Scaling of electric motor performance in theory and practice

Scaling laws offer key insights into the fundamental constraints shaping the performance of not only biological but also technological systems. Electric motors are a unique class of engineered systems owing to their ubiquity and large size range. While extensive derivations of expected scaling behaviour exist in electric motor design, few studies have compared theoretical predictions with empirical data. We compiled specifications for 168 electric motors ranging from 10−3 to 104 kg using manufacturer data sheets and determined the empirical scaling relationships for motor torque, power, current and speed as functions of motor mass. We then compared these results with theoretical expectations derived from established sizing equations, finding that many of the observed relationships deviated from their theoretical predictions, challenging the presumed universality of these engineering scaling laws. By highlighting the discrepancies between theoretical and observed scaling laws for these machines, this study underscores the need for advances in the theoretical understanding of the engineering design principles, informs the development of next-generation motors and advances the study of allometry in technology. Furthermore, the study raises questions related to the taxonomy of technology, defining a technological species as a group of devices with a preponderance of interchangeable parts.