Few Large and Many Small: Hierarchy in Movement on Earth

Movement on earth is effected by bodies (e.g. river channels, animals, vehicles) of seemingly random scales, large and small. Here we use the constructal law and the design of ‘distributed energy systems’ to show that the large must be few and the small many, in particular proportions that are required for greater access for movement on areas. First, we demonstrate that mass movement per kilogram moved and kilometer traveled requires less fuel on larger vehicles. The thermodynamics basis of this is the same as for the effect of size on the effi ciency of motors, vascular fl ow architectures and river basins. The same principle dictates that on every vehicle the motor mass must scale with the structural mass, and with the total mass. In addition, larger masses must move on areas to greater distances, and a characteristic number of smaller masses must be allocated to a larger mass to travel, on the same area element.