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Example ..'1 . The General /-"/'<■ Formula. An inter- 

 rogator equipment is used wiih 1 he radar of Example 



20. It operates on llil) me; the height Of the antenna 

 above the sea is 500 ft; and the distance to the shore 

 is 15,840 ft. The intervening land is too rough for 

 coherent reflection. The antenna consists of two 

 vertical radiating elements and parasitic reflectors. 

 The radiators are approximately a half wavelength 

 long and spaced a half wavelength apart. The maxi- 

 mum distance at which reliable interrogation may 

 be obtained in the absence of a reflecting surface 

 has been found to be 110 miles for this particular 

 equipment. It is desired to construct for this site 

 the vertical coverage diagram of the interrogator 

 system. 



The vertical pattern of a vertical half- wave dipole 

 is given by 



cos 



Sa = 



sin 7 



cos 7 



Since this factor is over 0.98 for angles up to 10 

 degrees, f(y) and /(7 — 20) will be taken as unity. 

 The lobe angles are then computed neglecting </> and 

 f, as in Example 11. Diffraction and divergence are 

 computed as in Example 15 and Section 15.6.17. The 

 results of these calculations are listed in Table 14. 



The values of p and <t> depend on 7' and are read 

 from Figures 69 and 70. Using equation (108), 4>' 

 is obtained and added to f. The sum 4>' + f is the 

 net phase shift of the reflected wave from the values 

 used in computing the lobe angles and is plotted 

 against 7 in Figure 72. For purposes of comparison 

 5 has also been plotted, but this curve is not required 

 otherwise. The product Dpz is the relative strength 

 of the reflected ray and is plotted in Figure 72. 



The points on the coverage diagram are obtained 

 in polar form from equation (107). 



d = 110\/l + {Dpzy - 2Dpz cos (</>'+ f + 8) . 



The vector representing the reflected wave is shifted 

 in the lagging direction by <j>' + f degrees when this 

 sum is positive, and in the leading direction when 

 the sum is negative. The effect of this phase shift 

 on the point on the lobe being considered may be 

 determined by inspection of Figure 72. 



Thus, to determine the first maximum point the 

 following procedure may be used. At n = 1 the 

 angle 7 is 0.0011 radian and 4>' + f is — 14.8 degrees. 

 This means that for the cosine term to be —1 the 

 path difference must be increased until 8 is 194.8 

 degrees. The angle jd at which this value of 8 occurs 



is fouiu 

 0.00492 

 interval, 

 angle <j>' 

 0.00141 

 the new 

 value of 

 and the 



[ by interpolating between 0.00110 and 

 since <5 changes from 180° to 360° in this 

 This angle is then 0.00141 radian. Had the 



+ f changed appreciably from 0.00110 to 

 the interpolation would be repeated using 

 value of <j>' + f. In most cases the new 

 <j>' + f may be estimated from the curve, 

 first approximation will be close enough. 



Table 14. The general lobe formula. (Example 21.) 



At 0.00141 radian Dpz is 0.501. Substituting this 

 value : 



d = llOVi + (0.501) 2 - 2 X 0.501 X (-1) 

 = 165.0 miles , 



which is laid off on the coverage diagram at an angle 

 of 0.00141 radian. As many other points as required 

 to sketch the diagram may be computed in a similar 

 fashion. For an intermediate point it is convenient 

 to use the net angle equal to 90° since the equation 

 then reduces to 



d = HOVl + {Dpz) 2 . 

 The angles of the lobes have been listed in Table 14 

 under y d and the lobe lengths under d. 



The vertical coverage diagram is shown in Figure 

 73. The lobe maxima and minima and the 90-degree 

 points have been sufficient for sketching the lobes 

 except on the first lobe where a few additional points 

 have been computed. When the net angle is 60 

 degrees, the field strength at the bottom of the first 



