A question which semi-regularly comes up here is "How [strong, fast, hungry, etc.] would [something] be if I scale its dimensions by [factor]?"
So we have some common language, let's call the scaling factor S in this question. Drawing from Gulliver's Travels, a Lilliputian (human, scaled down 10x) has S=0.1, and a typical resident of Brobdingnag (human, scaled up 10x) has S=10.
How can we easily distinguish between the following common cases when discussing this?
- S^0: [Attribute] is proportional to original size.
- S^1: [Attribute] is proportional to length. "How many rods laid end-to-end?"
- S^2: [Attribute] is proportional to area. "How much food will my field produce?"
- S^3: [Attribute] is proportional to volume. "How much will my creature eat?"
- S^(2/3): [Attribute] is proportional to area/mass. "How many of its own kind can an X lift when scaled, using the same muscles?"
- S^(3/2): [Attribute] is proportional to mass/area. "How much more efficient is using the same material to make a bigger gasbag for my airship?"
A good system will be fairly easily read by newcomers, and understood at a glance by anyone who is around regularly. A single-common-English-word description for each class which is easily distinguished would be ideal.
Tagged as science-based and hard-science for questions which require these explanations, and outdated-science for typical uses of this scaling. Not mentioning (say) inverse-square relationships because those tend not to be an entire system being size-changed, and typically are easier to communicate.