148 TECHNICAL SURVEY 
ground-based duct and by Figure 23 for an elevated 
duct. 
The detailed construction of a ray diagram in the 
case of am elevated duct is shown in Figure 23. It 
is assumed, for illustration, that the transmitter is 
placed at the point which produces the maximum 
amount of trapping, and this point turns out to be 
located at the maximum of the bend in the M curve. 
The vertical line for M, corresponding to h; is drawn 
as shown, and again the line 1 is drawn to the left 
of M, at the distance a,?/2, to represent ray 1 which 
departs from the transmitter at angle a: measured 
from the horizontal. As the ray proceeds outward 
and downward it is bent less and less, corresponding 
to the decreasing distance between the M and 1 
lines. Finally it reverses and rises to the height 
indicated. Ray 1 must therefore oscillate between 
the heights determined by the crossing of the M and 
1 lines. Ray 1’ starting upward at the same angle a; 
oscillates between the same height limits as ray 1. 
Rays 2 and 2’ emerging at angle a, are the limiting 
rays which are trapped in the duct between the 
heights h, and h,. Beyond the horizon ray 3 and 
below the duct lies the diffraction region for this 
case. Ray 4 emerging at an angle greater than a, is 
not trapped but atter reflection passes entirely 
through the duct. 
Ground-based ducts are likely to be found along 
coasts where warm, dry air from over land flows out 
over a colder sea. This situation, for instance, prevails 
in the summer months along the northeastern coast 
of the United States. Elevated ducts occur frequently 
along the southern California coast. 
An illustrative series of theoretical coverage 
diagrams as obtained by the ray tracing method 
described are collected in reference 448. A few of 
these diagrams are reproduced in Figure 24, for a 
frequency of 200 me and a transmitter elevation of 
hy = 100 ft, corresponding to an h;/) ratio of approxi- 
mately 20. The height scale is exaggerated in the 
ratio 40/1. Transmission over sea water is assumed. 
The coverage range is adjusted to “define the 
probable low-level zone of detection of a medium 
bomber with fair aspect by an SC-1 or SC-2 radar 
at 100-ft elevation. For SK radars and higher alti- 
tude installations, the diagrams are conservative. 
DISTANCE x 
Ficure 23. Rays with an elevated duct. 
