190 REFLECTION AND TRANSMISSION OF RADIO WAVES 



The first-order expansions of F in powers of sin 6 are limited in their 

 ranges of validity. This can be seen, for example, in Fig. 4-7. For vertical 

 polarization, the range of validity is limited to angles smaller than the 

 Brewster angle, while for horizontal polarization, the angular range is much 

 greater. For airborne radar frequencies, the range is about d < 30° for 

 horizontal polarization, and < 4° for vertical polarization. 



The results deduced above are based on the properties of plane waves. 

 In the case of the spherical waves radiated by an antenna, there is a surface 

 wave which should be added to the direct and reflected waves. For airborne 

 radar frequencies, however, this generally is unimportant. 



4-6 EFFECT OF EARTH'S CURVATURE 



The effect of the earth's curvature is twofold. First, it alters the geometry 

 so that the path difference between the direct and reflected waves is 

 decreased, and second, it decreases the amplitude of the reflected wave. 



The change from the plane to the spherical geometry is equivalent to a 

 reduction in the heights of radar and target, as illustrated in Fig. 4-14. 



Direct \Na\je /? 



Fig. 4-14 Curved Earth Geometry. 



The second ef^-ect of the earth's curvature is to decrease the amplitude of 

 the reflected wave, because the incident waves within a small range of 

 vertical angles are spread out, or diverged^ into a larger range of vertical 

 angles on reflection from the convex surface of the earth. 



For all distances encountered in airborne radar work, the reduced heights 

 Aj', Ao "^ay be calculated from 



7;; = /;i - A/;, = /;i - d,yia (4-42a) 



Ji'., = /;o - A/;2 = //2 - doVla (4-42b) 



where a is the earth's radius, and diidi) is the distance from the reflection 

 point to the transmitting (receiving) point. As will be shown in Paragraph 

 4-18, the effect of average or "standard" atmospheric refraction may be 



