solar Radiation GeometryLatitude or Angle of latitude(φ): The latitude angle is the angle between a line drawn from a point on the earth’s surface to the center of the earth and the earth’s equatorial plane.

Declination angle (δ): If a line is drawn between the center of the earth and the sun, the angle between this line and the earth's equatorial plane is called the declination angle (δ).

δ = 23.45 x sin[(360/365)(284+n)] degrees

Observer’s meridian at P

Hour angle (ω): is the angular distance between the meridian of the observer and the meridian whose plane contains the sun.(or) The hour angle at any moment is the angle through which the earth must turn to bring the meridian of the observer directly in line with the sun rays.ω=[Ts-12:00] x 15, where ω=Hour Angle(Degrees) , Ts = Solar time

ω +ve in afternoon and –ve in fore noon since at solar noon the hour angle is zero

Solar altitude angle (α): is defined as the angle between the central ray from the sun, and its projection on horizontal plane containing the observer.

Solar zenith angle (θz): Angle between the sun ray and the normal to the horizontal plane.

Solar azimuth angle (γs): measured clockwise on the horizontal plane, angle between due south and the projection of the sun’s central ray.

Slope or Tilt Angle(β): It is the angle between the inclined plane surface of collector and the horizontal.+ve when sloping is towards south

Surface azimuth angle(γ): It is the angle in the horizontal plane , between the line due south and the horizontal projection of the normal to the inclined plane surface.+ve when measured from south towards west.

Angle of incidence (θi): is the angle between the sun’s ray incident on the

earth plane surface and the normal to that surface. Expression for θi can be given as,

cos θi= (cos φ cos β + sin φ sin β cos γ) cosω cosδ +

cosδ sinω sin βsin γ + sinδ (sin φ cos β - cos φ sin β cos γ)

Special Cases: i) For surface facing due south, γ =0

cos θi= cos (φ- β) cosω cosδ + sinδ (sin φ- β)

ii) For a horizontal surface, β = 0, θi = θZ

cos θz= cos φ cosω cosδ + sinδ sin φ

iii) For a vertical surface facing due south

cos θi= - sinδ cos φ+cosω cosδ sin φ

Solar day Length:

At sunrise the rays are parallel to the horizontal surface. Then Angle of incidence, θi = θZ =900

, the corresponding hour angle, ωs from above eq. is

cos θi=0 = cos φ cosωs cosδ + sinδ sin φ

ωs =cos-1 (-tanφ tanδ)

The angle between sunrise and sunset,

2ωs =2cos-1 (-tanφ tanδ)

The daylight hours(td) is given by ,

td= (2/15) cos-1 (-tanφ tanδ)

Estimating Solar Radiation

Monthly And Daily Average Global Radiation:

The correlation for estimating monthly avg. daily total (global) radiation on a horizontal surface is given by

Because of the difficulties in defining a clear day , J. K. Page suggested that Hc is replaced by Ho, eq. becomes,

is the mean avg. of Ho for each day of the month, it is calculated by integrating Ho over the day length as follows:

Where ‘t’ is in hours and ‘ω’ is in radians

And hence, substituting the above we get,

Monthly And Daily Average Diffuse Radiation:

Monthly Avg. Clearness Index (KT): The ratio of

Solar Radiation on Tilted Surface

Measuring instruments give the value of solar radiation falling on a horizontal surface.But most of the solar equipment has titled surfaces for absorbing solar radiation, with some tilt angle with horizontal.So we have to calculate the flux on such surface.The flux is the sum of beam and diffused radiation falling directly on the surface and the radiation reflected on to the surface from the surroundings.

Beam Radiation: TILT FACTOR(rb): The ratio of beam radiation flux falling on the tilted surface to that of horizontal surface is called the TILT FACTOR for beam radiation.

For case of tilted surface facing due south γ=0

Diffuse Radiation:TILT FACTOR (rd): The ratio of diffuse radiation flux falling on the tilted surface to

that of horizontal surface is called the TILT FACTOR for diffuse radiation.Its value depends on the distribution of diffuse radiation over the sky and the portion of the sky dome seen by the tilted surface.Assuming that the sky is an isotropic source of diffuse radiation, for a tilted surface with slope β, we have

(1+ cosβ)/2 is the shape factor for a tilted surface w.r.t. sky