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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