Flying UltraSonic-A new way to measure the wind

Abstract. Measurements of flow conditions at complex sites that are difficult to install a met mast are expensive and can only be carried out with great effort. Concepts and new measuring methods are needed to evaluate these sites. This article presents an experiment in which an unmanned aerial vehicle (UAV), more precisely a helicopter, was equipped with a standard 3-D ultrasonic anemometer. This UAV was positioned closed to a meteorological measuring mast and remained stationary at a constant altitude to measure the wind speed components. The data of the UAV were compared with the measurements of an 5 ultrasonic sensor installed on the met mast. The measurements shows a deviation of 0.1 ms−1 for the horizontal speed. A comparison of the PSDs shows a very good agreement.

different flight patterns with high speed. The helicopter has its advantage in keeping a position during the flight. This results in different mission scenarios: -The main strengths of the fixed wing aircraft lie in its long range and flight time, which enables the survey of large areas.
-Because of its hovering characteristics, helicopters are ideal for measuring fixed positions / heights. For this experiment an existing helicopter system called AMPAIR was used. This helicopter system AMPAIR was equipped 5 with a 3-D ultrasonic sensor for the wind measurement. In comparison, a multi-hole probe is often used as a sensor for flow measurements in fixed wing aircraft [Wildmann et al. (2014[Wildmann et al. ( , 2017]. Such a combination of carrier system (helicopter) and measuring sensor (ultrasonic anemometer) has not yet been used for wind measurement. The aim of this experiment was to verify whether it is possible to determine the flow conditions with these alternative measuring methods. For the evaluation of the experiment data of a nearly located 95 m high meteorological mast 10 (met mast) with in-situ sensors was used.
In section 2 the experiment is described with an introduction of the helicopter system AMPAIR and a description of the location. In the section 3 the data preparation is described and in 4 the results are presented. Finally, the conclusion in section 5.
2 Experiment description 15 The aim of this experiment was to investigate whether it is possible to measure the flow conditions with an unnamed helicopter. To evaluate the measurements, flow measurements from a nearby stationary wind met mast are used. The two different measurement systems are compared with each other using statistical values such as mean value and standard deviation of the measurements, and the data are also examined in the frequency domain. The following section is structured as follows: In section 2.1 the used carrier system AMPAIR is introduced. Furthermore, in the section 2.2 the used measurement equip-20 ment is described, in the section 2.3 the site is characterized and in 2.4 the flight trajectory is presented.

AMPAIR Helicopter
AMPAIR is an electrically powered driven helicopter system, which was developed in the research project SOGRO -Sofortrettung bei Großunfall [Bergmann (2013)]. The AMPAIR is shown in Figure 1 and the technical parameters of the UAV are shown in Table 1. Due to the large rotor diameter and the powerful electric drive, the helicopter has sufficient thrust to be able to carry the sensors used for flow measurements, which are also used on wind met masts. The only question was how this sensor could 5 be mounted outside the main influence area of the rotor downwash. Furthermore, the mounting structure should not influence the flight aerodynamics, and no vibrations from the helicopter should not affect the performance of the sensor. Various concepts were developed and the final design was realized using in light-weight beam construction. A sensor boom with a length of approx. 2.22 m with a weight of approx. 0.5 kg was developed and built. This was be manufactured by using carbon fiber.
This had the further advantage that the mounting structure is extremely stiff with very low weight. In this experiment a 3-D 10 ultrasonic anemometer uSonic-3 Scientific from Metek was used. Due to vibrations and oscillations occurring during operation, the ultrasonic was not installed vertically as standard, but was mounted horizontally on the boom. Only the symmetrical arrangement of the ultrasonic anemometer on the longitudinal axis of the helicopter enables a nearly vibration-free operation of the sensor.
The flight time depends on the number of rechargeable battery packs carried. Since the maximum take-off mass is limited, 15 a compromise must be found between the payload used (e.g., equipped sensors) and the flight duration (number of batteries).
For this reason, the system is equipped with up to six battery packs and, depending on the flight time and required payload, it can be rearranged accordingly. One battery pack contains 11 A h each and has a mass of 4.8 kg. This allows a flight time in between 10 and 25 min with a variable payload of up to 10 kg.
The AMPAIR is equipped with an autopilot, which allows waypoint navigation as well as fully automatic flights. In addition 20 to an inertial sensor system, the helicopter also has an ultrasonic probe which is capable of measuring low altitudes for landing purposes. A telemetry connection to the system during the measurement flights allows a constant control of the flight and the adjustment of parameters in real time.

Measurement systems
This study compares data recorded with different measurement systems. To ensure that there is no time offset between the 25 different data sources, both systems synchronized with GPS time. The system on the wind met mast is a central data acquisition system that collects the data centrally at a sampling rate of 50 Hz.
Due to its size, the AMPAIR system does not need to be operated with miniaturized sensors, which, compared to commercially available sensor system (e.g., so called FirstClass sensors) show a larger deviation from the beginning. The used sensor in this campaign was a 3-D ultrasonic anemometer uSonic-3 Scientific from Metek, which is also used on met masts. The use of 30 proven and tested sensors that have been on the market for a long time should prevent negative influences from the measuring sensor. The AMPAIR contains two independently operating systems, to collect the required sensor data: The payload and the autopilot. -Payload: The payload contains the main components of the measuring system. The components are the electronics of the 3-D ultrasonic anemometer, the inertial measurement unit (IMU), the payload computer system electronic of the DGPS and the telemetry unit. The sensor head of the 3-D ultrasonic anemometer is connected to its evaluation electronics in the payload box and allows data recording up to 20 Hz. The AMPAIR is a mobile flying system with six degrees of freedom.
In order to transfer the measured wind speed data from the fixed system of the helicopter into the global reference system 5 of the met mast, the attitude is determined with the inertial measurement unit as well as the position via the DGPS. By recording accelerations and rotation rates via the IMU, the helicopter system's own movements can be recorded. Thus, wind speeds measured by the moving sensor can be corrected.
-Autopilot: The autopilots system logs all data of the autopilot system required for flight controller. These can be synchronized with the data of the payload via the GPS time. The following payload parameters are required for the post-10 processing of the measurement wind data: Position, altitude, acceleration, and heading of the helicopter

Site condition
The experiment was carried out near Grevesmühlen in the district of North-West Mecklenburg about 17 km south of the Baltic Sea. The site is shown in detail in Figure 2. At the time of the measurement, three wind turbines were installed at the site and one 95 m high met mast. The direct environment is not built-up and corresponds to an agricultural area with fragmented trees 15 and bushes. Further west, at about 1.3 km distance, there is a small settlement, and further south, at approx. 800 m distance, a densely forested area. The site corresponds to flat sites according to the IEC 61400-12 standard [International Electrotechnical Commission (2005)]. On the met mast there are several sensors at different heights for measuring wind speed, wind direction, pressure, and temperature ( Table 2). The sensor used for the comparison was the Thies Ultrassonic Anemometer 3D at 93.2 m.
The wind met mast has a large undisturbed sector which is not affected by the three wind turbines. This free sector extends from 121.83°to 355.17°(based on standard IEC 61400-12). The main wind direction at this site is in the free stream sector and is in the south-west direction (see Figure 3). In addition to the information of the direction, the wind rose also shows the wind speed bins in different colours. At this site wind speeds up to 14 m s −1 dominate. The data for the wind statistics were 5 collected from 04.09.2013 to 18.05.2014.

Flight Plan
The flight plan for this experiment is shown in Figure 4.

Data analysis
This section describes the steps to compare the measured data of the helicopter with the reference data of the met mast. The necessary coordinate transformations are described in 3.1 and in section 3.2 the correction of the induced velocities is discussed.
Induced velocities are additional velocities caused by the the helicopter's own motion, e.g. rotation around the body axes (see section 3.2). Furthermore, the measured signal must be corrected by the airspeed.

Coordinate Transformation
In order to be able to compare the measured wind speeds from the met mast with the measurements from the helicopter, the data must be available in a common coordinate system. The coordinate system of the met mast (Global subscript g) is a right-hand coordinate system, the x-axis points to the north, the y-axis to the west and the z-axis to the sky.
The helicopter has two different coordinate systems: The one from the sensor (subscript s) and the one from the body (body 10 subscript b). The two coordinate systems are right-hand systems. An overview of the individual coordinate systems is shown in Figure 6. In the sensor coordinate system the Z s axis points horizontally to the front, the Y s and X s axes are rotated by the mounting angle α to the horizontal plane. The Z b axes of the body coordinate system point downward, the X b points forward and the Y b points right. This is shown schematically in Figure 6b. The sensor coordinate system can be transferred to the body coordinate system with the fixed mounting angle α =30°. Additionally the axes X s to −Z b and the axis Z a to X b are swapped, 15 the wind speed components are also swapped accordingly. In the body coordinate system the X b -axis (roll) shows along the rump, the Z b -axis (yaw) is parallel to the shaft of the main rotor and shows downwards and the Y b -axis (pitch) accordingly.
The ZY X convention is used to transform the components in the body coordinate system into the components of the global coordinate system. This means a rotation around the roll, pitch and yaw angles. The following steps are necessary:   Transformation between the body and global coordinate system This transformation is shown schematically in Figure 6 b.1 to b.3 and can be described mathematically by the equations (1) and (2). From the components in the global coordinate system the wind direction (Equation (3)) and the horizontal wind speed 5 (Equation (4)) can be calculated.

Induced velocities
Due to the fluctuating flow conditions, the autopilot must constantly readjust to maintain the predefined position. The selfmotion induces additional velocities, which the ultrasonic also records. These induced velocities must be deducted from the recorded wind speed signal. The IMU of the helicopter records the rotation ratesφ,θ,ψ. These are needed to calculate the During the measurement phase, the rotation rates vary in the range of ±0.1 rad s −1 for the roll and yaw direction movement.
The pitch rotation is above ±0.2 rad s −1 and thus twice as large as the other two rotations (Figure 7). In Figure 8

Effect of rotation on the sonic measurements
The ultrasonic anemometer was installed for this application in a horizontal position and not vertically as it is originally designed. In principle, the position should not make any difference when evaluating the wind speed components. However, there 25 are considerable uncertainties as to which extent the ultrasonic anemometer will detect the induced rotational movements in the same way as assumed in this study. The functionality of a 3-D ultrasonic anemometer is simply described as follows: The ultrasonic anemometer has three transmitter-receiver pairs placed at 0°, 120°and 240°. Between the transmitter-receiver pairs there is a predefined distance. The transmitters emit sound waves and the receivers detect them again. The wind speed components u, v, w are calculated from the different running times of the sound waves. The measuring principle should determine the recording of the data of the met mast was continuous and not only during the flight campaign. In order to be able to compare the data with each other, they must be synchronized a second time. For the evaluation only the time period is used at which the AMPAIR has reached its target position and has entered the stationary mode for measurement.
For some evaluations such as cross correlation or coherence it is necessary that both signals have the same time resolution, so the wind speed components are resampled from 10 Hz to 50 Hz. A Fourier method is used [Hunter (2007)], the signal is 5 assumed to be periodic. Alternatively, the higher resolution signal could have been sampled down to the lower frequency. In this case, information would have been lost in the higher resolution signal. It was investigated if it makes a difference, but there was no noticeable difference between up-and downsampling in the results of covariance and Pearson correlations coefficient.
To compare the two sensors, the mean values (marked asx) and standard deviations (σ) are determined. Furthermore the turbulence intensity (T i) (Equation 7), the turbulent kinetic energy (TKE) (Equation 8) T KE = 1 2 σ u 2 + σ v 2 + σ w are transformed in main flow direction (necessary conditionv * = 0;w * = 0; values in the flow coordinate system are marked with * ). The length scales in v * , w * direction are evaluated with the wind speedū * in main flow direction.
The covariance (Equation 11 where E [x] is the expected value of variable X) and the Pearson's correlation coefficient To compare the data in the frequency domain, the Power Spectral Density (P SD) [Bendat and Piersol (2010);Hunter (2007)] for the wind speed components u * , v * , w * is determined as well as the coherence (C xy Equation 13) between the components of the sensors.

15
This section compares the measurements between the met mast and the AMPAIR.   Figure 10. Overview of the data processing workflow, form the measuring of the different system to the comparising of the results.
(2010); Hunter (2007)] for the wind speed components u * , v * , w * is determined as well as the coherence between the velocity components.
When evaluating the results, it should be noted that both measuring sensors are approx. 132 m apart from each other.
Before the results are looked at in detail, an overview is given of the distribution of the measurement data.

Distribution of the data 5
The distribution of the measurement data has a large influence on the statistical quantities such as σ, T i and T KE. The distribution depends significantly on how long the measurement is taken and whether the time series is stationary. The normalized probability density functions (PDF) of the v hor of the AMPAIR, that of the met mast ( evaluated time interval ) and for the whole 10 min period of the met mast are exemplarily presented in Figure 11. Furthermore the normalized normal distribution is shown. The PDFs are normalized with σ = 1 andv hor = 0. There are clear differences between the 10 min interval and the 10 evaluated time interval. The distributions of the AMPAIR and the 10 min interval resemble to the normal distribution. Quite in contrast, the distribution of the met mast for the evaluation period does not. Especially in the range of −3σ to −2σ the distribution shows larger deviations compared to the normal distribution, also in the region of 0.5σ. There is it more peaked.
The evaluated time interval overestimate the statistical parameter like the σ. For the evaluated time interval σ v hor = 1.61 m s −1 is compared to the 10 min period (σ v hor = 1.442 m s −1 ) 11.6 % higher. The more unstable conditions make it more difficult 15 for the AMPAIR to hover stationary and lead to more control interventions by the autopilot. Figure 12 shows the measured wind velocity components u, v, w in the global coordinate system for the measurement phase. In addition to subjective observation, the data is also statistically evaluated. The mean value and the standard deviation are used as criteria here. The statistical parameters are listed in the Table 3 and Table 4 shows slightly negative tendencies. The results give a conclusive picture. The integral length scale, as a quantity of how far the data correlates with itself, is much smaller as the distance between measurements systems. From this point of view, it is plausible that the values for ρ show no correlation.

Frequency domain
To compare the data in the frequency domain, the Power Spectral Density (PSD) is calculated from the data. It should be mentioned again that the sampling frequencies of the two measuring systems differ (UAV: 10 Hz; met mast: 50 Hz). When calculating the PSD S uu,vv,ww , efforts were made to take this into account and to adjust the resolution of the PSD. For the met mast, the PSD determined with N F F T = 1024 (NFFT: The number of data points used in each block for the FFT) data points the PSDs are shown in double-logarithmic scale. Additionally the theoretical spectrum for the ineratial subrange (∼ f −5/3 ) [Pope (2000)]. In comparison, the PSDs of the individual components u, v, w of the two measuring systems hardly differ from each other. The components v, w of the UAV have clear spikes between 1.5 to 3Hz, which do not occur in the met mast data.
The first assumption was, that these spikes were caused by the motion of the UAV (induced velocities), but these spikes are not visible in the PSDs of the roll, pitch and yaw rotation rates and also not in the PSDs of the induced velocities. Also possible 5 are oscillations, which are coupled in by the structure of the AMPAIR. However, it has not yet been possible to investigate this further. Definitely the influence of the rotor can be excluded because the rotor speed ranges from 780 rpm to 800 rpm, which exceeds the measurable frequency range of the ultrasonic (10 Hz). The spectra of the AMPAIR show a qualitatively good course with the theoretical spectrum. The measurements of the met mast also agree well up to approx. 5 Hz, at higher frequencies the spectrum drops.

10
In order to investigate the dependencies of the time series of the wind speed components u * , v * , w * in the frequency domain, the coherence ( Figure 15) was calculated. In addition, the coherence model according to Pielke and Panofsky coh(f ) = exp( −a·f ·D u ) [Pielke and Panofsky (1970)] was represented as a reference. The model uses as input parameters the frequency f , the mean wind speedū, the distance of the measuring points D and a decay parameter a in the order of 10 . The values here used are for the parameters a = 1 and a = 10 (see [Kristensen (1979)])and D = 132 m. For the parameter a two different 15 values were used, since the original proposed value (a = 10) appeared quite high compared to Simley [Simley and Pao (2015)].
Simley uses a modified model with a similar structure of terms, but only determined values between 0 to 2.5 for the parameter a depending on T i and the stability conditions. The measured coherence shows no significant correlation between the sensors.
The model after Pielke and Panofsky confirms this, that there should be no correlation at 132 m distance in the considered frequency range. When comparing the measured wind direction there are deviations of approx. 8.8°. A possible cause is that the compass heading (Yaw alignment) is disturbed by the electromagnetic field of the main rotor motor. The compass heading is a very central quantity in the transformation of wind components from the helicopter coordinate system to the global coordinate system. Another reason could be the wrong estimation of the v, w components during the rotation of the UAV body.

10
The other statistical quantities (e.g. ρ, cov ) show no similarities between the measurements. The reason for this is certainly the large spatial distance of 132 m and the relatively short common measurement period. The results of the integral length scales confirm this assumption. If the AMPAIR had come half closer to the met mast (distance of about 60 m), the agreement should be better.
The comparison of the energy of the met mast and the UAV data in the frequency domain also shows a very good agreement 15 among each other and also a very good agreement to the theoretical spectrum (∼ f −5/3 ). Due to the low sampling of the UAV ultrasonic, no influence of the rotation of main rotor on the wind measurement can be determined.
The comparison of the coherence shows no dependencies between the wind speed components. However, the theoretical model does not show any more dependencies in the representable frequency range at a distance of 132 m. For the representation of the low frequencies, where there should be a correlation, a higher sampling rate and a longer flight time are necessary for a 20 better resolution of the spectrum.
However, further improvements to the AMPAIR are needed. Sampling with 10 Hz is below the capability of the sensor (20 Hz). Furthermore, the effective measuring time must be increased. This is made possible by carrying more battery. However,