1. Chapter 4A: SOLAR RADIATION- GEOMETRY
Agami Reddy (rev- Dec 2017)
Earth’s tilt and rotation about the sun
Basic solar angles: solar declination, latitude, hour angle
Derived angles: solar altitude, solar azimuth
Sun path diagrams and shading from adjacent objects
Calculation of solar time
6. Angle of incidence on tilted planes
HCB-3 Chap 4A: Solar Radiation Geometry

2. HCB-3 Chap 4A: Solar Radiation Geometry
Equinox- equal day/night
Solstice- longest day/night
Figure 4.1.Geometry of the earth’s orbit and inclination of polar axis: (a) entire orbit and (b) enlarged detail, solstices.
HCB-3 Chap 4A: Solar Radiation Geometry

3. Elliptical orbit (+-1.7%)
From Boyle, 2004
Closer
Elliptical orbit (+-1.7%)
Time of year effect on solar radiation:
Sun not exact center of earth path (+-1.7%)
Eccentricity correction factor E0=(r0/rn)2
where r0 = mean-sun earth distance
and rn = actual distance on given day
From Goswami et al., 2004
HCB-3 Chap 4A: Solar Radiation Geometry

4. Solar Geometry- Basic Angles
Figure 4.2
(a) 3-D view. (b) Cross-sectional view at solar noon.
Latitude λ
Declination δ
Hour angle ω
difference between actual time of
day with respect to solar noon
Eq.4.4
O = center of earth,
N = north pole,
P = point on earth’s surface.
HCB-3 Chap 4A: Solar Radiation Geometry

5. Solar Declination
Equation for solar declination (Eq.4.3)
Declination causes seasonal effects
HCB-3 Chap 4A: Solar Radiation Geometry

6. Location of Sun in Sky Perspective of Local Observer
Solar zenith angle
Solar altitude angle
Solar azimuth angle
Eq. (4.9)
Eq. (4.11)
Eq. (4.10)
HCB-3 Chap 4A: Solar Radiation Geometry

7. HCB-3 Chap 4A: Solar Radiation Geometry
Example 4.2
HCB-3 Chap 4A: Solar Radiation Geometry

8. HCB-3 Chap 4A: Solar Radiation Geometry
Monthly Solar
Paths
Figure 4.4
Solar path diagrams over the day for three different periods of the year with respect to a local observer.
Mazria, 1979
HCB-3 Chap 4A: Solar Radiation Geometry

9. HCB-3 Chap 4A: Solar Radiation Geometry
Solar Sunrise Time and Day Length
Fig.4.7
from sunrise to noon
HCB-3 Chap 4A: Solar Radiation Geometry

10. HCB-3 Chap 4A: Solar Radiation Geometry

11. HCB-3 Chap 4A: Solar Radiation Geometry
Time of Day
Solar Paths
Mazria, 1979
HCB-3 Chap 4A: Solar Radiation Geometry

12. HCB-3 Chap 4A: Solar Radiation Geometry
Cylindrical projection
Figure 4.6
Cylindrical projection sun-path diagram: solar altitude angle (=90° − θs) versus azimuth ϕs. Time in legends is solar time. (a) Latitude λ = 30°
HCB-3 Chap 4A: Solar Radiation Geometry

13. Effect of Earth’s Tilt and Rotation about Sun
Declination of 23.5o
results in changes in day
length over year and
different solar paths
90 deg
0 deg
40 deg
Sun paths across the sky
for different latitudes
and times of year
HCB-3 Chap 4A: Solar Radiation Geometry

14. Using the sun-path diagram to determine shading from adjoining objects
Figure 4.9
Outline of horizon superimposed on the sun-path diagram to determine incidence of shading. αP and ϕP are the altitude and azimuth angles of point P as seen from the position of the observer
HCB-3 Chap 4A: Solar Radiation Geometry

15. HCB-3 Chap 4A: Solar Radiation Geometry
Greenwich Longitude = 00
HCB-3 Chap 4A: Solar Radiation Geometry

16. HCB-3 Chap 4A: Solar Radiation Geometry
Longitudes for U.S. Time Zones
UTC – coordinated universal time (same as Greenwich time)
HCB-3 Chap 4A: Solar Radiation Geometry

17. Solar Time Calculation
Definition of solar time:
time of day measured from solar noon;
due south (in Northern hemisphere) is zero;
towards east (-) towards west (+)
Diff. between local standard time and solar time is given by equation of time (ET)
For locations west of Greenwich:
(Local) solar time = standard time + 4’(Standard meridian-Local meridian) + ET
For locations east of Greenwich, this sign should be –ve.
Also standard time is watch time minus 1 hr (if daylight savings is in effect)
HCB-3 Chap 4A: Solar Radiation Geometry

18. Equation of Time Result of elliptical orbit of earth around sun
Fig. 4.3
HCB-3 Chap 4A: Solar Radiation Geometry

19. HCB-3 Chap 4A: Solar Radiation Geometry

20. HCB-3 Chap 4A: Solar Radiation Geometry
Solar Angles on Planes
A stationary tilted surface is defined by two angles:
Tilt angle (= zenith angle)
azimuth of plane and
Fig. 4.5
Incidence angle on tilted surface:
HCB-3 Chap 4A: Solar Radiation Geometry

21. Hourly Radiation on Tilted Surfaces
HCB-3 Chap 4A: Solar Radiation Geometry

22. HCB-3 Chap 4A: Solar Radiation Geometry
Outcomes
Understand the motion of the earth around the sun
Familiarity with the basic solar angles: declination, latitude and hour angles
Working knowledge of computing solar altitude and azimuth angles
Familiarity with the sun-path diagram
Working knowledge of solar time and standard time
Familiarity with how to define angles of a tilted surface
Working knowledge of how to compute angles of incidence on stationary tilted surfaces
HCB-3 Chap 4A: Solar Radiation Geometry