Scaling Laws for Mesoscale and Microscale Systems

The set of laws developed and presented here is by no means exhaustive. Techniques have been present to aid in the development of additional scaling laws and to combine these and other laws to produce additional useful relationships. Some of the relationships produced here have yielded perhaps surprising results. Examples include the fifth order scaling law for electromagnetic motor torque and the zero order scaling law for capacitive motor power. These laws demonstrate important facts about actuators in small-scale systems. The primary intent of this introduction into scaling law analysis is to provide needed tools to examine possible areas of the research in small-scale systems and direct research toward more fruitful areas. Numerous examples have been included to show the validity of developing scaling laws based on first principles and how real world systems tend to obey these laws even when many other variables may potentially come into play. Development of further laws may well serve to provide important high-level direction to the continued development of small-scale systems.