On the use of cup anemometers as wind speed sensors in stratospheric balloon missions

Stratospheric balloon missions have emerged as a cost-effective alternative to space missions for scientific research and technology development. These missions enable the collection of critical data from the Earth’s upper atmosphere while reducing financial and logistical burdens associated with traditional space missions. One key challenge in these missions is the accurate measurement of the relative-to-the-gondola wind speed in the tropopause and the stratosphere. This paper explores the viability of using cup anemometers as wind speed sensors in stratospheric balloon missions, offering an easy-to-calibrate, low-cost, and accurate solution. The present paper provides a short overview of stratospheric balloon missions and their relevance in atmospheric research and outlines the challenges and limitations of existing wind speed sensing technologies. The cup anemometer is also described, detailing its working principle, advantages, and limitations, and propose a methodology for incorporating the instrument into stratospheric balloon missions. To validate the proposed methodology, a stratospheric balloon mission (the Tasec-Lab experiment, onboard a B2Space balloon launched in 2021), was equipped with a cup anemometer whose performance was analyzed. The results prove that cup anemometers can provide accurate and reliable relative wind speed measurements in the tropopause and the stratosphere. Furthermore, the low power consumption and the ease of development and calibration of cup anemometers make them an attractive option for stratospheric balloon missions.


Introduction
Stratospheric balloon missions are nowadays a very popular low-cost solution for space systems analysis.They provide a cost-effective, quick, easier and less restrictive way of developing space missions which eases the way for academic and commercial institutions to the space sector [1].However, this type of mission can face different challenges regarding its design, which can differ significantly from those from traditional space missions.
One of the main differential challenges is the thermal characterization of the mission, which includes the definition of the cold and hot cases.For traditional space missions, the thermal characterization of the mission has been thoroughly studied over the time, with radiation and conduction as the main and only types of heat transfer [2,3].However, for stratospheric balloon missions, the definition of the cold case differs significantly.In this type of missions, the ascent phase has long residence periods on the different layers of the atmosphere which makes it necessary to study the presence of convective heat transfer for the definition of the cold case of the mission [4].
In the tropopause (about 11 km above ground), extreme environmental conditions are encountered.Very cold air temperatures are combined with high intensity winds with a non-negligible air density.Therefore, it has become necessary to measure the relative wind speed to which the balloon's gondola is exposed, with the aim to correctly estimate the forced convection on the gondola [5].
In addition, there are other circumstances where the wind speed needs to be measured in a lowdensity environment such as in meteorological applications and wind farm design and operation at high altitudes.
For the wind speed measurement in low density environments, the literature shows a lack of research.Sonic anemometers have been tested by Maruca et al., which show this type of instrument can make measures to a top altitude of 17 km, with poor measurements above 18 km [6].However, stratospheric balloons can reach higher altitudes (18-37 km commonly), which makes the sonic anemometer not-at-all ideal for the expected floating altitudes of the mission and for part of the ascent phases.Taking the above into account, the use of a modified cup anemometer was considered for this type of mission, as it is inexpensive, easy to calibrate, thoroughly tested and reliable instrument [7].An special cup anemometer was developed in order to assure its operation under very low-density environments, modifying its geometrical properties for an optimized working ceiling altitude.
The paper is divided as follows.In Section 2, the modified cup anemometer design process and result is described.In Section 3 the stratospheric balloon mission where the instrument was tested is described.In Section 4, results from the measurements of the instrument are presented.Finally, in Section 5, the conclusions of the work are presented.

Design of an anemometer for use in environments of very low density.
The design of a cup anemometer for low density environments was done following the conclusions of the previous research performed in the Instituto Universitario de Microgravedad "Ignacio Da Riva" (IDR/UPM) on the performance of the instrument at low densities [8].The research work analyzed the behavior of different anemometer geometries at very low wind speeds, in order to characterize the performance at very low air densities.Different configurations of the cup radius R c and arm radius Rrc (see Figure 1) of the anemometer were tested.
Research analyzed the starting and stopping points of the anemometer with different rotor configurations.For this, the dynamic pressure of the wind affecting the anemometer at the starting and stopping points was taken as the evaluation parameter.The starting and stopping points were analyzed via wind tunnel tests.For this, the IDR/UPM S4 wind tunnel facility was used.In Figure 2, the results of this analysis are shown.
From the results it can be stated that the start and stopping points behave differently for different anemometer geometries.The dynamic pressure for these points can vary significantly in some orders of magnitude.Results show that the stopping and starting points have quite stable values for values of Rc/Rrc lower than 0.4 and values of Rc of 40 mm.Taking the above into account, the modified anemometer was designed based on the body of a First Class Vector Instruments A100L2 cup anemometer.The cup anemometer rotor was designed with a cup radius Rc of 40 mm whilst its relationship Rrc/Rc was 0.41.The rotor was 3D printed with ABS.From the results obtained it was concluded that an anemometer with such geometry would be able to reach altitudes of at least 25 km in working conditions.

The TASEC-Lab experiment
The TASEC-Lab experiment is a CubeSat-Like experiment which was developed by the IDR/UPM with the aim to characterize the convective heat transfer in stratospheric balloon missions [9].The experiment characterized how the heat dissipates in the ascent and float phases of a stratospheric balloon flight using different heat plates.As the convective heat transfer is formed by the natural convection (the convection formed by temperature gradients inside the experiment) and by forced convection (the convection caused by the wind interacting with the gondola and the experiment), it was necessary to measure the relative-to-the-gondola wind to correctly characterize the contribution of each type of convection.
For this purpose, the anemometer described in Section 2 was developed, built and integrated into the gondola of the stratospheric balloon (see Figure 3) which was launched from the aerodrome of León (Spain) as part of the Be2Space mission in July 2021 (see Figure 4).Leaving aside the measurement of the relative-to-the-gondola horizontal wind speed during the most critical part of the ascent phase (the tropopause, at 11 km), it can be said that the aim of this mission was also to test the behavior of cup anemometers, to validate the use of this type of sensors at very high altitudes.The stratospheric balloon performed a flight of 1 h and 5 min, and reached an altitude of 18 km.The balloon did not reach its floating altitude as due to some external delays on the launch, the Spanish air authority ordered the early abortion of the mission.

Results and analysis
The output signal frequency of the anemometer during the mission in relation to the mission time is plotted in Figure 5.As it can be seen, the anemometer dropped measurements for the whole duration of the mission.In addition, a sudden increase in the output signal frequency is observed at some point in the mission, which coincides with the moment the tropopause altitude of 11 km is reached.
For the conversion of the frequency output of the cup anemometer to a wind speed measurement, the conventional transfer function was applied [10]: Following the transfer function stated in Equation ( 1), a correction needs to be made to the calibrated wind speed measurement in order to properly correct the measurements made at different air densities.The little literature on this subject refers commonly to the dynamic pressure as the variable to which the anemometer response is referred to [11,12].In accordance with the above results were preliminary corrected as follows: where V and ρ represent the actual wind speed and air density and V0 and ρ0 represent the calibration wind speed and air density.However, research is actually being performed to better analyze the influence of density in the performance of cup anemometers and to provide better confidence to the correction techniques.The results after the application of the transfer function stated in Equation ( 1) and the air density correction of Equation ( 2) are shown in Figure 6, related to the altitude of the stratospheric balloon.As it can be seen, the anemometer has been able to read high horizontal wind speed values at altitudes of above 11 km, which correspond to the level at which the tropopause is typically encountered.The registered wind speeds above 10 m/s are consistent with the literature from previous analysis of this phenomenon on stratospheric balloons [13].
However, for a better validation of the measurements of the cup anemometer at these altitudes, the measured wind speeds were correlated with the acceleration of the balloon gondola, which was derived from the GPS position data of the mission.This comparison was made as it is considered that the horizontal acceleration of the balloon gondola is related to the relative wind speed which acts as the force which moves the gondola, proportional to the dynamic pressure [14]: (3) Thus, considering Equations ( 1) and (2) it can be said that:   anemometer, related to the gondola acceleration derived from GPS data.For better read, the 3 min average values and their standard deviation are shown.Data shows quite a good relationship between the square of the output frequency and the acceleration of the gondola, which can be extracted from analysis of the 3 minute average values of both variables.This good correlation, based on Equation ( 4), shows that the anemometer readings correspond to actual measurements of the relative horizontal wind of the gondola, and that during the whole experiment and up to an altitude of 18 km, the instrument provided real readings of the relative wind, validating the work from Ramos Cenzano et al. [8] and stating that the cup anemometer is a viable instrument for the measurement of wind speeds in low density environments.
In addition, these measurements and relative wind speed estimations help to better analyze the thermal behaviour of stratospheric balloons in the ascent phase, as the encountered high wind speeds, together with the high enough air density (0.35 kg/m 3 ) create a non-negligible forced convection which needs to be considered for the cold case analysis of the mission.

Conclusions
In this paper, the process of developing a modified cup anemometer for measuring the relative wind speeds of a stratospheric balloon to measure winds speed up to a ceiling altitude of 25 km has been described.In the process, the optimal geometry of the rotor of the cup anemometer has been studied.The main conclusions of the above work are the following ones: • The optimal geometry was applied in the development of a 3D printed rotor for a cup anemometer which was installed together with the TASEC-Lab experiment onboard the stratospheric balloon mission of B2Space, which was launched from León in July 2021, and reached a ceiling altitude of 18 km.• The output data of the mission reveal the anemometer gave measurements for the whole duration of the flight.• The obtained data, after corrections for density revealed measurements of horizontal relative wind speeds of 10-15 m/s at and above the tropopause.• The recorded data was validated with comparison with data from horizontal acceleration of the gondola, caused by horizontal relative wind speeds.Both data tend to correlate, validating the output of the instrument.• The resulting measured relative horizontal wind speeds in the tropopause enhance the need to analyze the ascent phase and more precisely the tropopause in the cold case analysis of stratospheric balloon missions.

Figure 1 .
Figure 1.Detail on the parameters Rc and Rrc varied during the tests performed to analyze the performance of the cup-anemometer in a low air density environment.

Figure 2 .
Figure 2. Start (left) and stop (right) points of a modified Climatronics 100075 cup anemometer with different geometries (Rc and Rrc).The start and stop points are evaluated as the dynamic pressure of the air interacting with the anemometer [8].

Figure 3 .
Figure 3.The TASEC-Lab experiment and the cup anemometer onboard the Be2Space gondola before launch.July 2021.

Figure 4 .
Figure 4. Launch of the Be2Space mission, from the aerodrome of León, in July 2021.

Figure 5 .
Figure 5. Cup anemometer output signal frequency f related to the mission time t.The frequency was recorded at a rate of 1 Hz with the signal sampled at a rate of 3 kHz.
where f is the output frequency of the cup anemometer.The chart comparing the derived gondola acceleration with the measured wind is provided in Figure7.As the data measured contains a high .1088/1742-6596/2716/1/0121006 level of noise, the main values for a reference period of 3 minutes are included together with the standard deviation of the values for the same reference period.

Figure 6 .
Figure 6.Density corrected measured wind speed V, related to the balloon altitude h.The wind was measured at a rate of 1 Hz.

Figure 7 .
Figure 7.Comparison between the square of the output frequency of the cup