Hindawi Publishing CorporationThe Scientific World JournalVolume 2013 Article ID 197325 11 pageshttpdxdoiorg1011552013197325

Research ArticleAerodynamic Analysis of Cup Anemometers PerformanceThe Stationary Harmonic Response

Santiago Pindado Javier Cubas and Aacutengel Sanz-Andreacutes

Universidad Politecnica de Madrid ETSI Aeronauticos Instituto Universitario de Microgravedad ldquoIgnacio Da Rivardquo (IDRUPM)Plaza del Cardenal Cisneros 3 28040 Madrid Spain

Correspondence should be addressed to Santiago Pindado santiagopindadoupmes

Received 29 July 2013 Accepted 10 September 2013

Academic Editors D Missirlis and G Pascazio

Copyright copy 2013 Santiago Pindado et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The effect of cup anemometer shape parameters such as the cupsrsquo shape their size and their center rotation radius wasexperimentally analyzedThis analysis was based on both the calibration constants of the transfer function and the most importantharmonic termof the rotorrsquosmovement which due to the cup anemometer design is the third oneThis harmonic analysis representsa new approach to study cup anemometer performances The results clearly showed a good correlation between the averagerotational speed of the anemometerrsquos rotor and the mentioned third harmonic term of its movement

1 Introduction

The importance of wind energy for modern societies is todaya fact [1] Some countries have clearly supported this industryat the end of the twentieth century (Denmark GermanySpain ) and as a result they have led most of the technicaladvances on the scientific areas related towind energy On theother hand some other countries have started to invest moreand more in their wind energy sector the consequence beingthat at present these new players not only show the highestfigures of wind energy installed power but also the highestgrowing rates (China USA and India) see Table 1

As the extractable wind power is proportional to the thirdpower of the wind speed [2] the wind industry demands thebest instruments to measure it with special interest in twoparticular aspects wind energy forecast on the field and windturbine performance control [3]This fact has made the windenergy sector a mass consumer of cup anemometers all overthe world

Despite technological advances as LIDAR or SODAR [4ndash7] the cup anemometer invented in the XIX century formeteorological purposes [8] remains today the most properinstrument for the mentioned tasks of wind energy forecaston the field andwind turbine control Furthermore followingthe IEC-61400-12-1 standard [9] the power performance of

a wind turbine is preferred to be based on the wind speedmeasurements performed with a calibrated cup anemometer[10 11] Taking into account the great importance of the windspeed measurements accuracy a huge work was done duringthe XX century by researchers and scientists to improvethe cup anemometer and to have a better understanding ofits performance After initial efforts to study and optimizethe size of the anemometer [12ndash14] the cup aerodynamics[15 16] and the output frequency recording systems [17ndash21]the researchers focused on the analytical and experimentalanalysis of anemometer performance in the field [16 1922 23] Obviously the aforementioned studies were possiblethanks to the advances in experimental techniques achievedin the first part of the XX century

From the point of view of the wind energy industrythe cup anemometer performance is based on the transferfunction

119881 = 119860 sdot 119891 + 119861 (1)

where 119881 is the wind speed 119891 is the anemometerrsquos rotationfrequency output and 119860 (slope) and 119861 (offset) are thecalibration coefficientsThis linear equation which correlatesthe wind speed and the anemometerrsquos output frequency[24] must be defined by means of a calibration process

2 The Scientific World Journal

Table 1 Installed wind power per country (units in GW) of some of the biggest world producers from 2005 to 2012 The growing rates (withrespect to the preceding year) corresponding to 2011 and 2012 have been also added in brackets to illustrate the present status of the windenergy market (sources Global Wind Energy Council US Energy Information Administration)

Country 2005 2006 2007 2008 2009 2010 2011 2012

China 126 260 591 1220 1600 3110 6236(1005)

7556(212)

USA 871 1133 1652 2465 3430 3914 4692(199)

6004(280)

Germany 1843 2062 2225 2390 2570 2720 2908(69)

3151(84)

Spain 992 1172 1480 1660 1910 2070 2167(47)

2280(52)

India 530 620 780 1000 1100 1307 1608(231)

1842(145)

Italy 164 190 270 353 488 579 688(188)

815(185)

UK 157 196 248 341 442 538 647(203)

837(293)

Canada 068 146 177 237 332 397 565(422)

659(165)

Portugal 106 168 220 286 333 380 430(133)

445(34)

Brazil 003 024 025 041 060 093 151(628)

259(714)

[9 25ndash27] and was quite early defined for the Robinson-typeanemometer [28] The transfer function can be rewritten interms of the anemometerrsquos rotation frequency 119891

119903 instead of

the output frequency 119891 introducing in the expression thenumber of pulses per revolution given by the anemometer119873

119901

119881 = 119860 sdot 119873

119901sdot 119891

119903+ 119861 = 119860

119903sdot 119891

119903+ 119861 (2)

The expression above is preferable than the preceding oneas it has a clearer physical meaning Expression (2) alsoallows a direct comparison between anemometers [29] andbetween experimental results and analytical models [30 31]The number of pulses 119873

119901 is different depending on the

anemometerrsquos inner system for translating the rotation intoelectric pulses Magnet-based systems give 1 to 3 pulses perrevolution whereas optoelectronics-based systems normallygive higher pulse rates per revolution from 6 to 44 [29]

Leaving aside thewide acceptance of the industry it is alsofair to recognize the existence of some special uncertaintiesassociated with the cup anemometer wind speed measure-ments On the one handwe have the ldquooverspeedingrdquo problemwhich was detected and studied from the beginning of theXX century [32 33] The cup anemometer ldquooverspeedingrdquoconsists in a quicker response upon wind flow accelerationthan the one obtained after a wind flow deceleration Dueto the impact on the measured wind speed and turbulencethis effect (together with the problems related to the errorcaused by the vertical component of the wind) was one ofthe biggest concerns for meteorologists during the secondhalf of the XX century [34ndash41] All the researches done werequickly applied to the wind energy industry particularly to

the effect of the accuracy on the wind turbine power [42] andthe classification and improvement of cup anemometers [43]

From 2009 cup anemometer performances have beenanalyzed at the IDRUPM calibration lab focusing on theeffect of the rotor shape [29 44] the effect of air densityand climatic conditions [45] and the effect of aging [46]Recently research done at the IDRUPM has been focusedon the uniformity of anemometer rotation as even in a verylow turbulence and stationary wind flow the rotation speed isnot purely constant being composed by harmonic terms

The cup anemometer has a standardized configuration ofthree cups as the 3-cup anemometer has become the mostefficient solution when compared to the 4-cup anemometer(this was the initial configuration of the cup anemometerdeveloped in the XIX century) This 3-cup design makes therotational speed of this instrument not uniform [47] Therotational speed of a 3-cup anemometer 120596 under a perfectlyconstant and uniform wind speed can be decomposed alongone turn into a constant term 120596

0 plus a series of harmonic

terms that correspond to a frequency three times bigger thanthe one related to the mentioned constant term 3120596

0 and its

multiples 61205960 91205960 121205960

120596 (119905) = 120596

0+

infin

sum

119899=1

120596

3119899sin (3119899120596

0119905 + 120593

3119899) (3)

In Figure 1 the non-dimensional rotation speed 120596(119905)120596

0 of

a Thies 43303 anemometer at 8ms wind flow is shownThe third harmonic term can be clearly appreciated as themost important of the rotation speed obviously leavingaside the constant term 120596

0 The aforementioned study on

the regularity of the rotation speed of the anemometers at

The Scientific World Journal 3

120596120596

0

12

11

10

09

08

00 01 02 03 04 05 06 07 08 09 10

tT

(a)

120596i1205960

i

010

008

006

004

002

0001 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

(b)

Figure 1 Relative-to-the-average rotational speed120596120596

0 of aThies 43303 anemometer during one turn at 8ms wind speed [47] (a) and non-

dimensional values of the Fourier series decomposition performed on that rotational speed 120596119894120596

0(b) 119879 is the period of the anemometerrsquos

rotation

constant wind speed revealed the effect of the anemometerrsquosrotor shape on this third harmonic term of the rotation speed(these results were presented at the Alternative EnergiesSpecial Session of the 9th Conference on Diffusion in Solidsand Liquids Madrid 2013) Nevertheless the results werenot conclusive enough as the analysis was performed usingan Ornytion 107A anemometer This anemometer gives ananalog output consisting in 2-harmonic pulses per turngenerated by rotating magnets which is a good enough ratetomeasure correctly the average rotation speed120596

0 However

the process to extract the third harmonic term from theoutput had to be indirect and derived from Lenzrsquos law whichrelates the generated analog output of the anemometer to therotating magnetic field

The aim of the present study is to analyze the response ofan optoelectronic output anemometer (Climatronics 100075by Climatronics Corp also known as F460model) equippedwith different rotors to have a better understanding of theeffect of the geometry (size of the cups distance of the cupsto the rotation axis) on cup anemometer performances Alsothe third harmonic term of the rotation speed see expression(3) is studied as a possible new approach to analyze thementioned anemometer performances

2 Testing Configuration and Cases Studied

As said the Climatronics 100075 anemometer was used in thetesting campaign 32 different rotors were tested (see Table 2and Figure 2) 26 were equipped with conical cups (90∘ cone-angle 4 with cup radius 119877

119888= 20mm cup center rotation

radius varying from 119877

119903119888= 30mm to 119877

119903119888= 60mm 5 with

cup radius 119877119888= 25mm cup center rotation radius varying

from 119877

119903119888= 40mm to 119877

119903119888= 100mm 6 with cup radius

119877

119888= 30mm cup center rotation radius varying from 119877

119903119888=

40mm to 119877

119903119888= 120mm 5 with cup radius 119877

119888= 35mm cup

center rotation radius varying from 119877

119903119888= 50mm to 119877

119903119888=

120mm and 6 with cup radius 119877119888

= 40mm cup centerrotation radius varying from 119877

119903119888= 60mm to 119877

119903119888= 140mm)

3 were equipped with elliptical cups (front surface equal tothe conical cups 119878

119888= 19635mm2 and 119877

119903119888= 60mm)

Conical cupsRrc Rc

Porous cups

h

25

Elliptical cupsa

b

Rc

Rc

Rrc

Rrc

25

Figure 2 Sketch of the cups and rotor geometries tested Dimen-sions in mm See also Table 2

3 were equipped with porous cups (front surface includingthe empty area equal to the conical cups 119878

119888= 19635mm2

cup radius 119877119888= 25mm truncated shape with hole diameter

ℎ = 9mm ℎ = 19mm and ℎ = 24mm and 119877

119903119888= 60mm)

The cups used in this study were made of ABS plastic using a3D printer and the arm on each cup was made of aluminumtubing 5mm in diameter

The calibrations were carried out at the IDRUPMInstitute in the S4 wind tunnel (see Figure 3) This facilityis an open-circuit wind tunnel with a closed test sectionmeasuring 09 by 09m It is served by four 75 kW fanswith a flow uniformity under 02 in the testing area Moredetails concerning the facility and the calibration process areincluded in [29] The calibrations analyzed in the presentpaper were performed following the MEASNET [25 26]recommendations (over 13 points and from 4 to 16ms windspeed) In each point (wind speed) of every calibration

4 The Scientific World Journal

Table 2 Geometrical characteristics of the rotors tested cup center rotation radius 119877119903119888 front area of the cups 119878

119888 cup radius (conical and

porous cups)119877119888 ratio of cup radius to the cupsrsquo center rotation radius (conical cups)119877

119888119877119903119888 hole diameter of porous cups ℎ and semi-major

and semi-minor axes 119886 and 119887 of elliptical cups See also Figure 2

Conical cupsRotor 119877

119888[mm] 119878

119888[mm2] 119877

119903119888[mm] 119877

119888119877119903119888

c-2030 20 12566 30 0667c-2040 20 12566 40 0500c-2050 20 12566 50 0400c-2060 20 12566 60 0333c-2540 25 19635 40 0625c-2550 25 19635 50 0500c-2560 25 19635 60 0417c-2580 25 19635 80 0313c-25100 25 19635 100 0250c-3040 30 28274 40 0750c-3050 30 28274 50 0600c-3060 30 28274 60 0500c-3080 30 28274 80 0375c-30100 30 28274 100 0300c-30120 30 28274 120 0250c-3550 35 38485 50 0700c-3560 35 38485 60 0583c-3580 35 38485 80 0438c-35100 35 38485 100 0350c-35120 35 38485 120 0292c-4050 40 50265 50 0800c-4060 40 50265 60 0667c-4080 40 50265 80 0500c-40100 40 50265 100 0400c-40120 40 50265 120 0333c-40140 40 50265 140 0286

Elliptical cupsRotor 119886 [mm] 119887 [mm] 119878

119888[mm2] 119877

119903119888[mm]

a-2760 27 2315 19635 60a-3060 30 2083 19635 60a-3560 35 1786 19635 60

Porous cupsRotor 119877

119888[mm] 119878

119888[mm2] 119877

119903119888[mm] ℎ [mm]

h-960 25 19635 60 9h-1960 25 19635 60 19h-2460 25 19635 60 24

performed the anemometerrsquos output was sampled during 20seconds at 10000Hz

The Climatronics 100075 anemometer gives 30 squaredpulses per turn A plot of the output signal record in oneturn of this anemometer equipped with the h-2460 rotor isincluded in Figure 3 togetherwith the non-dimensional rota-tion speed 120596120596

0 once the output was post-processed The

non-dimensional rotation speed on one turn was calculatedaveraging groups of 30 pulses contained in the recorded datafor every point (ie every wind flow velocity) during thecalibration of all configurations analyzed

3 Results and Discussion

The calibration constants of the anemometer transfer func-tion 119860 and 119861 with regard to all cases tested are includedin Table 3 In Figure 4 the anemometer factor 119870 regardingthe calibrations performed in the present study to con-ical cups rotors is shown as a function of the param-eter 119903

119903(which represents the ratio between the cupsrsquo

radius 119877119888 and the cupsrsquo center rotation radius 119877

119903119888 119903119903

=

119877

119888119877

119903119888) This anemometer factor is defined as the ratio

between the wind speed 119881 and the rotation speed of

The Scientific World Journal 5

Vou

tput

tT

60

45

30

15

00

0 02 04 06 08 1

tT

0 02 04 06 08 1120596120596

0

110

105

100

095

090

(a)

(b)

(c)

Figure 3 Climatronics 100075 anemometer placed in the S4 wind tunnel of the IDRUPM Institute to carry out a calibration with the h-1960rotor (a) Anemometer voltage output signal 119881output in one turn (b) Relative-to-the-average rotational speed 120596120596

0 in one turn (c) 119879 is the

period of the anemometerrsquos rotation

rr

V = 4ms52

48

44

40

36

32

02 03 04 05 06 07 08 09

K

(a)

rr

52

48

44

40

36

32

02 03 04 05 06 07 08 09

V = 16ms

K

(b)

K

rr

52

48

44

40

36

32

02 03 04 05 06 07 08 09

K = 44139 minus 16573 middot r2c

K = 4438 minus 27174 middot r2c

Upper fitting

Lower fitting

V rarr infin

(c)

Figure 4 Anemometer factor 119870 regarding the conical cups rotors calculated for 119881 = 4ms (a) 119881 = 16ms (b) and 119881 rarr infin (c) as afunction of the parameter 119903

119903(119903119903= 119877

119888119877

119903119888) The symbols correspond to rotors equipped with the following cup radii 119877

119888= 20mm (rhombi)

119877

119888= 25mm (circles) 119877

119888= 30mm (squares) 119877

119888= 35mm (triangles) and 119877

119888= 40mm (crosses) The quadratic fittings to 119877

119888= 20mm rotors

(lower fitting) and to 119877

119888= 40mm rotors (upper fitting) have been also added (dotted lines) to the bottom graph

the cup center averaged in one complete rotation 120596

0119877

119903119888

[48]

119870 =

119881

120596

0119877

119903119888

=

119860

119903119891

119903+ 119861

2120587119891

119903119877

119903119888

=

119860

119903

2120587119877

119903119888

1

1 minus (119861119881)

(4)

where 119860

119903and 119861 are respectively the slope and the offset of

the transfer function see expression (2) The anemometerfactor 119870 was calculated for both limits of the wind speedcalibration range 4ms and 16ms and for very high windspeeds (119881 rarr infin) which in fact is the result of considering

6 The Scientific World Journal

Table 3 Calibration coefficients 119860 and 119861 measured for the rotors tested with Climatronics 100075 anemometer (see also Table 2 andFigure 2) The coefficient of determination 1198772 of the curve fittings and the slope of the transfer function based on the rotation frequency119860

119903(see expressions (1) and (2)) have also been included

Conical cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

c-2030 002021 060618 037096 099995c-2040 003177 095318 023328 099999c-2050 004186 125574 031148 099999c-2060 005180 155401 040091 099999c-2540 002963 088886 026760 099999c-2550 003932 117970 020786 099999c-2560 004961 148829 024245 099999c-2580 006964 208928 039438 099999c-25100 008952 268552 053685 099999c-3040 002861 085818 009551 099995c-3050 003861 115844 019606 099999c-3060 004850 145505 014823 099998c-3080 006836 205089 025403 100000c-30100 008697 260900 038253 099998c-30120 010738 322145 049053 099999c-3550 003720 111603 019081 099999c-3560 004719 141582 015354 099999c-3580 006827 204818 018132 099998c-35100 008737 262111 022168 099999c-35120 010742 322259 034171 099999c-4050 003539 106166 013714 099999c-4060 004586 137587 016652 099999c-4080 006663 199876 016932 099998c-40100 008668 260026 023292 099996c-40120 010638 319140 028805 099996c-40140 012639 379164 034162 099995

Elliptical cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

a-2760 005221 156617 019932 099999a-3060 005306 159167 023224 099998a-3560 005412 162361 021593 099998

Porous cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

h-0960 005445 163352 031414 099999h-1960 006579 197376 054539 099998h-2460 011763 352881 031563 099998

the offset constant of the transfer function 119861 negligible Itshould be said that the effect of this offset constant on similarcalculations has been considered negligible in past works[44 48] as it is only appreciated at lowwind speedsHoweverit was preserved in the present calculations in order to havea more accurate comparison between the different cases andnew conclusions have arisen

In Figure 4 three different cases can be observed Forlow wind speeds (119881 = 4ms) the cup anemometer is lessefficient in terms of transforming the wind velocity into

rotational speed than for higher wind speeds (ie highervalues of the anemometer factor 119870 are shown) Also thecurves corresponding to the different cup sizes seem to followthe samepath for ratios between the cupsrsquo radius and the cupsrsquocenter rotation radius lower than 119903

119903lt 065 The mentioned

lower performances of the anemometer can be explainedas an effect of the friction forces which are increasinglysignificant when compared to the aerodynamic forces forlow wind speeds (that obviously are translated into lowrotational speeds)

The Scientific World Journal 7

The situation changes for higher wind speeds as it canbe observed for 119881 = 16ms and even more clearly for thelimit case 119881 rarr infin (ie when the offset constant 119861 is leftaside) In this case the anemometer constant 119870 shows asecond-order polynomial dependence on the parameter 119903

119903

Also the effect of relative cup size is shown in the mentionedgraph The curves fitting to the results corresponding to therotors with the smallest and the largest cups (119877

119888= 20mm

and 119877

119888= 40mm resp) have been included in the graphThe

results corresponding to all the intermediate cup size rotors(119877119888= 25mm 119877

119888= 30mm and 119877

119888= 35mm) lie between

both curves revealing the aforementioned dependence onthe cupsrsquo size In tune with this effect it should also be saidthat other experimental results have already demonstratedthe direct relationship between the slope of the anemometertransfer function 119860 and the front area of the cups [44]

119860 =

1

119873

119901

119860

119903=

1

119873

119901

(

d119860119903

d119877119903119888

119877

119903119888+ 119860

1199030) (5)

where d119860119903d119877119903119888depends on the aerodynamic forces on the

cups (for rotors equipped with the same conical cups testedin the present work it was found that this coefficient hasconstant value with very little or no correlation to the cupsrsquosize) and 119860

1199030strongly depends on the cupsrsquo front area 119878

119888

Finally it should also be said that as far as the authorsknow this particular effect of the cupsrsquo size has not beenincluded in the different analyticalmodels developed to studycup anemometer behavior [30 31 33 38 40] These modelsare based on wind speed cup aerodynamic coefficientsand cup and rotor geometries and take as starting pointthat the behavior of cup anemometers is mainly driven byaerodynamic forces the frictional torque being much lowerin comparison [37 49] However these models are limiteddue to the complexity of rotating flows [48]

In order go to deeper into this problem the aerodynamicforces on each cup should be analyzed As the aerodynamictorque on the anemometerrsquos rotor is produced by the aerody-namic forces on the mentioned cups and the cups positionson the rotor have 120∘ phase separation it is logical to assumethat at constant wind speed equal rotational accelerations anddecelerationswill affect the anemometer rotor three times perrevolution (obviously these accelerations are responsible forthe third harmonic term of the anemometer wind speed 120596

3

see expression (3)) Therefore studying the third harmonicterm of the rotational speed is a way to analyze the effect ofthe cups on the rotor movement

In Figure 5 the non-dimensional third harmonic term120596

3120596

0 calculated for every wind speed of the calibrations

regarding the studied porous cups rotors (h-0960 h-1960and h-2460) is shown together with the results correspond-ing to the c-2560 rotor (included as it can be considered aspart of the porous cup series ie porosity equal to zero) Inthementionedfigure the differences among the performanceswith regard to the different rotors can be clearly observedThis figure has been chosen to illustrate two parameters usedin the present work to analyze the third harmonic term ofthe anemometer rotational speed (i) the non-dimensional

1205963 + 1205903

1205963

1205963 minus 1205903

V (ms)

900

800

700

600

500

400

300

200

100

0004 6 8 10 12 14 16

1205963120596

0(

)

Figure 5 Non-dimensional harmonic term 1205963120596

0 calculated at

every point of the calibrations performed on the Climatronics100075 anemometer equippedwith c-2560 (circles) h-0960 (trian-gles) h-1960 (squares) and h-2460 (rhombi) rotors The averagevalue line 120596

3 together with the standard deviation limits plusmn120590

3

corresponding to the h-1960 rotor values has been also included inthe graph

average value calculated with data from the 13 points of thecalibration procedure

120596

3=

1

13

13

sum

119894=1

120596

3

120596

0

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119894

(6)

and (ii) the corresponding standard deviation 1205903 calculated

using the general procedure

120590

3=

radic

sum

13

119894=1( (120596

3120596

0)

1003816

1003816

1003816

1003816119894minus 120596

3)

2

13 minus 1

(7)

In Figure 6 the averaged third non-dimensional har-monic term 120596

3 regarding the conical cups rotors and

the ratio of the standard deviation to the mentioned non-dimensional third harmonic term 120590

3120596

3 are shown as a

function of the ratio of the cup radius to the cupsrsquo centerrotation radius 119903

119903 The third harmonic term 120596

3 tends to be

smaller with higher values of 119903119903 that is for rotors whose cups

centers are closer to the rotation axisThe same tendency wasobserved on the anemometer factor 119870 (see Figure 4) so itcan be concluded that higher third harmonic terms have animmediate effect on the anemometer average performancereducing the average rotational speed 120596

0 This effect can be

explained in terms of energy as a bigger part of the energytransferred from the wind to the rotor movement is investedinto the mentioned third harmonic term and not into theconstant term of the rotational speed 120596

0 Also the effect

of the cupsrsquo size has the same pattern as the one for the

8 The Scientific World Journal

rr

180160140120100080060040

000 020 040 060 080 100

1205963(

)

(a)

rr

000 020 040 060 080 100

2000

1600

1200

800

400

000

1205903120596

3(

)

(b)

Figure 6 Averaged third harmonic term 1205963 regarding the conical cups rotors (a) and the corresponding standard deviation 120590

3120596

3(b)

both expressed as a function of the parameter 119903

119903(119903119903= 119877

119888119877

119903119888) The symbols correspond to rotors equipped with the following cup radii

119877

119888= 20mm (rhombi) 119877

119888= 25mm (circles) 119877

119888= 30mm (squares) 119877

119888= 35mm (triangles) and 119877

119888= 40mm (crosses)

anemometer constant graphs in Figure 4 Smaller cups withthe same parameter 119903

119903show smaller third harmonic terms

with higher rotational efficienciesFinally focusing on the standard deviationmeasuredwith

respect to the average third harmonic term 1205903120596

3 shown

in Figure 6 it seems that there is a minimum for every cupsize at a certain value of the parameter 119903

119903 located around

119903

119903= 05 In Figure 7 the third harmonic term measured for

every wind velocity during the calibration of four rotorsequipped with 119877

119888= 40mm cups is shown The data

correspond to the smallest and the largest cup rotation radiustested (119877

119903119888= 50mm and 119877

119903119888= 140mm resp) and two

intermediate cases (119877119903119888

= 80mm and 119877

119903119888= 100mm) It

can be observed that according to the information from thementioned graph in Figure 6 the dispersion of the results islower for the intermediate cases A linear tendency is alsoobserved with higher slopes for greater values of cup centerrotation radius Finally it should also be said that class-1commercial anemometers [47 50] have ratios between thecup radius and the cupsrsquo center rotation radius ranging from119903

119903= 04 to 119903

119903= 06 (Thies Clima 4335043351 119903

119903= 05

Vector Instruments A100L2 119903119903= 049 Vaisala WAA 151252

119903

119903= 042 WindSensor (Risoslash) P2546A 119903

119903= 059)

Concerning the effect of the cupsrsquo shape its effect onanemometer performance has been already analyzed Theaerodynamic forces on a single cup have been correlatedwith the aforementioned anemometer performance in twodifferent ways by means of analytical models correlated withexperimental testing [30 31 33 38] and by means of adirect comparison based on experimental calibration [48] InFigure 8 the anemometer constant at 16ms wind speed withregard to the calibrations performed on the anemometerequipped with elliptical and porous cups rotors has beenincluded respectively as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 and the ratio of the hole diameter to the cupdiameter ℎ2119877

119888 The non-dimensional third harmonic 120596

3

regarding these rotors has been also included in the figureAs it was previously measured [48] the effect of both theeccentricity and the porosity of the cups is translated into adecrease of the rotational efficiency of the cups (higher values

1205963120596

0

1205963

V (ms)

13

12

11

10

09

08

07

06

0 2 4 6 8 10 12 14 16 18

Rrc = 50mm (RcRrc = 08)

Rrc = 100mm (RcRrc = 04)

Rrc = 140mm (RcRrc = 0287)

Rrc = 80mm (RcRrc = 05)

Figure 7 Variation of the third harmonic term measured withrotors equipped with 119877

119888= 40mm conical cups as a function of the

wind speed within the calibration process

of 119870 that is lower rotational speed at a fixed wind speed)On the other hand the effect of both parameters on the thirdharmonic term has a reversed effect that is higher valuesof eccentricity and porosity increase the importance of thisharmonic term

4 Conclusions

In the present work the performance of a cup anemometerequipped with different rotors has been experimentally ana-lyzed On one hand the size of conical cups together withtheir distance to the anemometer rotation axis was studiedOn the other hand the shape of the rotor cups was alsostudied The analysis was based on two different parameters

The Scientific World Journal 9

K

e h2Rc

1000

950

900

850

800

750

700

650

600

550

500

450

400

000 020 040 060 080 100

(a)

1000

900

800

700

600

500

400

300

200

100

e h2Rc

000 020 040 060 080 100

1205963(

)(b)

Figure 8 Anemometer constant at 16ms wind speed119870 and non-dimensional third harmonic1205963 with regard to the calibrations performed

to the anemometer equipped with elliptical (squares) and porous (circles) cup rotors as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 andthe ratio of the hole diameter to the front cup area ℎ2119877

119888 respectively

the anemometer factor that takes into account the averagerotation of the anemometer and the third harmonic termresulting from the Fourier decomposition of the anemometerrotation speed The most relevant conclusions resulting fromthis work are as follows

(i) The average rotation speed is well correlated with thementioned third harmonic term resulting from theFourier decomposition of the anemometer rotationspeed Higher values of this third harmonic termresult in higher anemometer factors and thereforein lower rotational speeds This fact confirms thementioned third harmonic term as a useful parameterto study cup anemometer performance

(ii) Smaller cups with the same ratio of cup diameter tothe cupsrsquo center rotation radius 119903

119903 tend to produce

higher rotational speeds (lower anemometer factors)and lower third harmonic terms

(iii) The ratio of the third harmonic term to the averagerotational speed 120596

3120596

0 is more uniform (within the

wind speed calibration range) for values of the ratioof the cup diameter to the cupsrsquo center rotation radiusranging from 119903

119903= 04 to 119903

119903= 05 than for values of 119903

119903

beyond or below this bracket

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are truly indebted to Enrique Vega AlejandroMartınez Encarnacion Meseguer Luis Garcıa and EduardoCortes for the help and friendly support during the testingcampaign The authors are grateful to Anna Marıa Ballesterfor her kind help on improving the style of the text

References

[1] F Aminzadeh and S Pindado ldquoHow has Spain become a leaderin thewind energy industry during the last decade (An analysisof influential factors on the development of wind energy inSpain)rdquo in Proceedings of the EWEA Annual Event BrusselsBelgium 2011

[2] L Kristensen ldquoCan a cup anemometer ldquounderspeedrdquo A hereti-cal questionrdquo Boundary-Layer Meteorology vol 103 no 1 pp163ndash172 2002

[3] R V Coquilla J Obermeier and B R White ldquoCalibrationprocedures and uncertainty in wind power anemometersrdquoWind Engineering vol 31 no 5 pp 303ndash316 2007

[4] A Albers and H Klug ldquoOpen field cup anemometryrdquo DEWIMagazine vol 19 pp 53ndash58 2001

[5] A Albers H Klug and D Westermann ldquoOutdoor comparisonof cup anemometersrdquo DEWI Magazin vol 17 pp 5ndash15 2000

[6] S Lang and E McKeogh ldquoLIDAR and SODAR measurementsof wind speed and direction in upland terrain for wind energypurposesrdquo Remote Sensing vol 3 no 9 pp 1871ndash1901 2011

[7] R Wagner M Courtney J Gottschall and P Lindelow-Marsden ldquoAccounting for the speed shear in wind turbine

10 The Scientific World Journal

power performance measurementrdquoWind Energy vol 14 no 8pp 993ndash1004 2011

[8] T R Robinson ldquoOn a New Anemometerrdquo Proceedings of theRoyal Irish Academy (1836ndash1869 ) vol 4 pp 566ndash572 1847

[9] International Electrotechnical Commision International Stan-dard IEC-61400-12-1 Wind Turbines Part 12-1 Power Perfor-mance Measurements of Electricity Producing Wind TurbinesFirst Edition 2005ndash12 International Electrotechnical Commi-sion Geneva Switzerland 2005

[10] R V Coquilla and J Obermeier ldquoCalibration speed range forrotating anemometers used in wind energy applicationsrdquo inProceedings of the 46th AIAA Aerospace Sciences Meeting andExhibit pp 2ndash7 January 2008

[11] R V Coquilla A Havner J Obermeier and M SturgeonldquoVerification testing of Sonic anemometer wind speedmeasure-ments for wind energy applicationsrdquo in Proceedings of the 2010American Wind Energy Association Annual Conference (AWEAWINDPOWER rsquo10) pp 1ndash14 2010

[12] L J Fritschen ldquoA sensitive cup-type anemometerrdquo Journal ofApplied Meteorology vol 6 pp 695ndash698 1967

[13] M Sanuki and S Kimura ldquoSome aerodynamic aspects deducedfrom the start and stop experiment of three- and four-cupanemometerrdquo Papers in Meteorology and Geophysics vol 5 pp695ndash698 1954

[14] C F Marvin ldquoA rational theory of the cup anemometerrdquoMonthly Weather Review vol 60 pp 43ndash56 1932

[15] M J Brevoort and U T Joyner ldquoExperimental investigation ofthe Robinson-type cup anemometerrdquo NACA TN-513 1935

[16] C F Marvin ldquoRecent advances in anemometryrdquo MonthlyWeather Review vol 62 pp 115ndash120 1934

[17] C F Marvin ldquoAnemometer testsrdquoMonthlyWeather Review pp58ndash63 1900

[18] H Charnock and F E Pierce ldquoNew housing for the sensitivecup-contact anemometer Mk 1rdquo Journal of Scientific Instru-ments vol 36 no 7 p 329 1959

[19] P A Sheppard ldquoAn improved design of cup anemometerrdquoJournal of Scientific Instruments vol 17 no 9 pp 218ndash221 1940

[20] E L Deacon ldquoReply to two types of sensitive recording cupanemometersrdquo Journal of Scientific Instruments vol 25 no 8p 283 1948

[21] S G Crawford ldquoA simple form of sensitive electric contact cupanemometerrdquo Journal of Scientific Instruments vol 28 no 2 pp36ndash37 1951

[22] F Scrase and P Sheppard ldquoThe errors of cup anemometers influctuating windsrdquo Journal of Scientific Instruments vol 21 no9 pp 160ndash161 1944

[23] E L Deacon ldquoThe over-estimation error of cup anemometersin fluctuating windsrdquo Journal of Scientific Instruments vol 28no 8 pp 231ndash234 1951

[24] L KristensenThe Cup Anemometer and Other Exciting Instru-ments Risoslash-R-615 (EN) Risoslash National Laboratory RoskildeDenmark 1993

[25] MEASNET Cup Anemometer Calibration Procedure Version1 (September 1997 Updated 24112008) MEASNET MadridSpain 1997

[26] MEASNET Anemometer Calibration Procedure Version 2(October 2009) MEASNET Madrid Spain 2009

[27] ASTM International Standard Test Method for Determining thePerformance of a Cup Anemometer or Propeller Anemometer(ASTMD 5096-02) ASTM InternationalWest ConshohockenPa USA 2002

[28] M C-E Brazier ldquoSur la variation des indications desanemometres Robinson et Richard en fonction de lrsquoinclinaisondu ventrdquoComptes Rendus des Seances de LrsquoAcademie des Sciencesvol 170 pp 610ndash612 1920

[29] S Pindado E Vega A Martınez E Meseguer S Franchiniand I P Sarasola ldquoAnalysis of calibration results from cupand propeller anemometers Influence on wind turbine AnnualEnergy Production (AEP) calculationsrdquo Wind Energy vol 14no 1 pp 119ndash132 2011

[30] J Kondo G I Naito and Y Fujinawa ldquoResponse of cupanemometer in turbulencerdquo Journal of theMeteorological Societyof Japan vol 49 pp 63ndash74 1971

[31] S Ramachandran ldquoA theoretical study of cup and vaneanemometersrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 95 no 403 pp 163ndash180 1969

[32] M C-E Brazier ldquoSur la comparabilite des anemometresrdquoComptes Rendus des Seances de LrsquoAcademie des Sciences vol 172pp 843ndash845 1921

[33] O Schrenk ldquoUber die tragheitsfehler des Schalenkreuz-anemometers bei schwankender Windstarkerdquo Zeitschrift FurTechnische Physik vol 10 pp 57ndash66 1929

[34] H W Baynton ldquoErrors in wind run estimates from rotationalanemometersrdquo Bulletin of the American Meteorological Societyvol 57 no 9 pp 1127ndash1130 1976

[35] N E Busch and L Kristensen ldquoCup anemometer overspeed-ingrdquo Journal of AppliedMeteorology vol 15 pp 1328ndash1332 1976

[36] P Frenzen ldquoFast response cup anemometers for atmosphericturbulence researchrdquo in Proceedings of the 8th Symposium onTurbulence and Diffusion pp 112ndash115 1988

[37] E I Kaganov and A M Yaglom ldquoErrors in wind-speed mea-surements by rotation anemometersrdquo Boundary-Layer Meteo-rology vol 10 no 1 pp 15ndash34 1976

[38] J C Wyngaard ldquoCup propeller vane and sonic anemometersin turbulence researchrdquo Annual Review of Fluid Mechanics vol13 pp 399ndash423 1981

[39] P A Coppin ldquoAn examination of cup anemometer overspeed-ingrdquoMeteorologische Rundschau vol 35 pp 1ndash11 1982

[40] J CWyngaard J T Bauman and R A Lynch ldquoCup anemome-ter dynamicsrdquo in Flow Its Measurement and Control in Scienceand Industry vol 1 pp 701ndash708 1974

[41] L Kristensen ldquoCup anemometer behavior in turbulent environ-mentsrdquo Journal of Atmospheric and Oceanic Technology vol 15no 1 pp 5ndash17 1998

[42] R S Hunter ldquoThe accuracy of cup anemometer calibrationwithparticular regard to testing wind turbinesrdquo Wind Engineeringvol 14 no 1 pp 32ndash43 1990

[43] J-A Dahlberg J Gustavsson G Ronsten T F Pedersen US Paulsen and D Westermann Development of A Standard-ised Cup Anemometer Suited to Wind Energy Applications-(ClAsscup) vol 9 Technical University of Denmark LyngbyDenmark 2001

[44] S Pindado J Perez and S Avila-Sanchez ldquoOn cup anemometerrotor aerodynamicsrdquo Sensors vol 12 no 5 pp 6198ndash6217 2012

[45] S Pindado A Sanz and A Wery ldquoDeviation of cup andpropeller anemometer calibration results with air densityrdquoEnergies vol 5 no 3 pp 683ndash701 2012

[46] S Pindado A Barrero-Gil and A Sanz ldquoCup anemome-tersrsquoLoss of performance due to ageing processes and its effecton Annual Energy Production (AEP) estimatesrdquo Energies vol5 no 12 pp 1664ndash1685 2012

The Scientific World Journal 11

[47] J-A Dahlberg T F Pedersen and P Busche ACCUWIND-Methods for Classification of Cup Anemometers Risoslash-R-1555(EN) Risoslash National Laboratory Roskilde Denmark 2006

[48] S Pindado I Perez and M Aguado ldquoFourier analysis ofthe aerodynamic behavior of cup anemometersrdquo MeasurementScience and Technology vol 24 no 6 Article ID 065802 2013

[49] Y P Solovrsquoev A I Korovushkin and Y N Toloknov ldquoCharac-teristics of a cup anemometer and a procedure of measuring thewind velocityrdquo Physical Oceanography vol 14 no 3 pp 173ndash1862004

[50] T F Pedersen Development of A Classification System forCup Anemometers-CLASSCUP Risoslash-R-1348(EN) Risoslash NationalLaboratory Roskilde Denmark 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

2 The Scientific World Journal

Table 1 Installed wind power per country (units in GW) of some of the biggest world producers from 2005 to 2012 The growing rates (withrespect to the preceding year) corresponding to 2011 and 2012 have been also added in brackets to illustrate the present status of the windenergy market (sources Global Wind Energy Council US Energy Information Administration)

Country 2005 2006 2007 2008 2009 2010 2011 2012

China 126 260 591 1220 1600 3110 6236(1005)

7556(212)

USA 871 1133 1652 2465 3430 3914 4692(199)

6004(280)

Germany 1843 2062 2225 2390 2570 2720 2908(69)

3151(84)

Spain 992 1172 1480 1660 1910 2070 2167(47)

2280(52)

India 530 620 780 1000 1100 1307 1608(231)

1842(145)

Italy 164 190 270 353 488 579 688(188)

815(185)

UK 157 196 248 341 442 538 647(203)

837(293)

Canada 068 146 177 237 332 397 565(422)

659(165)

Portugal 106 168 220 286 333 380 430(133)

445(34)

Brazil 003 024 025 041 060 093 151(628)

259(714)

[9 25ndash27] and was quite early defined for the Robinson-typeanemometer [28] The transfer function can be rewritten interms of the anemometerrsquos rotation frequency 119891

119903 instead of

the output frequency 119891 introducing in the expression thenumber of pulses per revolution given by the anemometer119873

119901

119881 = 119860 sdot 119873

119901sdot 119891

119903+ 119861 = 119860

119903sdot 119891

119903+ 119861 (2)

The expression above is preferable than the preceding oneas it has a clearer physical meaning Expression (2) alsoallows a direct comparison between anemometers [29] andbetween experimental results and analytical models [30 31]The number of pulses 119873

119901 is different depending on the

anemometerrsquos inner system for translating the rotation intoelectric pulses Magnet-based systems give 1 to 3 pulses perrevolution whereas optoelectronics-based systems normallygive higher pulse rates per revolution from 6 to 44 [29]

Leaving aside thewide acceptance of the industry it is alsofair to recognize the existence of some special uncertaintiesassociated with the cup anemometer wind speed measure-ments On the one handwe have the ldquooverspeedingrdquo problemwhich was detected and studied from the beginning of theXX century [32 33] The cup anemometer ldquooverspeedingrdquoconsists in a quicker response upon wind flow accelerationthan the one obtained after a wind flow deceleration Dueto the impact on the measured wind speed and turbulencethis effect (together with the problems related to the errorcaused by the vertical component of the wind) was one ofthe biggest concerns for meteorologists during the secondhalf of the XX century [34ndash41] All the researches done werequickly applied to the wind energy industry particularly to

the effect of the accuracy on the wind turbine power [42] andthe classification and improvement of cup anemometers [43]

From 2009 cup anemometer performances have beenanalyzed at the IDRUPM calibration lab focusing on theeffect of the rotor shape [29 44] the effect of air densityand climatic conditions [45] and the effect of aging [46]Recently research done at the IDRUPM has been focusedon the uniformity of anemometer rotation as even in a verylow turbulence and stationary wind flow the rotation speed isnot purely constant being composed by harmonic terms

The cup anemometer has a standardized configuration ofthree cups as the 3-cup anemometer has become the mostefficient solution when compared to the 4-cup anemometer(this was the initial configuration of the cup anemometerdeveloped in the XIX century) This 3-cup design makes therotational speed of this instrument not uniform [47] Therotational speed of a 3-cup anemometer 120596 under a perfectlyconstant and uniform wind speed can be decomposed alongone turn into a constant term 120596

0 plus a series of harmonic

terms that correspond to a frequency three times bigger thanthe one related to the mentioned constant term 3120596

0 and its

multiples 61205960 91205960 121205960

120596 (119905) = 120596

0+

infin

sum

119899=1

120596

3119899sin (3119899120596

0119905 + 120593

3119899) (3)

In Figure 1 the non-dimensional rotation speed 120596(119905)120596

0 of

a Thies 43303 anemometer at 8ms wind flow is shownThe third harmonic term can be clearly appreciated as themost important of the rotation speed obviously leavingaside the constant term 120596

0 The aforementioned study on

the regularity of the rotation speed of the anemometers at

The Scientific World Journal 3

120596120596

0

12

11

10

09

08

00 01 02 03 04 05 06 07 08 09 10

tT

(a)

120596i1205960

i

010

008

006

004

002

0001 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

(b)

Figure 1 Relative-to-the-average rotational speed120596120596

0 of aThies 43303 anemometer during one turn at 8ms wind speed [47] (a) and non-

dimensional values of the Fourier series decomposition performed on that rotational speed 120596119894120596

0(b) 119879 is the period of the anemometerrsquos

rotation

constant wind speed revealed the effect of the anemometerrsquosrotor shape on this third harmonic term of the rotation speed(these results were presented at the Alternative EnergiesSpecial Session of the 9th Conference on Diffusion in Solidsand Liquids Madrid 2013) Nevertheless the results werenot conclusive enough as the analysis was performed usingan Ornytion 107A anemometer This anemometer gives ananalog output consisting in 2-harmonic pulses per turngenerated by rotating magnets which is a good enough ratetomeasure correctly the average rotation speed120596

0 However

the process to extract the third harmonic term from theoutput had to be indirect and derived from Lenzrsquos law whichrelates the generated analog output of the anemometer to therotating magnetic field

The aim of the present study is to analyze the response ofan optoelectronic output anemometer (Climatronics 100075by Climatronics Corp also known as F460model) equippedwith different rotors to have a better understanding of theeffect of the geometry (size of the cups distance of the cupsto the rotation axis) on cup anemometer performances Alsothe third harmonic term of the rotation speed see expression(3) is studied as a possible new approach to analyze thementioned anemometer performances

2 Testing Configuration and Cases Studied

As said the Climatronics 100075 anemometer was used in thetesting campaign 32 different rotors were tested (see Table 2and Figure 2) 26 were equipped with conical cups (90∘ cone-angle 4 with cup radius 119877

119888= 20mm cup center rotation

radius varying from 119877

119903119888= 30mm to 119877

119903119888= 60mm 5 with

cup radius 119877119888= 25mm cup center rotation radius varying

from 119877

119903119888= 40mm to 119877

119903119888= 100mm 6 with cup radius

119877

119888= 30mm cup center rotation radius varying from 119877

119903119888=

40mm to 119877

119903119888= 120mm 5 with cup radius 119877

119888= 35mm cup

center rotation radius varying from 119877

119903119888= 50mm to 119877

119903119888=

120mm and 6 with cup radius 119877119888

= 40mm cup centerrotation radius varying from 119877

119903119888= 60mm to 119877

119903119888= 140mm)

3 were equipped with elliptical cups (front surface equal tothe conical cups 119878

119888= 19635mm2 and 119877

119903119888= 60mm)

Conical cupsRrc Rc

Porous cups

h

25

Elliptical cupsa

b

Rc

Rc

Rrc

Rrc

25

Figure 2 Sketch of the cups and rotor geometries tested Dimen-sions in mm See also Table 2

3 were equipped with porous cups (front surface includingthe empty area equal to the conical cups 119878

119888= 19635mm2

cup radius 119877119888= 25mm truncated shape with hole diameter

ℎ = 9mm ℎ = 19mm and ℎ = 24mm and 119877

119903119888= 60mm)

The cups used in this study were made of ABS plastic using a3D printer and the arm on each cup was made of aluminumtubing 5mm in diameter

The calibrations were carried out at the IDRUPMInstitute in the S4 wind tunnel (see Figure 3) This facilityis an open-circuit wind tunnel with a closed test sectionmeasuring 09 by 09m It is served by four 75 kW fanswith a flow uniformity under 02 in the testing area Moredetails concerning the facility and the calibration process areincluded in [29] The calibrations analyzed in the presentpaper were performed following the MEASNET [25 26]recommendations (over 13 points and from 4 to 16ms windspeed) In each point (wind speed) of every calibration

4 The Scientific World Journal

Table 2 Geometrical characteristics of the rotors tested cup center rotation radius 119877119903119888 front area of the cups 119878

119888 cup radius (conical and

porous cups)119877119888 ratio of cup radius to the cupsrsquo center rotation radius (conical cups)119877

119888119877119903119888 hole diameter of porous cups ℎ and semi-major

and semi-minor axes 119886 and 119887 of elliptical cups See also Figure 2

Conical cupsRotor 119877

119888[mm] 119878

119888[mm2] 119877

119903119888[mm] 119877

119888119877119903119888

c-2030 20 12566 30 0667c-2040 20 12566 40 0500c-2050 20 12566 50 0400c-2060 20 12566 60 0333c-2540 25 19635 40 0625c-2550 25 19635 50 0500c-2560 25 19635 60 0417c-2580 25 19635 80 0313c-25100 25 19635 100 0250c-3040 30 28274 40 0750c-3050 30 28274 50 0600c-3060 30 28274 60 0500c-3080 30 28274 80 0375c-30100 30 28274 100 0300c-30120 30 28274 120 0250c-3550 35 38485 50 0700c-3560 35 38485 60 0583c-3580 35 38485 80 0438c-35100 35 38485 100 0350c-35120 35 38485 120 0292c-4050 40 50265 50 0800c-4060 40 50265 60 0667c-4080 40 50265 80 0500c-40100 40 50265 100 0400c-40120 40 50265 120 0333c-40140 40 50265 140 0286

Elliptical cupsRotor 119886 [mm] 119887 [mm] 119878

119888[mm2] 119877

119903119888[mm]

a-2760 27 2315 19635 60a-3060 30 2083 19635 60a-3560 35 1786 19635 60

Porous cupsRotor 119877

119888[mm] 119878

119888[mm2] 119877

119903119888[mm] ℎ [mm]

h-960 25 19635 60 9h-1960 25 19635 60 19h-2460 25 19635 60 24

performed the anemometerrsquos output was sampled during 20seconds at 10000Hz

The Climatronics 100075 anemometer gives 30 squaredpulses per turn A plot of the output signal record in oneturn of this anemometer equipped with the h-2460 rotor isincluded in Figure 3 togetherwith the non-dimensional rota-tion speed 120596120596

0 once the output was post-processed The

non-dimensional rotation speed on one turn was calculatedaveraging groups of 30 pulses contained in the recorded datafor every point (ie every wind flow velocity) during thecalibration of all configurations analyzed

3 Results and Discussion

The calibration constants of the anemometer transfer func-tion 119860 and 119861 with regard to all cases tested are includedin Table 3 In Figure 4 the anemometer factor 119870 regardingthe calibrations performed in the present study to con-ical cups rotors is shown as a function of the param-eter 119903

119903(which represents the ratio between the cupsrsquo

radius 119877119888 and the cupsrsquo center rotation radius 119877

119903119888 119903119903

=

119877

119888119877

119903119888) This anemometer factor is defined as the ratio

between the wind speed 119881 and the rotation speed of

The Scientific World Journal 5

Vou

tput

tT

60

45

30

15

00

0 02 04 06 08 1

tT

0 02 04 06 08 1120596120596

0

110

105

100

095

090

(a)

(b)

(c)

Figure 3 Climatronics 100075 anemometer placed in the S4 wind tunnel of the IDRUPM Institute to carry out a calibration with the h-1960rotor (a) Anemometer voltage output signal 119881output in one turn (b) Relative-to-the-average rotational speed 120596120596

0 in one turn (c) 119879 is the

period of the anemometerrsquos rotation

rr

V = 4ms52

48

44

40

36

32

02 03 04 05 06 07 08 09

K

(a)

rr

52

48

44

40

36

32

02 03 04 05 06 07 08 09

V = 16ms

K

(b)

K

rr

52

48

44

40

36

32

02 03 04 05 06 07 08 09

K = 44139 minus 16573 middot r2c

K = 4438 minus 27174 middot r2c

Upper fitting

Lower fitting

V rarr infin

(c)

Figure 4 Anemometer factor 119870 regarding the conical cups rotors calculated for 119881 = 4ms (a) 119881 = 16ms (b) and 119881 rarr infin (c) as afunction of the parameter 119903

119903(119903119903= 119877

119888119877

119903119888) The symbols correspond to rotors equipped with the following cup radii 119877

119888= 20mm (rhombi)

119877

119888= 25mm (circles) 119877

119888= 30mm (squares) 119877

119888= 35mm (triangles) and 119877

119888= 40mm (crosses) The quadratic fittings to 119877

119888= 20mm rotors

(lower fitting) and to 119877

119888= 40mm rotors (upper fitting) have been also added (dotted lines) to the bottom graph

the cup center averaged in one complete rotation 120596

0119877

119903119888

[48]

119870 =

119881

120596

0119877

119903119888

=

119860

119903119891

119903+ 119861

2120587119891

119903119877

119903119888

=

119860

119903

2120587119877

119903119888

1

1 minus (119861119881)

(4)

where 119860

119903and 119861 are respectively the slope and the offset of

the transfer function see expression (2) The anemometerfactor 119870 was calculated for both limits of the wind speedcalibration range 4ms and 16ms and for very high windspeeds (119881 rarr infin) which in fact is the result of considering

6 The Scientific World Journal

Table 3 Calibration coefficients 119860 and 119861 measured for the rotors tested with Climatronics 100075 anemometer (see also Table 2 andFigure 2) The coefficient of determination 1198772 of the curve fittings and the slope of the transfer function based on the rotation frequency119860

119903(see expressions (1) and (2)) have also been included

Conical cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

c-2030 002021 060618 037096 099995c-2040 003177 095318 023328 099999c-2050 004186 125574 031148 099999c-2060 005180 155401 040091 099999c-2540 002963 088886 026760 099999c-2550 003932 117970 020786 099999c-2560 004961 148829 024245 099999c-2580 006964 208928 039438 099999c-25100 008952 268552 053685 099999c-3040 002861 085818 009551 099995c-3050 003861 115844 019606 099999c-3060 004850 145505 014823 099998c-3080 006836 205089 025403 100000c-30100 008697 260900 038253 099998c-30120 010738 322145 049053 099999c-3550 003720 111603 019081 099999c-3560 004719 141582 015354 099999c-3580 006827 204818 018132 099998c-35100 008737 262111 022168 099999c-35120 010742 322259 034171 099999c-4050 003539 106166 013714 099999c-4060 004586 137587 016652 099999c-4080 006663 199876 016932 099998c-40100 008668 260026 023292 099996c-40120 010638 319140 028805 099996c-40140 012639 379164 034162 099995

Elliptical cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

a-2760 005221 156617 019932 099999a-3060 005306 159167 023224 099998a-3560 005412 162361 021593 099998

Porous cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

h-0960 005445 163352 031414 099999h-1960 006579 197376 054539 099998h-2460 011763 352881 031563 099998

the offset constant of the transfer function 119861 negligible Itshould be said that the effect of this offset constant on similarcalculations has been considered negligible in past works[44 48] as it is only appreciated at lowwind speedsHoweverit was preserved in the present calculations in order to havea more accurate comparison between the different cases andnew conclusions have arisen

In Figure 4 three different cases can be observed Forlow wind speeds (119881 = 4ms) the cup anemometer is lessefficient in terms of transforming the wind velocity into

rotational speed than for higher wind speeds (ie highervalues of the anemometer factor 119870 are shown) Also thecurves corresponding to the different cup sizes seem to followthe samepath for ratios between the cupsrsquo radius and the cupsrsquocenter rotation radius lower than 119903

119903lt 065 The mentioned

lower performances of the anemometer can be explainedas an effect of the friction forces which are increasinglysignificant when compared to the aerodynamic forces forlow wind speeds (that obviously are translated into lowrotational speeds)

The Scientific World Journal 7

The situation changes for higher wind speeds as it canbe observed for 119881 = 16ms and even more clearly for thelimit case 119881 rarr infin (ie when the offset constant 119861 is leftaside) In this case the anemometer constant 119870 shows asecond-order polynomial dependence on the parameter 119903

119903

Also the effect of relative cup size is shown in the mentionedgraph The curves fitting to the results corresponding to therotors with the smallest and the largest cups (119877

119888= 20mm

and 119877

119888= 40mm resp) have been included in the graphThe

results corresponding to all the intermediate cup size rotors(119877119888= 25mm 119877

119888= 30mm and 119877

119888= 35mm) lie between

both curves revealing the aforementioned dependence onthe cupsrsquo size In tune with this effect it should also be saidthat other experimental results have already demonstratedthe direct relationship between the slope of the anemometertransfer function 119860 and the front area of the cups [44]

119860 =

1

119873

119901

119860

119903=

1

119873

119901

(

d119860119903

d119877119903119888

119877

119903119888+ 119860

1199030) (5)

where d119860119903d119877119903119888depends on the aerodynamic forces on the

cups (for rotors equipped with the same conical cups testedin the present work it was found that this coefficient hasconstant value with very little or no correlation to the cupsrsquosize) and 119860

1199030strongly depends on the cupsrsquo front area 119878

119888

Finally it should also be said that as far as the authorsknow this particular effect of the cupsrsquo size has not beenincluded in the different analyticalmodels developed to studycup anemometer behavior [30 31 33 38 40] These modelsare based on wind speed cup aerodynamic coefficientsand cup and rotor geometries and take as starting pointthat the behavior of cup anemometers is mainly driven byaerodynamic forces the frictional torque being much lowerin comparison [37 49] However these models are limiteddue to the complexity of rotating flows [48]

In order go to deeper into this problem the aerodynamicforces on each cup should be analyzed As the aerodynamictorque on the anemometerrsquos rotor is produced by the aerody-namic forces on the mentioned cups and the cups positionson the rotor have 120∘ phase separation it is logical to assumethat at constant wind speed equal rotational accelerations anddecelerationswill affect the anemometer rotor three times perrevolution (obviously these accelerations are responsible forthe third harmonic term of the anemometer wind speed 120596

3

see expression (3)) Therefore studying the third harmonicterm of the rotational speed is a way to analyze the effect ofthe cups on the rotor movement

In Figure 5 the non-dimensional third harmonic term120596

3120596

0 calculated for every wind speed of the calibrations

regarding the studied porous cups rotors (h-0960 h-1960and h-2460) is shown together with the results correspond-ing to the c-2560 rotor (included as it can be considered aspart of the porous cup series ie porosity equal to zero) Inthementionedfigure the differences among the performanceswith regard to the different rotors can be clearly observedThis figure has been chosen to illustrate two parameters usedin the present work to analyze the third harmonic term ofthe anemometer rotational speed (i) the non-dimensional

1205963 + 1205903

1205963

1205963 minus 1205903

V (ms)

900

800

700

600

500

400

300

200

100

0004 6 8 10 12 14 16

1205963120596

0(

)

Figure 5 Non-dimensional harmonic term 1205963120596

0 calculated at

every point of the calibrations performed on the Climatronics100075 anemometer equippedwith c-2560 (circles) h-0960 (trian-gles) h-1960 (squares) and h-2460 (rhombi) rotors The averagevalue line 120596

3 together with the standard deviation limits plusmn120590

3

corresponding to the h-1960 rotor values has been also included inthe graph

average value calculated with data from the 13 points of thecalibration procedure

120596

3=

1

13

13

sum

119894=1

120596

3

120596

0

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119894

(6)

and (ii) the corresponding standard deviation 1205903 calculated

using the general procedure

120590

3=

radic

sum

13

119894=1( (120596

3120596

0)

1003816

1003816

1003816

1003816119894minus 120596

3)

2

13 minus 1

(7)

In Figure 6 the averaged third non-dimensional har-monic term 120596

3 regarding the conical cups rotors and

the ratio of the standard deviation to the mentioned non-dimensional third harmonic term 120590

3120596

3 are shown as a

function of the ratio of the cup radius to the cupsrsquo centerrotation radius 119903

119903 The third harmonic term 120596

3 tends to be

smaller with higher values of 119903119903 that is for rotors whose cups

centers are closer to the rotation axisThe same tendency wasobserved on the anemometer factor 119870 (see Figure 4) so itcan be concluded that higher third harmonic terms have animmediate effect on the anemometer average performancereducing the average rotational speed 120596

0 This effect can be

explained in terms of energy as a bigger part of the energytransferred from the wind to the rotor movement is investedinto the mentioned third harmonic term and not into theconstant term of the rotational speed 120596

0 Also the effect

of the cupsrsquo size has the same pattern as the one for the

8 The Scientific World Journal

rr

180160140120100080060040

000 020 040 060 080 100

1205963(

)

(a)

rr

000 020 040 060 080 100

2000

1600

1200

800

400

000

1205903120596

3(

)

(b)

Figure 6 Averaged third harmonic term 1205963 regarding the conical cups rotors (a) and the corresponding standard deviation 120590

3120596

3(b)

both expressed as a function of the parameter 119903

119903(119903119903= 119877

119888119877

119903119888) The symbols correspond to rotors equipped with the following cup radii

119877

119888= 20mm (rhombi) 119877

119888= 25mm (circles) 119877

119888= 30mm (squares) 119877

119888= 35mm (triangles) and 119877

119888= 40mm (crosses)

anemometer constant graphs in Figure 4 Smaller cups withthe same parameter 119903

119903show smaller third harmonic terms

with higher rotational efficienciesFinally focusing on the standard deviationmeasuredwith

respect to the average third harmonic term 1205903120596

3 shown

in Figure 6 it seems that there is a minimum for every cupsize at a certain value of the parameter 119903

119903 located around

119903

119903= 05 In Figure 7 the third harmonic term measured for

every wind velocity during the calibration of four rotorsequipped with 119877

119888= 40mm cups is shown The data

correspond to the smallest and the largest cup rotation radiustested (119877

119903119888= 50mm and 119877

119903119888= 140mm resp) and two

intermediate cases (119877119903119888

= 80mm and 119877

119903119888= 100mm) It

can be observed that according to the information from thementioned graph in Figure 6 the dispersion of the results islower for the intermediate cases A linear tendency is alsoobserved with higher slopes for greater values of cup centerrotation radius Finally it should also be said that class-1commercial anemometers [47 50] have ratios between thecup radius and the cupsrsquo center rotation radius ranging from119903

119903= 04 to 119903

119903= 06 (Thies Clima 4335043351 119903

119903= 05

Vector Instruments A100L2 119903119903= 049 Vaisala WAA 151252

119903

119903= 042 WindSensor (Risoslash) P2546A 119903

119903= 059)

Concerning the effect of the cupsrsquo shape its effect onanemometer performance has been already analyzed Theaerodynamic forces on a single cup have been correlatedwith the aforementioned anemometer performance in twodifferent ways by means of analytical models correlated withexperimental testing [30 31 33 38] and by means of adirect comparison based on experimental calibration [48] InFigure 8 the anemometer constant at 16ms wind speed withregard to the calibrations performed on the anemometerequipped with elliptical and porous cups rotors has beenincluded respectively as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 and the ratio of the hole diameter to the cupdiameter ℎ2119877

119888 The non-dimensional third harmonic 120596

3

regarding these rotors has been also included in the figureAs it was previously measured [48] the effect of both theeccentricity and the porosity of the cups is translated into adecrease of the rotational efficiency of the cups (higher values

1205963120596

0

1205963

V (ms)

13

12

11

10

09

08

07

06

0 2 4 6 8 10 12 14 16 18

Rrc = 50mm (RcRrc = 08)

Rrc = 100mm (RcRrc = 04)

Rrc = 140mm (RcRrc = 0287)

Rrc = 80mm (RcRrc = 05)

Figure 7 Variation of the third harmonic term measured withrotors equipped with 119877

119888= 40mm conical cups as a function of the

wind speed within the calibration process

of 119870 that is lower rotational speed at a fixed wind speed)On the other hand the effect of both parameters on the thirdharmonic term has a reversed effect that is higher valuesof eccentricity and porosity increase the importance of thisharmonic term

4 Conclusions

In the present work the performance of a cup anemometerequipped with different rotors has been experimentally ana-lyzed On one hand the size of conical cups together withtheir distance to the anemometer rotation axis was studiedOn the other hand the shape of the rotor cups was alsostudied The analysis was based on two different parameters

The Scientific World Journal 9

K

e h2Rc

1000

950

900

850

800

750

700

650

600

550

500

450

400

000 020 040 060 080 100

(a)

1000

900

800

700

600

500

400

300

200

100

e h2Rc

000 020 040 060 080 100

1205963(

)(b)

Figure 8 Anemometer constant at 16ms wind speed119870 and non-dimensional third harmonic1205963 with regard to the calibrations performed

to the anemometer equipped with elliptical (squares) and porous (circles) cup rotors as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 andthe ratio of the hole diameter to the front cup area ℎ2119877

119888 respectively

the anemometer factor that takes into account the averagerotation of the anemometer and the third harmonic termresulting from the Fourier decomposition of the anemometerrotation speed The most relevant conclusions resulting fromthis work are as follows

(i) The average rotation speed is well correlated with thementioned third harmonic term resulting from theFourier decomposition of the anemometer rotationspeed Higher values of this third harmonic termresult in higher anemometer factors and thereforein lower rotational speeds This fact confirms thementioned third harmonic term as a useful parameterto study cup anemometer performance

(ii) Smaller cups with the same ratio of cup diameter tothe cupsrsquo center rotation radius 119903

119903 tend to produce

higher rotational speeds (lower anemometer factors)and lower third harmonic terms

(iii) The ratio of the third harmonic term to the averagerotational speed 120596

3120596

0 is more uniform (within the

wind speed calibration range) for values of the ratioof the cup diameter to the cupsrsquo center rotation radiusranging from 119903

119903= 04 to 119903

119903= 05 than for values of 119903

119903

beyond or below this bracket

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are truly indebted to Enrique Vega AlejandroMartınez Encarnacion Meseguer Luis Garcıa and EduardoCortes for the help and friendly support during the testingcampaign The authors are grateful to Anna Marıa Ballesterfor her kind help on improving the style of the text

References

[1] F Aminzadeh and S Pindado ldquoHow has Spain become a leaderin thewind energy industry during the last decade (An analysisof influential factors on the development of wind energy inSpain)rdquo in Proceedings of the EWEA Annual Event BrusselsBelgium 2011

[2] L Kristensen ldquoCan a cup anemometer ldquounderspeedrdquo A hereti-cal questionrdquo Boundary-Layer Meteorology vol 103 no 1 pp163ndash172 2002

[3] R V Coquilla J Obermeier and B R White ldquoCalibrationprocedures and uncertainty in wind power anemometersrdquoWind Engineering vol 31 no 5 pp 303ndash316 2007

[4] A Albers and H Klug ldquoOpen field cup anemometryrdquo DEWIMagazine vol 19 pp 53ndash58 2001

[5] A Albers H Klug and D Westermann ldquoOutdoor comparisonof cup anemometersrdquo DEWI Magazin vol 17 pp 5ndash15 2000

[6] S Lang and E McKeogh ldquoLIDAR and SODAR measurementsof wind speed and direction in upland terrain for wind energypurposesrdquo Remote Sensing vol 3 no 9 pp 1871ndash1901 2011

[7] R Wagner M Courtney J Gottschall and P Lindelow-Marsden ldquoAccounting for the speed shear in wind turbine

10 The Scientific World Journal

power performance measurementrdquoWind Energy vol 14 no 8pp 993ndash1004 2011

[8] T R Robinson ldquoOn a New Anemometerrdquo Proceedings of theRoyal Irish Academy (1836ndash1869 ) vol 4 pp 566ndash572 1847

[9] International Electrotechnical Commision International Stan-dard IEC-61400-12-1 Wind Turbines Part 12-1 Power Perfor-mance Measurements of Electricity Producing Wind TurbinesFirst Edition 2005ndash12 International Electrotechnical Commi-sion Geneva Switzerland 2005

[10] R V Coquilla and J Obermeier ldquoCalibration speed range forrotating anemometers used in wind energy applicationsrdquo inProceedings of the 46th AIAA Aerospace Sciences Meeting andExhibit pp 2ndash7 January 2008

[11] R V Coquilla A Havner J Obermeier and M SturgeonldquoVerification testing of Sonic anemometer wind speedmeasure-ments for wind energy applicationsrdquo in Proceedings of the 2010American Wind Energy Association Annual Conference (AWEAWINDPOWER rsquo10) pp 1ndash14 2010

[12] L J Fritschen ldquoA sensitive cup-type anemometerrdquo Journal ofApplied Meteorology vol 6 pp 695ndash698 1967

[13] M Sanuki and S Kimura ldquoSome aerodynamic aspects deducedfrom the start and stop experiment of three- and four-cupanemometerrdquo Papers in Meteorology and Geophysics vol 5 pp695ndash698 1954

[14] C F Marvin ldquoA rational theory of the cup anemometerrdquoMonthly Weather Review vol 60 pp 43ndash56 1932

[15] M J Brevoort and U T Joyner ldquoExperimental investigation ofthe Robinson-type cup anemometerrdquo NACA TN-513 1935

[16] C F Marvin ldquoRecent advances in anemometryrdquo MonthlyWeather Review vol 62 pp 115ndash120 1934

[17] C F Marvin ldquoAnemometer testsrdquoMonthlyWeather Review pp58ndash63 1900

[18] H Charnock and F E Pierce ldquoNew housing for the sensitivecup-contact anemometer Mk 1rdquo Journal of Scientific Instru-ments vol 36 no 7 p 329 1959

[19] P A Sheppard ldquoAn improved design of cup anemometerrdquoJournal of Scientific Instruments vol 17 no 9 pp 218ndash221 1940

[20] E L Deacon ldquoReply to two types of sensitive recording cupanemometersrdquo Journal of Scientific Instruments vol 25 no 8p 283 1948

[21] S G Crawford ldquoA simple form of sensitive electric contact cupanemometerrdquo Journal of Scientific Instruments vol 28 no 2 pp36ndash37 1951

[22] F Scrase and P Sheppard ldquoThe errors of cup anemometers influctuating windsrdquo Journal of Scientific Instruments vol 21 no9 pp 160ndash161 1944

[23] E L Deacon ldquoThe over-estimation error of cup anemometersin fluctuating windsrdquo Journal of Scientific Instruments vol 28no 8 pp 231ndash234 1951

[24] L KristensenThe Cup Anemometer and Other Exciting Instru-ments Risoslash-R-615 (EN) Risoslash National Laboratory RoskildeDenmark 1993

[25] MEASNET Cup Anemometer Calibration Procedure Version1 (September 1997 Updated 24112008) MEASNET MadridSpain 1997

[26] MEASNET Anemometer Calibration Procedure Version 2(October 2009) MEASNET Madrid Spain 2009

[27] ASTM International Standard Test Method for Determining thePerformance of a Cup Anemometer or Propeller Anemometer(ASTMD 5096-02) ASTM InternationalWest ConshohockenPa USA 2002

[28] M C-E Brazier ldquoSur la variation des indications desanemometres Robinson et Richard en fonction de lrsquoinclinaisondu ventrdquoComptes Rendus des Seances de LrsquoAcademie des Sciencesvol 170 pp 610ndash612 1920

[29] S Pindado E Vega A Martınez E Meseguer S Franchiniand I P Sarasola ldquoAnalysis of calibration results from cupand propeller anemometers Influence on wind turbine AnnualEnergy Production (AEP) calculationsrdquo Wind Energy vol 14no 1 pp 119ndash132 2011

[30] J Kondo G I Naito and Y Fujinawa ldquoResponse of cupanemometer in turbulencerdquo Journal of theMeteorological Societyof Japan vol 49 pp 63ndash74 1971

[31] S Ramachandran ldquoA theoretical study of cup and vaneanemometersrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 95 no 403 pp 163ndash180 1969

[32] M C-E Brazier ldquoSur la comparabilite des anemometresrdquoComptes Rendus des Seances de LrsquoAcademie des Sciences vol 172pp 843ndash845 1921

[33] O Schrenk ldquoUber die tragheitsfehler des Schalenkreuz-anemometers bei schwankender Windstarkerdquo Zeitschrift FurTechnische Physik vol 10 pp 57ndash66 1929

[34] H W Baynton ldquoErrors in wind run estimates from rotationalanemometersrdquo Bulletin of the American Meteorological Societyvol 57 no 9 pp 1127ndash1130 1976

[35] N E Busch and L Kristensen ldquoCup anemometer overspeed-ingrdquo Journal of AppliedMeteorology vol 15 pp 1328ndash1332 1976

[36] P Frenzen ldquoFast response cup anemometers for atmosphericturbulence researchrdquo in Proceedings of the 8th Symposium onTurbulence and Diffusion pp 112ndash115 1988

[37] E I Kaganov and A M Yaglom ldquoErrors in wind-speed mea-surements by rotation anemometersrdquo Boundary-Layer Meteo-rology vol 10 no 1 pp 15ndash34 1976

[38] J C Wyngaard ldquoCup propeller vane and sonic anemometersin turbulence researchrdquo Annual Review of Fluid Mechanics vol13 pp 399ndash423 1981

[39] P A Coppin ldquoAn examination of cup anemometer overspeed-ingrdquoMeteorologische Rundschau vol 35 pp 1ndash11 1982

[40] J CWyngaard J T Bauman and R A Lynch ldquoCup anemome-ter dynamicsrdquo in Flow Its Measurement and Control in Scienceand Industry vol 1 pp 701ndash708 1974

[41] L Kristensen ldquoCup anemometer behavior in turbulent environ-mentsrdquo Journal of Atmospheric and Oceanic Technology vol 15no 1 pp 5ndash17 1998

[42] R S Hunter ldquoThe accuracy of cup anemometer calibrationwithparticular regard to testing wind turbinesrdquo Wind Engineeringvol 14 no 1 pp 32ndash43 1990

[43] J-A Dahlberg J Gustavsson G Ronsten T F Pedersen US Paulsen and D Westermann Development of A Standard-ised Cup Anemometer Suited to Wind Energy Applications-(ClAsscup) vol 9 Technical University of Denmark LyngbyDenmark 2001

[44] S Pindado J Perez and S Avila-Sanchez ldquoOn cup anemometerrotor aerodynamicsrdquo Sensors vol 12 no 5 pp 6198ndash6217 2012

[45] S Pindado A Sanz and A Wery ldquoDeviation of cup andpropeller anemometer calibration results with air densityrdquoEnergies vol 5 no 3 pp 683ndash701 2012

[46] S Pindado A Barrero-Gil and A Sanz ldquoCup anemome-tersrsquoLoss of performance due to ageing processes and its effecton Annual Energy Production (AEP) estimatesrdquo Energies vol5 no 12 pp 1664ndash1685 2012

The Scientific World Journal 11

[47] J-A Dahlberg T F Pedersen and P Busche ACCUWIND-Methods for Classification of Cup Anemometers Risoslash-R-1555(EN) Risoslash National Laboratory Roskilde Denmark 2006

[48] S Pindado I Perez and M Aguado ldquoFourier analysis ofthe aerodynamic behavior of cup anemometersrdquo MeasurementScience and Technology vol 24 no 6 Article ID 065802 2013

[49] Y P Solovrsquoev A I Korovushkin and Y N Toloknov ldquoCharac-teristics of a cup anemometer and a procedure of measuring thewind velocityrdquo Physical Oceanography vol 14 no 3 pp 173ndash1862004

[50] T F Pedersen Development of A Classification System forCup Anemometers-CLASSCUP Risoslash-R-1348(EN) Risoslash NationalLaboratory Roskilde Denmark 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Active and Passive Electronic Components

Control Scienceand Engineering

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Advances inOptoElectronics

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Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

The Scientific World Journal 3

120596120596

0

12

11

10

09

08

00 01 02 03 04 05 06 07 08 09 10

tT

(a)

120596i1205960

i

010

008

006

004

002

0001 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

(b)

Figure 1 Relative-to-the-average rotational speed120596120596

0 of aThies 43303 anemometer during one turn at 8ms wind speed [47] (a) and non-

dimensional values of the Fourier series decomposition performed on that rotational speed 120596119894120596

0(b) 119879 is the period of the anemometerrsquos

rotation

constant wind speed revealed the effect of the anemometerrsquosrotor shape on this third harmonic term of the rotation speed(these results were presented at the Alternative EnergiesSpecial Session of the 9th Conference on Diffusion in Solidsand Liquids Madrid 2013) Nevertheless the results werenot conclusive enough as the analysis was performed usingan Ornytion 107A anemometer This anemometer gives ananalog output consisting in 2-harmonic pulses per turngenerated by rotating magnets which is a good enough ratetomeasure correctly the average rotation speed120596

0 However

the process to extract the third harmonic term from theoutput had to be indirect and derived from Lenzrsquos law whichrelates the generated analog output of the anemometer to therotating magnetic field

The aim of the present study is to analyze the response ofan optoelectronic output anemometer (Climatronics 100075by Climatronics Corp also known as F460model) equippedwith different rotors to have a better understanding of theeffect of the geometry (size of the cups distance of the cupsto the rotation axis) on cup anemometer performances Alsothe third harmonic term of the rotation speed see expression(3) is studied as a possible new approach to analyze thementioned anemometer performances

2 Testing Configuration and Cases Studied

As said the Climatronics 100075 anemometer was used in thetesting campaign 32 different rotors were tested (see Table 2and Figure 2) 26 were equipped with conical cups (90∘ cone-angle 4 with cup radius 119877

119888= 20mm cup center rotation

radius varying from 119877

119903119888= 30mm to 119877

119903119888= 60mm 5 with

cup radius 119877119888= 25mm cup center rotation radius varying

from 119877

119903119888= 40mm to 119877

119903119888= 100mm 6 with cup radius

119877

119888= 30mm cup center rotation radius varying from 119877

119903119888=

40mm to 119877

119903119888= 120mm 5 with cup radius 119877

119888= 35mm cup

center rotation radius varying from 119877

119903119888= 50mm to 119877

119903119888=

120mm and 6 with cup radius 119877119888

= 40mm cup centerrotation radius varying from 119877

119903119888= 60mm to 119877

119903119888= 140mm)

3 were equipped with elliptical cups (front surface equal tothe conical cups 119878

119888= 19635mm2 and 119877

119903119888= 60mm)

Conical cupsRrc Rc

Porous cups

h

25

Elliptical cupsa

b

Rc

Rc

Rrc

Rrc

25

Figure 2 Sketch of the cups and rotor geometries tested Dimen-sions in mm See also Table 2

3 were equipped with porous cups (front surface includingthe empty area equal to the conical cups 119878

119888= 19635mm2

cup radius 119877119888= 25mm truncated shape with hole diameter

ℎ = 9mm ℎ = 19mm and ℎ = 24mm and 119877

119903119888= 60mm)

The cups used in this study were made of ABS plastic using a3D printer and the arm on each cup was made of aluminumtubing 5mm in diameter

The calibrations were carried out at the IDRUPMInstitute in the S4 wind tunnel (see Figure 3) This facilityis an open-circuit wind tunnel with a closed test sectionmeasuring 09 by 09m It is served by four 75 kW fanswith a flow uniformity under 02 in the testing area Moredetails concerning the facility and the calibration process areincluded in [29] The calibrations analyzed in the presentpaper were performed following the MEASNET [25 26]recommendations (over 13 points and from 4 to 16ms windspeed) In each point (wind speed) of every calibration

4 The Scientific World Journal

Table 2 Geometrical characteristics of the rotors tested cup center rotation radius 119877119903119888 front area of the cups 119878

119888 cup radius (conical and

porous cups)119877119888 ratio of cup radius to the cupsrsquo center rotation radius (conical cups)119877

119888119877119903119888 hole diameter of porous cups ℎ and semi-major

and semi-minor axes 119886 and 119887 of elliptical cups See also Figure 2

Conical cupsRotor 119877

119888[mm] 119878

119888[mm2] 119877

119903119888[mm] 119877

119888119877119903119888

c-2030 20 12566 30 0667c-2040 20 12566 40 0500c-2050 20 12566 50 0400c-2060 20 12566 60 0333c-2540 25 19635 40 0625c-2550 25 19635 50 0500c-2560 25 19635 60 0417c-2580 25 19635 80 0313c-25100 25 19635 100 0250c-3040 30 28274 40 0750c-3050 30 28274 50 0600c-3060 30 28274 60 0500c-3080 30 28274 80 0375c-30100 30 28274 100 0300c-30120 30 28274 120 0250c-3550 35 38485 50 0700c-3560 35 38485 60 0583c-3580 35 38485 80 0438c-35100 35 38485 100 0350c-35120 35 38485 120 0292c-4050 40 50265 50 0800c-4060 40 50265 60 0667c-4080 40 50265 80 0500c-40100 40 50265 100 0400c-40120 40 50265 120 0333c-40140 40 50265 140 0286

Elliptical cupsRotor 119886 [mm] 119887 [mm] 119878

119888[mm2] 119877

119903119888[mm]

a-2760 27 2315 19635 60a-3060 30 2083 19635 60a-3560 35 1786 19635 60

Porous cupsRotor 119877

119888[mm] 119878

119888[mm2] 119877

119903119888[mm] ℎ [mm]

h-960 25 19635 60 9h-1960 25 19635 60 19h-2460 25 19635 60 24

performed the anemometerrsquos output was sampled during 20seconds at 10000Hz

The Climatronics 100075 anemometer gives 30 squaredpulses per turn A plot of the output signal record in oneturn of this anemometer equipped with the h-2460 rotor isincluded in Figure 3 togetherwith the non-dimensional rota-tion speed 120596120596

0 once the output was post-processed The

non-dimensional rotation speed on one turn was calculatedaveraging groups of 30 pulses contained in the recorded datafor every point (ie every wind flow velocity) during thecalibration of all configurations analyzed

3 Results and Discussion

The calibration constants of the anemometer transfer func-tion 119860 and 119861 with regard to all cases tested are includedin Table 3 In Figure 4 the anemometer factor 119870 regardingthe calibrations performed in the present study to con-ical cups rotors is shown as a function of the param-eter 119903

119903(which represents the ratio between the cupsrsquo

radius 119877119888 and the cupsrsquo center rotation radius 119877

119903119888 119903119903

=

119877

119888119877

119903119888) This anemometer factor is defined as the ratio

between the wind speed 119881 and the rotation speed of

The Scientific World Journal 5

Vou

tput

tT

60

45

30

15

00

0 02 04 06 08 1

tT

0 02 04 06 08 1120596120596

0

110

105

100

095

090

(a)

(b)

(c)

Figure 3 Climatronics 100075 anemometer placed in the S4 wind tunnel of the IDRUPM Institute to carry out a calibration with the h-1960rotor (a) Anemometer voltage output signal 119881output in one turn (b) Relative-to-the-average rotational speed 120596120596

0 in one turn (c) 119879 is the

period of the anemometerrsquos rotation

rr

V = 4ms52

48

44

40

36

32

02 03 04 05 06 07 08 09

K

(a)

rr

52

48

44

40

36

32

02 03 04 05 06 07 08 09

V = 16ms

K

(b)

K

rr

52

48

44

40

36

32

02 03 04 05 06 07 08 09

K = 44139 minus 16573 middot r2c

K = 4438 minus 27174 middot r2c

Upper fitting

Lower fitting

V rarr infin

(c)

Figure 4 Anemometer factor 119870 regarding the conical cups rotors calculated for 119881 = 4ms (a) 119881 = 16ms (b) and 119881 rarr infin (c) as afunction of the parameter 119903

119903(119903119903= 119877

119888119877

119903119888) The symbols correspond to rotors equipped with the following cup radii 119877

119888= 20mm (rhombi)

119877

119888= 25mm (circles) 119877

119888= 30mm (squares) 119877

119888= 35mm (triangles) and 119877

119888= 40mm (crosses) The quadratic fittings to 119877

119888= 20mm rotors

(lower fitting) and to 119877

119888= 40mm rotors (upper fitting) have been also added (dotted lines) to the bottom graph

the cup center averaged in one complete rotation 120596

0119877

119903119888

[48]

119870 =

119881

120596

0119877

119903119888

=

119860

119903119891

119903+ 119861

2120587119891

119903119877

119903119888

=

119860

119903

2120587119877

119903119888

1

1 minus (119861119881)

(4)

where 119860

119903and 119861 are respectively the slope and the offset of

the transfer function see expression (2) The anemometerfactor 119870 was calculated for both limits of the wind speedcalibration range 4ms and 16ms and for very high windspeeds (119881 rarr infin) which in fact is the result of considering

6 The Scientific World Journal

Table 3 Calibration coefficients 119860 and 119861 measured for the rotors tested with Climatronics 100075 anemometer (see also Table 2 andFigure 2) The coefficient of determination 1198772 of the curve fittings and the slope of the transfer function based on the rotation frequency119860

119903(see expressions (1) and (2)) have also been included

Conical cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

c-2030 002021 060618 037096 099995c-2040 003177 095318 023328 099999c-2050 004186 125574 031148 099999c-2060 005180 155401 040091 099999c-2540 002963 088886 026760 099999c-2550 003932 117970 020786 099999c-2560 004961 148829 024245 099999c-2580 006964 208928 039438 099999c-25100 008952 268552 053685 099999c-3040 002861 085818 009551 099995c-3050 003861 115844 019606 099999c-3060 004850 145505 014823 099998c-3080 006836 205089 025403 100000c-30100 008697 260900 038253 099998c-30120 010738 322145 049053 099999c-3550 003720 111603 019081 099999c-3560 004719 141582 015354 099999c-3580 006827 204818 018132 099998c-35100 008737 262111 022168 099999c-35120 010742 322259 034171 099999c-4050 003539 106166 013714 099999c-4060 004586 137587 016652 099999c-4080 006663 199876 016932 099998c-40100 008668 260026 023292 099996c-40120 010638 319140 028805 099996c-40140 012639 379164 034162 099995

Elliptical cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

a-2760 005221 156617 019932 099999a-3060 005306 159167 023224 099998a-3560 005412 162361 021593 099998

Porous cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

h-0960 005445 163352 031414 099999h-1960 006579 197376 054539 099998h-2460 011763 352881 031563 099998

the offset constant of the transfer function 119861 negligible Itshould be said that the effect of this offset constant on similarcalculations has been considered negligible in past works[44 48] as it is only appreciated at lowwind speedsHoweverit was preserved in the present calculations in order to havea more accurate comparison between the different cases andnew conclusions have arisen

In Figure 4 three different cases can be observed Forlow wind speeds (119881 = 4ms) the cup anemometer is lessefficient in terms of transforming the wind velocity into

rotational speed than for higher wind speeds (ie highervalues of the anemometer factor 119870 are shown) Also thecurves corresponding to the different cup sizes seem to followthe samepath for ratios between the cupsrsquo radius and the cupsrsquocenter rotation radius lower than 119903

119903lt 065 The mentioned

lower performances of the anemometer can be explainedas an effect of the friction forces which are increasinglysignificant when compared to the aerodynamic forces forlow wind speeds (that obviously are translated into lowrotational speeds)

The Scientific World Journal 7

The situation changes for higher wind speeds as it canbe observed for 119881 = 16ms and even more clearly for thelimit case 119881 rarr infin (ie when the offset constant 119861 is leftaside) In this case the anemometer constant 119870 shows asecond-order polynomial dependence on the parameter 119903

119903

Also the effect of relative cup size is shown in the mentionedgraph The curves fitting to the results corresponding to therotors with the smallest and the largest cups (119877

119888= 20mm

and 119877

119888= 40mm resp) have been included in the graphThe

results corresponding to all the intermediate cup size rotors(119877119888= 25mm 119877

119888= 30mm and 119877

119888= 35mm) lie between

both curves revealing the aforementioned dependence onthe cupsrsquo size In tune with this effect it should also be saidthat other experimental results have already demonstratedthe direct relationship between the slope of the anemometertransfer function 119860 and the front area of the cups [44]

119860 =

1

119873

119901

119860

119903=

1

119873

119901

(

d119860119903

d119877119903119888

119877

119903119888+ 119860

1199030) (5)

where d119860119903d119877119903119888depends on the aerodynamic forces on the

cups (for rotors equipped with the same conical cups testedin the present work it was found that this coefficient hasconstant value with very little or no correlation to the cupsrsquosize) and 119860

1199030strongly depends on the cupsrsquo front area 119878

119888

Finally it should also be said that as far as the authorsknow this particular effect of the cupsrsquo size has not beenincluded in the different analyticalmodels developed to studycup anemometer behavior [30 31 33 38 40] These modelsare based on wind speed cup aerodynamic coefficientsand cup and rotor geometries and take as starting pointthat the behavior of cup anemometers is mainly driven byaerodynamic forces the frictional torque being much lowerin comparison [37 49] However these models are limiteddue to the complexity of rotating flows [48]

In order go to deeper into this problem the aerodynamicforces on each cup should be analyzed As the aerodynamictorque on the anemometerrsquos rotor is produced by the aerody-namic forces on the mentioned cups and the cups positionson the rotor have 120∘ phase separation it is logical to assumethat at constant wind speed equal rotational accelerations anddecelerationswill affect the anemometer rotor three times perrevolution (obviously these accelerations are responsible forthe third harmonic term of the anemometer wind speed 120596

3

see expression (3)) Therefore studying the third harmonicterm of the rotational speed is a way to analyze the effect ofthe cups on the rotor movement

In Figure 5 the non-dimensional third harmonic term120596

3120596

0 calculated for every wind speed of the calibrations

regarding the studied porous cups rotors (h-0960 h-1960and h-2460) is shown together with the results correspond-ing to the c-2560 rotor (included as it can be considered aspart of the porous cup series ie porosity equal to zero) Inthementionedfigure the differences among the performanceswith regard to the different rotors can be clearly observedThis figure has been chosen to illustrate two parameters usedin the present work to analyze the third harmonic term ofthe anemometer rotational speed (i) the non-dimensional

1205963 + 1205903

1205963

1205963 minus 1205903

V (ms)

900

800

700

600

500

400

300

200

100

0004 6 8 10 12 14 16

1205963120596

0(

)

Figure 5 Non-dimensional harmonic term 1205963120596

0 calculated at

every point of the calibrations performed on the Climatronics100075 anemometer equippedwith c-2560 (circles) h-0960 (trian-gles) h-1960 (squares) and h-2460 (rhombi) rotors The averagevalue line 120596

3 together with the standard deviation limits plusmn120590

3

corresponding to the h-1960 rotor values has been also included inthe graph

average value calculated with data from the 13 points of thecalibration procedure

120596

3=

1

13

13

sum

119894=1

120596

3

120596

0

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119894

(6)

and (ii) the corresponding standard deviation 1205903 calculated

using the general procedure

120590

3=

radic

sum

13

119894=1( (120596

3120596

0)

1003816

1003816

1003816

1003816119894minus 120596

3)

2

13 minus 1

(7)

In Figure 6 the averaged third non-dimensional har-monic term 120596

3 regarding the conical cups rotors and

the ratio of the standard deviation to the mentioned non-dimensional third harmonic term 120590

3120596

3 are shown as a

function of the ratio of the cup radius to the cupsrsquo centerrotation radius 119903

119903 The third harmonic term 120596

3 tends to be

smaller with higher values of 119903119903 that is for rotors whose cups

centers are closer to the rotation axisThe same tendency wasobserved on the anemometer factor 119870 (see Figure 4) so itcan be concluded that higher third harmonic terms have animmediate effect on the anemometer average performancereducing the average rotational speed 120596

0 This effect can be

explained in terms of energy as a bigger part of the energytransferred from the wind to the rotor movement is investedinto the mentioned third harmonic term and not into theconstant term of the rotational speed 120596

0 Also the effect

of the cupsrsquo size has the same pattern as the one for the

8 The Scientific World Journal

rr

180160140120100080060040

000 020 040 060 080 100

1205963(

)

(a)

rr

000 020 040 060 080 100

2000

1600

1200

800

400

000

1205903120596

3(

)

(b)

Figure 6 Averaged third harmonic term 1205963 regarding the conical cups rotors (a) and the corresponding standard deviation 120590

3120596

3(b)

both expressed as a function of the parameter 119903

119903(119903119903= 119877

119888119877

119903119888) The symbols correspond to rotors equipped with the following cup radii

119877

119888= 20mm (rhombi) 119877

119888= 25mm (circles) 119877

119888= 30mm (squares) 119877

119888= 35mm (triangles) and 119877

119888= 40mm (crosses)

anemometer constant graphs in Figure 4 Smaller cups withthe same parameter 119903

119903show smaller third harmonic terms

with higher rotational efficienciesFinally focusing on the standard deviationmeasuredwith

respect to the average third harmonic term 1205903120596

3 shown

in Figure 6 it seems that there is a minimum for every cupsize at a certain value of the parameter 119903

119903 located around

119903

119903= 05 In Figure 7 the third harmonic term measured for

every wind velocity during the calibration of four rotorsequipped with 119877

119888= 40mm cups is shown The data

correspond to the smallest and the largest cup rotation radiustested (119877

119903119888= 50mm and 119877

119903119888= 140mm resp) and two

intermediate cases (119877119903119888

= 80mm and 119877

119903119888= 100mm) It

can be observed that according to the information from thementioned graph in Figure 6 the dispersion of the results islower for the intermediate cases A linear tendency is alsoobserved with higher slopes for greater values of cup centerrotation radius Finally it should also be said that class-1commercial anemometers [47 50] have ratios between thecup radius and the cupsrsquo center rotation radius ranging from119903

119903= 04 to 119903

119903= 06 (Thies Clima 4335043351 119903

119903= 05

Vector Instruments A100L2 119903119903= 049 Vaisala WAA 151252

119903

119903= 042 WindSensor (Risoslash) P2546A 119903

119903= 059)

Concerning the effect of the cupsrsquo shape its effect onanemometer performance has been already analyzed Theaerodynamic forces on a single cup have been correlatedwith the aforementioned anemometer performance in twodifferent ways by means of analytical models correlated withexperimental testing [30 31 33 38] and by means of adirect comparison based on experimental calibration [48] InFigure 8 the anemometer constant at 16ms wind speed withregard to the calibrations performed on the anemometerequipped with elliptical and porous cups rotors has beenincluded respectively as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 and the ratio of the hole diameter to the cupdiameter ℎ2119877

119888 The non-dimensional third harmonic 120596

3

regarding these rotors has been also included in the figureAs it was previously measured [48] the effect of both theeccentricity and the porosity of the cups is translated into adecrease of the rotational efficiency of the cups (higher values

1205963120596

0

1205963

V (ms)

13

12

11

10

09

08

07

06

0 2 4 6 8 10 12 14 16 18

Rrc = 50mm (RcRrc = 08)

Rrc = 100mm (RcRrc = 04)

Rrc = 140mm (RcRrc = 0287)

Rrc = 80mm (RcRrc = 05)

Figure 7 Variation of the third harmonic term measured withrotors equipped with 119877

119888= 40mm conical cups as a function of the

wind speed within the calibration process

of 119870 that is lower rotational speed at a fixed wind speed)On the other hand the effect of both parameters on the thirdharmonic term has a reversed effect that is higher valuesof eccentricity and porosity increase the importance of thisharmonic term

4 Conclusions

In the present work the performance of a cup anemometerequipped with different rotors has been experimentally ana-lyzed On one hand the size of conical cups together withtheir distance to the anemometer rotation axis was studiedOn the other hand the shape of the rotor cups was alsostudied The analysis was based on two different parameters

The Scientific World Journal 9

K

e h2Rc

1000

950

900

850

800

750

700

650

600

550

500

450

400

000 020 040 060 080 100

(a)

1000

900

800

700

600

500

400

300

200

100

e h2Rc

000 020 040 060 080 100

1205963(

)(b)

Figure 8 Anemometer constant at 16ms wind speed119870 and non-dimensional third harmonic1205963 with regard to the calibrations performed

to the anemometer equipped with elliptical (squares) and porous (circles) cup rotors as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 andthe ratio of the hole diameter to the front cup area ℎ2119877

119888 respectively

the anemometer factor that takes into account the averagerotation of the anemometer and the third harmonic termresulting from the Fourier decomposition of the anemometerrotation speed The most relevant conclusions resulting fromthis work are as follows

(i) The average rotation speed is well correlated with thementioned third harmonic term resulting from theFourier decomposition of the anemometer rotationspeed Higher values of this third harmonic termresult in higher anemometer factors and thereforein lower rotational speeds This fact confirms thementioned third harmonic term as a useful parameterto study cup anemometer performance

(ii) Smaller cups with the same ratio of cup diameter tothe cupsrsquo center rotation radius 119903

119903 tend to produce

higher rotational speeds (lower anemometer factors)and lower third harmonic terms

(iii) The ratio of the third harmonic term to the averagerotational speed 120596

3120596

0 is more uniform (within the

wind speed calibration range) for values of the ratioof the cup diameter to the cupsrsquo center rotation radiusranging from 119903

119903= 04 to 119903

119903= 05 than for values of 119903

119903

beyond or below this bracket

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are truly indebted to Enrique Vega AlejandroMartınez Encarnacion Meseguer Luis Garcıa and EduardoCortes for the help and friendly support during the testingcampaign The authors are grateful to Anna Marıa Ballesterfor her kind help on improving the style of the text

References

[1] F Aminzadeh and S Pindado ldquoHow has Spain become a leaderin thewind energy industry during the last decade (An analysisof influential factors on the development of wind energy inSpain)rdquo in Proceedings of the EWEA Annual Event BrusselsBelgium 2011

[2] L Kristensen ldquoCan a cup anemometer ldquounderspeedrdquo A hereti-cal questionrdquo Boundary-Layer Meteorology vol 103 no 1 pp163ndash172 2002

[3] R V Coquilla J Obermeier and B R White ldquoCalibrationprocedures and uncertainty in wind power anemometersrdquoWind Engineering vol 31 no 5 pp 303ndash316 2007

[4] A Albers and H Klug ldquoOpen field cup anemometryrdquo DEWIMagazine vol 19 pp 53ndash58 2001

[5] A Albers H Klug and D Westermann ldquoOutdoor comparisonof cup anemometersrdquo DEWI Magazin vol 17 pp 5ndash15 2000

[6] S Lang and E McKeogh ldquoLIDAR and SODAR measurementsof wind speed and direction in upland terrain for wind energypurposesrdquo Remote Sensing vol 3 no 9 pp 1871ndash1901 2011

[7] R Wagner M Courtney J Gottschall and P Lindelow-Marsden ldquoAccounting for the speed shear in wind turbine

10 The Scientific World Journal

power performance measurementrdquoWind Energy vol 14 no 8pp 993ndash1004 2011

[8] T R Robinson ldquoOn a New Anemometerrdquo Proceedings of theRoyal Irish Academy (1836ndash1869 ) vol 4 pp 566ndash572 1847

[9] International Electrotechnical Commision International Stan-dard IEC-61400-12-1 Wind Turbines Part 12-1 Power Perfor-mance Measurements of Electricity Producing Wind TurbinesFirst Edition 2005ndash12 International Electrotechnical Commi-sion Geneva Switzerland 2005

[10] R V Coquilla and J Obermeier ldquoCalibration speed range forrotating anemometers used in wind energy applicationsrdquo inProceedings of the 46th AIAA Aerospace Sciences Meeting andExhibit pp 2ndash7 January 2008

[11] R V Coquilla A Havner J Obermeier and M SturgeonldquoVerification testing of Sonic anemometer wind speedmeasure-ments for wind energy applicationsrdquo in Proceedings of the 2010American Wind Energy Association Annual Conference (AWEAWINDPOWER rsquo10) pp 1ndash14 2010

[12] L J Fritschen ldquoA sensitive cup-type anemometerrdquo Journal ofApplied Meteorology vol 6 pp 695ndash698 1967

[13] M Sanuki and S Kimura ldquoSome aerodynamic aspects deducedfrom the start and stop experiment of three- and four-cupanemometerrdquo Papers in Meteorology and Geophysics vol 5 pp695ndash698 1954

[14] C F Marvin ldquoA rational theory of the cup anemometerrdquoMonthly Weather Review vol 60 pp 43ndash56 1932

[15] M J Brevoort and U T Joyner ldquoExperimental investigation ofthe Robinson-type cup anemometerrdquo NACA TN-513 1935

[16] C F Marvin ldquoRecent advances in anemometryrdquo MonthlyWeather Review vol 62 pp 115ndash120 1934

[17] C F Marvin ldquoAnemometer testsrdquoMonthlyWeather Review pp58ndash63 1900

[18] H Charnock and F E Pierce ldquoNew housing for the sensitivecup-contact anemometer Mk 1rdquo Journal of Scientific Instru-ments vol 36 no 7 p 329 1959

[19] P A Sheppard ldquoAn improved design of cup anemometerrdquoJournal of Scientific Instruments vol 17 no 9 pp 218ndash221 1940

[20] E L Deacon ldquoReply to two types of sensitive recording cupanemometersrdquo Journal of Scientific Instruments vol 25 no 8p 283 1948

[21] S G Crawford ldquoA simple form of sensitive electric contact cupanemometerrdquo Journal of Scientific Instruments vol 28 no 2 pp36ndash37 1951

[22] F Scrase and P Sheppard ldquoThe errors of cup anemometers influctuating windsrdquo Journal of Scientific Instruments vol 21 no9 pp 160ndash161 1944

[23] E L Deacon ldquoThe over-estimation error of cup anemometersin fluctuating windsrdquo Journal of Scientific Instruments vol 28no 8 pp 231ndash234 1951

[24] L KristensenThe Cup Anemometer and Other Exciting Instru-ments Risoslash-R-615 (EN) Risoslash National Laboratory RoskildeDenmark 1993

[25] MEASNET Cup Anemometer Calibration Procedure Version1 (September 1997 Updated 24112008) MEASNET MadridSpain 1997

[26] MEASNET Anemometer Calibration Procedure Version 2(October 2009) MEASNET Madrid Spain 2009

[27] ASTM International Standard Test Method for Determining thePerformance of a Cup Anemometer or Propeller Anemometer(ASTMD 5096-02) ASTM InternationalWest ConshohockenPa USA 2002

[28] M C-E Brazier ldquoSur la variation des indications desanemometres Robinson et Richard en fonction de lrsquoinclinaisondu ventrdquoComptes Rendus des Seances de LrsquoAcademie des Sciencesvol 170 pp 610ndash612 1920

[29] S Pindado E Vega A Martınez E Meseguer S Franchiniand I P Sarasola ldquoAnalysis of calibration results from cupand propeller anemometers Influence on wind turbine AnnualEnergy Production (AEP) calculationsrdquo Wind Energy vol 14no 1 pp 119ndash132 2011

[30] J Kondo G I Naito and Y Fujinawa ldquoResponse of cupanemometer in turbulencerdquo Journal of theMeteorological Societyof Japan vol 49 pp 63ndash74 1971

[31] S Ramachandran ldquoA theoretical study of cup and vaneanemometersrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 95 no 403 pp 163ndash180 1969

[32] M C-E Brazier ldquoSur la comparabilite des anemometresrdquoComptes Rendus des Seances de LrsquoAcademie des Sciences vol 172pp 843ndash845 1921

[33] O Schrenk ldquoUber die tragheitsfehler des Schalenkreuz-anemometers bei schwankender Windstarkerdquo Zeitschrift FurTechnische Physik vol 10 pp 57ndash66 1929

[34] H W Baynton ldquoErrors in wind run estimates from rotationalanemometersrdquo Bulletin of the American Meteorological Societyvol 57 no 9 pp 1127ndash1130 1976

[35] N E Busch and L Kristensen ldquoCup anemometer overspeed-ingrdquo Journal of AppliedMeteorology vol 15 pp 1328ndash1332 1976

[36] P Frenzen ldquoFast response cup anemometers for atmosphericturbulence researchrdquo in Proceedings of the 8th Symposium onTurbulence and Diffusion pp 112ndash115 1988

[37] E I Kaganov and A M Yaglom ldquoErrors in wind-speed mea-surements by rotation anemometersrdquo Boundary-Layer Meteo-rology vol 10 no 1 pp 15ndash34 1976

[38] J C Wyngaard ldquoCup propeller vane and sonic anemometersin turbulence researchrdquo Annual Review of Fluid Mechanics vol13 pp 399ndash423 1981

[39] P A Coppin ldquoAn examination of cup anemometer overspeed-ingrdquoMeteorologische Rundschau vol 35 pp 1ndash11 1982

[40] J CWyngaard J T Bauman and R A Lynch ldquoCup anemome-ter dynamicsrdquo in Flow Its Measurement and Control in Scienceand Industry vol 1 pp 701ndash708 1974

[41] L Kristensen ldquoCup anemometer behavior in turbulent environ-mentsrdquo Journal of Atmospheric and Oceanic Technology vol 15no 1 pp 5ndash17 1998

[42] R S Hunter ldquoThe accuracy of cup anemometer calibrationwithparticular regard to testing wind turbinesrdquo Wind Engineeringvol 14 no 1 pp 32ndash43 1990

[43] J-A Dahlberg J Gustavsson G Ronsten T F Pedersen US Paulsen and D Westermann Development of A Standard-ised Cup Anemometer Suited to Wind Energy Applications-(ClAsscup) vol 9 Technical University of Denmark LyngbyDenmark 2001

[44] S Pindado J Perez and S Avila-Sanchez ldquoOn cup anemometerrotor aerodynamicsrdquo Sensors vol 12 no 5 pp 6198ndash6217 2012

[45] S Pindado A Sanz and A Wery ldquoDeviation of cup andpropeller anemometer calibration results with air densityrdquoEnergies vol 5 no 3 pp 683ndash701 2012

[46] S Pindado A Barrero-Gil and A Sanz ldquoCup anemome-tersrsquoLoss of performance due to ageing processes and its effecton Annual Energy Production (AEP) estimatesrdquo Energies vol5 no 12 pp 1664ndash1685 2012

The Scientific World Journal 11

[47] J-A Dahlberg T F Pedersen and P Busche ACCUWIND-Methods for Classification of Cup Anemometers Risoslash-R-1555(EN) Risoslash National Laboratory Roskilde Denmark 2006

[48] S Pindado I Perez and M Aguado ldquoFourier analysis ofthe aerodynamic behavior of cup anemometersrdquo MeasurementScience and Technology vol 24 no 6 Article ID 065802 2013

[49] Y P Solovrsquoev A I Korovushkin and Y N Toloknov ldquoCharac-teristics of a cup anemometer and a procedure of measuring thewind velocityrdquo Physical Oceanography vol 14 no 3 pp 173ndash1862004

[50] T F Pedersen Development of A Classification System forCup Anemometers-CLASSCUP Risoslash-R-1348(EN) Risoslash NationalLaboratory Roskilde Denmark 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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4 The Scientific World Journal

Table 2 Geometrical characteristics of the rotors tested cup center rotation radius 119877119903119888 front area of the cups 119878

119888 cup radius (conical and

porous cups)119877119888 ratio of cup radius to the cupsrsquo center rotation radius (conical cups)119877

119888119877119903119888 hole diameter of porous cups ℎ and semi-major

and semi-minor axes 119886 and 119887 of elliptical cups See also Figure 2

Conical cupsRotor 119877

119888[mm] 119878

119888[mm2] 119877

119903119888[mm] 119877

119888119877119903119888

c-2030 20 12566 30 0667c-2040 20 12566 40 0500c-2050 20 12566 50 0400c-2060 20 12566 60 0333c-2540 25 19635 40 0625c-2550 25 19635 50 0500c-2560 25 19635 60 0417c-2580 25 19635 80 0313c-25100 25 19635 100 0250c-3040 30 28274 40 0750c-3050 30 28274 50 0600c-3060 30 28274 60 0500c-3080 30 28274 80 0375c-30100 30 28274 100 0300c-30120 30 28274 120 0250c-3550 35 38485 50 0700c-3560 35 38485 60 0583c-3580 35 38485 80 0438c-35100 35 38485 100 0350c-35120 35 38485 120 0292c-4050 40 50265 50 0800c-4060 40 50265 60 0667c-4080 40 50265 80 0500c-40100 40 50265 100 0400c-40120 40 50265 120 0333c-40140 40 50265 140 0286

Elliptical cupsRotor 119886 [mm] 119887 [mm] 119878

119888[mm2] 119877

119903119888[mm]

a-2760 27 2315 19635 60a-3060 30 2083 19635 60a-3560 35 1786 19635 60

Porous cupsRotor 119877

119888[mm] 119878

119888[mm2] 119877

119903119888[mm] ℎ [mm]

h-960 25 19635 60 9h-1960 25 19635 60 19h-2460 25 19635 60 24

performed the anemometerrsquos output was sampled during 20seconds at 10000Hz

The Climatronics 100075 anemometer gives 30 squaredpulses per turn A plot of the output signal record in oneturn of this anemometer equipped with the h-2460 rotor isincluded in Figure 3 togetherwith the non-dimensional rota-tion speed 120596120596

0 once the output was post-processed The

non-dimensional rotation speed on one turn was calculatedaveraging groups of 30 pulses contained in the recorded datafor every point (ie every wind flow velocity) during thecalibration of all configurations analyzed

3 Results and Discussion

The calibration constants of the anemometer transfer func-tion 119860 and 119861 with regard to all cases tested are includedin Table 3 In Figure 4 the anemometer factor 119870 regardingthe calibrations performed in the present study to con-ical cups rotors is shown as a function of the param-eter 119903

119903(which represents the ratio between the cupsrsquo

radius 119877119888 and the cupsrsquo center rotation radius 119877

119903119888 119903119903

=

119877

119888119877

119903119888) This anemometer factor is defined as the ratio

between the wind speed 119881 and the rotation speed of

The Scientific World Journal 5

Vou

tput

tT

60

45

30

15

00

0 02 04 06 08 1

tT

0 02 04 06 08 1120596120596

0

110

105

100

095

090

(a)

(b)

(c)

Figure 3 Climatronics 100075 anemometer placed in the S4 wind tunnel of the IDRUPM Institute to carry out a calibration with the h-1960rotor (a) Anemometer voltage output signal 119881output in one turn (b) Relative-to-the-average rotational speed 120596120596

0 in one turn (c) 119879 is the

period of the anemometerrsquos rotation

rr

V = 4ms52

48

44

40

36

32

02 03 04 05 06 07 08 09

K

(a)

rr

52

48

44

40

36

32

02 03 04 05 06 07 08 09

V = 16ms

K

(b)

K

rr

52

48

44

40

36

32

02 03 04 05 06 07 08 09

K = 44139 minus 16573 middot r2c

K = 4438 minus 27174 middot r2c

Upper fitting

Lower fitting

V rarr infin

(c)

Figure 4 Anemometer factor 119870 regarding the conical cups rotors calculated for 119881 = 4ms (a) 119881 = 16ms (b) and 119881 rarr infin (c) as afunction of the parameter 119903

119903(119903119903= 119877

119888119877

119903119888) The symbols correspond to rotors equipped with the following cup radii 119877

119888= 20mm (rhombi)

119877

119888= 25mm (circles) 119877

119888= 30mm (squares) 119877

119888= 35mm (triangles) and 119877

119888= 40mm (crosses) The quadratic fittings to 119877

119888= 20mm rotors

(lower fitting) and to 119877

119888= 40mm rotors (upper fitting) have been also added (dotted lines) to the bottom graph

the cup center averaged in one complete rotation 120596

0119877

119903119888

[48]

119870 =

119881

120596

0119877

119903119888

=

119860

119903119891

119903+ 119861

2120587119891

119903119877

119903119888

=

119860

119903

2120587119877

119903119888

1

1 minus (119861119881)

(4)

where 119860

119903and 119861 are respectively the slope and the offset of

the transfer function see expression (2) The anemometerfactor 119870 was calculated for both limits of the wind speedcalibration range 4ms and 16ms and for very high windspeeds (119881 rarr infin) which in fact is the result of considering

6 The Scientific World Journal

Table 3 Calibration coefficients 119860 and 119861 measured for the rotors tested with Climatronics 100075 anemometer (see also Table 2 andFigure 2) The coefficient of determination 1198772 of the curve fittings and the slope of the transfer function based on the rotation frequency119860

119903(see expressions (1) and (2)) have also been included

Conical cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

c-2030 002021 060618 037096 099995c-2040 003177 095318 023328 099999c-2050 004186 125574 031148 099999c-2060 005180 155401 040091 099999c-2540 002963 088886 026760 099999c-2550 003932 117970 020786 099999c-2560 004961 148829 024245 099999c-2580 006964 208928 039438 099999c-25100 008952 268552 053685 099999c-3040 002861 085818 009551 099995c-3050 003861 115844 019606 099999c-3060 004850 145505 014823 099998c-3080 006836 205089 025403 100000c-30100 008697 260900 038253 099998c-30120 010738 322145 049053 099999c-3550 003720 111603 019081 099999c-3560 004719 141582 015354 099999c-3580 006827 204818 018132 099998c-35100 008737 262111 022168 099999c-35120 010742 322259 034171 099999c-4050 003539 106166 013714 099999c-4060 004586 137587 016652 099999c-4080 006663 199876 016932 099998c-40100 008668 260026 023292 099996c-40120 010638 319140 028805 099996c-40140 012639 379164 034162 099995

Elliptical cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

a-2760 005221 156617 019932 099999a-3060 005306 159167 023224 099998a-3560 005412 162361 021593 099998

Porous cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

h-0960 005445 163352 031414 099999h-1960 006579 197376 054539 099998h-2460 011763 352881 031563 099998

the offset constant of the transfer function 119861 negligible Itshould be said that the effect of this offset constant on similarcalculations has been considered negligible in past works[44 48] as it is only appreciated at lowwind speedsHoweverit was preserved in the present calculations in order to havea more accurate comparison between the different cases andnew conclusions have arisen

In Figure 4 three different cases can be observed Forlow wind speeds (119881 = 4ms) the cup anemometer is lessefficient in terms of transforming the wind velocity into

rotational speed than for higher wind speeds (ie highervalues of the anemometer factor 119870 are shown) Also thecurves corresponding to the different cup sizes seem to followthe samepath for ratios between the cupsrsquo radius and the cupsrsquocenter rotation radius lower than 119903

119903lt 065 The mentioned

lower performances of the anemometer can be explainedas an effect of the friction forces which are increasinglysignificant when compared to the aerodynamic forces forlow wind speeds (that obviously are translated into lowrotational speeds)

The Scientific World Journal 7

The situation changes for higher wind speeds as it canbe observed for 119881 = 16ms and even more clearly for thelimit case 119881 rarr infin (ie when the offset constant 119861 is leftaside) In this case the anemometer constant 119870 shows asecond-order polynomial dependence on the parameter 119903

119903

Also the effect of relative cup size is shown in the mentionedgraph The curves fitting to the results corresponding to therotors with the smallest and the largest cups (119877

119888= 20mm

and 119877

119888= 40mm resp) have been included in the graphThe

results corresponding to all the intermediate cup size rotors(119877119888= 25mm 119877

119888= 30mm and 119877

119888= 35mm) lie between

both curves revealing the aforementioned dependence onthe cupsrsquo size In tune with this effect it should also be saidthat other experimental results have already demonstratedthe direct relationship between the slope of the anemometertransfer function 119860 and the front area of the cups [44]

119860 =

1

119873

119901

119860

119903=

1

119873

119901

(

d119860119903

d119877119903119888

119877

119903119888+ 119860

1199030) (5)

where d119860119903d119877119903119888depends on the aerodynamic forces on the

cups (for rotors equipped with the same conical cups testedin the present work it was found that this coefficient hasconstant value with very little or no correlation to the cupsrsquosize) and 119860

1199030strongly depends on the cupsrsquo front area 119878

119888

Finally it should also be said that as far as the authorsknow this particular effect of the cupsrsquo size has not beenincluded in the different analyticalmodels developed to studycup anemometer behavior [30 31 33 38 40] These modelsare based on wind speed cup aerodynamic coefficientsand cup and rotor geometries and take as starting pointthat the behavior of cup anemometers is mainly driven byaerodynamic forces the frictional torque being much lowerin comparison [37 49] However these models are limiteddue to the complexity of rotating flows [48]

In order go to deeper into this problem the aerodynamicforces on each cup should be analyzed As the aerodynamictorque on the anemometerrsquos rotor is produced by the aerody-namic forces on the mentioned cups and the cups positionson the rotor have 120∘ phase separation it is logical to assumethat at constant wind speed equal rotational accelerations anddecelerationswill affect the anemometer rotor three times perrevolution (obviously these accelerations are responsible forthe third harmonic term of the anemometer wind speed 120596

3

see expression (3)) Therefore studying the third harmonicterm of the rotational speed is a way to analyze the effect ofthe cups on the rotor movement

In Figure 5 the non-dimensional third harmonic term120596

3120596

0 calculated for every wind speed of the calibrations

regarding the studied porous cups rotors (h-0960 h-1960and h-2460) is shown together with the results correspond-ing to the c-2560 rotor (included as it can be considered aspart of the porous cup series ie porosity equal to zero) Inthementionedfigure the differences among the performanceswith regard to the different rotors can be clearly observedThis figure has been chosen to illustrate two parameters usedin the present work to analyze the third harmonic term ofthe anemometer rotational speed (i) the non-dimensional

1205963 + 1205903

1205963

1205963 minus 1205903

V (ms)

900

800

700

600

500

400

300

200

100

0004 6 8 10 12 14 16

1205963120596

0(

)

Figure 5 Non-dimensional harmonic term 1205963120596

0 calculated at

every point of the calibrations performed on the Climatronics100075 anemometer equippedwith c-2560 (circles) h-0960 (trian-gles) h-1960 (squares) and h-2460 (rhombi) rotors The averagevalue line 120596

3 together with the standard deviation limits plusmn120590

3

corresponding to the h-1960 rotor values has been also included inthe graph

average value calculated with data from the 13 points of thecalibration procedure

120596

3=

1

13

13

sum

119894=1

120596

3

120596

0

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119894

(6)

and (ii) the corresponding standard deviation 1205903 calculated

using the general procedure

120590

3=

radic

sum

13

119894=1( (120596

3120596

0)

1003816

1003816

1003816

1003816119894minus 120596

3)

2

13 minus 1

(7)

In Figure 6 the averaged third non-dimensional har-monic term 120596

3 regarding the conical cups rotors and

the ratio of the standard deviation to the mentioned non-dimensional third harmonic term 120590

3120596

3 are shown as a

function of the ratio of the cup radius to the cupsrsquo centerrotation radius 119903

119903 The third harmonic term 120596

3 tends to be

smaller with higher values of 119903119903 that is for rotors whose cups

centers are closer to the rotation axisThe same tendency wasobserved on the anemometer factor 119870 (see Figure 4) so itcan be concluded that higher third harmonic terms have animmediate effect on the anemometer average performancereducing the average rotational speed 120596

0 This effect can be

explained in terms of energy as a bigger part of the energytransferred from the wind to the rotor movement is investedinto the mentioned third harmonic term and not into theconstant term of the rotational speed 120596

0 Also the effect

of the cupsrsquo size has the same pattern as the one for the

8 The Scientific World Journal

rr

180160140120100080060040

000 020 040 060 080 100

1205963(

)

(a)

rr

000 020 040 060 080 100

2000

1600

1200

800

400

000

1205903120596

3(

)

(b)

Figure 6 Averaged third harmonic term 1205963 regarding the conical cups rotors (a) and the corresponding standard deviation 120590

3120596

3(b)

both expressed as a function of the parameter 119903

119903(119903119903= 119877

119888119877

119903119888) The symbols correspond to rotors equipped with the following cup radii

119877

119888= 20mm (rhombi) 119877

119888= 25mm (circles) 119877

119888= 30mm (squares) 119877

119888= 35mm (triangles) and 119877

119888= 40mm (crosses)

anemometer constant graphs in Figure 4 Smaller cups withthe same parameter 119903

119903show smaller third harmonic terms

with higher rotational efficienciesFinally focusing on the standard deviationmeasuredwith

respect to the average third harmonic term 1205903120596

3 shown

in Figure 6 it seems that there is a minimum for every cupsize at a certain value of the parameter 119903

119903 located around

119903

119903= 05 In Figure 7 the third harmonic term measured for

every wind velocity during the calibration of four rotorsequipped with 119877

119888= 40mm cups is shown The data

correspond to the smallest and the largest cup rotation radiustested (119877

119903119888= 50mm and 119877

119903119888= 140mm resp) and two

intermediate cases (119877119903119888

= 80mm and 119877

119903119888= 100mm) It

can be observed that according to the information from thementioned graph in Figure 6 the dispersion of the results islower for the intermediate cases A linear tendency is alsoobserved with higher slopes for greater values of cup centerrotation radius Finally it should also be said that class-1commercial anemometers [47 50] have ratios between thecup radius and the cupsrsquo center rotation radius ranging from119903

119903= 04 to 119903

119903= 06 (Thies Clima 4335043351 119903

119903= 05

Vector Instruments A100L2 119903119903= 049 Vaisala WAA 151252

119903

119903= 042 WindSensor (Risoslash) P2546A 119903

119903= 059)

Concerning the effect of the cupsrsquo shape its effect onanemometer performance has been already analyzed Theaerodynamic forces on a single cup have been correlatedwith the aforementioned anemometer performance in twodifferent ways by means of analytical models correlated withexperimental testing [30 31 33 38] and by means of adirect comparison based on experimental calibration [48] InFigure 8 the anemometer constant at 16ms wind speed withregard to the calibrations performed on the anemometerequipped with elliptical and porous cups rotors has beenincluded respectively as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 and the ratio of the hole diameter to the cupdiameter ℎ2119877

119888 The non-dimensional third harmonic 120596

3

regarding these rotors has been also included in the figureAs it was previously measured [48] the effect of both theeccentricity and the porosity of the cups is translated into adecrease of the rotational efficiency of the cups (higher values

1205963120596

0

1205963

V (ms)

13

12

11

10

09

08

07

06

0 2 4 6 8 10 12 14 16 18

Rrc = 50mm (RcRrc = 08)

Rrc = 100mm (RcRrc = 04)

Rrc = 140mm (RcRrc = 0287)

Rrc = 80mm (RcRrc = 05)

Figure 7 Variation of the third harmonic term measured withrotors equipped with 119877

119888= 40mm conical cups as a function of the

wind speed within the calibration process

of 119870 that is lower rotational speed at a fixed wind speed)On the other hand the effect of both parameters on the thirdharmonic term has a reversed effect that is higher valuesof eccentricity and porosity increase the importance of thisharmonic term

4 Conclusions

In the present work the performance of a cup anemometerequipped with different rotors has been experimentally ana-lyzed On one hand the size of conical cups together withtheir distance to the anemometer rotation axis was studiedOn the other hand the shape of the rotor cups was alsostudied The analysis was based on two different parameters

The Scientific World Journal 9

K

e h2Rc

1000

950

900

850

800

750

700

650

600

550

500

450

400

000 020 040 060 080 100

(a)

1000

900

800

700

600

500

400

300

200

100

e h2Rc

000 020 040 060 080 100

1205963(

)(b)

Figure 8 Anemometer constant at 16ms wind speed119870 and non-dimensional third harmonic1205963 with regard to the calibrations performed

to the anemometer equipped with elliptical (squares) and porous (circles) cup rotors as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 andthe ratio of the hole diameter to the front cup area ℎ2119877

119888 respectively

the anemometer factor that takes into account the averagerotation of the anemometer and the third harmonic termresulting from the Fourier decomposition of the anemometerrotation speed The most relevant conclusions resulting fromthis work are as follows

(i) The average rotation speed is well correlated with thementioned third harmonic term resulting from theFourier decomposition of the anemometer rotationspeed Higher values of this third harmonic termresult in higher anemometer factors and thereforein lower rotational speeds This fact confirms thementioned third harmonic term as a useful parameterto study cup anemometer performance

(ii) Smaller cups with the same ratio of cup diameter tothe cupsrsquo center rotation radius 119903

119903 tend to produce

higher rotational speeds (lower anemometer factors)and lower third harmonic terms

(iii) The ratio of the third harmonic term to the averagerotational speed 120596

3120596

0 is more uniform (within the

wind speed calibration range) for values of the ratioof the cup diameter to the cupsrsquo center rotation radiusranging from 119903

119903= 04 to 119903

119903= 05 than for values of 119903

119903

beyond or below this bracket

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are truly indebted to Enrique Vega AlejandroMartınez Encarnacion Meseguer Luis Garcıa and EduardoCortes for the help and friendly support during the testingcampaign The authors are grateful to Anna Marıa Ballesterfor her kind help on improving the style of the text

References

[1] F Aminzadeh and S Pindado ldquoHow has Spain become a leaderin thewind energy industry during the last decade (An analysisof influential factors on the development of wind energy inSpain)rdquo in Proceedings of the EWEA Annual Event BrusselsBelgium 2011

[2] L Kristensen ldquoCan a cup anemometer ldquounderspeedrdquo A hereti-cal questionrdquo Boundary-Layer Meteorology vol 103 no 1 pp163ndash172 2002

[3] R V Coquilla J Obermeier and B R White ldquoCalibrationprocedures and uncertainty in wind power anemometersrdquoWind Engineering vol 31 no 5 pp 303ndash316 2007

[4] A Albers and H Klug ldquoOpen field cup anemometryrdquo DEWIMagazine vol 19 pp 53ndash58 2001

[5] A Albers H Klug and D Westermann ldquoOutdoor comparisonof cup anemometersrdquo DEWI Magazin vol 17 pp 5ndash15 2000

[6] S Lang and E McKeogh ldquoLIDAR and SODAR measurementsof wind speed and direction in upland terrain for wind energypurposesrdquo Remote Sensing vol 3 no 9 pp 1871ndash1901 2011

[7] R Wagner M Courtney J Gottschall and P Lindelow-Marsden ldquoAccounting for the speed shear in wind turbine

10 The Scientific World Journal

power performance measurementrdquoWind Energy vol 14 no 8pp 993ndash1004 2011

[8] T R Robinson ldquoOn a New Anemometerrdquo Proceedings of theRoyal Irish Academy (1836ndash1869 ) vol 4 pp 566ndash572 1847

[9] International Electrotechnical Commision International Stan-dard IEC-61400-12-1 Wind Turbines Part 12-1 Power Perfor-mance Measurements of Electricity Producing Wind TurbinesFirst Edition 2005ndash12 International Electrotechnical Commi-sion Geneva Switzerland 2005

[10] R V Coquilla and J Obermeier ldquoCalibration speed range forrotating anemometers used in wind energy applicationsrdquo inProceedings of the 46th AIAA Aerospace Sciences Meeting andExhibit pp 2ndash7 January 2008

[11] R V Coquilla A Havner J Obermeier and M SturgeonldquoVerification testing of Sonic anemometer wind speedmeasure-ments for wind energy applicationsrdquo in Proceedings of the 2010American Wind Energy Association Annual Conference (AWEAWINDPOWER rsquo10) pp 1ndash14 2010

[12] L J Fritschen ldquoA sensitive cup-type anemometerrdquo Journal ofApplied Meteorology vol 6 pp 695ndash698 1967

[13] M Sanuki and S Kimura ldquoSome aerodynamic aspects deducedfrom the start and stop experiment of three- and four-cupanemometerrdquo Papers in Meteorology and Geophysics vol 5 pp695ndash698 1954

[14] C F Marvin ldquoA rational theory of the cup anemometerrdquoMonthly Weather Review vol 60 pp 43ndash56 1932

[15] M J Brevoort and U T Joyner ldquoExperimental investigation ofthe Robinson-type cup anemometerrdquo NACA TN-513 1935

[16] C F Marvin ldquoRecent advances in anemometryrdquo MonthlyWeather Review vol 62 pp 115ndash120 1934

[17] C F Marvin ldquoAnemometer testsrdquoMonthlyWeather Review pp58ndash63 1900

[18] H Charnock and F E Pierce ldquoNew housing for the sensitivecup-contact anemometer Mk 1rdquo Journal of Scientific Instru-ments vol 36 no 7 p 329 1959

[19] P A Sheppard ldquoAn improved design of cup anemometerrdquoJournal of Scientific Instruments vol 17 no 9 pp 218ndash221 1940

[20] E L Deacon ldquoReply to two types of sensitive recording cupanemometersrdquo Journal of Scientific Instruments vol 25 no 8p 283 1948

[21] S G Crawford ldquoA simple form of sensitive electric contact cupanemometerrdquo Journal of Scientific Instruments vol 28 no 2 pp36ndash37 1951

[22] F Scrase and P Sheppard ldquoThe errors of cup anemometers influctuating windsrdquo Journal of Scientific Instruments vol 21 no9 pp 160ndash161 1944

[23] E L Deacon ldquoThe over-estimation error of cup anemometersin fluctuating windsrdquo Journal of Scientific Instruments vol 28no 8 pp 231ndash234 1951

[24] L KristensenThe Cup Anemometer and Other Exciting Instru-ments Risoslash-R-615 (EN) Risoslash National Laboratory RoskildeDenmark 1993

[25] MEASNET Cup Anemometer Calibration Procedure Version1 (September 1997 Updated 24112008) MEASNET MadridSpain 1997

[26] MEASNET Anemometer Calibration Procedure Version 2(October 2009) MEASNET Madrid Spain 2009

[27] ASTM International Standard Test Method for Determining thePerformance of a Cup Anemometer or Propeller Anemometer(ASTMD 5096-02) ASTM InternationalWest ConshohockenPa USA 2002

[28] M C-E Brazier ldquoSur la variation des indications desanemometres Robinson et Richard en fonction de lrsquoinclinaisondu ventrdquoComptes Rendus des Seances de LrsquoAcademie des Sciencesvol 170 pp 610ndash612 1920

[29] S Pindado E Vega A Martınez E Meseguer S Franchiniand I P Sarasola ldquoAnalysis of calibration results from cupand propeller anemometers Influence on wind turbine AnnualEnergy Production (AEP) calculationsrdquo Wind Energy vol 14no 1 pp 119ndash132 2011

[30] J Kondo G I Naito and Y Fujinawa ldquoResponse of cupanemometer in turbulencerdquo Journal of theMeteorological Societyof Japan vol 49 pp 63ndash74 1971

[31] S Ramachandran ldquoA theoretical study of cup and vaneanemometersrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 95 no 403 pp 163ndash180 1969

[32] M C-E Brazier ldquoSur la comparabilite des anemometresrdquoComptes Rendus des Seances de LrsquoAcademie des Sciences vol 172pp 843ndash845 1921

[33] O Schrenk ldquoUber die tragheitsfehler des Schalenkreuz-anemometers bei schwankender Windstarkerdquo Zeitschrift FurTechnische Physik vol 10 pp 57ndash66 1929

[34] H W Baynton ldquoErrors in wind run estimates from rotationalanemometersrdquo Bulletin of the American Meteorological Societyvol 57 no 9 pp 1127ndash1130 1976

[35] N E Busch and L Kristensen ldquoCup anemometer overspeed-ingrdquo Journal of AppliedMeteorology vol 15 pp 1328ndash1332 1976

[36] P Frenzen ldquoFast response cup anemometers for atmosphericturbulence researchrdquo in Proceedings of the 8th Symposium onTurbulence and Diffusion pp 112ndash115 1988

[37] E I Kaganov and A M Yaglom ldquoErrors in wind-speed mea-surements by rotation anemometersrdquo Boundary-Layer Meteo-rology vol 10 no 1 pp 15ndash34 1976

[38] J C Wyngaard ldquoCup propeller vane and sonic anemometersin turbulence researchrdquo Annual Review of Fluid Mechanics vol13 pp 399ndash423 1981

[39] P A Coppin ldquoAn examination of cup anemometer overspeed-ingrdquoMeteorologische Rundschau vol 35 pp 1ndash11 1982

[40] J CWyngaard J T Bauman and R A Lynch ldquoCup anemome-ter dynamicsrdquo in Flow Its Measurement and Control in Scienceand Industry vol 1 pp 701ndash708 1974

[41] L Kristensen ldquoCup anemometer behavior in turbulent environ-mentsrdquo Journal of Atmospheric and Oceanic Technology vol 15no 1 pp 5ndash17 1998

[42] R S Hunter ldquoThe accuracy of cup anemometer calibrationwithparticular regard to testing wind turbinesrdquo Wind Engineeringvol 14 no 1 pp 32ndash43 1990

[43] J-A Dahlberg J Gustavsson G Ronsten T F Pedersen US Paulsen and D Westermann Development of A Standard-ised Cup Anemometer Suited to Wind Energy Applications-(ClAsscup) vol 9 Technical University of Denmark LyngbyDenmark 2001

[44] S Pindado J Perez and S Avila-Sanchez ldquoOn cup anemometerrotor aerodynamicsrdquo Sensors vol 12 no 5 pp 6198ndash6217 2012

[45] S Pindado A Sanz and A Wery ldquoDeviation of cup andpropeller anemometer calibration results with air densityrdquoEnergies vol 5 no 3 pp 683ndash701 2012

[46] S Pindado A Barrero-Gil and A Sanz ldquoCup anemome-tersrsquoLoss of performance due to ageing processes and its effecton Annual Energy Production (AEP) estimatesrdquo Energies vol5 no 12 pp 1664ndash1685 2012

The Scientific World Journal 11

[47] J-A Dahlberg T F Pedersen and P Busche ACCUWIND-Methods for Classification of Cup Anemometers Risoslash-R-1555(EN) Risoslash National Laboratory Roskilde Denmark 2006

[48] S Pindado I Perez and M Aguado ldquoFourier analysis ofthe aerodynamic behavior of cup anemometersrdquo MeasurementScience and Technology vol 24 no 6 Article ID 065802 2013

[49] Y P Solovrsquoev A I Korovushkin and Y N Toloknov ldquoCharac-teristics of a cup anemometer and a procedure of measuring thewind velocityrdquo Physical Oceanography vol 14 no 3 pp 173ndash1862004

[50] T F Pedersen Development of A Classification System forCup Anemometers-CLASSCUP Risoslash-R-1348(EN) Risoslash NationalLaboratory Roskilde Denmark 2003

International Journal of

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Journal of

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RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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DistributedSensor Networks

International Journal of

The Scientific World Journal 5

Vou

tput

tT

60

45

30

15

00

0 02 04 06 08 1

tT

0 02 04 06 08 1120596120596

0

110

105

100

095

090

(a)

(b)

(c)

Figure 3 Climatronics 100075 anemometer placed in the S4 wind tunnel of the IDRUPM Institute to carry out a calibration with the h-1960rotor (a) Anemometer voltage output signal 119881output in one turn (b) Relative-to-the-average rotational speed 120596120596

0 in one turn (c) 119879 is the

period of the anemometerrsquos rotation

rr

V = 4ms52

48

44

40

36

32

02 03 04 05 06 07 08 09

K

(a)

rr

52

48

44

40

36

32

02 03 04 05 06 07 08 09

V = 16ms

K

(b)

K

rr

52

48

44

40

36

32

02 03 04 05 06 07 08 09

K = 44139 minus 16573 middot r2c

K = 4438 minus 27174 middot r2c

Upper fitting

Lower fitting

V rarr infin

(c)

Figure 4 Anemometer factor 119870 regarding the conical cups rotors calculated for 119881 = 4ms (a) 119881 = 16ms (b) and 119881 rarr infin (c) as afunction of the parameter 119903

119903(119903119903= 119877

119888119877

119903119888) The symbols correspond to rotors equipped with the following cup radii 119877

119888= 20mm (rhombi)

119877

119888= 25mm (circles) 119877

119888= 30mm (squares) 119877

119888= 35mm (triangles) and 119877

119888= 40mm (crosses) The quadratic fittings to 119877

119888= 20mm rotors

(lower fitting) and to 119877

119888= 40mm rotors (upper fitting) have been also added (dotted lines) to the bottom graph

the cup center averaged in one complete rotation 120596

0119877

119903119888

[48]

119870 =

119881

120596

0119877

119903119888

=

119860

119903119891

119903+ 119861

2120587119891

119903119877

119903119888

=

119860

119903

2120587119877

119903119888

1

1 minus (119861119881)

(4)

where 119860

119903and 119861 are respectively the slope and the offset of

the transfer function see expression (2) The anemometerfactor 119870 was calculated for both limits of the wind speedcalibration range 4ms and 16ms and for very high windspeeds (119881 rarr infin) which in fact is the result of considering

6 The Scientific World Journal

Table 3 Calibration coefficients 119860 and 119861 measured for the rotors tested with Climatronics 100075 anemometer (see also Table 2 andFigure 2) The coefficient of determination 1198772 of the curve fittings and the slope of the transfer function based on the rotation frequency119860

119903(see expressions (1) and (2)) have also been included

Conical cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

c-2030 002021 060618 037096 099995c-2040 003177 095318 023328 099999c-2050 004186 125574 031148 099999c-2060 005180 155401 040091 099999c-2540 002963 088886 026760 099999c-2550 003932 117970 020786 099999c-2560 004961 148829 024245 099999c-2580 006964 208928 039438 099999c-25100 008952 268552 053685 099999c-3040 002861 085818 009551 099995c-3050 003861 115844 019606 099999c-3060 004850 145505 014823 099998c-3080 006836 205089 025403 100000c-30100 008697 260900 038253 099998c-30120 010738 322145 049053 099999c-3550 003720 111603 019081 099999c-3560 004719 141582 015354 099999c-3580 006827 204818 018132 099998c-35100 008737 262111 022168 099999c-35120 010742 322259 034171 099999c-4050 003539 106166 013714 099999c-4060 004586 137587 016652 099999c-4080 006663 199876 016932 099998c-40100 008668 260026 023292 099996c-40120 010638 319140 028805 099996c-40140 012639 379164 034162 099995

Elliptical cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

a-2760 005221 156617 019932 099999a-3060 005306 159167 023224 099998a-3560 005412 162361 021593 099998

Porous cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

h-0960 005445 163352 031414 099999h-1960 006579 197376 054539 099998h-2460 011763 352881 031563 099998

the offset constant of the transfer function 119861 negligible Itshould be said that the effect of this offset constant on similarcalculations has been considered negligible in past works[44 48] as it is only appreciated at lowwind speedsHoweverit was preserved in the present calculations in order to havea more accurate comparison between the different cases andnew conclusions have arisen

In Figure 4 three different cases can be observed Forlow wind speeds (119881 = 4ms) the cup anemometer is lessefficient in terms of transforming the wind velocity into

rotational speed than for higher wind speeds (ie highervalues of the anemometer factor 119870 are shown) Also thecurves corresponding to the different cup sizes seem to followthe samepath for ratios between the cupsrsquo radius and the cupsrsquocenter rotation radius lower than 119903

119903lt 065 The mentioned

lower performances of the anemometer can be explainedas an effect of the friction forces which are increasinglysignificant when compared to the aerodynamic forces forlow wind speeds (that obviously are translated into lowrotational speeds)

The Scientific World Journal 7

The situation changes for higher wind speeds as it canbe observed for 119881 = 16ms and even more clearly for thelimit case 119881 rarr infin (ie when the offset constant 119861 is leftaside) In this case the anemometer constant 119870 shows asecond-order polynomial dependence on the parameter 119903

119903

Also the effect of relative cup size is shown in the mentionedgraph The curves fitting to the results corresponding to therotors with the smallest and the largest cups (119877

119888= 20mm

and 119877

119888= 40mm resp) have been included in the graphThe

results corresponding to all the intermediate cup size rotors(119877119888= 25mm 119877

119888= 30mm and 119877

119888= 35mm) lie between

both curves revealing the aforementioned dependence onthe cupsrsquo size In tune with this effect it should also be saidthat other experimental results have already demonstratedthe direct relationship between the slope of the anemometertransfer function 119860 and the front area of the cups [44]

119860 =

1

119873

119901

119860

119903=

1

119873

119901

(

d119860119903

d119877119903119888

119877

119903119888+ 119860

1199030) (5)

where d119860119903d119877119903119888depends on the aerodynamic forces on the

cups (for rotors equipped with the same conical cups testedin the present work it was found that this coefficient hasconstant value with very little or no correlation to the cupsrsquosize) and 119860

1199030strongly depends on the cupsrsquo front area 119878

119888

Finally it should also be said that as far as the authorsknow this particular effect of the cupsrsquo size has not beenincluded in the different analyticalmodels developed to studycup anemometer behavior [30 31 33 38 40] These modelsare based on wind speed cup aerodynamic coefficientsand cup and rotor geometries and take as starting pointthat the behavior of cup anemometers is mainly driven byaerodynamic forces the frictional torque being much lowerin comparison [37 49] However these models are limiteddue to the complexity of rotating flows [48]

In order go to deeper into this problem the aerodynamicforces on each cup should be analyzed As the aerodynamictorque on the anemometerrsquos rotor is produced by the aerody-namic forces on the mentioned cups and the cups positionson the rotor have 120∘ phase separation it is logical to assumethat at constant wind speed equal rotational accelerations anddecelerationswill affect the anemometer rotor three times perrevolution (obviously these accelerations are responsible forthe third harmonic term of the anemometer wind speed 120596

3

see expression (3)) Therefore studying the third harmonicterm of the rotational speed is a way to analyze the effect ofthe cups on the rotor movement

In Figure 5 the non-dimensional third harmonic term120596

3120596

0 calculated for every wind speed of the calibrations

regarding the studied porous cups rotors (h-0960 h-1960and h-2460) is shown together with the results correspond-ing to the c-2560 rotor (included as it can be considered aspart of the porous cup series ie porosity equal to zero) Inthementionedfigure the differences among the performanceswith regard to the different rotors can be clearly observedThis figure has been chosen to illustrate two parameters usedin the present work to analyze the third harmonic term ofthe anemometer rotational speed (i) the non-dimensional

1205963 + 1205903

1205963

1205963 minus 1205903

V (ms)

900

800

700

600

500

400

300

200

100

0004 6 8 10 12 14 16

1205963120596

0(

)

Figure 5 Non-dimensional harmonic term 1205963120596

0 calculated at

every point of the calibrations performed on the Climatronics100075 anemometer equippedwith c-2560 (circles) h-0960 (trian-gles) h-1960 (squares) and h-2460 (rhombi) rotors The averagevalue line 120596

3 together with the standard deviation limits plusmn120590

3

corresponding to the h-1960 rotor values has been also included inthe graph

average value calculated with data from the 13 points of thecalibration procedure

120596

3=

1

13

13

sum

119894=1

120596

3

120596

0

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119894

(6)

and (ii) the corresponding standard deviation 1205903 calculated

using the general procedure

120590

3=

radic

sum

13

119894=1( (120596

3120596

0)

1003816

1003816

1003816

1003816119894minus 120596

3)

2

13 minus 1

(7)

In Figure 6 the averaged third non-dimensional har-monic term 120596

3 regarding the conical cups rotors and

the ratio of the standard deviation to the mentioned non-dimensional third harmonic term 120590

3120596

3 are shown as a

function of the ratio of the cup radius to the cupsrsquo centerrotation radius 119903

119903 The third harmonic term 120596

3 tends to be

smaller with higher values of 119903119903 that is for rotors whose cups

centers are closer to the rotation axisThe same tendency wasobserved on the anemometer factor 119870 (see Figure 4) so itcan be concluded that higher third harmonic terms have animmediate effect on the anemometer average performancereducing the average rotational speed 120596

0 This effect can be

explained in terms of energy as a bigger part of the energytransferred from the wind to the rotor movement is investedinto the mentioned third harmonic term and not into theconstant term of the rotational speed 120596

0 Also the effect

of the cupsrsquo size has the same pattern as the one for the

8 The Scientific World Journal

rr

180160140120100080060040

000 020 040 060 080 100

1205963(

)

(a)

rr

000 020 040 060 080 100

2000

1600

1200

800

400

000

1205903120596

3(

)

(b)

Figure 6 Averaged third harmonic term 1205963 regarding the conical cups rotors (a) and the corresponding standard deviation 120590

3120596

3(b)

both expressed as a function of the parameter 119903

119903(119903119903= 119877

119888119877

119903119888) The symbols correspond to rotors equipped with the following cup radii

119877

119888= 20mm (rhombi) 119877

119888= 25mm (circles) 119877

119888= 30mm (squares) 119877

119888= 35mm (triangles) and 119877

119888= 40mm (crosses)

anemometer constant graphs in Figure 4 Smaller cups withthe same parameter 119903

119903show smaller third harmonic terms

with higher rotational efficienciesFinally focusing on the standard deviationmeasuredwith

respect to the average third harmonic term 1205903120596

3 shown

in Figure 6 it seems that there is a minimum for every cupsize at a certain value of the parameter 119903

119903 located around

119903

119903= 05 In Figure 7 the third harmonic term measured for

every wind velocity during the calibration of four rotorsequipped with 119877

119888= 40mm cups is shown The data

correspond to the smallest and the largest cup rotation radiustested (119877

119903119888= 50mm and 119877

119903119888= 140mm resp) and two

intermediate cases (119877119903119888

= 80mm and 119877

119903119888= 100mm) It

can be observed that according to the information from thementioned graph in Figure 6 the dispersion of the results islower for the intermediate cases A linear tendency is alsoobserved with higher slopes for greater values of cup centerrotation radius Finally it should also be said that class-1commercial anemometers [47 50] have ratios between thecup radius and the cupsrsquo center rotation radius ranging from119903

119903= 04 to 119903

119903= 06 (Thies Clima 4335043351 119903

119903= 05

Vector Instruments A100L2 119903119903= 049 Vaisala WAA 151252

119903

119903= 042 WindSensor (Risoslash) P2546A 119903

119903= 059)

Concerning the effect of the cupsrsquo shape its effect onanemometer performance has been already analyzed Theaerodynamic forces on a single cup have been correlatedwith the aforementioned anemometer performance in twodifferent ways by means of analytical models correlated withexperimental testing [30 31 33 38] and by means of adirect comparison based on experimental calibration [48] InFigure 8 the anemometer constant at 16ms wind speed withregard to the calibrations performed on the anemometerequipped with elliptical and porous cups rotors has beenincluded respectively as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 and the ratio of the hole diameter to the cupdiameter ℎ2119877

119888 The non-dimensional third harmonic 120596

3

regarding these rotors has been also included in the figureAs it was previously measured [48] the effect of both theeccentricity and the porosity of the cups is translated into adecrease of the rotational efficiency of the cups (higher values

1205963120596

0

1205963

V (ms)

13

12

11

10

09

08

07

06

0 2 4 6 8 10 12 14 16 18

Rrc = 50mm (RcRrc = 08)

Rrc = 100mm (RcRrc = 04)

Rrc = 140mm (RcRrc = 0287)

Rrc = 80mm (RcRrc = 05)

Figure 7 Variation of the third harmonic term measured withrotors equipped with 119877

119888= 40mm conical cups as a function of the

wind speed within the calibration process

of 119870 that is lower rotational speed at a fixed wind speed)On the other hand the effect of both parameters on the thirdharmonic term has a reversed effect that is higher valuesof eccentricity and porosity increase the importance of thisharmonic term

4 Conclusions

In the present work the performance of a cup anemometerequipped with different rotors has been experimentally ana-lyzed On one hand the size of conical cups together withtheir distance to the anemometer rotation axis was studiedOn the other hand the shape of the rotor cups was alsostudied The analysis was based on two different parameters

The Scientific World Journal 9

K

e h2Rc

1000

950

900

850

800

750

700

650

600

550

500

450

400

000 020 040 060 080 100

(a)

1000

900

800

700

600

500

400

300

200

100

e h2Rc

000 020 040 060 080 100

1205963(

)(b)

Figure 8 Anemometer constant at 16ms wind speed119870 and non-dimensional third harmonic1205963 with regard to the calibrations performed

to the anemometer equipped with elliptical (squares) and porous (circles) cup rotors as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 andthe ratio of the hole diameter to the front cup area ℎ2119877

119888 respectively

the anemometer factor that takes into account the averagerotation of the anemometer and the third harmonic termresulting from the Fourier decomposition of the anemometerrotation speed The most relevant conclusions resulting fromthis work are as follows

(i) The average rotation speed is well correlated with thementioned third harmonic term resulting from theFourier decomposition of the anemometer rotationspeed Higher values of this third harmonic termresult in higher anemometer factors and thereforein lower rotational speeds This fact confirms thementioned third harmonic term as a useful parameterto study cup anemometer performance

(ii) Smaller cups with the same ratio of cup diameter tothe cupsrsquo center rotation radius 119903

119903 tend to produce

higher rotational speeds (lower anemometer factors)and lower third harmonic terms

(iii) The ratio of the third harmonic term to the averagerotational speed 120596

3120596

0 is more uniform (within the

wind speed calibration range) for values of the ratioof the cup diameter to the cupsrsquo center rotation radiusranging from 119903

119903= 04 to 119903

119903= 05 than for values of 119903

119903

beyond or below this bracket

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are truly indebted to Enrique Vega AlejandroMartınez Encarnacion Meseguer Luis Garcıa and EduardoCortes for the help and friendly support during the testingcampaign The authors are grateful to Anna Marıa Ballesterfor her kind help on improving the style of the text

References

[1] F Aminzadeh and S Pindado ldquoHow has Spain become a leaderin thewind energy industry during the last decade (An analysisof influential factors on the development of wind energy inSpain)rdquo in Proceedings of the EWEA Annual Event BrusselsBelgium 2011

[2] L Kristensen ldquoCan a cup anemometer ldquounderspeedrdquo A hereti-cal questionrdquo Boundary-Layer Meteorology vol 103 no 1 pp163ndash172 2002

[3] R V Coquilla J Obermeier and B R White ldquoCalibrationprocedures and uncertainty in wind power anemometersrdquoWind Engineering vol 31 no 5 pp 303ndash316 2007

[4] A Albers and H Klug ldquoOpen field cup anemometryrdquo DEWIMagazine vol 19 pp 53ndash58 2001

[5] A Albers H Klug and D Westermann ldquoOutdoor comparisonof cup anemometersrdquo DEWI Magazin vol 17 pp 5ndash15 2000

[6] S Lang and E McKeogh ldquoLIDAR and SODAR measurementsof wind speed and direction in upland terrain for wind energypurposesrdquo Remote Sensing vol 3 no 9 pp 1871ndash1901 2011

[7] R Wagner M Courtney J Gottschall and P Lindelow-Marsden ldquoAccounting for the speed shear in wind turbine

10 The Scientific World Journal

power performance measurementrdquoWind Energy vol 14 no 8pp 993ndash1004 2011

[8] T R Robinson ldquoOn a New Anemometerrdquo Proceedings of theRoyal Irish Academy (1836ndash1869 ) vol 4 pp 566ndash572 1847

[9] International Electrotechnical Commision International Stan-dard IEC-61400-12-1 Wind Turbines Part 12-1 Power Perfor-mance Measurements of Electricity Producing Wind TurbinesFirst Edition 2005ndash12 International Electrotechnical Commi-sion Geneva Switzerland 2005

[10] R V Coquilla and J Obermeier ldquoCalibration speed range forrotating anemometers used in wind energy applicationsrdquo inProceedings of the 46th AIAA Aerospace Sciences Meeting andExhibit pp 2ndash7 January 2008

[11] R V Coquilla A Havner J Obermeier and M SturgeonldquoVerification testing of Sonic anemometer wind speedmeasure-ments for wind energy applicationsrdquo in Proceedings of the 2010American Wind Energy Association Annual Conference (AWEAWINDPOWER rsquo10) pp 1ndash14 2010

[12] L J Fritschen ldquoA sensitive cup-type anemometerrdquo Journal ofApplied Meteorology vol 6 pp 695ndash698 1967

[13] M Sanuki and S Kimura ldquoSome aerodynamic aspects deducedfrom the start and stop experiment of three- and four-cupanemometerrdquo Papers in Meteorology and Geophysics vol 5 pp695ndash698 1954

[14] C F Marvin ldquoA rational theory of the cup anemometerrdquoMonthly Weather Review vol 60 pp 43ndash56 1932

[15] M J Brevoort and U T Joyner ldquoExperimental investigation ofthe Robinson-type cup anemometerrdquo NACA TN-513 1935

[16] C F Marvin ldquoRecent advances in anemometryrdquo MonthlyWeather Review vol 62 pp 115ndash120 1934

[17] C F Marvin ldquoAnemometer testsrdquoMonthlyWeather Review pp58ndash63 1900

[18] H Charnock and F E Pierce ldquoNew housing for the sensitivecup-contact anemometer Mk 1rdquo Journal of Scientific Instru-ments vol 36 no 7 p 329 1959

[19] P A Sheppard ldquoAn improved design of cup anemometerrdquoJournal of Scientific Instruments vol 17 no 9 pp 218ndash221 1940

[20] E L Deacon ldquoReply to two types of sensitive recording cupanemometersrdquo Journal of Scientific Instruments vol 25 no 8p 283 1948

[21] S G Crawford ldquoA simple form of sensitive electric contact cupanemometerrdquo Journal of Scientific Instruments vol 28 no 2 pp36ndash37 1951

[22] F Scrase and P Sheppard ldquoThe errors of cup anemometers influctuating windsrdquo Journal of Scientific Instruments vol 21 no9 pp 160ndash161 1944

[23] E L Deacon ldquoThe over-estimation error of cup anemometersin fluctuating windsrdquo Journal of Scientific Instruments vol 28no 8 pp 231ndash234 1951

[24] L KristensenThe Cup Anemometer and Other Exciting Instru-ments Risoslash-R-615 (EN) Risoslash National Laboratory RoskildeDenmark 1993

[25] MEASNET Cup Anemometer Calibration Procedure Version1 (September 1997 Updated 24112008) MEASNET MadridSpain 1997

[26] MEASNET Anemometer Calibration Procedure Version 2(October 2009) MEASNET Madrid Spain 2009

[27] ASTM International Standard Test Method for Determining thePerformance of a Cup Anemometer or Propeller Anemometer(ASTMD 5096-02) ASTM InternationalWest ConshohockenPa USA 2002

[28] M C-E Brazier ldquoSur la variation des indications desanemometres Robinson et Richard en fonction de lrsquoinclinaisondu ventrdquoComptes Rendus des Seances de LrsquoAcademie des Sciencesvol 170 pp 610ndash612 1920

[29] S Pindado E Vega A Martınez E Meseguer S Franchiniand I P Sarasola ldquoAnalysis of calibration results from cupand propeller anemometers Influence on wind turbine AnnualEnergy Production (AEP) calculationsrdquo Wind Energy vol 14no 1 pp 119ndash132 2011

[30] J Kondo G I Naito and Y Fujinawa ldquoResponse of cupanemometer in turbulencerdquo Journal of theMeteorological Societyof Japan vol 49 pp 63ndash74 1971

[31] S Ramachandran ldquoA theoretical study of cup and vaneanemometersrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 95 no 403 pp 163ndash180 1969

[32] M C-E Brazier ldquoSur la comparabilite des anemometresrdquoComptes Rendus des Seances de LrsquoAcademie des Sciences vol 172pp 843ndash845 1921

[33] O Schrenk ldquoUber die tragheitsfehler des Schalenkreuz-anemometers bei schwankender Windstarkerdquo Zeitschrift FurTechnische Physik vol 10 pp 57ndash66 1929

[34] H W Baynton ldquoErrors in wind run estimates from rotationalanemometersrdquo Bulletin of the American Meteorological Societyvol 57 no 9 pp 1127ndash1130 1976

[35] N E Busch and L Kristensen ldquoCup anemometer overspeed-ingrdquo Journal of AppliedMeteorology vol 15 pp 1328ndash1332 1976

[36] P Frenzen ldquoFast response cup anemometers for atmosphericturbulence researchrdquo in Proceedings of the 8th Symposium onTurbulence and Diffusion pp 112ndash115 1988

[37] E I Kaganov and A M Yaglom ldquoErrors in wind-speed mea-surements by rotation anemometersrdquo Boundary-Layer Meteo-rology vol 10 no 1 pp 15ndash34 1976

[38] J C Wyngaard ldquoCup propeller vane and sonic anemometersin turbulence researchrdquo Annual Review of Fluid Mechanics vol13 pp 399ndash423 1981

[39] P A Coppin ldquoAn examination of cup anemometer overspeed-ingrdquoMeteorologische Rundschau vol 35 pp 1ndash11 1982

[40] J CWyngaard J T Bauman and R A Lynch ldquoCup anemome-ter dynamicsrdquo in Flow Its Measurement and Control in Scienceand Industry vol 1 pp 701ndash708 1974

[41] L Kristensen ldquoCup anemometer behavior in turbulent environ-mentsrdquo Journal of Atmospheric and Oceanic Technology vol 15no 1 pp 5ndash17 1998

[42] R S Hunter ldquoThe accuracy of cup anemometer calibrationwithparticular regard to testing wind turbinesrdquo Wind Engineeringvol 14 no 1 pp 32ndash43 1990

[43] J-A Dahlberg J Gustavsson G Ronsten T F Pedersen US Paulsen and D Westermann Development of A Standard-ised Cup Anemometer Suited to Wind Energy Applications-(ClAsscup) vol 9 Technical University of Denmark LyngbyDenmark 2001

[44] S Pindado J Perez and S Avila-Sanchez ldquoOn cup anemometerrotor aerodynamicsrdquo Sensors vol 12 no 5 pp 6198ndash6217 2012

[45] S Pindado A Sanz and A Wery ldquoDeviation of cup andpropeller anemometer calibration results with air densityrdquoEnergies vol 5 no 3 pp 683ndash701 2012

[46] S Pindado A Barrero-Gil and A Sanz ldquoCup anemome-tersrsquoLoss of performance due to ageing processes and its effecton Annual Energy Production (AEP) estimatesrdquo Energies vol5 no 12 pp 1664ndash1685 2012

The Scientific World Journal 11

[47] J-A Dahlberg T F Pedersen and P Busche ACCUWIND-Methods for Classification of Cup Anemometers Risoslash-R-1555(EN) Risoslash National Laboratory Roskilde Denmark 2006

[48] S Pindado I Perez and M Aguado ldquoFourier analysis ofthe aerodynamic behavior of cup anemometersrdquo MeasurementScience and Technology vol 24 no 6 Article ID 065802 2013

[49] Y P Solovrsquoev A I Korovushkin and Y N Toloknov ldquoCharac-teristics of a cup anemometer and a procedure of measuring thewind velocityrdquo Physical Oceanography vol 14 no 3 pp 173ndash1862004

[50] T F Pedersen Development of A Classification System forCup Anemometers-CLASSCUP Risoslash-R-1348(EN) Risoslash NationalLaboratory Roskilde Denmark 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 The Scientific World Journal

Table 3 Calibration coefficients 119860 and 119861 measured for the rotors tested with Climatronics 100075 anemometer (see also Table 2 andFigure 2) The coefficient of determination 1198772 of the curve fittings and the slope of the transfer function based on the rotation frequency119860

119903(see expressions (1) and (2)) have also been included

Conical cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

c-2030 002021 060618 037096 099995c-2040 003177 095318 023328 099999c-2050 004186 125574 031148 099999c-2060 005180 155401 040091 099999c-2540 002963 088886 026760 099999c-2550 003932 117970 020786 099999c-2560 004961 148829 024245 099999c-2580 006964 208928 039438 099999c-25100 008952 268552 053685 099999c-3040 002861 085818 009551 099995c-3050 003861 115844 019606 099999c-3060 004850 145505 014823 099998c-3080 006836 205089 025403 100000c-30100 008697 260900 038253 099998c-30120 010738 322145 049053 099999c-3550 003720 111603 019081 099999c-3560 004719 141582 015354 099999c-3580 006827 204818 018132 099998c-35100 008737 262111 022168 099999c-35120 010742 322259 034171 099999c-4050 003539 106166 013714 099999c-4060 004586 137587 016652 099999c-4080 006663 199876 016932 099998c-40100 008668 260026 023292 099996c-40120 010638 319140 028805 099996c-40140 012639 379164 034162 099995

Elliptical cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

a-2760 005221 156617 019932 099999a-3060 005306 159167 023224 099998a-3560 005412 162361 021593 099998

Porous cupsRotor 119860 [mpulse] 119860

119903[mrev] 119861 [ms] 119877

2

h-0960 005445 163352 031414 099999h-1960 006579 197376 054539 099998h-2460 011763 352881 031563 099998

the offset constant of the transfer function 119861 negligible Itshould be said that the effect of this offset constant on similarcalculations has been considered negligible in past works[44 48] as it is only appreciated at lowwind speedsHoweverit was preserved in the present calculations in order to havea more accurate comparison between the different cases andnew conclusions have arisen

In Figure 4 three different cases can be observed Forlow wind speeds (119881 = 4ms) the cup anemometer is lessefficient in terms of transforming the wind velocity into

rotational speed than for higher wind speeds (ie highervalues of the anemometer factor 119870 are shown) Also thecurves corresponding to the different cup sizes seem to followthe samepath for ratios between the cupsrsquo radius and the cupsrsquocenter rotation radius lower than 119903

119903lt 065 The mentioned

lower performances of the anemometer can be explainedas an effect of the friction forces which are increasinglysignificant when compared to the aerodynamic forces forlow wind speeds (that obviously are translated into lowrotational speeds)

The Scientific World Journal 7

The situation changes for higher wind speeds as it canbe observed for 119881 = 16ms and even more clearly for thelimit case 119881 rarr infin (ie when the offset constant 119861 is leftaside) In this case the anemometer constant 119870 shows asecond-order polynomial dependence on the parameter 119903

119903

Also the effect of relative cup size is shown in the mentionedgraph The curves fitting to the results corresponding to therotors with the smallest and the largest cups (119877

119888= 20mm

and 119877

119888= 40mm resp) have been included in the graphThe

results corresponding to all the intermediate cup size rotors(119877119888= 25mm 119877

119888= 30mm and 119877

119888= 35mm) lie between

both curves revealing the aforementioned dependence onthe cupsrsquo size In tune with this effect it should also be saidthat other experimental results have already demonstratedthe direct relationship between the slope of the anemometertransfer function 119860 and the front area of the cups [44]

119860 =

1

119873

119901

119860

119903=

1

119873

119901

(

d119860119903

d119877119903119888

119877

119903119888+ 119860

1199030) (5)

where d119860119903d119877119903119888depends on the aerodynamic forces on the

cups (for rotors equipped with the same conical cups testedin the present work it was found that this coefficient hasconstant value with very little or no correlation to the cupsrsquosize) and 119860

1199030strongly depends on the cupsrsquo front area 119878

119888

Finally it should also be said that as far as the authorsknow this particular effect of the cupsrsquo size has not beenincluded in the different analyticalmodels developed to studycup anemometer behavior [30 31 33 38 40] These modelsare based on wind speed cup aerodynamic coefficientsand cup and rotor geometries and take as starting pointthat the behavior of cup anemometers is mainly driven byaerodynamic forces the frictional torque being much lowerin comparison [37 49] However these models are limiteddue to the complexity of rotating flows [48]

In order go to deeper into this problem the aerodynamicforces on each cup should be analyzed As the aerodynamictorque on the anemometerrsquos rotor is produced by the aerody-namic forces on the mentioned cups and the cups positionson the rotor have 120∘ phase separation it is logical to assumethat at constant wind speed equal rotational accelerations anddecelerationswill affect the anemometer rotor three times perrevolution (obviously these accelerations are responsible forthe third harmonic term of the anemometer wind speed 120596

3

see expression (3)) Therefore studying the third harmonicterm of the rotational speed is a way to analyze the effect ofthe cups on the rotor movement

In Figure 5 the non-dimensional third harmonic term120596

3120596

0 calculated for every wind speed of the calibrations

regarding the studied porous cups rotors (h-0960 h-1960and h-2460) is shown together with the results correspond-ing to the c-2560 rotor (included as it can be considered aspart of the porous cup series ie porosity equal to zero) Inthementionedfigure the differences among the performanceswith regard to the different rotors can be clearly observedThis figure has been chosen to illustrate two parameters usedin the present work to analyze the third harmonic term ofthe anemometer rotational speed (i) the non-dimensional

1205963 + 1205903

1205963

1205963 minus 1205903

V (ms)

900

800

700

600

500

400

300

200

100

0004 6 8 10 12 14 16

1205963120596

0(

)

Figure 5 Non-dimensional harmonic term 1205963120596

0 calculated at

every point of the calibrations performed on the Climatronics100075 anemometer equippedwith c-2560 (circles) h-0960 (trian-gles) h-1960 (squares) and h-2460 (rhombi) rotors The averagevalue line 120596

3 together with the standard deviation limits plusmn120590

3

corresponding to the h-1960 rotor values has been also included inthe graph

average value calculated with data from the 13 points of thecalibration procedure

120596

3=

1

13

13

sum

119894=1

120596

3

120596

0

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119894

(6)

and (ii) the corresponding standard deviation 1205903 calculated

using the general procedure

120590

3=

radic

sum

13

119894=1( (120596

3120596

0)

1003816

1003816

1003816

1003816119894minus 120596

3)

2

13 minus 1

(7)

In Figure 6 the averaged third non-dimensional har-monic term 120596

3 regarding the conical cups rotors and

the ratio of the standard deviation to the mentioned non-dimensional third harmonic term 120590

3120596

3 are shown as a

function of the ratio of the cup radius to the cupsrsquo centerrotation radius 119903

119903 The third harmonic term 120596

3 tends to be

smaller with higher values of 119903119903 that is for rotors whose cups

centers are closer to the rotation axisThe same tendency wasobserved on the anemometer factor 119870 (see Figure 4) so itcan be concluded that higher third harmonic terms have animmediate effect on the anemometer average performancereducing the average rotational speed 120596

0 This effect can be

explained in terms of energy as a bigger part of the energytransferred from the wind to the rotor movement is investedinto the mentioned third harmonic term and not into theconstant term of the rotational speed 120596

0 Also the effect

of the cupsrsquo size has the same pattern as the one for the

8 The Scientific World Journal

rr

180160140120100080060040

000 020 040 060 080 100

1205963(

)

(a)

rr

000 020 040 060 080 100

2000

1600

1200

800

400

000

1205903120596

3(

)

(b)

Figure 6 Averaged third harmonic term 1205963 regarding the conical cups rotors (a) and the corresponding standard deviation 120590

3120596

3(b)

both expressed as a function of the parameter 119903

119903(119903119903= 119877

119888119877

119903119888) The symbols correspond to rotors equipped with the following cup radii

119877

119888= 20mm (rhombi) 119877

119888= 25mm (circles) 119877

119888= 30mm (squares) 119877

119888= 35mm (triangles) and 119877

119888= 40mm (crosses)

anemometer constant graphs in Figure 4 Smaller cups withthe same parameter 119903

119903show smaller third harmonic terms

with higher rotational efficienciesFinally focusing on the standard deviationmeasuredwith

respect to the average third harmonic term 1205903120596

3 shown

in Figure 6 it seems that there is a minimum for every cupsize at a certain value of the parameter 119903

119903 located around

119903

119903= 05 In Figure 7 the third harmonic term measured for

every wind velocity during the calibration of four rotorsequipped with 119877

119888= 40mm cups is shown The data

correspond to the smallest and the largest cup rotation radiustested (119877

119903119888= 50mm and 119877

119903119888= 140mm resp) and two

intermediate cases (119877119903119888

= 80mm and 119877

119903119888= 100mm) It

can be observed that according to the information from thementioned graph in Figure 6 the dispersion of the results islower for the intermediate cases A linear tendency is alsoobserved with higher slopes for greater values of cup centerrotation radius Finally it should also be said that class-1commercial anemometers [47 50] have ratios between thecup radius and the cupsrsquo center rotation radius ranging from119903

119903= 04 to 119903

119903= 06 (Thies Clima 4335043351 119903

119903= 05

Vector Instruments A100L2 119903119903= 049 Vaisala WAA 151252

119903

119903= 042 WindSensor (Risoslash) P2546A 119903

119903= 059)

Concerning the effect of the cupsrsquo shape its effect onanemometer performance has been already analyzed Theaerodynamic forces on a single cup have been correlatedwith the aforementioned anemometer performance in twodifferent ways by means of analytical models correlated withexperimental testing [30 31 33 38] and by means of adirect comparison based on experimental calibration [48] InFigure 8 the anemometer constant at 16ms wind speed withregard to the calibrations performed on the anemometerequipped with elliptical and porous cups rotors has beenincluded respectively as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 and the ratio of the hole diameter to the cupdiameter ℎ2119877

119888 The non-dimensional third harmonic 120596

3

regarding these rotors has been also included in the figureAs it was previously measured [48] the effect of both theeccentricity and the porosity of the cups is translated into adecrease of the rotational efficiency of the cups (higher values

1205963120596

0

1205963

V (ms)

13

12

11

10

09

08

07

06

0 2 4 6 8 10 12 14 16 18

Rrc = 50mm (RcRrc = 08)

Rrc = 100mm (RcRrc = 04)

Rrc = 140mm (RcRrc = 0287)

Rrc = 80mm (RcRrc = 05)

Figure 7 Variation of the third harmonic term measured withrotors equipped with 119877

119888= 40mm conical cups as a function of the

wind speed within the calibration process

of 119870 that is lower rotational speed at a fixed wind speed)On the other hand the effect of both parameters on the thirdharmonic term has a reversed effect that is higher valuesof eccentricity and porosity increase the importance of thisharmonic term

4 Conclusions

In the present work the performance of a cup anemometerequipped with different rotors has been experimentally ana-lyzed On one hand the size of conical cups together withtheir distance to the anemometer rotation axis was studiedOn the other hand the shape of the rotor cups was alsostudied The analysis was based on two different parameters

The Scientific World Journal 9

K

e h2Rc

1000

950

900

850

800

750

700

650

600

550

500

450

400

000 020 040 060 080 100

(a)

1000

900

800

700

600

500

400

300

200

100

e h2Rc

000 020 040 060 080 100

1205963(

)(b)

Figure 8 Anemometer constant at 16ms wind speed119870 and non-dimensional third harmonic1205963 with regard to the calibrations performed

to the anemometer equipped with elliptical (squares) and porous (circles) cup rotors as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 andthe ratio of the hole diameter to the front cup area ℎ2119877

119888 respectively

the anemometer factor that takes into account the averagerotation of the anemometer and the third harmonic termresulting from the Fourier decomposition of the anemometerrotation speed The most relevant conclusions resulting fromthis work are as follows

(i) The average rotation speed is well correlated with thementioned third harmonic term resulting from theFourier decomposition of the anemometer rotationspeed Higher values of this third harmonic termresult in higher anemometer factors and thereforein lower rotational speeds This fact confirms thementioned third harmonic term as a useful parameterto study cup anemometer performance

(ii) Smaller cups with the same ratio of cup diameter tothe cupsrsquo center rotation radius 119903

119903 tend to produce

higher rotational speeds (lower anemometer factors)and lower third harmonic terms

(iii) The ratio of the third harmonic term to the averagerotational speed 120596

3120596

0 is more uniform (within the

wind speed calibration range) for values of the ratioof the cup diameter to the cupsrsquo center rotation radiusranging from 119903

119903= 04 to 119903

119903= 05 than for values of 119903

119903

beyond or below this bracket

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are truly indebted to Enrique Vega AlejandroMartınez Encarnacion Meseguer Luis Garcıa and EduardoCortes for the help and friendly support during the testingcampaign The authors are grateful to Anna Marıa Ballesterfor her kind help on improving the style of the text

References

[1] F Aminzadeh and S Pindado ldquoHow has Spain become a leaderin thewind energy industry during the last decade (An analysisof influential factors on the development of wind energy inSpain)rdquo in Proceedings of the EWEA Annual Event BrusselsBelgium 2011

[2] L Kristensen ldquoCan a cup anemometer ldquounderspeedrdquo A hereti-cal questionrdquo Boundary-Layer Meteorology vol 103 no 1 pp163ndash172 2002

[3] R V Coquilla J Obermeier and B R White ldquoCalibrationprocedures and uncertainty in wind power anemometersrdquoWind Engineering vol 31 no 5 pp 303ndash316 2007

[4] A Albers and H Klug ldquoOpen field cup anemometryrdquo DEWIMagazine vol 19 pp 53ndash58 2001

[5] A Albers H Klug and D Westermann ldquoOutdoor comparisonof cup anemometersrdquo DEWI Magazin vol 17 pp 5ndash15 2000

[6] S Lang and E McKeogh ldquoLIDAR and SODAR measurementsof wind speed and direction in upland terrain for wind energypurposesrdquo Remote Sensing vol 3 no 9 pp 1871ndash1901 2011

[7] R Wagner M Courtney J Gottschall and P Lindelow-Marsden ldquoAccounting for the speed shear in wind turbine

10 The Scientific World Journal

power performance measurementrdquoWind Energy vol 14 no 8pp 993ndash1004 2011

[8] T R Robinson ldquoOn a New Anemometerrdquo Proceedings of theRoyal Irish Academy (1836ndash1869 ) vol 4 pp 566ndash572 1847

[9] International Electrotechnical Commision International Stan-dard IEC-61400-12-1 Wind Turbines Part 12-1 Power Perfor-mance Measurements of Electricity Producing Wind TurbinesFirst Edition 2005ndash12 International Electrotechnical Commi-sion Geneva Switzerland 2005

[10] R V Coquilla and J Obermeier ldquoCalibration speed range forrotating anemometers used in wind energy applicationsrdquo inProceedings of the 46th AIAA Aerospace Sciences Meeting andExhibit pp 2ndash7 January 2008

[11] R V Coquilla A Havner J Obermeier and M SturgeonldquoVerification testing of Sonic anemometer wind speedmeasure-ments for wind energy applicationsrdquo in Proceedings of the 2010American Wind Energy Association Annual Conference (AWEAWINDPOWER rsquo10) pp 1ndash14 2010

[12] L J Fritschen ldquoA sensitive cup-type anemometerrdquo Journal ofApplied Meteorology vol 6 pp 695ndash698 1967

[13] M Sanuki and S Kimura ldquoSome aerodynamic aspects deducedfrom the start and stop experiment of three- and four-cupanemometerrdquo Papers in Meteorology and Geophysics vol 5 pp695ndash698 1954

[14] C F Marvin ldquoA rational theory of the cup anemometerrdquoMonthly Weather Review vol 60 pp 43ndash56 1932

[15] M J Brevoort and U T Joyner ldquoExperimental investigation ofthe Robinson-type cup anemometerrdquo NACA TN-513 1935

[16] C F Marvin ldquoRecent advances in anemometryrdquo MonthlyWeather Review vol 62 pp 115ndash120 1934

[17] C F Marvin ldquoAnemometer testsrdquoMonthlyWeather Review pp58ndash63 1900

[18] H Charnock and F E Pierce ldquoNew housing for the sensitivecup-contact anemometer Mk 1rdquo Journal of Scientific Instru-ments vol 36 no 7 p 329 1959

[19] P A Sheppard ldquoAn improved design of cup anemometerrdquoJournal of Scientific Instruments vol 17 no 9 pp 218ndash221 1940

[20] E L Deacon ldquoReply to two types of sensitive recording cupanemometersrdquo Journal of Scientific Instruments vol 25 no 8p 283 1948

[21] S G Crawford ldquoA simple form of sensitive electric contact cupanemometerrdquo Journal of Scientific Instruments vol 28 no 2 pp36ndash37 1951

[22] F Scrase and P Sheppard ldquoThe errors of cup anemometers influctuating windsrdquo Journal of Scientific Instruments vol 21 no9 pp 160ndash161 1944

[23] E L Deacon ldquoThe over-estimation error of cup anemometersin fluctuating windsrdquo Journal of Scientific Instruments vol 28no 8 pp 231ndash234 1951

[24] L KristensenThe Cup Anemometer and Other Exciting Instru-ments Risoslash-R-615 (EN) Risoslash National Laboratory RoskildeDenmark 1993

[25] MEASNET Cup Anemometer Calibration Procedure Version1 (September 1997 Updated 24112008) MEASNET MadridSpain 1997

[26] MEASNET Anemometer Calibration Procedure Version 2(October 2009) MEASNET Madrid Spain 2009

[27] ASTM International Standard Test Method for Determining thePerformance of a Cup Anemometer or Propeller Anemometer(ASTMD 5096-02) ASTM InternationalWest ConshohockenPa USA 2002

[28] M C-E Brazier ldquoSur la variation des indications desanemometres Robinson et Richard en fonction de lrsquoinclinaisondu ventrdquoComptes Rendus des Seances de LrsquoAcademie des Sciencesvol 170 pp 610ndash612 1920

[29] S Pindado E Vega A Martınez E Meseguer S Franchiniand I P Sarasola ldquoAnalysis of calibration results from cupand propeller anemometers Influence on wind turbine AnnualEnergy Production (AEP) calculationsrdquo Wind Energy vol 14no 1 pp 119ndash132 2011

[30] J Kondo G I Naito and Y Fujinawa ldquoResponse of cupanemometer in turbulencerdquo Journal of theMeteorological Societyof Japan vol 49 pp 63ndash74 1971

[31] S Ramachandran ldquoA theoretical study of cup and vaneanemometersrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 95 no 403 pp 163ndash180 1969

[32] M C-E Brazier ldquoSur la comparabilite des anemometresrdquoComptes Rendus des Seances de LrsquoAcademie des Sciences vol 172pp 843ndash845 1921

[33] O Schrenk ldquoUber die tragheitsfehler des Schalenkreuz-anemometers bei schwankender Windstarkerdquo Zeitschrift FurTechnische Physik vol 10 pp 57ndash66 1929

[34] H W Baynton ldquoErrors in wind run estimates from rotationalanemometersrdquo Bulletin of the American Meteorological Societyvol 57 no 9 pp 1127ndash1130 1976

[35] N E Busch and L Kristensen ldquoCup anemometer overspeed-ingrdquo Journal of AppliedMeteorology vol 15 pp 1328ndash1332 1976

[36] P Frenzen ldquoFast response cup anemometers for atmosphericturbulence researchrdquo in Proceedings of the 8th Symposium onTurbulence and Diffusion pp 112ndash115 1988

[37] E I Kaganov and A M Yaglom ldquoErrors in wind-speed mea-surements by rotation anemometersrdquo Boundary-Layer Meteo-rology vol 10 no 1 pp 15ndash34 1976

[38] J C Wyngaard ldquoCup propeller vane and sonic anemometersin turbulence researchrdquo Annual Review of Fluid Mechanics vol13 pp 399ndash423 1981

[39] P A Coppin ldquoAn examination of cup anemometer overspeed-ingrdquoMeteorologische Rundschau vol 35 pp 1ndash11 1982

[40] J CWyngaard J T Bauman and R A Lynch ldquoCup anemome-ter dynamicsrdquo in Flow Its Measurement and Control in Scienceand Industry vol 1 pp 701ndash708 1974

[41] L Kristensen ldquoCup anemometer behavior in turbulent environ-mentsrdquo Journal of Atmospheric and Oceanic Technology vol 15no 1 pp 5ndash17 1998

[42] R S Hunter ldquoThe accuracy of cup anemometer calibrationwithparticular regard to testing wind turbinesrdquo Wind Engineeringvol 14 no 1 pp 32ndash43 1990

[43] J-A Dahlberg J Gustavsson G Ronsten T F Pedersen US Paulsen and D Westermann Development of A Standard-ised Cup Anemometer Suited to Wind Energy Applications-(ClAsscup) vol 9 Technical University of Denmark LyngbyDenmark 2001

[44] S Pindado J Perez and S Avila-Sanchez ldquoOn cup anemometerrotor aerodynamicsrdquo Sensors vol 12 no 5 pp 6198ndash6217 2012

[45] S Pindado A Sanz and A Wery ldquoDeviation of cup andpropeller anemometer calibration results with air densityrdquoEnergies vol 5 no 3 pp 683ndash701 2012

[46] S Pindado A Barrero-Gil and A Sanz ldquoCup anemome-tersrsquoLoss of performance due to ageing processes and its effecton Annual Energy Production (AEP) estimatesrdquo Energies vol5 no 12 pp 1664ndash1685 2012

The Scientific World Journal 11

[47] J-A Dahlberg T F Pedersen and P Busche ACCUWIND-Methods for Classification of Cup Anemometers Risoslash-R-1555(EN) Risoslash National Laboratory Roskilde Denmark 2006

[48] S Pindado I Perez and M Aguado ldquoFourier analysis ofthe aerodynamic behavior of cup anemometersrdquo MeasurementScience and Technology vol 24 no 6 Article ID 065802 2013

[49] Y P Solovrsquoev A I Korovushkin and Y N Toloknov ldquoCharac-teristics of a cup anemometer and a procedure of measuring thewind velocityrdquo Physical Oceanography vol 14 no 3 pp 173ndash1862004

[50] T F Pedersen Development of A Classification System forCup Anemometers-CLASSCUP Risoslash-R-1348(EN) Risoslash NationalLaboratory Roskilde Denmark 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

The Scientific World Journal 7

The situation changes for higher wind speeds as it canbe observed for 119881 = 16ms and even more clearly for thelimit case 119881 rarr infin (ie when the offset constant 119861 is leftaside) In this case the anemometer constant 119870 shows asecond-order polynomial dependence on the parameter 119903

119903

Also the effect of relative cup size is shown in the mentionedgraph The curves fitting to the results corresponding to therotors with the smallest and the largest cups (119877

119888= 20mm

and 119877

119888= 40mm resp) have been included in the graphThe

results corresponding to all the intermediate cup size rotors(119877119888= 25mm 119877

119888= 30mm and 119877

119888= 35mm) lie between

both curves revealing the aforementioned dependence onthe cupsrsquo size In tune with this effect it should also be saidthat other experimental results have already demonstratedthe direct relationship between the slope of the anemometertransfer function 119860 and the front area of the cups [44]

119860 =

1

119873

119901

119860

119903=

1

119873

119901

(

d119860119903

d119877119903119888

119877

119903119888+ 119860

1199030) (5)

where d119860119903d119877119903119888depends on the aerodynamic forces on the

cups (for rotors equipped with the same conical cups testedin the present work it was found that this coefficient hasconstant value with very little or no correlation to the cupsrsquosize) and 119860

1199030strongly depends on the cupsrsquo front area 119878

119888

Finally it should also be said that as far as the authorsknow this particular effect of the cupsrsquo size has not beenincluded in the different analyticalmodels developed to studycup anemometer behavior [30 31 33 38 40] These modelsare based on wind speed cup aerodynamic coefficientsand cup and rotor geometries and take as starting pointthat the behavior of cup anemometers is mainly driven byaerodynamic forces the frictional torque being much lowerin comparison [37 49] However these models are limiteddue to the complexity of rotating flows [48]

In order go to deeper into this problem the aerodynamicforces on each cup should be analyzed As the aerodynamictorque on the anemometerrsquos rotor is produced by the aerody-namic forces on the mentioned cups and the cups positionson the rotor have 120∘ phase separation it is logical to assumethat at constant wind speed equal rotational accelerations anddecelerationswill affect the anemometer rotor three times perrevolution (obviously these accelerations are responsible forthe third harmonic term of the anemometer wind speed 120596

3

see expression (3)) Therefore studying the third harmonicterm of the rotational speed is a way to analyze the effect ofthe cups on the rotor movement

In Figure 5 the non-dimensional third harmonic term120596

3120596

0 calculated for every wind speed of the calibrations

regarding the studied porous cups rotors (h-0960 h-1960and h-2460) is shown together with the results correspond-ing to the c-2560 rotor (included as it can be considered aspart of the porous cup series ie porosity equal to zero) Inthementionedfigure the differences among the performanceswith regard to the different rotors can be clearly observedThis figure has been chosen to illustrate two parameters usedin the present work to analyze the third harmonic term ofthe anemometer rotational speed (i) the non-dimensional

1205963 + 1205903

1205963

1205963 minus 1205903

V (ms)

900

800

700

600

500

400

300

200

100

0004 6 8 10 12 14 16

1205963120596

0(

)

Figure 5 Non-dimensional harmonic term 1205963120596

0 calculated at

every point of the calibrations performed on the Climatronics100075 anemometer equippedwith c-2560 (circles) h-0960 (trian-gles) h-1960 (squares) and h-2460 (rhombi) rotors The averagevalue line 120596

3 together with the standard deviation limits plusmn120590

3

corresponding to the h-1960 rotor values has been also included inthe graph

average value calculated with data from the 13 points of thecalibration procedure

120596

3=

1

13

13

sum

119894=1

120596

3

120596

0

1003816

1003816

1003816

1003816

1003816

1003816

1003816

1003816

119894

(6)

and (ii) the corresponding standard deviation 1205903 calculated

using the general procedure

120590

3=

radic

sum

13

119894=1( (120596

3120596

0)

1003816

1003816

1003816

1003816119894minus 120596

3)

2

13 minus 1

(7)

In Figure 6 the averaged third non-dimensional har-monic term 120596

3 regarding the conical cups rotors and

the ratio of the standard deviation to the mentioned non-dimensional third harmonic term 120590

3120596

3 are shown as a

function of the ratio of the cup radius to the cupsrsquo centerrotation radius 119903

119903 The third harmonic term 120596

3 tends to be

smaller with higher values of 119903119903 that is for rotors whose cups

centers are closer to the rotation axisThe same tendency wasobserved on the anemometer factor 119870 (see Figure 4) so itcan be concluded that higher third harmonic terms have animmediate effect on the anemometer average performancereducing the average rotational speed 120596

0 This effect can be

explained in terms of energy as a bigger part of the energytransferred from the wind to the rotor movement is investedinto the mentioned third harmonic term and not into theconstant term of the rotational speed 120596

0 Also the effect

of the cupsrsquo size has the same pattern as the one for the

8 The Scientific World Journal

rr

180160140120100080060040

000 020 040 060 080 100

1205963(

)

(a)

rr

000 020 040 060 080 100

2000

1600

1200

800

400

000

1205903120596

3(

)

(b)

Figure 6 Averaged third harmonic term 1205963 regarding the conical cups rotors (a) and the corresponding standard deviation 120590

3120596

3(b)

both expressed as a function of the parameter 119903

119903(119903119903= 119877

119888119877

119903119888) The symbols correspond to rotors equipped with the following cup radii

119877

119888= 20mm (rhombi) 119877

119888= 25mm (circles) 119877

119888= 30mm (squares) 119877

119888= 35mm (triangles) and 119877

119888= 40mm (crosses)

anemometer constant graphs in Figure 4 Smaller cups withthe same parameter 119903

119903show smaller third harmonic terms

with higher rotational efficienciesFinally focusing on the standard deviationmeasuredwith

respect to the average third harmonic term 1205903120596

3 shown

in Figure 6 it seems that there is a minimum for every cupsize at a certain value of the parameter 119903

119903 located around

119903

119903= 05 In Figure 7 the third harmonic term measured for

every wind velocity during the calibration of four rotorsequipped with 119877

119888= 40mm cups is shown The data

correspond to the smallest and the largest cup rotation radiustested (119877

119903119888= 50mm and 119877

119903119888= 140mm resp) and two

intermediate cases (119877119903119888

= 80mm and 119877

119903119888= 100mm) It

can be observed that according to the information from thementioned graph in Figure 6 the dispersion of the results islower for the intermediate cases A linear tendency is alsoobserved with higher slopes for greater values of cup centerrotation radius Finally it should also be said that class-1commercial anemometers [47 50] have ratios between thecup radius and the cupsrsquo center rotation radius ranging from119903

119903= 04 to 119903

119903= 06 (Thies Clima 4335043351 119903

119903= 05

Vector Instruments A100L2 119903119903= 049 Vaisala WAA 151252

119903

119903= 042 WindSensor (Risoslash) P2546A 119903

119903= 059)

Concerning the effect of the cupsrsquo shape its effect onanemometer performance has been already analyzed Theaerodynamic forces on a single cup have been correlatedwith the aforementioned anemometer performance in twodifferent ways by means of analytical models correlated withexperimental testing [30 31 33 38] and by means of adirect comparison based on experimental calibration [48] InFigure 8 the anemometer constant at 16ms wind speed withregard to the calibrations performed on the anemometerequipped with elliptical and porous cups rotors has beenincluded respectively as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 and the ratio of the hole diameter to the cupdiameter ℎ2119877

119888 The non-dimensional third harmonic 120596

3

regarding these rotors has been also included in the figureAs it was previously measured [48] the effect of both theeccentricity and the porosity of the cups is translated into adecrease of the rotational efficiency of the cups (higher values

1205963120596

0

1205963

V (ms)

13

12

11

10

09

08

07

06

0 2 4 6 8 10 12 14 16 18

Rrc = 50mm (RcRrc = 08)

Rrc = 100mm (RcRrc = 04)

Rrc = 140mm (RcRrc = 0287)

Rrc = 80mm (RcRrc = 05)

Figure 7 Variation of the third harmonic term measured withrotors equipped with 119877

119888= 40mm conical cups as a function of the

wind speed within the calibration process

of 119870 that is lower rotational speed at a fixed wind speed)On the other hand the effect of both parameters on the thirdharmonic term has a reversed effect that is higher valuesof eccentricity and porosity increase the importance of thisharmonic term

4 Conclusions

In the present work the performance of a cup anemometerequipped with different rotors has been experimentally ana-lyzed On one hand the size of conical cups together withtheir distance to the anemometer rotation axis was studiedOn the other hand the shape of the rotor cups was alsostudied The analysis was based on two different parameters

The Scientific World Journal 9

K

e h2Rc

1000

950

900

850

800

750

700

650

600

550

500

450

400

000 020 040 060 080 100

(a)

1000

900

800

700

600

500

400

300

200

100

e h2Rc

000 020 040 060 080 100

1205963(

)(b)

Figure 8 Anemometer constant at 16ms wind speed119870 and non-dimensional third harmonic1205963 with regard to the calibrations performed

to the anemometer equipped with elliptical (squares) and porous (circles) cup rotors as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 andthe ratio of the hole diameter to the front cup area ℎ2119877

119888 respectively

the anemometer factor that takes into account the averagerotation of the anemometer and the third harmonic termresulting from the Fourier decomposition of the anemometerrotation speed The most relevant conclusions resulting fromthis work are as follows

(i) The average rotation speed is well correlated with thementioned third harmonic term resulting from theFourier decomposition of the anemometer rotationspeed Higher values of this third harmonic termresult in higher anemometer factors and thereforein lower rotational speeds This fact confirms thementioned third harmonic term as a useful parameterto study cup anemometer performance

(ii) Smaller cups with the same ratio of cup diameter tothe cupsrsquo center rotation radius 119903

119903 tend to produce

higher rotational speeds (lower anemometer factors)and lower third harmonic terms

(iii) The ratio of the third harmonic term to the averagerotational speed 120596

3120596

0 is more uniform (within the

wind speed calibration range) for values of the ratioof the cup diameter to the cupsrsquo center rotation radiusranging from 119903

119903= 04 to 119903

119903= 05 than for values of 119903

119903

beyond or below this bracket

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are truly indebted to Enrique Vega AlejandroMartınez Encarnacion Meseguer Luis Garcıa and EduardoCortes for the help and friendly support during the testingcampaign The authors are grateful to Anna Marıa Ballesterfor her kind help on improving the style of the text

References

[1] F Aminzadeh and S Pindado ldquoHow has Spain become a leaderin thewind energy industry during the last decade (An analysisof influential factors on the development of wind energy inSpain)rdquo in Proceedings of the EWEA Annual Event BrusselsBelgium 2011

[2] L Kristensen ldquoCan a cup anemometer ldquounderspeedrdquo A hereti-cal questionrdquo Boundary-Layer Meteorology vol 103 no 1 pp163ndash172 2002

[3] R V Coquilla J Obermeier and B R White ldquoCalibrationprocedures and uncertainty in wind power anemometersrdquoWind Engineering vol 31 no 5 pp 303ndash316 2007

[4] A Albers and H Klug ldquoOpen field cup anemometryrdquo DEWIMagazine vol 19 pp 53ndash58 2001

[5] A Albers H Klug and D Westermann ldquoOutdoor comparisonof cup anemometersrdquo DEWI Magazin vol 17 pp 5ndash15 2000

[6] S Lang and E McKeogh ldquoLIDAR and SODAR measurementsof wind speed and direction in upland terrain for wind energypurposesrdquo Remote Sensing vol 3 no 9 pp 1871ndash1901 2011

[7] R Wagner M Courtney J Gottschall and P Lindelow-Marsden ldquoAccounting for the speed shear in wind turbine

10 The Scientific World Journal

power performance measurementrdquoWind Energy vol 14 no 8pp 993ndash1004 2011

[8] T R Robinson ldquoOn a New Anemometerrdquo Proceedings of theRoyal Irish Academy (1836ndash1869 ) vol 4 pp 566ndash572 1847

[9] International Electrotechnical Commision International Stan-dard IEC-61400-12-1 Wind Turbines Part 12-1 Power Perfor-mance Measurements of Electricity Producing Wind TurbinesFirst Edition 2005ndash12 International Electrotechnical Commi-sion Geneva Switzerland 2005

[10] R V Coquilla and J Obermeier ldquoCalibration speed range forrotating anemometers used in wind energy applicationsrdquo inProceedings of the 46th AIAA Aerospace Sciences Meeting andExhibit pp 2ndash7 January 2008

[11] R V Coquilla A Havner J Obermeier and M SturgeonldquoVerification testing of Sonic anemometer wind speedmeasure-ments for wind energy applicationsrdquo in Proceedings of the 2010American Wind Energy Association Annual Conference (AWEAWINDPOWER rsquo10) pp 1ndash14 2010

[12] L J Fritschen ldquoA sensitive cup-type anemometerrdquo Journal ofApplied Meteorology vol 6 pp 695ndash698 1967

[13] M Sanuki and S Kimura ldquoSome aerodynamic aspects deducedfrom the start and stop experiment of three- and four-cupanemometerrdquo Papers in Meteorology and Geophysics vol 5 pp695ndash698 1954

[14] C F Marvin ldquoA rational theory of the cup anemometerrdquoMonthly Weather Review vol 60 pp 43ndash56 1932

[15] M J Brevoort and U T Joyner ldquoExperimental investigation ofthe Robinson-type cup anemometerrdquo NACA TN-513 1935

[16] C F Marvin ldquoRecent advances in anemometryrdquo MonthlyWeather Review vol 62 pp 115ndash120 1934

[17] C F Marvin ldquoAnemometer testsrdquoMonthlyWeather Review pp58ndash63 1900

[18] H Charnock and F E Pierce ldquoNew housing for the sensitivecup-contact anemometer Mk 1rdquo Journal of Scientific Instru-ments vol 36 no 7 p 329 1959

[19] P A Sheppard ldquoAn improved design of cup anemometerrdquoJournal of Scientific Instruments vol 17 no 9 pp 218ndash221 1940

[20] E L Deacon ldquoReply to two types of sensitive recording cupanemometersrdquo Journal of Scientific Instruments vol 25 no 8p 283 1948

[21] S G Crawford ldquoA simple form of sensitive electric contact cupanemometerrdquo Journal of Scientific Instruments vol 28 no 2 pp36ndash37 1951

[22] F Scrase and P Sheppard ldquoThe errors of cup anemometers influctuating windsrdquo Journal of Scientific Instruments vol 21 no9 pp 160ndash161 1944

[23] E L Deacon ldquoThe over-estimation error of cup anemometersin fluctuating windsrdquo Journal of Scientific Instruments vol 28no 8 pp 231ndash234 1951

[24] L KristensenThe Cup Anemometer and Other Exciting Instru-ments Risoslash-R-615 (EN) Risoslash National Laboratory RoskildeDenmark 1993

[25] MEASNET Cup Anemometer Calibration Procedure Version1 (September 1997 Updated 24112008) MEASNET MadridSpain 1997

[26] MEASNET Anemometer Calibration Procedure Version 2(October 2009) MEASNET Madrid Spain 2009

[27] ASTM International Standard Test Method for Determining thePerformance of a Cup Anemometer or Propeller Anemometer(ASTMD 5096-02) ASTM InternationalWest ConshohockenPa USA 2002

[28] M C-E Brazier ldquoSur la variation des indications desanemometres Robinson et Richard en fonction de lrsquoinclinaisondu ventrdquoComptes Rendus des Seances de LrsquoAcademie des Sciencesvol 170 pp 610ndash612 1920

[29] S Pindado E Vega A Martınez E Meseguer S Franchiniand I P Sarasola ldquoAnalysis of calibration results from cupand propeller anemometers Influence on wind turbine AnnualEnergy Production (AEP) calculationsrdquo Wind Energy vol 14no 1 pp 119ndash132 2011

[30] J Kondo G I Naito and Y Fujinawa ldquoResponse of cupanemometer in turbulencerdquo Journal of theMeteorological Societyof Japan vol 49 pp 63ndash74 1971

[31] S Ramachandran ldquoA theoretical study of cup and vaneanemometersrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 95 no 403 pp 163ndash180 1969

[32] M C-E Brazier ldquoSur la comparabilite des anemometresrdquoComptes Rendus des Seances de LrsquoAcademie des Sciences vol 172pp 843ndash845 1921

[33] O Schrenk ldquoUber die tragheitsfehler des Schalenkreuz-anemometers bei schwankender Windstarkerdquo Zeitschrift FurTechnische Physik vol 10 pp 57ndash66 1929

[34] H W Baynton ldquoErrors in wind run estimates from rotationalanemometersrdquo Bulletin of the American Meteorological Societyvol 57 no 9 pp 1127ndash1130 1976

[35] N E Busch and L Kristensen ldquoCup anemometer overspeed-ingrdquo Journal of AppliedMeteorology vol 15 pp 1328ndash1332 1976

[36] P Frenzen ldquoFast response cup anemometers for atmosphericturbulence researchrdquo in Proceedings of the 8th Symposium onTurbulence and Diffusion pp 112ndash115 1988

[37] E I Kaganov and A M Yaglom ldquoErrors in wind-speed mea-surements by rotation anemometersrdquo Boundary-Layer Meteo-rology vol 10 no 1 pp 15ndash34 1976

[38] J C Wyngaard ldquoCup propeller vane and sonic anemometersin turbulence researchrdquo Annual Review of Fluid Mechanics vol13 pp 399ndash423 1981

[39] P A Coppin ldquoAn examination of cup anemometer overspeed-ingrdquoMeteorologische Rundschau vol 35 pp 1ndash11 1982

[40] J CWyngaard J T Bauman and R A Lynch ldquoCup anemome-ter dynamicsrdquo in Flow Its Measurement and Control in Scienceand Industry vol 1 pp 701ndash708 1974

[41] L Kristensen ldquoCup anemometer behavior in turbulent environ-mentsrdquo Journal of Atmospheric and Oceanic Technology vol 15no 1 pp 5ndash17 1998

[42] R S Hunter ldquoThe accuracy of cup anemometer calibrationwithparticular regard to testing wind turbinesrdquo Wind Engineeringvol 14 no 1 pp 32ndash43 1990

[43] J-A Dahlberg J Gustavsson G Ronsten T F Pedersen US Paulsen and D Westermann Development of A Standard-ised Cup Anemometer Suited to Wind Energy Applications-(ClAsscup) vol 9 Technical University of Denmark LyngbyDenmark 2001

[44] S Pindado J Perez and S Avila-Sanchez ldquoOn cup anemometerrotor aerodynamicsrdquo Sensors vol 12 no 5 pp 6198ndash6217 2012

[45] S Pindado A Sanz and A Wery ldquoDeviation of cup andpropeller anemometer calibration results with air densityrdquoEnergies vol 5 no 3 pp 683ndash701 2012

[46] S Pindado A Barrero-Gil and A Sanz ldquoCup anemome-tersrsquoLoss of performance due to ageing processes and its effecton Annual Energy Production (AEP) estimatesrdquo Energies vol5 no 12 pp 1664ndash1685 2012

The Scientific World Journal 11

[47] J-A Dahlberg T F Pedersen and P Busche ACCUWIND-Methods for Classification of Cup Anemometers Risoslash-R-1555(EN) Risoslash National Laboratory Roskilde Denmark 2006

[48] S Pindado I Perez and M Aguado ldquoFourier analysis ofthe aerodynamic behavior of cup anemometersrdquo MeasurementScience and Technology vol 24 no 6 Article ID 065802 2013

[49] Y P Solovrsquoev A I Korovushkin and Y N Toloknov ldquoCharac-teristics of a cup anemometer and a procedure of measuring thewind velocityrdquo Physical Oceanography vol 14 no 3 pp 173ndash1862004

[50] T F Pedersen Development of A Classification System forCup Anemometers-CLASSCUP Risoslash-R-1348(EN) Risoslash NationalLaboratory Roskilde Denmark 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 The Scientific World Journal

rr

180160140120100080060040

000 020 040 060 080 100

1205963(

)

(a)

rr

000 020 040 060 080 100

2000

1600

1200

800

400

000

1205903120596

3(

)

(b)

Figure 6 Averaged third harmonic term 1205963 regarding the conical cups rotors (a) and the corresponding standard deviation 120590

3120596

3(b)

both expressed as a function of the parameter 119903

119903(119903119903= 119877

119888119877

119903119888) The symbols correspond to rotors equipped with the following cup radii

119877

119888= 20mm (rhombi) 119877

119888= 25mm (circles) 119877

119888= 30mm (squares) 119877

119888= 35mm (triangles) and 119877

119888= 40mm (crosses)

anemometer constant graphs in Figure 4 Smaller cups withthe same parameter 119903

119903show smaller third harmonic terms

with higher rotational efficienciesFinally focusing on the standard deviationmeasuredwith

respect to the average third harmonic term 1205903120596

3 shown

in Figure 6 it seems that there is a minimum for every cupsize at a certain value of the parameter 119903

119903 located around

119903

119903= 05 In Figure 7 the third harmonic term measured for

every wind velocity during the calibration of four rotorsequipped with 119877

119888= 40mm cups is shown The data

correspond to the smallest and the largest cup rotation radiustested (119877

119903119888= 50mm and 119877

119903119888= 140mm resp) and two

intermediate cases (119877119903119888

= 80mm and 119877

119903119888= 100mm) It

can be observed that according to the information from thementioned graph in Figure 6 the dispersion of the results islower for the intermediate cases A linear tendency is alsoobserved with higher slopes for greater values of cup centerrotation radius Finally it should also be said that class-1commercial anemometers [47 50] have ratios between thecup radius and the cupsrsquo center rotation radius ranging from119903

119903= 04 to 119903

119903= 06 (Thies Clima 4335043351 119903

119903= 05

Vector Instruments A100L2 119903119903= 049 Vaisala WAA 151252

119903

119903= 042 WindSensor (Risoslash) P2546A 119903

119903= 059)

Concerning the effect of the cupsrsquo shape its effect onanemometer performance has been already analyzed Theaerodynamic forces on a single cup have been correlatedwith the aforementioned anemometer performance in twodifferent ways by means of analytical models correlated withexperimental testing [30 31 33 38] and by means of adirect comparison based on experimental calibration [48] InFigure 8 the anemometer constant at 16ms wind speed withregard to the calibrations performed on the anemometerequipped with elliptical and porous cups rotors has beenincluded respectively as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 and the ratio of the hole diameter to the cupdiameter ℎ2119877

119888 The non-dimensional third harmonic 120596

3

regarding these rotors has been also included in the figureAs it was previously measured [48] the effect of both theeccentricity and the porosity of the cups is translated into adecrease of the rotational efficiency of the cups (higher values

1205963120596

0

1205963

V (ms)

13

12

11

10

09

08

07

06

0 2 4 6 8 10 12 14 16 18

Rrc = 50mm (RcRrc = 08)

Rrc = 100mm (RcRrc = 04)

Rrc = 140mm (RcRrc = 0287)

Rrc = 80mm (RcRrc = 05)

Figure 7 Variation of the third harmonic term measured withrotors equipped with 119877

119888= 40mm conical cups as a function of the

wind speed within the calibration process

of 119870 that is lower rotational speed at a fixed wind speed)On the other hand the effect of both parameters on the thirdharmonic term has a reversed effect that is higher valuesof eccentricity and porosity increase the importance of thisharmonic term

4 Conclusions

In the present work the performance of a cup anemometerequipped with different rotors has been experimentally ana-lyzed On one hand the size of conical cups together withtheir distance to the anemometer rotation axis was studiedOn the other hand the shape of the rotor cups was alsostudied The analysis was based on two different parameters

The Scientific World Journal 9

K

e h2Rc

1000

950

900

850

800

750

700

650

600

550

500

450

400

000 020 040 060 080 100

(a)

1000

900

800

700

600

500

400

300

200

100

e h2Rc

000 020 040 060 080 100

1205963(

)(b)

Figure 8 Anemometer constant at 16ms wind speed119870 and non-dimensional third harmonic1205963 with regard to the calibrations performed

to the anemometer equipped with elliptical (squares) and porous (circles) cup rotors as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 andthe ratio of the hole diameter to the front cup area ℎ2119877

119888 respectively

the anemometer factor that takes into account the averagerotation of the anemometer and the third harmonic termresulting from the Fourier decomposition of the anemometerrotation speed The most relevant conclusions resulting fromthis work are as follows

(i) The average rotation speed is well correlated with thementioned third harmonic term resulting from theFourier decomposition of the anemometer rotationspeed Higher values of this third harmonic termresult in higher anemometer factors and thereforein lower rotational speeds This fact confirms thementioned third harmonic term as a useful parameterto study cup anemometer performance

(ii) Smaller cups with the same ratio of cup diameter tothe cupsrsquo center rotation radius 119903

119903 tend to produce

higher rotational speeds (lower anemometer factors)and lower third harmonic terms

(iii) The ratio of the third harmonic term to the averagerotational speed 120596

3120596

0 is more uniform (within the

wind speed calibration range) for values of the ratioof the cup diameter to the cupsrsquo center rotation radiusranging from 119903

119903= 04 to 119903

119903= 05 than for values of 119903

119903

beyond or below this bracket

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are truly indebted to Enrique Vega AlejandroMartınez Encarnacion Meseguer Luis Garcıa and EduardoCortes for the help and friendly support during the testingcampaign The authors are grateful to Anna Marıa Ballesterfor her kind help on improving the style of the text

References

[1] F Aminzadeh and S Pindado ldquoHow has Spain become a leaderin thewind energy industry during the last decade (An analysisof influential factors on the development of wind energy inSpain)rdquo in Proceedings of the EWEA Annual Event BrusselsBelgium 2011

[2] L Kristensen ldquoCan a cup anemometer ldquounderspeedrdquo A hereti-cal questionrdquo Boundary-Layer Meteorology vol 103 no 1 pp163ndash172 2002

[3] R V Coquilla J Obermeier and B R White ldquoCalibrationprocedures and uncertainty in wind power anemometersrdquoWind Engineering vol 31 no 5 pp 303ndash316 2007

[4] A Albers and H Klug ldquoOpen field cup anemometryrdquo DEWIMagazine vol 19 pp 53ndash58 2001

[5] A Albers H Klug and D Westermann ldquoOutdoor comparisonof cup anemometersrdquo DEWI Magazin vol 17 pp 5ndash15 2000

[6] S Lang and E McKeogh ldquoLIDAR and SODAR measurementsof wind speed and direction in upland terrain for wind energypurposesrdquo Remote Sensing vol 3 no 9 pp 1871ndash1901 2011

[7] R Wagner M Courtney J Gottschall and P Lindelow-Marsden ldquoAccounting for the speed shear in wind turbine

10 The Scientific World Journal

power performance measurementrdquoWind Energy vol 14 no 8pp 993ndash1004 2011

[8] T R Robinson ldquoOn a New Anemometerrdquo Proceedings of theRoyal Irish Academy (1836ndash1869 ) vol 4 pp 566ndash572 1847

[9] International Electrotechnical Commision International Stan-dard IEC-61400-12-1 Wind Turbines Part 12-1 Power Perfor-mance Measurements of Electricity Producing Wind TurbinesFirst Edition 2005ndash12 International Electrotechnical Commi-sion Geneva Switzerland 2005

[10] R V Coquilla and J Obermeier ldquoCalibration speed range forrotating anemometers used in wind energy applicationsrdquo inProceedings of the 46th AIAA Aerospace Sciences Meeting andExhibit pp 2ndash7 January 2008

[11] R V Coquilla A Havner J Obermeier and M SturgeonldquoVerification testing of Sonic anemometer wind speedmeasure-ments for wind energy applicationsrdquo in Proceedings of the 2010American Wind Energy Association Annual Conference (AWEAWINDPOWER rsquo10) pp 1ndash14 2010

[12] L J Fritschen ldquoA sensitive cup-type anemometerrdquo Journal ofApplied Meteorology vol 6 pp 695ndash698 1967

[13] M Sanuki and S Kimura ldquoSome aerodynamic aspects deducedfrom the start and stop experiment of three- and four-cupanemometerrdquo Papers in Meteorology and Geophysics vol 5 pp695ndash698 1954

[14] C F Marvin ldquoA rational theory of the cup anemometerrdquoMonthly Weather Review vol 60 pp 43ndash56 1932

[15] M J Brevoort and U T Joyner ldquoExperimental investigation ofthe Robinson-type cup anemometerrdquo NACA TN-513 1935

[16] C F Marvin ldquoRecent advances in anemometryrdquo MonthlyWeather Review vol 62 pp 115ndash120 1934

[17] C F Marvin ldquoAnemometer testsrdquoMonthlyWeather Review pp58ndash63 1900

[18] H Charnock and F E Pierce ldquoNew housing for the sensitivecup-contact anemometer Mk 1rdquo Journal of Scientific Instru-ments vol 36 no 7 p 329 1959

[19] P A Sheppard ldquoAn improved design of cup anemometerrdquoJournal of Scientific Instruments vol 17 no 9 pp 218ndash221 1940

[20] E L Deacon ldquoReply to two types of sensitive recording cupanemometersrdquo Journal of Scientific Instruments vol 25 no 8p 283 1948

[21] S G Crawford ldquoA simple form of sensitive electric contact cupanemometerrdquo Journal of Scientific Instruments vol 28 no 2 pp36ndash37 1951

[22] F Scrase and P Sheppard ldquoThe errors of cup anemometers influctuating windsrdquo Journal of Scientific Instruments vol 21 no9 pp 160ndash161 1944

[23] E L Deacon ldquoThe over-estimation error of cup anemometersin fluctuating windsrdquo Journal of Scientific Instruments vol 28no 8 pp 231ndash234 1951

[24] L KristensenThe Cup Anemometer and Other Exciting Instru-ments Risoslash-R-615 (EN) Risoslash National Laboratory RoskildeDenmark 1993

[25] MEASNET Cup Anemometer Calibration Procedure Version1 (September 1997 Updated 24112008) MEASNET MadridSpain 1997

[26] MEASNET Anemometer Calibration Procedure Version 2(October 2009) MEASNET Madrid Spain 2009

[27] ASTM International Standard Test Method for Determining thePerformance of a Cup Anemometer or Propeller Anemometer(ASTMD 5096-02) ASTM InternationalWest ConshohockenPa USA 2002

[28] M C-E Brazier ldquoSur la variation des indications desanemometres Robinson et Richard en fonction de lrsquoinclinaisondu ventrdquoComptes Rendus des Seances de LrsquoAcademie des Sciencesvol 170 pp 610ndash612 1920

[29] S Pindado E Vega A Martınez E Meseguer S Franchiniand I P Sarasola ldquoAnalysis of calibration results from cupand propeller anemometers Influence on wind turbine AnnualEnergy Production (AEP) calculationsrdquo Wind Energy vol 14no 1 pp 119ndash132 2011

[30] J Kondo G I Naito and Y Fujinawa ldquoResponse of cupanemometer in turbulencerdquo Journal of theMeteorological Societyof Japan vol 49 pp 63ndash74 1971

[31] S Ramachandran ldquoA theoretical study of cup and vaneanemometersrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 95 no 403 pp 163ndash180 1969

[32] M C-E Brazier ldquoSur la comparabilite des anemometresrdquoComptes Rendus des Seances de LrsquoAcademie des Sciences vol 172pp 843ndash845 1921

[33] O Schrenk ldquoUber die tragheitsfehler des Schalenkreuz-anemometers bei schwankender Windstarkerdquo Zeitschrift FurTechnische Physik vol 10 pp 57ndash66 1929

[34] H W Baynton ldquoErrors in wind run estimates from rotationalanemometersrdquo Bulletin of the American Meteorological Societyvol 57 no 9 pp 1127ndash1130 1976

[35] N E Busch and L Kristensen ldquoCup anemometer overspeed-ingrdquo Journal of AppliedMeteorology vol 15 pp 1328ndash1332 1976

[36] P Frenzen ldquoFast response cup anemometers for atmosphericturbulence researchrdquo in Proceedings of the 8th Symposium onTurbulence and Diffusion pp 112ndash115 1988

[37] E I Kaganov and A M Yaglom ldquoErrors in wind-speed mea-surements by rotation anemometersrdquo Boundary-Layer Meteo-rology vol 10 no 1 pp 15ndash34 1976

[38] J C Wyngaard ldquoCup propeller vane and sonic anemometersin turbulence researchrdquo Annual Review of Fluid Mechanics vol13 pp 399ndash423 1981

[39] P A Coppin ldquoAn examination of cup anemometer overspeed-ingrdquoMeteorologische Rundschau vol 35 pp 1ndash11 1982

[40] J CWyngaard J T Bauman and R A Lynch ldquoCup anemome-ter dynamicsrdquo in Flow Its Measurement and Control in Scienceand Industry vol 1 pp 701ndash708 1974

[41] L Kristensen ldquoCup anemometer behavior in turbulent environ-mentsrdquo Journal of Atmospheric and Oceanic Technology vol 15no 1 pp 5ndash17 1998

[42] R S Hunter ldquoThe accuracy of cup anemometer calibrationwithparticular regard to testing wind turbinesrdquo Wind Engineeringvol 14 no 1 pp 32ndash43 1990

[43] J-A Dahlberg J Gustavsson G Ronsten T F Pedersen US Paulsen and D Westermann Development of A Standard-ised Cup Anemometer Suited to Wind Energy Applications-(ClAsscup) vol 9 Technical University of Denmark LyngbyDenmark 2001

[44] S Pindado J Perez and S Avila-Sanchez ldquoOn cup anemometerrotor aerodynamicsrdquo Sensors vol 12 no 5 pp 6198ndash6217 2012

[45] S Pindado A Sanz and A Wery ldquoDeviation of cup andpropeller anemometer calibration results with air densityrdquoEnergies vol 5 no 3 pp 683ndash701 2012

[46] S Pindado A Barrero-Gil and A Sanz ldquoCup anemome-tersrsquoLoss of performance due to ageing processes and its effecton Annual Energy Production (AEP) estimatesrdquo Energies vol5 no 12 pp 1664ndash1685 2012

The Scientific World Journal 11

[47] J-A Dahlberg T F Pedersen and P Busche ACCUWIND-Methods for Classification of Cup Anemometers Risoslash-R-1555(EN) Risoslash National Laboratory Roskilde Denmark 2006

[48] S Pindado I Perez and M Aguado ldquoFourier analysis ofthe aerodynamic behavior of cup anemometersrdquo MeasurementScience and Technology vol 24 no 6 Article ID 065802 2013

[49] Y P Solovrsquoev A I Korovushkin and Y N Toloknov ldquoCharac-teristics of a cup anemometer and a procedure of measuring thewind velocityrdquo Physical Oceanography vol 14 no 3 pp 173ndash1862004

[50] T F Pedersen Development of A Classification System forCup Anemometers-CLASSCUP Risoslash-R-1348(EN) Risoslash NationalLaboratory Roskilde Denmark 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

The Scientific World Journal 9

K

e h2Rc

1000

950

900

850

800

750

700

650

600

550

500

450

400

000 020 040 060 080 100

(a)

1000

900

800

700

600

500

400

300

200

100

e h2Rc

000 020 040 060 080 100

1205963(

)(b)

Figure 8 Anemometer constant at 16ms wind speed119870 and non-dimensional third harmonic1205963 with regard to the calibrations performed

to the anemometer equipped with elliptical (squares) and porous (circles) cup rotors as a function of the eccentricity 119890 =

radic

1 minus (119887119886)

2 andthe ratio of the hole diameter to the front cup area ℎ2119877

119888 respectively

the anemometer factor that takes into account the averagerotation of the anemometer and the third harmonic termresulting from the Fourier decomposition of the anemometerrotation speed The most relevant conclusions resulting fromthis work are as follows

(i) The average rotation speed is well correlated with thementioned third harmonic term resulting from theFourier decomposition of the anemometer rotationspeed Higher values of this third harmonic termresult in higher anemometer factors and thereforein lower rotational speeds This fact confirms thementioned third harmonic term as a useful parameterto study cup anemometer performance

(ii) Smaller cups with the same ratio of cup diameter tothe cupsrsquo center rotation radius 119903

119903 tend to produce

higher rotational speeds (lower anemometer factors)and lower third harmonic terms

(iii) The ratio of the third harmonic term to the averagerotational speed 120596

3120596

0 is more uniform (within the

wind speed calibration range) for values of the ratioof the cup diameter to the cupsrsquo center rotation radiusranging from 119903

119903= 04 to 119903

119903= 05 than for values of 119903

119903

beyond or below this bracket

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors are truly indebted to Enrique Vega AlejandroMartınez Encarnacion Meseguer Luis Garcıa and EduardoCortes for the help and friendly support during the testingcampaign The authors are grateful to Anna Marıa Ballesterfor her kind help on improving the style of the text

References

[1] F Aminzadeh and S Pindado ldquoHow has Spain become a leaderin thewind energy industry during the last decade (An analysisof influential factors on the development of wind energy inSpain)rdquo in Proceedings of the EWEA Annual Event BrusselsBelgium 2011

[2] L Kristensen ldquoCan a cup anemometer ldquounderspeedrdquo A hereti-cal questionrdquo Boundary-Layer Meteorology vol 103 no 1 pp163ndash172 2002

[3] R V Coquilla J Obermeier and B R White ldquoCalibrationprocedures and uncertainty in wind power anemometersrdquoWind Engineering vol 31 no 5 pp 303ndash316 2007

[4] A Albers and H Klug ldquoOpen field cup anemometryrdquo DEWIMagazine vol 19 pp 53ndash58 2001

[5] A Albers H Klug and D Westermann ldquoOutdoor comparisonof cup anemometersrdquo DEWI Magazin vol 17 pp 5ndash15 2000

[6] S Lang and E McKeogh ldquoLIDAR and SODAR measurementsof wind speed and direction in upland terrain for wind energypurposesrdquo Remote Sensing vol 3 no 9 pp 1871ndash1901 2011

[7] R Wagner M Courtney J Gottschall and P Lindelow-Marsden ldquoAccounting for the speed shear in wind turbine

10 The Scientific World Journal

power performance measurementrdquoWind Energy vol 14 no 8pp 993ndash1004 2011

[8] T R Robinson ldquoOn a New Anemometerrdquo Proceedings of theRoyal Irish Academy (1836ndash1869 ) vol 4 pp 566ndash572 1847

[9] International Electrotechnical Commision International Stan-dard IEC-61400-12-1 Wind Turbines Part 12-1 Power Perfor-mance Measurements of Electricity Producing Wind TurbinesFirst Edition 2005ndash12 International Electrotechnical Commi-sion Geneva Switzerland 2005

[10] R V Coquilla and J Obermeier ldquoCalibration speed range forrotating anemometers used in wind energy applicationsrdquo inProceedings of the 46th AIAA Aerospace Sciences Meeting andExhibit pp 2ndash7 January 2008

[11] R V Coquilla A Havner J Obermeier and M SturgeonldquoVerification testing of Sonic anemometer wind speedmeasure-ments for wind energy applicationsrdquo in Proceedings of the 2010American Wind Energy Association Annual Conference (AWEAWINDPOWER rsquo10) pp 1ndash14 2010

[12] L J Fritschen ldquoA sensitive cup-type anemometerrdquo Journal ofApplied Meteorology vol 6 pp 695ndash698 1967

[13] M Sanuki and S Kimura ldquoSome aerodynamic aspects deducedfrom the start and stop experiment of three- and four-cupanemometerrdquo Papers in Meteorology and Geophysics vol 5 pp695ndash698 1954

[14] C F Marvin ldquoA rational theory of the cup anemometerrdquoMonthly Weather Review vol 60 pp 43ndash56 1932

[15] M J Brevoort and U T Joyner ldquoExperimental investigation ofthe Robinson-type cup anemometerrdquo NACA TN-513 1935

[16] C F Marvin ldquoRecent advances in anemometryrdquo MonthlyWeather Review vol 62 pp 115ndash120 1934

[17] C F Marvin ldquoAnemometer testsrdquoMonthlyWeather Review pp58ndash63 1900

[18] H Charnock and F E Pierce ldquoNew housing for the sensitivecup-contact anemometer Mk 1rdquo Journal of Scientific Instru-ments vol 36 no 7 p 329 1959

[19] P A Sheppard ldquoAn improved design of cup anemometerrdquoJournal of Scientific Instruments vol 17 no 9 pp 218ndash221 1940

[20] E L Deacon ldquoReply to two types of sensitive recording cupanemometersrdquo Journal of Scientific Instruments vol 25 no 8p 283 1948

[21] S G Crawford ldquoA simple form of sensitive electric contact cupanemometerrdquo Journal of Scientific Instruments vol 28 no 2 pp36ndash37 1951

[22] F Scrase and P Sheppard ldquoThe errors of cup anemometers influctuating windsrdquo Journal of Scientific Instruments vol 21 no9 pp 160ndash161 1944

[23] E L Deacon ldquoThe over-estimation error of cup anemometersin fluctuating windsrdquo Journal of Scientific Instruments vol 28no 8 pp 231ndash234 1951

[24] L KristensenThe Cup Anemometer and Other Exciting Instru-ments Risoslash-R-615 (EN) Risoslash National Laboratory RoskildeDenmark 1993

[25] MEASNET Cup Anemometer Calibration Procedure Version1 (September 1997 Updated 24112008) MEASNET MadridSpain 1997

[26] MEASNET Anemometer Calibration Procedure Version 2(October 2009) MEASNET Madrid Spain 2009

[27] ASTM International Standard Test Method for Determining thePerformance of a Cup Anemometer or Propeller Anemometer(ASTMD 5096-02) ASTM InternationalWest ConshohockenPa USA 2002

[28] M C-E Brazier ldquoSur la variation des indications desanemometres Robinson et Richard en fonction de lrsquoinclinaisondu ventrdquoComptes Rendus des Seances de LrsquoAcademie des Sciencesvol 170 pp 610ndash612 1920

[29] S Pindado E Vega A Martınez E Meseguer S Franchiniand I P Sarasola ldquoAnalysis of calibration results from cupand propeller anemometers Influence on wind turbine AnnualEnergy Production (AEP) calculationsrdquo Wind Energy vol 14no 1 pp 119ndash132 2011

[30] J Kondo G I Naito and Y Fujinawa ldquoResponse of cupanemometer in turbulencerdquo Journal of theMeteorological Societyof Japan vol 49 pp 63ndash74 1971

[31] S Ramachandran ldquoA theoretical study of cup and vaneanemometersrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 95 no 403 pp 163ndash180 1969

[32] M C-E Brazier ldquoSur la comparabilite des anemometresrdquoComptes Rendus des Seances de LrsquoAcademie des Sciences vol 172pp 843ndash845 1921

[33] O Schrenk ldquoUber die tragheitsfehler des Schalenkreuz-anemometers bei schwankender Windstarkerdquo Zeitschrift FurTechnische Physik vol 10 pp 57ndash66 1929

[34] H W Baynton ldquoErrors in wind run estimates from rotationalanemometersrdquo Bulletin of the American Meteorological Societyvol 57 no 9 pp 1127ndash1130 1976

[35] N E Busch and L Kristensen ldquoCup anemometer overspeed-ingrdquo Journal of AppliedMeteorology vol 15 pp 1328ndash1332 1976

[36] P Frenzen ldquoFast response cup anemometers for atmosphericturbulence researchrdquo in Proceedings of the 8th Symposium onTurbulence and Diffusion pp 112ndash115 1988

[37] E I Kaganov and A M Yaglom ldquoErrors in wind-speed mea-surements by rotation anemometersrdquo Boundary-Layer Meteo-rology vol 10 no 1 pp 15ndash34 1976

[38] J C Wyngaard ldquoCup propeller vane and sonic anemometersin turbulence researchrdquo Annual Review of Fluid Mechanics vol13 pp 399ndash423 1981

[39] P A Coppin ldquoAn examination of cup anemometer overspeed-ingrdquoMeteorologische Rundschau vol 35 pp 1ndash11 1982

[40] J CWyngaard J T Bauman and R A Lynch ldquoCup anemome-ter dynamicsrdquo in Flow Its Measurement and Control in Scienceand Industry vol 1 pp 701ndash708 1974

[41] L Kristensen ldquoCup anemometer behavior in turbulent environ-mentsrdquo Journal of Atmospheric and Oceanic Technology vol 15no 1 pp 5ndash17 1998

[42] R S Hunter ldquoThe accuracy of cup anemometer calibrationwithparticular regard to testing wind turbinesrdquo Wind Engineeringvol 14 no 1 pp 32ndash43 1990

[43] J-A Dahlberg J Gustavsson G Ronsten T F Pedersen US Paulsen and D Westermann Development of A Standard-ised Cup Anemometer Suited to Wind Energy Applications-(ClAsscup) vol 9 Technical University of Denmark LyngbyDenmark 2001

[44] S Pindado J Perez and S Avila-Sanchez ldquoOn cup anemometerrotor aerodynamicsrdquo Sensors vol 12 no 5 pp 6198ndash6217 2012

[45] S Pindado A Sanz and A Wery ldquoDeviation of cup andpropeller anemometer calibration results with air densityrdquoEnergies vol 5 no 3 pp 683ndash701 2012

[46] S Pindado A Barrero-Gil and A Sanz ldquoCup anemome-tersrsquoLoss of performance due to ageing processes and its effecton Annual Energy Production (AEP) estimatesrdquo Energies vol5 no 12 pp 1664ndash1685 2012

The Scientific World Journal 11

[47] J-A Dahlberg T F Pedersen and P Busche ACCUWIND-Methods for Classification of Cup Anemometers Risoslash-R-1555(EN) Risoslash National Laboratory Roskilde Denmark 2006

[48] S Pindado I Perez and M Aguado ldquoFourier analysis ofthe aerodynamic behavior of cup anemometersrdquo MeasurementScience and Technology vol 24 no 6 Article ID 065802 2013

[49] Y P Solovrsquoev A I Korovushkin and Y N Toloknov ldquoCharac-teristics of a cup anemometer and a procedure of measuring thewind velocityrdquo Physical Oceanography vol 14 no 3 pp 173ndash1862004

[50] T F Pedersen Development of A Classification System forCup Anemometers-CLASSCUP Risoslash-R-1348(EN) Risoslash NationalLaboratory Roskilde Denmark 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 The Scientific World Journal

power performance measurementrdquoWind Energy vol 14 no 8pp 993ndash1004 2011

[8] T R Robinson ldquoOn a New Anemometerrdquo Proceedings of theRoyal Irish Academy (1836ndash1869 ) vol 4 pp 566ndash572 1847

[9] International Electrotechnical Commision International Stan-dard IEC-61400-12-1 Wind Turbines Part 12-1 Power Perfor-mance Measurements of Electricity Producing Wind TurbinesFirst Edition 2005ndash12 International Electrotechnical Commi-sion Geneva Switzerland 2005

[10] R V Coquilla and J Obermeier ldquoCalibration speed range forrotating anemometers used in wind energy applicationsrdquo inProceedings of the 46th AIAA Aerospace Sciences Meeting andExhibit pp 2ndash7 January 2008

[11] R V Coquilla A Havner J Obermeier and M SturgeonldquoVerification testing of Sonic anemometer wind speedmeasure-ments for wind energy applicationsrdquo in Proceedings of the 2010American Wind Energy Association Annual Conference (AWEAWINDPOWER rsquo10) pp 1ndash14 2010

[12] L J Fritschen ldquoA sensitive cup-type anemometerrdquo Journal ofApplied Meteorology vol 6 pp 695ndash698 1967

[13] M Sanuki and S Kimura ldquoSome aerodynamic aspects deducedfrom the start and stop experiment of three- and four-cupanemometerrdquo Papers in Meteorology and Geophysics vol 5 pp695ndash698 1954

[14] C F Marvin ldquoA rational theory of the cup anemometerrdquoMonthly Weather Review vol 60 pp 43ndash56 1932

[15] M J Brevoort and U T Joyner ldquoExperimental investigation ofthe Robinson-type cup anemometerrdquo NACA TN-513 1935

[16] C F Marvin ldquoRecent advances in anemometryrdquo MonthlyWeather Review vol 62 pp 115ndash120 1934

[17] C F Marvin ldquoAnemometer testsrdquoMonthlyWeather Review pp58ndash63 1900

[18] H Charnock and F E Pierce ldquoNew housing for the sensitivecup-contact anemometer Mk 1rdquo Journal of Scientific Instru-ments vol 36 no 7 p 329 1959

[19] P A Sheppard ldquoAn improved design of cup anemometerrdquoJournal of Scientific Instruments vol 17 no 9 pp 218ndash221 1940

[20] E L Deacon ldquoReply to two types of sensitive recording cupanemometersrdquo Journal of Scientific Instruments vol 25 no 8p 283 1948

[21] S G Crawford ldquoA simple form of sensitive electric contact cupanemometerrdquo Journal of Scientific Instruments vol 28 no 2 pp36ndash37 1951

[22] F Scrase and P Sheppard ldquoThe errors of cup anemometers influctuating windsrdquo Journal of Scientific Instruments vol 21 no9 pp 160ndash161 1944

[23] E L Deacon ldquoThe over-estimation error of cup anemometersin fluctuating windsrdquo Journal of Scientific Instruments vol 28no 8 pp 231ndash234 1951

[24] L KristensenThe Cup Anemometer and Other Exciting Instru-ments Risoslash-R-615 (EN) Risoslash National Laboratory RoskildeDenmark 1993

[25] MEASNET Cup Anemometer Calibration Procedure Version1 (September 1997 Updated 24112008) MEASNET MadridSpain 1997

[26] MEASNET Anemometer Calibration Procedure Version 2(October 2009) MEASNET Madrid Spain 2009

[27] ASTM International Standard Test Method for Determining thePerformance of a Cup Anemometer or Propeller Anemometer(ASTMD 5096-02) ASTM InternationalWest ConshohockenPa USA 2002

[28] M C-E Brazier ldquoSur la variation des indications desanemometres Robinson et Richard en fonction de lrsquoinclinaisondu ventrdquoComptes Rendus des Seances de LrsquoAcademie des Sciencesvol 170 pp 610ndash612 1920

[29] S Pindado E Vega A Martınez E Meseguer S Franchiniand I P Sarasola ldquoAnalysis of calibration results from cupand propeller anemometers Influence on wind turbine AnnualEnergy Production (AEP) calculationsrdquo Wind Energy vol 14no 1 pp 119ndash132 2011

[30] J Kondo G I Naito and Y Fujinawa ldquoResponse of cupanemometer in turbulencerdquo Journal of theMeteorological Societyof Japan vol 49 pp 63ndash74 1971

[31] S Ramachandran ldquoA theoretical study of cup and vaneanemometersrdquo Quarterly Journal of the Royal MeteorologicalSociety vol 95 no 403 pp 163ndash180 1969

[32] M C-E Brazier ldquoSur la comparabilite des anemometresrdquoComptes Rendus des Seances de LrsquoAcademie des Sciences vol 172pp 843ndash845 1921

[33] O Schrenk ldquoUber die tragheitsfehler des Schalenkreuz-anemometers bei schwankender Windstarkerdquo Zeitschrift FurTechnische Physik vol 10 pp 57ndash66 1929

[34] H W Baynton ldquoErrors in wind run estimates from rotationalanemometersrdquo Bulletin of the American Meteorological Societyvol 57 no 9 pp 1127ndash1130 1976

[35] N E Busch and L Kristensen ldquoCup anemometer overspeed-ingrdquo Journal of AppliedMeteorology vol 15 pp 1328ndash1332 1976

[36] P Frenzen ldquoFast response cup anemometers for atmosphericturbulence researchrdquo in Proceedings of the 8th Symposium onTurbulence and Diffusion pp 112ndash115 1988

[37] E I Kaganov and A M Yaglom ldquoErrors in wind-speed mea-surements by rotation anemometersrdquo Boundary-Layer Meteo-rology vol 10 no 1 pp 15ndash34 1976

[38] J C Wyngaard ldquoCup propeller vane and sonic anemometersin turbulence researchrdquo Annual Review of Fluid Mechanics vol13 pp 399ndash423 1981

[39] P A Coppin ldquoAn examination of cup anemometer overspeed-ingrdquoMeteorologische Rundschau vol 35 pp 1ndash11 1982

[40] J CWyngaard J T Bauman and R A Lynch ldquoCup anemome-ter dynamicsrdquo in Flow Its Measurement and Control in Scienceand Industry vol 1 pp 701ndash708 1974

[41] L Kristensen ldquoCup anemometer behavior in turbulent environ-mentsrdquo Journal of Atmospheric and Oceanic Technology vol 15no 1 pp 5ndash17 1998

[42] R S Hunter ldquoThe accuracy of cup anemometer calibrationwithparticular regard to testing wind turbinesrdquo Wind Engineeringvol 14 no 1 pp 32ndash43 1990

[43] J-A Dahlberg J Gustavsson G Ronsten T F Pedersen US Paulsen and D Westermann Development of A Standard-ised Cup Anemometer Suited to Wind Energy Applications-(ClAsscup) vol 9 Technical University of Denmark LyngbyDenmark 2001

[44] S Pindado J Perez and S Avila-Sanchez ldquoOn cup anemometerrotor aerodynamicsrdquo Sensors vol 12 no 5 pp 6198ndash6217 2012

[45] S Pindado A Sanz and A Wery ldquoDeviation of cup andpropeller anemometer calibration results with air densityrdquoEnergies vol 5 no 3 pp 683ndash701 2012

[46] S Pindado A Barrero-Gil and A Sanz ldquoCup anemome-tersrsquoLoss of performance due to ageing processes and its effecton Annual Energy Production (AEP) estimatesrdquo Energies vol5 no 12 pp 1664ndash1685 2012

The Scientific World Journal 11

[47] J-A Dahlberg T F Pedersen and P Busche ACCUWIND-Methods for Classification of Cup Anemometers Risoslash-R-1555(EN) Risoslash National Laboratory Roskilde Denmark 2006

[48] S Pindado I Perez and M Aguado ldquoFourier analysis ofthe aerodynamic behavior of cup anemometersrdquo MeasurementScience and Technology vol 24 no 6 Article ID 065802 2013

[49] Y P Solovrsquoev A I Korovushkin and Y N Toloknov ldquoCharac-teristics of a cup anemometer and a procedure of measuring thewind velocityrdquo Physical Oceanography vol 14 no 3 pp 173ndash1862004

[50] T F Pedersen Development of A Classification System forCup Anemometers-CLASSCUP Risoslash-R-1348(EN) Risoslash NationalLaboratory Roskilde Denmark 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

The Scientific World Journal 11

[47] J-A Dahlberg T F Pedersen and P Busche ACCUWIND-Methods for Classification of Cup Anemometers Risoslash-R-1555(EN) Risoslash National Laboratory Roskilde Denmark 2006

[48] S Pindado I Perez and M Aguado ldquoFourier analysis ofthe aerodynamic behavior of cup anemometersrdquo MeasurementScience and Technology vol 24 no 6 Article ID 065802 2013

[49] Y P Solovrsquoev A I Korovushkin and Y N Toloknov ldquoCharac-teristics of a cup anemometer and a procedure of measuring thewind velocityrdquo Physical Oceanography vol 14 no 3 pp 173ndash1862004

[50] T F Pedersen Development of A Classification System forCup Anemometers-CLASSCUP Risoslash-R-1348(EN) Risoslash NationalLaboratory Roskilde Denmark 2003

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of