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Solar Fundamentals Sun-Earth Geometry and Solar Position Part 3 Sun-Earth Geometry

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Solar Fundamentals Sun-Earth Geometry and Solar Position Part 3 Sun-Earth Geometry KTH ROYAL INSTITUTE OF TECHNOLOGY Solar Fundamentals Sun-Earth Geometry and Solar Position Part 3 Sun-Earth Geometry The direction of the incident beam radiation depends upon the position of the Sun, which varies throughout the day. Image Source: J. Spelling, 2009 MJ2411: RENEWABLE ENERGY TECHNOLOGY 2 Sun-Earth Geometry The path taken by the Sun depends on the observers latitude and the day of the year (through the declination angle δ) Image Source: J. Spelling, 2009 n 173 δ: declination angle [rad] arcsin0.39795cos2 365 n: calendar day (Gregorian) MJ2411: RENEWABLE ENERGY TECHNOLOGY 3 Sun-Earth Geometry The path taken by the Sun depends on the observers latitude and the day of the year (through the declination angle δ) Image based on: W.B.Stine and R.W.Harrigan, 1985 Equinoxes: 21st March / 21st September -> δ = 0 Summer Solstice: 21st June -> δ = +23.45° Winter Solstice: 21st December -> δ = -23.45° MJ2411: RENEWABLE ENERGY TECHNOLOGY 4 Sun-Earth Geometry Based on the declination angle and latitude, the length of a given day N can be calculated: 24 N arccos tan tan 180 N: day length [hrs] φ: latitude [°N] ψ: longitude [°W] Attention: Latitude in °N and longitude in °W. Image based on: Wikipedia, 2015 MJ2411: RENEWABLE ENERGY TECHNOLOGY 5 Sun-Earth Geometry The solar position can be defined using a number of angles: • Solar Azimuth Angle: γs • Solar Zenith Angle:θz • Solar Elevation Angle: θs = 90° - θz Image Source: J. Spelling, 2009 MJ2411: RENEWABLE ENERGY TECHNOLOGY 6 Sun-Earth Geometry The solar position can be defined using a number of angles: First step, convert local solar time into the: • Hour Angle: t 12 12 s Image based on: W.B.Stine and R.W.Harrigan, 1985 MJ2411: RENEWABLE ENERGY TECHNOLOGY 7 Sun-Earth Geometry The solar position can be defined using a number of angles: • Solar Zenith Angle: z arccoscos cos cos sin sin cos sin sin sgn() arccos z • Solar Azimuth Angle: s sin z cos Latitude: φ Declination: δ Hour Angle: ω Image Source: J. Spelling, 2009 MJ2411: RENEWABLE ENERGY TECHNOLOGY 8 Example: Solar Position It is 15:45 on the clock in Stockholm (59.3°N, 18.0°E) on the 26th July (n = 207). We already know that solar time is: 14h50 What is the solar position? • Solar Azimuth Angle • Solar Zenith Angle MJ2411: RENEWABLE ENERGY TECHNOLOGY 9 KTH ROYAL INSTITUTE OF TECHNOLOGY Calculate Example: Solar Position It is 15:45 on the clock in Stockholm (59.3°N, 18.0°E) on the 26th July (n = 207), what is the solar position (azimuth, zenith)? n 173 arcsin0.39795cos2 18.9 365 t 12 43.0 12 s 59.3 z arccoscos cos cos sin sin 50.2 cos sin sin z s sgn() arccos 56.1 sin z cos MJ2411: RENEWABLE ENERGY TECHNOLOGY 11 Solar Position Maps The path of the Sun can be plotted on solar maps - - - Image Source: J. Spelling, 2011 MJ2411: RENEWABLE ENERGY TECHNOLOGY 12 Solar Position Maps The path of the Sun can be plotted on solar maps - - Image Source: J. Spelling, 2011 MJ2411: RENEWABLE ENERGY TECHNOLOGY 13 Solar Position Maps When the clock time is used instead of solar time, the effects of longitude and the equation of time can become visible Solar Analemma Image Source: J. Spelling, 2012 MJ2411: RENEWABLE ENERGY TECHNOLOGY 14 KTH ROYAL INSTITUTE OF TECHNOLOGY Solar Fundamentals Sun-Earth Geometry and Solar Position Next: Solar Radiation Measurement .
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