Rear Suspension Compliance

[burgermeister]

I've been wondering about the semi trailing arm setups' compliance, and I finally got around to measuring it. I basically pushed on the jacking pad laterally, and measured deflection at 2 places on the car and at 2 places on the wheel. One basic assumption is that the load on the rear tires is equally distributed between both tires.

Tires: RE760 at 42 psi (it's what I seem to end up around on track)
New ERP rubber bushings all around
No measurable body roll during load application

The pictures should speak for themselves re. setup & calculations.

These are all for a load applied at the tire patch:
Camber Compliance 0.2 deg/kN
Tire Patch Compliance (with tire) 5.2 mm/kN
Tire Patch Compliance (without tire) 1.4 mm/kN
Toe Compliance: <0.02 deg/kN
Wheel Center Compliance 0.2 mm/kN (+- 0.1 mm/kN - the data is awfully noisy because deflections are so small)

There is a lot of camber compliance. There is very little toe compliance, which really surprised me. Whatever there is is less than the noise in my admittedly simple setup. The lateral compliance at tire patch with the tire is only for the linear range, and it obviously becomes nonlinear at bigger loads.

These numbers suggest that the majority of the camber compliance comes from the banana arm, wheel bearing, and wheel. If the bushings played the significant role, toe compliance should be similar to camber compliance, and wheel center compliance should be at around 1/2 of tire patch compliance (without tire).

So the bushings don't bother things all that much, is what I conclude. And one looses >1 deg of camber on the rear during max cornering just due to structural compliance.

You may conclude differently.





The calculation part of the camber spreadsheet. The corrections I made should be obvious from the column titles.

Load application:

The camber setup:

The toe setup:

[Flieger]

Interesting. So the spring plate flex + trailing arm rotation is the dominating factor rather than the bushing deflection?

[rusnak]

In my simple mind, would you not multiply the results by two?

[RWebb]

so.... is that why they are called "spring" plates?

[Chuck Moreland]

It's an interesting experiment.

But the maximum load of 425N is only about 95 lbs if we speak English, a trivially low cornering force.

What happens when the the cornering force is 1.1Gs = 3025 lbs (VIN weight of 2750 on say an '86)?

That's 32X the force applied in the test. Is bushing deflection still not important?

Also I don't see any control for movement of the chassis; body roll and yaw will mess up your camber and toe measures which are being taken relative to the floor.

Why not attach your dial indicators to the chassis to control for this?

[jrolstin]

Originally Posted by chuck moreland

it's an interesting experiment.

-

why not attach your dial indicators to the chassis to control for this?

+1

[RWebb]

also... is there any flex in the plywood or studs when you do this?

[burgermeister]

I will readily admit the setup is far from perfect. Obviously the wheel bearing is likely to be somewhat nonlinear, being softer at lower loads, and I can't capture what happens at higher loads. There is also likely considerable variation in bearings (bearing stiffness is probably a function of preload). But, I lack the equipment to apply any higher loads safely. Still, it is data. One could criticize almost any setup, no matter how elaborate. Or, one could make a better setup and produce better data.

Chuck, I didn't attach dial indicators to the car because I'm not clamping vise grips to painted surfaces, even wrapped in duct tape. But I did measure yaw of the car, and correct for it. I also measured roll - there wasn't any.
Yes, cornering loads are much higher (more like 2000# on the rear axle, maybe 1500# on outside wheel). But those bushings are mighty stiff. As evidence, my spring plate (clad in ERP rubber bushings BTW - thanks for selling the rears and especially the fronts) is perfectly centered in the spring plate cover, with the car sitting on the ground. That's > 1000# of load on the spring plate bushing, with no visible deformation.

The inner banana arm bushing is softer - not sure how much, let's rather conservatively pretend it's 1mm/1000lb and the outer is 0.25mm/1000lb. For a 1g corner, as rough easy-math numbers, load changes on the bushings are around 1000lb, so 1.25mm of total bushing compliance, over a 365mm span, is 0.2 degrees. My data suggests compliance of the banana arm / wheel / bearing assembly is >1 degree, which is almost an order of magnitude greater. So I conclude the bushings don't matter much - the stock banana arm assembly is a bigger gorilla.

If the same compliance occurs for toe, at 1g cornering, slip angles are probably in the 5 - 10 degree range. Another 0.2 degrees isn't going to be noticeable to me - the tire is the bigger gorilla in the room. If this was an F1 car, 0.2 deg would matter. On a track driven street car piloted by an amateur out for an adrenaline fix, I don't think I could tell if my life depended on it.

As I've stated, you may conclude differently - I have no horses in this race. I'm just interested in what makes the 911 tick, and I use the limited resources at my disposal

Rwebb, there is flex in the plywood, and one of the reasons I stop at 230lb of load on the car is that I don't want the bottom of the stud wall moving. But you will surely realize the applied load is whatever the scale measures, regardless of deformation of the plywood, the mil-spec "load applicator stick", or the wall.

[Flieger]

So you are saying the trailing arm is acting as a beam in bending and deflecting more at the wheel than the effect of the bushing times the lever arm?

[RWebb]

yes, the applied load is whatever the scale measures, regardless of deformation of the plywood or wall, as long as you got things to equilibrate (which is very likely)

"Or, one could make a better setup and produce better data." We all want you to do this... for example, you make dynamic measurements using laser interferometry or even something pedestrian like strain gages...

[burgermeister]

Yes, the trailing arm acts like a beam.

For camber compliance, the wheel bearing & wheel are also adding compliance. Not sure how to apportion it amongst the three - I suspect the bearing is the biggest, but that's a total guess.

For toe, it's just the arm & the bushings, and I'd guess the bushings are softer. But the overall toe compliance seems to be rather small. It is always in the oversteer direction, which is opposite any modern car, but I think it's small enough not to matter to me.

RWebb, I would if I could! But alas, I lack the sophistication and equipment to even use (or lay) strain gages. I'm more of a shade tree type ...

[petevb]

This is good work here.

I'm a little late, but I figured I'd jump in and add some thoughts.

I looked into this issue of rear end compliance last year by doing some simulation. It was relatively crude, not accurate enough to generate absolute values, but enough to get in the ballpark. I used a simplified model of the trailing arm and springplate to simulate, a stiff block stands in for the lever arm of the wheel:





When loaded with 700 kg of sideload (7 kn) the deflections look like this (10x magnification:





The result is right around half of what Burgermeister measured, or just under .1 degree per kn. However this model ignores important variables- no bearing deflection, no bushing deflection, no flex of the rear torsion tube. When I did further simulations including those I was getting numbers fairly close or a bit below the values Burgermeister measured here, though my car has ball joints at the A arm attachments so I'd expect some difference.

What I did was very rough- it was not intended to get to an exact value, only a relative understanding, but I feel pretty comfortable saying that the estimate above of .2 deg/kn is in the ballpark, and if anything I'd expect the compliance due to rubber bushings to be reduced as loads go up rather than increasing.

Comparing published data from other cars you can see that the measured value is actually relatively stiff, more than most street cars:



Not as stiff as more modern sports cars, however.

Now assuming the above is about right, what does it mean for suspension performance? There the answer is interesting:

In a relatively stiffly sprung car like mine the suspension generally doesn't move through a large range, only around +/- 20 mm or so. Over that range the stock 911 has limited camber gain built into the suspension, about .5 degrees. However the high side-loads seen in cornering (over 7 kn, depending on how heavy your car is and how sticky your tires are) mean you've actually lost much more camber to compliance (1.4 degrees in this example) than you gained in kinematic camber gain. Overall this doesn't sound too hot for running with limited static camber.

Of course the next question is what to do about it. The factory, of course asked the same question, and in some of the 935s the answer they came up with is shown below (excuse the poor cell phone pics taken from under cars at Rennsport last year).





These are fully fabricated A arms, and the "spring plate" in particular (responsible for much of the flex in the standard system) is much stiffer than the stock design. In addition to being stronger, one expects these would be significantly stiffer and hence have less camber loss than stock. Removing the flexibility under load also probably significantly helps the feel of the car- you can dial in more camber gain in multiple ways (by relocating the suspension pickups, etc) but I personally wonder what all this compliance feels like from behind the wheel.

After these experiments the factory ultimately went past the trailing arm entirely to go to the inherently stiffer multi-link designs we see from the 993 forward, which also offer the advantages of tunable compliance and toe curves. That's a different topic, however.

[Flieger]

Nice work, Pete. Thanks for sharing that with us. I had not seen those 935 rear A-arms before, either.

[RWebb]

thx - outstanding!


sounds like the added stiffness of the Al arms over steel is not such a big deal...

[petevb]

Originally Posted by RWebb

sounds like the added stiffness of the Al arms over steel is not such a big deal...

That's not really the conclusion I reached. While I didn't model the steel arms, so I don't know what the difference is, I concluded that anything that gives you more stiffness would be a good thing.

I see it as follows: If we want the outside tires roughly flat to the road in cornering, there are a few practical ways to achieve this.

Most obvious is static camber. We want the outside tires to be flat in the corner, so we start with them not flat in the staights. Unfortunately this has downsides- the not flat tires don't work as well in straight line acceleration and braking. So we'd like to minimize how much static camber we need. We can do this by:

1. Stiffer springs/ roll bars. These work primarilly by limiting body roll, and if the car rolls 2 degrees instead of 4 then we can use that much less static camber. The downside is that both ride and mechanical grip suffer.
   
2. Adding camber gain in the suspension. The 930, for example, has about .7 degrees of camber gain in 20mm of deflection (which is about what a stiff car sees in cornering) instead of a bit under .5 for the 911, so switching to a different rear suspension geometry like the 930 would allow you to reduce static camber by that difference, about .25 degrees. However increased camber gain isn't without downsides either- now when you go over a 20mm bump your wheels angle .7 degrees to the road and lose grip.
   
3. Decreased camber compliance. If we're losing ~1.4 degrees to camber compliance and we can double the stiffness, we need to run .7 degrees less static camber. That difference is larger than the gain easilly available with increased camber gain, and there is no downside other than the praticalities of achieving it (weight, complexity, cost, etc).

So all else being equal I'd go for as little camber compliance as possible, then add camber gain and static camber as needed. Modern car manufactures are getting religious on the subject of camber compliance from what I understand, and I tend to agree with that point of view.

Some ideas for ways 911s can address the issue:

1. Assuming the aluminum 911 trailing arm is actually stiffer I'd use it.
2. The 930 trailing arm will be stiffer still because it's shorter and also because the bearing package is larger and hence stiffer.
3. The next big one looks like going after the spring plate (especially if you're running coilovers, as this opens up options not available when the spring plate must still act like a spring).
4. Better than a spring plate is a fully fabricated trailing arm, like the 935s above. It looks like very large gains are available.
5. Supporting the torsion tube itself close to where the trailing arm attaches so that it flexes less (all of the suspension loads are trying to bend that tube).
6. Improved bushings/ ball joints at the attachment points.
7. Chucking it all and going to a multi-link...

[winders]

Originally Posted by petevb

Some ideas for ways 911s can address the issue:

1. Assuming the aluminum 911 trailing arm is actually stiffer I'd use it.
2. The 930 trailing arm will be stiffer still because it's shorter and also because the bearing package is larger and hence stiffer.
3. The next big one looks like going after the spring plate (especially if you're running coilovers, as this opens up options not available when the spring plate must still act like a spring).
4. Better than a spring plate is a fully fabricated trailing arm, like the 935s above. It looks like very large gains are available.
5. Supporting the torsion tube itself close to where the trailing arm attaches so that it flexes less (all of the suspension loads are trying to bend that tube).
6. Improved bushings/ ball joints at the attachment points.
7. Chucking it all and going to a multi-link...

Peter,

The rear suspension of my race car has coilovers, 930 trailing arms, spherical bearings, along with raised inner and out pickup points. The spring plates are modified stock spring plates.

What kind of gain would one expect to see by going with a stiffer (thicker) spring plate given the above setup? How much thicker would the spring plate need to be to make a significant difference. Any downside? Any of this change based on bias-ply versus radial tires?

Scott

[RWebb]

thx - since you found most of the flex in the spring plate, I figured the steel/Al arms was not a biggie

I did put Al arms on my '73 tho...

[petevb]

Originally Posted by winders

Any of this change based on bias-ply versus radial tires?

Are you running bias ply? They are much less camber sensitive, so it is less of an issue, however I don't understand those tires well enough to know how much less...

That said, the 935s shown above were also running bias-ply I assume, so that suggests it was worthwhile doing something. I also know of at least one heavilly modified early car running thicker springplates.

I personally wouldn't just go thicker- weight becomes an issue at some point, and you can create a more efficient structure by going out of plane.

I didn't get to a final design, but what I did play with showed the potential for up to a .04 kn/deg improvement from an optimized spring-plate. That's very rough, but it means you'd potentially have the ability to run in the range of 1/4 degree less static camber. That much improvement might come at around a 1 pound weight penatly per side, however. Also no guarentees here- a lot depends on the stiffness of the attachement to the trailing arm and other variables. I certainly felt it was worth looking at, however.

[petevb]

Originally Posted by RWebb

thx - since you found most of the flex in the spring plate, I figured the steel/Al arms was not a biggie

I did put Al arms on my '73 tho...

One could argue that, but I think I just feel like stiffer is better, so every little bit helps. The aluminum arms are probably helping...

[winders]

Originally Posted by petevb

Are you running bias ply? They are much less camber sensitive, so it is less of an issue, however I don't understand those tires well enough to know how much less...

That said, the 935s shown above were also running bias-ply I assume, so that suggests it was worthwhile doing something. I also know of at least one heavilly modified early car running thicker springplates.

I personally wouldn't just go thicker- weight becomes an issue at some point, and you can create a more efficient structure by going out of plane.

I didn't get to a final design, but what I did play with showed the potential for up to a .04 kn/deg improvement from an optimized spring-plate. That's very rough, but it means you'd potentially have the ability to run in the range of 1/4 degree less static camber. That much improvement might come at around a 1 pound weight penatly per side, however. Also no guarentees here- a lot depends on the stiffness of the attachement to the trailing arm and other variables. I certainly felt it was worth looking at, however.

Yes, I am running 11.5" front and 13" rear Goodyear bias-ply slicks so I would imagine that my car is generating a lot more lateral load than the average street car and probably not too far away from what the 935 generated.

We run very little (1 degree or less) static negative camber on these cars. More negative camber decreases lap times but the tire wear out to fast. So losing 1 degree of negative camber I would think is not such a good thing. My spring plates are mounted to the chassis a couple of inches more to the front of the car so they are longer. That means they probably deflect even more than stock.

What were you looking at as far as going out of plane? The rules for my class say I have to use the stock trailing arms but say nothing about the spring plates. I am not worried about a few pounds of weight....

Scott