just to confuse the imperial thinking:
if i take a metre (39.4" )
and divide that into 22.5 parts, i get 44.44 mm = millimetre (1.75" )
if i divide these 44.44 mm into 22.5 parts, i get 1.975 mm (0.08" )
using those numbers, i divide one metre by 1.975 mm ( = 0.001975 metres), i get 506.33
so, scale 1:506.3 it should be. (for ship modellers a quite normal relation)
just for the fun of it:
an inch should be built at about 0.005 mm
a foot would be about 0.6 mm long.
for modeling in that scale one would need additional tools.
absolutely needed a looking glas.
recommended a microscope.
or, to put it into relation: a loco in 1:506.3 would reach up to the trouser's seam of your LGB stationmaster.

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