GROUND REFLECTION 



57 



10"" mhos per meter for poorly conducting ground 

 like chalk or very dry soil and take a value of about 

 10"^ for good conductors like blue clay or water- 

 bogged marshy land. Fortunately, the amplitude 

 of the reflection coefficient is not ver}' sensitive to 

 minor changes in conductivitj^ when the frequency is 

 sufficiently high, saj' 200 mc or higher. Then the 

 real part of the dielectric constant is the most 

 important factor. 



4.2.8 



Dielectric Constant of Soil 



It is not possible to give a standard table of 

 dielectric constants of various types of soil, because 

 the variation with the moisture content is consider- 

 able. For very dry ground ir is likeh' to be about 4, 

 but this value may rise to 25 when the ground is 

 thoroughly soaked with water. The dielectric con- 

 stant of ground will normally decrease \\\i\\ increas- 

 ing frequency. 



Above 200 mc, the dielectric constant will dom- 

 inate the conductivity term, and for field conditions 

 the ground may be assumed to be a piu-e dielectric. 

 This is illustrated in Figure 16 for e, = 7; e, = 3 



40° 50° 60° 



Figure 17. Phase of the reflection coefficient for 

 moist and dry soil. 



and e.- = 0; and for e, = 25, f,- = 19 and e,- = 0. 

 Except for values close to the Brewster angle, the 

 zero conductivity curves give a usable approxima- 

 tion. 



In Figure 17, the phase, 4>, of the reflection coeffi- 

 cient corresponding to the above values of tr and e, 

 is also given. 



4.2.9 



The Divergence Factor 



The preceding considerations apply only to 

 reflection from plane surfaces. For reflection from a 

 sphere like the earth, the divergence of a bundle of 

 rays is increased when it suffers reflection, and the 

 plane earth reflection coefficient, R, must be multi- 

 plied by a divergence factor denoted by D, which 

 accounts for the earth curvature. This factor ranges 

 from unity at close range where the earth can be 

 considered plane to zero at points just above the 

 tangent luie. [Note: Whew the divergence factor 

 approaches zero at grazing angles less than the last 

 minimum, other components of the wave must be 



Figure 18. Geometry for divergence factor. 



considered.] To a sufficient approximation B is 

 given by the expression 



2/u 



D = 



1 + 



dka 



tan' \p J 



(24) 



where (see Figure 18), 



/?/, 1h' = heights of transmitter and receiver above 

 tangent plane at reflection point. 

 d = distance between transmitter and re- 

 ceiver measured along the surface of 

 the earth. 

 \p = grazing angle above tangent plane. 

 ka = equivalent earth radius. 



4.2.10 



Irregularity of Ground 



The formulas for reflection from a plane or a 

 spherical earth can only be applied with confidence 

 granting a certain smoothness of the reflecting 

 surface, depending on the wavelength. A rule of 



