Scale and Gauge
A theoretical dissertation on model railway manufacturing
standards.
With reference to the anomolous specification of metric to
imperial ratios, eg. 3.5mm to the foot.
My model train collection happens to include three "sizes", which are generally known by gauge (track width) as "0" (zero, or oh), 00 (zero zero, or oh oh) and H0 (half zero, or half oh, or haitch oh).
Track gauge is one thing that needs to be defined in a model railway. The
other criteria is scale, or what ratio is used to build the
rolling stock.
But the basic standard required in the manufacture of toy trains was the track,
which took precedent over the scale of the rolling stock for both practical
and marketing reasons. Within limits, it did not matter if each piece of rolling
stock differed in scale (ratio), so long as they ran on the same track, and
ran without mishap. So how these track gauges, and their associated scales
came into the toy market is quite interesting.
The overall question of how scales or ratios in drawings, and plans evolved into use over time, is equally fascinating. It also involves models of all types. Models of boats, farm implements, and structures are as old as mankind. Examples from thousands of years ago, made of lasting materials such as bone, exist in museums everywhere. Our model scales today, still relate to the British imperial measurement system, where a foot is divided into 12 parts, or inches. Engineering and architectural plans were drawn at various scales depending on the size of the real object, and the size of the drawing material to be used. A bridge may be drawn at 1/8 of an inch (1/8") to the foot (1/96th); detail of a locomotive firebox may be at 1inch to the foot (1/12th). So most scales are derivatives of 1/12th part, even in scale plastic modelling, where 1:48 and 1:72 are ubiquitous.
To illustrate the concept, I include a photo of 2 traction engine models taken from a Christies catalogue for 1997. The first traction/ploughing engine is called a 2" model, or 2 inches to the foot (1/6th scale or 1:6)  two inches on the model is equivalent to 1 foot on the real machine. The second model is a 3" model, or 1/4 scale. This method of describing a model in inches, usually applies only to road machines. Railway models use other nomenclatures.
I have a theory that all our modern model train scales
have devolved from the English architectural and engineering drawing reliance
on imperial 12ths of a foot. An example
scale of 1/8 of an inch equals 1 foot (12 inches), was widely used in building
and engineering. It is termed an imperial scale,
and it goes without saying, that the ratio of drawing or
model:fullsize is therefore 1:96. Equally used scales were 1/4" to the
foot (1:48), 3/8" to the foot (1:32),
and even 1.1/2" to the foot (1:8, or 1/8th scale). It is the latter scale
that is used in live steam engines running on 7.1/4 inch gauge track. And
below is an example of half that size, running on 3.1/2 inch gauge track,
at a ratio of 1/16th. (If you multiply 3.1/2 inch x 16, you get 56 inches,
which is close enough to the 4' 8.1/2 inches of the full size railway gauge).
The photo is from a Christies catalogue, 1997.
The evolution of modelling railways starts at the largest, and devolves to the smallest. So for model trains suitable for playing in the home, at first we had gauge 1, then 0, then half0, and so on down to TT, N and Z scales. I use the English as the pivotal factor in my theory, because it is they whose blossoming market for toy trains in the late 1800s, early 1900s, could dictate some terms to continental manufacturers. It was people like Marklin, Bing and Carette on the continent, who had the production facility and expertise to satisfy English demands.
1 gauge (called the Royal gauge by Marklin to this day) is 1:32, or 3/8 (0.375) inch to the foot. 1/32nd of the real standard railway gauge of 1435mm, is exactly 45mm! The imperial specification for 1 gauge track is 1.3/4 inches, which is out of gauge by 0.9mm, and is probably not of sufficient an error to cause running problems at this size. I am not sufficiently familiar with this gauge to make further comment. (Side note: S scale or gauge, was half the size of gauge 1, at a ratio of 1:64 with track of 22.43mm (imperial 7/8 inch), widely used in the USA and elsewhere).
Let us suppose that Mr BassettLowke (a well known British modelling engineer
of the early 1900s) approached a continental manufacturer XX to make models
to run on 1 gauge track, at a scale of 1:32,or 3/8 (0.375)
inch to the foot. XX does not have imperial measuring equipment,
so what is the nearest metric equivalent by which Mr BLs order will be satisfied?
3/8 inch is basically 10mm. So British 1 gauge was built
to plans drawn at 10mm to the foot, a ratio that is a mix
of metric and imperial! It runs on a gauge 1 track of 45mm,
or perhaps more precisely, 44.1mm (1.3/4 inches).
And the same theory of metric:imperial ratios applies through
0 (zero) gauge, and H0 (half zero).
So we get to the smaller 0 (zero) gauge:  this is 1:48, or 1/4 inch to the foot. Specifying 7mm to the foot (as leaning to a slightly larger construction for reasons practical for mechanisms) would have been the best means of instructing a continental manufacturer as regards scale (ratio). On this basis, 0 gauge in England ends up being 1:43.5, running on 32mm gauge track.
H0  halfzero (H0) is 3.5mm (half of 7mm) to the foot, and instead of being true to the architectural 1:96, ends up being 1:87, and runs on track close to scale at 16.5mm. Considering that 16.5mm track was already in use in Britain by virtue of Bing's introductory tabletop railways in 1923 (marketed by BassetLowke), it seems sensible then (as in 0 gauge), to specify a slightly larger construction scale.
So in Britain, trains running on 16.5mm track will henceforth be built at
4mm to the foot (1:76), instead of 3.5mm. So 4mm to the foot is 00 ratio
models, running on H0 gauge track. By 1938, you have people like Meccano Ltd
(Hornby Dublo) producing 00 gauge/scale trains for 16.5mm track. Even though
the marketing is for 00 model trains, the English language is eqully satisfied
with the term "oh oh", and Meccano made use of this fact by calling
their tabletop model trains "Dublo", the phonetic equivalent.
Henry Greenly, and his compatriot Ernest Steel*, both figureheads in English
model standards and consumer production in the 1900s, actually quoted scales
thus:
Gauge 1  1/30
Gauge 0 – 1/44
Gauge 00 – 1/77
It appears that in the tiny world of minaturisation, with then available materials
and technology, rigid specification was not necessary, so long as the things
worked. In my theory above, the variation from architectural/engineering true
scales, occurred both out of the metric:imperial ratios,
and the practicalities of fitting mechanisms.
Footnote* From a booklet "Planning and Layout" by Henry Greenly, new edition published 1947.
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How do real world modellers view scale and gauge?
An interview with an 80 year old Märklin employee:
Here's an extract from an interview with Friedrich Rieker, the inventor of the Märklin crocodile. He made the first Crocodiles in gauge 0 and I, and the quote is taken from 'Märklin: Die Legende lebt', published in 2009 and edited by Klaus Eckert. I have the book, but I am indebted to Mark of Luxembourg for the translation and words in italics:
"Alles is ganz neu konstruiert worden. Es war ja auch nichts vorrätig. Also, es hat schon Schwierigkeiten gegeben bei der Entwicklung. Man hat genau berechnen müssen, wie lang man die Lok macht und wie hoch, damit sie überall durchkommt. [...] Es hat nicht genau aufs Zehntel gestimmt. Hauptsache, die Lok hat ein gutes Bild abgegeben und auch funktioniert. Das war das Wichtigste."
Mr Rieker was talking about the first Crocodile prototype he made. Translation: "Everything had to be built from scratch. There was nothing in stock. There were definitely problems in designing this locomotive. One had to calculate exactly how long and how high the locomotive needed to be to make sure that it would pass everywhere. [He probably means tunnels, bridges, curves and turnovers.] [...] The measurements were not 100% exact. The main thing was that the locomotive looked good and worked as well. Those were the most important points."
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Some mathematical musings:
So 1:87 (H0) ends up being an odd scale, unlike 1:100 which would seem to
be more in keeping with continental metrics!
Nominally, it is quoted in the world of modelling (outside of the European
continent) as 3.5mm:1foot. The use of metric:imperial as
a ratio, is explained above.
1:87 does not make any sense in the metric world. 1:100, or 1:80 might make
some sense. Yes, 1:80 is used for HO modelling in Japan, running on 16.5mm
track, and continental brands widely used a scale of anything between 1:82
and 1:96 depending on the size of the model, to ensure troublefree running
on that gauge.
In the imperial measurement world, 1:96 makes sense, because that is 1/8inch:1foot.
If English or US model makers who first ventured in to something small, and
tabletop, for their own markets, sent plans to German manufacturers, with
imperial measurements of feet, they may have simply instructed as follows

this 72.1/2 foot engine has to be 10 inches long, and it has to run on tracks
of 2/3 of an inch.
72.5 feet at 10 inches = 1:87
2/3 of an inch gauge track = 16.5mm, and at 4' 8.1/2"(1435mm) = 86.96
times (1:87).
Now if you take 12 inches = 1 foot = 302.4mm, divide by 3.5mm (3.5mm:1foot),
then the ratio is 1:86.4.
What a fascinating subject (for a rainy afternoon).
Of course, it does not matter much what we think, this information is not
going to turn the modelling world on its head.
What do you think?
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