Sun Angles on a Fixed Tilt

A fixed collector sees the sun through four angles that change on two different clocks. Declination δ moves with the season, while altitude β and azimuth φS move through the day, and the incidence angle θ collects all of them against the panel normal. Angle conventions and equations follow Masters chapter on The Solar Resource.

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Site and time

Collector

Angles

δDeclination
HHour angle
βSolar altitude
φSSolar azimuth
θIncidence angle
cos θBeam fraction
IBCClear-sky beam

Declination through the year

The seasonal clock: δ = 23.45° sin[360(n − 81)/365].

Beam fraction through the day

The daily clock: cos θ on this fixed tilt, sunrise to sunset.

Declinationδ = 23.45° sin[(360/365)(n − 81)]
Hour angleH = (15°/h) · (hours before solar noon)
Altitudesin β = cos L cos δ cos H + sin L sin δ
Azimuthsin φS = cos δ sin H / cos β
Incidence anglecos θ = cos β cos(φS − φC) sin Σ + sin β cos Σ
Clear-sky beam on the collectorIBC = A e−km cos θ,   m = 1/sin β