SITING 475 
DECLINATION Im DEGREES 
CousTion OF Tut m= muRUTES 
Figure 1. Calculation of solar azimuth. 
The hour angle HA is the local apparent time 
(LAT) minus 12 hours. To convert the observed 
time into LAT, the civil time at Greenwich (GCT) 
must be found and combined with the equation of 
time to correct for the apparent irregular motion of 
the sun. This gives Greenwich apparent time. 
GAT, which is converted to LAT, by allowing for 
the longitude. The equation of time and the decli- 
nation of the sun are plotted for 1945 in Figure 1. 
The annual change is small and these curves may 
be used for most orientations without regard to the 
year. Standard time meridians are given every 
15 degrees east or west of Greenwich, each zone 
corresponding to one hour. Care should be used to 
take daylight saving or other changes from standard 
into account correctly. 
The calculations may be illustrated from the 
following data: date, 16 March; time, 1345 hours 
PWT; latitude, 40° north; longitude, 118° west. 
The HA is computed first. 
Observed time (PWT) 13 hr 45 min 
Zone difference + 7hr 
Greenwich civil time 20 hr 45 min 
Equation of time (Figure 1) — 9 min 
Greenwich apparent time 20 hr 36 min 
Longitude difference (for 118° W) — Thr 52min 
Local apparent time (LAT) 12hr 44 min 
LAT —12 hours = HA —12hr 
Hour angle of sun 
HA in are +11° 
Latitude p + 40° 
Declination of sun 6 (Figure 1) —) 2° 
Substituting in equation (1), 
sin 11° 
cos 40° - tan (—2°) — sin 40°- cos 11° 
B = 16° 10’ 
Since @ — 6 is positive, 6 is the bearing from the 
EARTH d; Ss h 
ka 
tan 6 = — 
Figure 2. Geometry for horizon distance for zero 
height transmitter. 
+ Ohr 44min 
Ficurz 3. Geometry for horizon distance with ele- 
vated transmitter. 
south. The bearing is west of south, since HA is 
positive (p.m.). The azimuth ot the sun is 
180° + 16°10’ = 196° 10’.* 
The equal altitude method is less convenient but 
requires no calculation. This method consists in 
measuring the horizontal angles between the sun 
and a mark taken when the sun is at the same alti- 
tude on both sides of the meridian of the observer. 
The bisector of the horizontal angle between the 
two equal altitude positions of the sun during the 
observations is very close to true south, and the 
azimuth of the mark may be determined. 
GEOMETRICAL LIMITS OF VISIBILITY 
Horizon Formula 
It is assumed throughout that the earth radius is 
ka (see Chapter 4). Whenever numerical examples 
are given, the standard value, k = 4/3, is used. 
The alternate method of accounting for refraction 
givenin Chapter 4 may also be used in connection 
with the following equations if k ~ 4/3. 
When 2a horizontal ray, tangential to the earth, is 
drawn, the earth slopes away (Figure 2) at the rate of 
ad? 
hs == 2 
2ka @) 
Hence the horizon distance dr for a transmitter at a 
height h above level ground is equal to 
dr = V2kah. (3) 
Numerically, when all the lengths are in meters 
_ 4 
dy = 4,120 Vh fork = ae (4) 
With fA in feet and dz in statute miles, by a curious 
numerical coincidenee, 
— 4 
drp=NV2h fork = 3° (5) 
When both terminals of a path are elevated above 
the ground (Figure 3), the horizon distance is 
dy, = V2ka (Vi, + Vin), (6) 
where again V2ka = 4,120 in the metric system. | 
8 This result could have been obtained directly from 
Azimuths of the Sun, HO71, U.S. Naval Department, Hydro- 
graphic Office. The equation of time may be obtained from a 
current copy of The American Nautical Almanac, U.S. Naval 
Observatory, Washington, D.C. 
