Earth sun angle &observer sun angle

useful for the technical students

1. EARTH SUN ANGLE & OBERVER ANGLE PREPARED BY:- SONU KUMAR BAIRWA

2. Sun Earth Angles The angle between the earth- sun line and the earth’s equatorial plane is known as the angle of declination. This varies with the date; and the orbital velocity of the earth traveling around the elliptic plane also varies slightly. The two angles that completely describe the sun position are the solar altitude b, measured from 0° to 90° above the horizon, and the solar azimuth f, measured from 0° to 180° from the south with positive sign eastwards and negative sign westwards. To determine these two angles from data on Latitude, date and time, the following calculation is carried out: Instead of being expressed in time units, true solar time can be expressed in angular terms related to the earth"s rotation as the hour angle, H, where

3. Since in one minute the earth rotates 0.25°. Values a.m. are + ve and p.m. + ve . Then , sin b = cos L cos d cos H + sin L sin d And sin f = ( cos d sin H) / cos b

4. L Latitude, degrees D declination, degrees (northern hemisphere =+ ve , southern hemisphere = - ve ) Values of b and f may be available from tables in publications or graphical techniques for finding them are also available .

5. OBSERVER SUN ANGLES The Solar Altitude  ( α s α s) measures the angle between the central ray from the Sun (beam radiation), and a horizontal plane containing the observer. Note that the subscript `` ss' ' is there to indicate that the altitude relative to the observer of the Sun . This will become important in evaluating the altitude angles of other objects projected onto the  sky dome , like buildings, overhangs, wing walls, and arrays of solar receivers. sin α s=sin δ sin ϕ+ cos δ cos ϕ cos ω sin α s=sin δ sin ϕ+ cos δ cos ϕ cos ω cos α ssin γ s=− cos δ sin ω cos α ssin γ s=− cos δ sin ω α s=sin−1[sin δ sin ϕ+ cos δ cos ϕ cos ω ]

6. The Zenith Angle  ( θzθz ) is the geometric complement of the solar altitude angle . We direct your attention to the use of  θθ  here, as the general concept of the angular deviation of the Sun's ray from the  normal  projection of a surface is called the angle of incidence,  θθ . In effect, the zenith angle represents the angle of incidence for a horizontal surface. Recall: "normal" means perpendicular to a surface. cosθz = sinδsinϕ+cosδcosϕcosωcosθz = sinδsinϕ+cosδcosϕcosω θz =cos −1[ sinδsinϕ+cosδcosϕcosω ]

7. The Solar Azimuth   measures the angle on the horizontal plane between the meridian of the 0 degrees axis (South, for the Northern hemisphere, opposite Down Under) and the meridional projection of the Sun's central beam (the Sun's meridian ). The convention we will use is also used in the advanced design tools for solar energy, TRNSYS (UW-Madison: Transient eNergy Simulation Software), PVSyst , and SAM (NREL:  System Advisor Model ). The angle varies from 0 degrees at the South-pointing coordinate axis to ± 180±180 degrees. East (earlier than noon) is  negative  and west (later than noon) is  positive  in this basis.

8. THANK YOU