# Solar radiation with a clear sky

Solar radiation with a clear sky consists of three parts:

Total solar radiation on a horizontal surface, GtH GtH = Gdh + GdH, Gr=0 Total radiation on a tilted surface Gte = G ne + Gde + Gr All the three parts are the functions of normal direct radiation, Gnd

G A

110 exp(B / sin Я)

Where A = apparent solar radiation (TTable 6-1, ATable 8)

B = atmospheric extinction coefficient (T Table 6-1, A Table 8)

Я = solar altitude

Direct solar radiation on a surface of arbitrary orientation

Gd6 = Gnd Cn cos 0

 Where

Cn = clearness number (T Figure 6-7)

0 = incident angle

On a horizontal surface, cos 0 = sin (3

Gdh = Gnd Cn sin (3

 W-Winter Figure 6-7 Estimated atmospheric clearness numbers CN in the United States for nonindustrial localities, percent. (Reprinted by permission from ASHRAE Handbook, Fundamentals Volume, 1989)

Diffuse radiation On a horizontal surface:

GdH = CGND/CN2

 Where

C = ratio of diffuse on a horizontal surface to direct nonnal radiation (T Table 6-1, A Table 8)

On a tilted surface

Gde = (C Gnd / Cn2) Fws

Fws = view factor between the surface and the sky Fws= (1 + cos Z)/2

For a horizontal surface Fws = 1 and for a vertical surface Fws = 0.5.

Gr = (Gdh + GdH) pg Fwg

Where pg = reflectance of ground

Fwg — view factor between the surface and the ground

FWg = (1 — cos Z)/2

For a horizontal surface Fwg = 0 and for a vertical surface Fwg = 0.5.

Example 7-4

Continue from Example 7-3. If the ground reflectivity is 0.3, find the total solar radiation on the vertical window surface.

Solution

From T Table 6-1 or A Table 8, A = 1187 W/m2, B = 0.142, and C = 0.104.

From T Figure 6-7, Cn = 1.0

G A

ND exp (B / sin Я)

________ H87_______

~~ exp(0.142/sin37.85°)

= 942 W/m2

Gdg = Gnd Cn cos 0

= 0 No direct solar radiation

GdH = C Gnd / Cn2 = 0.104×942/ 1.02 =98 W/m2

Gde = GdH F = Gd (1 + cos X)/2 = 98 (1 + cos 90°)/2 = 49 W/m2

Gr = (Gdh + GdH) pg Fwg = (Gnd Cn sin Я + Gd) pg (1 — cos X)/2 = (942 x 1.0 x sin 37.85 ° + 49) x 0.3 x (1 — cos 90°)/2 = 94 W/m2

Gte — Gdg + Gde + Gr

= 0 + 49 + 94 = 143 W/m2