38 



STANDARD PROPAGATION 



quately by an idealized model is that of a sudden 

 change of the dielectric properties of the ground, as 

 at a coast line. 340 " 346 If the land is rough while the 

 sea surface produces full specular reflection, the 

 coast line can be considered as a diffracting straight 

 edge with respect to the image antenna, rays of which 

 represent the field reflected by the sea surface. The 

 straight edge serves to cut off that part of the radia- 

 tion from the image that would represent reflection 

 from the land area. The geometrical conditions are 

 shown schematically in Figure 8. For the details of 



VERTICAL SECTION 





PLAN VIEW 



Figure 8. Diffraction by a coast line. 



the analytical treatment the reader is referred to the 

 comprehensive report on standard propagation con- 

 tained in Volume 3 of the Summary Technical Re- 

 port of the Committee on Propagation. The distor- 

 tion of the coverage diagram of a radar set caused by 

 this type of diffraction is often quite large and be- 

 comes important operationally at frequencies of 100 

 to 200 mc. This is illustrated here by a computed 

 coverage diagram shown in Figure 9. If diffraction is 



WITH DIFFRACTION 

 ■WITHOUT DIFFRACTION 



////// '/;;///////, / / , 



Figure 9. Coverage diagram for coast line diffraction 

 (relative field strength). (Heights exaggerated 3.5 to 1.) 



not taken into account the coverage pattern shows a 

 constant amplitude through higher angular elevations 

 reached only by the direct rays since the ground re- 

 flection is negligible. At lower angular elevations 



rays reflected from the sea add to the direct rays, 

 and the "lobe" type of pattern appears. It is clear 

 that if the diffraction effect were neglected very 

 serious errors of the estimated coverage would result. 

 Similar methods can be used to treat diffraction 

 caused by cliffs, edges of wooded areas, lakes, etc., 

 but these cases are not so often of importance in 

 radar practice. 



54 THE ELECTROMAGNETIC FIELD 



Field Strength Distribution 



If a transmitter is erected over a plane, ideally re- 

 flecting earth, the well-known lobe pattern results 



Figure 10. Typical coverage diagram (lobes) over 

 plane earth. 



(Figure 10), the curves being ones of constant field 

 strength. The field is given by 



E = E ■ 2 sin 



( 2irh i h: 

 \ Xd 



(22) 



where hi and h% are the transmitter and receiver 

 heights, and d the distance from transmitter to 

 receiver. The maxima and minima occur at the 

 positions in space where 



hjii — j Xd 

 4 



(23) 



with n=l, 3, 5 

 ra=0, 2, 4 



for the maxima, 



for the minima. 

 If h 2 » hi, the angle of elevation is ^ = h 2 /d and 

 the formula for the maxima and minima can be 



written 



nX 



* = 



47u 



(24) 



If the earth curvature is taken into account the 

 pattern remains essentially the same above the line 

 of sight, but a number of corrections enter which 

 change somewhat the position and strength of the 



