Mass Scaling Laws for Energy-Optimal Horizontal Multirotor Flight

Multicopters are a type of aerial robot seeing extensive real-world applications but with range and endurance as critical bottlenecks. Optimization of its energy efficiency through energy-aware flight planning (e.g. cruise speed-scheduling) has hence been an important topic. The mass of the multicopter is an important factor to consider, as it has a significant impact on efficiency, and many common applications are subject to frequent mass variation due to payload change. This work derives closed-form scaling relationships between the energy-optimal steady horizontal flight behavior of a multicopter and its vehicle mass, and validates them experimentally on two multirotor platforms. Specifically, for mass-only variation, i.e., when payload changes the vehicle mass while the airframe geometry, aerodynamic characteristics, and rotor configuration remain unchanged, we show through a combination of numerical simulation, theoretical derivation, and experimental validation that (1) the energy-optimal velocity is proportional to the square root of vehicle mass; (2) the energy-optimal pitch angle is constant with respect to mass; and (3) the optimal energy per meter is proportional to mass. The analysis shows that these three relationships arise from a common mass-similarity property of the steady-state flight and rotor-aerodynamic equations. Furthermore, the obtained scaling relationships enable simple yet effective cruise-speed planning to optimize energy efficiency and extend the range and endurance of the multicopter.