OK, I started doing this to try and figure out the minimum distance I had to make the chassis brackets apart for a Jeep spring swap on the back of an LJ81 using Suzuki standard shackles. Considering I have seen a few RUF's go wrong, and a few types of lifted springs being too long for standard hanger positions, I thought I'd throw this out there for possible use, or discussion...
(before reading any of this, be aware of manufacturing differences, so measurements of components may differ!).
I figured I didn't need to simulate this super accurately, so I just treated the suspension geometry as a regular triangle.
The main leaf being side L (actually distance from eye to eye)
The shackle being side S (pin to pin)
and side C being the straight line distance between the shackle hanger and spring hanger on the chassis.
This of course is for the spring being totally flat, which is when the spring stands its biggest chance of inverting anyway.
A simple Theoretical model:
The most simplest dumbed down theory would be, when S+C =< L, inversion will occur. This however is crap, as it tells you very little information.
Instead I wanted to find out what the shackle angle would be with certain geometries. So using the law of cosines (click here if you don't know it), I rearranged it to get a way of determining the angle between the shackle and the main leaf when the leaf spring is flat.
A = arcos((L^2 + S^2 - C^2)/(2LS))
'A' being the angle. If the angle is 90 degrees, then your shackle is 90 degrees to your leaf spring, which is close to vertical on the front of a leaf sprung Suzuki (close enough anyway). If the angle is 0 degrees, it will invert; If you get a mathematical impossibility, then it will definitely invert!
Standard Suspension:
Front: L = 940mm, C = 910mm, S = 70mm........ A = 63 degrees.
Rear: L = 1000mm, C = 975mm, S = 70mm........ A = 67 degrees.
This shows why longer aftermarket springs are feasible, the angles are large (ie closer to vertical). Take one of the longer aftermarket rear leaves which causes inversion problems on some vehicles.... EFS.
EFS Rear: L = 1040mm, C = 975mm, S = 70mm........ A = 21 degrees.
A much much flatter shackle when the leaf spring is flat. However it is not 0 degrees, so why do they invert on some cars? The answer has to be spring bushes.
Accounting for Spring Bush compression:
I don't know typical stiffness values for spring bushes, but I wanted to make sure when I get around to welding brackets on the chassis, inversion is not going to be possible. So I went conservative, and assumed there were no spring bushes left in the shackle.
Introducing a new parameter, I'll call B for bush.....
B is the thickness of spring bush between the centre pin and the leaf or chassis eye. For a small size Suzuki bush this is about 8mm, 17mm for a large type bush. Add B to the effective L, and subtract from the effective C, to represent non existant spring bushes, and the shackle pins pushing hard against the outside of the eyes.
A = arcos(((L+B)^2 + S^2 - (C-B)^2)/(2(L-B)S))
Above examples redone:
Front: L = 940mm, C = 910mm, S = 70mm, B = 8mm........ A = 47 degrees.
Rear: L = 1000mm, C = 975mm, S = 70mm, B = 8mm........ A = 53 degrees.
EFS Rear: L = 1040mm, C = 975mm, S = 70mm, B = 8mm........ A = Not possible, ie will invert.
If the rear chassis bracket spacing was changed to 986mm, the EFS rear attained an angle of 0 degrees, meaning a C of greater than 986mm would not be able to invert one of these springs. I have measured one WT Sierra chassis with rear spacing of ~985mm which is close, and considering total failure of the spring bushes to the extent I am assuming is unlikely, these 985mm chassis would probably be fine.
Its also worth noting I run these springs on the back of my LJ80 which definitely has 975mm chassis bracket spacing, and they cannot quite invert. The reason for this is I have extended bumpstops which don't allow the leaf spring to completely flatten out (just something else to consider).
Anyway the numbers I was originally after:
Jeep CJ-7 front springs
I did some buggerising around in excel using these little relations, and came up with this:
CJ-7: L = 1130mm, C = 1075mm, S = 70mm, B = 6.5mm........
A = 37mm without spring bush deformation
A = 13 degrees without spring bushes.
So I got 1075mm as a minimum chassis distance (to the nearest 5mm) which won't invert a spring. The CJ-7 chassis uses about 1032mm from what I have found, but I believe they use longer shackles...
This is the minimum value, I could make the distance slightly larger to maintain a more vertical shackle. I still don't have a clue what it will be like at ride height though
Thats why I get the computer to do all the work for me 
thanks
