Minimum Radius of Model Train Track Curves

For some time now I have been trying to work out a mathematical formula to give and indication of the "Minimum Radius of Track curves" so that for say "G" or G1" locos I could use as a starting point to determine what curve of track I could layout in my garage and then test a loco on a piece of track set to that calculation.

I have thought that the minimum curve radius must be related to :-

  1. the side movement possible of a set of wheels relative to the frames holding the wheels and
  2. the distance between the outer most set of driving wheels and
  3. excluding any widening of the gauge in a curve.
Looking through Tubal Cain's book "Model Engineer's Handbook" I came across the formula relating the above mentioned items and introducing to me a term that I had not come across before VERSIN !!!.

Then I thought how on earth do I transpose the formula, as it was a long time ago that I did "A" level maths at school so I emailed a radio amateur friend who took a look at it and came up with:

It works out curves as I would have expected !