## Example

Calculate the apparent solar time on March 10 at 2:30 pm for the city of Athens, Greece (23°40' E longitude).

Solution

The equation of time for March 10 (N = 69) is calculated from Eq. (2.1), in which the factor B is obtained from Eq. (2.2) as

B = 360/364(N - 81) = 360/364(69 - 81) = -11.87 ET = 9.87sin(2B) - 7.53cos(B) - 1.5sin(B)

= 9.87sin(-2 X 11.87) - 7.53 cos(-11.87) - 1.5cos(-11.87)

Therefore,

The standard meridian for Athens is 30°E longitude. Therefore, the apparent solar time at 2:30 pm, from Eq. (2.3), is

AST = 14:30 + 4(30 - 23.66) - 0:13 = 14:30 + 0:25 - 0:13 = 14:42, or 2:42pm

SoLAR ALTITuDE ANGLE, a

The solar altitude angle is the angle between the sun's rays and a horizontal plane, as shown in Figure 2.8. It is related to the solar zenith angle, which is the angle between the sun's rays and the vertical. Therefore,

The mathematical expression for the solar altitude angle is sin(a) = cos(\$) = sin(L) sin(6) + cos(L) cos(6) cos(h) (2.12)

where L = local latitude, defined as the angle between a line from the center of the earth to the site of interest and the equatorial plane. Values north of the equator are positive and those south are negative.