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Old 10-01-2013, 06:24 PM   #1
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Caster, SAI, Steering and Camber

So there’s been some recent discussion on camber and how it changes based on suspension articulation. Here’s one piece of the puzzle – the camber change due to steering inputs (the other piece being the camber change due to bump/droop travel).

There are two different parameters that define the camber change through steering– caster and SAI/Included Angle (IA) (both define the angle of the steering axis). Caster is the angle of the steering axis as viewed from the side of the car (side view). If it is perfectly vertical, caster is zero, and if the axis is tilted backward (top of strut farther back than the balljoint) then there is positive caster. Our cars nominally have 5.6 degrees of caster. Caster affects steering in that the more positive caster there is, the more the outside wheel in a turn will gain negative camber as the wheels are steered (and the inside wheel gains positive camber). It’s easier to imagine if caster were 90 degrees (parallel to the ground), “steering” the wheels in this scenario would result in pure camber change (completely unrealistic scenario but useful for illustrating the effect). And with zero caster, all steering inputs result in pure toe change. So caster angles between will result in some component of steer contributing to toe change and some component contributing to camber change.

Here is the equation that defines the camber as a function of caster:

CamberChange = SteerAngle*sin(CasterAngle)

Note that SteerAngle is the steer angle of the wheels, as opposed to the angle of the steering wheel. Our cars have a steering ratio of 13.2:1, so you can calculate the SteerAngle by looking at video of your driving (for autocross, steering wheel angle tends approach 90 degrees frequently – slalomy stuff, 180 degrees somewhat frequently, and occasionally can flirt with 270 degrees in the tightest of stuff, for tracking, it seems steering wheel angles are limited to ~90 degrees or less).

Assuming 5.6 degrees of caster, here is the camber gain of the outside wheel as a function of Steering Angle (all in degrees):
Code:
Steering
Wheel    Steer  Camber
Angle    Angle  Change
----------------------
0	  0	0.00
13	  1	-0.10
26	  2	-0.20
40	  3	-0.29
53	  4	-0.39
66	  5	-0.49
79	  6	-0.59
92	  7	-0.68
106	  8	-0.78
119	  9	-0.88
132	  10	-0.98
145	  11	-1.07
158	  12	-1.17
172	  13	-1.27
185	  14	-1.37
198	  15	-1.46
211	  16	-1.56
224	  17	-1.66
238	  18	-1.76
251	  19	-1.85
264	  20	-1.95
So at 6 degrees of steer angle, you gain about 0.6 degrees of camber, at 12 degrees of steer angle, you gain about 1.17 degrees of camber, and at 20 degrees of steer angle, you get almost 2 degrees of camber. The more you steer the wheel, the more camber change you will get.

Unfortunately, the other steering axis parameter, the SAI (really Included Angle), works the opposite way – as you steer, the outside wheel will lose negative camber. The SAI (also called the Kingpin Angle) is the tilt of the steering axis as viewed from the front of the vehicle. If the axis is tilted inward (upper mount inboard of the balljoint), this angle is positive. On our cars this is nominally 15.5 degrees. But SAI alone isn’t the driving factor, it’s actually the angle between the wheel and the steering axis, which is the Included Angle. This can be calculated by SAI+Wheel Camber (static wheel camber). So, with the nominal SAI of 15.5 degrees, and assuming a static wheel camber of -1.5 degrees, the Included Angle would be 15.5 + (-1.5) = 14 degrees (this is close to the scenario of a stock setup with the factory crash bolts).

So trying to envision why the camber changes due to Included Angle is a little more difficult than envisioning the change due to caster. I can kind of see it but admittedly it’s not crystal clear in my head. But here is the equation that defines the relationship:

CamberChange = IncludedAngle*(1-cos(SteerAngle))

Assuming 14 degrees of Included Angle, here is the camber change for the outside wheel as a function of Steer Angle (all in degrees):
Code:
Steering
Wheel    Steer  Camber
Angle    Angle  Change
----------------------
0	  0	0.00
13	  1	0.00
26	  2	0.01
40	  3	0.02
53	  4	0.03
66	  5	0.05
79	  6	0.08
92	  7	0.10
106	  8	0.14
119	  9	0.17
132	  10	0.21
145	  11	0.26
158	  12	0.31
172	  13	0.36
185	  14	0.42
198	  15	0.48
211	  16	0.54
224	  17	0.61
238	  18	0.69
251	  19	0.76
264	  20	0.84
So comparing the same checkpoints used from the Caster table, at 6 degrees of steer angle, you lose 0.08 degrees of camber, at 12 degrees of steer angle, you lose 0.31 degrees of camber, and at 20 degrees of steer angle, you lose about 0.8 degrees of camber. So overall these effects are less than the Caster “gains” - comparing the values at 12 degrees of steer you gain 1.17 degrees of camber due to caster but lose 0.31 degrees due to IA, for a net gain of 0.86 degrees.

So here’s a combined table that lays out the effects of Caster and IA, and shows the net effect (still assuming 5.6 deg caster and 14 deg IA) (all in degrees):
Code:
Steering        Camber Camber Camber
Wheel    Steer  Change Change Change
Angle    Angle (Caster) (IA)   (Net)
--------------------------------------
0	  0	0.00	0.00	0.00
13	  1	-0.10	0.00	-0.10
26	  2	-0.20	0.01	-0.19
40	  3	-0.29	0.02	-0.27
53	  4	-0.39	0.03	-0.36
66   	  5	-0.49	0.05	-0.43
79	  6	-0.59	0.08	-0.51
92	  7	-0.68	0.10	-0.58
106	  8	-0.78	0.14	-0.64
119	  9	-0.88	0.17	-0.70
132	  10	-0.97	0.21	-0.76
145	  11	-1.07	0.26	-0.81
158	  12	-1.16	0.31	-0.86
172	  13	-1.26	0.36	-0.90
185	  14	-1.35	0.42	-0.94
198	  15	-1.45	0.48	-0.97
211	  16	-1.54	0.54	-1.00
224	  17	-1.64	0.61	-1.03
238	  18	-1.73	0.69	-1.05
251	  19	-1.82	0.76	-1.06
264	  20	-1.92	0.84	-1.07
So depending on your setup – camber plates, camber bolts, static camber setting – there are a lot of different combinations of Caster/IA (i.e. getting camber at the camber bolt vs. the strut top, canted camber plates), but overall caster has more of an effect than SAI does, and the effects of both are less significant the lesser you need to use the steering wheel (track vs. autocross). Since the equations are all laid out you guys should be able to run through all of the hypotheticals of your setup options and conclude which path would be optimal for your intended usage.

Just to get an idea of the sensitivity of camber and IA, here's a camber table that assumes 7 degrees of caster (all in degrees):
Code:
Steering
Wheel    Steer  Camber
Angle    Angle  Change
----------------------
0	0	0.00
13	1	-0.12
26	2	-0.24
40	3	-0.37
53	4	-0.49
66	5	-0.61
79	6	-0.73
92	7	-0.85
106	8	-0.97
119	9	-1.10
132	10	-1.22
145	11	-1.34
158	12	-1.46
172	13	-1.58
185	14	-1.71
198	15	-1.83
211	16	-1.95
224	17	-2.07
238	18	-2.19
251	19	-2.32
264	20	-2.44
A quick check at 12 degrees of steer shows a camber gain of 1.46 degrees - about 0.3 more degrees of camber gained than when we had 5.6 degrees of caster - quite a bit.

And to see the sensitivity of IA, here's what the camber change looks like where IA is assumed to be 15 degrees (about what the factory stock IA would be without the camber bolt):
Code:
Steering
Wheel    Steer  Camber
Angle    Angle  Change
----------------------
0	0	0.00
13	1	0.00
26	2	0.01
40	3	0.02
53	4	0.04
66	5	0.06
79	6	0.08
92	7	0.11
106	8	0.15
119	9	0.18
132	10	0.23
145	11	0.28
158	12	0.33
172	13	0.38
185	14	0.45
198	15	0.51
211	16	0.58
224	17	0.66
238	18	0.73
251	19	0.82
264	20	0.90
So the sensitivity here isn't great. At 12 degrees of steer, we lost 0.33 degrees of camber, compared to losing 0.31 degrees of camber with 14 degrees of IA. So increasing IA by 1 degree only resulted in a camber change of 0.02 degrees at 12 degrees of steer... basically negligible.

As always, math checks are welcome.

(and I prefer tables to graphs because graphs require pic hosting and pics have a tendency to disappear over time, esp in older threads).
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Old 10-01-2013, 07:42 PM   #2
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question, if the IA is the steering axis angle - the static camber of the wheel, does that mean leaning the strut tops in without changing IA does not affect camber loss when steering wheel is turned?

So maybe the camber plates that only add camber but not caster are okay to use as long as IA isn't increased from stock?
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Old 10-01-2013, 11:30 PM   #3
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Quote:
Originally Posted by autobrz View Post
question, if the IA is the steering axis angle - the static camber of the wheel, does that mean leaning the strut tops in without changing IA does not affect camber loss when steering wheel is turned?

So maybe the camber plates that only add camber but not caster are okay to use as long as IA isn't increased from stock?
Correct, the camber change with steering from front-view effects are a function of IA, so if you dial in camber with a camber plate (change SAI) and don't change any adjustment at the camber bolt location (IA is the same), then the camber change with steering would be the same as before.

I think any camber plate would help, but the numbers indicate that additional caster can help a good bit, and has a lot more influence than IA. I think it can be more of a question of if you want to get more camber or more caster (as this is the tradeoff due to spring interference if a plate can adjust both independently). With more caster you can run less static camber and maybe improve tire wear and braking.
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Old 10-02-2013, 10:35 AM   #4
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Yeah, I never thought SAI/IA was as big of a deal as people were making it. Even in AutoX I rarely need more than 180 degrees of steering input. That's 0.4 on the outside tire which is easily compensated for with camber. And using crash bolts or a slotted coilover will reduce that as well by enabling the damper to stand up more for the same amount of negative camber.

So SAI/IA still gets a big *shrug* from me.
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Old 10-02-2013, 04:18 PM   #5
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Excellent post. I'd give you two likes if I could
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Old 10-02-2013, 06:03 PM   #6
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Sticky?
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Old 10-03-2013, 11:59 AM   #7
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Quote:
Originally Posted by Draco-REX View Post
Yeah, I never thought SAI/IA was as big of a deal as people were making it. Even in AutoX I rarely need more than 180 degrees of steering input. That's 0.4 on the outside tire which is easily compensated for with camber. And using crash bolts or a slotted coilover will reduce that as well by enabling the damper to stand up more for the same amount of negative camber.

So SAI/IA still gets a big *shrug* from me.
I was expecting the IA sensitivity to be a little greater, but I think the reality is that with our struts and baseline SAI/IA, it starts "high", and due to practical issues like tire/strut/spring interference there's not a lot of range of flexibility for IA. Sure, we probably have the freedom to adjust it +/- 2 degrees, but even so it doesn't make that much of a difference.

I think there's value in having a "low" SAI, but our cars will never be able to achieve that.

I think there are other benefits for low SAI other than just the camber affect - wishbones have low SAI (I think the 350Z has something like 8 deg of caster and only 6-7 deg SAI ), and of the wishbone cars I've driven the steering feels fantastic. The steering on the BRZ is awesome, it's accurate and quick and steady with good weighting and decent feedback, but there still seems to be some quality missing from it that I get from wishbone cars.

There have been some recent fancy strut designs (GM's HiPer Strut and Ford's RevoKnuckle) which reduce SAI quite a bit and seem to be "better" designs. I know they cite reduced or zero scrub radius and minimized torque steer as the main benefit. But I think it's possible to achieve minimal or zero scrub with wheel offset, so there must be some other benefit from making the SAI more vertical.

BMW has always run a lot of caster on their sporty strut, and they had some interesting things going on with their balljoint - IIRC it had dual ball joints that defined a virtual pivot point - I haven't researched enough to know what their reasoning was but they were definitely going out of their way to define a particular steering axis.

I'm kind of curious now to go see what Porsche strut/steering geometry looks like.
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Old 10-07-2013, 03:57 PM   #8
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Something else to consider is that changing camber vs. SAI also changes the effective lever arm length the spindle has on the strut. This will impact strut side loading and the friction that goes with it.

You can use camber adjustment at the strut and top mount to balance scrub radius, strut side loads, and camber change. For caster, I've heard run as much as you can tolerate. More caster means a duller turn-in feeling, some of which can be offset with toe out in the front.

Ultimately, if you can get the dynamic camber you need by adding caster while reducing static camber, it will improve braking performance. Strut cars suffer here as you have to run a ton of static camber to keep the tire happy under body roll and then braking performance suffers.

Something to consider, increasing SAI has a "leveling" effect on the camber gain. You can combine it with caster and less static camber so that camber starts lower for braking performance, builds quickly to accommodate steering loads, then levels off as body roll will hit a limit with tire adhesion limits and further camber gain will reduce tire contact patch.

I've heard of guys having good results with up to 20* SAI and 8-9* of caster on other strut platforms.
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Old 10-30-2013, 11:58 PM   #9
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From Speed Secrets:
“The more positive castor, the more the steering will self-center—which, generally, is a desirable effect. However, the more positive castor, the more effort it takes to turn the steering against this castor. There has to be a compromise between easy self-centering and heavy steering.
Castor also affects the camber when the steering is turned. The more positive castor, the more negative camber on the outside tire during cornering. This must be kept in mind when adjusting for the “optimum camber setting. Perhaps, instead of dialing in more static camber, you may be better off adjusting in more castor. Remember, this will result in more negative camber on the outside tire during cornering. This can be an important factor. Learn and understand castor.”
Excerpt From: Ross Bentley. “Speed Secrets.” iBooks. https://itun.es/us/ZuKhz.l

This seems to jive with your numbers. Agreed?

This topic is beginning to really interest me. Fantastic post BTW but I really need to study it more, a lot of info!

I'm thinking a good place to start is adding some caster via Whiteline's anti-drive caster kit and also getting some camber bolts. This should give some immediate benefit from the moderate caster increase and provide further adjustability through the bolts. Then, for the rear, possibly an adjustable Lower Control Arm kit.

Thoughts?
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Old 10-31-2013, 10:48 AM   #10
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Yeah, I think it all jives. If you did the WL ADK and the camber bolts you would be increasing caster and reducing IA so overall it would be a win-win in gaining negative camber through steering. I know the WL ADK kit has had some issues on other chassis, so just watch out for that.

So you can use the equations above to quantify the effects of what you're changing. In theory the more caster you have the less static camber you "need", but it also depends on a lot of other things, and also keep in mind the radius of your corners (and how much you will need to steer the wheels) will also affect that analysis.

For cars I've had in the past I could add around 0.5-0.75 degree of caster without it affecting the steering feel that much. Adding 1-1.5 deg of caster, while I'm sure it was good for camber, just started making things feel very... weird (not to mention making me steering pump groan). I think there's something to be said for keeping caster change within a certain %range from factory.
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Old 10-31-2013, 10:54 AM   #11
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i still don't think it jives

i mean, the net-effect of what is said is absolutely true.

but i can't help but think that the tire is forced to work harder and the contact patch isn't being as optimized on a car with heavy castor... it just seems that if you don't get it JUST RIGHT.. given castor, camber, sai, AND the vehicle body roll in degrees, to get the wheel flat on the ground, then you're gonna be scrubbing one part of the tire more than the other.

my own personal inclination is that the more roll stiffness you get.. (and drive on smooth tracks), the less you have to rely on static castor, camber and what not.

i just wish there was an animated 3-d model of this i could see...
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Old 10-31-2013, 01:05 PM   #12
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Quote:
Originally Posted by Wepeel View Post
Yeah, I think it all jives. If you did the WL ADK and the camber bolts you would be increasing caster and reducing IA so overall it would be a win-win in gaining negative camber through steering. I know the WL ADK kit has had some issues on other chassis, so just watch out for that.

For cars I've had in the past I could add around 0.5-0.75 degree of caster without it affecting the steering feel that much. Adding 1-1.5 deg of caster, while I'm sure it was good for camber, just started making things feel very... weird (not to mention making me steering pump groan). I think there's something to be said for keeping caster change within a certain %range from factory.
What sort of issues with the ADK? What else would you recommend to get .5 degree of positive caster?

I agree, just light variation from stock is preferrable.
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Old 10-31-2013, 01:53 PM   #13
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Good post. I find it useful because I use my car for drifting I run a good amount of front camber (-3 right now). The goal is to get the leading edge wheel as close to 0 degrees as possible at full lock under load to maintain as much contact patch and front end grip as possible mid drift.

On stock knuckles and steering components and -3 camber, I still have a bit of wheel flop (positive camber). Going with more negative camber will eliminate that, which gets more noticeable when you have more steering angle. Increasing/changing caster will also have an affect on the camber changes during steering.

The post/tables above give me a good idea of about where I need to be to get the desired effect that I'm looking for.

Thanks
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Old 10-31-2013, 02:29 PM   #14
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Quote:
Originally Posted by 7thgear View Post
i still don't think it jives

i mean, the net-effect of what is said is absolutely true.

but i can't help but think that the tire is forced to work harder and the contact patch isn't being as optimized on a car with heavy castor... it just seems that if you don't get it JUST RIGHT.. given castor, camber, sai, AND the vehicle body roll in degrees, to get the wheel flat on the ground, then you're gonna be scrubbing one part of the tire more than the other.

my own personal inclination is that the more roll stiffness you get.. (and drive on smooth tracks), the less you have to rely on static castor, camber and what not.

i just wish there was an animated 3-d model of this i could see...
You also have to take into account tire deflection as well. If you look at a Formula 1 car, you know it has virtually zero body roll and the best suspension geometry, but they still run multiple degrees of static camber. Watching the new infrared cameras this year, you can see tha the inside of the tires is heavily loaded with the outsides barely touching, but under heavy cornering loads the whole contact patch heats up.

Ultimately, there is no perfect setup or geometry. Even once you take the car, suspension design, and tires into account, you still have to tune for the track itself. Every corner is different, so everything is an exercise in compromise.

And THEN! after all that, there's the "black magic" of using those limitations in an "less-than-ideal" suspension geometry to gain favorable results out on track. Have a driver that's a little heavy on the throttle but has good slide control? A little mid-corner understeer would help balance power oversteer, and maybe help that driver through the tighter parts of the track.

Suspension tuning is an art because there is no ideal.
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