Simplified Spring Rate Selection for an Existing Suspension

[Miatav8,MstrASE,A&P,F]

Okay, you've got a suspension now and just want to figure out an appropriate spring rate for garden variety coilover shocks. The following bases the rate on the dimensions of what you have built and your sporting intentions (CPM).
There may be errors and I'm not going too deep. I'm just trying to simplify the process.

If building a suspension around a particular coilover, such as used sportbike monoshocks with stiff springs and little travel, the math can be flipped around to help with that also.

I apologize if this seems to be an exact duplicate of some other topic.

Desired Cycles Per Minute, CPM

The higher the CPM, the higher the spring rate and damping requirement.

60-80: grandma cars to average vehicles, touring cars
80-100: sport touring cars to sports cars
100-130: limited use racing cars

Wheel Rate Required, WR

WR = ( desired CPM / 187.8 ) squared x sprung corner weight

Effective Spring Rate Required, ESR

ESR = WR x COS x ( MR ) squared

Coilover Mount Angles, Degrees from vertical and Cosine, COS

The greater the angle, the higher the spring rate and damping requirement.

(i.e., for 10 degree mount, 1 inch lower coilover pivot movement to .985 inch coilover piston movement)
10, .985
11, .982
12, .978
13, .974
14, .970
15, .966
16, .961
17, .956
18, .951
19, .946
20, .940

Motion Ratio, MR

The further the lower coilover pivot is from the LBJ, the higher the spring rate and damping requirement.

Examples in Print:

Champion LCA Dims:
LCA pivot cl to LBJ cl: 13.37"
LCA pivot cl to lower coilover pivot cl: 10.37"
MR: 1.29:1 (.77 coilover movement to 1 inch LBJ movement)

Gibbs LCA Dims:
LCA pivot cl to LBJ cl: 420 mm
LCA pivot cl to lower coilover pivot cl: 300 mm
MR: 1.4:1 ( .71 inch coilover movement to 1 inch LBJ movement)

Typical Example:
300 lb sprung corner weight (350 - 50 lbs unsprung weight, 1400 curb weight, 50/50 distribution)
100 CPM Goal (Good choice IMHO)
Gibbs LCA dims (could be improved)
20 degree coilover mounting angle (could be much better)

WR = ( 100/187.8 ) squared x 300
WR = ( .532 ) squared x 300
WR = .28328 x 300
WR = 84.984 # / "

ESR = WR x ( MR ) squared / COS
ESR = 84.984 x (1.41) squared / .940
ESR = 84.984 x 1.988 / .940
ESR = 168.948 / .940
ESR = 179.73 # / "

There is .667" of coilover piston movement for each inch of wheel movement at ride height (the ratio decreases in droop and increases in bump, but I am trying to keep this simple).
For 3 inches of droop, the coilover with a 179 # / " spring must compress 2 inches to sit at ride height, requiring a load of 358 lbs. Replacing the 179 # / " spring with a 150 # / " spring will achieve the desired ride height and reduce the CPM to 91.3.

ESR = 150
WR = 150 x .940 / 1.988
WR = 141 / 1.988
WR = 70.92 # / "
CPM = 187.8 x square root of WR / Sprung weight
CPM = 187.8 x square root of 70.92 / 300
CPM = 187.8 x square root of 236
CPM = 187.8 x .486
CPM = 91.3

[KB58]

It's a great starting point, but the problem is the +/-25% personal preference factor that makes the precision much less useful. The important thing to know is that the above will get you in the ballpark, but not necessarily give you the spring rate that you want.

[Rein]

Hey MiataV8, I know this thread is very old, but I'd like you ask you a favour. Would you perhaps be able to clarify what all the acronyms mean, and if possible a diagram would be a lot of help!

Another question regarding this; having a push rod working through a rocker arm, would this method also work?

Thanks

[Warpspeed]

My approach to this is to first stick any old available springs in at one end of the car and measure the compressed length at ride height. Also measure the bounce frequency with some dummy shocks and those very same springs.
With the springs removed from the car, measure the free length and measure an accurate spring rate.

You can then calculate the actual compressive load on those springs at ride height, which for me at least eliminates all this (often non linear) motion ratio squared stuff that can lead to errors.

The figures for bounce frequency, static compressive spring load, and spring rate should all tie in together if all the measured numbers are correct. You then have a starting point for selecting some new springs to give the required bounce frequency and ride height.

Most of the reference books work with direct wheel rates and vehicle corner weights, but few if any suspension linkages give a linear wheel to spring motion ratio. That is why I prefer to work with the loads on the actual springs themselves at ride height. Once you know what is happening right at the spring, spring rates and free lengths can make far more intuitive sense.