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Updated : 16/10/2016

Anemometer Theory and Calibration

Introduction

Rotation anemometers, such as cup and propeller anemometers, are the most commonly used instruments for wind speed measurements. Three cup anemometers are currently used as the industry standard for wind resource assessment studies. Thanks to their linearity and accuracy they are optimal for a large number of applications in the wind energy sector, from routine observations to field measurements. For the home enthusiast the cup or cone anemometer is the simplest and most reliable.

A rotation anemometer consists of a rotor arm or disc to which two or more (generally 3) cups are radially attached. A second internal rotor arm or disc is attached to the first via a shaft suppoted by bearings. The rotation speed of the internal rotor is measured by a rotation detector. Several type of rotation detectors are commonly used from rotary encoders to pulse generators which produce a signal pulse for each revolution of the rotor. The pulse generator may be a magnetic reed switch or hall effect ic, triggered by a magnet attached to the internal rotor, or optical detector. It is important to note that anemometers may have more than one detector to produce multiple pulses per revolution. The AAG anemometer is such a device and produces two pulses per revolution.

Theory of Cup Anemometers

Considering the simple case of a two cup anemometer as shown then under conditions of aerodynamic balance the forces F1 and F2 are equal and opposite and the situation can be described by the following expression:-

where V is the wind speed, ω is the rotor’s angular velocity, Rrc is the cups’ center rotation radius, Sc is the front area of the cups, and Cd1 and Cd2 are the drag coefficients of the cups, respectively at 0° and 180° regarding the wind direction.

This equation can be simplified to obtain the transfer function of the anemometer:

Where Ar is the calibration constant and fr is the rotation frequency.

The ratio between the wind speed, V, and the rotation speed of the cups’ center, ωRrc, is called the anemometer factor, K:

The above figure shows the coefficient of drag for cones as a function of the cone half angle.
Note: A half angle of 90° is a flat disc with a CD of 1.17. A cone moving the opposite direction will have a CD equivalent to a halve angle of 180 - cone half angle

The above figure shows the 2-cup anemometer model and the anemometer factor K, as a function of the ratio between the aerodynamic drag coefficient of the cups at 0° wind angle, cd1, and at 180° wind angle, cd2.

The K value for an anemometer with two cone cups of 45 degree half-angle is 6 as compared to a typical value of 4.77 for a 3-cup anemometer. Extensive research has been conducted to develop an accurate methematical model for anemometers but to date no model has been able to satifactorily predict the transfer function of cup anemometers.

Even amongst high end anemometers significant variablity exists since even slight variations in cup shape, the existence of an edge bead etc. produce unpredictable changes to the drag coefficients resulting in a large scatter of the K value and transfer function as shown in the figure below.

Anemometer factor, K, of different commercial cup anemometers (big open circles) as a function of the ratio between the cups’ radius, Rc, and the cups’ center rotation radius, Rrc. The experimental data corresponding to different conical-cups rotors tested on an Ornytion 107A anemometer have been added to the graph. The symbols correspond to the following cups radius: Rc = 20 mm (open squares), Rc = 25 mm (closed squares), Rc = 30 mm (open triangles), Rc = 35 mm (closed triangles), Rc = 40 mm (open rhombi). A quadratic fit to this experimental data has been also added (dotted line). The analytical value calculated for the tested cases using Ramachandran’s method has been also included in the graph (solid line).

Calibration

It must be concluded that at present there is no satisfactory method of predicting the transfer function of cup anemometers and therefore, an anemometer must be individually calibrated before use, either in a wind tunnel or by direct comparison with a certified instrument. It should also be noted that manufacturers of lower cost anemometers used by hobbyist may have had a master model independently calibrated but it is unlikely that the instrument you receive will have been calibrated against that master. More likely, is that you will be given the tranfer function of the master and there is ample evidence that your instrument, whilst outwardly similar to the master, may have a markedly different transfer function.

A comparison of the calibration and transfer function of the Inspeed Vortex and AAG anemometers is shown in the following table:

V (kph) = A . Pr
Where A = 2 . π . K . Rrc . 3.6
2-cup theory    
Anemometer Data Inspeed AAG K = 4.77 Inspeed Spec.
Radius Rrc (m) 0.056 0.060 0.060 0.060
Cup diameter (m) 0.050 0.072 - -
Cup Depth (m) 0.028 0.048 - -

Calculations

Cup half-angle (θ)° 41.760 36.870 - -
Cup  reverse half-angle (180-θ)° 138.240 143.130 - -
CDs 0.715 0.658 - -
CDl 1.348 1.363 - -
Alpha 0.728 0.695 - -
Anemometer factor K 6.354 5.553 4.770 2.947
Transfer Function A 8.048 7.536 6.474 4.000
Rotation speed (rad/sec) per (m/s) 2.811 3.002 3.494 5.655
Rotation (rps) per  (m/s) 0.447 0.478 0.556 0.900
Rotation (rps)  per (km/hr) 0.124 0.133 0.154 0.250
No of pulses per revolution 1.000 1.000 1.000 1.000
Counts per second per (km/hr) 8.048 7.536 6.474 4.000

If your anemometer is a commercial product then contact the supplier for the transfer function. If this is not available then use a value of 3 for the anemometer factor K.

To determine the wind speed measured by the Inspeed anemometer in miles per hour the manual from Hobby Boards indicates that the counts per minute (RPM) be multiplied by 2.5. To obtain the output in kph the factor should be increased to 4.023. Comparisons of the output with a local airport (FAOR 10 km away) and the conditions noted in the Beaufort scale below over a period of several weeks indicate that a factor of 4.023 provided a reasonable correspondence to the values from the Beafort scale and the local airport.

Beaufort Wind Scale

Beaufort number Description Wind speed kph Land conditions
0 Calm < 1 Calm. Smoke rises vertically.
1 Light air 1.1–5.5 Smoke drift indicates wind direction. Leaves and wind vanes are stationary.
2 Light breeze 5.6–11 Wind felt on exposed skin. Leaves rustle. Wind vanes begin to move.
3 Gentle breeze 12–19 Leaves and small twigs constantly moving, light flags extended.
4 Moderate breeze 20–28 Dust and loose paper raised. Small branches begin to move.
5 Fresh breeze 29–38 Branches of a moderate size move. Small trees in leaf begin to sway.
6 Strong breeze 39–49 Large branches in motion. Whistling heard in overhead wires. Umbrella use becomes difficult. Empty plastic bins tip over.
7 High wind, moderate gale, near gale

50–61

Whole trees in motion. Effort needed to walk against the wind.
8 Gale, fresh gale 62–74 Some twigs broken from trees. Cars veer on road. Progress on foot is seriously impeded.
9 Strong gale 75–88 Some branches break off trees, and some small trees blow over. Construction/temporary signs and barricades blow over.
10 Storm, whole gale 89–102 Trees are broken off or uprooted, structural damage likely.
11 Violent storm 103-117 Widespread vegetation and structural damage likely.
12 Hurricane force ≥ 118 Severe widespread damage to vegetation and structures. Debris and unsecured objects are hurled about.

Sources

  • Santiago Pindado *, Javier Pérez and Sergio Avila-Sanchez,On Cup Anemometer Rotor Aerodynamics
    Available Online at Sensors
  • Santiago Pindado, Imanol P´erez and Maite Aguado, Fourier analysis of the aerodynamic behavior of cup anemometers.
    Available Online
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