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.

中文翻译：

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升力螺旋桨最小功率飞行编队研究

本研究深入研究了独立、非铰接、升力螺旋桨在边缘飞行中的最小功率形成问题。自由飞行固定翼的编队飞行已经得到很好的解决，证明了相互诱导上洗流的重要性。然而，需要了解该机制如何与任意数量的自由飞行旋翼的最佳飞行编队相关。初始分析是使用低保真度空气动力学性能预测器与粒子群优化相结合进行的。根据优化结果可以推断，当所有螺旋桨不共享旋转方向时，最小功率配置呈倒V形形式。另一方面，当所有螺旋桨共享旋转方向时，最小功率配置类似于梯队编队。与常规 V 形相比，逆 V 形可降低功率需求。根据自由涡尾流模型，四旋翼的下降幅度约为 1.8%，六旋翼的下降幅度为 3.1%，八旋翼的下降幅度为 3.2%。在所有情况下，当下游螺旋桨位于上游螺旋桨的前进侧（而不是后退侧）后面时，上洗流的好处会最大化。 V 形角度对沿叶片跨度的载荷分布有影响。随着形成角变得更加锐利，叶片的外侧部分逐渐向中跨卸载。