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 ω=[Ts-12:00] x 15. angle between due south and the projection of the sun’s central ray. and its projection on horizontal plane containing the observer. 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. Solar azimuth angle (γs): measured clockwise on the horizontal plane. (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. where ω=Hour Angle(Degrees) . Solar zenith angle (θz): Angle between the sun ray and the normal to the horizontal plane. .Hour angle (ω): is the angular distance between the meridian of the observer and the meridian whose plane contains the sun. Slope or Tilt Angle(β): It is the angle between the inclined plane surface of collector and the horizontal. between the line due south and the horizontal projection of the normal to the inclined plane surface. . +ve when sloping is towards south Surface azimuth angle(γ): It is the angle in the horizontal plane . +ve when measured from south towards west. β) ii) For a horizontal surface.β) cosω cosδ + sinδ (sin φ. β = 0. γ =0 cos θi= cos (φ. 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 .Angle of incidence (θi): is the angle between the sun’s ray incident on the earth plane surface and the normal to that surface.cos φ sin β cos γ) Special Cases: i) For surface facing due south.sinδ cos φ+cosω cosδ sin φ . θi = θZ cos θz= cos φ cosω cosδ + sinδ sin φ iii) For a vertical surface facing due south cos θi= . 2ωs =2cos-1 (-tanφ tanδ) The daylight hours(td) is given by . the corresponding hour angle. θi = θZ =900 . Then Angle of incidence. ωs from above eq.Solar day Length: At sunrise the rays are parallel to the horizontal surface. td= (2/15) cos-1 (-tanφ tanδ) . is cos θi=0 = cos φ cosωs cosδ + sinδ sin φ ωs =cos-1 (-tanφ tanδ) The angle between sunrise and sunset. daily total (global) radiation on a horizontal surface is given by .Estimating Solar Radiation Monthly And Daily Average Global Radiation: The correlation for estimating monthly avg. eq. is the mean avg. it is calculated by integrating Ho over the day length as follows: Where ‘t’ is in hours and ‘ω’ is in radians And hence. becomes. Page suggested that Hc is replaced by Ho. . J. substituting the above we get.Because of the difficulties in defining a clear day . of Ho for each day of the month. K. Monthly And Daily Average Diffuse Radiation: Monthly Avg. Clearness Index (KT): The ratio of . But most of the solar equipment has titled surfaces for absorbing solar radiation. For case of tilted surface facing due south γ=0 . 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.Solar Radiation on Tilted Surface Measuring instruments give the value of solar radiation falling on a horizontal surface. 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. with some tilt angle with horizontal. Assuming that the sky is an isotropic source of diffuse radiation.t. for a tilted surface with slope β. sky . Its value depends on the distribution of diffuse radiation over the sky and the portion of the sky dome seen by the tilted surface. we have (1+ cosβ)/2 is the shape factor for a tilted surface w.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.r.