# The numerical value of direct radiation

In order to evaluate the amount of solar radiation normally incident upon a surface, it is first necessary to know the value of the intensity, /, which is normally incident on a surface held at right angles to the path of the rays. The values of I can be established only by referring to experimental results for different places over the surface of the earth. These seem to suggest that I is independent of the place and that it depends only on the altitude of the sun. There is sense in this, since the amount of direct radiation reaching the surface of the earth will clearly depend on how much is absorbed in transit through the atmosphere, and the atmospheric path length is greater when the sun is lower in the sky; that is, when its altitude is less.

Numerical values for the intensity of direct solar radiation are given in Table 7.1, and Table 7.2 gives correction factors that account for the increased intensity with ascending altitude from the same source.

Figure 7.10 shows curves based on Curtis and Lawrence (1972) and ASHRAE (1993a) using equation (7.9):

/ = A/exp(S/sin a) kW nT2 (7.9)

In which the constant A is the apparent solar radiation in the absence of an atmosphere and the constant B is an atmospheric correction factor. A and B (see Table 7.3) depend upon

 Sun altitude (degrees) 5° 10° 15° 20° 25° O O CO 35° 4^ O O 50° O O VO O O R- O O OO : Inclination and Intensity of basic direct solar radiation with a clear sky for a place Orientation of surface 0-300 m above sea level (W m 2) 1. Normal to sun 210 388 524 620 688 740 782 814 860 893 912 920 2. Horizontal roof 18 67 136 212 290 370 450 523 660 773 857 907 3. Vertical wall: Orientation from Sun in degrees 0° 210 382 506 584 624 642 640 624 553 447 312 160 (wall-solar 10° 207 376 498 575 615 632 630 615 545 440 307 158 Azimuth angle) 20° 197 360 475 550 586 603 602 586 520 420 293 150 30° 182 330 438 506 540 556 555 540 480 387 270 140 40° 160 293 388 447 478 492 490 478 424 342 240 123 45° 148 270 358 413 440 454 453 440 390 316 220 113 50° 135 246 325 375 400 413 412 400 355 287 200 103 55° 120 220 290 335 358 368 368 358 317 256 180 92 60° 105 190 253 292 312 210 320 312 277 224 156 80 65° 90 160 214 247 264 270 270 264 234 190 132 68 O O R- 72 130 173 200 213 220 220 213 190 153 107 55 75° 54 100 130 150 160 166 166 160 143 116 80 40 O O 00 36 66 88 100 108 110 110 108 96 78 54 28 (Reproduced by kind permission from the CIBSE Guide A2 (1986)) Table 7.2 Percentage increase in direct solar radiation at varying heights above sea level Height above Solar altitude Sea level 10′ 3 20° 25c ’ 30 O 35° O O U © O 60c 5 70 O OO O 0 1000 m 32 22 18 16 14 13 12 11 10 10 1500 m 50 31 26 23 21 18 16 15 14 14 2000 m 65 40 33 29 27 24 21 19 18 18 3000 m 89 52 43 37 34 31 27 24 23 22
 Note that sky radiation decreases by approximately 30 per cent at 1000 m and by about 60 per cent at 1500 m above sea level.

Seasonal variations in the earth-sun distance, the atmospheric moisture content and dust pollution according to Moon (1940). The equation does not give the maximum intensity but the value likely on an average cloudless day: the maximum intensity of direct radiation on a very clear day can be 15 per cent higher. The equation gives more accurate results than Moon.

CIBSE values for the intensity of direct radiation on a plane normal to the sun’s rays, taken from Table 7.1, are in good agreement with the curve for May in Figure 7.10, for solar altitudes exceeding 10°, in northern latitudes.

If data which have been determined for the northern hemisphere are to be used for an application in the southern hemisphere, corrections must be applied to take account of the reduced sun-earth distance in the southern summer. Thus a solar intensity value (or a value

 Solar altitude (a) Fig. 7.10 Numerical values of direct solar radiation, incident on a surface at right angles to the sun’s rays, at sea level in the northern hemisphere.

Table 7.3 Constants for determining the values of direct and scattered radiation at sea level, to be used in equations (7.9) and (7.14)

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Units

C 0.058 0.060 0.071 0.097 0.121 0.134 0.136 0.122 0.092 0.073 0.063 0.057 —

A 1.230 1.213 1.186 1.136 1.104 1.088 1.085 1.107 1.152 1.192 1.220 1.233 kW nT2

В 0.142 0.144 0.156 0.180 0.196 0.205 0.207 0.201 0.177 0.160 0.149 0.142 —

Of cooling load due to solar gain through windows) for the month of July in the northern hemisphere, should be multiplied by the ratio of the intensity in January to that in July, if it is to be used for the month of January in the southern hemisphere.

Correction factors for this purpose, based on the ratio of solar intensities outside the limits of the earth’s atmosphere according to ASHRAE (1993a), for corresponding months, are given in Table 7.4.

Table 7.4 Correction factors for solar radiation data based on the northern hemisphere, when applied to the southern hemisphere

Month ratio Dec/Jun Jan/Jul Feb/Aug Mar/Sep Apr/Oct

Correction factor 1.07 1.07 1.06 1.02 0.98

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