Comprehensive Solar Energy & Sky Dome Simulation

1. Eccentricity Correction (E0)
E0 = 1 + 0.033 * cos((360 * n) / 365)
Accounts for Earth-Sun distance variation across day of year n.

2. Solar Declination (delta)
delta = 23.45° * sin(360° * (284 + n) / 365)
Angular position of the sun relative to Earth's equator.

3. Solar Hour Angle (omega)
omega = 15° * (Solar Time - 12)
Angular displacement (15°/hour) from local solar noon.

4. Zenith Angle (theta_z) & Elevation (alpha)
cos(theta_z) = sin(phi)*sin(delta) + cos(phi)*cos(delta)*cos(omega)
alpha = 90° - theta_z

5. Angle of Incidence (theta)
cos(theta) = sin(delta)*sin(phi)*cos(beta) - sin(delta)*cos(phi)*sin(beta)*cos(gamma) + cos(delta)*cos(phi)*cos(beta)*cos(omega) + cos(delta)*sin(phi)*sin(beta)*cos(gamma)*cos(omega) + cos(delta)*sin(beta)*sin(gamma)*sin(omega)
Where beta is tilt and gamma is surface azimuth.

6. Air Mass (AM) & Direct Normal (G_bn)
AM = 1 / [cos(theta_z) + 0.50572 * (90 - theta_z + 6.07995)^(-1.6364)]
G_bn = G_sc * E0 * (0.7)^(AM^0.678)
Hottel clear-sky attenuation model (G_sc = 1367 W/m²).

7. Global Horizontal Irradiance (GHI)
GHI = G_bn * cos(theta_z) + G_dh
Sum of direct horizontal beam and clear-sky diffuse.

8. Total Tilted Irradiance (G_t)
G_t = G_b,t + G_d,t + G_r,t
G_b,t = G_bn * max(0, cos(theta))
G_d,t = G_dh * [(1 + cos(beta)) / 2]
G_r,t = GHI * rho * [(1 - cos(beta)) / 2]