2040:=48.2°. While the summertime AM number for mid-latitudes during the middle parts of the day is less than 1.5, higher figures apply in the morning and evening and at other times of the year. Therefore, AM1.5 is useful to represent the overall yearly average for mid-latitudes. The specific value of 1.5 has been selected in the 1970s for standardization purposes, based on an analysis of solar irradiance data in the conterminous United States. Since then, the solar industry has been using AM1.5 for all standardized testing or rating of terrestrial solar cells or modules, including those used in concentrating systems. The latest AM1.5 standards pertaining to photovoltaic applications are the ASTM G-173 and IEC 60904, all derived from simulations obtained with the
131:
direct path, giving the sun a yellow tinge. The greater the distance in the atmosphere through which the sunlight travels, the greater this effect, which is why the sun looks orange or red at dawn and sunset when the sunlight is travelling very obliquely through the atmosphere — progressively more of the blues and greens are removed from the direct rays, giving an orange or red appearance to the sun; and the sky appears pink — because the blues and greens are scattered over such long paths that they are highly attenuated before arriving at the observer, resulting in characteristic pink skies at dawn and sunset.
1882:
1297:
1877:{\displaystyle {\begin{aligned}\int _{0}^{\infty }\exp((-2x\cos z-(\sin z)^{2}x^{2}/r)/2)dx&=\exp((r\cot ^{2}z)/2)\int _{0}^{\infty }\exp(-({\sqrt {r}}\cot z+x\sin z/{\sqrt {r}})^{2}/2)dx\\&=-\exp(r(\cot z)^{2}/2){\frac {\sqrt {r\pi /2}}{\sin z}}{\text{ erfc}}(({\sqrt {r}}\cot z+x\sin z/{\sqrt {r}})/{\sqrt {2}}){\Bigg |}_{x}^{\infty }\\&=\exp(r(\cot z)^{2}/2){\frac {\sqrt {r\pi /2}}{\sin z}}{\text{ erfc}}\left({\sqrt {r/2}}\cot z\right)\\\end{aligned}}}
84:
294:
100:
2107:=70°) is a useful range for estimating the overall average performance of solar cells installed at high latitudes such as in northern Europe. Similarly AM2 to AM3 is useful to estimate wintertime performance in temperate latitudes, e.g. airmass coefficient is greater than 2 at all hours of the day in winter at latitudes as low as 37°.
3159:, per unit of sunlight energy is greater than in space. This means that solar cells are more efficient at AM1 than AM0. This apparently counter-intuitive result arises simply because silicon cells can't make much use of the high energy radiation which the atmosphere filters out. As illustrated below, even though the
2012:
Solar panels do not generally operate under exactly one atmosphere's thickness: if the sun is at an angle to the Earth's surface the effective thickness will be greater. Many of the world's major population centres, and hence solar installations and industry, across Europe, China, Japan, the United
130:
Atmospheric scattering plays a role in removing higher frequencies from direct sunlight and scattering it about the sky. This is why the sky appears blue and the sun yellow — more of the higher-frequency blue light arrives at the observer via indirect scattered paths; and less blue light follows the
2177:
Solar intensity at the collector reduces with increasing airmass coefficient, but due to the complex and variable atmospheric factors involved, not in a simple or linear fashion. For example, almost all high energy radiation is removed in the upper atmosphere (between AM0 and AM1) and so AM2 is not
126:
As the sunlight travels through the atmosphere, chemicals interact with the sunlight and absorb certain wavelengths changing the amount of short-wavelength light reaching the Earth's surface. A more active component of this process is water vapor, which results in a wide variety of absorption bands
3139:
are suitable for use only to altitudes of a few kilometres above sea level, implying as they do reduction to AM0 performance levels at only around 6 and 9 km respectively. By contrast much of the attenuation of the high energy components occurs in the ozone layer - at higher altitudes around
2164:
region, it is possible to use a lower absolute AM numbers than for the corresponding latitude at sea level: AM numbers less than 1 towards the equator, and correspondingly lower numbers than listed above for other latitudes. However, this approach is approximate and not recommended. It is best to
1120:
These simple models assume that for these purposes the atmosphere can be considered to be effectively concentrated into around the bottom 9 km, i.e. essentially all the atmospheric effects are due to the atmospheric mass in the lower half of the
2186:. Depending on level of pollution in the air, overall attenuation can change by up to ±70% towards the horizon, greatly affecting performance particularly towards the horizon where effects of the lower layers of atmosphere are amplified manyfold.
3174:) for a typical solar cell is still highest at AM0. Conversely, the shape of the spectrum does not significantly change with further increases in atmospheric thickness, and hence cell efficiency does not greatly change for AM numbers above 1.
1286:
2159:
air mass, equal to the relative air mass multiplied by the local atmospheric pressure and divided by the standard (sea-level) pressure, decreases with elevation above sea level. For solar panels installed at high altitudes, e.g. in an
2041:
2978:
3154:
The earth's atmosphere absorbs a considerable amount of the ultraviolet light. The resulting spectrum at the Earth's surface has fewer photons, but they are of lower energy on average, so the number of photons, above the
127:
at many wavelengths, while molecular nitrogen, oxygen and carbon dioxide add to this process. By the time it reaches the Earth's surface, the spectrum is strongly confined between the far infrared and near ultraviolet.
874:
490:
3873:
3779:
2263:
626:
285:
The air mass number is thus dependent on the Sun's elevation path through the sky and therefore varies with time of day and with the passing seasons of the year, and with the latitude of the observer.
3052:
2757:
764:
1302:
1913:. This gives a lower value, of around 33, when the sun is on the horizon. However, neither this model nor the previous take into consideration the bending of light rays due to refraction (see
347:
227:
2137:=90°, i.e. sunset) at sea level. However, in practice there is a high degree of variability in the solar intensity received at angles close to the horizon as described in the next section
3599:
911:
3898:
The ASTM G-173 standard measures solar intensity under "rural aerosol loading" i.e. clean air conditions - thus the standard value fits closely to the maximum of the expected range.
3101:
1132:
is the distance along the light ray from where it meets the ground, divided by the equivalent thickness of the atmosphere (approximately 9 km), then the height of a point is:
706:
71:
under standardized conditions, and is often referred to using the syntax "AM" followed by a number. "AM1.5" is almost universal when characterizing terrestrial power-generating
412:
up to around 75°. A number of refinements have been proposed to more accurately model the path thickness towards the horizon, such as that proposed by Kasten and Young (1989):
2308:
671:
272:
1954:
The spectrum after travelling through the atmosphere to sea level with the sun directly overhead is referred to, by definition, as "AM1". This means "one atmosphere". AM1 (
1907:
3268:
This illustrates the more general point that given that solar energy is "free", and where available space is not a limitation, other factors such as total output power
1107:
1138:
392:
The above approximation overlooks the atmosphere's finite height, and predicts an infinite air mass at the horizon. However, it is reasonably accurate for values of
2583:
This illustrates that significant power is available at only a few degrees above the horizon. For example, when the sun is more than about 60° above the horizon (
2816:
2793:
2627:
2601:
2359:
2335:
2135:
2105:
2085:
2038:
1992:
1972:
942:
530:
410:
383:
177:
157:
2178:
twice as bad as AM1. Furthermore, there is great variability in many of the factors contributing to atmospheric attenuation, such as water vapor, aerosols,
3402:
1938:
The spectrum outside the atmosphere is referred to as "AM0", meaning "zero atmospheres". Solar cells used for space power applications, like those on
2843:
772:
420:
116:
3807:
3713:
2629:=75°) the solar intensity is still about 600 W/m or 60% of its maximum level; and at only 5° above the horizon still 27% of the maximum.
2197:
297:
Atmospheric effects on optical transmission can be modelled as if the atmosphere is concentrated in approximately the lower 9 km.
3933:
3607:
3455:
2310: = 1.353 kW/m, and the factor of 1.1 is derived assuming that the diffuse component is 10% of the direct component.
543:
95:
temperature, of the Sun (5777 K) is the temperature a black body of the same size must have to yield the same total emissive power.
3908:
3435:
of blue — yellow is the aggregate color of what remains after scattering removes some blue from the "white" light from the sun.
2052:
30:
This article is about practical application in the solar energy industry. For more comprehensive theoretical treatment, see
2999:
2645:
2155:
air mass is only a function of the sun's zenith angle, and therefore does not change with local elevation. Conversely, the
711:
2637:
One approximate model for intensity increase with altitude and accurate to a few kilometres above sea level is given by:
1910:
309:
187:
3527:
Gueymard, C.; Myers, D.; Emery, K. (2002). "Proposed reference irradiance spectra for solar energy systems testing".
3140:
30 km. Hence these approximations are suitable only for estimating the performance of ground-based collectors.
111:
radiator of the same size at about 5,800 K. As it passes through the atmosphere, sunlight is attenuated by
3399:
1939:
3124:
for average, polluted or clean air respectively) can be used to estimate intensity from AM in the normal way.
3500:
Schoenberg, E. (1929). Theoretische
Photometrie, g) Über die Extinktion des Lichtes in der Erdatmosphäre. In
882:
3057:
512:, for various atmospheric models and experimental data sets. At sea level the air mass towards the horizon (
3952:
3419:
3343:
3308:
3149:
2183:
676:
88:
3313:
3282:
per unit of invested money (e.g. per dollar), are often more important considerations than efficiency (
53:
2284:
647:
248:
3957:
3536:
3303:
38:
31:
3624:
3576:
3333:
2017:
latitudes. An AM number representing the spectrum at mid-latitudes is therefore much more common.
1890:
49:
1125:. This is a useful and simple model when considering the atmospheric effects on solar intensity.
2179:
2013:
States of
America and elsewhere (including northern India, southern Africa and Australia) lie in
1995:
1918:
2313:
This formula fits comfortably within the mid-range of the expected pollution-based variability:
83:
3468:
1281:{\displaystyle {\sqrt {(r\sin z)^{2}+(r\cos z+x)^{2}}}-r\approx x\cos z+(\sin z)^{2}x^{2}/(2r)}
3929:
3603:
3592:
Planning and installing photovoltaic systems: a guide for installers, architects and engineers
3451:
2055:) under AM1.5 is given as 109,870 lux (corresponding with the AM1.5 spectrum to 1000.4 W/m).
766: ≈ 708. To avoid taking the difference of two large numbers, this can be written as
1092:
3544:
3406:
3358:
535:
Modelling the atmosphere as a simple spherical shell provides a reasonable approximation:
61:
3540:
2798:
3432:
3323:
2778:
2612:
2586:
2344:
2320:
2120:
2090:
2070:
2023:
1977:
1957:
927:
515:
395:
368:
162:
142:
3548:
3946:
3692:
3363:
3328:
2996:
where the normalized heights of the atmosphere and of the collector are respectively
60:. The air mass coefficient can be used to help characterize the solar spectrum after
17:
3348:
386:
56:, expressed as a ratio relative to the path length vertically upwards, i.e. at the
2609:
as shown in the above table), whereas when the sun is only 15° above the horizon (
2189:
One empirical approximation model for solar intensity versus airmass is given by:
1128:
One can also assume that the air density falls off exponentially with height. If
3909:
The measurement of solar spectral irradiance at different terrestrial elevations
3665:
The ASTM G-173 standard measures solar intensity over the band 280 to 4000
3353:
2973:{\displaystyle AM={\sqrt {(r+c)^{2}\cos ^{2}z+(2r+1+c)(1-c)}}\;-\;(r+c)\cos z\,}
2165:
simulate the actual spectrum based on the relative air mass (e.g., 1.5) and the
1122:
120:
72:
3656:
reference uses 1367 W/m as the solar intensity external to the atmosphere.
293:
3338:
3318:
2169:
atmospheric conditions for the specific elevation of the site under scrutiny.
112:
108:
92:
68:
3561:
2117:
AM38 is generally regarded as being the airmass in the horizontal direction (
67:
The air mass coefficient is commonly used to characterize the performance of
3666:
3517:
reports values in the range 8 to 10 km for different atmospheric models
3373:
2161:
2014:
1914:
279:
179:
relative to the normal to the Earth's surface, the air mass coefficient is:
99:
2831:
Alternatively, given the significant practical variabilities involved, the
869:{\displaystyle AM={\frac {2r+1}{{\sqrt {(r\cos z)^{2}+2r+1}}\;+\;r\cos z}}}
2020:"AM1.5", 1.5 atmosphere thickness, corresponds to a solar zenith angle of
485:{\displaystyle AM={\frac {1}{\cos \,z+0.50572\,(96.07995-z)^{-1.6364}}}\,}
3378:
2048:
1999:
508:
A more comprehensive list of such models is provided in the main article
3868:{\displaystyle I=1.1\times I_{\mathrm {o} }\times 0.76^{(AM^{0.618})}\,}
3774:{\displaystyle I=1.1\times I_{\mathrm {o} }\times 0.56^{(AM^{0.715})}\,}
3514:
3488:
3156:
2832:
2258:{\displaystyle I=1.1\times I_{\mathrm {o} }\times 0.7^{(AM^{0.678})}\,}
509:
3491:
reports values in the range 36 to 40 for different atmospheric models
1994:=25°) is a useful range for estimating performance of solar cells in
275:
57:
2603:<30°) the solar intensity is about 1000 W/m (from equation
673: = 6371 km, the effective height of the atmosphere
292:
98:
82:
3409:
retrieved 27 April 2011 "Effective
Temperature ... 5777 K"
119:; the more atmosphere through which it passes, the greater the
3368:
159:
through the atmosphere, and solar radiation incident at angle
3627:
retrieved 1 May 2011, Stuart Bowden and
Christiana Honsberg,
3595:
621:{\displaystyle AM={\sqrt {(r\cos z)^{2}+2r+1}}\;-\;r\cos z\,}
107:
The overall intensity of solar radiation is like that of a
2795:
is the solar collector's height above sea level in km and
3469:
Revised optical air mass tables and approximation formula
2281:
where solar intensity external to the Earth's atmosphere
103:
Solar irradiance spectrum above atmosphere and at surface
3400:
3600:
International
Institute for Environment and Development
3106:
And then the above table or the appropriate equation (
3810:
3716:
3628:
3060:
3047:{\displaystyle r=R_{\mathrm {E} }/y_{\mathrm {atm} }}
3002:
2846:
2801:
2781:
2752:{\displaystyle I=1.1\times I_{\mathrm {o} }\times \,}
2648:
2615:
2589:
2347:
2323:
2287:
2200:
2123:
2093:
2073:
2026:
1980:
1960:
1893:
1300:
1141:
1095:
930:
885:
775:
759:{\displaystyle r=R_{\mathrm {E} }/y_{\mathrm {atm} }}
714:
679:
650:
546:
518:
423:
398:
371:
312:
301:
A first-order approximation for air mass is given by
251:
190:
165:
145:
3915:, vol. 13, no. 1, pp. 43-50, IN1-IN4, 51-57, 1970.
3867:
3773:
3095:
3046:
2972:
2810:
2787:
2751:
2621:
2595:
2353:
2329:
2302:
2257:
2129:
2099:
2079:
2032:
1986:
1966:
1901:
1876:
1280:
1101:
936:
905:
868:
758:
700:
665:
620:
524:
484:
404:
377:
341:
266:
221:
171:
151:
3562:Reference Solar Spectral Irradiance: Air Mass 1.5
1729:
342:{\displaystyle AM\approx {\frac {1}{\cos \,z}}\,}
3683:
3681:
3679:
3677:
3675:
1917:). A more realistic model would be based on the
222:{\displaystyle AM={\frac {L}{L_{\mathrm {o} }}}}
3577:Reference Solar Spectral Irradiance: ASTM G-173
3398:or more precisely 5,777 K as reported in
920:Estimates of airmass coefficient at sea level
916:These models are compared in the table below:
879:which also shows the similarity to the simple
37:"AM0" redirects here. Not to be confused with
8:
3587:
3585:
3928:, section 6.4. Kluwer Academic Publishers.
3602:, Deutsche Gesellschaft für Sonnenenergie.
3629:Solar Power Labs, Arizona State University
3620:
3618:
3616:
3504:. Band II, erste Hälfte. Berlin: Springer.
2944:
2940:
2828:the collector was installed at sea level.
850:
846:
604:
600:
3864:
3853:
3842:
3828:
3827:
3809:
3770:
3759:
3748:
3734:
3733:
3715:
3080:
3079:
3070:
3059:
3031:
3030:
3021:
3014:
3013:
3001:
2969:
2884:
2874:
2856:
2845:
2800:
2780:
2748:
2737:
2720:
2706:
2691:
2666:
2665:
2647:
2614:
2588:
2346:
2322:
2293:
2292:
2286:
2254:
2243:
2232:
2218:
2217:
2199:
2122:
2092:
2072:
2025:
1979:
1959:
1942:, are generally characterized using AM0.
1894:
1892:
1846:
1841:
1831:
1809:
1800:
1789:
1783:
1739:
1734:
1728:
1727:
1716:
1711:
1701:
1696:
1665:
1654:
1632:
1623:
1612:
1606:
1548:
1542:
1531:
1526:
1495:
1474:
1469:
1454:
1439:
1396:
1385:
1379:
1369:
1314:
1309:
1301:
1299:
1261:
1255:
1245:
1197:
1163:
1142:
1140:
1094:
929:
902:
895:
886:
884:
823:
802:
785:
774:
743:
742:
733:
726:
725:
713:
685:
684:
678:
656:
655:
649:
617:
577:
556:
545:
517:
481:
469:
452:
442:
433:
422:
397:
370:
338:
331:
322:
311:
278:(i.e., normal to the Earth's surface) at
257:
256:
250:
210:
209:
200:
189:
164:
144:
3639:Meinel, A. B. and Meinel, M. P. (1976).
3176:
2835:could be applied to estimate AM, using:
2315:
918:
708: ≈ 9 km, and their ratio
3572:
3570:
3391:
906:{\displaystyle {\frac {1}{\cos \,z}}\,}
3483:
3481:
3096:{\displaystyle c=h/y_{\mathrm {atm} }}
3178:Output power vs. airmass coefficient
64:has traveled through the atmosphere.
7:
3801:
3707:
3467:Kasten, F. and Young, A. T. (1989).
2837:
2639:
2191:
2138:
537:
414:
303:
181:
27:A term in the solar energy industry
3829:
3735:
3087:
3084:
3081:
3038:
3035:
3032:
3015:
2667:
2489:
2486:
2481:
2478:
2475:
2294:
2219:
1740:
1475:
1315:
1096:
750:
747:
744:
727:
701:{\displaystyle y_{\mathrm {atm} }}
692:
689:
686:
657:
258:
211:
25:
2317:Solar intensity vs. zenith angle
3926:Astronomical photometry: a guide
3054: ≈ 708 (as above) and
2303:{\displaystyle I_{\mathrm {o} }}
666:{\displaystyle R_{\mathrm {E} }}
267:{\displaystyle L_{\mathrm {o} }}
3859:
3843:
3765:
3749:
3687:Interpolated from data in the
2957:
2945:
2935:
2923:
2920:
2899:
2871:
2858:
2745:
2726:
2717:
2707:
2699:
2679:
2676:
2249:
2233:
1797:
1780:
1767:
1761:
1723:
1708:
1662:
1659:
1620:
1603:
1590:
1584:
1556:
1539:
1492:
1486:
1462:
1451:
1429:
1426:
1404:
1393:
1366:
1353:
1329:
1326:
1275:
1266:
1242:
1229:
1194:
1172:
1160:
1144:
820:
804:
644:where the radius of the Earth
574:
558:
466:
453:
1:
3697:
3643:Addison Wesley Publishing Co.
3594:, 2nd Ed. (2008), Table 1.1,
3549:10.1016/S0038-092X(03)00005-7
3135:
3129:
3120:
3114:
3108:
2820:
2605:
2371:
1902:{\displaystyle {\text{erfc}}}
980:
971:
962:
1911:complementary error function
532:= 90°) is approximately 38.
2833:homogeneous spherical model
2337:and airmass coefficient AM
3974:
3924:R.L.F. Boyd (Ed.) (1992).
3447:The Physics of Solar Cells
3147:
36:
29:
3691:reference using suitable
3579:ASTM retrieved 1 May 2011
3564:NREL retrieved 1 May 2011
1940:communications satellites
3502:Handbuch der Astrophysik
3127:These approximations at
2452:780 .. 1100 = 940 ± 17%
2422:840 .. 1130 = 990 ± 15%
389:, typically in degrees.
2547:200 .. 660 = 430 ± 53%
2501:560 .. 970 = 770 ± 27%
2483:680 .. 1050 = 870 ± 21%
2467:710 .. 1060 = 880 ± 20%
2437:800 .. 1110 = 960 ± 16%
2366:range due to pollution
1102:{\displaystyle \infty }
3869:
3775:
3693:Least squares estimate
3449:. Weinheim: Wiley-VCH.
3097:
3048:
2974:
2812:
2789:
2753:
2623:
2597:
2561:85 .. 480 = 280 ± 70%
2532:330 .. 800 = 560 ± 41%
2516:430 .. 880 = 650 ± 34%
2355:
2331:
2304:
2259:
2184:temperature inversions
2131:
2101:
2081:
2034:
1988:
1968:
1903:
1878:
1291:The air mass is then:
1282:
1103:
938:
907:
870:
760:
702:
667:
622:
526:
486:
406:
379:
343:
298:
274:is the path length at
268:
223:
173:
153:
104:
96:
3870:
3776:
3695:variants of equation
3445:Peter Würfel (2005).
3420:Diffuse sky radiation
3418:See also the article
3344:Solar cell efficiency
3309:Diffuse sky radiation
3150:Solar cell efficiency
3144:Solar cell efficiency
3098:
3049:
2975:
2818:is the airmass (from
2813:
2790:
2754:
2624:
2598:
2356:
2332:
2305:
2260:
2132:
2102:
2082:
2035:
1989:
1969:
1904:
1879:
1283:
1104:
939:
913:formula given above.
908:
871:
761:
703:
668:
623:
527:
487:
407:
380:
344:
296:
269:
224:
174:
154:
102:
89:effective temperature
86:
3907:Laue, E. G. (1970),
3808:
3714:
3641:Applied Solar Energy
3386:Notes and references
3304:Air mass (astronomy)
3163:is lower at AM0 the
3058:
3000:
2844:
2799:
2779:
2646:
2613:
2587:
2345:
2321:
2285:
2198:
2121:
2091:
2071:
2047:The illuminance for
2024:
1978:
1958:
1891:
1298:
1139:
1093:
928:
883:
773:
712:
677:
648:
544:
516:
421:
396:
369:
310:
249:
188:
163:
143:
46:air mass coefficient
32:Air mass (astronomy)
18:Air mass coefficient
3541:2002SoEn...73..443G
3475:28:4735–4738.
3334:Rayleigh scattering
3179:
2633:At higher altitudes
2338:
2182:and the effects of
2146:At higher altitudes
1744:
1479:
1319:
949:Kasten & Young
921:
50:optical path length
48:defines the direct
3865:
3771:
3405:2015-07-03 at the
3314:Earth's atmosphere
3177:
3165:total output power
3093:
3044:
2970:
2811:{\displaystyle AM}
2808:
2785:
2749:
2619:
2593:
2351:
2327:
2316:
2300:
2255:
2180:photochemical smog
2127:
2097:
2077:
2030:
1984:
1964:
1919:barometric formula
1899:
1874:
1872:
1726:
1465:
1305:
1278:
1099:
934:
919:
903:
866:
756:
698:
663:
618:
522:
482:
402:
375:
339:
299:
264:
219:
169:
149:
139:For a path length
105:
97:
54:Earth's atmosphere
3889:
3888:
3795:
3794:
3704:for polluted air:
3513:The main article
3487:The main article
3266:
3265:
2994:
2993:
2938:
2788:{\displaystyle h}
2773:
2772:
2622:{\displaystyle z}
2596:{\displaystyle z}
2581:
2580:
2533:
2517:
2484:
2468:
2438:
2354:{\displaystyle z}
2330:{\displaystyle z}
2279:
2278:
2130:{\displaystyle z}
2100:{\displaystyle z}
2080:{\displaystyle z}
2033:{\displaystyle z}
1987:{\displaystyle z}
1967:{\displaystyle z}
1897:
1854:
1834:
1829:
1817:
1721:
1706:
1670:
1657:
1652:
1640:
1536:
1500:
1203:
1118:
1117:
937:{\displaystyle z}
900:
864:
844:
642:
641:
598:
525:{\displaystyle z}
506:
505:
479:
405:{\displaystyle z}
378:{\displaystyle z}
363:
362:
336:
243:
242:
217:
172:{\displaystyle z}
152:{\displaystyle L}
16:(Redirected from
3965:
3937:
3922:
3916:
3905:
3899:
3896:
3890:
3883:
3874:
3872:
3871:
3866:
3863:
3862:
3858:
3857:
3834:
3833:
3832:
3802:
3789:
3780:
3778:
3777:
3772:
3769:
3768:
3764:
3763:
3740:
3739:
3738:
3708:
3685:
3670:
3663:
3657:
3650:
3644:
3637:
3631:
3622:
3611:
3589:
3580:
3574:
3565:
3559:
3553:
3552:
3524:
3518:
3511:
3505:
3498:
3492:
3485:
3476:
3465:
3459:
3450:
3442:
3436:
3429:
3423:
3416:
3410:
3396:
3186:Solar intensity
3180:
3102:
3100:
3099:
3094:
3092:
3091:
3090:
3074:
3053:
3051:
3050:
3045:
3043:
3042:
3041:
3025:
3020:
3019:
3018:
2988:
2979:
2977:
2976:
2971:
2939:
2889:
2888:
2879:
2878:
2857:
2838:
2817:
2815:
2814:
2809:
2794:
2792:
2791:
2786:
2767:
2758:
2756:
2755:
2750:
2741:
2730:
2729:
2725:
2724:
2695:
2672:
2671:
2670:
2640:
2628:
2626:
2625:
2620:
2602:
2600:
2599:
2594:
2531:
2515:
2482:
2466:
2436:
2360:
2358:
2357:
2352:
2339:
2336:
2334:
2333:
2328:
2309:
2307:
2306:
2301:
2299:
2298:
2297:
2273:
2264:
2262:
2261:
2256:
2253:
2252:
2248:
2247:
2224:
2223:
2222:
2192:
2136:
2134:
2133:
2128:
2106:
2104:
2103:
2098:
2086:
2084:
2083:
2078:
2039:
2037:
2036:
2031:
1993:
1991:
1990:
1985:
1973:
1971:
1970:
1965:
1908:
1906:
1905:
1900:
1898:
1895:
1883:
1881:
1880:
1875:
1873:
1869:
1865:
1855:
1850:
1842:
1835:
1832:
1830:
1828:
1813:
1802:
1801:
1793:
1788:
1787:
1748:
1743:
1738:
1733:
1732:
1722:
1717:
1715:
1707:
1702:
1700:
1671:
1666:
1658:
1655:
1653:
1651:
1636:
1625:
1624:
1616:
1611:
1610:
1568:
1552:
1547:
1546:
1537:
1532:
1530:
1501:
1496:
1478:
1473:
1458:
1444:
1443:
1400:
1389:
1384:
1383:
1374:
1373:
1318:
1313:
1287:
1285:
1284:
1279:
1265:
1260:
1259:
1250:
1249:
1204:
1202:
1201:
1168:
1167:
1143:
1131:
1108:
1106:
1105:
1100:
952:Spherical shell
943:
941:
940:
935:
922:
912:
910:
909:
904:
901:
899:
887:
875:
873:
872:
867:
865:
863:
845:
828:
827:
803:
800:
786:
765:
763:
762:
757:
755:
754:
753:
737:
732:
731:
730:
707:
705:
704:
699:
697:
696:
695:
672:
670:
669:
664:
662:
661:
660:
636:
627:
625:
624:
619:
599:
582:
581:
557:
538:
531:
529:
528:
523:
500:
491:
489:
488:
483:
480:
478:
477:
476:
434:
415:
411:
409:
408:
403:
384:
382:
381:
376:
357:
348:
346:
345:
340:
337:
335:
323:
304:
273:
271:
270:
265:
263:
262:
261:
237:
228:
226:
225:
220:
218:
216:
215:
214:
201:
182:
178:
176:
175:
170:
158:
156:
155:
150:
21:
3973:
3972:
3968:
3967:
3966:
3964:
3963:
3962:
3943:
3942:
3941:
3940:
3923:
3919:
3906:
3902:
3897:
3893:
3881:
3849:
3838:
3823:
3806:
3805:
3787:
3755:
3744:
3729:
3712:
3711:
3686:
3673:
3664:
3660:
3651:
3647:
3638:
3634:
3623:
3614:
3590:
3583:
3575:
3568:
3560:
3556:
3526:
3525:
3521:
3512:
3508:
3499:
3495:
3486:
3479:
3466:
3462:
3444:
3443:
3439:
3430:
3426:
3417:
3413:
3407:Wayback Machine
3397:
3393:
3388:
3383:
3359:Solar radiation
3299:
3291:
3287:
3280:
3273:
3220:
3216:
3209:
3202:
3172:
3152:
3146:
3075:
3056:
3055:
3026:
3009:
2998:
2997:
2986:
2880:
2870:
2842:
2841:
2797:
2796:
2777:
2776:
2765:
2716:
2702:
2661:
2644:
2643:
2635:
2611:
2610:
2585:
2584:
2343:
2342:
2319:
2318:
2288:
2283:
2282:
2271:
2239:
2228:
2213:
2196:
2195:
2175:
2173:Solar intensity
2139:Solar intensity
2119:
2118:
2089:
2088:
2069:
2068:
2022:
2021:
1976:
1975:
1974:=0°) to AM1.1 (
1956:
1955:
1927:
1889:
1888:
1871:
1870:
1840:
1836:
1818:
1779:
1746:
1745:
1641:
1602:
1566:
1565:
1538:
1435:
1413:
1375:
1365:
1296:
1295:
1251:
1241:
1193:
1159:
1137:
1136:
1129:
1091:
1090:
926:
925:
891:
881:
880:
819:
801:
787:
771:
770:
738:
721:
710:
709:
680:
675:
674:
651:
646:
645:
634:
573:
542:
541:
514:
513:
498:
465:
438:
419:
418:
394:
393:
367:
366:
355:
327:
308:
307:
291:
252:
247:
246:
235:
205:
186:
185:
161:
160:
141:
140:
137:
81:
62:solar radiation
42:
35:
28:
23:
22:
15:
12:
11:
5:
3971:
3969:
3961:
3960:
3955:
3945:
3944:
3939:
3938:
3917:
3900:
3891:
3887:
3886:
3877:
3875:
3861:
3856:
3852:
3848:
3845:
3841:
3837:
3831:
3826:
3822:
3819:
3816:
3813:
3800:
3799:
3798:for clean air:
3793:
3792:
3783:
3781:
3767:
3762:
3758:
3754:
3751:
3747:
3743:
3737:
3732:
3728:
3725:
3722:
3719:
3706:
3705:
3671:
3658:
3645:
3632:
3612:
3581:
3566:
3554:
3535:(6): 443–467.
3519:
3506:
3493:
3477:
3473:Applied Optics
3460:
3437:
3433:color negative
3431:Yellow is the
3424:
3411:
3390:
3389:
3387:
3384:
3382:
3381:
3376:
3371:
3366:
3361:
3356:
3351:
3346:
3341:
3336:
3331:
3326:
3324:Mie scattering
3321:
3316:
3311:
3306:
3300:
3298:
3295:
3289:
3285:
3278:
3271:
3264:
3263:
3260:
3257:
3254:
3250:
3249:
3246:
3243:
3240:
3236:
3235:
3232:
3229:
3226:
3222:
3221:
3218:
3214:
3211:
3207:
3204:
3200:
3197:
3194:
3193:
3190:
3187:
3184:
3170:
3148:Main article:
3145:
3142:
3089:
3086:
3083:
3078:
3073:
3069:
3066:
3063:
3040:
3037:
3034:
3029:
3024:
3017:
3012:
3008:
3005:
2992:
2991:
2982:
2980:
2968:
2965:
2962:
2959:
2956:
2953:
2950:
2947:
2943:
2937:
2934:
2931:
2928:
2925:
2922:
2919:
2916:
2913:
2910:
2907:
2904:
2901:
2898:
2895:
2892:
2887:
2883:
2877:
2873:
2869:
2866:
2863:
2860:
2855:
2852:
2849:
2807:
2804:
2784:
2771:
2770:
2761:
2759:
2747:
2744:
2740:
2736:
2733:
2728:
2723:
2719:
2715:
2712:
2709:
2705:
2701:
2698:
2694:
2690:
2687:
2684:
2681:
2678:
2675:
2669:
2664:
2660:
2657:
2654:
2651:
2634:
2631:
2618:
2592:
2579:
2578:
2575:
2573:
2570:
2566:
2565:
2562:
2559:
2556:
2552:
2551:
2548:
2545:
2542:
2538:
2537:
2534:
2529:
2526:
2522:
2521:
2518:
2513:
2510:
2506:
2505:
2502:
2499:
2496:
2492:
2491:
2488:
2485:
2480:
2477:
2473:
2472:
2469:
2464:
2461:
2457:
2456:
2453:
2450:
2447:
2443:
2442:
2439:
2434:
2431:
2427:
2426:
2423:
2420:
2417:
2413:
2412:
2409:
2406:
2403:
2400:
2396:
2395:
2392:
2389:
2386:
2384:
2380:
2379:
2376:
2367:
2364:
2361:
2350:
2326:
2296:
2291:
2277:
2276:
2267:
2265:
2251:
2246:
2242:
2238:
2235:
2231:
2227:
2221:
2216:
2212:
2209:
2206:
2203:
2174:
2171:
2149:
2148:
2126:
2115:
2114:
2096:
2087:=60°) to AM3 (
2076:
2065:
2064:
2029:
2010:
2009:
1983:
1963:
1952:
1951:
1936:
1935:
1926:
1923:
1885:
1884:
1868:
1864:
1861:
1858:
1853:
1849:
1845:
1839:
1827:
1824:
1821:
1816:
1812:
1808:
1805:
1799:
1796:
1792:
1786:
1782:
1778:
1775:
1772:
1769:
1766:
1763:
1760:
1757:
1754:
1751:
1749:
1747:
1742:
1737:
1731:
1725:
1720:
1714:
1710:
1705:
1699:
1695:
1692:
1689:
1686:
1683:
1680:
1677:
1674:
1669:
1664:
1661:
1650:
1647:
1644:
1639:
1635:
1631:
1628:
1622:
1619:
1615:
1609:
1605:
1601:
1598:
1595:
1592:
1589:
1586:
1583:
1580:
1577:
1574:
1571:
1569:
1567:
1564:
1561:
1558:
1555:
1551:
1545:
1541:
1535:
1529:
1525:
1522:
1519:
1516:
1513:
1510:
1507:
1504:
1499:
1494:
1491:
1488:
1485:
1482:
1477:
1472:
1468:
1464:
1461:
1457:
1453:
1450:
1447:
1442:
1438:
1434:
1431:
1428:
1425:
1422:
1419:
1416:
1414:
1412:
1409:
1406:
1403:
1399:
1395:
1392:
1388:
1382:
1378:
1372:
1368:
1364:
1361:
1358:
1355:
1352:
1349:
1346:
1343:
1340:
1337:
1334:
1331:
1328:
1325:
1322:
1317:
1312:
1308:
1304:
1303:
1289:
1288:
1277:
1274:
1271:
1268:
1264:
1258:
1254:
1248:
1244:
1240:
1237:
1234:
1231:
1228:
1225:
1222:
1219:
1216:
1213:
1210:
1207:
1200:
1196:
1192:
1189:
1186:
1183:
1180:
1177:
1174:
1171:
1166:
1162:
1158:
1155:
1152:
1149:
1146:
1116:
1115:
1112:
1109:
1098:
1088:
1084:
1083:
1080:
1077:
1074:
1070:
1069:
1066:
1063:
1060:
1056:
1055:
1052:
1049:
1046:
1042:
1041:
1038:
1035:
1032:
1028:
1027:
1024:
1021:
1018:
1014:
1013:
1010:
1007:
1004:
1000:
999:
996:
993:
990:
986:
985:
976:
967:
958:
954:
953:
950:
947:
944:
933:
898:
894:
890:
877:
876:
862:
859:
856:
853:
849:
843:
840:
837:
834:
831:
826:
822:
818:
815:
812:
809:
806:
799:
796:
793:
790:
784:
781:
778:
752:
749:
746:
741:
736:
729:
724:
720:
717:
694:
691:
688:
683:
659:
654:
640:
639:
630:
628:
616:
613:
610:
607:
603:
597:
594:
591:
588:
585:
580:
576:
572:
569:
566:
563:
560:
555:
552:
549:
521:
504:
503:
494:
492:
475:
472:
468:
464:
461:
458:
455:
451:
448:
445:
441:
437:
432:
429:
426:
401:
374:
361:
360:
351:
349:
334:
330:
326:
321:
318:
315:
290:
287:
260:
255:
241:
240:
231:
229:
213:
208:
204:
199:
196:
193:
168:
148:
136:
133:
80:
77:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3970:
3959:
3956:
3954:
3951:
3950:
3948:
3935:
3934:0-7923-1653-3
3931:
3927:
3921:
3918:
3914:
3910:
3904:
3901:
3895:
3892:
3885:
3878:
3876:
3854:
3850:
3846:
3839:
3835:
3824:
3820:
3817:
3814:
3811:
3804:
3803:
3797:
3796:
3791:
3784:
3782:
3760:
3756:
3752:
3745:
3741:
3730:
3726:
3723:
3720:
3717:
3710:
3709:
3703:
3702:
3700:
3699:
3694:
3690:
3684:
3682:
3680:
3678:
3676:
3672:
3668:
3662:
3659:
3655:
3649:
3646:
3642:
3636:
3633:
3630:
3626:
3621:
3619:
3617:
3613:
3609:
3608:1-84407-442-0
3605:
3601:
3597:
3593:
3588:
3586:
3582:
3578:
3573:
3571:
3567:
3563:
3558:
3555:
3550:
3546:
3542:
3538:
3534:
3530:
3523:
3520:
3516:
3510:
3507:
3503:
3497:
3494:
3490:
3484:
3482:
3478:
3474:
3470:
3464:
3461:
3457:
3456:3-527-40857-6
3453:
3448:
3441:
3438:
3434:
3428:
3425:
3421:
3415:
3412:
3408:
3404:
3401:
3395:
3392:
3385:
3380:
3377:
3375:
3372:
3370:
3367:
3365:
3364:Solar tracker
3362:
3360:
3357:
3355:
3352:
3350:
3347:
3345:
3342:
3340:
3337:
3335:
3332:
3330:
3329:Photovoltaics
3327:
3325:
3322:
3320:
3317:
3315:
3312:
3310:
3307:
3305:
3302:
3301:
3296:
3294:
3292:
3281:
3274:
3261:
3258:
3255:
3252:
3251:
3247:
3244:
3241:
3238:
3237:
3233:
3230:
3227:
3224:
3223:
3212:
3205:
3198:
3196:
3195:
3191:
3189:Output power
3188:
3185:
3182:
3181:
3175:
3173:
3166:
3162:
3158:
3151:
3143:
3141:
3138:
3137:
3132:
3131:
3125:
3123:
3122:
3117:
3116:
3111:
3110:
3104:
3076:
3071:
3067:
3064:
3061:
3027:
3022:
3010:
3006:
3003:
2990:
2983:
2981:
2966:
2963:
2960:
2954:
2951:
2948:
2941:
2932:
2929:
2926:
2917:
2914:
2911:
2908:
2905:
2902:
2896:
2893:
2890:
2885:
2881:
2875:
2867:
2864:
2861:
2853:
2850:
2847:
2840:
2839:
2836:
2834:
2829:
2827:
2823:
2822:
2805:
2802:
2782:
2769:
2762:
2760:
2742:
2738:
2734:
2731:
2721:
2713:
2710:
2703:
2696:
2692:
2688:
2685:
2682:
2673:
2662:
2658:
2655:
2652:
2649:
2642:
2641:
2638:
2632:
2630:
2616:
2608:
2607:
2590:
2576:
2574:
2571:
2568:
2567:
2563:
2560:
2557:
2554:
2553:
2549:
2546:
2543:
2540:
2539:
2535:
2530:
2527:
2524:
2523:
2519:
2514:
2511:
2508:
2507:
2503:
2500:
2497:
2494:
2493:
2474:
2470:
2465:
2462:
2459:
2458:
2454:
2451:
2448:
2445:
2444:
2440:
2435:
2432:
2429:
2428:
2424:
2421:
2418:
2415:
2414:
2410:
2407:
2404:
2401:
2398:
2397:
2393:
2390:
2387:
2385:
2382:
2381:
2377:
2374:
2373:
2368:
2365:
2362:
2348:
2341:
2340:
2324:
2314:
2311:
2289:
2275:
2268:
2266:
2244:
2240:
2236:
2229:
2225:
2214:
2210:
2207:
2204:
2201:
2194:
2193:
2190:
2187:
2185:
2181:
2172:
2170:
2168:
2163:
2158:
2154:
2147:
2144:
2143:
2142:
2140:
2124:
2113:
2110:
2109:
2108:
2094:
2074:
2063:
2060:
2059:
2058:
2056:
2054:
2050:
2045:
2043:
2027:
2018:
2016:
2008:
2005:
2004:
2003:
2001:
1997:
1981:
1961:
1950:
1947:
1946:
1945:
1943:
1941:
1934:
1931:
1930:
1929:
1924:
1922:
1921:for density.
1920:
1916:
1912:
1866:
1862:
1859:
1856:
1851:
1847:
1843:
1837:
1825:
1822:
1819:
1814:
1810:
1806:
1803:
1794:
1790:
1784:
1776:
1773:
1770:
1764:
1758:
1755:
1752:
1750:
1735:
1718:
1712:
1703:
1697:
1693:
1690:
1687:
1684:
1681:
1678:
1675:
1672:
1667:
1648:
1645:
1642:
1637:
1633:
1629:
1626:
1617:
1613:
1607:
1599:
1596:
1593:
1587:
1581:
1578:
1575:
1572:
1570:
1562:
1559:
1553:
1549:
1543:
1533:
1527:
1523:
1520:
1517:
1514:
1511:
1508:
1505:
1502:
1497:
1489:
1483:
1480:
1470:
1466:
1459:
1455:
1448:
1445:
1440:
1436:
1432:
1423:
1420:
1417:
1415:
1410:
1407:
1401:
1397:
1390:
1386:
1380:
1376:
1370:
1362:
1359:
1356:
1350:
1347:
1344:
1341:
1338:
1335:
1332:
1323:
1320:
1310:
1306:
1294:
1293:
1292:
1272:
1269:
1262:
1256:
1252:
1246:
1238:
1235:
1232:
1226:
1223:
1220:
1217:
1214:
1211:
1208:
1205:
1198:
1190:
1187:
1184:
1181:
1178:
1175:
1169:
1164:
1156:
1153:
1150:
1147:
1135:
1134:
1133:
1126:
1124:
1113:
1110:
1089:
1086:
1085:
1081:
1078:
1075:
1072:
1071:
1067:
1064:
1061:
1058:
1057:
1053:
1050:
1047:
1044:
1043:
1039:
1036:
1033:
1030:
1029:
1025:
1022:
1019:
1016:
1015:
1011:
1008:
1005:
1002:
1001:
997:
994:
991:
988:
987:
983:
982:
977:
974:
973:
968:
965:
964:
959:
956:
955:
951:
948:
945:
931:
924:
923:
917:
914:
896:
892:
888:
860:
857:
854:
851:
847:
841:
838:
835:
832:
829:
824:
816:
813:
810:
807:
797:
794:
791:
788:
782:
779:
776:
769:
768:
767:
739:
734:
722:
718:
715:
681:
652:
638:
631:
629:
614:
611:
608:
605:
601:
595:
592:
589:
586:
583:
578:
570:
567:
564:
561:
553:
550:
547:
540:
539:
536:
533:
519:
511:
502:
495:
493:
473:
470:
462:
459:
456:
449:
446:
443:
439:
435:
430:
427:
424:
417:
416:
413:
399:
390:
388:
372:
359:
352:
350:
332:
328:
324:
319:
316:
313:
306:
305:
302:
295:
288:
286:
283:
281:
277:
253:
239:
232:
230:
206:
202:
197:
194:
191:
184:
183:
180:
166:
146:
134:
132:
128:
124:
122:
118:
114:
110:
101:
94:
90:
85:
78:
76:
74:
70:
65:
63:
59:
55:
51:
47:
40:
33:
19:
3953:Solar energy
3925:
3920:
3913:Solar Energy
3912:
3903:
3894:
3879:
3785:
3696:
3688:
3661:
3653:
3648:
3640:
3635:
3591:
3557:
3532:
3529:Solar Energy
3528:
3522:
3509:
3501:
3496:
3472:
3463:
3446:
3440:
3427:
3414:
3394:
3349:Solar energy
3283:
3276:
3269:
3267:
3168:
3164:
3160:
3153:
3134:
3128:
3126:
3119:
3113:
3107:
3105:
2995:
2984:
2830:
2825:
2819:
2774:
2763:
2636:
2604:
2582:
2370:
2312:
2280:
2269:
2188:
2176:
2166:
2156:
2152:
2150:
2145:
2116:
2111:
2066:
2061:
2057:
2053:this version
2046:
2019:
2011:
2006:
1953:
1948:
1944:
1937:
1932:
1928:
1886:
1290:
1127:
1119:
979:
970:
961:
915:
878:
643:
632:
534:
507:
496:
391:
387:zenith angle
364:
353:
300:
284:
244:
233:
138:
129:
125:
106:
66:
52:through the
45:
43:
3958:Solar cells
3354:Solar power
3192:Efficiency
2378:ASTM G-173
1123:Troposphere
946:Flat Earth
289:Calculation
121:attenuation
79:Description
69:solar cells
3947:Categories
3339:Solar cell
3319:Insolation
3161:efficiency
1996:equatorial
1833: erfc
1656: erfc
135:Definition
117:absorption
113:scattering
109:black body
93:black body
3836:×
3821:×
3742:×
3727:×
3689:Earthscan
3654:Earthscan
3598:with the
3596:Earthscan
3374:Sun chart
2964:
2942:−
2930:−
2891:
2686:−
2674:×
2659:×
2369:formula (
2226:×
2211:×
2162:Altiplano
2015:temperate
2002:regions.
1915:Levelling
1860:
1823:
1807:π
1774:
1759:
1741:∞
1691:
1676:
1646:
1630:π
1597:
1582:
1576:−
1521:
1506:
1490:−
1484:
1476:∞
1467:∫
1446:
1424:
1360:
1351:−
1345:
1333:−
1324:
1316:∞
1307:∫
1236:
1221:
1212:≈
1206:−
1182:
1154:
1097:∞
858:
814:
612:
602:−
568:
471:−
460:−
320:≈
280:sea level
3403:Archived
3379:Sun path
3297:See also
2157:absolute
2153:relative
2049:Daylight
2000:tropical
457:96.07995
3625:PVCDROM
3537:Bibcode
3515:Airmass
3489:Airmass
3157:bandgap
2490:1000.4
2411:1347.9
2383:degree
1909:is the
957:degree
510:Airmass
450:0.50572
385:is the
3932:
3606:
3454:
3275:, and
2775:where
2476:48.2°
2167:actual
2044:code.
2042:SMARTS
1887:where
474:1.6364
365:where
276:zenith
245:where
73:panels
58:zenith
3855:0.618
3761:0.715
3242:1000
3228:1350
2826:as if
2722:0.678
2463:1.41
2455:1010
2449:1.15
2441:1020
2433:1.09
2425:1040
2408:1353
2405:1367
2245:0.678
2067:AM2 (
2062:AM2~3
2007:AM1.5
1925:Cases
1114:37.6
1111:37.9
1082:20.3
1079:19.4
1076:28.7
1068:10.6
1065:10.3
1062:11.5
91:, or
3930:ISBN
3840:0.76
3746:0.56
3652:The
3604:ISBN
3452:ISBN
3262:15%
3259:120
3256:800
3248:15%
3245:150
3234:12%
3231:160
3210:W/m
3203:W/m
3133:and
2569:90°
2564:270
2555:85°
2550:470
2544:5.6
2541:80°
2536:620
2528:3.8
2525:75°
2520:710
2512:2.9
2509:70°
2504:840
2495:60°
2487:930
2479:1.5
2471:950
2460:45°
2446:30°
2430:23°
2394:W/m
2391:W/m
2388:W/m
2151:The
2112:AM38
1998:and
1896:erfc
1087:90°
1073:88°
1059:85°
1054:5.6
1051:5.6
1048:5.8
1045:80°
1040:3.8
1037:3.8
1034:3.9
1031:75°
1026:2.9
1023:2.9
1020:2.9
1017:70°
1012:2.0
1009:2.0
1006:2.0
1003:60°
998:1.0
995:1.0
992:1.0
115:and
87:The
44:The
3882:I.4
3818:1.1
3788:I.3
3724:1.1
3698:I.1
3545:doi
3369:Sun
3293:).
3286:out
3279:out
3272:out
3217:/ P
3215:out
3208:out
3183:AM
3171:out
3136:A.4
3130:I.2
3121:I.4
3118:or
3115:I.3
3112:or
3109:I.1
2987:A.4
2961:cos
2882:cos
2821:A.2
2766:I.2
2743:7.1
2704:0.7
2697:7.1
2656:1.1
2606:I.1
2577:20
2572:38
2558:10
2416:0°
2372:I.1
2363:AM
2272:I.1
2230:0.7
2208:1.1
1949:AM1
1933:AM0
1857:cot
1820:sin
1771:cot
1756:exp
1688:sin
1673:cot
1643:sin
1594:cot
1579:exp
1518:sin
1503:cot
1481:exp
1437:cot
1421:exp
1357:sin
1342:cos
1321:exp
1233:sin
1218:cos
1179:cos
1151:sin
989:0°
981:A.3
972:A.2
963:A.1
893:cos
855:cos
811:cos
635:A.3
609:cos
565:cos
499:A.2
440:cos
356:A.1
329:cos
236:A.1
39:AMO
3949::
3911:,
3701::
3674:^
3667:nm
3615:^
3584:^
3569:^
3543:.
3533:73
3531:.
3480:^
3471:.
3290:in
3288:/P
3253:2
3239:1
3225:0
3219:in
3201:in
3103:.
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2498:2
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2399:-
2375:)
2141:.
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975:)
966:)
282:.
123:.
75:.
3936:.
3884:)
3880:(
3860:)
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3786:(
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3753:A
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3721:=
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3669:.
3610:.
3551:.
3547::
3539::
3458:.
3422:.
3284:P
3277:P
3270:P
3213:P
3206:P
3199:P
3169:P
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2985:(
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2924:(
2921:)
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2051:(
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1982:z
1962:z
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817:z
808:r
805:(
798:1
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789:2
783:=
780:M
777:A
751:m
748:t
745:a
740:y
735:/
728:E
723:R
719:=
716:r
693:m
690:t
687:a
682:y
658:E
653:R
637:)
633:(
615:z
606:r
596:1
593:+
590:r
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559:(
554:=
551:M
548:A
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497:(
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454:(
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431:=
428:M
425:A
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358:)
354:(
333:z
325:1
317:M
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259:o
254:L
238:)
234:(
212:o
207:L
203:L
198:=
195:M
192:A
167:z
147:L
41:.
34:.
20:)
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