A Coherent System of Modeling Scales

This is just a thought experiment. It is NOT a proposal of any kind. I'm NOT advocating for the creation of any new modeling scales! That would only create an even bigger mess than we already have!

Having once owned and operated a hobby shop, it always struck me as odd how our common modeling scales are a huge mess of arbitrary proportions. Every community of modelers has their own preferred modeling scales (mostly owing to the desire to maintain compatibility with existing models, parts, and tooling), and so it's often difficult to combine models from different genres, franchises, or manufacturers in the same scene without something being disproportionate. The existing scales are an incoherent mess.

GenreIncoherent Scales
aircraft1/32, 1/72, 1/72, 1/144, 1/100, 1/200, 1/400
boats1/48, 1/50, 1/96, 1/144, 1/200, 1/350, 1/700
cars1/18, 1/24, 1/32, 1/43, 1/64
construction and farm equipment1/16, 1/32, 1/50
mecha1/35, 1/48, 1/60, 1/72, 1/100, 1/144
military1/16, 1/35, 1/48, 1/72, 1/87, 1/144
model railroadsX (1/5.5), III (1/18), II (1/22.5), F (1/23.32), G (1/22.5 to 1/32), H (1/24), A (1/29), 1 (1/32), US O (1/48), O (1/45), UK O (1/43.5), S (1/64), OO (1/76.2), HO (1/87.1), TT (1/120), UK N (1/148), JP N (1/150), N (1/160), Z (1/220), ZZ (1/300), T (1/450 to 1/500)
spacecraft1/48, 1/72, 1/100, 1/144, 1/200, 1/250-1/350

I've often wondered what a coherent system of modeling scales would look like in an ideal alternate reality, so I set about figuring this out.

My desired criteria:

  1. Scales should be equally-spaced logarithmically (i.e., the proportions of adjacent scales should always differ by the same factor).
  2. Fractional powers of 2 (e.g., 1/64, 1/128) are nice, but too far apart, so intermediate scales are needed.
  3. Scale identifiers should be numerical, and directly related to (but not necessarily directly proportional to) the scale they represent.
  4. Precision scratchbuilding materials (e.g., styrene and metal sheets, rods, and tubes) with round dimensions in one scale should also have round dimensions in as many other scales as possible, so suppliers and hobby shops aren't unduly burdened with needing to maintain too many SKUs.
  5. Large scales, such as those used by rideable miniature train clubs / attractions, should be accommodated as well.

The natural consequence of criteria 1 and 2 is that adjacent scales should differ by a factor of either √2 or √3. In the interest of criteria 4, I chose a factor of √2 (just like how ISO paper sizes work) so only two sets of SKUs would be needed for precision scratchbuilding materials (one for even-numbered scales and one for odd-numbered scales).

In this system, the exact proportion of a scale numbered n is calculated as 2-n/2 = 12n/2 = 1(√2)n.

Hypothetical ScaleComparable Incoherent Scales
#Proportionin / ft
020= 1/112″full-scale / prototype
12-1/2≈ 1/1.418.49″
22-2/2= 1/26″
32-3/2≈ 1/2.834.24″
42-4/2= 1/43″rideable rolling stock
52-5/2≈ 1/5.662.12″rideable rolling stock, X (1/5.5), 2-1/2" (1/4.8)
62-6/2= 1/81-1/2″rideable rolling stock, V gauge (≈1/8)
72-7/2≈ 1/11.31.06″IV gauge (≈1/11), 1” (1/12)
82-8/2= 1/163/4″III gauge (≈1/18)
92-9/2≈ 1/22.60.530″F (1/20.32), II gauge (1/22.5), G (1/22.5 to 1/32), 1/2" or H (1/24), A (1/29)
102-10/2= 1/323/8″1/35, I gauge (≈1/32)
112-11/2≈ 1/45.30.265″US O (1/48), O (1/45), UK O (1/43.5), 1/50
122-12/2= 1/643/16″1/60, S (1/64), 1/72
132-13/2≈ 1/90.50.133″OO (1/76.2), HO (1/87.1), 1/96, 1/100
142-14/2= 1/1283/32″TT (1/120), 1/144
152-15/2≈ 1/1810.0663″UK N (1/148), JP N (1/150), N (1/160), 1/200
162-16/2= 1/2563/64″Z (1/220), 1/250, ZZ (1/300)
172-17/2≈ 1/3620.0331″1/350, 1/400
182-18/2= 1/5123/128″T (1/450 to 1/500)
192-19/2≈ 1/7240.0166″1/700
202-20/2= 1/10243/256″1/1000

Benefits of these hypothetical modeling scales:

The system could be extended backwards (with negative integers) to accommodate larger-than-life models, though I'm not sure how useful that would be. If you're building something larger-than-life, it's probably something esoteric that doesn't need to be compatible with other models.