78 



CALCULATION OF RADIO GAIN 



The divergence factor D is given by 

 1 



D = 



where 

 and 



q = 



Vi + 4pV(i-p')' 



p = SI' 



''-JiA^ = 1 _ 1' = 1 - s. 



d d 



for a particular frequency and reflecting surface. 

 The grazing angle xp may be expressed in terms of 

 (102) s, u, and v, as follows. From equation (60), 



tan ^ ^ ^ = ^ f 1 - ^ . (105) 



1 - s-v'-) = — I - - sr 1 



dx \sv / 



(103) 



Hence 



tarn/' = 



fti 



Since s is a function of u and v only, it follows that D 

 may be plotted in u , v coordinates. This may be 

 accomplished by solving equation (96) with respect 

 to q, which gives 



(1 - p'-) (1 - DO 



or 



dfisd/dx) 



tan i/' 

 It 



(1 



1 V2fca \-?'' ^7' 



and for k = 4/3, 



^ 4p-D= 



Equation (103) gives s = 1 



(104) 

 q; V = p/s, and u 



tan li 



-7=r- = 2.4 X 10 





(106) 



(107) 



may be read from Figure 19 or 20. Contours of From Figure 24, 4' may be obtained for given values 



constant D are shown in Figures 21, 22, and 23. of /h and sv = p. 



The grazing angle i is important in calculations The generalized coordinates described in this 



for vertical polarization since it determines the section will be found highly useful both in field 



magnitude and phase of the reflection coefficient strength and coverage calculations. 



0=999.08X1 7.0 6.0 



5.0 4.5 D=.95 4.0 



3.0 D=l9 2.7 



2.5 



Figure 21. Contours of constant divergence factor D and path difference variable R. (Radiation Laboratory.) 



