IIT Bombay
DESE
Solar Geometry
Lecture #7
04/08/2011
EN 601: Lecture 7: Solar Geometry
Slide 1
IIT Bombay
Learning Objective and Outcome sheet
Topic
DESE
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
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.
Problem/Assignment
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
04/08/2011
This lecture enables learner to understand the relative motion of the sun
around the earth to determine the incident radiation on any plane.
EN 601: Lecture 7: Solar Geometry
Slide 2
Geographical coordinates
IIT Bombay
DESE

 : Latitude
04/08/2011
EN 601: Lecture 7: Solar Geometry
Slide 3
IIT Bombay
DESE
04/08/2011
EN 601: Lecture 7: Solar Geometry
Slide 4
Rotation of earth
04/08/2011
EN 601: Lecture 7: Solar Geometry
IIT Bombay
DESE
Slide 5
IIT Bombay
Rotation of earth
DESE
Sunrise
Noon
Sunset
04/08/2011
EN 601: Lecture 7: Solar Geometry
Slide 6
IIT Bombay
DESE
04/08/2011
EN 601: Lecture 7: Solar Geometry
Slide 7
IIT Bombay
Latitude angle
04/08/2011
DESE
EN 601: Lecture 7: Solar Geometry
Slide 8
IIT Bombay
Geographical coordinates
DESE

-ve
+ve
 : Longitude angle
04/08/2011
EN 601: Lecture 7: Solar Geometry
Slide 9
Sun path in cylindrical coordinate
04/08/2011
EN 601: Lecture 7: Solar Geometry
IIT Bombay
DESE
Slide 10
Sun path in polar coordinate
04/08/2011
EN 601: Lecture 7: Solar Geometry
IIT Bombay
DESE
Slide 11
IIT Bombay
Tilt surface
DESE
N
 = Tilt angle

W
E
s
S
04/08/2011
 s =Surface azimuth angle
EN 601: Lecture 7: Solar Geometry
Slide 12
IIT Bombay
Sun positions
DESE
z
N
W
E

S
04/08/2011
 z= Zenith angle
 =Azimuth angle
90   z = Altitude angle
EN 601: Lecture 7: Solar Geometry
Slide 13
IIT Bombay
Sun positions

DESE
z
 z= Zenith angle

 = Tilt angle
W

E
s
S
04/08/2011
N
 =Azimuth angle
 s =Surface azimuth angle
EN 601: Lecture 7: Solar Geometry
Slide 14
Angle betwn tilted surface & sun ray
IIT Bombay
DESE
cos   sin  sin  cos   cos  cos  s cos  sin  
 cos  cos  cos  cos   sin  cos  s sin  
 cos  sin  sin  s sin 
Zenith angle (z) is given by
cosz  sin  sin   cos cos  cos 
04/08/2011
EN 601: Lecture 7: Solar Geometry
Slide 15
Angle betwn tilted surface & sun ray
IIT Bombay
DESE
cos   sin  sin  cos   cos  cos  s cos  sin  
 cos  cos  cos  cos   sin  cos  s sin  
 cos  sin  sin  s sin 
Azimuth angle () is given by
sin  cos  cos   cos  sin 
cos  
sin  z
04/08/2011
EN 601: Lecture 7: Solar Geometry
Slide 16