Robotics meets Fluid Dynamics: A Characterization of the Induced Airflow below a Quadrotor as a Turbulent Jet

TL;DR

The paper addresses the problem of quantifying the mean induced flow below a quadrotor in hover to improve safety and multi-agent coordination. It proposes a computationally lightweight approach that models the far-field flow as a turbulent jet, with normalization by the hover-induced velocity $U_H$ and a motor-distance length scale $l$, validated on over 16 hours of flight data from six drones. The key contributions include a unified analytic far-field model that requires only mass, propeller diameter, and vehicle size, experimental validation showing jet-like behavior after about 2.5 length scales, and demonstration of a downwash compensation controller that yields up to a 4× improvement in altitude tracking when passing below another drone. The approach enables safer proximity operations, improved sensor placement, and scalable multi-drone planning without reliance on expensive CFD simulations or exhaustive measurements.

Abstract

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.

Figures (10)

• Figure 1: Smoke visualization of the flow (left) and corresponding measured velocity field (right) of the Kolibri drone at hover. The individual propellers flows are separated close to the drone. After 2.5 motor-to-motor distances $l$ the individual flows merge into one turbulent jet (far-field) for which the velocity field and half-width (distance where the velocity is half the centerline velocity) can be calculated with our proposed method.
• Figure 2: Diagram for the drone and the flow coordinate system and geometry. The bodyframe$\mathcal{B}$ of a quadrotor is such that the x-axis faces forward, and the z-axis upwards in thrust direction. The flow coordinate system is oriented such that its longitudinal axis $\mathbf{\hat{s}_\mathcal{F}}$ is aligned with flow direction (i.e., points in negative $\mathbf{\hat{z}_\mathcal{B}}$ direction). The flow is described in cylindrical coordinates $[s~~r~~\theta]^\top$ by its longitudinal (axial), radial, and azimuthal velocity components $U$, $V$ and $W$, respectively. The vehicle's propeller radius $r_\text{prop}$, diameter $d$ and motor-distance $l$ are defined as depicted.
• Figure 3: The DJI Matrice 300 drone hovers in proximity to the flow probe. The inset shows a close-up view of the Testo hot ball probe. The flow probe measures the speed of the airflow.
• Figure 4: Visualization of the near field of (a) the Offboard 1 drone and (b) the Matrice 300. The length and velocity scales are normalized. The influence of the individual propellers is clearly visible at $z=0$ and diminishes at a normalized distance of about 2.5 as indicated by the dotted white line.
• Figure 5: Distance $\tilde{\delta}$ of the flow tube centerline to the $\mathbf{z}_\mathcal{B}$ axis. Close to the rotor-plane of the vehicle (left side) the flow has not fully developed. From 2 to 3 length scales below the drone the flow fully develops with the highest velocity being measured on the negative z-axis of the drone.