Angular Symbols for Standard Solar Relations

General Angles

Summarized below are angle notations that will be used in readings and problems throughout the course. In the literature, you may encounter some variation of symbols and their interpretation, so in the attempt of better consistency, we will try to stick this table as a reference guide.

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

Earth-Sun Angles

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

Sun-Observer Angles

Sun-Observer Angles
Angular Measure	Symbol	Range and Sign Convention
solar altitude angle (complement)	$α_{s} = 1 - θ_{z}$ $α_{s} = 1 - θ_{z}$ (alpha_s is the complement of theta_z)	0^o to + 90^o
solar azimuth angle	$γ_{s}$ (gamma_s)	0^o to + 360^o; clockwise from North origin
zenith angle	$θ_{z}$ (theta_z)	0^o to + 90^o; vertical is zero

Collector-Sun Angles

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

Angular Symbols for Standard Solar Relations

General Angles

Earth-Sun Angles

Sun-Observer Angles

Collector-Sun Angles

Navigation

EMS

Programs

Related Links