LOW-ANGLE AND SURFACE COVERAGE 



163 



the end of this chapter, noise figures and bandwidths 

 of various sets are given. An important correction to 

 Pnii.. as determined from the noise figure and band- 

 width is the scanning loss. This loss for various 

 scanning speeds and beamwidths is represented in 

 Figure 4. Another source of loss is deviation of the 

 product of bandwidth B (mc) and the pulse width 

 t (microseconds) from the optimum value of 1.2. 

 The losses for various values of the product are tabu- 

 lated in Table 2. 



Table 2. Loss resulting from band- and pulse widths. 



Bt 



Loss (db) 



0.1 

 0.3 

 0.7 

 1.2 

 2.5 

 5.0 

 10.0 

 20.0 



5.0 

 1.5 

 0.5 

 0.0 

 0.8 

 3.0 

 5.0 

 8.0 



*B = i-f bandwidth (mc) ; t = pulse width (microseconds) . 



A field measure of the performance figure of a 

 radar can be determined by the use of a target of 

 known radar cross section, such as a silvered balloon 

 and equation (7). A check on variability of per- 

 formance can be made by finding the maximum 

 range on a plane (using a constant aspect, such as 

 nose or tail). 



7.2.4 



Radar Cross Section 



An important but troublesome factor in calculat- 

 ing c^max of a radar from a knowledge of the perform- 

 ance figure is cr, the radar cross section (see Section 

 2.4.1 and Chapter 9). The value of o-can be found by: 



1. Laboratory measurement of the factors which 

 constitute the performance figure and field determi- 

 nation of the maximum range (imax- The value of 

 ff is then given by equation (7). 



2. Measuring the signal returned by the target 

 at a convenient distance on a calibrated A scope or 

 by direct comparison with a pulsed signal generator. 

 In this method neither Pmin nor dmax enter. 



The equations involving a assume a point target. 

 Since an airplane intercepts a small solid angle over 

 which the beam strength varies little, the assumption 

 of a point target is adequate for aircraft. 



7^ LOW-ANGLE AND SURFACE 



COVERAGE 



^■^■' Maximum Range 



Since the gain factor A for this case is more 

 complicated than for free space, the relation be- 

 tween dniax and the performance figure cannot be 

 given in general by a simple expression, as can be 

 seen from equations (172) and (184) in Chapter 5. 

 For ranges such that the shadow factor Fj ~ 1, i.e., 

 distances d less than lO^X^'^, X, and d in meters, and 

 both antennas low, or antenna and target low {hi,h2 < 

 SOX^'^), the fomi of A is simplified so that a simple 

 relation can be given for rfmax- Otherwise, the 

 methods of Sections 5.6, 5.7.3, and 5.7.4 must be 

 employed, especially of Sections 5.6.5 and 5.7.3. 



7.3.2 



Ducts and Set Performance 



It has been found from field tests that atmospheric 

 ducts are Ukely to be found close to the surface of the 

 sea. The consequent increase in range may mask 

 subnormal set performance. If the antenna is 

 tilted upward so that no radiation reaches the earth, 

 then the free-space discussion of Section 7.2 applies 

 to the field determination or check of the per- 

 formance figure. Otherwise field testing, when condi- 

 tions are normal, can be accomplished by the use of 

 permanent echoes or the use of a ship of known 

 target cross section (see Section 7.3.7). 



7.3 3 



Low Heights and Plane Earth Ranges 



For these conditions, the following relations must 

 hold: 



(/ii,2 < 30X2 ^ rf < loV^), 



where h, d and X are in meters (see Section 5.7.1). 



In the dielectric case (see Section 5.7.3), generally 

 applicable to radar, the value of A [ec^uation (172) 

 in Chapter 5] for Fs = landg = 1, becomes 



3 /ll/l2 



A = 



2 d' 



(9) 



Ap = 4ir- 



(10) 



Since A = A^Ap and Ao = 3X/87rrf, the preceding 

 ecjuation is equivalent to a path-gain factor value of 



\d ' 



[See equation (55) in Chapter 5.] Instead of equa- 

 tions (4) and (5), we now have [from equations (3) 

 and (5) in Chapter 5] for a dielectric earth. 



