MATLAB Programming Fundamentals - MathWorks

The sun's declination (δ) is the angle of the sun relative to the earth's equatorial plane.

The solar declination is 0 ∘ at the vernal and autumnal equinoxes and rises to a maximum

of23.45∘ at the summer solstice. On any given day of the year (d), declination can be
calculated from the following formula:

δ= sin−^1 sin(23.45)sin

360

365

(d−81)

From the declination (δ) and the latitude (φ) we can calculate the sun's elevation (α) at
the current time.

α= sin−^1 sinδsinφ+cosδcosφcosω

Here ω is the hour angle, which is the number of degrees of rotation of the earth between
the current solar time and solar noon.

delta = asind(sind(23.45)sind(360(d - 81)/365)); % Declination
omega = 15(solarTime.Hour + solarTime.Minute/60 - 12); % Hour angle
alpha = asind(sind(delta)sind(phi) + ... % Elevation
cosd(delta)cosd(phi)cosd(omega));
disp(['Solar Declination = ' num2str(delta) ' Solar Elevation = ' num2str(alpha)])

Solar Declination = 21.9634 Solar Elevation = 69.2589

Knowing the sun's declination and the local latitude allows us to calculate the time of
sunrise and sunset. Sunrise and sunset are calculated in Standard Time.

sunrise= 12−

cos−^1 −tanφtanδ

15 ∘

−

TC

60

sunset= 12+

cos−^1 −tanφtanδ

15 ∘

−

TC

60

midnight = dateshift(localTime,'start','day');
sr = 12 - acosd(-tand(phi)tand(delta))/15 - solarCorr/60;
sunrise = timeofday(midnight + hours(sr));
ss = 12 + acosd(-tand(phi)tand(delta))/15 - solarCorr/60;
sunset = timeofday(midnight + hours(ss));
disp(['Sunrise = ' datestr(sunrise,'HH:MM:SS') ' Sunset = ' datestr(sunset,'HH:MM:ss') ])

Sunrise = 04:15:34 Sunset = 19:08:11

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