94 



DETERMINATION OF STANDARD COVERAGE CHARTS 



nate all but h 2 and S, denning our coverage diagram. 

 We may substitute the approximate value for D 

 into equation (5) and also use equation (4) to elimi- 

 nate S from the equation 



IQ-. 4/20 _ 



10 3 



1 



.VZrhi (1 - a) 



_A*1 

 iirhla* J 



X 



( 4 



We may now set 



= (n - i) r; 



3a) 



sin-* 



V 



■ 



(6) 



* = 



12 3 



±, 4j, U, 



(7a) 



which correspond to the maxima of the lobes. We 

 may alternatively take 



* = mr , (7b) 



corresponding to lobe minima or, more generally 



* = (n. + 6) tv (7c) 



to represent any specific position on the lobe. 



With A , hi, X*, and a as variables, we may throw 

 equation (6) into the form of a nomogram, from 

 which we determine a, first for the lobe tips, second 

 for the minima, and third for as many intermediate 

 points as are necessary. 



With the a's so determined, proceed to equation 

 (4), also in nomographic form, to get S. Finally, use 



equation (2), to determine h%. This equation can also 

 be thrown into nomographic form if we set 





h' 2 



(8) 



where h' 2 is measured vertically from the line tangent 

 to the base of the transmitter. 



Another somewhat simpler type of coverage dia- 

 gram is possible. If we take 



10-**no = 10 



4irti 2 



(9) 



as defining the intensity for a transmitter in free 

 space, we get for the ratio of the two 



Iq-(a-a *)/io _ io B/1 ° = 



1 



s;n- 



3a 



2 ' 



n 2 



+ 



(10) 



where B is the number of decibels by which the 

 actual field exceeds the free space value. Coverage 

 diagrams of this type consist of lines radiating from 

 the transmitter, rather than contours. For non- 

 standard propagation the drawings have some com- 

 plications, but the procedures are clear. This method 

 has the additional advantage of fitting in with the 

 theory used for surface targets, for which it is simpler 

 to use free space intensities and lump the field 

 strength integrated over the target area as an 

 "effective" target area in a uniform field. 



