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298 CHAPTER 13 1957 Guide Table 4. Values of /Dn, Direct Solar Radiation Received at Normal Incidence at the Earth's Surface, and Values of 7d, Diffuse or Sky Solar Radia tion, Received by Variously Oriented Surfaces Btu per (hour) (square foot) Solar Altitude 0, Degrees For Clear Atmospheres Direct 4 Normal Radi ation Diffuse obSkt Radiation15 Fob Industrial Atmospheres Direct*1. Normal Radi ation Diffuse or Sky Radiation- AM -* 1 5 10 15 20 25 30 35 40 45 50 60: 70 80 90 N E s w Hobiz. N E 8 W Hobiz. 67 6 11 4 4 7 123 11 20 8 7 14 166 14 27 11 10 19 197 15 32 13 12 23 218 16 35 15 13 26 34 4 11 5 3 9 58 8 22 9 7 18 80 11 28 13 9 24 103 13 36 17 12 31 121 16 43 21 16 38 235 17 ` 36 17 15 28 248 17 36 19 16 . 30 258 18 36 21 17 31 266 19 35 23 18 32 273 19 33 25 19 33 136 18 .47 24 18 44 148 19 50 27 21 48 158 20 . 50 30 23 52 165 21 49 31 25 55 172 22 47 34 27 58 283 21 28 27 21 34 i 181' 22 41 37 30 63 289 22 23 29 23 35 188 22 34 41 34 69 292 __ -- -- -- -- 195 -- -- -- -- -- 294 -- ---- -- 200 -- -- -- -- -- pll-* N . W S E .. Hobiz. N * W 8 E Hobiz. 4 Moon's4 proposed standard for sea level, 20 mm precipitable water vapor, 300 dust particles per cu cm, 2.8 mm Hg partial pressure of ozone. b For 40 deg north latitude on about August 1. c Based on observations by ASHAE Laboratory at Cleveland on cloudless days during which the observed normal incidence values closely approximated the normal incidence values tabulated. d Derived from recommended design sol-air temperatures4 for New York City for a horizontal surface with bsorptivity of 1.0. values of the order of those given for industrial atmospheres are usually associated with dry-bulb and wet-bulb temperatures near the design values of 95 F and 75 F (67 F dew-point). On the other hand, values approaching or exceeding those for a clear atmosphere are often encountered during Cleveland summers, but with dew-point and maximum dry-bulb temperatures 10 to 15 deg lower. Considerable judgment, therefore, is required in selecting solar intensity values for design purposes. Data regarding the irradiation of vertical and horizontal surfaces by diffuse or sky radiation are few. Suggested design values for a 40-deg latitude on August 1 (18 deg declination, north) are given ih Table 4 for the two types of atmospheres. These are based upon observations mad on cloudless days in Cleveland over a period of several summers. Since less extensive data were available for industrial atmospheres, there is more' uncertainty regarding these values. In both instances, the values include an unknown amount of ground reflection, which may be expected to. vary with location. It should be noted that clouds which do not obscure the sun tend to increase diffuse radiation values. Nearby buildings may reduce diffuse irradiation by partial shading. Calculation Tables The irradiation of a surface by the sun is the product of 7dd, the direct normal radiation (see Table 4), and the cosine K of the incident angle,#-1 For horizontal surfaces, the cosine A equals the sine of the solar altitude-; Cooling Load 299 jl 40 D bg N orth Table 5. Values of K, the Cosine of the Incident Angle, for Variously Oriented Walls and a Horizontal Surface Computed for 18 Deg Declination, North (August 1) BAP Sun Time . Cosine K of the Incident Angle P AM - l N NE E 8E S sw Hobiz. a 6 BJU. 6 DJD. co 7 8 Z9 5 4 3 a0 Q CO 10 11 12 2 1 5 ajn. 6 7 8 7 pjn. 6 5 4 93 10 2 11 12 0.267 0.144 0.030 0.862 0.752 0.604 0.427 0.234 0.039 0.406 0.237 - 0.079 0.934 0.840 0.705 0.533 0.837 0.129 0.952 0.919 0.824 0.672 0.476 0.246 0.000 0.914 0.951 0.919 0.824 0.673 0.475 0.246 0.000 0.484 0.548 0.561 0.524 0.438 0.310 0.147 0.358 0.505 0.594 0.631 0.614 0.542 0.424 0.265 0.068 0.144 0.192 0.208 0.069 0.196 0.292 0.354 0.375 0.147 0.156 0.367 0.566 0.737 0.866 0.951 0.978 0.076 0.265 0.009 . 0.199 0.391 0.566 0.713 0.829 0.903 0.927 ttB 5 am. 7 p.m. 66 O7 5 Z8 4 ao Q 9 10 23 s 11 12 1 0.385 0.199 0.010 0.922 0.813 0.656 0.465 0.252 0.030 0.920 0.951 0.918 0.824 0.673 0.475 0.247 0.000 0.378 0.532 0.643 0.700 0.699 0.642 0.532 0.375 0.166 0.316 0.433 0.505 0.530 0.183 0.375 0.078 0.233 0.399 0.545 0.669 0.766 0.829 0.848 . pii- N NW W 8W S SE Horzs. For vertical walls, K ia a function of the solar altitude 0 and the wall solar azimuth 7, thus -- -- , --. , \.u These three angles are defined in Fig. 1. Values of K are given in Table 5 and values of 0 and 7 are given in Table 6 for 18 deg north declination (August 1).. To compute K values for orientations other than those given in Table 5, "fled angle <j>, the solar azimuth, is required! In' this discussion, <j> will be measured east from south in the morning, and west from south in the after noon. Hence, $ values are equal to 90 deg minus the 7 values for an east v, feeing wall, except when Table 6 shows the south walls to be in the cnade. In this case <f> equals 90 + 7, that is, <f> is greater than 90 deg. The wall azimuth $ is the angle, measured east from south to the per pendicular to the wall for walls which have an easterly component, and west irom south for those having a westerly component. For example, $ for a wall facing northeast is 135 deg. solar azimuth 7 may be found according to the following For walls facing east of south: For walls facing west of south: y = ^ ^ a.m. y = 0 + f a.m. y =(/> + # p.m. y = * -- * P-m- Treat negative values of 7 as if they were positive. If 7 is greater than deji, the wall is in the shade.