Solar angle

1. Solar Geometry
Lecture #7

2. Learning Objective and Outcome sheet
Topic Solar geometry
Learning Objectives
 Sun position and movement of the earth around the sun
 Standard time and local time
 Angles associated with the solar geometry and plane
Learning Outcome
 Equation of time
 Sun path in cylindrical coordinate and polar coordinate
 Analysis of shading
Problem/Assignment
7.1 Calculate the date and time when the air mass at Mumbai (Latitude : 18oN, Longitude:
72oE) is maximum solar radiation. Given, Std. Longitude for India: 82.5 oE.
7.2 You plan to install a solar energy converter on the equator. There is a hill (180 m high and
0.95 km wide) on the east side at a distance 1 km from the site of the installation. Estimate the
energy loss in percent due to obstruction Write down the assumption adopted for estimation
Learning Resources
Summary
This lecture enables learner to understand the relative motion of the sun
around the earth to determine the incident radiation on any plane.

3. Geographical coordinates

Latitude
:


5. Rotation of earth

6. Sunrise
Noon
Sunset
Rotation of earth

8. Latitude angle

9. Geographical coordinates

-ve +ve
 : Longitude angle

10. Sun path in cylindrical coordinate

11. Sun path in polar coordinate

12. E
S
W
N
Tilt surface
s


s
 =Surface azimuth angle
= Tilt angle


13. E
S
W
N
Sun positions
z


z

=Azimuth angle
= Zenith angle
z


90 = Altitude angle

14. s


N
E
S
W
Sun positions
z


z

=Azimuth angle
= Zenith angle


s
 =Surface azimuth angle
= Tilt angle

15. Zenith angle (z) is given by





 cos
cos
cos
sin
sin
cos 

z
 
 



















sin
sin
sin
cos
sin
cos
sin
cos
cos
cos
cos
sin
cos
cos
cos
cos
sin
sin
cos
s
s
s





Angle betwn tilted surface & sun ray

16. Azimuth angle () is given by
z







sin
sin
cos
cos
cos
sin
cos


 
 



















sin
sin
sin
cos
sin
cos
sin
cos
cos
cos
cos
sin
cos
cos
cos
cos
sin
sin
cos
s
s
s





Angle betwn tilted surface & sun ray