188 



SITING 



The azimuth of the sun may be calculated from 

 the formula, 



sin (HA) 



tan |8 = - 



(1) 



cos tan 5 — sin <^ cos (HA) 

 where fi = bearing of the sun. The bearing is east or 

 west of south when 4> — 8 is positive. 

 The bearing is east or west of north when 

 — 5 is negative. The bearing is east 

 in the morning (/3 will be negative) and 

 west in the afternoon (/S will be positive) . 

 HA = hour angle of the sun. During the morn- 

 ing hours when the hour angle is greater 

 than 12 hours, its value should be sub- 

 tracted from 2-t hours for use in the 

 formula. 

 (b = latitude of the place of observation. 

 5 = declination of the sun at the time of 

 observation. The signs of (j) and 8 are 

 important and each is positive when 

 north of the eciuator and negative when 

 south. 

 The hour angle HA is the local apparent time 

 (LAT) minus 12 hours. To convert the observed 

 time into LAT, the civil time at Green^vich (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 allo\\-ing 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 

 j^ear. 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 + 7 hr 



Greenwich civil time 



Equation of time (Figure 1) 



Greenwich apparent time 



Longitude difTerence (for 118° W) 



Local apparent time (LAT) 



LAT -12 hours = HA 



Hour angle of sun 



HA in arc 



Latitude <f> 



Declination of sun 5 (Figure 1) 



Substituting in equation (1), 



, ^ sin ir 



tan /3 = — - 



cos 40° . tan (-2°) - sin 40° • cos 11° 



13 = 16° 10' 



Since — o is positive, (3 is the l3earing from the 

 south. The bearing is west of south, since HA is 

 positi^■e (p.m.). The azimuth of the sun is 

 180°+ 16° 10' = 196° lO'.'" 



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 «'hen the sun is at the same alti- 

 tude on both sides of the meridian of the observer. 

 The iDisector 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 maj'' be determined. 



'«^ GEOMETRICAL LIMITS OF VISIBILITY 



10.3.1 



Horizon Formula 



It is assumed throughout that the earth radius is 

 ka (see Section 4.1). Whenever numerical examples 

 are given, the standard value, k = 4/3, is u.sed. 

 The alternate method of accounting for refraction 

 given in Section 4.1.5 may also be used in connection 

 with the following equations if k t^ 4/3. 



When a horizontal ray, tangential to the earth, is 

 drawn, the earth slopes away (Figure 2) at the rate of 



h 



2ka 



(2) 



Hence the horizon distance dr for a transmitter at a 

 height h above level ground is equal to 



dr = V2ta/!. (3) 



Numerically, when all the lengths are in metere 



dr = 4,120 V/i for/: = -. 



(4) 



With h in feet and dr in statute miles, by a curious 



numerical coincidence, 



,- 4 



dr = V2/!. for k = -- 



(5) 



^ This result could have been obtained directlj- from 

 Azimuths of the Sun. H071, U.S. Xaval Department, Hydro- 

 graphic Office. The equation of time may be obtained from a 

 current cop}- of The American Nautical Almanac, U.S. Naval 

 Observatorv. Washington. D.C. 



