34
SYSTEM
•
D
= solar declination (
), which ranges from +0.409 radians (+23.45°) at summer
solstice to -0.409 radians (-23.45°) at winter solstice:
Equation 26
=
+
+
+
D
J
J
arcsin{0.39785sin(4.869 0.0172
0.03345sin(6.224 0.0172 )]}
where
J
is the day of the year.
• 2.618 = conversion of hours to radians (Earth turns at a rate of 0.2618 radians/h)
•
t
= time (in hours from 0 to 24).
•
t
0
= time of solar noon:
Equation 27
=
−
−
LC ET
12
t
0
where
LC
is the longitude correction and
ET
is the Equation of Time.
Longitude correction is +4 min, or +1/15 h for each degree east of the standard meridian and
-1/15 h for each degree west of the standard meridian. Standard meridians are at 0°, 15°,
30°... etc. Generally, time zones run approxi7.5° to -7.5° on either side of a standard
meridian, but this varies depending on political boundaries, so check an atlas to find both
standard meridian and longitude. Typically, longitudes in the Eastern Hemisphere are given
as negative values.
The Equation of Time is a 15- to 20-min correction that depends on the day of the year. It can
be calculated from:
Equation 28
φ
φ
φ
φ
φ
φ
φ
=
−
+
+
−
−
−
+
ET
104.7sin
596.2sin2
4.3sin3 12.7sin4
429.3cos
2.0cos2
19.3cos3
3,600
where
φ
=(279.575 + 0.986
J
)π/180. Some values for
ET
are given in
Table 1 Solar Declination and Equation of Time
Date
Day of Year
D
(Radians)
ET Hour
Jan 1
1
–0.403
–0.057
Jan 10
10
–0.386
–0.123
Jan 20
20
–0.355
–0.182
Jan 30
30
–0.312
–0.222
Feb 0
40
–0.261
–0.238
Feb 19
50
–0.202
–0.232
Mar 1
60
–0.138
–0.208
Mar 11
70
–0.071
–0.117
Mar 21
80
–0.002
–0.122
Mar 31
90
0.067
–0.072
Apr 10
100
0.133
–0.024
Apr 20
110
0.196
0.017