Scaling and Arithmetic for Scale Models
by Ora Lassila / So Many Aircraft
Since all scale models use some particular scale, it is a good idea to learn what this actually means and to be able to do conversions between different scales. For example, the scale 1/72nd (often also written 1:72) means that the “real thing” is 72 times bigger than the model (or, conversely, the size of the model is 1/72nd of the real thing). Scaling means that every dimension changes in the same ratio. Since most scales originate from the Imperial measurement system, they can also be expressed differently, using inches and feet. For example, 1/72nd scale: 1 inch in the model is 6 feet in the real thing because 1 foot is 12 inches, and 6 x 12 = 72. This is also why 1/48th scale is sometimes (somewhat erroneously) referred to as "quarter scale" (1 inch in the model is 4 feet in the real thing, or ¼" is 1', so maybe "quarter inch scale" would be more appropriate).
Conversions between scales are easy. For example, if you want to convert from 1/72nd scale to 1/48th scale, you need to multiply every dimension by 1.5, because 72/48 = 1.5, and going in the opposite direction you divide everything by 1.5 (or multiply by ⅔; now aren't you glad that you paid attention in elementary school when they were explaining about fractions). Remembering whether to multiply or divide is easy to remember when you keep in mind that models in 1/72nd scale are smaller than models in 1/48th scale (in other words, the greater the denominator, the smaller the models).
If you need to figure out the scale of some scale plans you have, you need at least one known measurement of the real thing. For example, if you know that the wingspan is 15.7 m and the same dimension in your plans is 217 mm, then 15.7 m / 217 mm = 15700 mm / 217 mm = 72.35, and your scale is 1:72.35 (so almost exactly 1/72nd). I usually use multiple known dimensions just to confirm that I really know what the scale is, and that (say) the side view is in the same scale as the top view, etc.
Graphics programs let you scale dimensions using percentages. So if you need to scale up from 1/72nd to 1/48th, or 1.5 times as we discussed earlier, you scale by 150%. Similarly, if you go from 1/48th to 1/72nd, or 2/3rds, you scale by 66.67% (⅔ = 0.66666… ≈ 66.67/100 = 66.67%).
Scaling dialog in Adobe Illustrator.