
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, R_{rc} is the cups’ center rotation
radius, S_{c} is the front area of the cups, and C_{d1} and C_{d2} 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 A_{r} is the calibration constant and f_{r} is the rotation frequency.
The ratio between the wind speed, V, and the rotation speed of the cups’ center, ωR_{rc}, 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 2cup 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 halfangle is 6 as compared to a typical value
of 4.77 for a 3cup 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 conicalcups 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 . P_{r} 
Where A = 2 . π . K . R_{rc }. 3.6 

2cup theory 


Anemometer Data 
Inspeed 
AAG 
K = 4.77 
Inspeed Spec. 
Radius R_{rc} (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 halfangle (θ)° 
41.760 
36.870 
 
 
Cup reverse halfangle (180θ)° 
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 
103117 
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 AvilaSanchez,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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