Science Laws

5 Pages 1293 Words

Scaling laws are extremely simple observations about how physics works at different sizes. A well-known example is that a flea can jump dozens of times its height, while an elephant can't jump at all. Scaling laws tell us that this is a general rule: smaller things are less affected by gravity. This essay explains how scaling laws work, shows how to use them, and discusses the benefits of tinyness with regard to speed of operation, power density, functional density, and efficiency—four very important factors in the performance of any system.

Scaling laws provide a very simple, even simplistic approach to understanding the nanoscale. Detailed engineering requires more intricate calculations. But basic scaling law calculations, used with appropriate care, can show why technology based on nanoscale devices is expected to be extremely powerful by comparison with either biology or modern engineering.

Let's start with a scaling-law analysis of muscles vs. gravity in elephants and fleas. As a muscle shrinks, its strength decreases with its cross-sectional area, which is proportional to length times length. We write that in shorthand as strength ~ L2. (If you aren't comfortable with 'proportional to', just think 'equals': strength = L squared.) But the weight of the muscle is proportional to its volume: weight ~ L3. This means that strength vs. weight, a crude indicator of how high an organism can jump, is proportional to area divided by volume, which is L2 divided by L3 or L-1 (1/L). Strength-per-weight gets ten times better when an organism gets ten times smaller. A nanomachine, nearly a million times smaller than a flea, doesn't have to worry about gravity at all. If the number after the L is positive, then the quantity becomes larger or more important as size increases. If the number is negative, as it is for strength-per-weight, then the quantity becomes larger or more important as the system gets smaller.

Notice what just happ...