Chapter 4A: SOLAR RADIATION- GEOMETRY

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Presentation transcript:

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

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

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

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

Solar Declination http://www.physicalgeography.net/fundamentals/6h.html Equation for solar declination (Eq.4.3) Declination causes seasonal effects HCB-3 Chap 4A: Solar Radiation Geometry

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

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

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

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

HCB-3 Chap 4A: Solar Radiation Geometry

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

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

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

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

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

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

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

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

HCB-3 Chap 4A: Solar Radiation Geometry

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

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

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