EME 810
Solar Resource Assessment and Economics

2.3 Basic Solar Jargon for Angular Relations

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When we want a shorthand to describe spatial relationships on continuous surfaces that are sphere-like, as with the Earth and the surrounding sky and stars, we choose to use Greek letters. In contrast, when we are trying to communicate things like linear distances, lengths, time, or simple Cartesian coordinates, then we will tend to use Roman letters for our shorthand.

You may notice in your reading of older textbooks that several systems of sign convention for the angles have emerged for practical use. Also, the various systems can have different approaches to azimuth that we should be aware of. For instance, the software SAM (System Advisor Model) will use both the $360^\circ$ clockwise standard (from Meteorology) as well as the $\pm180^\circ$ standard used extensively in the component-based models of TRNSYS and SAM. We will be sure to become familiar with both.

Below are four tables showing the Angular Symbols for Standard Solar Relations.

General Angles

Table 2.2: General Angles
Angular Measure Symbol Range and Sign Convention
altitude angle α (alpha) 0o to + 90o; horizontal is zero
azimuth angle γ (gamma) 0o to + 360o; clockwise from North origin
azimuth (alternate) γ (gamma) 0o to ±180o; zero (origin) faces the equator, East is + ive, West is - ive

Earth-Sun Angles

Table 2.3: Earth-Sun Angles
Angular Measure Symbol Range and Sign Convention
latitude ϕ (phi) 0o to ± 90o; Northern Hemisphere is +ive
longitude λ (lambda) 0o to ± 180o; Prime Meridian is zero, West is -ive
declination δ (delta) 0o to ± 23.45o; Northern Hemisphere is +ive
hour angle ω (omega) 0o to ± 180o; solar noon is zero, afternoon is +ive, morning is -ive

Sun-Observer Angles

Table 2.4: Sun-Observer Angles
Angular Measure Symbol Range and Sign Convention
solar altitude angle (complement) α s = 1 −  θ z
α s =1− θ z
(alphas is the complement of thetaz)		 0o to + 90o
solar azimuth angle γ s
(gammas)		 0o to + 360o; clockwise from North origin
zenith angle θ z
(thetaz)		 0o to + 90o; vertical is zero

Collector-Sun Angles

Table 2.5: Collector-Sun Angles
Angular Measure Symbol Range and Sign Convention
surface altitude angle α (alpha) 0o to + 90o
slope or tilt (of collector surface) β (beta) 0o to ±90o; facing equator is +ive
surface azimuth angle γ (gamma) 0o to + 360o; clockwise from North origin
angle of incidence θ (theta) 0o to + 90o
glancing angle (complement) α=1−θ
(alpha)		 0o to + 90o