LOBE-ANGLE METHOD 



139 



trated in Figure 9 for two stations A and B with 

 heights equal to 146.5 meters and 302 meters and 

 wavelengths X = 1.50 meters and X = 1.42 meters 

 respectively. 



2. From equation (58) in Chapter 5, a second curve 

 may be plotted with rfi as abscissa and the equivalent 

 height hi' as ordinate as shown in Figure 10. To illus- 

 trate, computed data for station A are given in 

 Table 4, for a free-space range of do = 100 km. d is 

 calculated from equations (IG) and (17). 



where 



Hence by equation (32) 



ka 



n\ 



V 2/.T// 





(35) 



(36) 



Table 4. Data for station A of Figure 9.' 



* Antenna gain and directivity factors have been omitted from the above calculatio 

 tSee Sec;ion 6.6.4. 



3. For any n, including integral and fractional where odd values of n give maxima and even values 



values, di may be found from Figure 9 and the 

 corresponding hi' from Figiu'e 10. The angles y' 

 corresponding to lobe maxima may then be calculated 

 from equation (32). 



6.6.4 



Lobe Angles with Horizontal 



The angle y' given by equation (32) is measured 

 with respect to the tangent plane through the reflec- 

 tion point shown m Figure 8. This plane is inclined 

 at an angle 6 ■with the horizontal at the base of the 

 transmitter. The true angle y which the lobe-center 

 line makes with the hoiizontal is 



7' - 



(34) 



mmima, provided the reflection phase shift is t 

 radians. The angle maj^ be either positive or nega- 

 tive, as shown by equation (36). 



6.6.5 



Use of Modified Divergence Factor 



The value of the divergence factor must be de- 

 termined in order to calculate the maximum and 

 minimum lobe lengths by equation (46) in Chapter 5. 

 A convenient formula for the divergence factor at 

 the angles of lobe maxima is obtained by substitut- 

 ing y' for \l/ in equation (92) in Chapter 5. The 

 errors involved in this assumption have been given 

 in Section 6.2.3. Substituting y' =\f/in equation (92) 



