136 



COVERAGE DIAGRAMS 



If p = 1, and the effect of antenna directivity is 

 neglected, K = D, and 



= — = V G\do J (1 - D)' + iD sin2 - . (22) 



Cty ' 2 



given bj' Figure 12 in Chapter 5. Equation (22) 

 then gives the value of v. These quantities together 

 with R = nr may convenientlj' be tabulated, as in 

 Table 2. Corresponding values of D and v are plotted 

 as crosses on Figure 7. The line drawn through these 



Figure 7. D-v loci and lobes. 



The following discussion illustrates how one con- 

 tour of a coverage diagram, corresponding to a 

 particular value of radio gain, may be plotted on 

 Figure 4 or its equivalent. Figure 7. The result is a 

 curve similar to Figure 2, but plotted in u,v coordi- 

 nates instead of h« and d. See also Figures 16 to 39. 



For illustration, let the transmitter gain, Gi = 1 and 

 let the radio gain be such a \'alue that do = do/dx = 2. 

 Further, let X = 0.1 meter and hi = 20 meters. 

 From Figure 15 it is seen that r = l,030X//ii^- = 1.2. 

 Select one of the curves for sin- (12/2) in Figure 12, 

 Chapter 5, say sin- (0/2) = 1, for which Q = Tr,3ir, 

 Sir, etc. These values correspond to tips of the lobes 

 for which n = 1, 3, 5, etc., since, for perfect reflec- 

 tion, Q = nir by equation (116) in Chapter 5. 



Next select values oi K = D and note the corre- 

 sponding value of the radical 



Table 2. Values of v and R for sin=(S2, 2) = 1, d„ =2. 



xl (1 - A')^ + 4/v' sin= - 

 > 2 



points is the locus of the tips of the lobes. The 

 actual position of each lobe tip is then marked with a 

 circle where the corresponding value of R crosses 

 the locus in Figure 7. 



