Numerical values of scattered radiation
The total amount of solar radiation (/t) normally incident on a surface is given by
7t = / cos i + Is + /r (7.14)
Where /s is sky radiation and /r is radiation reflected from surrounding surfaces. ASHRAE (1993b) evaluates /s and /r according to
Is + /r = CIFS + p/(C + sin a)Fs (7.15)
The value of the dimensionless constant, C, varies through the year and is given in Table 7.3. The angle factor for the ground with relation to the particular surface, Fg, is complementary to Fs, the factor between the surface and the sky and is given by
Fg = 0.5(1 — cos 8) (7.16)
Note that the sum of all the angle factors between a surface and its surroundings is unity. Hence, Fs = 1 — Fg for any surface seeing only the ground and the sky. 8 is the angle between the ground and the horizontal.
The reflectivity, p, of the ground depends on solar altitude and on the type of surface. Over the range of solar altitudes from 30° to 60° it has values of about 0.32 for new concrete, 0.22 for old concrete, 0.23 for green grass and 0.1 for asphalt according to ASHRAE (1993c).
Calculate the total scattered radiation normally incident on a vertical surface in July for a solar altitude of 40°, a height above sea level of 2000 m and a ground reflectivity of 0.2.
From Table 7.1 or equation (7.9), / = 814 W m 2 (CIBSE figure) or 786 W m 2 (an
American-derived figure) at sea level and from Table 7.2 the increase in these values is 24 per cent at a height of 2000 m. Also, from Table 7.3, C = 0.136 and by equation (7.16),
Fg = 0.5(1 — cos 90°) = 0.5
Hence, by equation (7.15), using the CIBSE figure,
Is + Ir= 1.24[0.136 x 814 x (1 — 0.5) + 0.2 x 814 x (0.136 + sin 40) x 0.5]
= 1.24(55.4 + 63.4)
— 147 W m-2
Note that Table 7.7 quotes values of 53 and 61 W m-2 at sea level for sky and ground radiation in July with 40° solar altitude. These are less than the values calculated because they are based on / = 786 W m-2, the American-derived figure, used when compiling the table.
The CIBSE Guide A2 (1999) uses solar data from measurements at Bracknell.
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