Sun Earth Relationships

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1 1 ESCI-61 Introduction to Photovoltaic Technology Sun Earth Relationships Ridha Hamidi, Ph.D.

2 Spring (sun aims directly at equator) Winter (northern hemisphere tilts away from sun) Solar radiation Summer (northern hemisphere tilts toward sun) Fall (sun aims directly at equator)

3 3 Earth s Orbit Ecliptic Plane: the plane of Earth s orbit around the Sun Perihelion: point of the Earth s orbit when it is closest to the Sun (around Jan. 3 rd ) Aphelion: point in Earth s orbit when it is farthest from the Sun (around July 4 th ) Equatorial Plane: plane containing Earth s equator and extending outward into space Earth s axis is tilted by 23.5 (constant angle bet ween ecliptic & equatorial planes) This causes the seasonal variations in Earth s climate Solar Declination: angle between the equatorial plane and the line joining the centers of the Sun & Earth Changes continuously as Earth orbits the Sun, ranging from 23.5 to Apparent change as viewed from the Sun Visit for more info

4 4 Earth s Orbit Solstices: Earth s orbit position when solar declination is at minimum or maximum At any location in the Northern hemisphere, the Sun is 47 lower in the sky at solar noon on the winter solstice than at solar noon on the summer solstice The rate of change in declination is small, so daily change in Sun path is at minimum

5 5 Earth s Orbit Summer solstice: maximum solar declination (+23.5 ), around June 21 Northern hemisphere is at its maximum tilt toward the Sun Days are longer than nights in the Northern hemisphere All points south the Antarctic circle are in total darkness The Sun is at Zenith at solar noon at locations at 23.5 N latitude, aka Tropic of Cancer Winter solstice: minimum solar declination (-23.5 ), around December 21 Northern hemisphere is at its maximum tilt away from the Sun Days are shorter than nights in the Northern hemisphere All points north the Arctic circle are in total darkness The Sun is at Zenith at solar noon at locations at 23.5 S latitude, aka Tropic of Capricorn

6 6 Earth s Orbit Equinoxes: Earth s orbital position when solar declination is zero Spring Equinox: around March 21 Fall Equinox: around September 23 Every location on Earth has equal length days & nights The Sun is at zenith at solar noon on the equator and rises and sets due East and due West, resp., everywhere on Earth The rate of change in declination is large, so daily change in Sun path is at maximum

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12 12 Solar Time Meridian: a plane formed by a due North-South longitude line through a location on Earth and projected out into space Local Meridian: meridian at the observer s exact location Solar Time: timescale based on the apparent motion of the Sun crossing a local meridian Solar noon: the moment when the Sun crosses a local meridian and is at its highest position of the day Solar Day: the interval of time between sun crossings of local meridian, which is approximately 24h

13 13 Standard Time Standard Meridian: a meridian located at a multiple of 15 East or West of zero longitude (Greenwich, England), aka Prime Meridian Standard Time: a timescale based on the apparent motion of the Sun crossing standard meridians The Earth rotates 360 in approximately 24h Each 15 of longitude is equal to one hour of solar time Each 1 of longitude is equal to 4mn of solar time Standard time zones are at one hour multiples ahead of or behind the time at the Prime Meridian, aka Greenwich Mean Time (GMT) or Universal Time (UT)

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15 15 Standard Time vs Solar Time Longitude Time Correction t λ = (λ local λ s ) x 4 t λ : longitude time correction (mn) λ local : local longitude (deg) λ s : longitude of standard meridian (deg) Equation of Time Correction Caused by eccentricities in Earth s rotation during its orbit around the Sun difference between actual solar noon and theoretical solar noon based on uniform Earth motion t s = t 0 t E + t λ t s : Local Standard Time t 0 : Solar Time t E : Equation of Time Value t λ : Longitude Time Correction

16 16 Solar Time Calculators

17 Calculating Solar Time 17

18 18 Sun Position Two angles are used to define the Sun s position in the sky Solar Altitude: vertical angle between zero and 90 Solar Azimuth: horizontal angle between a reference direction (typically due South in the Northern hemisphere) and the Sun varies between -180 and +180 Sun position to the East of due South is represented as a positive angle, and to the West as a negative angle

19 19

20 Sun Path Charts 20

21 Sun Path Charts 21

22 Sun Path Charts 22

23 23

24 24 Array Orientation Array orientation is defined by two angles: Array Tilt: vertical angle between horizontal and the array surface Array Azimuth: horizontal angle between a reference direction (typically due South in the Northern hemisphere) and the direction an array surface faces Incidence Angle: angle between the direction of direct radiation and a line exactly perpendicular to the array surface

25 25

26 26 Array Tilt Angle Smaller tilt angles can be required by applications with high energy loads in the summer, like airconditioning Average declination during the summer is +15, so the optimal tilt angle for the summer is (latitude - 15 ) Larger tilt angles can be required by applications with high energy loads in the winter, like artificial lighting Average declination during the winter is -15, so the optimal tilt angle for the winter is (latitude + 15 )

27 Solar Radiation Data Manual 27

28 28 Array Tilt Angle The geometry of the solar window is such that the Sun is in the sky for longer in the summer than in the winter Climate and atmospheric factors result in a slightly lower optimal tilt angle to maximize the annual energy production Summer skies are clearer than winter skies Less air mass in the summer

29 Optimal Tilt Angle 29

30 30 Optimal Tilt Angle

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