36 



STANDARD PROPAGATION 



Figure 5. Graph: 1/k versus RH gradient and temperature for 100 per cent RH at ground. Add correction tabulated to 

 obtain 1/fc for RH at ground ^ 100%. 



is only one case out of several that may, and do, 

 arise in the atmosphere. A full appreciation of the 

 limitations of the concept of standard refraction 

 requires some knowledge of the phenomena of non- 

 standard propagation which will be dealt with ex- 

 tensively in later chapters. 



Roughness of the Ground 



In order to estimate how closely the ground ap- 

 proximates the condition of an ideal reflecting sur- 

 face, a rule is required that gives results sufficiently 

 accurate to be used in radio and radar practice. The 

 subject has not been very thoroughly explored, but 

 Rayleigh's criterion for roughness, originally devel- 

 oped for optical purposes, has been applied with good 

 success. Since it seems to be the only criterion of its 

 kind and since it is often necessary to decide whether 

 the terrain in front of a given radio or radar site is 

 reflecting, it deserves some detailed consideration. 



The principle of Rayleigh's criterion is illustrated 

 in Figure 6. The roughness is assumed to be pro- 

 duced by a large number of elevations in the reflect- 

 ing plane of average height H. One such "hump" 



is shown in the figure together with two rays one of 

 which is assumed to be reflected from the ground sur- 

 face and one from the top of the "hump." The dif- 

 ference in phase between the two rays is 2H\f/(2ir/\). 



Figure 6. Geometry for Rayleigh's criterion for rough 

 ground. 



The criterion now requires that the surface be con- 

 sidered as rough when this phase difference exceeds 

 ir/4 radians. This gives for the critical value of H, 

 when ^ is in degrees, X in meters, 



H = 



X 

 16+ 



(19) 



If n is the "lobe variable," that is, a quantity equal 

 to 1, 3 • • • (2w — 1), • • ■ at the first, second, 



