I find this entire discussion fascinating on a purely theoretical level, although the higher math is way beyond my long ago and now forgotten high school math.
Rich's simple method will create a natural easement with flex track, but don't the variables have to be fixed before it is of any use? That is you need a tangent section, a curved section, an offset, and then some way to determine where to start the easement and at what angle (slope?) to meet at a tangent with the curve. I know this is what Melgar is getting at, but I'll be ****ed if I understand it.
Karl has given us useful graphs for fixed radius track to show how little extra width you need to do a 180deg curve with easements. What would be useful are diagrams using sectional track that show which pieces are used and the overall width and length for both 90deg and 180deg turns. For example, if I want to do a layout with sectional track and a minimum radius of O-54. What are my options for easements of various lengths using wider radius? There would be several ways to do this depending on what radii were available and how gradual I wanted to make the easement or maybe how much real estate I had available without crowding my aisles.
An easement is actually a piece of a spiral, isn't that correct? And an easement using decreasing radii or arcs that meet is a sort of Fibonacci spiral.
