A bit more on transition curves. The wikipedia page has a very useful animated GIF:

https://en.wikipedia.org/wiki/Track_transition_curve#/media/File:CornuSprialAnimation.gif

If you imagine two such curves connected back to back then the result would be a sweeping "S" curve, just like the real railway! Without going into the math (I was never very good at calculus) it would appear that it is possible to work backwards from previously defined minimum radii, even drawing the curves by hand.

In my working life I did a lot of hand contouring of maps - this technique often proved to be more acceptable than computer driven contouring (which tries to honor all the data all the time, even using smoothing and gridding algorithms). I have come to the conclusion that hand contouring is more acceptable because it uses a combination of three distinct radii that are built in to all of us - Simply put, the pencil is held in the hand and curves are made by rotating the pen using the shoulder, elbow and wrist joints. In this way it is possible to emulate a Euler Curve.

The next challenge would be to transfer the scaled down plan to the real terrain, particularly is the terrain is relatively rough. That now becomes a work in progress.