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Solar radiation geometry Solar radiation geometry is the determining factor of heat gain, Shading and the potential of day light penetration. Direction of beam radiation is useful in establishing geometric relationship between a plane and incoming beam solar radiation. Direction of beam radiation can be described in terms of several angles. Angles useful in solar radiation analysis (a)

Basic solar angles: I. II. III.

(b)

Latitude angle (ф) Declination angle (δ) Hour angle(ω) Derived solar angles:

I. II. III. (c)

Altitude angle(α) Zenith angle(θz) Solar azimuth angle (γs) Surface angles:

I. II. III.

Surface azimuth angle(γ) Slope (β) Incidence(θ)

Angle made by radial line joining the location to the (1) Latitude angle (ф): “Angle centre of earth and the projection of that line on equatorial plane”. It varies from 00° at equator to 90° at poles (north positive).

Fig.1: the position of any point on earth.

Fig.2: Basic angles.

(2) Declination angle (δ): ( It is the angle between a line extending from centre of sun to centre of earth and the projection of this line upon earth’s equatorial plane. It is due to tilt of Earth’s axis and it varies between 23.45° (summer solstice: 22 June) to -23.45° (winter solstice: December 22). On equinoxes, Declination=0 =0 It is given by

=

.

°.

.( +

)

Fig.3: The variation in declination angle throughout year.

(3) Hour angle (ω): ): The angle through which earth must turn to bring the meridian of a point directly in line with Sun’s rays. The angle through which earth must turn to bring the meridian of a point directly in line with Sun’s rays. At solar noon ω = 0°. It is measures from m noon, (+)ve before noon and (-)ve )ve after noon.

Vertical angle between direction of sun ray and it’s (4) Altitude angle (α): ( “Vertical projection on horizontal plane on earth’s surface”. surface It is maximum at solar noon.

Fig.4: Derived angles.

(5) Zenith angle (θ θz): Complementary omplementary angle of solar altitude angle, i.e. Vertical angle between Sun’s rays and a line perpendicular to horizontal plane through the point.

(6) Solar azimuth angle (γs ( or Az): It is the horizontal angle measured from north to horizontal projection of Sun’s rays. It is considered (+)ve west side. Also can be defined as solar angle in degrees along the horizon east or west of north. Relation between basic solar angles

cosθz = cosф cosω cosδ cos +sinф sinδ = sinα α = 90- θz cosγs = secα (cosф sinδ sin – cosδ sinф cosω ) sinγs = secα cosδ sinω ω

(7) Surface azimuth angle (γ): For tilted surfaces. It is angle of deviation of the normal to the surface from the local meridian, or It is the angle between the normal to the surface and south. For south facing surface γ= 0°. For west facing surface γ= 90° and so on. Eastward: (+)ve, West-ward : (-)ve.

Fig.5: Surface angles.

(8) Slope (β): “Angle made by the plane surface with the horizontal”. (+)ve : for surface slopping toward south . (-)ve : for surface slopping toward north.

(9) Incidence (θ) : Used when tilted surfaces are involved. Angle between sun rays and normal to surface under consideration. General equation for angle of incidence (θ): cosθ = sinф ( sinδcosβ + cosδcosγcosωsinβ ) + cosф(cosδcosωcosβ – sinδcosγsinβ) + cos δsinγsinωsinβ

By: Kailash Singh Jhinkwan Mtech (Thermal engineering) GBPUAT PANTNAGAR Uttarakhand

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Basic solar angles: I. II. III.

(b)

Latitude angle (ф) Declination angle (δ) Hour angle(ω) Derived solar angles:

I. II. III. (c)

Altitude angle(α) Zenith angle(θz) Solar azimuth angle (γs) Surface angles:

I. II. III.

Surface azimuth angle(γ) Slope (β) Incidence(θ)

Angle made by radial line joining the location to the (1) Latitude angle (ф): “Angle centre of earth and the projection of that line on equatorial plane”. It varies from 00° at equator to 90° at poles (north positive).

Fig.1: the position of any point on earth.

Fig.2: Basic angles.

(2) Declination angle (δ): ( It is the angle between a line extending from centre of sun to centre of earth and the projection of this line upon earth’s equatorial plane. It is due to tilt of Earth’s axis and it varies between 23.45° (summer solstice: 22 June) to -23.45° (winter solstice: December 22). On equinoxes, Declination=0 =0 It is given by

=

.

°.

.( +

)

Fig.3: The variation in declination angle throughout year.

(3) Hour angle (ω): ): The angle through which earth must turn to bring the meridian of a point directly in line with Sun’s rays. The angle through which earth must turn to bring the meridian of a point directly in line with Sun’s rays. At solar noon ω = 0°. It is measures from m noon, (+)ve before noon and (-)ve )ve after noon.

Vertical angle between direction of sun ray and it’s (4) Altitude angle (α): ( “Vertical projection on horizontal plane on earth’s surface”. surface It is maximum at solar noon.

Fig.4: Derived angles.

(5) Zenith angle (θ θz): Complementary omplementary angle of solar altitude angle, i.e. Vertical angle between Sun’s rays and a line perpendicular to horizontal plane through the point.

(6) Solar azimuth angle (γs ( or Az): It is the horizontal angle measured from north to horizontal projection of Sun’s rays. It is considered (+)ve west side. Also can be defined as solar angle in degrees along the horizon east or west of north. Relation between basic solar angles

cosθz = cosф cosω cosδ cos +sinф sinδ = sinα α = 90- θz cosγs = secα (cosф sinδ sin – cosδ sinф cosω ) sinγs = secα cosδ sinω ω

(7) Surface azimuth angle (γ): For tilted surfaces. It is angle of deviation of the normal to the surface from the local meridian, or It is the angle between the normal to the surface and south. For south facing surface γ= 0°. For west facing surface γ= 90° and so on. Eastward: (+)ve, West-ward : (-)ve.

Fig.5: Surface angles.

(8) Slope (β): “Angle made by the plane surface with the horizontal”. (+)ve : for surface slopping toward south . (-)ve : for surface slopping toward north.

(9) Incidence (θ) : Used when tilted surfaces are involved. Angle between sun rays and normal to surface under consideration. General equation for angle of incidence (θ): cosθ = sinф ( sinδcosβ + cosδcosγcosωsinβ ) + cosф(cosδcosωcosβ – sinδcosγsinβ) + cos δsinγsinωsinβ

By: Kailash Singh Jhinkwan Mtech (Thermal engineering) GBPUAT PANTNAGAR Uttarakhand

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