Development of a Brushless DC Motor Sizing Algorithm for a Small UAS Design Framework

This paper describes the development of a semi-empirical sizing algorithm for the outrunner brushless DC (BLDC) motors used in electric unmanned aerial systems (UAS) with a maximum gross takeoff weight of 25 kg (55 lb.). Given an operating torque and a desired geometric aspect ratio (stator diameter/length), the algorithm can predict the mass, geometry, and figure of merit (km) of a motor rated for the applied torque. Given an operating voltage and operating speed, the algorithm can predict the optimal torque constant (kt ), speed constant (kv), and winding resistance (R). To develop, tune, and validate the algorithm, complementary theoretical and experimental methods were used to overcome two key barriers: (1) motor performance theory was used to generate non-existent performance data, and (2) empirical trends in motor design were leveraged to connect independent theoretical torque, volume, and mass models. The resulting mass and figure of merit predictions are within ±20% of actual values for motors ranging in mass from 25 - 500 g (1-18 oz.) and varying geometries. Moreover, the derived electrical constants can be fed into equivalent circuit performance models to validate the output of the sizing algorithm and drive optimization feedback in a broader UAS conceptual design tool. The validated algorithm also revealed that motor size (and therefore mass) grows with torque, not power, which is a critical distinction for vehicle designers in the VTOL industry who are increasingly transitioning to electric powertrains.