solar spectrum and effect of azimuth angle

Spectrum of sunlight or solar spectrum

Solar Spectrum

Solar Spectrum

The light energy from the sun occupies a wide range of frequencies. It extends from Infra red to ultraviolet region. A graph of spectral irradiance to wavelength is shown in the figure. The sun acts as a black body radiator with temperature of black body equal to 5250 Degrees Centigrade approximately fits the spectrum of sun light. The spectral power density (power per hertz) of a black body radiator is given as

                             u (λ) = (2*h*C25)*1/(eh*ν/(K*T)-1)

Where λ is the wavelength of incident light in m,

h is Planck’s constant = 6.626*10-34 J.s,

ν is the frequency of light in hertz,

K is Boltzmann’s constant = 1.38*10^-23 J/K,

T is the absolute temperature in Kelvin,

C is the velocity of light = 3*108 m/s

Most of the usable portion of solar energy occupies visible portion of spectrum. The energy available in sunlight in terms of solar spectral irradiance for the air mass one condition for different range of frequencies is shown in the table

Wavelength (nm)


Solar spectral irradiance(milli watts/cm2)

Higher than 1150

(Far infrared region)




(Near infrared region)




(visible region)




(ultraviolet, X-rays e.t.c)





Total=107 mW/cm2

Wavelengths in solar spectrum higher than 1150 nm are termed as far infrared region with energies 0-1.08 eV. This range of frequencies will not be available to solar cells as a energy source. This is one of the major limitations on the efficiency of solar cells. The range of frequencies in the range 1150-700 nm corresponds to near infrared region. From the table it is obvious that the solar irradiance in the visible region is higher followed by near infrared region, far infrared region, and ultraviolet region in the decreasing order of solar irradiance. Most of the energy in the ultraviolet and X-ray region will be absorbed by Ozone layer in upper parts of atmosphere.

Solar power flux

The sun’s energy output will be slightly fluctuating by a few percent from time to time. Hence a common average value is assigned to the power density available to detector positioned just outside earth’s atmosphere. This is called as solar constant and is given as

                                      Solar constant = 0.1353 w/cm2

Once the sunlight reaches earth’s atmosphere a number of additional effects become important. They will reduce the energy density in the sunlight at the earth’s surface. Under these conditions the power flux at earth’s surface with sun directly overhead on the zenith and cloudless day is

                                                 Power Flux = 0.0107 w/cm2

The other factors influencing the solar energy availability are geometric in nature. They are

  • The earth rotates on its axis with a time period of 24 hours of which the sun light is available for only 12 hours a day
  • The earth’s axis of rotation is tilted approximately 23.5 degrees to the normal to the plane of its rotation about the sun.

Together these effects act to produce a shift in the number of hours of daylight and a geometrical situation in which sun is almost never on the zenith, thereby enhancing light losses due to atmospheric phenomena surveyed.

Effect of azimuth angle on solar energy output

Effect of azimuth angle on solar energy output

Effect of azimuth angle on solar energy output

Effect of azimuth angle on solar energy output

Effect of azimuth angle on solar energy output

For vertical orientation of sun and horizontal orientation for the collectors relative to earth’s surface the solar input power is 1.07 kW/m2. The condition of vertical orientation of sun and cloudless day (atmospheric effects are negligible on cloudless day) is known as air-mass-one. The air mass coefficient defines the direct optical path length through the Earth’s atmosphere, expressed as a ratio relative to the path length vertically upwards, i.e. at the zenith. If the sun makes an angle Ф with the normal of the detector lying flat on the earth’s surface, the air mass coefficient  and available solar power P is

                            AM = 1/cos (Ф), P = α (Ф) *cos (Ф) = α (Ф)/AM.

Where α(Ф) is multiplication factor which depends on angle Ф can be used to characterize the solar spectrum after solar radiation has travelled through the atmosphere, greater the angle Ф greater the length of atmosphere which must be traversed and the more light is scattered and absorbed, thus, value of α decreases. α(Ф) has the units of power density W/m^2. Its value is 1.07 kW/m^2 for air-mass-one (When the sun is directly overhead, the Air Mass is 1).

Total solar insolation

The total solar insolation is defined as the energy received directly from the sun. Total Solar insolation can be estimated approximately for the condition that the sun makes an angle Ф with the normal of the detector lying flat on the earth’s surface by the following equation

                                         S.I = 2×\int_{0}^{T/2}\alpha (\phi )*cos(\phi )*dt


T is the daylight period of a given day approximately 12 hours.

For a detector mounted at an angle θ with respect to earth’s surface, sun making an angle of Ф with respect to normal of the detector the Total solar insolation is given as

                                         SI = 2*\int_{0}^{T/2}\alpha (\phi )*cos(\theta ' )*dt

Where θ’ = Ф –θ.

In the solar energy impinging on earth only around 19 percent is available at the land surfaces after reflection from the atmosphere, oceans e.t.c.

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