156 



SITING AND COVERAGE OF GROUND RADARS 



30,000 



20,000 



u 



§ 10,000 



-i 

 < 



CENTER OF ANTENNA 



80 100 120 



DISTANCE IN MILES 



140 



160 



180 



200 



Figure 55. Lobe and null lines. (Example 13.) 



/<; 



For a perfect reflector and horizontal polarization 

 the phase lag is equal to +x + (2ir/X) X (raX/2) 

 which adds up to nir + %. Odd integral values of 

 n give lobe maxima, and intermediate values give 

 other points on the lobes. 



The sum of the two vectors practically parallel 

 and of equal magnitude, Ei/d, is 



= ~i cos [(n + 1) |1 , (72) 



where Ey is the electric intensity (microvolts per 

 meter) in the equatorial plane 1 mile from the 

 antenna in free space, that is, without a reflecting 

 surface. E is the electric intensity at the point 

 considered in microvolts per meter, d is the distance 

 to the point, in miles, n is a number related to the 

 angle of elevation. It is an odd integer for lobe 

 maximums and an even integer for nulls. For a 

 given antenna and radar the electric intensity E 

 will produce at the input of the receiver a voltage, 



V t = 



d 



sin (90°/i) 



(73) 



where fci is a proportionality factor for the voltage 

 applied to the receiver input. If F 2 is set equal to 

 the minimum operating voltage of the receiver 

 equation (73) becomes 



d = ^1 sin (90°n) . 



' mln 



The term kiEi/V mln is usually obtained from test 



flights on the particular radar or on radars of the 

 same type. The usual form is 



d = fLax sin (90°?i) , (74) 



where d max stands for kiEi/V min and is a measure 

 of the performance of the radar set. 



The lobes will be polar sinusoids and the minima 

 will go to zero only when the amplitude of the direct 

 and indirect waves are equal. These conditions will 

 not obtain if the vertical directivity of the antenna 

 affects the rays unequally, if the reflected wave 

 suffers imperfect reflection or divergence, or the 

 atmosphere or terrain has unequal effects on the 

 two waves. Low sites are generally free from the 

 above effects and equation (74) may be used with 

 acceptable accuracy. 



Example 14- Low Site Lobes. A radar operating on 

 200 mc is 25 ft high and has a maximum range of 

 60 miles. The lobes occur at 2.82°, 8.46°, and 14.1° 

 and the nulls at 0°, 5.64°, 11.28°. The method of 

 plotting a lobe is shown in Figure 56. n may be 

 divided into as many parts as desired, and the 

 corresponding range for each obtained from equa- 

 tion (74). Thus at n = 0.7 the angle is 



0.7 X 4 92 



= 0.0344 radian 



4 X 25 

 d = 60 sin (90° X 0.7) = 53.46 miles. 



A line is drawn at this angle, and a point is marked 

 off at a range of 53.46 miles. 



