Bob, thanks for your reply. The project is to taper a cylindrical barrel to meet IBS rules. The barrel o.d. is 1.235'' but the muzzle end has to be reduced to .9584'' or less in a straight taper over 18 inches. I don't have a taper attachment for the lathe so I will be offsetting the tail stock center. There will be an insert in the chamber end and the muzzle will be recut after the tapering job is done.
My calculations indicate that the tail stock center has to be offset by .1383''. Although it probably can be done with conventional centres, I would like to try ball centres because of the offset. Plus, I want to stick with a 60 deg. chamfer because it seems to balance axial and radial forces nicely.
My noggin got sore from trying to do the trig calculations so I consulted the tables in my Machinery handbook for segments of a circle and got a royal headache. But I stuck with it and calculated that a 9/32'' ball would have a ring of contact in the 60 deg chamfer of .244''. So 9/32'' looks like the smallest I could use. Since the chamfer can be cut any width, a 5/16th ball could work also but with a contact ring of .270''.
Thanks very much for the links and your comments, much appreciated, it got me back in the game. Mike