In modelling, why are the scales used so random?

When choosing a scale model, you'll be confronted with a huge range of scales to choose from, the most common aircraft, boats and cars etc will fall into a spectrum between 1:148 and 1:24 scale with 1:72, 1:50, 1:48 and 1:32 representing most of the middle ground. But where do these scales come from? and why do they seem so random?

The truth is, they are not manufacturer's random choices of scale that have coincidently ended up becoming common sizes on the model shop's shelves, and there is often a logical explanation for the seemingly 'plucked out of the air' scales used by manufacturers of scale models.

When dissected, 1:48 scale equates to 1/4 inch of model representing 1 foot of prototype. This measurement ends up being represented as 1:48 scale because there are 48 quarters of an inch in one foot meaning the prototype is 48 times larger than the model. When 1:72 scale is dissected, it equates to 1 inch of model to 6 foot of prototype, there are 72 inches in 6 feet, therefore the scale becomes 1:72 and so on. When thought of in inches, both these sizes make for sensible and logical choices when manufacturing a scale model, but if feet and inches were used as a key, you would be presented with 1/4"/1' vs 1"/6' which doesn't help the end-user to identify how large the scale of a model is in comparison to each other. The much simpler scale representation is much more to the point, comparable and understandable for the end-user.

While this explanation goes some way to justifying the use of some of the more odd scales, others scales such as 1:50 or 1:100 need no adjustment to be understood due to their countries of origin using the metric system which doesn't have complicated fractions to deal with, these scales were probable born from the use of a nice round number which fits neatly into our idea of the norm, this explains why these days we have 1:48 and 1:50 scales so close together, a simple case of two countries producing a desirably sized model but using different metrics to achieve it.

Other scales were specifically designed for an intended purpose, 1:144 scale, for example, was commissioned by the War Department to produce models in a scale that had the correct trade-off between size and detail for use as aircraft identification models for American soldiers and the scale simply remained in production after WWII.

The oddballs of scale seem to be ones known as box scale, here the scale does appear to be random, but with a good excuse. These now rare scales was produced to cut costs and were manufactured to fit models into pre-existing box sizes, hence the name.

There are many perceived random scales with no obvious explanation as to how they came about, but dig a little deeper and there will be a reason for their existence.