To desing a good swithch isfor Lego is very dificult. So it would be much better to decide the distance betwen the radiuses after we have a persuading switch system. The most imprtent thig for swithes tht the track distence nad the end of the swithch have to be on round stud. I think it is importatn tdemand for the seith that we have to be able to use it to build multiple track stations.
So there are two Pythagorean round number what we can use for switch design:
(1) 3,4,5 stud sided triangle with arc of 33,87 deg and
(2) 5,12,13, stud sided triangle with arc of 22.62 deg (22,5 deg is acceptabel).
If we have such a good switch design it give us the track distance of 9, 10, 12 or 15 stud. Maybe not 12 stud is the best.