188 REFLECTION AND TRANSMISSION OF RADIO WAVES 



lag of the reflected wave is an even or odd multiple, respectively, of 180°. 

 The height interval between an adjacent maximum and minimum is 



Ml = X/4 sin d. (4-29) 



This succession of maximums and minimums of the resultant field gives rise 

 to the lobe structure in the vertical coverage of the radar, which is especially- 

 important for search radars. The location of a given maximum or minimum 

 is different for vertical and horizontal polarization because of the phase of 

 the reflection coefficient p. For airborne radar work with pencil beam 

 antennas, the lobe structure usually is of importance only for targets at 

 small depression angles, since otherwise the narrow beamwidth of the 

 antenna would not illuminate the indirect path strongly. The lobe structure 

 is pronounced only if the value of Ah is large compared with the vertical 

 extent of the target. If the target covers more than one lobe, it effectively 

 averages out the field variation over the lobe. This actually produces a net 

 increase of gain over the free-space field acting alone, which is due to the 

 field reflected from the surface. 



A similar oscillation in the propagation factor is observed with fixed radar 

 and target altitudes and a continuously varying range as the target passes 

 through the lobe pattern. In this case the angle 6 can be expressed as 



H -\- h H -\- h 



^^^ ^ = ^WTUH ^ -R- ^""^^^ 



where H = radar altitude 

 h = target altitude 

 R = target range. 



Neglecting the change in the phase angle of the reflection coefficient p, the 

 range interval between an adjacent maximum and minimum is 



where R is the mean range. Thus for a target flying at a constant height, 

 the lobes become packed more densely as the range is decreased. The 

 oscillations of received power caused by the lobes are superimposed on a 

 free-space variation which is proportional to the inverse fourth power of 

 range as indicated in Equation 4-1. 



The situation is somewhat different when the target lies below the first 

 lobe. In this case, the angle Q will be small and an expansion of F in powers 

 of sin Q can be used. To obtain this expansion, we note first that ph and pr, 

 which are given in Equations 4-24 and 4-25, can be approximated as 



p// = -1 +2(6- l)-i/2sine (4-32) 



PK = -1 + 2e(e - ])-■/- sin Q. (4-33) 



