THE CALCILATION ()!•' \ KHTIC A I. COVEKAtJK 



L55 



To use this method it is best to arrange the calcu- 

 lations in a tabular form. Points along the lobe center 

 are selected by using various values of ch for the 

 value of n desired. Next ty is obtained from equation 

 (08) and substituted in equation (09), and B and 

 * are substituted in equation (70) yielding SE^, which 

 is combined with 6 to obtain y. The curve of constant- 

 path difference is then plotted from y and rj, which 

 are now known. 



Example IS. The General Lobe Angle Formula. To 

 illustrate this method a radar 3,000 ft high and 

 operating at 100 mc will be used. A trial value of 

 60 miles is arbitrarily selected for di and substituted 

 in equation (68), giving 



* = 



3,000 - \ X (60) - 

 5,280 X 60 



= 0.003788 radian 



In equation (69) using n = 1 and A = 9.84 ft, 



B = 



1 X 9.84 

 10,560 



X 60 



2 X 60(0.003788) 2 



1 X 9.84 

 10,560 



= 70.85 miles . 



*d 



70.85 - 60 

 70.85 + 60 



X 0.003788 = 0.000314 radian 



60 



= -0.01136 radian . 



5,280 



y = 0.000314 - 0.01136 = -0.01105 radian . 



r d = 60 + 70.85 = 130.85 miles . 



Laying out the angle y from the antenna and 

 marking off the distance r d gives one point on the 

 curve of constant path difference. Enough other 



points are computed to enable one to draw a smooth 

 curve. The computations may be arranged as shown 

 in Table 8. The values selected for d\ should be 

 small enough so that the denominator of equation 

 (69) is positive. 



These two curves are plotted in Figure 55. For 

 comparison is shown the first lobe as computed from 

 equation (62), and it can be seen that this equation 

 may lead to appreciable error in estimating low 

 coverage. For most purposes it will suffice to calcu- 

 late lobes higher than the first one or two by means 

 of equation (62). 



15.6.1 



The Calculation of Lobes 



Three methods of computing lobe angles were 

 given corresponding to low, medium, and high sites, 

 in order to relate the labor of the computations to 

 the complexity of the problem. A similar procedure 

 will be followed in the calculation of the lobe shapes. 



The lobe diagram represents the locus of all points 

 along a particular azimuth of a definite field intensity, 

 usually the threshold of detection. If the site has 

 horizontal symmetry throughout its sector of opera- 

 tion one diagram will suffice. Usually several dia- 

 grams are required, and it is common practice to 

 prepare a diagram for the central azimuth of the 

 sector and for 10 degrees inside of each limit of scan. 



156 7 Low Site Lobes 



The electric field intensity at the target is the 

 resultant of the direct and reflected waves which 

 have the same amplitude and a phase angle which 

 varies continually as the lobe angle y is increased. 



Table 8. General lobe angle formula. (Example 13.) 



