THE CAI.Cl LATION OF VERTICAL COVERAGE 



159 



therefore neglected. This is equivalent to termination 

 o!' the reflecting surface at t he shore line. 



In order to describe diffraction at a shore line a 

 system of Fresnel zones for each lobe is considered 

 to be formed on the sea with the reflection point of 

 the lobe as their center. The zones will be ellipses 

 because of the. inclination of the rays. The influence 

 of the shore line will be determined by the number 

 of zones which are not interfered with by the shore. 



Thus a low angle lobe which has its central Fresnel 

 zone far out to sea would be virtually unaffected by 

 the limited reflection area, as numerous zones are 

 formed on the sea. This is indicated by A in Figure 

 57, which represents the reflected wave. At B, a 

 higher angle lobe, there are only two zones intact, 

 and the reflected wave is weak. Had only one zone 

 been complete, the reflected wave would have been 

 stronger than A. At C only portions of outer zones 

 are formed on the sea, and the reflected wave is 

 negligible. 



The effect of the reflecting surface may be repre- 

 sented by an image antenna located in the earth 

 under the radar antenna at a depth hi below the 



surface as in Figure 58. The nonreflecting land surface 

 then acts precisely as a straight diffracting edge for 

 the image antenna and indirect ray. A general 

 formula will be developed which gives the situation 

 of any Fresnel zone of any lobe for a given radar 

 station. From this formula and the distance to the 

 shoreline it may be determined for each lobe which 

 zone is intercepted by the shore. In the graph in 

 Figure 58 is plotted the relative intensity of the 

 reflected ray as a function of to, the number of the 

 zone touching the shore. In the illuminated region 

 at large angles, as A, the relative intensity is close 

 to unity. Approaching the shore it oscillates about 

 unity, reaching a maximum of 1.18. In the shadow 

 region, the intensity drops to low values. Thus, 

 knowing to, the effect of shoreline diffraction on the 

 reflected ray may be obtained. The derivation will 

 be developed for a plane reflecting surface, since, as 

 it has been shown in Section 15.6.4, for lobe angles 

 corrected for standard earth curvature, the effect of 

 earth curvature may be taken into account by using 

 hi [equation (59)] instead of hi. In most cases di will 

 be small and h x may be used with little error. 



IMAGE ANTENNA 



Figure 58. Shore line diffraction. 



