F and R roll center height relationships

In reply to Curmudgeon:

The roll center isn't the problem? What else would cause it to need shorter shocks or limit straps to rein in the jacking? Most vehicles don't approach their usable droop travel during braking/corning...

Sure, the RC goes even higher under braking as the back end comes up, but if it wasn't for the high roll center creating jacking forces, you wouldn't have any need of droop limiters or "camber compensators" or the other voodoo created for the Spitfire.

It probably isn't an ideal example for a discussion of roll center heights in general, but I couldn't resist the picture...

EDIT: While what I've said above seems pretty clear to me, the bottom line is that I haven't played with a Spit and you have, so I've gotta recognize the possibility that I'm Just Plain Wrong, but unfortunately that notion of a sane droop-limited Spitfire doesn't do much for my understanding of roll axis inclination, though if I think hard, I'm sure I can learn something from it.

The roll center going higher than the center of gravity definitely WAS the problem.

The suspensions' motion pivoted around the inner joint of the swingaxle, so the roll center was a point somewhere around the top edge of the differential, right next to the ring gear. Oops.

Then you get into the Z-bar, aka a PRO-sway bar, that simultaneously promoted vehicle lean as well as discouraged two-wheel motion.

Puhn's book seems like it has a whole chapter dedicated to the problem Come to think of it, if that's not the same Spitfire photo from his book, then it must have been a common sight when those were around.

Y'all are both missing the point. The reason the rear roll center got to be in low Earth orbit was due to the rear suspension's excessive droop. If you control the droop, you control the roll center change. I know that works on those cars because I have done it. That's what I was referring to earlier as the roll center moving around due to suspension changes. On the Spitfire, the rear roll center moves up about 6" or so (IN RELATION TO THE CAR! very important!) when the rear suspension is in full droop like that. In relation to the ground it moves way up, to like 18" or so. But again that's not what really drives the Spitfire's inherent rear suspension problem.

It's also what I was referring to when I said the roll axis tilt is only one of many factors and when it's within reason the other suspension settings and tires etc have a much bigger role to play in handling. If the roll center were at that 6" higher figure but the rear tires didn't droop, then you probably wouldn't notice a whole lot going on.

Also, if you look at the Spitfire picture again you will notice the front tires are pointed almost dead ahead. That tells me the rear end attitude was caused by hard braking. I know first hand that's what starts the problem: braking hard. Then you turn, which loads the outside tires, and the outside rear tire does not have enough contact patch to transfer the weight and load placed on it and the tire slides. Oopsie. Once the gyrations start, now the roll center thing jumps into the fight and (again from first hand experience) that makes the driver feel most uncomfortable. I suppose that's where the whole thing about the roll axis making the car 'feel' better to the driver came from.

Kas Kastner's original camber compensator: http://www.fairpoint.net/~herald948/database/cc/

From the article:

The original swing-axle independent rear suspension of the Triumph Herald and its derivatives (Vitesse/Sport 6, Spitfire and GT6) had its limitations. Setting of "static camber" was critical. There was a tendency of the rear wheels to tuck under during certain cornering conditions, such as quick transitions. This was due largely to the inherent limitations of a swing-axle suspension as well as the high effective roll center created by a solidly mounted transverse leaf spring atop the differential.

Standard-Triumph USA's Competition Manager "Kas" Kastner developed a beautifully simple solution to the problem: the camber compensator. This single leaf spring, bolted to each axle's vertical link at the radius arm mount and fastened by a single bolt to a mount on the bottom of the differential, was an easy, bolt-on modification that greatly reduced the tendency of the rear wheels to tuck under.

The camber compensator did NOT change the original position of the roll center. All it did was control the droop which definitely helped control the roll center's height change but most importantly got rid of the roughly 20 degree camber change possible with the early Spitfire setup, thus allowing the tires to maintain a larger contact patch. By the way, the same thing can be accomplished by using shocks with less travel (early Corvette shocks will work, for instance) or, as in my case, make travel limiters for the shocks from cable.

An epic battlethread about Spitfire rear suspension: http://www.triumphexperience.com/phorum/read.php?8,688383 The funny thing, both sides of that argument had valid points.

Mercedes was credited with taming the swing axle. Actually, it shared the same basic design flaws as the early Spitfire and Beetle swing setups: excessive positive camber at the worst possible moment.

http://www.mbzponton.org/valueadded/maintenance/swingaxle.htm

Here, let me help, I'll throw some gasoline on the fire ... ;)
While it's true that the rear roll center rises a bit with positive camber changes, it's not by much relative to the center of gravity (which remains unchanged unless the car starts to deform). This, because the effective pivot points of the rear UJoints are only about 11" apart. So even at 30 degrees positive camber, the RC only rises 2.75". Maybe that still sounds like a lot, but once 'jacking' takes place, RC, etc become meaningless, as other forces prevail. The truly important measure is the angle formed by line through outside contact patch and UJ pivot, and road surface. The Tangent of that angle, times the lateral force developed at the contact patch results in a jacking force causing the rear to rise a bit. Once that jacking force exceeds the weight force at the RC, then the rear will start to rise uncontrollably. Call that the critical angle. Note that when the rear rises, the entire car including CG rises, and also the RC rises relative to the road surface. And once that happens, the angle increases, which degenerately causes even more jacking, causing the rear to rise more, the angle to increase, and so on and so on until some physical travel limit is reached (In stock Spitfires, depending on the travel limit of the shocks fitted, that is often when the axle contacts the frame, there's even a little clearance dimple in the frame from the factory!).
If you can somehow manage that angle to stay below the critical angle, then runaway jacking does not occur.
Camber compensator does this, Z-bar does this, stiffer spring does this, smaller diameter tires does this, lowering block does this, and limiting devices do this.
In 45 years of owning and racing Spitfires, I've seen several limiting methods used: Cables (with and without pulleys), chains, short travel shocks, even seat belt webbing (if you are clever, the buckles can be retained for easy adjustment!) I don't care for limiting devices, because their effect is sudden rather than continuous (reach the end of travel, and SNAP).
But they have worked very well for some people.

The roll center moves down nearly to the bottom of the diff when the rear suspension is at full compression. It then goes up to the top at full droop. The total up/down travel is somewhere around 6".

I once bought a stillborn AX project Spitfire with the pulley/cable system. It ran right where the fuel tank needed to be The pulley system also had to be under constant tension so the cable couldn't come off if both rear wheels went up at the same time and the guy hadn't designed it that way, there was no droop at all (it needed some to keep the rear tires from leaving the ground over stutter bumps, etc) meaning it had more than a few bugs that needed to be worked out. Since I was driving a street car I used individual cables to limit the travel instead. Yes it could be abrupt but it had the intended effect.

Roll Center on swing axle cars is generally accepted to be the intersection of the two lines from centroid of tire contact patch through the swing axle UJoint pivot center. Let's use some simple trig to calculate the RC at zero camber, then at max compression, then at max droop.

Visualize right triangle ABC, where A is the centroid of the tire contact patch, B is the point on road surface directly under the RC, and C is the UJ pivot center. 90 degree between segment A-B and B-C. Now visualize another right triangle CDE, where C is the same UJ pivot center, D is the midpoint between the two UJ pivot centers, and E is the RC. Triangles ABC and CDE are similar, in the Geometric sense, i.e. both have same set of interior angles, and thus ratio's of sides are also proportional.

Let's plug in some actual dimensions, and get calculating!

Assume Spitfire track = 48", tire diameter = 24", and that UJ pivot center-center distance along diff axle centerline is 11" (I just measured this on one of the several Spitfire diffs decorating my workspace).

segment A-B = 18.5" (half the 48" track, minus half the 11" UJ c-c distance) segment B-C = 12" (zero camber, so UJ pivot center is same height as hub center, half the tire diameter) segment A-C = 22.1" (Pythagorean formula for hypotenuse, rounded)

segment C-D = 5.5" (half of the UJ c-c distance) segment D-E = 3.6" ( (5.512)/18.5, similar triangle, rounded) segment C-E = 6.6" ( (5.522.1)/18.5, similar triangle, rounded)

Segment D-E is distance from diff axle centerline to RC. So the RC height above road surface at zero camber = sum of segments B-C and D-E, about 15.6"

Now for max compression, assume that ground clearance is 5", so that's the compression limit, let's recalculate:

segment A-C = 22.1" (stays the same) segment B-C = 7" (zero camber height minus 5") segment A-B = 21" (Pyth, rounded)

segment C-D = 5.5" (stays the same) segment D-E = 1.8" ( (5.57)/21, rounded) segment C-E = 5.8" ( (5.522.1)/21, rounded)

Segment D-E is distance from diff axle centerline to RC, which moved 1.8", from 3.6" above axle centerline to 1.8" above it. So the RC height above road surface at max compression = sum of segments B-C and D-E, about 8.8", moved from 15.6" to 8.8" above road surface.

Now for max droop, assume that the wheels can droop 7", let's recalculate:

segment A-C = 22.1" (stays the same) segment B-C = 19" (zero camber height of 12" plus 7" droop) segment A-B = 11.3" (Pyth, rounded)

segment C-D = 5.5" (stays the same) segment D-E = 9.2" ( (5.519)/11.3, rounded) segment C-E = 10.8" ( (5.522.1)/11.3, rounded)

Segment D-E is distance from diff axle centerline to RC, which moved 5.6", from 3.6" above axle centerline to 9.2" above it. So the RC height above road surface at max droop = sum of segments B-C and D-E, about 28.2", moved from 15.6" to 28.2" above road surface.

To summarize, from full compression to full droop:
Total RC movement with respect to chassis/CG is 7.4", from 1.8" below static, to 5.6" above static.
Total RC movement with respect to road surface is 19.4" from in 8.8" in full compression to 28.2" in full droop.

Looks like my numbers were off in previous post, sorry.

But that doesn't matter, because once you droop past the 'critical angle', RC is meaningless, eventually the inside tire lifts off the ground, while the outside axle tire tries to tuck all the way under the car.

It's like runaway anti-squat/dive on steroids.

BTW, the trick with the pulley/cable system is to run a steel retaining strip around the outside of each pulley to keep the cable from escaping, in conjunction with a coil spring (like throttle return spring) attached to the center of the cable. When the cable goes loose, the spring takes up the slack, while the strips keep the cable from jumping off of the pulley.

Regarding the fixed cables, as long as you know they are there, and how the car behaves at that limit, they can be very effective.

Carter

28.2 inches off the ground in full droop? Wow. My 'eye-crometer' measurements were way off.

I could have probably gotten the cable/pulley setup to work but damn it was going to be a pain. I went with cheap and simple. I was even too cheap to buy the Corvette shocks.

The later Mk IV and 1500 Spits with the 'swing spring' did something I never liked; they had a HEAP of negative camber, I'd say 3 or so degrees, in the rear when driving. The front (and this is true of all of them, '62 to '80) also had a bunch of positive camber in the front on acceleration. Maybe the car handled OK that way but it sure looked funky and would wear the outside edges of the tires fast.

GT6's with Rotoflexes had a strange camber curve in the rear too, the upper control arm was the spring and not only was it longer than the lower arm (bass ackwards) it could also vary in length. Here's how that worked: as the suspension compressed, the extra leaves would come in, change the bend point of the spring and basically move the pivot point outboard. Nothing like variable suspension geometry, it wakes you up better'n coffee. I swear my GT6+ was way looser in the rear than any of my Spitfires and it wasn't all due to the extra HP. The swing axle GT6's aped the Spitfires.

Wow, I'm inspiring a thread! It's funny that this came up today because I spent a good deal of this afternoon Googling about roll axis inclination because I also have many questions. There's a lot of info in Mark Ortiz's chassis newsletter, found here: http://www.eviltwinmotorsports.com/?page_id=204
It's mostly over my head but I did read somewhere that having the rear RC higher than the front allows you to soften the rear suspension wheel rate, thus making the car seem more planted while at the same time keeping the car from being understeery.

When I plug the numbers into my suspension program, if I stiffen the rear suspension, I have to lower the rear roll center. When I soften the rear suspension, I can balance the handling by raising the rear roll center. A local FSAE suspension guy said that the rear RC is higher because it makes the rear transfer weight quicker, which is necessary to keep up with what the front of the car is doing.

I'm not sure how this jives with what some say about mid or rear engine cars having a front RC higher than the rear but maybe it gives us a window into understanding roll axis inclination? Maybe you need the roll center lower at the end of the car that has higher mass (not neccessarily weight, but mass) because lower roll center transfers weight less abruptly?

Thinking about it that way helps me visualize it, bear with me, I'm spitballing here. The front of the car has a lower RC than the rear because it has higher mass (engine/trans) and by lowering the roll center, the weight of the mass is transferred more slowly. The rear has less mass and by raising the RC, weight transfer occurs more quickly and matches the "volume" (I can't think of a better word for it) of weight being transferred at the front. If I lowered the rear roll center, weight would not be transferred as quickly and the car would understeer. I could be way out on this but it makes sense to me.

Evil Twin says basically this roll center debate has been raging for years.

Keep in mind the roll center is the axis about which the weight moves side to side. If you put that roll center down at, say, 3" above the ground the car should feel stable. Of course there is a lot more which goes into that.

If you move the roll center to, say, 10" above the ground then the weight moving from side to side will be felt more strongly.

That's like the difference between holding a 5 pound weight at your chest, then holding it at the end of your outstretched arm. There's a big difference in the effort required to hold it steady. You haven't changed the weight only its leverage.

A live axle rear car's rear roll center won't change a whole bunch as the body rolls, but the independent front suspension's RC will. That means the axis as viewed from above can swing side to side on a point centered at the rear roll center. That indicates to me that with a higher rear roll center (within reason!)the rear weight actually resists the front's tendency to roll (unless the car has the torsional strength of spaghetti), which should theoretically help the car feel more stable, but also have the effect of keeping weight off of the outside front tire which can lead to understeer. Softening the rear suspension spring rate (to a point) would allow the rear to roll more easily and help with weight transfer to the outside front tire, which will be doing most of the work anyway.

Or I could be dead assed wrong (it wouldn't be the first time, just ask my ex). I need to get that program you mentioned and go through it.

Loss of traction can come from either not enough or too much weight on a given tire contact patch. That's why it's possible to tune understeer in/out with sway bars, springs etc. Unless they are huge, height differences in the front/rear roll centers don't have a whole lot of say in the matter, always assuming that body roll is kept to a minimum. Again I point out that the higher the speeds the closer to the razor's edge you get the more critical every part of the equation becomes and yes that means working the posterior off to level the roll axis becomes more and more important.

OBTW: An IRS car can have the roll centers move together or even in opposite directions. Now wouldn't that be interesting.