» TECHNICAL SURVEY 
selected. Wherever this line intersects the M curve 
the corresponding rays become horizontal and there- 
after reverse the sign of dh/dz. In the case of Figure 
3 these reversals combine with reflections from the 
ground to make a family of rays oscillate between 
an upper limit, different for each ray, and the ground. 
The limiting angle of emergence beyond which re- 
ALTITUDE IN FEET 
7000 
(a 
GROUND BASED DUCT, 
GROUND BASED DUCT) _ 
TRANSMITTER HEIGHT+100 FEET 
FREQUENCY- 200 MC 
ELevateD pucTi 000 
NORMAL LIMITING COVERAGE 
RANGE IN NAUTICAL MILES 50 
Ficure 5. Calculated coverage diagram. 
versal no longer occurs is designated by (2 or’ 2’) 
in Figures 3 and 4. The duct is the vertical interval 
cut out by the intersection of the vertical line desig- 
nated by 2 with the M curve or with the ground. 
The terms trapping, superrefraction, or guided pro- 
pagation aré often employed to describe these phe- 
nomena. 
A word might be said here about the substandard 
case which, although much less frequent than the 
duct, is of operational significance. It is readily seen 
that in this case the rays undergo a strong upward 
curvature in the layer in which there is a substandard 
slope of the M curve. As a result of this the apparent 
horizon distance is reduced, and the ranges of radar 
and radio equipment for targets or receivers near 
the ground are greatly diminished. M curves of the 
substandard type occur often when fog is present but 
are not uniquely correlated with fog. i 
In order to compute coverage diagrarhs on this 
basis it is necessary to know the phases associated 
with the rays so as to determine their mutual inter- 
ference. If this is done by an appropriate graphical 
or numerical method, contours of constant field 
strength can be drawn. Figure 5 shows, typical cov- 
erage diagrams computed in this way,!4° correspond- 
ing to a value of hi/A = 20. The lines separating 
the ‘detection zones” from the “blind zones’’ indi- 
cate ranges at which a medium bomber would just 
become visible to the particular radar to which these 
diagrams apply. Diagram 1 shows the undistorted 
lobe diagram for standard refraction while dia- 
grams 2, 3, 4, 5 show the coverage diagram for 
various types of ground-based and elevated ducts. 
In Figure 6 is shown the variation of field strength 
with height for various distances for the M curve 
shown on the left-hand side of the figure.7? The 
transmitter is at a height of 60 m. 
In all diagrams shown in this section the vertical 
scale is vastly exaggerated as compared to the 
horizontal scale. It may readily be shown that when 
the representation is such that the earth is curved, 
the contours of constant height can be represented 
by parabolas in the approximation where the true 
vertical elevations are small compared to the hori- 
zontal distances involved. 
GENERAL CHARACTERISTICS 
OF DUCTS 
It is evident that the number of types of M curves 
that one can construct a priori is almost unlimited., 
In practice both the types actually occurring and 
their variability within each type of classification 
are severely limited by meteorological conditions. 
M, as defined by equation (4), is the sum of two 
parts, the true refractive part (n — 1) and the earth 
curvature part h/a. At higher elevations the absolute 
moisture in the atmosphere decreases, and irregular 
variations of temperature become more and more 
exceptional so that eventually, at a relatively great 
height, any M curve approaches the standard curve. 
An additional limitation comes from the fact that 
both the temperature and moisture variations in any. 
one climate are subject to definite limitations. An 
extreme moisture change occurs when there is a 
boundary separating a nearly or fully saturated 
