Model Scale, Part 1 – Scale

Scale is the most important term in model making. It is the main model’s characteristic, describing a size of the model in relation to life-size of the origin.
In US architecture scale usually based to inch/foot measurements and looks like, for example, 1” – 20’ or 1/8” – 1’, where, in this particular sample 1” on the model represents 20’ of life scale size, or 1/8” on the model is the equivalent of 1’ in life-size.
Communicating with architects we are using this system as well. However, we prefer to use scale system that is not based on any particular measurement. This scale called international, or engineering, or, sometimes, metric, although, like it was said before, this system is universal for any system as long as measurement units are the same. This scale represents how many measurement points of the origin are represented by one measurement point on the model and its record looks:

1 : X, or 1 / X and reads “one to X”

The scale describes by the following formula:

Scale = Lo/Lm

where Lo is Length of the origin and Lm is Length of the model.

It is important for model maker to operate with scale related calculations freely, as such calculations sometimes tricky and may lead to mistake.
Let’s analyze a situation where we have a set of drawings in 1:Y scale and have to build model in 1:X scale. In order to recalculate drawing into model size easily we have to use the formula above. Let’s put into the formula all that known to us.
Lo in this case will look like this:

Lo = Ld x Y

where Ld is Length on the drawing and the whole formula for scale X will look like this:

X = Ld x Y/Lm

The only unknown in the equation above is Lm, which is the measurement that we will have to calculate multiple times during the model’s fabrication.
Than

Lm = Ld x Y/ X

Let’s separate Y / X from this formula as it is a part of calculation which will be constant for finding each particular measurement, and let’s call it recalculation coefficient k, where

k = Y/X

Than our main formula transforms into:

Lm = Ld x k

All we have to do now is to take any measurement from the drawing, multiply it to k and to find its equivalent in model’s scale in a simple and elegant way.

It is important to remember that scale applies only on linear measurements. Never apply scale on area measurements or, God forbid, value – it will be a grave mistake.