The wind tunnel experiments were conducted in the Open Jet Facility (OJF) at the Faculty of Aerospace Engineering of Delft University of Technology from 1 to 10 April 2024. The facility is a closed-loop wind tunnel, featuring an octagonal jet exhaust nozzle with maximum dimensions of 2.85m×2.85m and a contraction ratio of 3:1, as illustrated in Fig. . The jet discharges into a test section room with dimensions 13m in width and 8m in height. The wind tunnel is equipped with a 500 kW electric motor driving a large fan, which generates a controlled streamwise velocity of up to 35 ms-1 in the test section. Corner vanes and wire meshes guide the flow to ensure uniform flow conditions, resulting in a turbulence intensity of 0.5 % in the test section .

As the original TU Delft LEI V3 kite is 8.3 m wide and the width of the OJF exhaust nozzle is only 2.85 m, a scale model had to be used. With the main purpose of the measurement campaign being the acquisition of validation data for numerical tools, the scale model was manufactured to match the wing geometry used in earlier CFD simulations . This geometry was adapted from the original design CAD model to facilitate mesh smoothness in the simulations. Notably, the bridle line system was omitted, the trailing edge connecting the upper and lower canopy surfaces was rounded, and an edge fillet was applied at all canopy–tube junctions. The only difference between the CFD and manufactured geometries is the use of a canopy with increased thickness for structural integrity – 3 to 4 mm instead of 1 mm. The model geometry was verified using a laser tracker with a spatial resolution of 0.5µm . Figure  compares the manufactured physical model with the rendered geometry and the overlaid laser-tracked outline of the physical model. The agreement between the manufactured and rendered geometry was within 1 mm in chord, height, and width, corresponding to errors of less than 0.25% in all cases, as detailed in Table .

Considering manufacturing costs, handling limitations, Reynolds number scaling, and wind tunnel blockage, further detailed in Appendix , we decided on a 1:6.5 scaling of the wind tunnel model, leading to the dimensions listed in Table . The anhedral swept wing with a bow-shaped leading edge and double-curved canopy was manufactured by Curveworks B.V. using carbon-fibre-reinforced plastic laid up in a 3D-milled mould from structural foam. The canopy is 3 mm thick, except for the two central panels, which are 4 mm as they need to sustain a higher load. The outer layers provided the most structural support and were made of carbon fibre. The 1 or 2 mm inner layers were made of a glass-fibre-reinforced polymer. Structural foam was used inside the chordwise struts, except for the two inner struts, which incorporate two parallel steel rods. These rods slide into the two aluminium sleeve tubes of the support frame, as illustrated in Fig. a.

The support frame is a truss structure assembled from custom-cut aluminium profiles. The angle of attack α quantifies the inclination of the mid-span chord line with respect to the inflow and can be adjusted as illustrated in Fig. . The angle was measured with an accuracy of 0.1° by placing two digital inclinometers on the aluminium sleeve tubes. The measured value is converted to the angle of attack α by subtracting the offset angle 6.3° between the chord line and the parallel steel rods of the model. The support structure was placed aft of the kite to minimize flow interference and mounted onto a six-component load balance, as illustrated in Fig. . The balance operates at 2000 Hz and is equipped with six load cells able to measure the longitudinal, inflow-aligned Fx, transverse Fy, and vertical Fz forces and the roll Mx, pitch My, and yaw Mz moments. The entire assembly was mounted on a rotary table, allowing a remote adjustment of the sideslip angle β with an angular resolution of 0.01°. The sideslip angle was defined in a body-fixed reference frame. A counter-clockwise rotation of the turn-table, which appeared as a positive rotation in Fig. , therefore corresponded to a negative inflow angle β in the body-fixed reference frame.

The experiments were conducted for most combinations of α, β, and U∞ listed in Table , although time constraints prevented testing all β values at every α. The test matrix was designed to cover the full range of inflow conditions encountered in flight. Based on in-flight measurements, the angle of attack α typically varied between 1° during reel-in and 8° during reel-out , while observed sideslip angles β generally remained within -10 to 10° . Table , therefore, includes these operational ranges of α and β to ensure that the inflow conditions experienced by the V3 kite are represented, and additional values of both angles are incorporated to provide further data points for model validation.

The Reynolds number, 1Re=U∞crefν, was used to characterize the flow regime, recalculating the kinematic viscosity ν for each value of U∞ using Sutherland's law . Multiple inflow speeds were included to assess the influence of varying Re, and those listed in Table  were selected to approach in-flight values. The experimental setup did not permit matching the in-flight Re, which for the V3 kite was around Re=3×106 .

Measurements without the kite were performed across the full parameter range to quantify the aerodynamic loads on the support structure alone. As the load measurement setup did not permit quantification of the interference between the structure and the kite, these effects were assumed to be negligible. To ensure consistency, measurements taken with α=5.7° at U∞=20 ms-1 and β=-20, 0, and 20° were repeated three times. Furthermore, the sensor drift of the load balance during the campaign was analysed through six measurements done over a 30s time interval each morning and evening with U∞=0 ms-1 for 3 consecutive days. A zero-wind measurement was performed before each measurement set, and by using this as a baseline, any sensor drift present in the system was inherently accounted for in the subsequent data.

A measuring period of 10s was selected for all tests. Given that approximately 125–625 fluid parcels pass within this time, combined with the agreement between repeated measurements and the outcome of a dedicated convergence analysis, the measuring period was deemed statistically sufficient; further details are provided in Appendix .

Using two-dimensional (2D) CFD simulations, showed that incorporating a boundary layer transition model significantly affects the aerodynamic predictions for Re<2×107. This motivated the use of natural transition modelling in subsequent three-dimensional (3D) CFD simulations of the V3 kite . In practice, transition may be influenced by the zigzag-patterned stitching seam connecting the canopy to the tube along the span, as shown in Fig. a. Whether this seam height would be sufficient to induce transition remained uncertain, however. As the scale model did not incorporate this stitching seam, additional measurements using zigzag tape were conducted to address this issue. The setup is shown in Fig. b.

The critical roughness Reynolds number Rek,crit is commonly used to quantify the height threshold at which a surface roughness element induces boundary layer transition. The numerical estimation of this number is non-trivial, as it depends on local pressure gradients, freestream disturbances, geometry, and roughness characteristics . In practice, trip heights are often estimated through empirical correlations . reported typical values of Rek,crit ranging between 300–600. For zigzag or wavy-patterned 2D roughness, adopted a value of 300, while others found 200 to be sufficient . Given a value of Rek,crit, the corresponding roughness height k can be computed using the relation 2k=Rek,critνUk, where Uk denotes the local velocity at the roughness height, which lies within the boundary layer and is therefore different from the external velocity U∞, i.e. generally somewhat smaller; nonetheless, it is often approximated by U∞ for practical purposes . For a more precise assessment, the local velocity profile within the boundary layer could be employed to determine Uk directly; however, this typically necessitates either supplementary measurements or detailed boundary layer computations, which were not available in the present study. The resulting functional dependency of k is shown in Fig.  for two different values of Rek,crit. The diagram also includes the selected tape height of 0.2 mm to trigger transition from approximately Re≥3.9×105 according to the estimate Rek,crit=200. The tape, produced by Glasfaser Flugzeug-Service GmbH with a 60° tooth angle, was applied at 5 % chord, following the approach in , , , and .

The measured load data were converted to the non-dimensional aerodynamic coefficients as follows:

subtract zero-wind measurements

This section quantifies the main sources of measurement uncertainty to ensure data reliability and repeatability, including sensor drift, support-to-kite load proportion, vibration analysis, coefficient of variation, and measurement repeatability. Although a load balance sensor drift was detected, it was concluded not to affect the results, as detailed in Appendix . Analysing the proportions of support-structure loads to kite loads as signal-to-noise ratio, one finds high certainty for lift and lower certainty for CM,y and CM,z, as detailed in Appendix .

For some measurements at U∞=25 ms-1 and high values of α and β, the wind tunnel model started to vibrate considerably. To avoid physical damage, these specific measurements were not completed, which is why some data points are missing at Re=6.1×105. A vibration analysis revealed structural resonance at 4–5 Hz, close to the resonance frequency of the supporting blue table shown in Fig. , as reported in . This frequency band was not filtered to avoid introducing processing artefacts. See Appendix  for further details, i.e. time series and power spectral density analyses.

The coefficient of variation, denoted as CV, offers a dimensionless metric for comparing variability across different datasets by normalizing the standard deviation relative to the mean . For each aerodynamic force or moment coefficient, CVi=σi‾μi,i∈{L,D,S,Mx,My,Mz}, where σi‾ is the average standard deviation of coefficient i, and μi is its mean value, both computed over the ensemble of measurements. Table  lists CVi for each Re, except for Re=6.1×105, which is excluded due to incomplete data. The means μi were computed over the full range of α and β for CVL, CVD, and CVM,y. For CVS, CVM,x, and CVM,z, only positive values of β were considered to avoid including near-zero loads at β=0°, which could lead to inflated values of CVi and skew the statistical averages.

The decline in CVi values from Re=1.3 to 2.5×105 reflects a reduction in relative measurement uncertainty, as the standard deviation becomes smaller relative to the mean. In this work, force measurements exhibited lower relative uncertainty compared to moment measurements, which can be attributed to their inherently higher signal-to-noise ratios. The cases at Re=3.8 and 5×105 exhibit the smallest values of CVi, indicating the highest relative measurement precision. However, it should be noted that a low CV reflects only the precision – that is, the spread or random uncertainty of the measurements – and does not account for possible systematic errors or constant offsets that may affect accuracy.

At Re=5×105; α=5.7°; and β=-20, 0, and 20°, measurements were made three times to check the repeatability. For each of these measurements, the standard deviation within these repeated measurements σrm is shown in Table . The authors conclude that the measurement repeatability is overall high, as evidenced by the orders of magnitude difference between the averaged standard deviation, 1×10-1, and the repeatability standard deviation, 1×10-4. The smallest uncertainties are for β=0°.

The measured aerodynamic force coefficients with and without zigzag tape are shown in Fig.  for β=0° and α=9.4°, selected for its proximity to the nominal reel-out angle of α=8° . The Re=6.1×105 case was excluded due to missing data. In addition to the mean values, a confidence interval (CI) is plotted, indicating with 99 % certainty that the mean lies within the given range. As detailed in Sect. , the load balance records data over a 10s time interval, thereby capturing between 125–625 fluid parcels passing through. The resulting samples are regarded as temporally correlated; one supporting argument is that each fluid element traverses the measurement region over 16–80ms, while data are sampled at much finer 0.5ms intervals. To accurately estimate the sample measurement uncertainty of this correlated time series, the heteroskedasticity and autocorrelation-consistent (HAC) estimator by is employed. The method requires an estimate of the time lag. A time lag of 11 samples was found from taking the integer value of Nsamples14 .

For context, the theoretical analysis leading to Fig.  indicated that a zigzag tape height of 0.2mm would be insufficient to force transition at Re=2.5×105, marginally sufficient at 3.8×105, and sufficient at 5×105. The three horizontally separated regions in Fig.  correspond to these different Re, with black and red symbols indicating measurements obtained without and with zigzag tape, respectively. At β=0°, adding zigzag tape resulted in higher lift and lower drag for Re=2.5 and 3.8×105, whereas the opposite trend was observed at Re=5×105, including a 12% increase in drag. This latter observation is consistent with the literature, where the introduction of zigzag tape led to decreased lift and increased drag .

Definitive conclusions cannot be drawn for the non-zero sideslip cases, where data are limited to Re=3.8×105 at α=9.4° for β=±10°. Nonetheless, based on the measured increase in lift and side force, along with an observed 50 % reduction in drag, the authors hypothesize that, in the sideslip configuration, the zigzag tape may locally promote a laminar-to-turbulent transition that delays flow separation.

Without zigzag tape and under sideslip, the measured CS value remains near zero, independent of Re. In contrast, with zigzag tape, a negative CS is observed at Re=5×105. This difference suggests that the zigzag tape introduces a setup asymmetry, possibly due to imperfect tape application.

Figure  presents the measured force and moment coefficients as functions of α for various Re. In the measurements, the lift coefficient CL increases with Re but so does the drag coefficient CD, resulting in a CL/CD ratio that does not show a consistent increasing trend with Re, except for the Re=6.1×105 case. This finding contrasts with the 3D numerical simulations of , in which both an increase in lift and a decrease in drag were observed from Re=1×105 to 1×106, leading to higher CL/CD with increasing Re. The absence of a similar trend in the present measurements may be attributed to the smaller range of Re realized experimentally, differences in canopy thickness, and/or drag underprediction in the simulations, as discussed in Sect. .

The Re=1.3×105 case exhibits the least smooth curves, attributable to a less favourable signal-to-noise ratio; i.e. the load magnitudes are relatively small compared to the support-structure loads. The CL–α plot suggests that, compared to higher Re, stall development may occur at lower angles, as evidenced by the earlier decrease in slope of the CL–α curve for Re=1.3×105, indicating reduced lift growth and hence the possible onset of local flow separation. This aligns with aerodynamic theory predicting earlier separation in laminar flows due to lower sensitivity to adverse pressure gradients .

Although small in magnitude, the non-zero values of CM,x and CM,z may have indicated an asymmetry in the setup. For coefficients of smaller magnitude, the non-smoothness of the curves was amplified, which was consistent with the higher relative uncertainties found, as indicated by the coefficient of variation in Table . The pitching moment coefficient CM,y exhibited an increasing trend with increasing α.

The influence of β, shown in Fig. , was examined at α=7.4°, as this condition most closely resembled the average angle of attack of 8° observed during the reel-out phase of a V3 kite flight . A perfectly symmetric setup would yield coefficients CL, CD, and CM,y symmetric about β=0° and coefficients CS, CM,x, and CM,z that are antisymmetric. In practice, slight asymmetries in the experimental setup caused small deviations from this ideal symmetry, notably non-zero values of CS, CM,x, and CM,z at β=0°, as well as minor asymmetries of CL, CD, and CM,y about the vertical axis. The largest deviations from ideal symmetry were observed at the lowest Re=1.3×105, with overall increasing symmetry as Re increased.

The CL plot reveals an overall increase in lift coefficient with increasing Re, consistent with the findings when varying α. Notably, around β=8°, the CS curve exhibits both positive and negative peaks, suggesting a nonlinear relationship with β. At this same angle, a local maximum is observed in CM,x for the Re=5×105 case, and off-trend behaviour can be seen for CD and CM,z. Similar off-trend behaviour near β=±8° also appears in β sweeps at other values of α. The potential underlying causes of this phenomenon are examined further in Sect. .

Among the tested cases with complete measurement sets, Re=5×105 represents the highest Reynolds number and is therefore the closest to actual in-flight operational conditions, which is around Re=3×106 . Consequently, this case is used as the basis for comparison with the numerical simulations. Additional arguments for choosing this specific measurement run are the low measurement uncertainty, as indicated by the CVi values in Table ; its high repeatability, demonstrated in Table ; and the high degree of symmetry and antisymmetry in the positive and negative β measurements.

In Fig. , the force coefficients CL, CD, and L/D are plotted against α for the VSM, CFD, and wind tunnel (WT) data, along with 99 % CI bands, evaluated using the autocorrelation-consistent method by . The CI band is rather narrow for CL compared to the mean values, indicating high certainty. For CD, the band is wider, aligning with the difference in the CV listed in Table . The numerical data match the measured lift coefficient trend well from α=-11 to around 11°. Above α=11°, the numerical VSM predicts lower lift, whereas the RANS CFD predicts substantially higher lift. The differences in numerical predictions around stall are considered to arise, in part, from discrepancies in turbulence modelling. The VSM employs fully turbulent 2D RANS CFD as input, whereas the 3D RANS CFD simulations both incorporate a transition model .

The numerical and measured drag coefficients start deviating more above around α=10°, where the lift slope also changes. Both VSM and CFD predictions with and without struts agree well but do not show the same expected change in drag slope when entering the stall regime. The change of slope is not reproduced by the VSM predictions to the same extent, attributed to inherent limitations of lifting-line-based methods in this regime , e.g. its inviscid nature.

From α=1 to 10°, the measured lift-to-drag ratio plateaus at the maximum value range between L/D=8 and 8.5, sharply dropping outside this α range. All numerical models predict a higher maximum L/D: the CFD simulations reach a value of 10.5, while the VSM predicts a maximum of 9.5.

In Fig. , the force coefficients CL, CD, and CS are plotted against β for α=12.5°. CFD data were only available at a different angle of attack, α=13.02°, but is included regardless to enable trend comparison. Furthermore, the WT data are plotted for both positive and negative β ranges to illustrate the effect of the asymmetric measurement setup, e.g. due to geometry, surface condition, or inflow.

The measurements confirm and closely follow the trends predicted by the numerical simulations. With increasing sideslip angle, CL decreases, while CD and the absolute value of CS increase. The measured data at negative β form an exception, showing an off-trend lift, drag, and side force behaviour above around β=8°. This off-trend behaviour appears across multiple Re values, as shown in Fig. , and is smaller for the lower-α case. Since this behaviour was not observed in the CFD or VSM predictions, and as an increase in lift and side force and a decrease in drag were measured, it suggests the presence of local separated flow in the positive β case and attached flow in the negative β case. These differences are attributed to asymmetry in the measurement setup and surface imperfections on the scale model.

The moment coefficients CM,x, CM,y, and CM,z are plotted over an α sweep in Fig. . Compared to the force measurements, the confidence intervals are wider due to higher measurement uncertainty, the same conclusion as drawn from analysing CV shown in Table . No CFD data are available; therefore, only VSM data are used. The numerical data predict no roll or yaw moment, where the measurements do show, on average, a negative roll moment coefficient CM,x and a positive yaw moment coefficient CM,z, indicating asymmetries in the setup. The experimental pitch moment coefficients CM,y fluctuate significantly, yet on average exhibit a positive slope. The numerical predictions differ in magnitude but exhibit a similar positive and increasing moment trend up to the stall point.

In Fig. , the moment coefficients CM,x, CM,y, and CM,z are plotted over a β sweep. Similar to the forces, the measured moments differ between positive and negative β ranges. The numerical and experimental data match well for the roll moment coefficient CM,x. Less agreement in trend is shown for the pitch moment coefficient CM,y, where the measurements indicate an increasing moment up to β=10° and above this threshold a decreasing moment. The VSM, on the other hand, predicts a higher value that changes less with increasing β. For the yaw moment coefficient CM,z, the measurements and numerical predictions show opposite trends; it is unclear why this is the case. The currently measured negative slope suggests that the anhedral kite shape was yaw statically stable, which is identical to the findings of , where a negative slope was measured for an anhedral rigidized paraglider in wind tunnel experiments. Possible factors contributing to the prediction discrepancy include observed setup asymmetry; high uncertainty, as shown in Table ; and a low signal-to-noise ratio, as presented in Fig.  in Appendix . Furthermore, because the moments are computed about a prescribed reference point, any mismatch between the centre of gravity definition in the measurements and that used in the simulations would directly affect the predicted moment levels and could therefore contribute to the observed discrepancy.