Variable pitch spring calculations

[Malaps]

Hi,
does anyone know how to calculate the current spring constant of a variable pitch spring when under compression. Since some of its coils get inactive when compressed the stiffness is increasing and consequently “k” is changing as well, is there an equation I can use to calculate the new spring value after the spring is compressed by a distance x?

 

[Tom.G]

Optimization Design and Calculation of the
Variable Stiffness Coil Spring Applied to Vehicles
https://www.ijsr.net/archive/v3i6/MDIwMTQ4MTk=.pdf

(above, and many more, found with:
http://www.google.com/search?&q=calculating+variable+pitch+spring)

Cheers,
Tom