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Old 10-01-2013, 05:24 PM   #1
Wepeel
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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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