# On the Variation of Cup Anemometer Performance Due to Changes in the Air Density
## 4 Conclusions  
In the present paper, the uncoupled effects of changes in the air density and temperature on cup anemometer performance are analyzed. The most relevant outlines are as follows:  
* The effect of air density changes on the cup anemometer measurements (this effect being uncoupled with the cup anemometer's temperature, which affects the friction torque on the rotor's shaft) has been studied by analyzing data available from open sources. The results indicate a change in the performance of the cup anemometer at air densities of around 0.65 kg\(\cdot\)m\({}^{-3}\). This change can be attributed to the ratio between aerodynamic and friction forces, as when the last ones are of the same order as the first ones; the classic aerodynamic theory that is applied to this instrument (the average dynamic torque is zero in one turn of the anemometer's rotor), is no longer valid.
* Additionally, the effect of the wind speed measurement bias on the Annual Energy Production of three wind generators due to air density variation with respect to the one from the instrument calibration has been estimated. The maximum impact is reached at wind speeds around 6 m\(\cdot\)s\({}^{-1}\), the consequences being a 1.5% AEP decrease at air densities corresponding to 2917 m above sea level. For higher altitudes, the effect is much more severe (3.5% decrease at around 5000 m above sea level). Larger wind generators (9000 kW instead of 3000-4500 kW) are less affected by the discrepancy  
Figure 11: Percentage variation of the Annual Energy Production, \(\Delta\)AEP, of wind turbines W2E Wind to Energy W2E-215/9.0 (**Top-Left**), Enercon E112/4500 (**Top-Right**) and Vestas V112/3000 (**Bottom**), due to the error of the measured wind speed caused by the air density change (related to the air density during the instrument calibration process), in relation to the annual average wind speed at hub height, \(V_{\alpha,hub}\), for heights over the sea level \(h\), =550, 1100, 2917 and 4999 m.  
between measured and true wind speed due to the difference in the air density between where the anemometer is operated and where it was calibrated.
* More research is required to properly model the cup anemometer performance at air densities below 0.7 kg\(\cdot\)m\({}^{-3}\). This could help to extend the use of the cup anemometer to stratospheric balloons, bearing in mind the errors of sonic anemometers in these conditions due to the problems related to the sonic transmittance in low-density air.  
Conceptualization, S.P., D.A.-C., I.T.-G. and F.M.-G.; methodology, S.P. and D.A.-C.; validation, S.P. and D.A.-C.; formal analysis, S.P. and D.A.-C.; investigation, S.P. and D.A.-C.; data curation, S.P., D.A.-C., I.T.-G. and F.M.-G.; writing--original draft preparation, S.P., D.A.-C., I.T.-G. and F.M.-G.; writing--review and editing, S.P., D.A.-C., I.T.-G. and F.M.-G.; supervision, S.P. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors gratefully acknowledge [PERSON] for his encouraging support regarding the research program on cup anemometer performance. The authors are indebted to the reviewers, whose comments helped to improve the present paper.  
The authors declare no conflict of interest.