190 



SITING 



above the straight line connecting the terminals while the second term again Ijecomes il'd" 12 for 



given by 



h 



/d' + d'y / d' - d'y 



2ka 



2ka 



or, after a simple reduction, 

 d'd" 



I: = 4/3. 



I'^riuation (13) is used to decide whether and by 

 how much an obstacle such as a hill will obstruct a 

 (9) gi\-en transmission path. 



10 i 3 Extended Obstacle 



When the obstacle is of apprecialile horizontal 

 extension, it may not possess a single peak to which 

 equation (13) can be applied without ambiguit^^ 

 The case of twin mountains is show n in Figure 6 for 

 straight rays (earth's radius ka). 



Figure 4. Height of eartli as an obstacle. 



where h, d', and d" are given in meters. If /) is in 

 feet and d' in statute miles, 

 , d'd' 



for /.- = 4/3. 



(11) 



Secondly, assume that the terminals are elevated 

 (Figure 5). The elevation of the straight line con- 

 necting the terminals, for a flat earth, is eciual to 



h = 



d'h - d"Iu 



(12) 



d' - d" 



where d', d" are again the distances to the terminals, 

 and hi, h^, are the corresponding elevations. 



In order to account for the effect of the earth's 

 curvature, Figure 5 may be; considered as a plane 

 earth diagram on which a ray will appear curved, the 

 deviation from a straight line being downward and 

 given by equation (10). This is indicated by the 

 dashed line in Figure 5. 



Figure 5. Ileiglit for elevated terminals. 



Hence, the total height above the theoretical 

 ground is 



d' h - d"hi d'd" 

 ~ 2ka ' 



h = 



d' - d" 2ka ' ^^^-^ 



When the heights are expressed in feet and the dis- 

 tances in miles, the first term remains unaltered, 



Figure 6. Height of equivalent (liffiacting edge. 



The optical peak P of the obstacle for radio or radar 

 transmission is the point from which both terminals 

 are just visible. For a given profile, the limiting rays 

 to the terminals may be foimd by trial and error by 

 applying equation (13) to those points of the profile 

 which are most likely to represent limiting elevatioas. 

 In the theory of diffraction given in Chapter 8, 

 P marks the position of the equivalent diffracting 

 edge. 



10.3.4 Degree of Shielding 



As a measure of the degree of shielding, the angle 

 between the two limiting rays drawn from the 

 terminals to the (actual or eciuivalent) peak of the 

 obstacle of height hp may be used. 



Since all angles considered are small, the sine or 

 tangent of the angle may be replaced by the angle 

 in radians. Consider first the ray going from the 

 first terminal to P (Figure 7). The angle of the ray 

 with the horizontal at the terminal is 

 hp-hi _ d/_ 

 2ka 



"1 



d' 



(14) 



and its angle with the horizontal at P is 



d' _ hp - )H ^ d' 

 ka d' 2ka 



(15) 



The angle of the ra.y going from the sec(jud terminal 

 to P is determined correspondingly. 



