142 



COVERAGE DIAGRAMS 



consists in ijlottiiig point by puint the lobe-center Equations [(■44a to e)] are obtained by insijection of 

 lines and angles of lobe maxima. The points will be Figure 13. Equations (44f) and (44g) are derived as 

 located by polar coordinates with the pole at the follows: 



1.0 

 0.9 

 0.8 

 0.7 



0.6 



I 

 0.5 



0.4 

 0.3 

 0.2 

 0.1 



1.0 



0.5 



0.2 



0.1 



nX 



.0 5 



.0 2 



JS\ 



FiniJRE 12. Contours of 7' as a function of D and nX. 



transmitter. The coordinates are shown in Figure 

 13 as Td and 71. 



Referring to Figure 13, the following relations 

 hold when the angle i/- is less than 10 degrees : 



sin 21/- Ti 2yp 



sinf^+^j) B f+rp/ 

 2^B 



(a) 



(b) 

 (c) 

 (tl) 

 (e) 

 (f) 



(g) 







A ~ d/ 



(h^A 

 kn ka 



7i = 4',! " 9^ 



III = //i - ^ 

 2ka 



r,i ^A + B = <h+ B 



h 



B = 



{n\/2)di 

 2rl4"- - »\.''2 



^ + ^d = 



Td 



(f) 



--C-^')-('^^l 



(44) 



Figure 13. Geometry for ratlio propagation over 

 spherical earth. See Figure 14 in Chapter 5. 



