One of the more difficult tasks in spring winding is to determine what size arbor to use. Since the newly-wound spring will "uncoil" a bit when removed from the winding arbor, the arbor generally needs to have an OD smaller than the desired final ID for the spring.
Kozo Hiraoka, the genius builder of model locomotives, addressed this problem some years ago in HSM and produced a set of nomographs to determine the required arbor size from the spring specifications.
I converted his work into equations and programmed them. They're available from my page - look for the MANDREL archive. I've used this program to make several springs and it's worked very well for me.