World estimates of PV optimal tilt angles and ratios of ...
Solar Energy 169 (2018) 55?66
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World estimates of PV optimal tilt angles and ratios of sunlight incident T
upon tilted and tracked PV panels relative to horizontal panels
Mark Z. Jacobson, Vijaysinh Jadhav
Department of Civil and Environmental Engineering, Stanford University, Stanford, CA 94305-4020, USA
ARTICLE INFO
Keywords: Solar photovoltaics Tracking Optimal tilt Solar radiation
ABSTRACT
This study provides estimates of photovoltaic (PV) panel optimal tilt angles for all countries worldwide. It then estimates the incident solar radiation normal to either tracked or optimally tilted panels relative to horizontal panels globally. Optimal tilts are derived from the National Renewable Energy Laboratory's PVWatts program. A simple 3rd-order polynomial fit of optimal tilt versus latitude is derived. The fit matches data better above 40? N latitude than do previous linear fits. Optimal tilts are then used in the global 3-D GATOR-GCMOM model to estimate annual ratios of incident radiation normal to optimally tilted, 1-axis vertically tracked (swiveling vertically around a horizontal axis), 1-axis horizontally tracked (at optimal tilt and swiveling horizontally around a vertical axis), and 2-axis tracked panels relative to horizontal panels in 2050. Globally- and annuallyaveraged, these ratios are 1.19, 1.22, 1.35, and 1.39, respectively. 1-axis horizontal tracking differs from 2-axis tracking, annually averaged, by only 1?3% at most all latitudes. 1-axis horizontal tracking provides much more output than 1-axis vertical tracking below 65? N and S, whereas output is similar elsewhere. Tracking provides little benefit over optimal tilting above 75? N and 60? S. Tilting and tracking benefits generally increase with increasing latitude. In fact, annually averaged, more sunlight reach tilted or tracked panels from 80 to 90? S than any other latitude. Tilting and tracking benefit cities of the same latitude with lesser aerosol and cloud cover. In sum, for optimal utility PV output, 1-axis horizontal tracking is recommended, except for the highest latitudes, where optimal tilting is sufficient. However, decisions about panel configuration also require knowing tracking equipment and land costs, which are not evaluated here. Installers should also calculate optimal tilt angles for their location for more accuracy. Models that ignore optimal tilting for rooftop PV and utility PV tracking may underestimate significantly country or world PV potential.
1. Introduction
Global solar photovoltaic (PV) installations on rooftops and in power plants are growing rapidly and will grow further as the world transitions from fossil fuels to clean, renewable energy (Jacobson et al., 2017). A critical parameter for installing fixed-tilt panels is the tilt angle, since PV panel output increases with increasing exposure to direct sunlight. Energy modelers also need to know the optimal tilt angle of a panel for calculating regional or global PV output in a given location or worldwide.
Another issue for installers and modelers is whether 1-axis vertical tracked PV panels (panels that face south or north and swivel vertically around a horizontal axis) receive more incident radiation than 1-axis horizontal tracked panels (panels at optimal tilt angle that swivel horizontally around a vertical axis), and the extent to which incident radiation to 1-axis- and 2-axis-tracked panels (which combine 1-axis vertical and horizontal tracking capabilities to follow the sun perfectly
during the day) exceeds that of optimally tilted panels. Finally, because global and regional weather and climate models almost all calculate radiative transfer assuming that radiation impinges on horizontal surfaces, energy modelers also need estimates of the ratio of incident solar radiation to panels that track the sun or are optimally-tilted to that of panels that are placed horizontally on a flat surface.
This study first provides estimates of optimal tilt angles derived from the NREL PVWatts program (NREL, 2017) at 1?4 sites in each country of the world. These optimal tilt angles are representative of assumed historic meteorological conditions near a given site, so are only approximate. Although installers would need to make more precise calculations at each site, the results provided here are still useful rough estimates. The study then provides convenient albeit rough polynomial fits to the PVWatts data of the optimal tilt angle as a function of latitude for both the Northern and Southern Hemispheres. The optimal tilt data by country and by latitude are then input into a global climate model, GATOR-GCMOM for year 2050 meteorological and air quality
Corresponding author. E-mail address: jacobson@stanford.edu (M.Z. Jacobson).
Received 18 December 2017; Received in revised form 4 April 2018; Accepted 13 April 2018 0038-092X/ ? 2018 Elsevier Ltd. All rights reserved.
M.Z. Jacobson, V. Jadhav
Solar Energy 169 (2018) 55?66
conditions, to provide ratios of incident solar radiation normal to an optimally tilted, 1-axis vertically-tracked, 1-axis horizontally-tracked, and 2-axis tracked PV panel relative to a horizontal panel.
The reasons for using GATOR-GCMOM rather than PVWatts for the global calculations are (1) GATOR-GCMOM covers the entire world, whereas PVWatts covers locations only near specific meteorological stations, (2) GATOR-GCMOM is used here to examine a future 2050 scenario, where aerosol, cloud, temperature, and wind speed properties differ from today, whereas PVWatts treats only past conditions, and (3) we want to use GATOR-GCMOM to calculate incident solar radiation for the two components of 1-axis horizontal tracking that, when combined, exactly comprise the components of 2-axis tracking, and this cannot be done with current PVWatts output. Specifically, one way for a panel to follow the sun exactly throughout the day (2-axis tracking), is for the panel to swivel horizontally around a vertical axis and, independently, swivel vertically around a horizontal axis. In this study, we calculate incident radiation for both cases ? namely vertical tracking (swiveling vertically around a horizontal axis with the panel facing south or north) and horizontal tracking (swiveling horizontally around a vertical axis with the panel at optimal south-north tilt), and separately calculate incident radiation for 2-axis tracking. Whereas PVWatts calculates incident radiation for 2-axis tracking, it does not consider either of the above 1-axis options; instead, it invokes a third option, which is to swivel east-to-west around an axis parallel to a specified tilt, not necessarily the optimal tilt, of the panel. That option is not examined here, but the 1-axis horizontal tracking option treated here results in incident radiation within 1?3% of the 2-axis tilting option at most latitudes, thus may be close to optimal, if not optimal, for 1-axis tracking.
Many studies have provided equations that allow for the theoretical calculation of the optimal tilt angle over time of a solar collector based on Earth-sun geometry (e.g., Kern and Harris, 1975; Koronakis, 1986; Lewis, 1987; Gunerhan and Hepbash, 2009; Chang, 2009; Talebizadeh et al., 2011; Yadav and Chandel, 2013). Some of these studies have derived simple linear expressions of optimal tilt angle versus latitude (Chang, 2009; Talebizadeh et al., 2011). However, optimal tilt depends not only on latitude but also on weather conditions, including cloud cover (Kern and Harris, 1975) and the altitude above sea level (Yadav and Chandel, 2013). Because of the difficulty in determining optimal tilt angle as a function of cloud cover and weather conditions, calculators such as PVWatts (NREL, 2017), are often used to estimate optimal tilt angles at specific locations (Yadav and Chandel, 2013). Here, we first use PVWatts to estimate 1?4 optimal tilt angles for each country of the world.
Breyer and Schmid (2010a) combined satellite data with geometric and radiative equations to map global estimates of optimal tilt angles for solar PV. Similarly, Breyer and Schmid (2010a, 2010b), Breyer (2012), Bogdanov and Breyer (2016), Kilickaplan et al. (2017), Breyer et al. (2017a, 2017b), Sadiqa et al. (2018) have applied tilting, singleaxis, and/or 2-axis tracking equations to regionally- or globally-gridded solar radiation satellite datasets for energy analysis. However, it appears that no 3-D global or regional climate, weather, or air pollution model has included tilting, 1-axis horizontal tracking, 1-axis vertical tracking, or 2-axis tracking interactively within it. Pelland et al. (2011) used horizontal-plate solar radiation output from a downscaled climate model to estimate PV output from fixed-tilt panels. However, the calculation was done offline (after the 3-D model simulation was performed) rather than online (interactive within the 3-D model), thus it could not examine the effects of, for example, instantaneous temperature and wind speed, on panel performance. This study offers the opportunity to estimate global PV output anywhere in the world with tilted or tracked panels relative to horizontal panels using consistent meteorology and accounting for temperature and wind speed on panel performance.
The ideal tracking or tilting option depends not only on the incident solar radiation relative to a horizontal surface but also on the land or roof area needed to avoid shading, and the cost of tracking versus
tilting. For example, 2-axis tracking in a utility PV plant requires more land area to avoid shading panels behind the front row than do 1-axis tracking or optimal tilting, and 2-axis equipment is more expensive than is 1-axis equipment or optimal tilting. Shading depends not only on panel tilting, but also on the height that panels are placed relative to each other. For example, panels that track the sun placed on a southfacing hillside will likely see less shading than will panels on uniformly elevated ground. Shading further depends on the number of panels placed on each single platform that tracks the sun. In sum, the decision about what type of tracking or tilting option is best ultimately depends not only on the incident radiation received normal to each panel, but also on the land or roof area required to avoid shading and on the cost. In this study, we examine only the ratios of incident radiation with different tilting and tracking options relative to horizontal panels. We do not consider areas required or costs. However, these topics are discussed at length in Breyer (2012).
2. Methodology for determining optimal tilt angles
We first use PVWatts (NREL, 2017), which combines solar resource data from a specific location with 30 years of historic temperature and wind speed data from a nearby meteorological station, characteristics of a solar panel, and orientation of the panel relative to the sun. PVWatts uses `typical year' meteorology from each station, which is relevant, since the data have considerable inter-annual variability. For example, in the U.S., solar output during the lowest 10th percentile solar output meteorological year is on average, 4.8% less than that during the 50th percentile year (Ryberg et al., 2015). PVWatts uses solar data from the National Solar Radiation Database 1961?1990 for the U.S., the Canadian Weather for Energy Calculations database for Canada, and both ASHRAE International Weather for Energy Calculations Version 1.1 data and Solar and Wind Energy Resource Assessment Program data for all other countries. "Typical year" solar radiation values from these databases are updated by PVWatts to account for the reduction in sunlight due to clouds and air pollution at each site. Panel altitude, latitude, longitude, and angle relative to the sun are used to estimate exposure of the panel to sunlight. Air temperature and wind speed data are used to estimate panel temperature.
Here, PVWatts is used to estimate annually averaged solar output in all countries of the world assuming tilted panels. The optimal tilt angle in each location is found by calculating panel output with different tilt angles until the tilt angle giving the maximum output is found. That tilt angle is the optimal tilt angle. In most countries, an optimal tilt angle is estimated for only one location. For several large countries, estimates are obtained for 2?4 locations (Table 1). The optimal tilt angles calculated here are not necessarily the most cost-effective fixed tilt angles because they do not account for the additional land needed to minimize shading between panels (Section 3.2 of Breyer (2012)).
The main assumptions for the calculations with PVWatts include the following: 10 kW of premium panels with a temperature coefficient of -0.0035/K and 10% efficiency losses. Such losses include soiling (2%), wiring (2%), connections (0.5%), mismatch (2%), light-induced degradation (1.5%), nameplate rating (1%), shading (0.5%), and availability (0.5%). All panels are assumed to face due south in the Northern Hemisphere (180? azimuth angle) or due north in the Southern hemisphere (0? azimuth angle), with the exception of Nairobi, Kenya, which is slightly in the Southern Hemisphere (-1.32 S), but has an optimal tilt angle calculated to face 4? southward.
3. Optimal tilt angle results
Table 1 provides all optimal tilt angle results from PVWatts. Fig. 1 shows the resulting optical tilt angles versus latitude for each location in each country of the world in Table 1. The results are approximate for each location, so installers would need to make more exact calculations at their location of interest. 3rd-order polynomials are fit through the
56
M.Z. Jacobson, V. Jadhav
Table 1 Optimal tilt angles for fixed tilt solar PV panels for all countries of the world.
Country
Representative City
Nearest Meteorological Station
Iceland Afghanistan Albania Algeria Andorra Angola Antigua and Barbuda Argentina Armenia Australia Australia Australia Austria Azerbaijan Bahamas Bahrain Bangladesh Barbados Belarus Belgium Belize Benin Bhutan Bolivia Bosnia Herzegovina Botswana Brazil Brazil Brunei Darussalam Bulgaria Burkina Faso Burundi Cabo Verde Cambodia Cameroon Canada Canada Canada Central Afr. Republic Chad Chile China China China China Colombia Comoros Congo Congo Dem Rep of Costa-Rica Croatia Cuba Cyprus Czech Republic Denmark Djibouti Dominica Dominican Republic Dutch-Antilles Ecuador Egypt El Salvador Equatorial Guinea Eritrea Estonia Ethiopia Fiji Finland France France Gabon Gambia Georgia Germany
Reykjav?k Kandahar Sarande Algiers Andorra La Vella Luanda St. Johns Buenos Aires Yerevan Darwin Perth Sydney Graz Lankaran Nassau Riffa Chittagong Bridgetown Minsk Saint Hubert Belize City Port Novo Thimphu La Paz Banja Luka Gaborone Manaus Rio De Janeiro Bandar Seri Begaw Plovdiv Banfora Bujumbura Praia Phnom Penh Douala Calgary Vancouver Montreal Carnot N'Djamena Antofagasta Beijing Shanghai Lhasa Kunming Bogota Moroni Owando Lubumbashi San Jose Zadar Sancti Spiritus Larnaca Ostrava Copenhagen Djibouti Roseau Santo Domingo Willemstad Quito Aswan Ilopango Bata Keren Tartu Gondar Nadi Helsinki Lyon Bordeaux Libreville Banjul Tbilisi Cologne
Reykjav?k Karachi, Pakistan S Maria Di Leuca Algiers Gerona, Spain Harare, Zimbabwe Fort-De-France Buenos Aires Tabriz, Iran Darwin Perth Sydney Graz Tabriz, Iran Saua La Grande Riyadh Chittagong Fort-De-France Minsk Saint Hubert Belize Accra, Ghana Pagri, China La Paz Banja Luka Johannesburg Manaus Rio De Janeiro Bandar Seri Begawan Plovdiv Accra, Ghana Kisii, Kenya Dakar, Senegal Bangkok, Thailand Accra, Ghana Calgary Vancouver Montreal Accra, Ghana Accra, Ghana Antofagasta Beijing Shanghai Lhasa Kunming Bogota Antananarivo Accra, Ghana Harare, Zimbabwe Rivas, Nicaragua Ancona, Italy Sancti Spiritus Larnaca Ostrava Copenhagen Combolcha/Dessie Fort-De-France Aquadilla Borinquen Caracas, Venezuela Quito Aswan Ilopango Accra, Ghana Gondar, Ethiopia Helsinki, Finland Gondar Nadi Helsinki Lyon Bordeaux Accra, Ghana Dakar, Senegal Tabriz, Iran Cologne
57
Station Lat. (deg.)
64.13 24.9 39.65 36.72 41.9 -17.92 14.6 -34.82 38.05 -12.42 -31.93 -33.95 47 38.05 22.82 24.7 22.27 14.6 53.87 50.03 17.53 5.6 27.73 -16.52 44.78 -26.13 -3.13 -22.9 4.93 42.13 5.6 -0.67 14.73 13.92 5.6 51.12 49.18 45.5 5.6 5.6 -23.43 39.93 31.17 29.67 25.02 4.7 -18.8 5.6 -17.92 11.42 43.62 21.93 34.88 49.72 55.63 11.08 14.6 18.5 10.6 -0.15 23.97 13.7 5.6 12.53 60.32 12.53 -17.75 60.32 45.73 44.83 5.6 14.73 38.05 50.87
Solar Energy 169 (2018) 55?66
StationLon. (deg.)
Opt tilt
-21.9 67.13 18.35 3.25 2.77 31.13 -61 -58.53 46.17 130.88 115.95 151.18 15.43 46.17 -80.08 46.8 91.82 -61 27.53 5.4 -88.3 -0.17 89.08 -68.18 17.22 28.23 -60.02 -43.17 114.93 24.75 -0.17 34.78 -17.5 100.6 -0.17 -114.02 -123.17 -73.62 -0.17 -0.17 -70.43 116.28 121.43 91.13 102.68 -74.13 47.48 -0.17 31.13 85.83 13.37 -79.45 33.63 18.18 12.67 39.72 -61 -67.13 -66.98 -78.48 32.78 -89.12 -0.17 37.43 24.97 37.43 177.45 24.97 5.08 -0.7 -0.17 -17.5 46.17 7.17
43 25 30 31 37 -22 14 -30 30 -18 -27 -31 33 30 21 26 25 14 32 35 16 6a 32 -22 33 -29 -7a -22 5a 30 6a -3a 14 15 6a 45 34 37 6a 6a -22 37 23 31 25 5a -18 6a -22 14 30 21 30 33 36 15 14 20 10 -3a 24 18 6a 18 39 18 -18 39 30 33 6a 14 30 32
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M.Z. Jacobson, V. Jadhav
Table 1 (continued)
Country
Germany Ghana Gibraltar Greece Guatemala Guinea Guinea-Bissau Guyana Haiti Honduras Hong Kong Hungary India India Indonesia Iran Iran Iraq Ireland Israel Italy Ivory Coast Jamaica Japan Jordan Kazakhstan Kenya Kiribati Korea Korea DPR Kosovo Kuwait Kyrgyz Republic Laos Latvia Lebanon Lesotho Liberia Libyan Arab Jamahiriya Liechtenstein Lithuania Luxembourg Macedonia Malaysia Maldives Mali Malta Marshall Islands Mauritania Mauritius Mexico Mexico Micronesia Moldova Republic Monaco Mongolia Montenegro Morocco Mozambique Myanmar Namibia Nauru Nepal Netherlands New Zealand Nicaragua Niger Nigeria Norway Oman Pakistan Palau Palestine Panama Papua New Guinea
Representative City
Munich Accra Catalan Bay Athens Guatemala City Conakry Bissau Dadanawa Port-Au-Prince Catacamas Hong Kong Debrecen Rajkot Chennai Balikpapan Tehran Yazd Baghdad Kilkenny Be'Er Sheva Catania Yamoussoukro Kingston Osaka Amman Zhezqazghan Nairobi South Tarawa Kwangju Pyongyang Prishtina Kuwait City Jalal-Abad Vientiane Daugavpils Beirut Maseru Monrovia Tripoli Vaduz Kaunas Luxembourg Bitola Kuala Lumpur Gan Island Bamako Rabat Kwajalein Atoll Nouakchott Port Louis Mexico City Merida Palikir Chisinau Monaco-Ville Ulaanbaatar Podgorica Casablanca Maputo Yangon Windhoek Yaren Kathmandu Beek Auckland Rivas Niamey Lagos Oslo Salalah Karachi Koror Jerusalem Panama City Port Moresby
Nearest Meteorological Station
Munich Accra, Ghana Ceuta, Spain Athens Guatemala City Dakar, Senegal Dakar, Senegal Boa Vista (Civ/Mil) Punta Maisi, Cuba Catacamas Hong Kong Debrecen Rajkot Chennai Bandar Seri Begawan Tehran Yazd Tabriz, Iran Kilkenny Be'Er Sheva Catania Accra, Ghana Santiago De Cuba Osaka Jerusalem, Israel Tashkent Nairobi Kwajalein Atoll Kwangju Pyongyang Podgorica Shiraz, Iran Kashi, China Hanoi, Vietnam Kaunas, Lithuania Damascus, Syria Johannesburg Dakar, Senegal Tripoli Innsbruck, Austria Kaunas St Hubert Thessaloniki Kuala Lumpur Gan Island Dakar, Senegal Cozzo Spadaro Kwajalein Atoll Dakar, Senegal Antananarivo Mexico City Belize Guam, Hi Odessa, Ukraine Nice, France Ulaanbaatar Podgorica Casablanca Johannesburg Bangkok, Thailand Cape Town Kwajalein Atoll Kathmandu Beek Auckland Rivas Accra, Ghana Accra, Ghana Oslo Abu Dhabi, UAE Karachi Koror Island Jerusalem Rivas, Nicaragua Weipa, Australia
58
Station Lat. (deg.)
48.13 5.6 35.89 37.9 14.58 14.73 14.73 2.83 20.25 14.9 22.32 47.48 22.31 13.07 4.93 35.41 31.88 38.05 52.67 31.25 37.47 5.6 19.97 34.78 31.87 41.27 -1.32 8.73 35.13 39.03 42.37 29.32 39.47 21.2 54.88 33.42 -26.13 14.73 32.67 42.27 54.88 50.03 40.52 3.12 -0.68 14.73 36.68 8.73 14.73 -18.8 19.43 17.53 13.55 46.45 43.65 47.93 42.37 33.37 -26.13 13.92 -33.98 8.73 27.7 50.92 -37.02 11.42 5.6 5.6 59.9 24.43 24.9 7.33 31.87 11.42 -12.68
Solar Energy 169 (2018) 55?66
StationLon. (deg.)
Opt tilt
11.7 -0.17 -5.29 23.73 -90.52 -17.5 -17.5 -60.7 -74.15 -85.93 114.17 21.63 70.8 80.24 114.93 51.19 54.28 46.17 -7.27 34.8 15.05 -0.17 -75.85 135.45 35.22 69.27 36.82 167.73 126.92 125.78 19.25 52.36 75.98 105.8 23.88 36.52 28.23 -17.5 13.5 11.35 23.88 5.4 22.97 101.55 73.15 -17.5 15.13 167.73 -17.5 47.48 -99.08 -88.3 144.83 30.7 7.2 106.98 19.25 -7.58 28.23 100.6 18.6 167.73 85.37 5.78 174.8 85.83 -0.17 -0.17 10.62 54.65 67.13 134.48 35.22 85.83 141.92
33 6a 31 29 18 14 14 6a 19 15 20 30 24 13 5a 31 26 30 36 29 27 6a 20 30 28 32 4a 12 29 36 36 26 35 16 33 29 -29 14 27 37 33 35 33 1a -2a 14 28 12 14 -18 17 16 14 31 35 43 36 28 -29 15 -30 12 29 34 -30 14 6a 6a 40 25 25 8a 28 14 -17
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M.Z. Jacobson, V. Jadhav
Table 1 (continued)
Country
Paraguay Peru Philippines Poland Portugal Qatar Romania Russia Russia Russia Rwanda Saint Kitts And Nevis Saint Lucia Samoa San Marino Sao Tome & Principe Saudi Arabia Senegal Serbia Seychelles Sierra Leone Singapore Slovakia Slovenia Solomon Islands Somalia South Sudan South Africa South Africa Spain Spain Sri-Lanka St. Vincent/Grenadines Sudan Suriname Swaziland Sweden Switzerland Syrian Arab Republic Taiwan Tajikistan Tanzania Thailand Timor-Leste Togo Tonga Trinidad and Tobago Tunisia Turkey Turkey Turkmenistan Tuvalu Uganda Ukraine Ukraine United States United States United States United Arab Emirates United Kingdom United Kingdom Uruguay Uzbekistan Vanuatu Vatican City Venezuela Vietnam Yemen Zambia
Solar Energy 169 (2018) 55?66
Representative City
Asuncion Lima Manila Bielsko-Biala Lisbon Doha Bucharest St Petersburg Moscow Omsk Nyagatare Basseterre Castries Apia Fiorentino Sao Tome Riyadh Dakar Belgrade Victoria Freetown Singapore Kosice Ljubljana Honiara Mogadishu Juba Johannesburg Cape Town Castell?n Ceuta Colombo Kingstown Khartoum Kabalebo Mbabane Stockholm Geneva Damascus Taipei Dushanbe Arusha Bangkok Dili Lome Nukunuku San Fernando Tunis Ankara Diyarbakir Ashgabat Vaitupu Kampala Kiev Odessa Raleigh, NC Bakersfield, CA Austin, TX Abu Dhabi Hemsby London Montevideo Tashkent Elia Vatican City Caracas Hanoi Sana'A Lusaka
Nearest Meteorological Station
Asuncion Lima Manila Bielsko-Biala Lisbon Abu Dhabi, UAE Bucharest St Petersburg Moscow Omsk Kisii, Kenya Charlotte Amalie Fort-De-France Nadi, Fiji Rimini, Italy Accra, Ghana Riyadh Dakar Belgrade Lamu/Manda Island Dakar, Senegal Singapore Kosice Ljubljana Weipa, Australia Marsabit, Kenya Lowdar, Kenya Johannesburg Cape Town Castell?n Ceuta Colombo Fort-De-France Gondar, Ethiopia Boa Vista, Brazil Johannesburg Stockholm Geneva Damascus Taipei Tashkent Makindu, Kenya Bangkok Darwin, Australia Accra, Ghana Nadi, Fiji Fort-De-France Tunis Ankara Tabriz, Iran Tehran Mehrabad, Nadi, Fiji Kisii, Kenya Kiev Odessa Raleigh, NC Bakersfield, CA Austin, TX Abu Dhabi Hemsby London Montevideo Tashkent Nadi, Fiji Roma-Ciampino Caracas Hanoi Gondar, Ethiopia Harare, Zimbabwe
Station Lat. (deg.)
-25.25 -12 14.52 49.67 38.73 24.43 44.5 59.97 55.75 54.93 -0.67 18.35 14.6 -17.75 44.03 5.6 24.7 14.73 44.82 -2.27 14.73 1.37 48.7 46.22 -12.68 2.3 3.12 -26.13 -33.98 39.95 35.89 6.82 14.6 12.53 2.83 -26.13 59.65 46.25 33.42 25.07 41.27 -2.28 13.92 -12.42 5.6 -17.75 14.6 36.83 40.12 38.05 35.41 -17.75 -0.67 50.4 46.45 35.86 35.43 30.29 24.43 52.68 51.15 -34.83 41.27 -17.75 41.8 10.6 21.2 12.53 -17.92
StationLon. (deg.)
Opt tilt
-57.57 -77.12 121 19.25 -9.15 54.65 26.13 30.3 37.63 73.4 34.78 -64.97 -61 177.45 12.62 -0.17 46.8 -17.5 20.28 40.83 -17.5 103.98 21.27 14.48 141.92 37.9 35.62 28.23 18.6 -0.07 -5.29 79.88 -61 37.43 -60.7 28.23 17.95 6.13 36.52 121.55 69.27 37.83 100.6 130.88 -0.17 177.45 -61 10.23 32.98 46.17 51.19 177.45 34.78 30.45 30.7 -78.78 -119.05 -97.74 54.65 1.68 -0.18 -56 69.27 177.45 12.58 -66.98 105.8 37.43 31.13
-23 -7a 9a 31 35 25 32 40 37 42 -3a 18 14 -18 31 6a 24 14 34 -2a 14 0a 33 29 -17 4a 5a -29 -30 36 31 9a 14 18 6a -29 41 32 29 17 32 -4a 15 -18 6a -18 14 28 29 30 31 -18 -3a 35 31 32 29 28 25 34 34 -32 32 -18 30 10 16 18 -22
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