// Compute apparent sunset on a titled surface facing the equator
// Duffie and Beckman (1991) eqn 2.19.3b
public static double GetApparentSunsetHourAngleEquator // (o) apparent sunset hour angle [radians]
(double Slope // (i) slope of receiving surface [radians]
, double Lat // (i) latitude [radians, N > 0]
, double Decl // (i) declination [radians]
)
{
double IsNorth, Aux1, Aux2;
IsNorth = (Lat > 0) ? 1 : -1;
Aux1 = Astro.GetSunsetHourAngle(Lat, Decl);
Aux2 = Astro.GetSunsetHourAngle(Lat - IsNorth * Slope, Decl);
return(Math.Min(Aux1, Aux2));
}
// Compute apparent sunrise and sunset times on a tilted surface of any orientation
// Duffie and Beckman (1991) eqn 2.20.5e to 2.20.5i
public static void CalcApparentSunsetHourAngle
(double Lat // (i) latitude [radians]
, double Decl // (i) declination [radians]
, double Slope // (i) slope of receiving surface [radians]
, double Azimuth // (i) azimuth angle of receiving surface [radians]
, out double AppSunrise // (o) apparent sunrise hour angle [radians]
, out double AppSunset // (o) apparent sunset hour angle [radians]
, out double Sunset // (o) true sunset hour angle [radians]
)
{
// Declarations
double aux1, aux2, aux3, disc;
double cosInc, SunZenith, SunAzimuth;
double A, B, C;
// Calculate true sunset and parameters A, B and C
Sunset = Astro.GetSunsetHourAngle(Lat, Decl);
A = Math.Cos(Slope) + Math.Tan(Lat) * Math.Cos(Azimuth) * Math.Sin(Slope);
B = Math.Cos(Sunset) * Math.Cos(Slope) + Math.Tan(Decl) * Math.Sin(Slope) * Math.Cos(Azimuth);
C = Math.Sin(Slope) * Math.Sin(Azimuth) / Math.Cos(Lat);
// Pathological case: the sun does not rise
if (Sunset == 0)
{
AppSunrise = AppSunset = 0;
return;
}
// Normal case
aux1 = A * A + C * C;
disc = aux1 - B * B;
// Check discriminant. If it is positive or zero, the sun rises (tangentially)
// on the surface. In that case, calculate apparent sunrise and apparent
// sunset
if (disc >= 0)
{
aux2 = C * Math.Sqrt(disc) / aux1;
aux3 = A * B / aux1;
AppSunrise = Math.Min(Sunset, Math.Acos(aux3 + aux2));
AppSunset = Math.Min(Sunset, Math.Acos(aux3 - aux2));
if ((A > 0 && B > 0) || (A >= B))
{
AppSunrise = -AppSunrise;
}
else
{
AppSunset = -AppSunset;
}
}
// If discriminant is negative, the surface is either always or never
// illuminated during the day. To find which case applies, compute the
// cosine of the angle of incidence on the surface at noon. If it is less
// than zero, then the surface is always in the dark. If it is greater
// than zero, then the surface is always illuminated
else
{
Astro.CalcSunPositionHourAngle(Decl, 0, Lat, out SunZenith, out SunAzimuth);
cosInc = GetCosIncidenceAngle(SunZenith, SunAzimuth, Slope, Azimuth);
if (cosInc < 0)
{
AppSunrise = AppSunset = 0;
}
else
{
AppSunrise = -Sunset;
AppSunset = Sunset;
}
}
}