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)

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

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

The numerical value of direct radiation

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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