High-resolution vertical wind and turbulence measurements with quadcopter uncrewed aerial systems: wind tunnel calibration and field validation

Abstract

The SWUF-3D drone fleet is used in the atmospheric boundary layer (ABL) for in situ turbulence measurements of complex flows, such as in mountainous terrain or wind turbine wakes. Previous calibrations for measuring vertical wind speed $w$ using the drones' avionics data were performed on field data, limiting applicability to low winds ($\leq 8~\mathrm{m}\,\mathrm{s}^{-1}$) and being prone to high uncertainties. To overcome these limitations, we calibrate $w$ measurement in a wind tunnel and validate it in field measurements. Calibration is performed in a wind tunnel with an active grid used to deflect horizontal flow into the vertical. This wind is measured with a multi hole probe, while wind forces acting on the drone are determined from the avionics data, allowing an empirical relationship between these quantities. For validation, we conduct comparative fleet measurements with up to 10 drones simultaneously around an array of meteorological masts equipped with sonic anemometers. The results show high accuracy for turbulence statistics: the variance determination for $w$ has a root mean square error (RMSE) of 0.12~$\mathrm{m^2\,s^{-2}}$ and a normalized RMSE (nRMSE) of 17.0~\%, for the horizontal wind components the RMSEs are $\sim$0.3~$\mathrm{m^2\,s^{-2}}$ and nRMSEs $\sim$25~\%. The RMSEs for the covariances of the components are $<\,$0.3~$\mathrm{m^2\,s^{-2}}$. The variance spectra of $w$ measured with drones and reference sensors agree in all frequency ranges, the RMSE for covariances between different measurement points is $\sim$0.1~$\mathrm{m^2\,s^{-2}}$. Accurate $w$ retrieval at all wind speeds sustainable by the drone enables studies of strongly three-dimensional flows, supports eddy-covariance flux estimation, enables resolving diurnal turbulence evolution in the ABL, and improves spatial turbulence characterization.

Figures (13)

• Figure 1: The geodetic coordinate system (black) and the body-fixed coordinate system with Euler angles (blue) of the QAV250 drone in the 5.5$^{\prime\prime}$ setup (adapted from Hofmann2025, Hofmann2025).
• Figure 2: QAV250 drone in the 5.0$^{\prime\prime}$ setup hovering in front of the wind tunnel nozzle equipped with the active grid.
• Figure 3: Schematic representation of the measurement mast array. The arrows indicate the sonic anemometers selected as references at heights of 20, 25, 90, and 100 m.
• Figure 4: Flight patterns of the fleet for the validation measurements around the measurement mast array with wind rose from the reference sensor system of the corresponding flights. The dashed blue lines represent the alignments of the drones relative to each other and to the sensors on the masts.
• Figure 5: Calibration curve for the QAV250 drone in the 5.5$^{\prime\prime}$ setup (blue) for determining the longitudinal wind speed in the drone's body-fixed coordinate system $u_{\mathrm{b}}$ based on the acceleration data in the x-direction of the drone's coordinate system $a_{\mathrm{x}}$. The curve (blue) is composed of various calibration curves (grayscale), each of which is fitted for different speed ranges using the data points from calibration flights (gray dots). The dashed black lines indicate the thresholds $a_{\mathrm{L1}}$ and $a_{\mathrm{L2}}$ for the accelerations at which between curves is switched and, in some cases, interpolated between them.