling on top of itself creating instability.

In reply to RedS13Coupe:

That's an interesting observation about the temporal aspect of modes of anti-roll:

• roll center/geometric: based on force
• dampers: based on rate of roll
• springs/bars: based on displacement of roll

So the geometric force is essentially instant, the dampers affect weight transfer during the change of attitude of the unsprung mass, and springs and bars become effective as roll occurs.

You lost me a bit in the last couple of paragraphs... Without a flexy body, one end can't roll more than the other end, can it? Due to high roll centers, cars can take some funny attitudes but the overall body still has only one roll angle, and it's the end with the high roll center which takes a funny attitude (jacking up and eventually moving outward relative to the outside contact patch), and thus losing traction, both relative to the low-RC end and in absolute terms.

NASCAR crews change the rear roll center by adjusting the height of the panhard bar.

ransom wrote: You lost me a bit in the last couple of paragraphs... Without a flexy body, one end can't roll more than the other end, can it? Due to high roll centers, cars can take some funny attitudes but the overall body still has only one roll angle, and it's the end with the high roll center which takes a funny attitude (jacking up and eventually moving outward relative to the outside contact patch), and thus losing traction, both relative to the low-RC end and in absolute terms.

Ohhh hell, I dunno... Just some E36 M3 I read in a book that I recite at parties to sound smart to other people

Most of that is more or less as explained by Race Car Vehicle Dynamics... Makes sense to me, but I am not going to pretend I can show you equations to prove it true...

I will say if nothing else we are talking about small changes making the difference in something that is otherwise near equal (front and rear grip, roll front vs rear, ect...) and to some degree EVERYTHING flexes.

And perhaps saying the front rolls more causing the car to yaw to the outside isn't particularly as correct as saying the front WANTS to roll more, creating a yaw moment (but perhaps not the actual yaw movement) towards the outside of the turn.

If nothing else, dumbed down... The fact that the end of the car that wants to roll more would try and turn the car in a direction that would move that end towards the outside of the turn just seems right

Huh... Dug out a couple more books. I don't own Milliken's RCVD, but I clearly need to.

Can't find any discussion of F vs R roll center heights in Staniforth's "Race and Rally Car Source Book", Puhn's "How to Make Your Car Handle", or much to my surprise, Smith's "Tune To Win". I half think I need to go through a bit more thoroughly in case that particular discussion is hiding somewhere I haven't looked in that book...

Interesting discussion of the same topic over at fsae.com.

From a tuning standpoint, I'm really curious about whether it makes sense to stick to relatively low roll centers at both ends so that the geometric contribution stays small (to avoid complicating things with interactions), but use it to tune that very initial turn-in moment.

I wonder whether that's the part that feels good to a driver: If it's a small contribution, it shouldn't necessarily make the car oversteer at the limit, but it might contribute to a feeling of responsiveness if it tunes the car slightly towards oversteer just as the tires are loading up...

This is fascinating...

RedS13Coupe wrote: If nothing else, dumbed down... The fact that the end of the car that wants to roll more would try and turn the car in a direction that would move that end towards the outside of the turn just seems right

But if that's the end with less net roll stiffness, then it's the end which is experiencing less transfer of weight to the outside wheel. In short, it's the definition of the end that should benefit in traction from this whole thing.

In any case, your observation about the near-instantaneous nature of geometric anti-roll shook some stuff loose in my head. After all, when we're tuning a car's behavior, we're not strictly concerned with whether it oversteers or understeers or is neutral in a steady-state corner; we're concerned with turn-in, early corner, mid-corner, corner exit, and how it behaves on the brakes on they way in and on power on the way out...

So when you look at what state the car will be in with respect to roll or rate of roll at any given instant, you can create a sort of "overlay" for the effects of the different systems (meaning at any instant, the total anti-roll forces are the sum of the separate geometric, damper, and spring/bar forces). The magnitude of the effect of a small change in roll center height may be small, but when the car hasn't rolled at all yet, then the contribution from springs and bars is zero, and the dampers' contribution only comes in as roll motion occurs, so at the instant of corner initiation, geometric anti-roll is 100% of the anti-roll, so the magnitude of differences between front are rear is momentarily more important than it will be as the other systems load up.

ransom wrote: But if that's the end with less net roll stiffness, then it's the end which is experiencing less transfer of weight to the outside wheel. In short, it's the definition of the end that should *benefit* in traction from this whole thing.

Roll stiffness is more then just the moment created about the RC by the CG, its that combined with wheel rate (spring rate)... Other then saying that loading is transferred over time when done through the springs there has been no discussion of the added effect of spring rates to the situation. Tons of stuff effecting this basic picture, roll stiffness and gradients/rc migration is simply an additional layer of complexity that will further shape the outcome...

If your not scared of by trig/vectors and some integration pick up Race Car Vehicle Dynamics by Milliken and Milliken. While there may be some charm in my half assed dumbed down version this book is pretty much considered the bible of vehicle dynamics. Its expensive, but given its contents probably under priced in all honesty. Less moral people may even try and find it for free in PDF form online, its a popular book and I am sure many copies are out there... but stealing is wrong, and its an impressive piece for the book shelf.

ransom wrote: Huh. This gives a compelling argument for the rear roll center being higher, but is, if anything, contrary to the "feels better" argument. Or not, depending on how much time you spend being frustrated by understeer...

"Feels better" meaning "the car's motions are intuitive to the driver".

It's similar-ish to how it's easier to drive a car if you are sitting upright instead of laid back. In that case, the brain does a better job of interpreting the forces that are acting on the body.

In the case of the suspension geometry, it's something to do with the way the car rolls into a corner. It just "feels" better.

ransom wrote: In reply to RedS13Coupe: That's an interesting observation about the temporal aspect of modes of anti-roll: * roll center/geometric: based on force * dampers: based on rate of roll * springs/bars: based on displacement of roll So the geometric force is essentially instant, the dampers affect weight transfer during the change of attitude of the unsprung mass, and springs and bars become effective as roll occurs. You lost me a bit in the last couple of paragraphs... Without a flexy body, one end can't roll more than the other end, can it? Due to high roll centers, cars can take some funny attitudes but the overall body still has only one roll angle, and it's the end with the high roll center which takes a funny attitude (jacking up and eventually moving outward relative to the outside contact patch), and thus losing traction, both relative to the low-RC end and in absolute terms.

The Spitfire is not a good comparison point for this because the roll center was not the true cause of what you see here. Its problem (along with early swing axle Beetles) was the shocks had too much downward travel. That is what led to the craziness in that picture.The rear roll center went up under hard braking as a result. Combine that with tires which could only grip with about 1" of the outside edge due to the massive camber change and it was a scary situation. But again the roll center is NOT the root cause of this problem! BTW, I learned that you could fab up some travel limiters out of stainless cable and big flat washers which would get rid of about 90% of what you see in that picture.