120 



CALCULATION OF RADIO GAIN 



Comparing equations (202) and (203) with height [i.e., /(O) = 1] and equation (205) is now of 



the form 



equations (193) and (194), we find that 



P'd =\5\ s^ 

 Hence, equation (192) may be written as 



(204) 



E = 2E,A,F, 



(208) 



If 5 is large (e.g., X small), 2r„/5 in equation (207) 

 may be neglected and t„ replaced by r„.„ so that the 



E = 2£'o(27r)^''-i^ V ^ '^ fnUh)fn{hd (205) shadow factor is practically independent of ground 

 2)'d I -^^ 1 + 2t„/5 j constants. The shadow factor is represented graphi- 



V^) 



10000 



Figure 55. V 9(5) and g' as functions of magnitude and phase. 



If p'd is hirge, we see from Figure 56 that 



A, oi 



p d 



(206) 



so that the physical significance of 1/p'd in equation 

 (205) becomes apparent. 



The factor 



e '^n^ 



(207) 



represents the effect of earth curvature in increasing 

 the attenuation over that of a plane earth at zero 



cally in Figures 32 and 58. Where the factor 2t„/5 

 cannot be neglected, as in the \TIF range, vertical 

 polarization over sea \\'ater, the dependence of 

 Fs on 5 is accommodated by changing the abscissa 

 from i = sd to V = s'd where s' = s/(6), and by 

 representing F^ by a family of curves in Figure 58, 

 whose parameter is given by dotted lines in Figure 

 57. f(S) is represented also in Figure 57. For V < 0.4, 

 Fs is less than 1 db Ijelow unity. This corresponds 

 to a distance over \-\hich the earth maj' be considered 

 plane, i.e., d < 10"'X^''^, as given in Section 5.7.1. 

 The greater the wavelength, the smaller the effect 

 of the earth's curvature. 



