On minimum power flight formations of lifting propellers

Abstract

The present study delves into the problem of minimum-power formation of independent, non-articulated, lifting propellers in edgewise flight. Formation flight of free-flying fixed wings has been well addressed, demonstrating the importance of mutually induced upwash. However, there is a need to understand how this mechanism relates to the optimal flight formation of an arbitrary number of free-flying rotary wings. The initial analysis is carried out using a lower-fidelity aerodynamic performance predictor coupled with Particle Swarm Optimization. Based on the optimization results, it can be inferred that the minimum power configuration takes the form of an inverse V-shape when the direction of rotation is not shared among all propellers. On the other hand, when the direction of rotation is shared among all propellers, the minimum power configuration resembles an echelon formation. The inverse V formation leads to a decrease in power requirements compared to the regular V formation. For the tetra-rotor, the decrease is approximately 1.8%, for the hexa-rotor it is 3.1%, and for the octa-rotor, it is 3.2%, based on the free-vortex wake model. In all cases, the benefits of upwash are maximized when the downstream propellers are located behind the advancing side of the upstream propellers, instead of the retreating side. The V formation angle has an impact on the load distribution along the blade span. As the formation angle becomes more acute, the outboard section of the blade is increasingly offloaded towards the mid-span.