# Technical literature

Here you find technical notes and scientific documents, all in PDF format.

**Technical notes**

The Working of the Cup Anemometer

This note discusses the cup-anemometer dynamics in a slightly different presentation. Further it contains af presentation of the oversimplified Schrenk model which illustrates in detail how the non-linearity of the anemometer causes overspeeding and also shows that without this property is responsible for the ability for the rotor to start rotating from zero wind speed. There is a short discussion of the spectral analysis, necessary for the understanding of the dynamics. The equations for overspeeding is derived for the neutral atmospheric surface layer and extended to include overspeeding in wind tunnel calibrations, albeit the turbulence here is in general very small.

Deficit of Wind-Speed Variance and Standard Deviation as measured by a Cup Anemometer

The dynamics of a cup anemometer can In its simplest form be described as a first-order filter with a time constant equal to the distance constant divided by the mean wind speed. This means that the Instrument is unable to capture the contributions from highest frequencies or largest wave numbers of the turbulence to the variance. Using a standard model for the surface-layer turbulence the loss of variance and standard deviation are determined as functions of the ratio of the distance constant and the height of the measurement. Two cup anemometers and a sonic are compared.

**Refereed papers, reports and proceedings**

The Cup Anemometer and Other Exciting Instruments

This report is mainly a discussion of dynamics of a cup anemometer. It is pointed out that the so-called overspeeding, caused by the atmospheric turbulence, is due to the fact that the cup rotor will speed-up more readily by an increase in the wind velocity than speed-down by a decrease of the same amount. The result is that, in principle, the measured wind speed with a given mean is larger than corresponding that obtained in a laminar (low-turbulence) wind tunnel with the same wind speed. This is a manifestation of the non-linearity of the cup anemometer response. In other words, the equation for the dynamics of a cup anemometer includes the wind fluctuations of second order. From a practical point of view the overspeeding is seldom important. Only when the wind speed is small, as in very convective conditions, it might be a problem. This is discussed in detail. The most important source of wind-speed bias is the non-ideal angular response. The cup-anemometer response to fluctuations in the (up-down) direction perpendicular to the rotor is in general important. To eliminate this bias it requires that the cup anemometer has a cosine response. Apart from this complication, the cup anemometer can be considered a spatial first-order filter, responding to fluctuations in the mean-wind direction, with a linear mean-wind calibration. The filter effect is described in terms of the distance constant, which is an instrument constant. The discussion is extended to the dynamics of instruments with non-linear calibration and instruments with second-order response.

Cup Anemometer Behaviour in Turbulent Environments

This article is an extract from the report Risø-R-615. It is entirely about the cup anemometer in a neutrally stratified atmospheric surface layer (from 0 to about 100 meter over the surface). Usually this state of the atmosphere corresponds to wind speeds of more than about 5 m/s with a corresponding well-defined mean-wind direction. This Is relevant to many wind power applications.

The Perennial Cup Anemometer

Here we apply an intuitive approach to an understanding of cup-anemometer dynamics and overspeeding. After a short historical presentation, the (somewhat unrealistic) Schrenk model and its consequences are discussed. It is shown how the wind-direction fluctuations always will cause a positive bias on the measured mean wind velocity i.e., the mean-velocity component in the direction of the wind. This bias is the so-called DP-error (data-processing error), the expression being coined by Paul MacCready who, in the early seventies, constructed the first man powered aircraft, Gossamer Condor. It is shown that the DP-error can be eliminated by using a wind vane together with the cup anemometer. This is supported by full-scale field measurements.

Wind Tunnel Calibration of Cup Anemometers, AWEA 201206

The paper describes wind tunnel calibrations of cup anemometers and classification of cup anemometers based on wind tunnel measurements of their tilt angular response and rotor torque characteristics. The results are used for power-performance and wind-resource estimates, and all measurements applied follow the procedures specified in IEC 61400-12-1 and are carried out in wind tunnels being accredited and Measnet approved.

Cup anemometer aerodynamics and wind tunnel aerodynamics are considered and used to evaluate the uncertainties involved in cup anemometer calibrations. The IEC procedure for cup anemometer calibrations specifies flow requirements of the empty working section, e.g. requirements concerning flow homogeneity and upper limit of flow turbulence, and tunnel size in form of maximum blockage ratios. The paper documents that deviation between fullscale and model-scale air turbulence and the interference effects between tunnel boundaries and rotating rotors of cup anemometers including their mounting systems may introduce a significant bias on the calibration results. This, however, is not taken into consideration by the specifications of the IEC procedure.

The importance of distance from cup anemometer rotor to tunnel boundaries is illustrated for both open and closed tunnels. It is shown that a certain minimum distance from rotor to tunnel boundary is crucial for avoiding significant contributions from these interference effects. If this distance is too small the tunnel boundary may be sucked towards the rotor in open tunnels or a friction force may be generated in closed tunnels. The suction towards the rotor in open tunnels may lead to accelerated flow in the central part of the cross section, and thereby increased rotation rate of the rotor. The friction force in closed tunnels will decrease the rotation rate of the rotor. Thus, interference effects as the ones described above will systematically bias the calibration results obtained significantly for small wind tunnels with a short distance from rotor to tunnel boundaries.

The present IEC procedure is based on a number of assumptions, which may lead to deviating calibration results. We recommend that the ongoing revision of the IEC procedure takes the new findings into consideration and that the effects shall be quantified by carrying out reference calibrations in very large wind tunnels with negligible contributions from blockage and tunnel boundary interference effects. In this way the updated procedure will reduce calibration uncertainties to a minimum and thereby minimize the uncertainties inherent in wind resources estimated for a specific site.

Distance Constant of the Risø Cup Anemometer

The distance constant, which is a true instrument constant, can in principle be determined in a wind tunnel by recording, at a particular wind speed, the time it takes to be for the rotor to obtain equilibrium with the wind after starting from zero rotation rate. It seems easier to use the method applied here, namely the power-spectrum method. A field experiment where the output from a sonic anemometer and a cup anemometer at the height of about 2 m and laterally displaced by approximately 2 m measured simultaneously the wind velocity with high temporal resolution. The duration of each of the 19 runs varied between 5.5 h and 37 h. The wind velocity in these periods varied from 1.76 m/s to 8.64 m/s. The result was that the distance constant was measured to be 1.81 m with the standard deviation 0.04 m.

Cups, Props and Vanes

The dynamics of the cup anemometer and the wind vane are discussed, the first in terms of the semi-empirical model developed in Risø-R-615. The basic equation for the vane is re-derived. This equation is a second-order differential equation which means that it has both distance constant and a damping ratio. The most interesting result of the analysis is that if we can design a wind vane with a damping ration of 0.38 we have constructed an instrument with an overshoot which, in the atmospheric surface layer, compensate exactly for the loss of lateral variance due to low-pass filtering.

Measuring Higher-Order Moments with a Cup Anemometer

The overspeeding is a bias on the mean-wind velocity. However, a cup anemometer can be sampled with so high a rate that it is possible to determine higher-order moments. It is therefore useful to know if these moments are bias free. A rather complicated theoretical analysis shows they actually are. This is documented by field measurements where the signals from a cup anemometer and a sonic anemometer are used to compute second, third,-and fourth order moments. Also skewness and kurtosis are determined form the data and compared. It is quite obvious that there is a statistical spread, in particular for the highest moments. But there is no discernible bias.