Roll center heights - I apologize in advance

[mark512]

I've been scouring textbooks and the internet regarding roll center heights, and in particular the front-rear difference (roll axis inclination) and why the rear roll center is often higher than the front. I've organized what I found into several theories:


Theory 1 - Other suspension requirements are more important and the RC's just happen to fall out of the numbers:

Front RC Low - The front axle steers, so low RC, long equivalent swing arm lengths means predictable steering due to minimal track change, minimal RC height change, minimal camber change with suspension motion, minimal jacking forces, etc.

Rear RC High - In the case of live axle, Watts linkage or Panhard rod determines roll center, and needs to be high to avoid physically scraping the road. In the case of IRS, needs to be higher especially in the case of RWD where keeping the wheels square to the road / squarer to the road than the front is important.


Discarded Theory - Roll moment distribution: I've seen a lot of this type of explanation on forums, and it makes sense that it affects the roll moment distribution if you literally hold everything else constant and only vary the roll axis inclination, but there are many other ways to adjust the distribution other than by purely roll center heights.


Unhelpful Theory - The rear roll center needs to be higher than the front because it makes the car "feel right"


Interesting Theory - This one apparently comes from Maurice Olley, that roll axis inclination controls roll-yaw coupling, and that having the RCH higher in the rear stabilizes the vehicle by causing yaw in the opposite direction of the turn as the car rolls.


Theory 2 - Geometric weight transfer "kick in the rear end"

Front RC Low - The weight transfer in the front end is almost entirely elastic, so starts small and builds with body roll

Rear RC High - The high roll center means lots of nearly instantaneous geometric weight transfer at the rear end, causing transient oversteer that compensates for other sources of (perceived) steering sluggishness.

There was an explanation on this forum by NormPeterson that seems to jive with this theory (in particular, combining this with high(er) front roll stiffness to have initial oversteer that transitions to limit understeer.) Also, looking at some race car setups (non-downforce) plus a detailed analysis of the Ferarri F355 suspension that's floating around the internet, it seems that if this interpretation is correct, quite a few designers subscribe to it - putting the front roll center slightly above or slightly below ground level, with the rear more substantially (~100mm-200mm) above ground.

The question then becomes how much of a "kick in the rear end" is necessary? The AP1 (first gen) Honda S2000 seems to subscribe to this, with a rear roll center 190mm above ground, however many have described this car as "trying to kill you." The Ferarri F355 and NA (first gen) Mazda Miata both have their rear roll centers at 120mm above ground (though the Miata front RC is high at 60mm) and I've heard no such complaints about these.

I'd be very interested in your thoughts on the validity of these theories and assumptions. Thanks!

 

[GregLocock]

Raising the front roll centre certainly improves on centre steering feel, so I like Theory 2, as getting the rear to actually start steering ASAP is useful, and it is tedious to have to wait for roll steer to kick in.

However I must admit roll centre heights may mean something, but I'm not sure what is really being measured. For instance we had a live rear axle car (watts link) with the RCH at 420mm or whatever, and the IRS in that vehicle had an RCH of 180. Yet the front suspension didn't really need retuning around that lowered RCH. So if you can change something by a factor 150% and not thoroughly upset the car I'd say either it isn't important or there's a problem with measuring it. In this case I suspect the latter.


Cheers

Greg Locock


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[cibachrome]

Historically, from my own personal experience, an inclined roll axis results from several body and chassis considerations.

1) Ride balance at a designated speed demands that there be a rear to front ride frequency ratio. For hiway driving this number is often set at 1.2 for 'flat ride'.
2) Once the chassis is defined, 3 levels of suspension are usually offered: Base (Level I) handling, level II with a base tire and a rear bar to reduce the roll gradient from 6.5 - 7 deg/g to 5 - 6 deg/g, and a Level III car with Summer Tires, stiffer springs (same R/F ride ratio) and a roll gradient of 3.5 - 4.5 deg/g (just for the sake of argument). So: pick roll centers which simultaneously achieve the ride balance and the TLLTD with a small front bar and no rear bar. Without changing trim heights or wheelhouse clearances, add a rear bar with only slight ride frequency changes (suspension bushings most likely and taking into account a larger motor (maybe 2 more cylinders). Drop the TLLTD maybe down to 3 points over the weight distribution. Then there is the level III car, with much stiffer suspension (springs and bars all around) with a Summer class tire on wider and larger wheels, maybe split tires, TLLTD dropped to within a point or 2 of weight distribution. All this without re-configuring the body line at the plant and without a lot of extra holes or slots (net build, please). The simultaneous solution to delivering ride frequencies (structural and wheel travel windows, plus roll gradients at several tune-able TLLTDs hands you roll center locations. Its called synthesis: Spec what performance you want, compute the hardware you need with specific constraints. From my perspective, many car makers grab a crate of parts, build up a car, patch and play car-car until start of production and then quit. This is folowed by next year's "refined, modified and optimized" suspension packages. Then they use the same words to describe the ding chassis as a new and improved model is prepared.

3) Paying attention to body (sprung mass) inertia defined by power-train mounting and accessory locations plus passenger, payload and fuel mass properties also gives you something to think about in terms of the roll axis location. Want roll or roll with lateral translation ?

Once you tell the computers what you are after, its just 'turn the crank'.

Don't have your Ferrari 335 , but an F430 was 60mm front and 140 rear at 2 passenger. Porsche Cayman was 22 mm front and 88 mm rear, Carrera -7 front and 70 rear. Miata 25 mm front and 110 rear. There have been a few Hondas with inverted roll axis inclinations, but didn't stick around long.

FWIW.

 

[GregLocock]

Some Mercedes were higher at the front than the rear

Cheers

Greg Locock


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[cibachrome]

Merc S500 comes to mind. Also Hyundai Santa Fe, Lexus RX300, Ford Explorer, Saturn Vue and BMW M5. But these center heights are just a couple a dozen mm and not VERY different front/rear and from each other as well. Even a Land Rover. The true measure of a vehicle platform (IMHO) is whether the roll axis stays the same year to year and among a few samples of the same car or truck. Some manufacturers seem oblivious to the consistency of their 'specifications ??', clearly not interested in repeatability or caring about where the roll center actually is. They get real hand wavely and right brained, though, when testifying in court aboat why their works of art rolled over and turned Rembrandt into a vegetable.

 

[mark512]

Raising the front roll centre certainly improves on centre steering feel

That's something I haven't thought of before, but it does makes sense. The F355 analysis

http://rejsa.nu/forum/viewtopic.php?t=60154

claims that the very low roll center results in next to no tire scrub (track change) so as to not adulter the "contact patch feel" but it would follow that having some track change with suspension movement would result in on-center "road feel." I've heard other sources talk about "road feel" via particular steering geometry aspects (i.e. large scrub radius, etc.) but this way seems more sensible to me.

So if you can change something by a factor 150% and not thoroughly upset the car I'd say either it isn't important or there's a problem with measuring it.

Agreed - thus my advance apologies regarding bringing up a controversial topic.

an F430 was 60mm front and 140 rear at 2 passenger. Porsche Cayman was 22 mm front and 88 mm rear, Carrera -7 front and 70 rear. Miata 25 mm front and 110 rear

Those are some good sanity-checking numbers. Competition Car Suspension (Staniforth) says something in the order of -25mm to 50mm on the lighter/lower end, 0mm to 100mm on the heavier/higher end which seems to be ballpark.

Merc S500 comes to mind. Also Hyundai Santa Fe, Lexus RX300, Ford Explorer, Saturn Vue and BMW M5. But these center heights are just a couple a dozen mm and not VERY different front/rear and from each other as well.

Also, a lot of people would consider only one of those to be a "driver's car"
But I could see a case where a car with an approximately even F/R weight distribution has stiffer springs on the rear (for flat ride or whatever) you could incline the roll axis upward toward the front to level out the TLLTD instead of doing it entirely with anti-roll bars.

 

[mark512]

I like Theory 2, as getting the rear to actually start steering ASAP is useful, and it is tedious to have to wait for roll steer to kick in.

So I'm experimenting with how high I can raise the rear roll center, but keeping the front and rear spring rates the same, front anti-roll bar stiffness goes up to compensate for the rear roll center rising...but how stiff I can go?

Steve Lyman did a Formula SAE presentation where he says: "My philosophy: the springs contribute 60%-75% of the roll stiffness, use anti-roll bars to trim out the roll couple distribution." I'm not sure if he's referring to the overall roll stiffness, or the roll stiffness at a particular axle.

Currently, I've arbitrarily decided to limit the front anti-roll bar roll stiffness to that of the roll stiffness due to the springs, so the contribution of each to the total front axle roll stiffness is 50/50. I'm wondering if this is a reasonable limit, or should it be lower or can it be higher?

 

[GregLocock]

Is this for racing or street? For racing the usual advice for a RWD is to use no rear bar, add enough front bar to keep the rear wheels stable out of corners with the power on. The usual advice for FWD is to sell it and buy a RWD.

Cheers

Greg Locock


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[BrianPetersen]

You haven't told us what type of suspension layout you are working with, or what vehicle you are working with, etc.

Bear in mind that a live-axle suspension design will tolerate a high roll center but an independent design will always have a "jacking" effect (see: first generation Chevrolet Corvair and Ralph Nader's book "Unsafe at Any Speed"). The reason is that with a live-axle, the various forces that would otherwise lead to "jacking" are contained within the axle, which is unsprung, whereas with an independent design, those forces go to suspension linkage attachment points on each side of the chassis, and those forces have a vertical component due to the high roll center and since the outer wheel is always more heavily loaded than the inner one when going around a corner, the net result is an upward force on the chassis (and the chassis actually does move upward, because this force represents a net unloading of the springs and the only way that happens, is for the springs to become longer, i.e. the body moves up).

Millions of cars were built with live rear axles and a very high rear roll center. The traditional diagonal 4-link design with trailing lower links and diagonal upper links have a roll center in the vicinity of where those upper links attach to the axle, near the top of the differential housing.

Just because a live axle can get away with having a high roll center doesn't mean it is without bad side effects. In one-wheel bump, the whole axle shifts to the side, which kicks the bodyshell to the other side. The millions of cars with live rear axles and a very high rear roll center were typically built with very compliant bushings and tires which covers up the ride motion. The floppy handling wasn't much of a concern with a '71 Ford Galaxie. It was a concern with the Fox-body Mustang ... and the S197 design (3-link plus panhard) works better by practically all accounts, and it has a lower roll center.

Which is better - Stiff springs and soft antiroll bar, or soft springs and stiff antiroll bar - is a subject of plenty of debate and there are advocates on both sides. I think there is reasonable consensus that in most normal applications (Heavy trucks are a big exception!) the roll center height can be a little above ground level, let's say low-single-digits inches, but much beyond that, the bad side effects start becoming ugly.

Heavy truck suspensions - which are with few exceptions solid axles all around! - have high roll centers and a ton of roll stiffness but that is because they have to, not because it's a good thing to be doing.

 

[mark512]

Is this for racing or street? For racing the usual advice for a RWD is to use no rear bar, add enough front bar to keep the rear wheels stable out of corners with the power on. The usual advice for FWD is to sell it and buy a RWD.

I'm pretty much sold on having no rear bar - you mention it a few times in your various posts, and in the Steve Lyman presentation I quoted before he also mentions he's not a fan of designs with rear bars. Looking at the math, it seems that if the CG is reasonably low and close to the middle of the car, good performance is definitely achievable with only a front bar.

Bear in mind that a live-axle suspension design will tolerate a high roll center but an independent design will always have a "jacking" effect see: first generation Chevrolet Corvair

This does seem to be the case, as with Greg's example where the car with a live axles had a RCH at 420mm, and the IRS had an RCH of 180mm and the front didn't need to change. But yes, it seems that a rear-heavy car with swing axles is a very bad idea, like the Corvair a.k.a. "Unsafe at any speed" or the Tatra a.k.a. "the Czech secret weapon."

I think there is reasonable consensus that in most normal applications (Heavy trucks are a big exception!) the roll center height can be a little above ground level, let's say low-single-digits inches, but much beyond that, the bad side effects start becoming ugly.

A list that I've compiled so far (green is at the low end, red is at the high end, white is in the middle, ordered by roll axis inclination.) So yes, makes sense.


The vehicle in question is a roadster-type sports car, mostly for street use (but track use is always a possibility), with a typically low CG, very near 50/50 weight distribution, RWD, and double wishbones all around.

(I try to ask questions as generally as possible in order for these discussions (and the information presented within) to be applicable to as many readers as possible, but since both of you have asked, this is what I'm working with.)

 

[BrianPetersen]

From the diagrams that I see (and I know only what google can tell me) of the Honda S2000 rear suspension, I don't see how the rear RCH is 190mm with the car at nominal ride height. The lower arm looks like it is nearly horizontal. The video that I found seems to indicate the upper arm being not a whole lot out of parallel with the lower arm. That's a recipe for a pretty low roll center, which is what I would expect in that application.

The arms are quite short, which would make the roll center quite sensitive to ride height. Lowering the car would drastically lower the roll center. Raising it would raise the roll center, but that's not usually what folks do to these cars.

https://www.youtube.com/watch?v=fGKCo6nQ24g

 

[mark512]

It's hard to trust random information on the internet, and it's difficult to even get a second source for any of them.

For the S2000 this image seems to be floating around the S2KI forums:

And this guy seems to do a lot of work with the S2000:

https://robrobinette.com/S2000RollCenters.htm

https://robrobinette.com/S2000Info.htm

Though I'm fairly certain for the independent rear suspension I'm not going to go anywhere near 190mm RCH anyways.

 

[NormPeterson]

If that rear geometry sketch is anywhere near to scale laterally, it's got an awfully short FVSA . . . probably wouldn't want to get out of the throttle at 8/10ths cornering.


Norm

 

[BrianPetersen]

The S2000 is known to be rather skittish.