BLDG365-#7 Solar radiation-W2021-Handout.pdf - BLDG 365...

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BLDG 365 Building Science 2021-03-08 Chang-Seo Lee 1 BLDG 365 Building Science Solar Radiation and Buildings Winter 2021 Chang-Seo Lee, Ph.D., P.Eng. Dept. of Building, Civil & Environmental Engineering Concordia University 1 Part A. Solar Angles 2
BLDG 365 Building Science 2021-03-08 Chang-Seo Lee 2 Solar Radiation Direction of sun’s ray changes Day of the year Time of the day Location on the earth’s surface Sun’s position in the sky is expressed by Solar Altitude or Elevation ( ) above the horizon Solar Azimuth ( ) measured from South : E= -90°, W= 90° & are determined by Solar declination ( ), Apparent Solar Time (AST) and Local Latitude (L) 3 Apparent Solar Time (AST) Based on the apparent motion of the actual Sun, measured by sundial (= true solar time) 𝐴𝑆𝑇 = 𝐿𝑆𝑇 + 𝐸𝑇 ௠௜௡ + 4 ȉ 𝐿𝑆𝑀 − 𝐿𝑂𝑁 ௠௜௡ AST: Apparent solar time LST: Local standard time LSM: Local standard meridian [deg]: Eastern Time LSM = 75°W LON: Local longitude of the site [deg] - [email protected] = 78°W ET: Equation of time [min] 3/8/2021 4
BLDG 365 Building Science 2021-03-08 Chang-Seo Lee 3 Apparent Solar Time (AST) Equation of Time [ET] corrects for the eccentricity of the Earth's orbit and the Earth's axial tilt 5 - sunlight/suns-position Apparent Solar Time (AST) Daylight saving time (DST) 𝐿𝑆𝑇 = 𝐷𝑆𝑇 − 1ℎ𝑟 3/8/2021 6
BLDG 365 Building Science 2021-03-08 Chang-Seo Lee 4 Apparent Solar Time (AST) Ex) What is the AST corresponding to 10:30 central standard time (LSM=90°W) on Feb. 2 at Madison, WI (LON=89.4°W)? 3/8/2021 7 Solar Angles Solar Declination ( ) Northern hemisphere n: the day number of the year (e.g., n=1 on Jan.1) 8 - energy/part-3-calculating-solar-angles/ 𝛿 = 23.45° sin 𝑛 + 284 365 × 360°
BLDG 365 Building Science 2021-03-08 Chang-Seo Lee 5 Solar Angles Hour Angle (H) Angular displacement of the sun east or west of the local meridian due to the rotation of the earth, and expressed in degrees Sun moves through 15° of longitude in 1 hour 𝐻 = 𝐴𝑆𝑇 ௛௥ − 12 × 15° = 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑚𝑖𝑛𝑢𝑡𝑒𝑠 𝑓𝑟𝑜𝑚 𝑙𝑜𝑐𝑎𝑙 𝑠𝑜𝑙𝑎𝑟 𝑛𝑜𝑜𝑛 × 0.25° AST : Apparent solar time [hr] Hour angle is negative in the morning, positive in the afternoon AST= 9:00, H= -45° AST=18:00, H= 90° 9 Solar Angles 10 Caution – Different notations used in these figures
BLDG 365 Building Science 2021-03-08 Chang-Seo Lee 6 Solar Angles Solar Altitude Angle ( ) Apparent angular height of the sun in the sky if you are facing it sin 𝛽 = sin 𝐿 sin 𝛿 + cos 𝐿 cos 𝛿 cos 𝐻 L = latitude (positive in either hemisphere) [0° to +90°], δ = declination angle (negative for Southern Hemisphere) [–23.45° to +23.45°], H = hour angle [deg] At solar noon, H=0 ∴ 𝛽 = 90° − 𝐿 + 𝛿 11 Solar Angles Solar Azimuth Angle ( ) Angular displacement from south of the projection, on the horizontal plane, of the earth/sun line sin 𝜙 = sin 𝐻 cos 𝛿 cos 𝛽 = solar altitude [deg] δ = declination angle [deg] H = hour angle [deg] 12
BLDG 365 Building Science 2021-03-08 Chang-Seo Lee 7 Solar Angles Angle of Incidence ( ) Angle between the line normal to the irradiated surface and the earth-sun line 13 important in fenestration, load calculations, and solar technology

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