The widespread adoption of quadrotors for diverse applications, from agriculture to public safety, necessitates an understanding of the aerodynamic disturbances they create. This paper introduces a computationally lightweight model for estimating the time-averaged magnitude of the induced flow below quadrotors in hover. Unlike related approaches that rely on expensive computational fluid dynamics (CFD) simulations or drone specific time-consuming empirical measurements, our method leverages classical theory from turbulent flows. By analyzing over 16 hours of flight data from drones of varying sizes within a large motion capture system, we show for the first time that the combined flow from all drone propellers is well-approximated by a turbulent jet after 2.5 drone-diameters below the vehicle. Using a novel normalization and scaling, we experimentally identify model parameters that describe a unified mean velocity field below differently sized quadrotors. The model, which requires only the drone's mass, propeller size, and drone size for calculations, accurately describes the far-field airflow over a long-range in a very large volume which is impractical to simulate using CFD. Our model offers a practical tool for ensuring safer operations near humans, optimizing sensor placements and drone control in multi-agent scenarios. We demonstrate the latter by designing a controller that compensates for the downwash of another drone, leading to a four times lower altitude deviation when passing below.

翻译：四旋翼飞行器在从农业到公共安全等众多领域的广泛应用，亟需对其产生的空气动力学扰动进行深入理解。本文提出一种计算轻量化的模型，用于估算悬停状态下四旋翼飞行器下方诱导气流的时间平均强度。与依赖昂贵的计算流体动力学（CFD）模拟或针对特定无人机进行耗时经验测量的相关方法不同，我们的方法借鉴了湍流经典理论。通过分析大型运动捕捉系统内不同尺寸无人机超过16小时的飞行数据，我们首次证明：在飞行器下方2.5倍机身直径距离处，所有螺旋桨产生的合成气流可被湍流射流模型精确近似。采用创新的归一化与标度方法，我们通过实验确定了描述不同尺寸四旋翼飞行器下方统一平均速度场的模型参数。该模型仅需无人机质量、螺旋桨尺寸和机身尺寸即可进行计算，能精确描述大尺度空间内远场气流的长期特性，而此类大体积模拟对CFD方法而言极不现实。我们的模型为保障近人操作安全、优化多智能体场景中的传感器布置与飞行控制提供了实用工具。我们通过设计一种能补偿其他无人机下洗气流的控制器验证了后一应用，实验表明当飞行器从下方通过时，其高度偏差降低了四倍。