Length halves, weight drops by eight
Why Is a Model Never Quite Right?
Shrinking a thing shrinks its length, its area and its volume by three different amounts.
-
Step 1 of 5
Length is the only thing that halves.
Halve a model and every measurement along it halves — height, width, the length of a leg. That much is intuitive.
-
Step 2 of 5
Area falls by four.
Surfaces are two lengths multiplied together, so halving both halves twice. A model at half scale has a quarter of the paint to cover.
-
Step 3 of 5
Volume falls by eight.
Volume is three lengths multiplied. Half scale means an eighth of the material, and so an eighth of the weight.
-
Step 4 of 5
That is why models do not behave right.
A model boat is far too light for its sail area and bobs wrongly. A model bridge is far too strong for its weight and cannot fall down properly.
-
Step 5 of 5
And why giants could not exist.
Double a person and their weight goes up eight times while their bone cross-section goes up only four. The legs cannot carry it.
This is why insects can be thin-legged and elephants cannot, and why a mouse survives a fall that kills a horse.
The short version
Halving a length quarters the area and cuts the volume to an eighth, so models never behave like the thing they copy.
Try it yourself
Build a cube from 8 sugar cubes, then one from 27. The side went up by half again; the weight more than tripled.
Topics