I paged through, but didn't read closely, the book Jon recommended and, while it seems a comprehensive treatment of the subject, I didn't see any mention of how to calculate the size of the mandrel on which the spring is wound.
Such a mandrel must have a diameter less than the desired ID of the finished spring since, due to spring-back, the spring diameter will increase once removed from the mandrel.
Kozo Hiraoka, a master builder of miniature live steam locomotives, studied the subject of mandrel sizing in depth and developed a set of equations for use by the DIY spring maker. His work was published in Home Shop Machinist, July/August 1987, pg. 30.
I converted his graphs and equations to computer code and developed a program to calculate mandrel size. Here's an example of the output...
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Kozo Hiraoka's SPRING WINDING MANDREL DIAMETER CALCULATION
Wire type: music wire [0] or phosphorus bronze (1) [0] ?
Wire diameter [0.04 in] ?
Spring inside diameter [0.203 in] ?
Recommended mandrel diameter = 0.180 in
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The program, MANDREL, is available for free on my page, the URL for which is in my sig.

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