FE = flat map = euclidean geometry = no deformation = no projection, only a scale.

If you'd have to draw a map of a FE, just imagine 26 rows with the numbers 1 to 26 and 26 columns with the letters A to Z, forming 26 x 26 squares, each representing roughly 1,000 miles.

Using the simples laws of geometry (and why should it be different because we are dealing with flat surfaces), we know that any distance in square F12 = the ones in V5.

This is valid using any scale.

I don't see the reason why you want to use anything more complicated than this.