19 An additional angle of interest is the profile angle, α p , of beam radiation on a receiver plane R that has a surface azimuth angle of γ . It is the angle through which a plane that is initially horizontal must be rotated about an axis in the plane of the surface in question in order to include the sun. The profile angle is useful in calculating shading by overhangs and can be determined from: ANGLE RELATIONS – Profile angle, α p (13) Three types of shading problems typically occur: a) shading of a collector, window, or other receiver by nearby trees, buildings or other obstructions. The geometries may be irregular and systematic calculations of shading of the receiver in question may be difficult. Recourse is made to diagrams of the position of the sun in the sky, for example plots of solar altitude, α s , versus solar azimuth γ s , on which shapes of obstructions (shading profiles) can be superimposed to determine when the path from the sun to the point in question is blocked. b) The second type includes shading of collectors in other than the first row of multi-row arrays by the collectors on the adjoining row. c) shading of windows by overhangs and wingwalls. When the geometries are regular, shading problems can be assessed through analytical calculation, and the results can be presented in general form. SHADING - 1 IDES-EDU
20 SHADING - Solar plots Solar plots are a 2D representation of the sun paths over the sky dome. These paths are plotted for different periods of the year and are the projection of the sun orbits over the horizontal plane. Each solar plot is draw for a specific location (that is, for a certain latitude, φ ) and allows to assess the sun position for every hour of the day and for every day of the year, by means of the solar altitude angle, α s , and of the solar azimuth, γ s . Solar plots may be plotted in either polar or rectangular coordinate charts. Solar position plot of θ z and α s , versus γ s , for latitudes of ± 45°is shown in Figure. Lines of constant declination, δ , are labeled by dates of mean days of the months (see Table 1.6.1). Lines of constant hour angles, ω , are labeled by hours. (plots for latitudes from 0 to ± 70°are included in App endix H of Duffie & Beckman). SHADING - Type a) – Use of Solar plots (rectangular coordinate plot) The angular position of buildings, wingwalls, overhangs, or other obstructions can be entered on the same plot (the angular coordinates corresponding to altitude and azimuth angles of points on the obstruction - the object azimuth angle, γ o , and object altitude angle, α o ) can be calculated from trigonometric considerations and drawn on the plot). For obstructions such as buildings, the points selected must include corners or limits that define the extent of obstruction. It may or may not be necessary to select intermediate points to fully define shading. IDES-EDU
21 SHADING - Type a) – Use of Solar plots
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- Fall '19