Solar Geometry 5f37u

Solar Radiation Geometry

Ch.Bhanu prakash, Assistant Prof. Department of ME VIT R41033

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Solar Geometry • Solar Geometry describes the relationship between the sun and earth or more importantly • The relationship of solar radiation. • The product of the sun with any location on the earth.

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Important geometrical parameters, which describe Earth-Sun relations

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Nature of the solar resource Earth’s orbit ain’t circular

Nature of the solar resource Earth’s orbit: Variation in radiation

Irradiance (W/m 2)

1,450

1,400

1,350

1,300 Jan

Feb

Mar

Apr

May

Jun

Jul

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Oct

Nov

Dec

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Nature of the solar resource 0 Earth is tilted 23. 45

solstice • Either of the two times in the year, the summer solstice and the winter solstice, when the sun reaches its highest or lowest point in the sky at noon, marked by the longest and shortest days. • Either of the two times a year when the sun is at its greatest distance from the celestial equator: about June 21, when the sun reaches its northernmost point on the celestial sphere, or about December 22, when it reaches its southernmost point. 9M606C.5

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Nature of the solar resource Earth is tilted 23.45 •

•

•

On the winter solstice (December 21) – The north pole has its maximum angle of inclination away from the sun – Everywhere above 66.55 N (90-23.45) is in darkness for 24 hours, Everywhere above 66.55 S is in sunlight for 24 hours – the sun es directly overhead over the tropic of Capricorn (23.45 S) On the equinox (March 22 & September 22) – Both poles are equidistant – the day is exactly 12 hours long – the sun es directly overhead over the equator – The sun tracks a straight line across the sky On the summer solstice (June 22) 14 – The reverse of the winter solstice R41033

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Nature of the solar resource Solar geometry

 

Beam radiation

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Nature of the solar resource Solar geometry: Hour angle

Beam radiation



Rotation

Meridian • A meridian (or line of longitude) is the half of an imaginary great circle on the Earth's surface, terminated by the North Pole and the South Pole, connecting points .

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Meridian

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Hour angle • It is the angle through which the earths must turn to bring the meridian of a point directly in line with the sun rays. • It is the angle measured in the earths equatorial plane.  LST

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LST

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Nature of the solar resource Solar geometry: Sun angles Zenith

z

W

N

s s

South

E

Nature of the solar resource Solar geometry: Sun angles z s s

= Zenith angle – the angle between the vertical (zenith) and the line of the sun = Solar attitude angle – the angle between the horizontal and the line to the sun = Solar azimuth angle – the angle of the projection of beam radiation on the horizontal plane (with zero due south, east negative and west positive)

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Incident angle

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Incident angle • It is the angle being measured b/w the beam of rays and normal to the plane

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Nature of the solar resource Solar geometry: Sun angles

cos z  cos  cos  cos   sin  sin  Z

cos  s 

sin  cos  cos   sin  sin  cos  s

   s

s

= Zenith Angle = Latitude = Declination = Hour angle = Solar azimuth angle = Solar attitude angle

Note:  &  should be the same sign

Nature of the solar resource Solar geometry: Sun angles: Sunset angle and day length

cos s   tan  tan 

s  

= Sunset angle = Declination = Latitude

2 Day length  cos 1   tan  tan   15 Note: Day length is in hours

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Nature of the solar resource Solar geometry: Collector angles Zenith

z

W

N

s s

South





 E

Nature of the solar resource Solar geometry: Collector angles  



= Slope – the angle between the plane of the collector and the horizontal = Surface azimuth angle – the deviation of the projection on a horizontal plane of the normal to the collector from the local meridian (with zero due south, east negative and west positive) = Angle of incidence – the angle between the beam radiation on the collector and the normal R41033

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Nature of the solar resource Solar geometry: Collector angles Sun angles

cos   cos  s sin  sin  sin  s  cos  s cos  sin  cos  s  sin  s cos  Earth angles

cos   sin   sin  cos   cos  sin  cos  

 cos  cos   cos  cos   sin  sin  cos    cos  sin  sin  sin 

 s  s    

= Angle of incidence = Solar attitude angle = Surface azimuth angle = Solar azimuth angle = Collector slope = Declination = Latitude = Hour angle

Nature of the solar resource Solar geometry: Collector angles Northern Hemisphere

cos ss   tan  tan     

Southern Hemisphere

cos ss   tan  tan     

ss   

= Sunset angle = Declination = Latitude = Collector slope

System design Irradiance: Variables • Latitude at the point of observation • Orientation of the surface in relation to the sun • Day of the year • Hour of the day • Atmospheric conditions

System design Irradiance on a horizontal surface Gb ,n Gb Gb  Gb,n cos  z

Gb Gb,n z

= Beam Irradiance normal to the earth’s surface (W/m2) = Beam Irradiance (W/m2) = Zenith angle

System design Tilt: Beam radiation Gb ,n Gb,T

Gb,t  Gb, n cos Gb,t Gb,n 

= Beam Irradiance normal to a tilted surface (W/m2) = Beam Irradiance (W/m2) = Angle of incidence

System design Tilt: Beam radiation Gb ,n Gb ,t Gb ,n Gb

Rb,t

Gb ,n cos

cos     Gb Gb ,n cos z cos  z Gb ,t

Solar Angles Describe the sun position relative to a vertical surface

Solar Altitude: β (beta) Vertical angle to sun position

Solar Azimuth: Φ (phi) Horizontal bearing angle from south

Surface Azimuth: Ψ (psi) Surface horizontal bearing angle from south

Surface Solar Azimuth: γ (gamma) Angle between solar and surface azimuths γ=Φ-Ψ

Sign Conventions Angles east of south are negative Angles west of south are positive

90º

-90º

45º +

-45º S0º

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