Fundamental parameters of a steam loco

During the construcion of my model I perpetualy came back to questioning myself and people around, how does the scaled model work as compared to protoype and how should it be optimally tuned for best effects.

Some questions of this sort can be answered straight away by observing certain scaling laws. Below I will derive some of them.


In a faithful model all details are reproduced in the same scale 1:k. Thus all distances decrase by k, all areas by k2 and volumes (and masses approximately too) by k3. This is illustated in a table below:
Scale Gauge Surface Volume
1:1 1435 1m2 1m3
VI 1:5,5260 (10¼") 331cm2 6.01dm3
V 1:8 184 (7¼") 156cm2 1.95dm3
IV 1:11 127 (5") 82.6cm2 751cm3
III 1:16 89 (3½") 39.1cm2 244cm3
II 1:22,5 64 (2½") 19.8cm2 87.8cm3
I 1:32 45 (1¾") 9.77cm2 30.5cm3
O 1:45 32 (1¼") 4.94cm2 11cm3
S 1:64 22,5 2.44cm2 3.81cm3
HO 1:87 16,5 1.32cm2 1.52cm3
TT 1:120 12 69.4mm2 0.579cm3
The rest will be translated...