First Identification and Quantification of Detached Tip Vortices Behind a WEC Using Fixed Wing UAS

Abstract. Quantifying blade tip vortices helps to understand the process of vortices detaching from the wind converter blade and their development in the wake until finally dissipating in the far wake, contributing to overall turbulence. This is especially interesting for set-ups of numerical simulations when setting the spatial resolution of the simulation grid. The MASC MK 3 (Multi-purpose Airborne Sensor Carrier Mark 3) UAS (Unmanned Aircraft System) by the University 5 of Tübingen measured atmospheric and meteorological quantities during the HeliOW campaign in July 2018 data behind a wind energy converter (WEC) (Enercon E-112) north of Wilhelmshaven, Germany, at the Jade Wind Park. Aside turbulence distribution, air temperature, humidity and the three wind components u, v, w in front of the WEC and in the wake were measured. By evaluation of the wind components, detached blade tip vortices were identified in the time series. The presented data were captured under a dominating marine stratification about 2 km from the North Sea coast line with northern wind 10 direction. The measured vortices are compared to the analytical Burnham-Hallock model for two vortices spinning in opposite direction. The model has its origin in aviation, where it describes two aircraft wake vortices. It will be shown that the BH model can be used to describe wake vortices behind a WEC. An evaluation method is presented to measure detached tip vortices with a fixed wing UAS. Also an improvement for the model in WEC wake use will be proposed.


Introduction
The wind energy sector has been growing world wide for decades and the produced power from wind energy is still growing.
Not only the amount of installed wind energy converters (WECs) is increasing but also the capacity of a single turbine. Also the field of application has widely increased with WEC. There are systems available for homogeneous terrain, off or near shore, 20 or even complex terrain with a high amount of additional turbulence stress that is induced onto the wind turbine's blades.
A WEC, especially in a stable marine ABL (atmospheric boundary layer), acts as a turbulence generator. The added turbulence has two main sources. On the one hand the increased wind shear in the wake that results from the wind deficit in the near wake and the low pressure bulb that develops behind the WEC nacelle. On the other hand turbulence is created by expansion and dissipation of detached blade-tip vortices that transfer their kinetic energy to the surrounding flow. A proper understanding 25 of these vortices and their induced load onto the converter blade is of great importance for future enhancement of life span and working loads of wind energy converters in wind farms. Blade-tip vortices follow a helical pattern into the wake, detaching from each converter blade. These detached eddies can be measured with the mounted five-hole-probe on the MASC UAS. Subramanian et al. (2015) detected tip vortices via pressure fluctuations qualitatively in a flight pattern along the wake, also using a small UAS. In this study an evaluation method is presented to measure the core radius r c , circulation Γ and maximum 30 tangential velocity V t,max of a tip vortex using in-situ wind measurements from UAS flights perpendicular to the mean wind velocity.  The research UAS MASC Mk 3 (cf. Fig. 1 and Tab. 1) is a fixed wing airborne measurement system of the University of Tübingen that has been used in several measurement campaigns and has been described by Wildmann et al. (2014a, b). The third iteration of this platform features some changes to the fuselage. The electrical pusher motor has been moved from a centre 5 position behind the wings to the tail, accelerating the aircraft along the centre axis and increasing flight stability. The MASC Mk 3 system allows in-situ high frequency measurements of the atmospheric flow and its transported properties. A detailed description of the improved UAS and its instruments can be found in Rautenberg et al. (2019b). The latest iteration MASC Mk 3 is using an improved IMU (Inertial Measurement Unit) and positioning system.
Aside the changes in fuselage design, the former ROCS autopilot operating on the MASC Mk 2 system has been changed to  The E-112 WEC is the most powerful converter in the Jade-Wind-Park north of Wilhemshaven, Germany. The particular 5 converter is a former near-shore prototype with a rotor diameter D of 114 m delivering up to 4.5 MW of electrical power and thus comparable to an actual off-shore WEC. The Jade-Wind-Park is located about 2 km from the North Sea coast line and a maritime influence in the wind profile can be expected.

Measurement site
Apart from surrounding WECs (to the south of the E-112 WEC) power lines to the east and north and industrial buildings to the north and north-east (not in the picture) restricted the flight path to the ones depicted in Fig. 3.

10
For this study of the near wake of a WEC, the wind turbine described above, has been chosen. This specific converter and its location near the coast is comparable with off-shore converters in marine flow which was a requirement when choosing the WEC. The measurements are part of the HeliOW project, in which the atmospheric turbulence in front of and in the wake

Available data
For the tip vortex evaluation five flight legs (straight and level fly-by's) are available 0.25 D downstream the WEC rotor plane.
Only one of these legs shows the necessary criterion for the circulation and core radius calculation (cf. the following sections).
This one leg (two vortex measurements) that fits the criterion will be shown exemplary to present the evaluation method and the analytical solution using the BH model approach, including also the approach by Sørensen et al. (2014).

5
With the goal to measure detached tip vortices behind a WEC, it is helpful to have at first an understanding of the behaviour of those vortices. Fig. 4 shows the helical vortex pattern forming behind a WEC, by representing the iso-surfaces of the λ 2 -criterion of detached tip vortices from CFD simulation. The fully resolved URANS simulation has been performed by the University of Stuttgart with the compressible flow solver FLOWer (Kroll and Fassbender, 2005), using the Menter SST (Menter, 1994) turbulence model. The modelled rotor is a stand alone generic model of the Enercon E-112 WEC rotor, based 10 on free access airfoil data. For more details regarding the numerical methods, please refer to Cormier et al. (2018) in which the same methods have been applied and described. Figures 5 and 6 give a qualitative impression of the presence of the WEC wake.
In both, horizontal wind velocity and turbulence kinetic energy (TKE), the wake and its effects are visible. Farther downstream the helical pattern will start to meander and the symmetrical pattern will dissipate into turbulence. In the near vicinity of the WEC nacelle, these vortices follow a helical pattern. The helical structure is shown simplified by a ring vortex in Fig. 7 which is 15 an approximation of the wake vorticity at high tip-speed ratio. The tangential velocity in this sketch can be split in its horizontal components at hub height (nacelle height). Here the y axis points north (ideally antiparallel to the main wind direction) similar to the conditions at the HeliOW campaign (cf. Fig. 3) and the x axis points east along the UAS flight path. Note that, at hub height, the tip vortex ideally has no w component (Fig. 7) under the vortex ring assumption. Thus, at this height, the tangential velocity can be split into its horizontal components u and v. The red rectangle indicates a change of perspective, showing a 20 top view of a vortex spinning in the x − y plane. In reality, from planing flight paths until take-off of the UAS and the actual measurement, the wind direction changes slightly. Therefore, for later evaluations the coordinate system has been rotated into the main wind direction.

Vortex model
To measure and evaluate tip vortices from UAS data an analytical vortex model has to be found. Previous efforts to define 25 a vortex were reviewed e.g. by Jeong and Hussain (1995), comparing several definitions with data from direct numerical simulations and exact solutions of the Navier-Stokes Equations. A universal definition of a vortex or a generally applicable model does not exist. Assuming incompressible flow and an irrotational velocity field, where the curl of the gradient of the velocity is zero, the circulation Γ, representing the strength of a vortex around a contour C, can be connected to the vorticity flux by Stoke's theorem. For any surface S that spans the curve C and dI being an infinitesimal tangential element along C,  The circulation Γ is the line integral of the tangential velocity along the curve C which is equal to the vorticity flux ω = ∇ × V t through the surface S, with n being the normal vector of the surface. A circular integration in a cylindrical polar coordinate system with the azimuthal angle φ and the radius r yields: For a two dimensional, axisymmetric vortex, the circulation is a simple function of the radius and the tangential velocity V t . Since real vortices in fluids experience viscous effects, the Figure 7. Simplified sketch of a vortex pair passed by the UAS to the right. In reality it would rather have a helical pattern than a ring shape.
Velocities and axis according to meteorological standards, therefore axis and orientation according to the in-situ conditions. y axis pointing north, x axis pointing east. At hub height the w component (along z axis) vanishes. The red rectangle illustrates a top view of a tip vortex with distance ∆y to the UAS.
(1982). Fischenberg concludes that both models show the ageing processes of a vortex wake known from theory. In general the model by Burnham-Hallock shows a slightly better agreement in circulation and tangential velocity to the conducted measurements by Fischenberg. Also Vermeer (1992) uses the BH vortex model successfully to describe WEC wake vortices.
According to these findings and its simplicity it has been decided to use the analytical solution for wake vortices by Burnham-Hallock in this study. While the two counter rotating vortices in the BH model used in aviation interact with each other, the two 5 opposite vortices in a WEC wake do not do that. This is an important detail to point out. So for the identification of the vortex parameters (Γ, r c ) a model of two counter-spinning vortices is not necessary. Here, a stand alone vortex is considered. For the later analytical solution of the whole flight path perpendicular to the WEC wake, the BH model for two vortices is consulted.
The BH model does not provide a solution for the whole wake structure, but for an idealised 2D cut. Describing two (independent) counter rotating wake vortices with a simple analytical model and comparing it to in-situ measurements is a new 10 approach in studying wind turbine wake structures. Figure 8. Qualitative plot of the tangential velocity from the vortex core outwards. The tangential velocity increases from zero (left) to a maximum at a distance rc and decreases to zero for large distances (to the right).
Having a look at the BH model, a vortex is described by its circulation Γ, tangential velocity V t and its core radius r c . The tangential velocity is the velocity of the air circling the vortex centre and is a function of the distance r to the vortex core.
The core radius r c is defined as the distance from the vortex centre (or core) at which the tangential velocity is at its maximum (circular symmetry). So the radius r c is also the radius at which the surface integral (cf. Eq. 1) is maximal, considering a 5 circular surface. For r = r c the maximum tangential velocity becomes (Eq. 5) Figure 8 shows the tangential velocity V t distribution of a BH modelled vortex with the highest tangential velocity at the distance r = r c . The distribution is circle symmetric with the vortex core (r = 0) in its centre.
In order to estimate the circulation and size of r c from transects through the vortices with MASC in the wake of a WEC, the 10 following procedure is proposed.

Evaluation method
As shown above, it is likely to measure tip vortices at hub height. At this height a simplification of the two vortices can be made. The blade-tip vortices can be considered as two dimensional vortices of circular shape in the horizontal plane and ideally the w component can be neglected. After subtracting the mean wind v ∞ the vortex tangential velocity is The norm of the tangential velocity then is When measuring with a UAS the measurement can be considered a snap shot of the in-situ conditions. Figure 9 differentiates between two different scenarios of the UAS passing a vortex. Both shown from a top view. Both scenarios will be explained in detail in the following paragraphs, with first focussing on Fig. 9a. Here the UAS passes the vortex at its closest distance (∆y), 5 marked point 3 in the sketch, with ∆y > r c , thus the vortex core radius is not reached. Point 1 and 2 mark the position of two corresponding tangential velocities of identical absolute value, when approaching the vortex and moving away from it again.
The measured signal is similar to the dashed black line in Fig. 10 that is an example for ∆y = 2r c . From such data only point 3 can be identified, since it is the point at which the measured tangential velocity is at its maximum. Point 1 and 2 are somewhere left and right of the maximum with L being unknown. There are indefinite combinations of Γ and r c that could describe the 10 vortex using Eq. 4.
The three equations 8, 9, 10 are known to describe the velocities and geometry of the measurement. V t,1 ( V t,2 ) is the tangential 15 velocity at the point 1 (and 2). Since there are four unknown parameters Γ, r c , L, and r 1,2 the problem is not solvable.
Now we consider the case, when the UAS passes a vortex at ∆y < r c , as shown in Fig. 9b. The measured tangential velocity now provides a distinct feature; a double peak in the horizontal wind measurement. This double peak is caused by passing the maximum tangential velocity at r = r c at position 1 and 2. Since the tangential velocity decreases from that point inwards at a distance double the core radius (black dashed line). The peak to peak distance is 2 L (cf. Fig. 9), above illustrated for the black solid line.
(towards the vortex core), the velocity at point 3 is a local minimum, leading to a visible 'dent' in the data (cf. red line in Fig. 10). Additionally the ground speed of the UAS is known, hence the distance L can be calculated. The three equations previously described above, then become: With now only 3 (Γ, r c and ∆y) unknown parameters it is possible to solve the equations.
Dividing Eq. 12 by Eq. 11 eliminates Γ. Inserting Eq. 13 gives: Equation 14 describes a tangential velocity ratio that is a function of L. Also L is known to range from 0 to r c . A dimensionless 10 relationship L r −1 c can be plotted and is shown in Fig. 11. By passing the vortex with ∆y < r c , and plotting the measured V t against the distance to the vortex (Fig. 10), we can determine L, V t,max , V t , ∆y. Using diagram Fig.11, we finally determine L r −1 c and thus r c .

Analytical reconstruction
As shown above, blade-tip vortices are theoretically measurable. They :::: blade ::: tip ::::::: vortices can be identified by their distinct  Figure 11. Dimensionless relationship between the ratio of the minimum (dent) tangential velocity and the maximum tangential velocity versus half the peak to peak distance (L), in percentage of rc.
(analytical solution) of the individually measured vortex, which is helpful to verify the measurements and evaluation technique.
Examining both vortices, the velocity distribution pattern of the UAS passing at distance r < r c ::::: r < r c : is visible in the v h 5 measurement. The horizontal wind velocity v h is a superposition of the tangential velocity, turbulence and the horizontal wind of the undisturbed inflow. The characteristics of the tangential velocity of vortex 1 (Fig. 14a,c) is almost solely determined by the v : v component, while in Fig. 14b,d the u : u component inheres an equal part. In the plain UAS measurement (i.e. before coordinate transformation) vortex 2 has a significant non-zero w component (Fig. 14b), indicating that the vortex did not rotate in the x − y plane, hence the coordinate transformation into the vortex coordinate system :::: x − y :::::: plane. Especially Fig. 14d 10 shows a significant reduction of the w component after the coordinate transformation ::: data ::::::: rotation. Purple dashed lines indicate the velocity deficit dV t ::: dV t : (dent), grey dashed lines the peak-to-peak distance. The dot-dashed purple line can be interpreted as an extension of the horizontal wind velocity by the w component, essentially giving the norm of the wind vector: The described coordinate system rotation was applied with respect to the area between the grey dashed lines (Fig. 14) i.e. 15 between entering and leaving the vortex. A good indicator that the data rotation was successful is when the norm of the wind vector (purple dashed line) and the v h in-between the grey dashed lines are about the same magnitude. Then it can be concluded that the two dimensional vortex rotation (u and v components) includes the entire kinetic energy, i.e. the vertical wind component is now neglectable. Table 2 shows the derived parameters from the vortices depicted in Fig. 14. It has to be mentioned that vortex 1 made for a 20 better and clearer measurement, since vortex 2 is influenced by the wind deficit and turbulence inside the wake. Vortex 1 shows a sharp jump in the tangential velocity which makes it easier to obtain the necessary quantities and provides more reliable results. The average of the obtained circulations is Γ = 74.17 m 2 s −1 , the average core radius is r c = 0.61 m. Figure 16 shows a two dimensional cut through a skewed or canted vortex that results in an ellipse where the peak to peak distance is 2 L . This peak to peak distance is under-predicted (2 L < 2 L). The introduced error ∆y is visualised in Fig. 16 25 by dotted red lines. To overcome this issue the measured data are rotated into the vortex hose if necessary. This simulates the UAS canting to follow the oblique vortex hose.

Quality control and error estimation
The wake of a WEC, especially as close as 0.25 D behind the nacelle, is a highly turbulent region. When measuring with an autonomous UAS, it is of interest whether the UAS is capable of manoeuvring stably in such an environment and if the 30 measurement instrument (e.g. 5-hole probe) is operating within its operational specifications. Figure 15 shows the attitude of the UAS (a) while passing the WEC for the consulted flight leg and the angle of attack, sideslip and true air speed (b). The The same measurement split into the three wind components u, v, w. ::: The ::::: x-axis :: is :::::: relative ::::: easting :::: with ::: the :::: WEC :::::: position :: as ::::: origin :::: (∆x : in :::: Fig. :: 7). UAS is affected by the wake entry and exit. The motions of the UAS are well recognised by the IMU and auto-pilot (cf. Fig.   15a) and taken into account for the later post-processing. The UAS handles these motions without loss of control. Fig. 15b indicate the limit of the calibrated range of ±20 • of the 5-hole probe. Passing a tip vortex at ∆y < r c is an extreme event, not only for the aircraft, but also for the pressure probe. Angle of attack and sideslip are within the calibrated ranges with one exception of vortex 1. Here, the sideslip is extrapolated. An examination of the true air speed 5 (TAS) for the measurement (blue line in Fig. 15b) shows clearly the entry and exit of the wake. Changes in true air speed cannot be avoided. Usually small deviations from the calibrated TAS value of the 5-hole probe do not result in significant changes in the calculated wind speed. The peaks visible in the TAS measurement however, will have an effect on the wind velocity calculation. The influence of different air speed calibrations on UAS measurements is studied by Rautenberg et al. (2019a).

Grey dashed lines in
There it is concluded that the deviation from the "true" wind speed is about 10% or at most 1 m s −1 , e.g. for a TAS error 10 measured at vortex 2 of about 8 m s −1 . So the peak velocities may be underestimated by 1 m s −1 .
While this error has no significant influence on the ratio V t,∆y /V t,max it is significant when calculating the circulation Γ from Eq. 5. In the presented case the circulation of vortex 2 is under predicted by about 10%.   The BH model provides a solution for two vortices spinning in opposite direction, as, for example, found in an aircraft wake. A similar constellation of vortex pairs can be found in a WEC wake at hub-height (cf. Fig. 7), with their vortex cores positioned along the x axis. This approximation can only be done, when the flight path is perpendicular to the wind (wake) direction to assure that the measured vortices are of the same age. 5 With the average values Γ and r c retrieved from Tab. 2 the minimum measured tangential velocity between the two peaks (position '3' in Fig. 14) as well as a distance ∆y can be derived. The resulting distance to the vortex core ∆y can then be fed to a model, based on the BH approach. Figure 17 shows the analytical solution of u and v overlain measured data of u an v.
Overlain to the in-situ data the tangential velocity still contains the mean horizontal wind V t = √ u 2 + v 2 . For the analytical solution the measured data has been rotated slightly (ca. 10 • ) into the mean wind direction to fit the meteorological coordinate system with the vortex coordinate system, so the u component equals zero in average and v is the predominant horizontal wind direction. In addition to the solely BH solution for the v component (dotted line in Fig. 17b), the long dashed line shows the same solution, but multiplied with a correction factor to satisfy for the wind deficit in the wake. The general vortex model does not consider the mean horizontal velocity, so it needs to be accounted for, especially when there is a artificially induced drop behind the WEC in the wake (wake deficit). In the present case the velocity deficit was measured to be about 65 %. It 15 is visible as a jump in the mean horizontal wind between the two measured vortices. Similar deficits were already measured by Wildmann et al. (2014a) or Bartl et al. (2012). The velocity correction function is simply an upside down Tukey window.
The analytical solution remains uncorrected until entering the wake of the WEC. After incorporating a deficit correction to the analytical solution, it is visible that the deficit in the wake plays an important role to the structure (placement, intensity, etc.) of the vortex. Especially since the two vortices do not interact with each other, as the two vortices in the BH model for aircraft 20 wakes do.

Discussion
Here we compare the airborne measured circulation Γ with data of the WEC itself. Equation 20 allows for a calculation of the blade-tip vortex strength by given parameters and describes the circulation for a rotor of constant thrust coefficient, e.g. (Sørensen et al., 2014): N b being the number of blades and Ω the rotational velocity provided by the owner of the WEC. For the determination of the thrust coefficient C T the following estimation is done: The relatively low wind speed (v ∞ = 8.8 m s −1 by UAS measurement) implies a pitch angle of β = 0°when approximating the E-112 with the NREL 5 MW offshore WEC (Jonkman et al., 2009). The tip-speed ratio (T SR = ΩR v∞ ) can also be calculated and thus a thrust coefficient C T ≈ 0.8 can be estimated from the C T to T SR relationship by Al-Solihat and Nahon (2018).
The BH vortex model does work for aircraft induced vortices as shown by Ahmad et al. (2014) as well as Fischenberg (2011) and as the results imply, it can be used to describe WEC wake vortex properties. Not least, both phenomena can be described by two vortices spinning in opposite direction, yet there is no interaction of the two opposite vortices, as in the aircraft wake model usually intended. Vortex patterns of a WEC wake show higher complexity than aircraft wake vortices. The whole wake is in 10 motion and different turbulence and shear forces interact with each other. Therefore, for the wake vortices some simplifications had to be made, e.g. the shown evaluation method is only valid for a 2-D cut of the whole vortex hose. Also the blade root vortex was not analysed any further.
In this study also the fact that the UAS experiences a change in true air speed (TAS) when entering the wake is addressed.
Theoretically the calibration range of the used five hole probe is for a fixed air speed which changes when entering the wake. 15 Since this evaluation uses the ratio of two velocities the influence of a different calibration for the five hole probe does not lead to a significant error. For the calculation of the circulation Γ, however, absolute velocities are necessary and a small error can be expected due to a change in TAS when entering and leaving the wake velocity deficit. The error is estimated to be ±10 % for the calculated wind velocities (Rautenberg et al., 2019a). An error estimation is given in Section 4.2.

20
The resulting circulation strength Γ derived from UAS data shows good accordance to the results obtained from Eq. 20. It can be concluded that the evaluation method, using the basic geometrical properties of a vortex, can be used to derive vortex properties in a WEC wake. Turbulence acting on the vortex and on the surrounding atmospheric flow can aggravate an evaluation since the evaluation is done mainly graphically. For example the second tip vortex is embedded in a relatively high level of turbulence 5 (wake deficit, shear, etc.). It also does not show a clear border to the undisturbed atmosphere as tip vortex 1 does. The reference velocity levels for the evaluation are therefore harder to extract from the measurements. Also a hit of a blade-tip vortex in flight changes the true air speed (TAS) locally and temporally, resulting in a (small) :: an error in the velocity measurement ::::::: (usually ::::::: 5 − 10% ::: off).
In addition, this method still has to be proven at larger distances to the WEC nacelle, where the vortices might begin to 10 meander and get unstable. However, to our knowledge, this is the first quantitative analysis of WEC tip vortices using in situ measured turbulence data by a fixed wing UAS.
The MASC Mk 3 system is capable of measuring detached tip vortices in the wake of a WEC. The spatial and temporal resolution is sufficient to detect vortex patterns in the measurements. However, on many occurrences, the measured sideslip β left the calibration range of the 5-hole probe and the corresponding pressure sensor was outside the measuring range, leaving 15 data lags in the time series. In conclusion, those measurements could not been used. For future measurements the calibration of the 5-hole probes could simply be expanded to larger angles. This also allows for a lower TAS (true air speed) of the UAV, which in turn results in a better spacial resolution of the data. The path accuracy of the UAS will be upped by using an RTK (real time kinematic) GPS : . :::: This :::: will ::::: allow ::: for :::::: precise ::::::::::::::: back-calculations :: of ::: the :::::::: positions :: of :::: the ::::::: vortices. ::::: Wake ::::::::::: meandering, :::: wake :::: and ::::: vortex :::::::: widening ::: can :::: then ::: be :::::::::: documented. 20 The proposed analytical vortex model by Burnham and Hallock is capable of describing WEC wake vortices. Yet, as for most analytical models, the analytical solution shown in this paper can and should be improved. E.g. to better fit the WEC wake (velocity deficit, blade root vortex near the nacelle). This evaluation was conducted with data obtained at 0.25 D from the nacelle. For a future additional field campaign blade-tip vortices in the farther wake shall be investigated.

Section 2
p.3,l.5: I think the link to Pixhawk should be given as a proper reference. The reference has been implemented.
p.5, Fig.3: Please label or mark the WEC more clearly in the picture. An updated graphic, containing a clear indication of the WEC, is now being used.
p.5,l.6: You state that only a single flight leg is presented, but then say the presented data was captured within 15 minutes. I do not think the one flight leg took that long, so pleases be more precise in the description of the data. The TKE seems very low, even for a quasi-marine boundary layer. Can you please add information about the time of day and any kind of information about the synoptic or mesoscale situation. You say that TKE was calculated from a ten second measurement which would be way too short for a point measurement. I assume you calculated it along a flight leg, but you have to let the reader know, including the length of the leg.
We have now implemented more information about the flight leg and set it apart from the flight pattern that took 15 min. The flight took place approximately at 6.30 PM at a usual summer day with clear sky and 25 • C air temperature. The TKE calculation has been done at hub height in the undisturbed, free atmospheric flow, averaged over approximately 200 m distance. Regarding the relatively low value for TKE: Depending on the calculation window (±100 indices) the TKE is about 0.1 m 2 s −2 . This corresponds to a standard deviation of the horizontal wind of ≈ 0.3 m 2 s −2 which should be alright for an evening transition with decreasing turbulence.
To clarify the mesoscale weather situation we can provide weather maps of the day of the field campaign ( Fig. 1) and if needed, implement it to the manuscript.
p.12,l.9: "blade-tip vortices are theoretically measurable." -I recommend to eliminate this sentence. It is trivial and does not add any The sentence has been altered.
Thank you, their position has been corrected.
p.14,l.14f: Changing the name of the new coordinate system is not enough. There is still an explanation of the new coordinate system required and this should probably go to section 3, because it is a method and not a result. In line 22 it is still called vortex coordinate system by the way.
We want to argue that this data rotation into the vortex plane is less a method than a reaction to the measurement reality, since the method assumes a ring vortex instead of a helical vortex pattern. It ought to be understood as the UAS canting into the vortex rotational plane to catch the whole rotational energy in a 2D-plane, whatever its orientation, and therefore minimising the w component. It is here described as the transformation of the UAS coordination system into the vortex coordination system (e.g. in line 22). This (individual) transformation introduces an error in the residual time series, but at a distance of ± r c around the vortex core where the evaluation takes place, the data is corrected. Meaning, the purple dashed and purple solid line overlay.
The section has been re-written and is now better structured. The purpose of this data rotation has been explained in separate paragraphs, followed by the presentation and explanation of the figures/data.
p.15, Fig.13: Please explain the x-axis in the caption. A more detailed description has been added.
p. 15,l.19f: I think this is a critical finding, because it looks like during the pass through tip vortex 1, the measured sideslip angle is outside the calibration range. In the conclusion and the data availability section it is said that data outside the calibration range cannot be used. In Figure 13, wind speeds in that range where sideslip is out of range is definitely shown. Thank you, I can understand how this might be confusing. So we have to be more clear hear. Therefore, I want to distinguish between to kinds of "out of range". The more severe type of "out of range" measurement is, when the 5-hole probe gets is measuring extreme pressure fluctuations due to the tip vortex. Sometimes those angles (and pressures) are so steep and and the pressures very high, that the pressure sensor itself is simply out of range. As a consequence, the data shows NAs or a data lag in the time series, when plotted. These data can not be used, since a part of the single most important feature, the vortex measurement, is missing. Then, there exist measurements, where the 5-hole probe is exposed "near critical". The flow angles are steep, but the pressure sensor can still handle it. No data lags are produced. Usually the flow angles are interpolated inside the calibrated range. But when a measurement is outside of the calibrated range, the flow angle can be extrapolated using the ninth order polynomial equation.

Section 5
p.19,l.17: I still think that from an experiment with a single sample it cannot be stated as a fact that a model is valid.
We can see the point. The sentence has been rephrased.

Section 6
p.20,l.21: What is a (small) error? Please be more objective.
As shown in the section covering the measurement error, the measurement uncertainty is about 5 to 10 %. We will be more precise on p.20,l.21. And still, only for high variations of the true air speed.
p.20,l.28: I disagree that a calibration range of a 5-hole probe can "simply" be expanded to larger angles. The characteristics of the probe geometry have to allow this. This is correct, different 5-hole probe geometries excel at different "measurement environments". The 5-hole probe operating on the MASC-3 UAS allows for an extension of the calibration range to ±40 • .
p.20,l.30: I do not understand why path accuracy and RTK GPS is relevant for this study. It is not mentioned as an issue.
The position of the UAS is used for the analytical BH model, e.g. Fig. 17. For future evaluation the position of the vortex can be calculated. Possible vortex or wake meandering could be derived from these positions, also the widening of the core radius can then be well documented.