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{ RCSid $Id: sun2.cal,v 1.1 2019/10/17 03:53:10 greg Exp $ } |
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{ |
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Improved solar angle calculations based on "The Astronomical Almanac's |
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Algorithm for Approximate Solar Position (1950-2050)" by Joseph J. |
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Michalsky, published in 1988 in Solar Energy, Vol. 40, No. 3 |
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Translated by G.Ward, October 2019 |
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Inputs: |
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LAT = Site latitude (degrees north of Equator) |
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LON = Site longitude (degrees west of Greenwich) |
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SM = Standard meridian (degrees west of Greenwich) |
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TIME = Standard time (fractional hours 0-24) |
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DAY = Day of the month |
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MONTH = Month (January == 1) |
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YEAR = Calendar year AD (1950-2050) |
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Outputs: |
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SAZI = Solar altitude (degrees above horizon) |
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SALT = Solar azimuth (degrees west of south) |
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} |
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{ Defaults for San Francisco, CA } |
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LAT = 37.8152145; |
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LON = 122.04; |
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SM = 120; |
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DEG : PI/180; |
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{ Constants and functions } |
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normcir(a,c) : if(-a, normcir(a+c, c), if(c-a, a, normcir(a-c, c))); |
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and(a,b) : if(a, b, a); |
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leap(yr) : floor(yr/4 + .125) - yr/4 + .125; |
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{ Julian date } |
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delta = YEAR - 1949; |
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subjd = DAY + select(MONTH,0,31,59,90,120,151,181,212,243,273,304,334) + |
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if(and(MONTH-2.5,leap(YEAR)), 1, 0); |
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UTIME = TIME + SM/15; |
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jd = 2432916.5 + delta*365 + floor(delta/4) + subjd + UTIME/24; |
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{ Ecliptic coordinates } |
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n = jd - 2451545; |
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L = normcir(280.460 + 0.9856474*n, 360); |
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g = normcir(357.528 + 0.9856003*n, 360); |
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l = normcir(L + 1.915*sin(g*DEG) + 0.020*sin(2*DEG*g), 360); |
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ep = 23.439 - 4e-7*n; |
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{ Reused values } |
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sin_l = sin(l*DEG); |
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sin_LAT = sin(LAT*DEG); |
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{ Right ascension and declination angles } |
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ra = normcir(atan2(sin_l*cos(ep*DEG), cos(l*DEG))/DEG, 360); |
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sin_dec = sin(ep*DEG)*sin_l; |
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cos_dec = sqrt(1 - sin_dec*sin_dec); |
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dec = asin(sin_dec) / DEG; |
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{ Greenwich mean sidereal time } |
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gmst = normcir(6.697375 + 0.0657098242*n + UTIME, 24); |
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lmst = normcir(gmst - LON/15, 24); |
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ha = 15*(normcir(lmst - ra/15 + 12, 24) - 12); |
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{ Final solar angles } |
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sin_SALT = sin_dec*sin_LAT + cos_dec*cos(LAT*DEG)*cos(ha*DEG); |
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SALT = asin(sin_SALT) / DEG; |
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az = asin(-cos_dec*sin(ha*DEG)/cos(SALT*DEG)) / DEG; |
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SAZI = normcir(if(sin_dec-sin_SALT*sin_LAT, az, 180-az), 360) - 180; |
