Hog away, I love this kind of discussion (ask Uwe

)
First point, the 'ratio squared' thing. I was given that calculation by 'Pooky' (on northloop.co.uk and bmwtrackzone.com). He's a suspension designer/engineer for Jaguar. I used it as rote initially, but thinking about it further it does make sense. Not only does the coilover spring have more static leverage than the OE spring, but
it is also compressed more in the same ratio.
Here's a simple diagram :
Let's assume the lower position in the diagram is with the suspension fully unloaded and the upper is at static sag.
Each spring must provide a force, in the compressed position, sufficient to support the weight of the car. We'll assume for simplicity's sake that this weight acts through the coilover point as opposed to the hub (which sits a short way pivot-ward) and also that the OE spring perch is half-way between the coilover point and the pivot.
One side of the rear of an E30 weighs c. 250Kg, so this is the force that must be developed.
The OE spring is at a disadvantage here as it acts on a point half-way up the trailing arm; it must therefore develop 500Kg in order to support the car, where the coilover spring need develop only 250Kg. This is the static leverage ratio.
Now let's consider how these forces are developed. Look at the arcs described by the movement of the spring attachment points - these show how much each spring is compressed. Notice that the coilover spring is compressed twice as much as the OE spring for the same suspension movement. This means that it will develop the same force as the OE spring with only half the spring rate.
The coilover spring therefore need only develop half the force of the OE spring on being compressed twice as much, so its rate will be 1/4 as high - the
square of the ratio of distance from the pivot.
Does that make sense now?
Aaaand back to ARBs
If I was serious about going fast on this upcoming track day, I'd either leave the stock rear ARB in place or fit an even softer one.
But I'm not. The day was organised on Scoobynet; most of the cars there will have twice as much power as me, some even more, so I'm just going to go as sideways as I can and have a laugh. To this end, a stiffer rear bar will reduce rear grip nicely and let me play
I'm in full agreement with the comments made about high spring rates making ARBs redundant.
Re : Jhonno's point about using ARBs to tune suspension....
What you
can do with adjustable bars is to move the roll centre forward or backward. This can have a large impact on the car's handling; see my point above about using stiff rear bars in FWD hatches.
I would hesitate to attempt altering the weight distribution of a car by meddling with spring perch heights, though this adjustment is useful for corner-weighting. If weight distribution needs altering, move some weight!
The pic of Jhonno's car is a little misleading; it's about mid-way around the Karussell so it's cornering at over a G, on 45 degree banking.
I'm fairly Welsh......