- Email: [email protected]
Determination of the optimum tilt angle of solar collectors for building applications
ARTICLE IN PRESS
Building and Environment 42 (2007) 779–783 www.elsevier.com/locate/buildenv
Determination of the optimum tilt angle of solar collectors for building applications Huseyin Gunerhan, Arif Hepbasli Faculty of Engineering, Department of Mechanical Engineering, Ege University, 35100 Bornova, Izmir, Turkey Received 25 August 2005; received in revised form 14 September 2005; accepted 15 September 2005
Abstract Solar energy technologies offer a clean, renewable and domestic energy source, and are essential components of a sustainable energy future. This paper deals with the determination of the optimum tilt angle of solar collectors for building applications. The optimum angle is calculated by searching for the values for which the total radiation on the collector surface is a maximum for a particular day or a specific period. An application of the model is done using the experimental data measured for Izmir in Turkey. The best orientation for solar collectors in Izmir is due south. For increasing the utilization efficiency of solar collectors, it is recommended that, if it is possible, the solar collector should be mounted at the monthly average tilt angle and the slope adjusted once a month. r 2005 Elsevier Ltd. All rights reserved. Keywords: Tilt angle; Solar radiation; Solar energy; Solar collector; Solar house; Solar greenhouse; Izmir (Turkey)
1. Introduction Generally, domestic solar water heaters are installed to supply 70–80% of the energy and may reach a value of 90–95% in warm and hot climates [1]. The performance of a solar collector is highly influenced by its orientation and its angle of tilt with the horizontal. This is due to the fact that both the orientation and tilt angle change the solar radiation reaching the surface of the collector. The orientation and tilt angle with horizontal of a solar collector highly influence its performance. Therefore in the design, simulation and operation of solar collectors, it is very essential to know the optimum tilt angle. Optimum tilt angle is applied to a variety of systems, such as flat or parabolic collectors, photovoltaic (PV)-systems, solar houses and solar greenhouses installed in a fixed position. In addition to these, it is crucial in the determination of the Corresponding author. Tel./fax: +90 232 388 85 62.
E-mail addresses: [email protected] (H. Gunerhan), [email protected] (A. Hepbasli). URL: http://bornova.ege.edu.tr/gunerhan. 0360-1323/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2005.09.012
lengths of the shading elements to be placed above the windows in buildings as well as in the right selection of the angles of these elements if they are located angular. Turkey lies in a sunny belt between 361 and 421N latitudes and is geographically well situated with respect to solar energy potential. Turkey’s yearly average total sunshine duration is 2640 h and the yearly average solar radiation is 1311 kWh/m2 yr (3.6 kWh/m2 day). The majority of solar thermal applications in Turkey are in the field of solar heaters, with total annual production capacities of 700,000–1,000,000 m2 between 1998 and 2001. Turkey’s PV market potential is very large due to the suitability of the country for solar radiation and the large availability of the land for solar farms [2]. A number of studies have been carried out by various investigators in order to optimize the tilt angle around the world [1,3–10], while the studies related to Turkey are few in numbers. The main objective of this study is to determine the optimum tilt angle for solar collectors in Izmir, which is located in the western part of Turkey and is the third biggest city in the country by population.
ARTICLE IN PRESS H. Gunerhan, A. Hepbasli / Building and Environment 42 (2007) 779–783
780
I* n
Nomenclature I Ic I1 I2 I3 I4 I5 I6
daily extraterrestrial solar radiation on a tilted surface (J/m2) solar constant (¼ 1373 W=m2 ) daily extraterrestrial solar radiation on an optimum tilt (MJ/m2) daily total solar radiation on an optimum tilt (MJ/m2) daily total solar radiation on a horizontal surface (MJ/m2) daily extraterrestrial solar radiation at latitude (¼ 38:461) (MJ/m2) daily extraterrestrial solar radiation at an angle of 38.461+151 (MJ/m2) daily extraterrestrial solar radiation at an angle of 38.461151 (MJ/m2)
extraterrestrial solar radiation (W/m2) number of the day of the year starting from the first of January (dimensionless)
Greek letters d bopt bopt(m) bopt(y) f g y o or os
solar declination (deg) optimum tilt angle (deg) monthly optimum tilt angle (deg) yearly optimum tilt angle (deg) latitude of site (deg) surface azimuth angle (deg) angle of incidence (deg) hour angle (deg) hour angle for sunrise (deg) hour angle for sunset (deg)
with 2. Methodology The extraterrestrial solar radiation on a tilted surface for a day (I) was calculated from the equation [11,12] Z 24:3600 os n I¼ I cos y do (1) 2p or with 360n n I ¼ I c 1 þ 0:034 cos , 365:25
(2)
where I* is the extraterrestrial solar radiation, Ic the solar constant (¼ 1373 W=m2 ), n the number of the day of the year starting from the first January, y the angle of incidence, or and os are the hour angles for sunrise and sunset, respectively. The angle of incidence of the direct solar radiation on the tilted surface, y and the solar declination, d were estimated by the following equations, respectively [13]: cos y ¼ sin d sin f cos b sin d cos f sin b cos g þ cos d cos f cos b cos o þ cos d sin f sin b cos g cos o þ cos d sin b sin g sin o, 284 þ n d ¼ 23:45 sin 360 . 365
ð3Þ (4)
The hour angles for sunrise (or) and sunset (os) on a south facing (g ¼ 0) tilted surface were computed from the relations, respectively [13]. ) o1 ¼ arccos ½A=ð2BÞ or ¼ max ðo1 ; o2 Þ; o2 ¼ arccos ð tan f tan dÞ os ¼ min ðo1 ; o2 Þ; (5)
A ¼ 2ðsin d sin f cos b sin d cos f sin b cos gÞ ðcos d cos f cos b þ cos d sin f sin b cos gÞ
ð6Þ
and B ¼ ðcos d cos f cos b þ cos d sin f sin b cos gÞ2 þ ðcos d sin b sin gÞ2 .
ð7Þ
In this study, the experimental data measured in the Solar-Meteorological Station of Solar Energy Institute in Ege University over a 3-year period from 1994 to 1996 were used to determine the optimum tilt angle. The specifications of this station are given in detail elsewhere [14]. 3. Results and discussion Based on the analysis presented above, a Fortran 90 computer program was constructed to calculate Eqs. (1)–(7) for Izmir, Turkey (f ¼ 38:461). In this regard, the calculations were made for a south-facing solar collector for 365 days. The tables were prepared for the days of year representing each month. The optimum angle was calculated by searching for the values for which the extraterrestrial solar radiation on the collector surface is a maximum for a particular day or a specific period. The results obtained are shown in Table 1, where the average values for the total solar radiation measured in the SolarMeteorological Station of Solar Energy Institute in Ege University over a 3-year period from 1994 to 1996 are also included. The variation of the optimum tilt according to days of year is shown in Fig. 1, while the variations of daily extraterrestrial solar radiation at various angles are illustrated in Figs. 2–5. In the northern hemisphere, the optimum orientation for solar collectors is south facing. The optimum tilt angle
ARTICLE IN PRESS H. Gunerhan, A. Hepbasli / Building and Environment 42 (2007) 779–783
781
Table 1 Calculated values for the optimum tilt angles according to days of year Months
Day of year
bopt(m) (calculated) (deg)
Daily extraterrestrial solar radiation on an optimum tilt (I1) (calculated) (MJ/m2)
Daily total solar radiation on an optimum tilt (I2) (measured) (MJ/m2)
Daily total solar radiation on a horizontal surface (I3) (calculated) (MJ/m2)
Daily extraterrestrial solar radiation at latitude (I4) (calculated) (MJ/m2)
Daily extraterrestrial solar radiation at an angle of 38.461+151 (I5) (calculated) (MJ/m2)
Daily extraterrestrial solar radiation at an angle of 38.461151 (I6) (calculated) (MJ/m2)
Jan. Feb. Mar. Apr. May June Jul. Aug. Sep. Oct. Nov. Dec.
17 47 75 105 135 162 198 228 258 288 318 344
65.3 56.4 42.2 23.4 06.6 00.0 01.3 16.6 35.0 52.2 63.2 67.4
38.9 38.9 38.1 38.2 40.2 41.9 40.8 38.4 37.5 38.3 38.7 38.6
8.1 16.1 21.0 20.0 25.0 26.7 27.9 22.6 23.0 22.0 9.0 8.8
7.0 12.1 17.9 18.4 24.7 26.6 27.7 22.0 20.0 14.5 7.5 7.1
34.7 37.0 (38.1) 37.0 34.9 33.6 34.1 35.8 (37.4) 37.2 35.2 33.7
(38.1) (38.9) 37.4 33.2 29.0 26.9 27.7 31.2 35.5 (38.3) (38.2) (37.4)
29.0 32.7 36.1 (38.2) (38.7) (38.5) (38.4) (38.2) 36.7 33.6 29.8 27.7
Optimum tilt (˚)
Maximum value.
90 80 70 60 50 40 30 20 10 0 1
29 57 85 113 141 169 197 225 253 281 309 337 365 Day of year
Daily extraterrestrial solar radiation (MJ/m²)
Fig. 1. Variation of the optimum tilt according to days of year.
43 42 42 41 41 40 40 39 39 38 38 37 1
29 57 85 113 141 169 197 225 253 281 309 337 365 Day of year
Fig. 2. Variation of daily extraterrestrial solar radiation on the optimum tilt according to days of year.
varies according to the latitude and the days of year. It is suggested that for the systems, which utilize solar energy throughout the year, the optimum tilt angle (bopt) is taken to be equal to the latitude of the location (f), while for
summer bopt ¼ f þ 151 and for winter bopt ¼ f 151 [1,2–10]. As can be seen from Table 1, the values of the monthly optimum tilt angle, bopt(m) for the months of March and September are approximately equal to the latitude (f ¼ 38:461). For these months, a solar collector tilted at an angle equal to the latitude will receive solar radiation nearly normally. It is also noted from Table 1 that bopt(m) increases towards the beginning and end of the year. This indicates the times when the greatest improvement is made on the amount of solar radiation incident on a solar collector tilted at an optimum angle. Further, the energy loss will occur if we take boptðmÞ ¼ f throughout the year. Therefore the values for bopt(m) given in Table 1 should be taken into account for receiving a maximum amount of solar energy. The values for bopt(m) obtained from the present study were compared to those estimated by the correlations of Nijegorodor et al. [7], who gave a set of 12 relations for any location that lies between a latitude of 601 south to 601 north, as illustrated in Table 2. It may be concluded that the results obtained from the two were in a good agreement. 4. Conclusions The optimum tilt angle plays an important role in enhancing the energy collection of solar collectors. In this study, the optimum values of tilt angles for solar collectors in Izmir, Turkey were determined using the data measured in the Solar-Meteorological Station of Solar Energy Institute in Ege University over a 3-year period from 1994 to 1996.
ARTICLE IN PRESS H. Gunerhan, A. Hepbasli / Building and Environment 42 (2007) 779–783
Daily extraterrestrial solar radiation (MJ/m²)
782
39 38 37 36 35 34 33 1
29
57
85
113
141
169 197 Day of year
225
253
281
309
337
365
Daily extraterrestrial solar radiation (MJ/m²)
Fig. 3. Variation of daily extraterrestrial solar radiation at latitude (38.461) according to days of year.
40 39 38 37 36 35 34 33 32 31 30 29 28 27 1
29
57
85
113
141
169 197 225 Day of year
253
281
309
337
365
Fig. 4. Variation of daily extraterrestrial solar radiation at an angle of 38.461151 according to days of year.
41 Daily extraterrestrial solar radiation (MJ/m²)
39 37 35 33 31 29 27 25 1
29
57
85
113
141
169 197 225 Day of year
253
281
309
337
365
Fig. 5. Variation of daily extraterrestrial solar radiation at an angle of 38.461+151 according to days of year.
The following main conclusions may be drawn from the results of the present study: (a) The best orientation for solar collectors in Izmir is due south. For increasing the utilization efficiency of solar collectors, it is recommended that, if
it is possible, the solar collector should be mounted at the monthly average tilt angle and the slope adjusted once a month, as also denoted by Yakup and Malik [10]. (b) It may also be concluded that the analysis reported here will provide the solar investigators with knowledge
ARTICLE IN PRESS H. Gunerhan, A. Hepbasli / Building and Environment 42 (2007) 779–783
783
Table 2 A comparison of the optimum tilt angles of the present study with those estimated by the correlations of Nijegorodor et al. [7] Months
Day of year
Jan. 17 Feb. 47 Mar. 75 Apr. 105 May 135 June 162 July 198 Aug. 228 Sep. 258 Oct. 288 Nov. 318 Dec. 344 Yearly optimum tilt angle bopt(y)
Using Nijegorodor et al.’s correlations for Izmir [7] bopt(m) (deg)
bopt(m) estimated for Izmir, Turkey (f ¼ 38:461) (deg)
Present study bopt(m) (deg)
0.89f+291 0.97f+171 f+41 f101 0.93f241 0.87f341 0.89f301 0.97f171 f21 f+121 0.93f+251 0.87f+341
63.2 54.3 42.5 28.5 11.8 0.5 4.2 20.3 36.5 50.5 60.8 67.5 36.6
65.3 56.4 42.2 23.4 6.6 0.0 1.3 16.6 35.0 52.2 63.2 67.4 35.8
about optimizing the tilted solar collector systems. This knowledge is also needed for identifying energy efficiency and/or energy conservation opportunities of these systems. References [1] Shariah AM, Al-Akhras A, Al-Omari IA. Optimizing the tilt angle of solar collectors. Renewable Energy 2002;26:587–98. [2] Hepbasli A, Ulgen K, Eke R. Solar energy applications in Turkey. Energy Sources 2004;26:551–61. [3] Lewis G. Optimum tilt of a solar collectors. Solar and Wind Technology 1987;4:407. [4] Saraf GR, Hamad FAW. Optimum tilt angle for a flat plate solar collector. Energy Conversion and Management 1998;28: 185–91. [5] Prasad M, Chandra KS. Optimum tilt of solar collector for maximum natural flow. Energy Conversion and Managememt 1990;30:369–79. [6] Soulayman SSH. On the optimum tilt of solar absorber plates. Renewable Energy 1991;1:551–4.
[7] El-Kassaby MM, Hassab MH. Investigation of a variable tilt angle Australian type solar collector. Renewable Energy 1994;4: 327–32. [8] Nijegorodov N, Devan KRS, Jain PK, Carlsson S. Atmospheric transmittance models and an analytical method to predict the optimum slope on an absorber plate, variously orientated at any latitude. Renewable Energy 1994;4:529. [9] Hussein HMS, Ahmad GE, Mohamad MA. Optimization of operational and design parameters of plane reflector-tilted flat plate solar collector systems. Energy 2000;25:529–42. [10] Yakup MABHM, Malik AQ. Optimum tilt angle and orientation for solar collector in Brunei Darussalam. Renewable Energy 2001;24: 223–34. [11] Atagunduz G. Solar Energy Fundamentals and Applications. Izmir, Turkey: Ege University Press Unit; 1989 [in Turkish]. [12] Goswami DY, Kreith F, Kreider JF. Principles of Solar Engineering. 2nd ed. Philadelphia: Taylor & Francis; 2000. [13] Duffie JA, Beckman WA. Solar Engineering of Thermal Processes. 2nd ed. New York: Wiley; 1991. [14] Ulgen K, Hepbasli A. Comparison of solar radiation correlations for Izmir, Turkey. International Journal of Energy Research 2002;3(26): 413–30.
Building and Environment 42 (2007) 779–783 www.elsevier.com/locate/buildenv
Determination of the optimum tilt angle of solar collectors for building applications Huseyin Gunerhan, Arif Hepbasli Faculty of Engineering, Department of Mechanical Engineering, Ege University, 35100 Bornova, Izmir, Turkey Received 25 August 2005; received in revised form 14 September 2005; accepted 15 September 2005
Abstract Solar energy technologies offer a clean, renewable and domestic energy source, and are essential components of a sustainable energy future. This paper deals with the determination of the optimum tilt angle of solar collectors for building applications. The optimum angle is calculated by searching for the values for which the total radiation on the collector surface is a maximum for a particular day or a specific period. An application of the model is done using the experimental data measured for Izmir in Turkey. The best orientation for solar collectors in Izmir is due south. For increasing the utilization efficiency of solar collectors, it is recommended that, if it is possible, the solar collector should be mounted at the monthly average tilt angle and the slope adjusted once a month. r 2005 Elsevier Ltd. All rights reserved. Keywords: Tilt angle; Solar radiation; Solar energy; Solar collector; Solar house; Solar greenhouse; Izmir (Turkey)
1. Introduction Generally, domestic solar water heaters are installed to supply 70–80% of the energy and may reach a value of 90–95% in warm and hot climates [1]. The performance of a solar collector is highly influenced by its orientation and its angle of tilt with the horizontal. This is due to the fact that both the orientation and tilt angle change the solar radiation reaching the surface of the collector. The orientation and tilt angle with horizontal of a solar collector highly influence its performance. Therefore in the design, simulation and operation of solar collectors, it is very essential to know the optimum tilt angle. Optimum tilt angle is applied to a variety of systems, such as flat or parabolic collectors, photovoltaic (PV)-systems, solar houses and solar greenhouses installed in a fixed position. In addition to these, it is crucial in the determination of the Corresponding author. Tel./fax: +90 232 388 85 62.
E-mail addresses: [email protected] (H. Gunerhan), [email protected] (A. Hepbasli). URL: http://bornova.ege.edu.tr/gunerhan. 0360-1323/$ - see front matter r 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.buildenv.2005.09.012
lengths of the shading elements to be placed above the windows in buildings as well as in the right selection of the angles of these elements if they are located angular. Turkey lies in a sunny belt between 361 and 421N latitudes and is geographically well situated with respect to solar energy potential. Turkey’s yearly average total sunshine duration is 2640 h and the yearly average solar radiation is 1311 kWh/m2 yr (3.6 kWh/m2 day). The majority of solar thermal applications in Turkey are in the field of solar heaters, with total annual production capacities of 700,000–1,000,000 m2 between 1998 and 2001. Turkey’s PV market potential is very large due to the suitability of the country for solar radiation and the large availability of the land for solar farms [2]. A number of studies have been carried out by various investigators in order to optimize the tilt angle around the world [1,3–10], while the studies related to Turkey are few in numbers. The main objective of this study is to determine the optimum tilt angle for solar collectors in Izmir, which is located in the western part of Turkey and is the third biggest city in the country by population.
ARTICLE IN PRESS H. Gunerhan, A. Hepbasli / Building and Environment 42 (2007) 779–783
780
I* n
Nomenclature I Ic I1 I2 I3 I4 I5 I6
daily extraterrestrial solar radiation on a tilted surface (J/m2) solar constant (¼ 1373 W=m2 ) daily extraterrestrial solar radiation on an optimum tilt (MJ/m2) daily total solar radiation on an optimum tilt (MJ/m2) daily total solar radiation on a horizontal surface (MJ/m2) daily extraterrestrial solar radiation at latitude (¼ 38:461) (MJ/m2) daily extraterrestrial solar radiation at an angle of 38.461+151 (MJ/m2) daily extraterrestrial solar radiation at an angle of 38.461151 (MJ/m2)
extraterrestrial solar radiation (W/m2) number of the day of the year starting from the first of January (dimensionless)
Greek letters d bopt bopt(m) bopt(y) f g y o or os
solar declination (deg) optimum tilt angle (deg) monthly optimum tilt angle (deg) yearly optimum tilt angle (deg) latitude of site (deg) surface azimuth angle (deg) angle of incidence (deg) hour angle (deg) hour angle for sunrise (deg) hour angle for sunset (deg)
with 2. Methodology The extraterrestrial solar radiation on a tilted surface for a day (I) was calculated from the equation [11,12] Z 24:3600 os n I¼ I cos y do (1) 2p or with 360n n I ¼ I c 1 þ 0:034 cos , 365:25
(2)
where I* is the extraterrestrial solar radiation, Ic the solar constant (¼ 1373 W=m2 ), n the number of the day of the year starting from the first January, y the angle of incidence, or and os are the hour angles for sunrise and sunset, respectively. The angle of incidence of the direct solar radiation on the tilted surface, y and the solar declination, d were estimated by the following equations, respectively [13]: cos y ¼ sin d sin f cos b sin d cos f sin b cos g þ cos d cos f cos b cos o þ cos d sin f sin b cos g cos o þ cos d sin b sin g sin o, 284 þ n d ¼ 23:45 sin 360 . 365
ð3Þ (4)
The hour angles for sunrise (or) and sunset (os) on a south facing (g ¼ 0) tilted surface were computed from the relations, respectively [13]. ) o1 ¼ arccos ½A=ð2BÞ or ¼ max ðo1 ; o2 Þ; o2 ¼ arccos ð tan f tan dÞ os ¼ min ðo1 ; o2 Þ; (5)
A ¼ 2ðsin d sin f cos b sin d cos f sin b cos gÞ ðcos d cos f cos b þ cos d sin f sin b cos gÞ
ð6Þ
and B ¼ ðcos d cos f cos b þ cos d sin f sin b cos gÞ2 þ ðcos d sin b sin gÞ2 .
ð7Þ
In this study, the experimental data measured in the Solar-Meteorological Station of Solar Energy Institute in Ege University over a 3-year period from 1994 to 1996 were used to determine the optimum tilt angle. The specifications of this station are given in detail elsewhere [14]. 3. Results and discussion Based on the analysis presented above, a Fortran 90 computer program was constructed to calculate Eqs. (1)–(7) for Izmir, Turkey (f ¼ 38:461). In this regard, the calculations were made for a south-facing solar collector for 365 days. The tables were prepared for the days of year representing each month. The optimum angle was calculated by searching for the values for which the extraterrestrial solar radiation on the collector surface is a maximum for a particular day or a specific period. The results obtained are shown in Table 1, where the average values for the total solar radiation measured in the SolarMeteorological Station of Solar Energy Institute in Ege University over a 3-year period from 1994 to 1996 are also included. The variation of the optimum tilt according to days of year is shown in Fig. 1, while the variations of daily extraterrestrial solar radiation at various angles are illustrated in Figs. 2–5. In the northern hemisphere, the optimum orientation for solar collectors is south facing. The optimum tilt angle
ARTICLE IN PRESS H. Gunerhan, A. Hepbasli / Building and Environment 42 (2007) 779–783
781
Table 1 Calculated values for the optimum tilt angles according to days of year Months
Day of year
bopt(m) (calculated) (deg)
Daily extraterrestrial solar radiation on an optimum tilt (I1) (calculated) (MJ/m2)
Daily total solar radiation on an optimum tilt (I2) (measured) (MJ/m2)
Daily total solar radiation on a horizontal surface (I3) (calculated) (MJ/m2)
Daily extraterrestrial solar radiation at latitude (I4) (calculated) (MJ/m2)
Daily extraterrestrial solar radiation at an angle of 38.461+151 (I5) (calculated) (MJ/m2)
Daily extraterrestrial solar radiation at an angle of 38.461151 (I6) (calculated) (MJ/m2)
Jan. Feb. Mar. Apr. May June Jul. Aug. Sep. Oct. Nov. Dec.
17 47 75 105 135 162 198 228 258 288 318 344
65.3 56.4 42.2 23.4 06.6 00.0 01.3 16.6 35.0 52.2 63.2 67.4
38.9 38.9 38.1 38.2 40.2 41.9 40.8 38.4 37.5 38.3 38.7 38.6
8.1 16.1 21.0 20.0 25.0 26.7 27.9 22.6 23.0 22.0 9.0 8.8
7.0 12.1 17.9 18.4 24.7 26.6 27.7 22.0 20.0 14.5 7.5 7.1
34.7 37.0 (38.1) 37.0 34.9 33.6 34.1 35.8 (37.4) 37.2 35.2 33.7
(38.1) (38.9) 37.4 33.2 29.0 26.9 27.7 31.2 35.5 (38.3) (38.2) (37.4)
29.0 32.7 36.1 (38.2) (38.7) (38.5) (38.4) (38.2) 36.7 33.6 29.8 27.7
Optimum tilt (˚)
Maximum value.
90 80 70 60 50 40 30 20 10 0 1
29 57 85 113 141 169 197 225 253 281 309 337 365 Day of year
Daily extraterrestrial solar radiation (MJ/m²)
Fig. 1. Variation of the optimum tilt according to days of year.
43 42 42 41 41 40 40 39 39 38 38 37 1
29 57 85 113 141 169 197 225 253 281 309 337 365 Day of year
Fig. 2. Variation of daily extraterrestrial solar radiation on the optimum tilt according to days of year.
varies according to the latitude and the days of year. It is suggested that for the systems, which utilize solar energy throughout the year, the optimum tilt angle (bopt) is taken to be equal to the latitude of the location (f), while for
summer bopt ¼ f þ 151 and for winter bopt ¼ f 151 [1,2–10]. As can be seen from Table 1, the values of the monthly optimum tilt angle, bopt(m) for the months of March and September are approximately equal to the latitude (f ¼ 38:461). For these months, a solar collector tilted at an angle equal to the latitude will receive solar radiation nearly normally. It is also noted from Table 1 that bopt(m) increases towards the beginning and end of the year. This indicates the times when the greatest improvement is made on the amount of solar radiation incident on a solar collector tilted at an optimum angle. Further, the energy loss will occur if we take boptðmÞ ¼ f throughout the year. Therefore the values for bopt(m) given in Table 1 should be taken into account for receiving a maximum amount of solar energy. The values for bopt(m) obtained from the present study were compared to those estimated by the correlations of Nijegorodor et al. [7], who gave a set of 12 relations for any location that lies between a latitude of 601 south to 601 north, as illustrated in Table 2. It may be concluded that the results obtained from the two were in a good agreement. 4. Conclusions The optimum tilt angle plays an important role in enhancing the energy collection of solar collectors. In this study, the optimum values of tilt angles for solar collectors in Izmir, Turkey were determined using the data measured in the Solar-Meteorological Station of Solar Energy Institute in Ege University over a 3-year period from 1994 to 1996.
ARTICLE IN PRESS H. Gunerhan, A. Hepbasli / Building and Environment 42 (2007) 779–783
Daily extraterrestrial solar radiation (MJ/m²)
782
39 38 37 36 35 34 33 1
29
57
85
113
141
169 197 Day of year
225
253
281
309
337
365
Daily extraterrestrial solar radiation (MJ/m²)
Fig. 3. Variation of daily extraterrestrial solar radiation at latitude (38.461) according to days of year.
40 39 38 37 36 35 34 33 32 31 30 29 28 27 1
29
57
85
113
141
169 197 225 Day of year
253
281
309
337
365
Fig. 4. Variation of daily extraterrestrial solar radiation at an angle of 38.461151 according to days of year.
41 Daily extraterrestrial solar radiation (MJ/m²)
39 37 35 33 31 29 27 25 1
29
57
85
113
141
169 197 225 Day of year
253
281
309
337
365
Fig. 5. Variation of daily extraterrestrial solar radiation at an angle of 38.461+151 according to days of year.
The following main conclusions may be drawn from the results of the present study: (a) The best orientation for solar collectors in Izmir is due south. For increasing the utilization efficiency of solar collectors, it is recommended that, if
it is possible, the solar collector should be mounted at the monthly average tilt angle and the slope adjusted once a month, as also denoted by Yakup and Malik [10]. (b) It may also be concluded that the analysis reported here will provide the solar investigators with knowledge
ARTICLE IN PRESS H. Gunerhan, A. Hepbasli / Building and Environment 42 (2007) 779–783
783
Table 2 A comparison of the optimum tilt angles of the present study with those estimated by the correlations of Nijegorodor et al. [7] Months
Day of year
Jan. 17 Feb. 47 Mar. 75 Apr. 105 May 135 June 162 July 198 Aug. 228 Sep. 258 Oct. 288 Nov. 318 Dec. 344 Yearly optimum tilt angle bopt(y)
Using Nijegorodor et al.’s correlations for Izmir [7] bopt(m) (deg)
bopt(m) estimated for Izmir, Turkey (f ¼ 38:461) (deg)
Present study bopt(m) (deg)
0.89f+291 0.97f+171 f+41 f101 0.93f241 0.87f341 0.89f301 0.97f171 f21 f+121 0.93f+251 0.87f+341
63.2 54.3 42.5 28.5 11.8 0.5 4.2 20.3 36.5 50.5 60.8 67.5 36.6
65.3 56.4 42.2 23.4 6.6 0.0 1.3 16.6 35.0 52.2 63.2 67.4 35.8
about optimizing the tilted solar collector systems. This knowledge is also needed for identifying energy efficiency and/or energy conservation opportunities of these systems. References [1] Shariah AM, Al-Akhras A, Al-Omari IA. Optimizing the tilt angle of solar collectors. Renewable Energy 2002;26:587–98. [2] Hepbasli A, Ulgen K, Eke R. Solar energy applications in Turkey. Energy Sources 2004;26:551–61. [3] Lewis G. Optimum tilt of a solar collectors. Solar and Wind Technology 1987;4:407. [4] Saraf GR, Hamad FAW. Optimum tilt angle for a flat plate solar collector. Energy Conversion and Management 1998;28: 185–91. [5] Prasad M, Chandra KS. Optimum tilt of solar collector for maximum natural flow. Energy Conversion and Managememt 1990;30:369–79. [6] Soulayman SSH. On the optimum tilt of solar absorber plates. Renewable Energy 1991;1:551–4.
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