Estimation of the degree of direct shading

For further calculations, it is assumed that the surroundings of the point of reference are given by the approximated polygonal shape shown in Figure 2.21. A horizontal ray originating at the position of the sun is used for testing whether the position of the sun is inside or outside the polygon describing the shading objects (Figure 2.22). The number of times the ray crosses the polygon boundary lines is determined. All boundary lines to the left from the position of the sun must be considered. If the number of intersections is even, the position of the sun is outside the polygon. If the number of intersections is odd, the position of the sun is inside the polygon and direct sunlight is blocked.

However, not all objects between the sun and the observer block the direct irradiance completely; in this case, the transmittance must be considered. As an example, a part of the direct irradiance may pass through trees. The transmittance t describes the fraction that passes through trees. The transmittance of deciduous trees has been investigated (see Sattler and Sharples, 1987):

90 80

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90 80

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21 June J

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21 March „

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21 Feb

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21 Dec ^J

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Solar azim uth angle in degrees

Solar azim uth angle in degrees

Figure 2.21 Solar Position Diagram of Berlin with an Approximation of the

Surroundings

For further calculations, the degree of direct shading Sdir is introduced. The degree of shading describes the portion of the direct irradiance that is reduced by shading:

if (yS,aS) is outside the object polygon if (yS,aS) is inside an opaque object polygon t if (yS,aS) is inside a semi-transparent object polygon

Figure 2.22 Shading Test for Two Different Positions of the Sun A and B (Position A has 5 Intersections, Position B has 4)

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