History of the Scales

Before the plastic model kit industry

Hobbyists' scale models derive from those used by the firms which made the full-sized products. Originally, a "scale" was a physical measuring instrument, a notion which survives as concerns weight. First among scales are the rulers that are triangular in cross-section and called architect's scales or engineer's scales. The terminology used was of this manner: "scale size to full size", or the reverse. An architect's scale was used to make the first affordable models: doll houses and their furniture. Its popular scales for these miniatures were "one inch to the foot" and "one-half inch to the foot"; there is also "three-quarters inch to the foot".

The proportion of the model to the prototype was originally called "size", as in "full-sized" or "half-sized", as used on a blueprint for making something that would fit on a workbench.

Shipyards were the first to use the scales to make models of things larger than a house. The scales they used were expressed in a different manner: "one-foot-to-the-inch" through "six-feet-to-the-inch" were common. During the Second World War, battleship models were made "eight-foot-to-the-inch", in the later phrasing, "one-eighth-inch to the foot"; you will find these models used for training workers in maritime museums. The model ship would be referred to as "one-ninety-sixth size", or "1/96th", but rarely, as there were few scales commonly used; it couldn't possibly be "1/98th scale", for example.

There were also rotary instruments in which one would line up marks on two dials to be able to translate measurements from units on the prototype to units on the model. After the production of kits to make plastic models became an industry, there were developed rulers marked in the model units and which are called scales.
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Comparing scales

Phrases used are those of "larger" and "smaller" scales. The scale of 1/8"-to-the-foot is a larger scale than 1/16"-to-the-foot, even though the denominator is smaller. So a larger model is made to a larger scale. You can remember this in that a full-size, or full-scale, model is larger than a half-size model.
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Origins of the plastic model kit

For aircraft recognition in the Second World War, the RAF selected making models to the scale of "one-sixth inch to the foot" (which was two British lines, a legal division of length which didn't make it to America, besides being a standard shipyard scale). Although some consumer models were sold pre-war in Britain to this scale, the airmens' models were pressed out of ground-up old rubber tires. This is of course the still-popular "one-seventy-second size".

It wasn't predestined to succeed; there were competitors. The US Navy, in contrast, had metal models made to the proportion 1:432, which is "nine-feet-to-the-quarter-inch". At this scale, a model six feet away looked as the prototype would at about half a statute mile; and at seven feet, at about half a nautical mile.

After the war, firms that moulded models from polystyrene entered the consumer marketplace, the American firm Revell notably offering a model of the Royal Coach around the time of the 1953 coronation. In the early years, firms offered models of aircraft and ships in "fit-the-box" size. A box that would make an impressive gift was specified, and a mould was crafted to make a model that wouldn't ludicrously slide around inside. Modellers could not compare models, nor switch parts from one kit to another. It was the British firm Airfix that brought the idea of the constant scale to the marketplace, and they picked the RAF's scale.

In the 1960s, the company Monogram offered an aircraft actually labeled as ¼" scale, which may have been a common contraction in factories. They meant "one-quarter-inch to the foot", or "one-forty-eighth size". Shortly thereafter, hobbyists lost the ability to distinguish the two, and now the proportion is referred to as scale.
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Terminology

The terms and the means of writing them down have changed, and for model kits they are now standardized for the European Union. In English-speaking countries, such terms as "1/72" were used, but the format with a colon as "1:72" is often preferred. The slash format is usually avoided with decimal fractions: "1/76.2" is usually not used; it's "1:76.2" instead. That hybrid OO gauge can also be expressed by explicitly using a mixed system of units as "4 mm:1 ft" or "1 mm:3 in", but the dimensionless form makes comparison with other scales easier.
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Rational choice of scales

The nominal height of a man is simple in the inch-based system: six feet. Many traditional scales are derived so that a figure of such a height against the model can be readily imagined as a simple relation to an inch. Although the metric system has specified a limited series of scales for blueprints and maps, when it comes to models, there may be a problem with these scales for a readily imagined person of 180 centimetres. Model railways have the additional difficulty of having to present the rail gauge as a simple number, the height of a person being secondary. Trade authorities in metric countries are attempting to specify scales that are simple mulitiples of 2 and 5, but neither tracks nor people seem to fit. Or it could be that they are using the statement of rationalization for competitive advantage, so that people will buy models of their scale and not those of another manufacturing country?

On the other hand, wargaming scales have traditionally been traced to metric system, where the number of millimetres relate to the relative height of the human figure based on 180 cm standard man. Therefore 25 mm scale (popular in historical and fantasy wargaming) refers to 1:72 scale, whilst the 15 mm scale (nowadays the most popular scake in ancient, medieval and Renaissance wargaming) refers to 1:120 scale. Likewise, 50 mm scale is the same as 1:35 military model scale, and 5 mm equals 1:350 naval scale.