Azimuth angle conversion from east to west
ajit.nayak87
Posts: 76
Dear all.
I am trying to convert solar azimuth angle in +90 degree to -90 degree format to get sun Desired potion.Here i am attaching relevant images. i searched from Google.
How to convert azimuth angle from +90 degree to -90 degree fomat
sun position will be 0 @ NORTH
90@ east
180 @ south
270 @ West.
Since tracking should be from east to west.so my azimuth angle changes from +90 to zero from East to North and 0 to -90 degree from North to West. .
Sun angle will Be zero around 12.30 of the day. i.e north point.
Question Here is how to convert Elevation angle or desired angle in +90 t0 -90 degree format.
Form East to north angle will be +ve and north to south it will be negative.
pveducation.org/pvcdrom/properties-of-sunlight/suns-position
I am trying to convert solar azimuth angle in +90 degree to -90 degree format to get sun Desired potion.Here i am attaching relevant images. i searched from Google.
How to convert azimuth angle from +90 degree to -90 degree fomat
sun position will be 0 @ NORTH
90@ east
180 @ south
270 @ West.
Since tracking should be from east to west.so my azimuth angle changes from +90 to zero from East to North and 0 to -90 degree from North to West. .
Sun angle will Be zero around 12.30 of the day. i.e north point.
Question Here is how to convert Elevation angle or desired angle in +90 t0 -90 degree format.
Form East to north angle will be +ve and north to south it will be negative.
pveducation.org/pvcdrom/properties-of-sunlight/suns-position
Comments
If you want to use a -90 to +90 format, if the azimuth from the table is less than 180 deg, use the value as is. If it's greater than 180 degrees, subtract 360 from it. For example if the azimuth is 275 deg, 275 - 360 = -85 deg. Be careful though, since the azimuth of the sunrise and sunset points can go beyond +90 and -90 (in your format). If you want to see what the range is for your location, use the website calculator to generate tables for the solstices (Dec 21 and June 21). Be sure to generate both.
So, for the present, I'm not sure why you want to convert the noon azimuth to north, rather than south, unless you also need to convert the altitude to an angle greater than 90 degrees.
-Phil
My tracking Period Will be Morning 7Am to Eving 18. I.e i am tracking sun from east to west . SInce my strcture will be placed in North -SOuth Direction.SInce I am getting From Top. azimuth angle (eastward from N) i.e 0 @ north and 180 @ SOuth. 90@ east and 270@ west . And my Sensor to which comparing result measure from +90degre to-90 degree format So i am converting it to +90 to -90 degree format
So the rotation axis of your tracking device is oriented north-south? Are you saying that from the east horizon to the meridian (noon) the sensor gives an angle that decreases from +90 to 0 and then after noon it goes from 0 to -90?
If that's the case, I wouldn't use alt-az coordinates for the sun's position. It sounds like what you need is the hour angle. That's the angle (it can be expressed as hours or degrees) between the object (the sun) and the meridian so the eastern horizon is -90, the meridian (~noon) is 0, and the western horizon is +90. If I understood you correctly, that means you need to multiply the hour angle (in degrees) by -1 to change the sign. Converting from hour angle in hours to degrees is just 15 degrees per hour. This site defines solar hour angle: http://www.princeton.edu/~achaney/tmve/wiki100k/docs/Hour_angle.html and this one goes through the math: http://pveducation.org/pvcdrom/properties-of-sunlight/suns-position
Edit: I see on your attached file that you have zenith angles greater than 90 degrees. From my understanding of zenith angle, that puts the sun below the horizon so I guess I'm still clueless as to what you're trying to do.
As a first approximation:
The Earth rotates 360 degrees per day. Which is 15 degrees per hour. Or 0.25 degrees per minute or 0.00417 degrees per second.
So, just fix up you machine to rotate at that rate.
From your tables you know at what time to start at sunrise in the morning.
Job done.
Back in the day (1970's) we were doing this with clockwork mechanisms wound up with springs driving solar concentrators.
Check below link. What i am trying to do:
INPUT data:
This tracking application i am trying to implement. structure will be placed in north south direction. i will get azimuth, zenith angle from above calculator.That i can implement in C.Question is how to use the zenith and azimuth angle used to track sun position.
Here i am attaching my location snapshot which can be used in calculator for latitude and longitude
. We know the sunrise and sunset position from Table. my sensor read value from +or- 90 degree. How to convert these angle from table to sensor angle format, since I am staying in Bangalore,INDIA, How i could use above angle???
@ jones.
I am staying in Bangalore INDIA.
Below point you understand properly.
the table i have attached i got from NREL spa calculator Who details attached Above. Just put the date/time , latitude, longitude other parameter you get table.
As you only have a single axis of rotation you don't need to make it complicated. As I posted above:
As a first approximation:
The Earth rotates 360 degrees per day. Which is 15 degrees per hour. Or 0.25 degrees per minute or 0.00417 degrees per second.
So, just fix up you machine to rotate at that rate.
From your tables you know at what time to start at sunrise in the morning. Just make sure everything is turned back to that position in the morning at start the motors at the right time.
How to covert those angle to+or-90 degree fromat
-Phil
main
void setup() { Serial.begin(9600); // rtcSetup(); } void loop() { /* Check_RTC(); getRTCDateTime(); */ Check_minute(); /* Serial.print("Julian Day:"); Serial.println(spa.jd); Serial.print("Zenith:"); Serial.println(spa.zenith); Serial.print("Azimuth:"); Serial.println(spa.azimuth); */ spa_tester(); Serial.println("......................"); delay(100); } int spa_tester() { // print_result(); //declare the SPA structure int result; //enter required input values into SPA structure spa.year = yy; spa.month = mm; spa.day = dd; spa.hour = 9; spa.minute = 50; spa.second = s; spa.timezone = 5.50; spa.delta_t = 67; spa.longitude = 80.27; spa.latitude = 13.08; spa.elevation = 1000.0; spa.pressure = 835; spa.temperature = 10; spa.slope = 30; spa.azm_rotation = -10; spa.atmos_refract = 0.5667; spa.function = SPA_ALL; //call the SPA calculate function and pass the SPA structure result = spa_calculate(&spa); if (result == 0) //check for SPA errors { // Serial.println("In SPA DATA read"); Serial.print("spa Date:"); Serial.print(spa.day); Serial.print("/"); Serial.print(spa.month); Serial.print("/"); Serial.println(spa.year); Serial.print("time:"); Serial.print(spa.hour); Serial.print("-"); Serial.print(spa.minute); Serial.print("-"); Serial.println(spa.second); Serial.print("Julian Day:"); Serial.println(spa.jd); Serial.print("Zenith:"); Serial.println(spa.zenith); Serial.print("Azimuth:"); Serial.println(spa.azimuth); elevation=90-latitude+spa.delta; Serial.print("elevation north :"); Serial.println(elevation); elevation=90+latitude-spa.delta; Serial.print("elevation south "); Serial.println(elevation); Serial.print("WELCOME"); } else Serial.print("SPA Error Code:"); Serial.println(result); return 0; } void print_result() { Print_Date(); Print_Time(); } void Print_Date(){ Serial.print("Local Date:"); Serial.print(dd); Serial.print("/"); Serial.print(mm); Serial.print("/"); Serial.println(yy); } void Print_Time() { Serial.print("local_time is:"); Serial.print(h); Serial.print("-"); Serial.print(m); Serial.print("-"); Serial.println(s); }spa.h#ifndef __solar_position_algorithm_header #define __solar_position_algorithm_header //enumeration for function codes to select desired final outputs from SPA enum { SPA_ZA, //calculate zenith and azimuth SPA_ZA_INC, //calculate zenith, azimuth, and incidence SPA_ZA_RTS, //calculate zenith, azimuth, and sun rise/transit/set values SPA_ALL, //calculate all SPA output values }; typedef struct { //----------------------INPUT VALUES------------------------ int year; // 4-digit year, valid range: -2000 to 6000, error code: 1 int month; // 2-digit month, valid range: 1 to 12, error code: 2 int day; // 2-digit day, valid range: 1 to 31, error code: 3 int hour; // Observer local hour, valid range: 0 to 24, error code: 4 int minute; // Observer local minute, valid range: 0 to 59, error code: 5 int second; // Observer local second, valid range: 0 to 59, error code: 6 double delta_t; // Difference between earth rotation time and terrestrial time // It is derived from observation only and is reported in this // bulletin: http://maia.usno.navy.mil/ser7/ser7.dat, // where delta_t = 32.184 + (TAI-UTC) + DUT1 // valid range: -8000 to 8000 seconds, error code: 7 double timezone; // Observer time zone (negative west of Greenwich) // valid range: -18 to 18 hours, error code: 8 double longitude; // Observer longitude (negative west of Greenwich) // valid range: -180 to 180 degrees, error code: 9 double latitude; // Observer latitude (negative south of equator) // valid range: -90 to 90 degrees, error code: 10 double elevation; // Observer elevation [meters] // valid range: -6500000 or higher meters, error code: 11 double pressure; // Annual average local pressure [millibars] // valid range: 0 to 5000 millibars, error code: 12 double temperature; // Annual average local temperature [degrees Celsius] // valid range: -273 to 6000 degrees Celsius, error code; 13 double slope; // Surface slope (measured from the horizontal plane) // valid range: -360 to 360 degrees, error code: 14 double azm_rotation; // Surface azimuth rotation (measured from south to projection of // surface normal on horizontal plane, negative west) // valid range: -360 to 360 degrees, error code: 15 double atmos_refract;// Atmospheric refraction at sunrise and sunset (0.5667 deg is typical) // valid range: -5 to 5 degrees, error code: 16 int function; // Switch to choose functions for desired output (from enumeration) //-----------------Intermediate OUTPUT VALUES-------------------- double jd; //Julian day double jc; //Julian century double jde; //Julian ephemeris day double jce; //Julian ephemeris century double jme; //Julian ephemeris millennium double l; //earth heliocentric longitude [degrees] double b; //earth heliocentric latitude [degrees] double r; //earth radius vector [Astronomical Units, AU] double theta; //geocentric longitude [degrees] double beta; //geocentric latitude [degrees] double x0; //mean elongation (moon-sun) [degrees] double x1; //mean anomaly (sun) [degrees] double x2; //mean anomaly (moon) [degrees] double x3; //argument latitude (moon) [degrees] double x4; //ascending longitude (moon) [degrees] double del_psi; //nutation longitude [degrees] double del_epsilon; //nutation obliquity [degrees] double epsilon0; //ecliptic mean obliquity [arc seconds] double epsilon; //ecliptic true obliquity [degrees] double del_tau; //aberration correction [degrees] double lamda; //apparent sun longitude [degrees] double nu0; //Greenwich mean sidereal time [degrees] double nu; //Greenwich sidereal time [degrees] double alpha; //geocentric sun right ascension [degrees] double delta; //geocentric sun declination [degrees] double h; //observer hour angle [degrees] double xi; //sun equatorial horizontal parallax [degrees] double del_alpha; //sun right ascension parallax [degrees] double delta_prime; //topocentric sun declination [degrees] double alpha_prime; //topocentric sun right ascension [degrees] double h_prime; //topocentric local hour angle [degrees] double e0; //topocentric elevation angle (uncorrected) [degrees] double del_e; //atmospheric refraction correction [degrees] double e; //topocentric elevation angle (corrected) [degrees] double eot; //equation of time [minutes] double srha; //sunrise hour angle [degrees] double ssha; //sunset hour angle [degrees] double sta; //sun transit altitude [degrees] //---------------------Final OUTPUT VALUES------------------------ double zenith; //topocentric zenith angle [degrees] double azimuth180; //topocentric azimuth angle (westward from south) [-180 to 180 degrees] double azimuth; //topocentric azimuth angle (eastward from north) [ 0 to 360 degrees] double incidence; //surface incidence angle [degrees] double suntransit; //local sun transit time (or solar noon) [fractional hour] double sunrise; //local sunrise time (+/- 30 seconds) [fractional hour] double sunset; //local sunset time (+/- 30 seconds) [fractional hour] } spa_data; //Calculate SPA output values (in structure) based on input values passed in structure int spa_calculate(spa_data *spa); #endifspa.cpp
#include <math.h> #include "spa.h" #define PI 3.1415926535897932384626433832795028841971 #define SUN_RADIUS 0.26667 #define L_COUNT 6 #define B_COUNT 2 #define R_COUNT 5 #define Y_COUNT 63 #define L_MAX_SUBCOUNT 64 #define B_MAX_SUBCOUNT 5 #define R_MAX_SUBCOUNT 40 enum {TERM_A, TERM_B, TERM_C, TERM_COUNT}; enum {TERM_X0, TERM_X1, TERM_X2, TERM_X3, TERM_X4, TERM_X_COUNT}; enum {TERM_PSI_A, TERM_PSI_B, TERM_EPS_C, TERM_EPS_D, TERM_PE_COUNT}; enum {JD_MINUS, JD_ZERO, JD_PLUS, JD_COUNT}; enum {SUN_TRANSIT, SUN_RISE, SUN_SET, SUN_COUNT}; #define TERM_Y_COUNT TERM_X_COUNT const int l_subcount[L_COUNT] = {64,34,20,7,3,1}; const int b_subcount[B_COUNT] = {5,2}; const int r_subcount[R_COUNT] = {40,10,6,2,1}; /////////////////////////////////////////////////// /// Earth Periodic Terms /////////////////////////////////////////////////// const double L_TERMS[L_COUNT][L_MAX_SUBCOUNT][TERM_COUNT]= { { {175347046.0,0,0}, {3341656.0,4.6692568,6283.07585}, {34894.0,4.6261,12566.1517}, {3497.0,2.7441,5753.3849}, {3418.0,2.8289,3.5231}, {3136.0,3.6277,77713.7715}, {2676.0,4.4181,7860.4194}, {2343.0,6.1352,3930.2097}, {1324.0,0.7425,11506.7698}, {1273.0,2.0371,529.691}, {1199.0,1.1096,1577.3435}, {990,5.233,5884.927}, {902,2.045,26.298}, {857,3.508,398.149}, {780,1.179,5223.694}, {753,2.533,5507.553}, {505,4.583,18849.228}, {492,4.205,775.523}, {357,2.92,0.067}, {317,5.849,11790.629}, {284,1.899,796.298}, {271,0.315,10977.079}, {243,0.345,5486.778}, {206,4.806,2544.314}, {205,1.869,5573.143}, {202,2.458,6069.777}, {156,0.833,213.299}, {132,3.411,2942.463}, {126,1.083,20.775}, {115,0.645,0.98}, {103,0.636,4694.003}, {102,0.976,15720.839}, {102,4.267,7.114}, {99,6.21,2146.17}, {98,0.68,155.42}, {86,5.98,161000.69}, {85,1.3,6275.96}, {85,3.67,71430.7}, {80,1.81,17260.15}, {79,3.04,12036.46}, {75,1.76,5088.63}, {74,3.5,3154.69}, {74,4.68,801.82}, {70,0.83,9437.76}, {62,3.98,8827.39}, {61,1.82,7084.9}, {57,2.78,6286.6}, {56,4.39,14143.5}, {56,3.47,6279.55}, {52,0.19,12139.55}, {52,1.33,1748.02}, {51,0.28,5856.48}, {49,0.49,1194.45}, {41,5.37,8429.24}, {41,2.4,19651.05}, {39,6.17,10447.39}, {37,6.04,10213.29}, {37,2.57,1059.38}, {36,1.71,2352.87}, {36,1.78,6812.77}, {33,0.59,17789.85}, {30,0.44,83996.85}, {30,2.74,1349.87}, {25,3.16,4690.48} }, { {628331966747.0,0,0}, {206059.0,2.678235,6283.07585}, {4303.0,2.6351,12566.1517}, {425.0,1.59,3.523}, {119.0,5.796,26.298}, {109.0,2.966,1577.344}, {93,2.59,18849.23}, {72,1.14,529.69}, {68,1.87,398.15}, {67,4.41,5507.55}, {59,2.89,5223.69}, {56,2.17,155.42}, {45,0.4,796.3}, {36,0.47,775.52}, {29,2.65,7.11}, {21,5.34,0.98}, {19,1.85,5486.78}, {19,4.97,213.3}, {17,2.99,6275.96}, {16,0.03,2544.31}, {16,1.43,2146.17}, {15,1.21,10977.08}, {12,2.83,1748.02}, {12,3.26,5088.63}, {12,5.27,1194.45}, {12,2.08,4694}, {11,0.77,553.57}, {10,1.3,6286.6}, {10,4.24,1349.87}, {9,2.7,242.73}, {9,5.64,951.72}, {8,5.3,2352.87}, {6,2.65,9437.76}, {6,4.67,4690.48} }, { {52919.0,0,0}, {8720.0,1.0721,6283.0758}, {309.0,0.867,12566.152}, {27,0.05,3.52}, {16,5.19,26.3}, {16,3.68,155.42}, {10,0.76,18849.23}, {9,2.06,77713.77}, {7,0.83,775.52}, {5,4.66,1577.34}, {4,1.03,7.11}, {4,3.44,5573.14}, {3,5.14,796.3}, {3,6.05,5507.55}, {3,1.19,242.73}, {3,6.12,529.69}, {3,0.31,398.15}, {3,2.28,553.57}, {2,4.38,5223.69}, {2,3.75,0.98} }, { {289.0,5.844,6283.076}, {35,0,0}, {17,5.49,12566.15}, {3,5.2,155.42}, {1,4.72,3.52}, {1,5.3,18849.23}, {1,5.97,242.73} }, { {114.0,3.142,0}, {8,4.13,6283.08}, {1,3.84,12566.15} }, { {1,3.14,0} } }; const double B_TERMS[B_COUNT][B_MAX_SUBCOUNT][TERM_COUNT]= { { {280.0,3.199,84334.662}, {102.0,5.422,5507.553}, {80,3.88,5223.69}, {44,3.7,2352.87}, {32,4,1577.34} }, { {9,3.9,5507.55}, {6,1.73,5223.69} } }; const double R_TERMS[R_COUNT][R_MAX_SUBCOUNT][TERM_COUNT]= { { {100013989.0,0,0}, {1670700.0,3.0984635,6283.07585}, {13956.0,3.05525,12566.1517}, {3084.0,5.1985,77713.7715}, {1628.0,1.1739,5753.3849}, {1576.0,2.8469,7860.4194}, {925.0,5.453,11506.77}, {542.0,4.564,3930.21}, {472.0,3.661,5884.927}, {346.0,0.964,5507.553}, {329.0,5.9,5223.694}, {307.0,0.299,5573.143}, {243.0,4.273,11790.629}, {212.0,5.847,1577.344}, {186.0,5.022,10977.079}, {175.0,3.012,18849.228}, {110.0,5.055,5486.778}, {98,0.89,6069.78}, {86,5.69,15720.84}, {86,1.27,161000.69}, {65,0.27,17260.15}, {63,0.92,529.69}, {57,2.01,83996.85}, {56,5.24,71430.7}, {49,3.25,2544.31}, {47,2.58,775.52}, {45,5.54,9437.76}, {43,6.01,6275.96}, {39,5.36,4694}, {38,2.39,8827.39}, {37,0.83,19651.05}, {37,4.9,12139.55}, {36,1.67,12036.46}, {35,1.84,2942.46}, {33,0.24,7084.9}, {32,0.18,5088.63}, {32,1.78,398.15}, {28,1.21,6286.6}, {28,1.9,6279.55}, {26,4.59,10447.39} }, { {103019.0,1.10749,6283.07585}, {1721.0,1.0644,12566.1517}, {702.0,3.142,0}, {32,1.02,18849.23}, {31,2.84,5507.55}, {25,1.32,5223.69}, {18,1.42,1577.34}, {10,5.91,10977.08}, {9,1.42,6275.96}, {9,0.27,5486.78} }, { {4359.0,5.7846,6283.0758}, {124.0,5.579,12566.152}, {12,3.14,0}, {9,3.63,77713.77}, {6,1.87,5573.14}, {3,5.47,18849.23} }, { {145.0,4.273,6283.076}, {7,3.92,12566.15} }, { {4,2.56,6283.08} } }; //////////////////////////////////////////////////////////////// /// Periodic Terms for the nutation in longitude and obliquity //////////////////////////////////////////////////////////////// const int Y_TERMS[Y_COUNT][TERM_Y_COUNT]= { {0,0,0,0,1}, {-2,0,0,2,2}, {0,0,0,2,2}, {0,0,0,0,2}, {0,1,0,0,0}, {0,0,1,0,0}, {-2,1,0,2,2}, {0,0,0,2,1}, {0,0,1,2,2}, {-2,-1,0,2,2}, {-2,0,1,0,0}, {-2,0,0,2,1}, {0,0,-1,2,2}, {2,0,0,0,0}, {0,0,1,0,1}, {2,0,-1,2,2}, {0,0,-1,0,1}, {0,0,1,2,1}, {-2,0,2,0,0}, {0,0,-2,2,1}, {2,0,0,2,2}, {0,0,2,2,2}, {0,0,2,0,0}, {-2,0,1,2,2}, {0,0,0,2,0}, {-2,0,0,2,0}, {0,0,-1,2,1}, {0,2,0,0,0}, {2,0,-1,0,1}, {-2,2,0,2,2}, {0,1,0,0,1}, {-2,0,1,0,1}, {0,-1,0,0,1}, {0,0,2,-2,0}, {2,0,-1,2,1}, {2,0,1,2,2}, {0,1,0,2,2}, {-2,1,1,0,0}, {0,-1,0,2,2}, {2,0,0,2,1}, {2,0,1,0,0}, {-2,0,2,2,2}, {-2,0,1,2,1}, {2,0,-2,0,1}, {2,0,0,0,1}, {0,-1,1,0,0}, {-2,-1,0,2,1}, {-2,0,0,0,1}, {0,0,2,2,1}, {-2,0,2,0,1}, {-2,1,0,2,1}, {0,0,1,-2,0}, {-1,0,1,0,0}, {-2,1,0,0,0}, {1,0,0,0,0}, {0,0,1,2,0}, {0,0,-2,2,2}, {-1,-1,1,0,0}, {0,1,1,0,0}, {0,-1,1,2,2}, {2,-1,-1,2,2}, {0,0,3,2,2}, {2,-1,0,2,2}, }; const double PE_TERMS[Y_COUNT][TERM_PE_COUNT]={ {-171996,-174.2,92025,8.9}, {-13187,-1.6,5736,-3.1}, {-2274,-0.2,977,-0.5}, {2062,0.2,-895,0.5}, {1426,-3.4,54,-0.1}, {712,0.1,-7,0}, {-517,1.2,224,-0.6}, {-386,-0.4,200,0}, {-301,0,129,-0.1}, {217,-0.5,-95,0.3}, {-158,0,0,0}, {129,0.1,-70,0}, {123,0,-53,0}, {63,0,0,0}, {63,0.1,-33,0}, {-59,0,26,0}, {-58,-0.1,32,0}, {-51,0,27,0}, {48,0,0,0}, {46,0,-24,0}, {-38,0,16,0}, {-31,0,13,0}, {29,0,0,0}, {29,0,-12,0}, {26,0,0,0}, {-22,0,0,0}, {21,0,-10,0}, {17,-0.1,0,0}, {16,0,-8,0}, {-16,0.1,7,0}, {-15,0,9,0}, {-13,0,7,0}, {-12,0,6,0}, {11,0,0,0}, {-10,0,5,0}, {-8,0,3,0}, {7,0,-3,0}, {-7,0,0,0}, {-7,0,3,0}, {-7,0,3,0}, {6,0,0,0}, {6,0,-3,0}, {6,0,-3,0}, {-6,0,3,0}, {-6,0,3,0}, {5,0,0,0}, {-5,0,3,0}, {-5,0,3,0}, {-5,0,3,0}, {4,0,0,0}, {4,0,0,0}, {4,0,0,0}, {-4,0,0,0}, {-4,0,0,0}, {-4,0,0,0}, {3,0,0,0}, {-3,0,0,0}, {-3,0,0,0}, {-3,0,0,0}, {-3,0,0,0}, {-3,0,0,0}, {-3,0,0,0}, {-3,0,0,0}, }; /////////////////////////////////////////////// double rad2deg(double radians) { return (180.0/PI)*radians; } double deg2rad(double degrees) { return (PI/180.0)*degrees; } double limit_degrees(double degrees) { double limited; degrees /= 360.0; limited = 360.0*(degrees-floor(degrees)); if (limited < 0) limited += 360.0; return limited; } double limit_degrees180pm(double degrees) { double limited; degrees /= 360.0; limited = 360.0*(degrees-floor(degrees)); if (limited < -180.0) limited += 360.0; else if (limited > 180.0) limited -= 360.0; return limited; } double limit_degrees180(double degrees) { double limited; degrees /= 180.0; limited = 180.0*(degrees-floor(degrees)); if (limited < 0) limited += 180.0; return limited; } double limit_zero2one(double value) { double limited; limited = value - floor(value); if (limited < 0) limited += 1.0; return limited; } double limit_minutes(double minutes) { double limited=minutes; if (limited < -20.0) limited += 1440.0; else if (limited > 20.0) limited -= 1440.0; return limited; } double dayfrac_to_local_hr(double dayfrac, double timezone) { return 24.0*limit_zero2one(dayfrac + timezone/24.0); } double third_order_polynomial(double a, double b, double c, double d, double x) { return ((a*x + b)*x + c)*x + d; } /////////////////////////////////////////////////////////////////////////////////////////////// int validate_inputs(spa_data *spa) { if ((spa->year < -2000) || (spa->year > 6000)) return 1; if ((spa->month < 1 ) || (spa->month > 12 )) return 2; if ((spa->day < 1 ) || (spa->day > 31 )) return 3; if ((spa->hour < 0 ) || (spa->hour > 24 )) return 4; if ((spa->minute < 0 ) || (spa->minute > 59 )) return 5; if ((spa->second < 0 ) || (spa->second > 59 )) return 6; if ((spa->pressure < 0 ) || (spa->pressure > 5000)) return 12; if ((spa->temperature <= -273) || (spa->temperature > 6000)) return 13; if ((spa->hour == 24 ) && (spa->minute > 0 )) return 5; if ((spa->hour == 24 ) && (spa->second > 0 )) return 6; if (fabs(spa->delta_t) > 8000 ) return 7; if (fabs(spa->timezone) > 18 ) return 8; if (fabs(spa->longitude) > 180 ) return 9; if (fabs(spa->latitude) > 90 ) return 10; if (fabs(spa->atmos_refract) > 5 ) return 16; if ( spa->elevation < -6500000) return 11; if ((spa->function == SPA_ZA_INC) || (spa->function == SPA_ALL)) { if (fabs(spa->slope) > 360) return 14; if (fabs(spa->azm_rotation) > 360) return 15; } return 0; } /////////////////////////////////////////////////////////////////////////////////////////////// double julian_day (int year, int month, int day, int hour, int minute, int second, double tz) { double day_decimal, julian_day, a; day_decimal = day + (hour - tz + (minute + second/60.0)/60.0)/24.0; if (month < 3) { month += 12; year--; } julian_day = floor(365.25*(year+4716.0)) + floor(30.6001*(month+1)) + day_decimal - 1524.5; if (julian_day > 2299160.0) { a = floor(year/100); julian_day += (2 - a + floor(a/4)); } return julian_day; } double julian_century(double jd) { return (jd-2451545.0)/36525.0; } double julian_ephemeris_day(double jd, double delta_t) { return jd+delta_t/86400.0; } double julian_ephemeris_century(double jde) { return (jde - 2451545.0)/36525.0; } double julian_ephemeris_millennium(double jce) { return (jce/10.0); } double earth_periodic_term_summation(const double terms[][TERM_COUNT], int count, double jme) { int i; double sum=0; for (i = 0; i < count; i++) sum += terms[i][TERM_A]*cos(terms[i][TERM_B]+terms[i][TERM_C]*jme); return sum; } double earth_values(double term_sum[], int count, double jme) { int i; double sum=0; for (i = 0; i < count; i++) sum += term_sum[i]*pow(jme, i); sum /= 1.0e8; return sum; } double earth_heliocentric_longitude(double jme) { double sum[L_COUNT]; int i; for (i = 0; i < L_COUNT; i++) sum[i] = earth_periodic_term_summation(L_TERMS[i], l_subcount[i], jme); return limit_degrees(rad2deg(earth_values(sum, L_COUNT, jme))); } double earth_heliocentric_latitude(double jme) { double sum[B_COUNT]; int i; for (i = 0; i < B_COUNT; i++) sum[i] = earth_periodic_term_summation(B_TERMS[i], b_subcount[i], jme); return rad2deg(earth_values(sum, B_COUNT, jme)); } double earth_radius_vector(double jme) { double sum[R_COUNT]; int i; for (i = 0; i < R_COUNT; i++) sum[i] = earth_periodic_term_summation(R_TERMS[i], r_subcount[i], jme); return earth_values(sum, R_COUNT, jme); } double geocentric_longitude(double l) { double theta = l + 180.0; if (theta >= 360.0) theta -= 360.0; return theta; } double geocentric_latitude(double b) { return -b; } double mean_elongation_moon_sun(double jce) { return third_order_polynomial(1.0/189474.0, -0.0019142, 445267.11148, 297.85036, jce); } double mean_anomaly_sun(double jce) { return third_order_polynomial(-1.0/300000.0, -0.0001603, 35999.05034, 357.52772, jce); } double mean_anomaly_moon(double jce) { return third_order_polynomial(1.0/56250.0, 0.0086972, 477198.867398, 134.96298, jce); } double argument_latitude_moon(double jce) { return third_order_polynomial(1.0/327270.0, -0.0036825, 483202.017538, 93.27191, jce); } double ascending_longitude_moon(double jce) { return third_order_polynomial(1.0/450000.0, 0.0020708, -1934.136261, 125.04452, jce); } double xy_term_summation(int i, double x[TERM_X_COUNT]) { int j; double sum=0; for (j = 0; j < TERM_Y_COUNT; j++) sum += x[j]*Y_TERMS[i][j]; return sum; } void nutation_longitude_and_obliquity(double jce, double x[TERM_X_COUNT], double *del_psi, double *del_epsilon) { int i; double xy_term_sum, sum_psi=0, sum_epsilon=0; for (i = 0; i < Y_COUNT; i++) { xy_term_sum = deg2rad(xy_term_summation(i, x)); sum_psi += (PE_TERMS[i][TERM_PSI_A] + jce*PE_TERMS[i][TERM_PSI_B])*sin(xy_term_sum); sum_epsilon += (PE_TERMS[i][TERM_EPS_C] + jce*PE_TERMS[i][TERM_EPS_D])*cos(xy_term_sum); } *del_psi = sum_psi / 36000000.0; *del_epsilon = sum_epsilon / 36000000.0; } double ecliptic_mean_obliquity(double jme) { double u = jme/10.0; return 84381.448 + u*(-4680.93 + u*(-1.55 + u*(1999.25 + u*(-51.38 + u*(-249.67 + u*( -39.05 + u*( 7.12 + u*( 27.87 + u*( 5.79 + u*2.45))))))))); } double ecliptic_true_obliquity(double delta_epsilon, double epsilon0) { return delta_epsilon + epsilon0/3600.0; } double aberration_correction(double r) { return -20.4898 / (3600.0*r); } double apparent_sun_longitude(double theta, double delta_psi, double delta_tau) { return theta + delta_psi + delta_tau; } double greenwich_mean_sidereal_time (double jd, double jc) { return limit_degrees(280.46061837 + 360.98564736629 * (jd - 2451545.0) + jc*jc*(0.000387933 - jc/38710000.0)); } double greenwich_sidereal_time (double nu0, double delta_psi, double epsilon) { return nu0 + delta_psi*cos(deg2rad(epsilon)); } double geocentric_sun_right_ascension(double lamda, double epsilon, double beta) { double lamda_rad = deg2rad(lamda); double epsilon_rad = deg2rad(epsilon); return limit_degrees(rad2deg(atan2(sin(lamda_rad)*cos(epsilon_rad) - tan(deg2rad(beta))*sin(epsilon_rad), cos(lamda_rad)))); } double geocentric_sun_declination(double beta, double epsilon, double lamda) { double beta_rad = deg2rad(beta); double epsilon_rad = deg2rad(epsilon); return rad2deg(asin(sin(beta_rad)*cos(epsilon_rad) + cos(beta_rad)*sin(epsilon_rad)*sin(deg2rad(lamda)))); } double observer_hour_angle(double nu, double longitude, double alpha_deg) { return limit_degrees(nu + longitude - alpha_deg); } double sun_equatorial_horizontal_parallax(double r) { return 8.794 / (3600.0 * r); } void sun_right_ascension_parallax_and_topocentric_dec(double latitude, double elevation, double xi, double h, double delta, double *delta_alpha, double *delta_prime) { double delta_alpha_rad; double lat_rad = deg2rad(latitude); double xi_rad = deg2rad(xi); double h_rad = deg2rad(h); double delta_rad = deg2rad(delta); double u = atan(0.99664719 * tan(lat_rad)); double y = 0.99664719 * sin(u) + elevation*sin(lat_rad)/6378140.0; double x = cos(u) + elevation*cos(lat_rad)/6378140.0; delta_alpha_rad = atan2( - x*sin(xi_rad) *sin(h_rad), cos(delta_rad) - x*sin(xi_rad) *cos(h_rad)); *delta_prime = rad2deg(atan2((sin(delta_rad) - y*sin(xi_rad))*cos(delta_alpha_rad), cos(delta_rad) - x*sin(xi_rad) *cos(h_rad))); *delta_alpha = rad2deg(delta_alpha_rad); } double topocentric_sun_right_ascension(double alpha_deg, double delta_alpha) { return alpha_deg + delta_alpha; } double topocentric_local_hour_angle(double h, double delta_alpha) { return h - delta_alpha; } double topocentric_elevation_angle(double latitude, double delta_prime, double h_prime) { double lat_rad = deg2rad(latitude); double delta_prime_rad = deg2rad(delta_prime); return rad2deg(asin(sin(lat_rad)*sin(delta_prime_rad) + cos(lat_rad)*cos(delta_prime_rad) * cos(deg2rad(h_prime)))); } double atmospheric_refraction_correction(double pressure, double temperature, double atmos_refract, double e0) { double del_e = 0; if (e0 >= -1*(SUN_RADIUS + atmos_refract)) del_e = (pressure / 1010.0) * (283.0 / (273.0 + temperature)) * 1.02 / (60.0 * tan(deg2rad(e0 + 10.3/(e0 + 5.11)))); return del_e; } double topocentric_elevation_angle_corrected(double e0, double delta_e) { return e0 + delta_e; } double topocentric_zenith_angle(double e) { return 90.0 - e; } double topocentric_azimuth_angle_neg180_180(double h_prime, double latitude, double delta_prime) { double h_prime_rad = deg2rad(h_prime); double lat_rad = deg2rad(latitude); return rad2deg(atan2(sin(h_prime_rad), cos(h_prime_rad)*sin(lat_rad) - tan(deg2rad(delta_prime))*cos(lat_rad))); } double topocentric_azimuth_angle_zero_360(double azimuth180) { return azimuth180 + 180.0; } double surface_incidence_angle(double zenith, double azimuth180, double azm_rotation, double slope) { double zenith_rad = deg2rad(zenith); double slope_rad = deg2rad(slope); return rad2deg(acos(cos(zenith_rad)*cos(slope_rad) + sin(slope_rad )*sin(zenith_rad) * cos(deg2rad(azimuth180 - azm_rotation)))); } double sun_mean_longitude(double jme) { return limit_degrees(280.4664567 + jme*(360007.6982779 + jme*(0.03032028 + jme*(1/49931.0 + jme*(-1/15300.0 + jme*(-1/2000000.0)))))); } double eot(double m, double alpha, double del_psi, double epsilon) { return limit_minutes(4.0*(m - 0.0057183 - alpha + del_psi*cos(deg2rad(epsilon)))); } double approx_sun_transit_time(double alpha_zero, double longitude, double nu) { return (alpha_zero - longitude - nu) / 360.0; } double sun_hour_angle_at_rise_set(double latitude, double delta_zero, double h0_prime) { double h0 = -99999; double latitude_rad = deg2rad(latitude); double delta_zero_rad = deg2rad(delta_zero); double argument = (sin(deg2rad(h0_prime)) - sin(latitude_rad)*sin(delta_zero_rad)) / (cos(latitude_rad)*cos(delta_zero_rad)); if (fabs(argument) <= 1) h0 = limit_degrees180(rad2deg(acos(argument))); return h0; } void approx_sun_rise_and_set(double *m_rts, double h0) { double h0_dfrac = h0/360.0; m_rts[SUN_RISE] = limit_zero2one(m_rts[SUN_TRANSIT] - h0_dfrac); m_rts[SUN_SET] = limit_zero2one(m_rts[SUN_TRANSIT] + h0_dfrac); m_rts[SUN_TRANSIT] = limit_zero2one(m_rts[SUN_TRANSIT]); } double rts_alpha_delta_prime(double *ad, double n) { double a = ad[JD_ZERO] - ad[JD_MINUS]; double b = ad[JD_PLUS] - ad[JD_ZERO]; if (fabs(a) >= 2.0) a = limit_zero2one(a); if (fabs(b) >= 2.0) b = limit_zero2one(b); return ad[JD_ZERO] + n * (a + b + (b-a)*n)/2.0; } double rts_sun_altitude(double latitude, double delta_prime, double h_prime) { double latitude_rad = deg2rad(latitude); double delta_prime_rad = deg2rad(delta_prime); return rad2deg(asin(sin(latitude_rad)*sin(delta_prime_rad) + cos(latitude_rad)*cos(delta_prime_rad)*cos(deg2rad(h_prime)))); } double sun_rise_and_set(double *m_rts, double *h_rts, double *delta_prime, double latitude, double *h_prime, double h0_prime, int sun) { return m_rts[sun] + (h_rts[sun] - h0_prime) / (360.0*cos(deg2rad(delta_prime[sun]))*cos(deg2rad(latitude))*sin(deg2rad(h_prime[sun]))); } //////////////////////////////////////////////////////////////////////////////////////////////// // Calculate required SPA parameters to get the right ascension (alpha) and declination (delta) // Note: JD must be already calculated and in structure //////////////////////////////////////////////////////////////////////////////////////////////// void calculate_geocentric_sun_right_ascension_and_declination(spa_data *spa) { double x[TERM_X_COUNT]; spa->jc = julian_century(spa->jd); spa->jde = julian_ephemeris_day(spa->jd, spa->delta_t); spa->jce = julian_ephemeris_century(spa->jde); spa->jme = julian_ephemeris_millennium(spa->jce); spa->l = earth_heliocentric_longitude(spa->jme); spa->b = earth_heliocentric_latitude(spa->jme); spa->r = earth_radius_vector(spa->jme); spa->theta = geocentric_longitude(spa->l); spa->beta = geocentric_latitude(spa->b); x[TERM_X0] = spa->x0 = mean_elongation_moon_sun(spa->jce); x[TERM_X1] = spa->x1 = mean_anomaly_sun(spa->jce); x[TERM_X2] = spa->x2 = mean_anomaly_moon(spa->jce); x[TERM_X3] = spa->x3 = argument_latitude_moon(spa->jce); x[TERM_X4] = spa->x4 = ascending_longitude_moon(spa->jce); nutation_longitude_and_obliquity(spa->jce, x, &(spa->del_psi), &(spa->del_epsilon)); spa->epsilon0 = ecliptic_mean_obliquity(spa->jme); spa->epsilon = ecliptic_true_obliquity(spa->del_epsilon, spa->epsilon0); spa->del_tau = aberration_correction(spa->r); spa->lamda = apparent_sun_longitude(spa->theta, spa->del_psi, spa->del_tau); spa->nu0 = greenwich_mean_sidereal_time (spa->jd, spa->jc); spa->nu = greenwich_sidereal_time (spa->nu0, spa->del_psi, spa->epsilon); spa->alpha = geocentric_sun_right_ascension(spa->lamda, spa->epsilon, spa->beta); spa->delta = geocentric_sun_declination(spa->beta, spa->epsilon, spa->lamda); } //////////////////////////////////////////////////////////////////////// // Calculate Equation of Time (EOT) and Sun Rise, Transit, & Set (RTS) //////////////////////////////////////////////////////////////////////// void calculate_eot_and_sun_rise_transit_set(spa_data *spa) { spa_data sun_rts; double nu, m, h0, n; double alpha[JD_COUNT], delta[JD_COUNT]; double m_rts[SUN_COUNT], nu_rts[SUN_COUNT], h_rts[SUN_COUNT]; double alpha_prime[SUN_COUNT], delta_prime[SUN_COUNT], h_prime[SUN_COUNT]; double h0_prime = -1*(SUN_RADIUS + spa->atmos_refract); int i; sun_rts = *spa; m = sun_mean_longitude(spa->jme); spa->eot = eot(m, spa->alpha, spa->del_psi, spa->epsilon); sun_rts.hour = sun_rts.minute = sun_rts.second = 0; sun_rts.timezone = 0.0; sun_rts.jd = julian_day (sun_rts.year, sun_rts.month, sun_rts.day, sun_rts.hour, sun_rts.minute, sun_rts.second, sun_rts.timezone); calculate_geocentric_sun_right_ascension_and_declination(&sun_rts); nu = sun_rts.nu; sun_rts.delta_t = 0; sun_rts.jd--; for (i = 0; i < JD_COUNT; i++) { calculate_geocentric_sun_right_ascension_and_declination(&sun_rts); alpha[i] = sun_rts.alpha; delta[i] = sun_rts.delta; sun_rts.jd++; } m_rts[SUN_TRANSIT] = approx_sun_transit_time(alpha[JD_ZERO], spa->longitude, nu); h0 = sun_hour_angle_at_rise_set(spa->latitude, delta[JD_ZERO], h0_prime); if (h0 >= 0) { approx_sun_rise_and_set(m_rts, h0); for (i = 0; i < SUN_COUNT; i++) { nu_rts[i] = nu + 360.985647*m_rts[i]; n = m_rts[i] + spa->delta_t/86400.0; alpha_prime[i] = rts_alpha_delta_prime(alpha, n); delta_prime[i] = rts_alpha_delta_prime(delta, n); h_prime[i] = limit_degrees180pm(nu_rts[i] + spa->longitude - alpha_prime[i]); h_rts[i] = rts_sun_altitude(spa->latitude, delta_prime[i], h_prime[i]); } spa->srha = h_prime[SUN_RISE]; spa->ssha = h_prime[SUN_SET]; spa->sta = h_rts[SUN_TRANSIT]; spa->suntransit = dayfrac_to_local_hr(m_rts[SUN_TRANSIT] - h_prime[SUN_TRANSIT] / 360.0, spa->timezone); spa->sunrise = dayfrac_to_local_hr(sun_rise_and_set(m_rts, h_rts, delta_prime, spa->latitude, h_prime, h0_prime, SUN_RISE), spa->timezone); spa->sunset = dayfrac_to_local_hr(sun_rise_and_set(m_rts, h_rts, delta_prime, spa->latitude, h_prime, h0_prime, SUN_SET), spa->timezone); } else spa->srha= spa->ssha= spa->sta= spa->suntransit= spa->sunrise= spa->sunset= -99999; } /////////////////////////////////////////////////////////////////////////////////////////// // Calculate all SPA parameters and put into structure // Note: All inputs values (listed in header file) must already be in structure /////////////////////////////////////////////////////////////////////////////////////////// int spa_calculate(spa_data *spa) { int result; result = validate_inputs(spa); if (result == 0) { spa->jd = julian_day (spa->year, spa->month, spa->day, spa->hour, spa->minute, spa->second, spa->timezone); calculate_geocentric_sun_right_ascension_and_declination(spa); spa->h = observer_hour_angle(spa->nu, spa->longitude, spa->alpha); spa->xi = sun_equatorial_horizontal_parallax(spa->r); sun_right_ascension_parallax_and_topocentric_dec(spa->latitude, spa->elevation, spa->xi, spa->h, spa->delta, &(spa->del_alpha), &(spa->delta_prime)); spa->alpha_prime = topocentric_sun_right_ascension(spa->alpha, spa->del_alpha); spa->h_prime = topocentric_local_hour_angle(spa->h, spa->del_alpha); spa->e0 = topocentric_elevation_angle(spa->latitude, spa->delta_prime, spa->h_prime); spa->del_e = atmospheric_refraction_correction(spa->pressure, spa->temperature, spa->atmos_refract, spa->e0); spa->e = topocentric_elevation_angle_corrected(spa->e0, spa->del_e); spa->zenith = topocentric_zenith_angle(spa->e); spa->azimuth180 = topocentric_azimuth_angle_neg180_180(spa->h_prime, spa->latitude, spa->delta_prime); spa->azimuth = topocentric_azimuth_angle_zero_360(spa->azimuth180); if ((spa->function == SPA_ZA_INC) || (spa->function == SPA_ALL)) spa->incidence = surface_incidence_angle(spa->zenith, spa->azimuth180, spa->azm_rotation, spa->slope); if ((spa->function == SPA_ZA_RTS) || (spa->function == SPA_ALL)) calculate_eot_and_sun_rise_transit_set(spa); } return result; }Here Mr. Jone Understand problem properly. I have attached the youtube links. for refernce