Presentation On

Solar Geometry

Presented by-MADHAV SHARMA

481671

Solar Geometry can be explained with help of-

• Solar Context• Earth Context• Solar Angle Context• Sunpath Diagrams

2

3 1. POSITION

A. SOLAR CONTEXT

4 1. POSITION

A. SOLAR CONTEXT

5 1. POSITION

A. SOLAR CONTEXT

6 1. POSITION

A. SOLAR CONTEXT

7 1. POSITION

A. SOLAR CONTEXT

8 1. POSITION

B. EARTH CONTEXT

Latitude and Longitude as linear unit

One latitudinal second measures 30.715 metres, one latitudinal minute is 1843 metres and one latitudinal degree is110.6 kilometres. The circles of longitude, meridians, meet at the geographical poles, with the west-east width of a second naturally decreasing as latitude increases. On the equator at sea level, one longitudinal second measures 30.92 metres, a longitudinal minute is 1855 metres and a longitudinal degree is 111.3 kilometres. At 30° a longitudinal second is 26.76 metres, at Greenwich (51° 28' 38" N) 19.22 metres, and at 60° it is 15.42 metres.

9 1. POSITION

B. EARTH CONTEXT

10 2. TIME AND SOLAR PATH

B. EARTH CONTEXT

11 1. ALTITUDE & AZIMUTH

C. SOLAR ANGLES

Solar altitude is the angular distance of the sun to the horizon from the view of an observer. Of course, every other heavenly body also has its altitude.

12 1. ALTITUDE & AZIMUTH

C. SOLAR ANGLES

13 1. ALTITUDE & AZIMUTH

C. SOLAR ANGLES

Solar Azimuth is the angular position of the sun measured around the Horizon with North being 0 degrees, East 90 degrees, South 180 degrees and West 270 degrees.

14 2. CONVENTION

C. SOLAR ANGLES Azimuth angle is usually measured from South (in architecture) … but sometimes from the North

South is always “solar” South (not magnetic South or plan South)

Altitude angle is measured from the horizontal

Times are always “solar” times

153. SOLAR SOUTH

C. SOLAR ANGLES SOLAR SOUTH

Defined by the position of the sun at solar noon

Marks the center of symmetry for the daily solar path

Differs from magnetic South by the magnetic deviation value

Plan South is totally arbitrary

16 3. SOLAR SOUTH

C. SOLAR ANGLES

17 4. SOLAR TIME

C. SOLAR ANGLES

AST (clock time) = Local solar time + Equation of time value + (4)(local standard meridian – local longitude) +/-daylight saving time

18 5. DESCRIPTION

C. SOLAR ANGLES

Sign ConventionsAngles east of south are negative

Angles west of south are positive

+ -

S

-90º90º

0º

-45º45º

19 5. CONVETION DESCRIPTION

C. SOLAR ANGLES

Calculating Surface Solar Azimuth

γ = Φ – Ψ

For example:Building façade is oriented south east (Ψ =-45º)Solar azimuth (ϕ) is 30º west of south γ = 30º – (-45º) = 75ºNote: |γ|≥ 90º, façade in shade

-45º30º

20 5. CONVETION DESCRIPTION

C. SOLAR ANGLES

21 1. MODEL

D. SUNPATH DIAGRAMSun path diagrams or sun charts are projections of the sky dome onto a surface1. Cylindrical projection Show the Sun's appearent path for an observer who is looking due South. Useful for conducting shading calculations, especially for high geographical altitudes. It is very confusion when the sun is high up in the sky, i.e. in tropical situations.

22 1. MODEL

D. SUNPATH DIAGRAM

23 1. MODEL

D. SUNPATH DIAGRAM

2. Polar diagram The sky dome is projected onto a horizontal plane with the observer being in the center. Ideal for visualising the compass direction of the Sun at any point in time, especially at tropical latitudes and during the summer months

24 1. MODEL

D. SUNPATH DIAGRAM

25 1. MODEL

D. SUNPATH DIAGRAM

261. MODEL

D. SUNPATH DIAGRAM

27 1. MODEL

D. SUNPATH DIAGRAM

282. DERIVATION

D. SUNPATH DIAGRAM

29 2. DERIVATION

D. SUNPATH DIAGRAM

30 2. DERIVATION

D. SUNPATH DIAGRAM

31 2. DERIVATION

D. SUNPATH DIAGRAM

32 2. DERIVATION

D. SUNPATH DIAGRAM

33 2. DERIVATION

D. SUNPATH DIAGRAM

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.

Solar AnglesDescribe 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