Bob, I measured the mandrel I used - it is .155". I used this mandrel for both the intake spring, using 7 turns of .013" music wire, and for the exhaust spring, using 9 turns of .022" music wire - both of these as called for in the Webster plans. I was pleasantly surprised by how well they turned out, since this was my first experience with making springs.
As noted in my build log, I made and used a simple "gripper" to guide and keep tension on the wire and set the lathe up to the closest tpi for the resulting spring. A couple of turns by hand to establish a flat beginning, then engaged the half nuts, let it turn the 7 or 9 turns, disengaged, and a couple of more turns to establish a flat ending. It helped tremendously that my lathe goes down to 30 rpm at its low end - much faster and I would have had difficulty controlling it. (If I didn't have the low speed, I would have turned the spindle by handle.)