3. Solstices
June solstice - North Pole is tilted 23.5o
towards the Sun
relative to the circle of illumination. All places above a
latitude of 66.5o
N are in 24 hours of sunlight, while
locations below a latitude of 66.5o
S are in darkness.
4. Equinoxes
Equinoxes – Earth’s axis is not tilted toward or away
from the Sun and the circle of illumination cuts through
the poles. Red circles are the Arctic Circle.
8. Relationship of maximum Sun height to latitude for the
equinox (left) and June solstice (right). The red values
on the right of the globes are maximum solar altitudes at
solar noon. During the equinox, the equator is the
location on the Earth with a Sun angle of 90 degrees for
solar noon
9. Solar Altitude
α = Sin-1[Sin δ Sin φ + Cos δ Cos ω Cos φ]
φ is latitude
Hour Angle
ω = 15 (ts – 12) (degrees)
ts is local solar time in hours
Declination Angle
δ = Sin-1 [0.39795 Cos [0.98563 (N-173)]]
16. Total Daily Extraterrestrial Solar Radiation on a
Horizontal Surface
Ho,h = 86,400 Io [ωs Sin Φ Sin δ + Cos δ Cos Φ Sin ωs] / π (J/m2
)
Io = Isc [1 + 0.34 cos {2πN / 365.25}] is the solar constant
Isc = 1367 Watt
ωs = cos–1
[- tan(δ) tan(Φ)] is the hour angle of sunset in radians
-Ve before noon & +Ve after noon
Instantaneous Extraterrestrial Solar Radiation on a Horizontal
Surface
Ioh = Io [cos δ cos Φ cos ω + sin δ sin Φ]
29. Effect of Air
Mass on
Spectral
Irradiance
on the
Ground
Air Mass = 1
for sea level
normal
Irradiance
Sun rise &
Sun set > 30
air mass
30. Air mass
AM = 1/[cos θz + 0.50572 (96.07995 – θz) -1.6364
]
θz = Zenith angle = 90o
at sunset
Solar Radiation Attenuation Due to Air Mass
I = 1.1 x Ioh x 0.7(AM)**(0.678)
factor of 1.1 accommodates the 10% diffused radiation
31. Attenuation of Normal Solar Radiation Versus
Azimuth Angle
0
5
10
15
20
25
30
35
40
45
0 20 40 60 80 100
Azimuth Angle (degrees)
AirMass/SolarRadiation
Air Mass
Solar Radiation
(25 W units)
