6 TECHNICAL SURVEY 
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. 
Ficure 6. Geometry for Rayleigh’s criterion for rough 
ground. 
ROUGHNESS OF THE GROUND 
In order to estimate how closely the ground ap- 
proximates the condition of an ideal reflecting sur- 
facé, 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” 
1s 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 2Hy(27/)). 
The criterion now requires that the surface be con- 
sidered as rough when this phase difference exceeds 
a/4 radians. This gives for the critical value of H, 
when y is in degrees, \ in meters, 
r 
el Sra 
(19) 
If n is the ‘‘lobe variable,” that is, a quantity equal 
to 1 3 .---(2n — 1), ---at the first, second, 
nth interference maximum of the direct and ground- 
reflected rays, namely, 
_ 4hy 
Saha 
(20) 
where h; is the height of the transmitter above the 
-ground, the criterion can be written in the form 
So 6 (21) 
Although admittedly rough, the criterion indicates 
the order of magnitude of the angle above which 
specular reflection will be- greatly reduced in favor 
of diffuse scattering of the type which, in ordinary 
optics, is produced by a dull, white surface. It is 
reasonably safe to assume that for angles exceeding 
the critical angle the amount of specular reflection 
will be reduced to a small fraction, perhaps to the 
order of one-fifth, of the value of the reflection under 
ideal conditions. 
DIFFRACTION BY TERRAIN 
A number of the influences of the earth’s surface 
upon wave propagation have the common charac- 
teristic that they represent deviations of the actual 
earth from the idealized model of a smooth sphere 
endowed with homogeneous electrical constants. 
Diffraction by the earth’s average curvature is not 
included among the effects considered here since it 
is dealt with extensively in Volume 3. 
There are two main classes of phenomena that fall 
under the general heading of diffraction. One is the 
diffraction by obstacles, such as hills, trees or houses, 
and the other is the diffraction by the structure of 
an otherwise fairly level ground, in particular, rough- 
ness and horizontal variations of dielectric constant. 
The diffraction by hills and similar obstacles of the 
terrain is commonly treated theoretically by means 
of the Fresnel-Kirchhoff diffraction theory as found 
in textbooks on optics. The only problem which is 
sufficiently simple to admit of a direct application to 
FIELD §N SHADOW BEHIND DIFFRACTING RIDGE 
K\ 
OB BELOW FREE SPACE 
NUN 
ah NY 
45 
015 02 03 0.4 0.6 08 1 2 a 1G 6 
Ficure 7. Field in shadow behind a diffracting ridge. 
