Scale: The Universal Laws of Life and Death in Organisms, Cities and Companies

by Geoffrey West

He realized that the volume of cargo a ship could carry increases as the cube of its dimensions (like its weight), whereas the strength of the drag forces it experiences as it travels through water increases as the cross-sectional area of its hull and therefore only as the square of its dimensions. This is just like Galileo’s conclusions for how the strength of beams and limbs scale with body weight. In both cases the strength increases more slowly than the corresponding weight following a 2⁄3 power scaling law. Thus the strength of the hydrodynamic drag forces on a ship relative to the weight of the cargo it can carry decreases in direct proportion to the length of the ship. Or to put it the other way around: the weight of its cargo relative to the drag forces its engines need to overcome systematically increases the bigger the ship. In other words, a larger ship requires proportionately less fuel to transport each ton of cargo than a smaller ship.