so 



CALCULATION OF RADIO GAIN 



D=.99 



D=95 



Figure 23. Contours of constant divergence factor D and path difference variable R. (Radiation Laboratory.) 



section. However, the a.ssumption is made generalh' 

 that the reflection coefficient is equal to —1 (i.e., 

 p = 1 and (^ = 180 degrees) and that the direct and 

 reflected rays do not differ appreciably^ on account 

 of the shape of the antenna beam pattern {F« = Fi). 

 Foi- large distances over sea water, these assumptions 

 are approximately realized. For most of the calcula- 

 tions it offers no inherent difficulty to consider the 

 effect of directivity or of a reflection coefficient 

 different from — 1 but may require considerable 

 additional calculation (see Sections 5.6.2 and 5.6.5). 

 For convenience, the formulas required in the 

 calculations are recapitulated here. Putting p = Fi 

 = F2 = 1, equation (108) takes the form 



A 



= ^o>J 



(1 - D)- + 4D sin^ 



(110) 



or, in decibels, 



20 log .4 = 20 log Ao + 10 log 



The reflection point variable 

 dr ^2kahi 



V 



(111) 



<h 



^^ (when fc = 4/3) 



(4120 V/)i 



will be used extensively. It has been found that the 

 interference pattern is very sensitive to slight changes 

 in p, so that an accuracy to the fourth significant 

 figure is generally required. 



The path difference variable R is related to p = rfi/rfy 

 and V = d/dr by the equation 



R 



= (--) 



\p V / 



(1 - v")"-. 



(112) 



Resolved with respect to 1/v, this equation assumes 

 the form 



(l-Z))^ + 4Dsin"-^ . - = -(1- ,, nO ^^ 



2 J V p\ (l-p-)-/ 



-g 

 P 



(113) 



