Research Article

Mathematical Analysis of the Effect of Rotor Geometry on Cup Anemometer Response

Table 1

Research carried out on cup anemometer behavior/performances. References classified by areas of study and research. Some references regarding applications have also been included.

ResearchMathematical modelExperimental research

Static and dynamic response
Aerodynamic force on the cups; shape of the anemometer(i) Schrenk 1929 [28]
(ii) Ramachandran 1969 [23]
(iii) Kondo et al. 1971 [24]
(iv) Dahlberg et al. 2001 [8]
(v) Winkel et al. 2007 [29]
(vi) Pindado et al. 2012 [21]
(vii) Pindado et al. 2013 [22]
(viii) Potsdam et al. 2013 [30]
(i) Patterson 1926 [31]
(ii) Schrenk 1929 [28]
(iii) Pinkerton 1930 [32]
(iv) Hubbard and Brescoll 1934 [33]
(v) Brevoort and Joyner 1935 [27]
(vi) Fergusson 1939 [34]
(vii) Albright and Klein 1941 [35]
(viii) Fritschen 1967 [36]
(ix) Ramachandran 1969 [23]
(x) Kondo et al. 1971 [24]
(xi) Lindley 1975 [37]
(xii) Lockhart 1985 [38]
(xiii) Pedersen and Paulsen 1999 [39]
(xiv) Dahlberg et al. 2001 [8]
(xv) Hunter et al. 2003 [40]
(xvi) Winkel et al. 2007 [29]
(xvii) Pindado et al. 2011 [20]
(xviii) Pindado et al. 2012 [21]
(xix) Pindado et al. 2013 [22]
(xx) Pindado et al. 2013 [4]

Average rotational speed estimation; vertical component of the wind speed; overspeeding. turbulence(i) Schrenk 1929 [28]
(ii) Scrase and Sheppard 1944 [41]
(iii) Sanuki 1952 [42]
(iv) Ramachandran 1969 [23]
(v) Ramachandran 1969 [43]
(vi) Torochkov and Surazhskiy 1969 [44]
(vii) Acheson 1970 [45]
(viii) Kondo et al. 1971 [24]
(ix) Hyson 1972 [15]
(x) Wyngaard et al. 1974 [13]
(xi) Kaganov and Yaglom 1976 [11]
(xii) Busch and Kristensen 1976 [18]
(xiii) Busch et al. 1980 [46]
(xiv) Wyngaard 1981 [14]
(xv) Coppin 1982 [16]
(xvi) Hayashi 1987 [47]
(xvii) Frenzen 1988 [48]
(xviii) Snow et al. 1989 [49]
(xix) Chang and Frenzen 1990 [17]
(xx) Hunter 1990 [50]
(xxi) Skarstein et al. 1992 [51]
(xxii) Kristensen 1993 [52]
(xxiii) Kristensen 1994 [53]
(xxiv) Fabian 1995 [54]
(xxv) Westermann 1996 [55]
(xxvi) Kristensen 1998 [19]
(xxvii) Hristov et al. 2000 [56]
(xxviii) Kristensen 2000 [57]
(xxix) Dahlberg et al. 2001 [8]
(xxx) Kristensen 2002 [3]
(xxxi) Kristensen and Hansen 2002 [58]
(xxxii) Pedersen 2003 [10]
(xxxiii) Kristensen et al. 2003 [59]
(xxxiv) Pedersen 2004 [60]
(xxxv) Solov’ev et al. 2004 [12]
(xxxvi) Yahaya and Frangi 2004 [61]
(xxxvii) Kristensen and Hansen 2005 [62]
(xxxviii) Dahlberg et al. 2006 [9]
(xxxix) Bégin-Drolet et al. 2011 [63]
(xl) Pindado et al. 2012 [21]
(xli) Bégin-Drolet et al. 2013 [64]
(i) Brazier 1921 [65]
(ii) Schrenk 1929 [28]
(iii) Marvin 1932 [66]
(iv) Marvin 1934 [67]
(v) Spilhaus and Rossby 1934 [68]
(vi) Brevoort and Joyner 1935 [27]
(vii) Fergusson 1939 [34]
(viii) Scrase and Sheppard 1944 [41]
(ix) Deacon 1951 [69]
(x) MacCready 1966 [70]
(xi) Bernstein 1967 [71]
(xii) Izumi and Barad 1970 [72]
(xiii) Camp et al. 1970 [73]
(xiv) Kondo et al. 1971 [24]
(xv) Hyson 1972 [15]
(xvi) Lindley and Bowen 1974 [74]
(xvii) Wyngaard et al. 1974 [13]
(xviii) Lindley 1975 [37]
(xix) Baynton 1976 [75]
(xx) Busch et al. 1980 [46]
(xxi) Coppin 1982 [16]
(xxii) Hayashi 1987 [47]
(xxiii) Hunter 1990 [50]
(xxiv) Morris et al. 1992 [76]
(xxv) Fabian 1995 [54]
(xxvi) Westermann 1996 [55]
(xxvii) Kristensen 2000 [57]
(xxviii) Dahlberg et al. 2001 [8]
(xxix) Pedersen 2003 [10]
(xxx) Hunter et al. 2003 [40]
(xxxi) Pedersen 2004 [60]
(xxxii) Solov’ev et al. 2004 [12]
(xxxiii) Pedersen and Paulsen 1999 [39]
(xxxiv) Kristensen 2002 [58]
(xxxv) Yahaya and Frangi 2004 [61]
(xxxvi) Dahlberg et al. 2006 [9]
(xxxvii) Pedersen et al. 2006 [77]
(xxxviii) Bégin-Drolet et al. 2011 [63]
(xxxix) Pindado et al. 2012 [21]
(xl) Bégin-Drolet et al. 2013 [64]
(xli) Pindado et al. 2013 [22]
(xlii) Pindado et al. 2013 [4]

Effect of bearings system; friction.(i) Fabian 1995 [54]
(ii) Pedersen and Paulsen 1999 [39]
(iii) Dahlberg et al. 2001 [8]
(iv) Pedersen 2003 [10]
(v) Pedersen 2004 [60]
(vi) Dahlberg et al. 2006 [9]
(i) Baynton 1976 [75]
(ii) Fabian 1995 [54]
(iii) Pedersen and Paulsen 1999 [39]
(iv) Dahlberg et al. 2001 [8]
(v) Pedersen 2003 [10]
(vi) Pedersen 2004 [60]
(vii) Dahlberg et al. 2006 [9]
(viii) Pedersen et al. 2006 [77]

Performance degradation(i) Siegel and Lee 2011 [78]
(ii) Cassity et al. 2012 [79]
(iii) Sun et al. 2012 [80]
(i) Zlatanovic and Zlatanovic 2012 [81]
(ii) Pindado et al. 2012 [82]

Output signal post-processing
Sampling; filtering; correction of the measured velocity(i) Wieringa 1980 [83]
(ii) Wyngaard et al. 1982 [84]
(iii) Moore 1986 [85]
(iv) Hayashi 1987 [47]
(v) Skarstein et al. 1992 [51]
(vi) Ebert et al. 1995 [86]
(vii) Barnard et al. 1998 [87]
(viii) Hristov et al. 2000 [56]
(ix) Kristensen et al. 2003 [59]
(x) Selyaninov 2004 [88]
(xi) Solov’ev et al. 2004 [12]
(xii) Yahaya and Frangi 2004 [61]
(xiii) Siegel and Lee 2011 [78]
(xiv) Bégin-Drolet et al. 2013 [64]
(i) Bernstein 1967 [71]
(ii) Wieringa 1980 [83]
(iii) Wyngaard et al. 1982 [84]
(iv) Hayashi 1987 [47]
(v) Ebert et al. 1995 [86]
(vi) Solov’ev et al. 2004 [12]
(vii) Yahaya and Frangi 2004 [61]
(viii) Bégin-Drolet et al. 2013 [64]

Performance on the field
Climatic conditions (change of air density, rain, ice, extreme weather conditions, etc.)(i) Dentler 1978 [89]
(ii) Fortin et al. 2005 [90]
(i) Gates and Thompson 1986 [91]
(ii) Kimura et al. 2001 [92]
(iii) Makkonen et al. [93]
(iv) Fortin et al. 2005 [90]
(v) Pindado et al. 2012 [94]
(vi) Hobby et al. 2013 [95]

Anemometer allocation on towers(i) Wieringa 1980 [83]
(ii) Wyngaard 1981 [96]
(iii) Wyngaard et al. 1982 [84]
(iv) Hansen and Pedersen 1999 [97]
(v) Lubitz 2009 [98]
(i) Izumi and Barad 1970 [72]
(ii) Burt 1975 [99]
(iii) Wieringa 1980 [83]
(iv) Wyngaard et al. 1982 [84]
(v) Morris et al. 1992 [76]
(vi) Pedersen et al. 1992 [100]
(vii) Hunter et al. 2003 [40]
(viii) Orlando et al. 2011 [101]
(ix) Farrugia and Sant 2013 [102]

Performance on the field; recalibration on the field; comparison with Lidar and Sodar (and other instruments)(i) Kristensen et al. 1991 [103]
(ii) Siegel and Lee 2011 [78]
(iii) Cassity et al. 2012 [79]
(iv) Sun et al. 2012 [80]
(i) Camp 1966 [104]
(ii) Kristensen et al. 1991 [103]
(iii) Petersen et al. 1998 [105]
(iv) Albers et al. 2000 [7]
(v) Albers and Klug 2001 [6]
(vi) Papadopoulos et al. 2001 [106]
(vii) Hunter et al. 2001 [107]
(viii) Paulsen et al. 2007 [108]
(ix) Wagner et al. 2011 [109]
(x) Lang and McKeogh 2011 [110]
(xi) Bradley 2013 [111]
(xii) Hasager et al. 2013 [112]
(xiii) Sanz Rodrigo et al. 2013 [113]

Wind tunnel testing and calibration
Description; procedure; uncertainties(i) Robinson 1878 [114]
(ii) Robinson 1880 [115]
(iii) Brazier 1920 [116]
(iv) Hunter 1990 [50]
(v) López Peña and Duro 2003 [117]
(vi) Eecen and De Noord 2005 [118]
(vii) Coquilla et al. 2007 [2]
(viii) Piccato et al. 2010 [119]
(ix) Piccato et al. 2011 [120]
(x) Coquilla 2012 [121]
(i) Robinson 1878 [114]
(ii) Robinson 1880 [115]
(iii) Brazier 1920 [116]
(iv) Camp 1966 [104]
(v) Baynton 1976 [75]
(vi) Lockhart 1985 [38]
(vii) Lockhart 1987 [122]
(viii) Gates and Thompson 1986 [91]
(ix) Hunter 1990 [50]
(x) Makkonen and Helle 1994 [123]
(xi) Fabian 1995 [54]
(xii) MEASNET 1997 [26]
(xiii) Pedersen and Paulsen 1999 [39]
(xiv) Hunter et al. 2001 [107]
(xv) ASTM International 2002 [124]
(xvi) Hunter et al. 2003 [40]
(xvii) Eecen and De Noord 2005 [118]
(xviii) International Electrotechnical Commision 2005 [5]
(xix) Dahlberg 2006 [125]
(xx) Coquilla et al. 2007 [2]
(xxi) Coquilla and Obermeier 2008 [126]
(xxii) MEASNET 2009 [25]
(xxiii) Piccato et al. 2010 [119]
(xxiv) Pindado et al. 2011 [20]
(xxv) Piccato et al. 2011 [120]
(xxvi) Westermann et al. 2011 [127]
(xxvii) Hansen et al. 2012 [128]
(xxviii) Coquilla 2012 [121]
(xxix) Gkanias and Katsanevakis 2012 [129]

Instrumentation(i) McBean 1972 [130]
(ii) Sheppard et al. 1972 [131]
(iii) Lockhart 1985 [38]
(iv) Moore 1986 [85]
(i) Sheppard et al. 1972 [131]
(ii) Hobby et al. 2013 [95]

Design and performance
Design; anemometer classification(i) Pedersen and Paulsen 1999 [39]
(ii) Kristensen 2002 [58]
(iii) Pedersen 2003 [10]
(iv) Pedersen 2004 [60]
(v) Dahlberg et al. 2006 [9]
(vi) Pindado et al. 2013 [22]
(i) Frenzen 1968 [132]
(ii) Wellman 1968 [133]
(iii) Mazzarella 1972 [134]
(iv) Lindley 1975 [37]
(v) Pedersen and Paulsen 1999 [39]
(vi) Dahlberg et al. 2001 [8]
(vii) Kristensen 2002 [58]
(viii) Pedersen 2003 [10]
(ix) Pedersen 2004 [60]
(x) Dahlberg et al. 2006 [9]
(xi) Pedersen et al. 2006 [77]
(xii) Choon et al. 2012 [135]
(xiii) Pindado et al. 2013 [22]