## Sinhss

2nhOI

where r = ratio of hourly total radiation to daily total radiation.

a = G.4G9 + G.5G16sin(hss ß = G.66G9 - G.4767 sin(hss

Example 2.15

Given the following empirical equation,

1.39G

where HD is the monthly average daily diffuse radiation on horizontal surface—see Eq. (2.105a)—estimate the average total radiation and the average diffuse radiation between 11:00 am and 12:00 pm solar time in the month of July on a horizontal surface located at 35°N latitude. The monthly average daily total radiation on a horizontal surface, H, in July at the surface location is 23.14 MJ/m2-d.

Solution

From Table 2.5 at 35° N latitude for July, Ho

40.6 MJ/m2. Therefore,

H 23.14

4G.6

Therefore, H

G.57G

^ = 1.39G - 4.G27(G.57) + 5.531(G.57)2 - 3.1G8(G.57)3 = G.316 H

From Table 2.5, the recommended average day for the month is July 17 (N = 199). The solar declination is calculated from Eq. (2.5) as

23.45sin

The sunset hour angle is calculated from Eq. (2.15) as cos(hss) = -tan(L)tan(6) ^ hss = cos_1[-tan(35)tan(21)] = 106°

The middle point of the hour from 11:00 am to 12:00 pm is 0.5 h from solar noon, or hour angle is -7.5°. Therefore, from Eqs. (2.84b), (2.84c), and (2.84a), we have a = 0.409 + 0.5016 sin(hss - 60) = 0.409 + 0.5016sin(106 - 60)

(3 = 0.6609 - 0.4767sin(hss - 60) = 0.6609 - 0.4767sin(106 - 60)

,, xx cos(h) - cos(hss) r = — (a + ß cos(h))--ss

sin(106)

2n(106)

cos(106)

n 24

sin(hss)

cos(hss)

sin(hss)

cos(hss)