OK, this is truly Off Topic, but...

I am struggling with an analysis of a double spring problem.

The issue at hand is the Morgan front suspension. It has a sliding stub axle on a fixed kingpin (see this drawing). So the kingpin is fixed to the frame at both the upper and lower ends, and the stub axle holding the wheel slides up and down on the kingpin.

There are 2 springs, the upper main spring carrying the weight of the vehicle, and a shorter, stiffer rebound spring at the bottom. Now comes the hard part - there is a pre-compression load on the springs. So for the first part of motion, the springs interact (pushing against each other), until the rebound spring is fully extended. From then on the rebound spring is out of the picture and the wheel is riding the main spring.

What I have been trying to figure out is what the effective spring rate is for the initial part where the springs interact. There seems to be two opinions - that it is stiffer than the "only main spring" scenario because of the preload, and that it is less because the springs partially cancel each other.

I would imagine there is a simple standard formula for this, but I haven't ben able to find anything...