468 : PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
(12) and the path lengths being different in each case. 
From Figure 9, the diffracted field is found to be 
14 db below the free-space field at the same distance. 
Example 
Assume that from a topographic map the profile 
shown in Figure 12 has been drawn. The horizontal 
scale is in kilometers and the vertical scale in meters 
above sea level. From this profile, combined with 
inspection of the terrain, it has been found that the 
ground is so rough that the reflected rays may be 
METERS ABOVE 
SEA LEVEL 
90 
60 ; 2 
' 
30 «7 a 
= 541 72 5 «KILOMETERS 
Ficurs 12. Assumed profile. 
disregarded. ‘Ine ueights above sea level of trans- 
mitter, receiver, and obstacle, are respectively 
hi = 24 meters, ho = 33 meters, h = 69 meters. 
Since d, = 9,000 meters, d, = 5,400 meters, d = 
14,400 meters, we find from equation (12) that 
ho = —39 meters. Assume a wavelength of 1 meter: 
Fy oe LRA NN 
Vid d 
DIFFRACTION BY COASTS 
Introduction 
Diffraction occurring at coast lines is significant 
for coverage problems of coastal radars. It becomes 
particularly important when the sets are used for 
height-finding purposes where an accurate knowledge 
of the lobe angle and possible deformation of the 
lobes is required. 
The diffraction might be due either to the fact 
that the radar is sited on a cliff or to the sudden 
change in surface properties. Reflection from rough 
ground is diffuse, so that there is no interference 
between direct and reflected rays when the reflection 
point lies on this type of terrain, but interference 
does occur when the reflection point lies on the sea 
surface from which regular reflection is obtained. A 
situation commonly occurring is that of a search 
radar sited on rough terrain a few miles inland from 
the coast. Here coastal diffraction may result in an 
appreciable deformation (shortening or lengthening) 
of the lobes. 
More generally, diffraction occurs with level 
ground whenever there is a change, especially a 
sudden change, of ground properties along the trans- 
mission path. The formulas developed for coast- 
line diffraction may equally be applied to the case 
where rough ground suddenly changes into smooth, 
reflecting ground. Similarly, the effect of patches 
of smooth ground in rough surroundings, such as a 
lake in wooded country and, vice versa, rough 
patches in smooth terrain, may be treated by means 
of the Fresnel-Kirchhoff theory. Here, attention 
will be confined to the case of a straight boundary, 
applving the diffraction theory developed in the 
first section of this Chapter . 
Level Site Near Coast 
Assume a transmitter sited on rough ground near 
a coast. If diffraction were disregarded, the coverage 
pattern would appear as. follows. When the reflec- 
tion point is on the land, the reflected ray is diffusely 
scattered and its field at the receiver is negligible. 
Again, if the reflection point falls on the sea, the 
reflected ray will be present and will interfere with 
the direct ray with its full or nearly its full intensity. 
The ray leaving the transmitter at an angle yo 
(Figure 13), such that its reflected counterpart 
undergoes reflection right at the shore line, divides 
the coverage diagram into two parts. For angles of 
VERTICAL SECTION 
ane eas 
PLAN VIEW 
Ficure 13. Diffraction by a coast line. 
elevation larger than y = yo the field will be essen- 
tially the free-space field; for angles of elevation less 
than Y = y the familiar lobe pattern, for complete 
reflection, will appear with maxima equal to twice 
the free-space field. When diffraction by the coast 
line is taken into account, the discontinuity expressed 
by this rough picture is replaced by a smooth transi- 
tion of the field from one region to the other. 
The land surface may be considered as an opaque 
screen for the image transmitter from which the 
reflected rays seem to come (Figure 13). This prob- 
lem is somewhat different from the diffraction prob- 
lem treated previously since the trace of the screen 
in the vertical plane through 7’ and FR is no longer 
perpendicular to the line T’F as it was, for instance, 
in Figure 2, upper part. In the present case, the 
effective height ho of the diffracting edge for any 
given ray is the perpendicular projection from the 
coast line upon this ray, as shown in Figure 13. 
The slant distance of the coast from the trans- 
mitter is d;. Assuming that the receiver (target) is 
far distant, a condition usually fulfilled in radar 
