ATTENUATION DIAGRAMS FOR SURFACE DUCTS 179 
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Gl Sa Se 
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M DEFICIT 
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eR AUNGINNNANINN 
Sn : 
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|| AAAS 
TMA Vi 
0 
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100 
' ATTENUATION THOUSAND YARDS 
===TRAPPING INDEX 
DUCT THICKNESS IN FEET 
Ficure 3. Horizontal attenuation of first mode and trapping index, 3,000 me, standard attenuation (0 M deficit): 
1.23 db per 1,000 yd. 
is frequently dominant. The results presented apply 
primarily to this situation 
The type of M curve considered is the bilinear 
model in which the M curve consists of two straight- 
line segments, the upper being assumed to possess 
standard slope. This model M curve is completely 
characterized by two parameters: duct thickness and 
M deficit. Figures 2, 3 and 4 refer to three 
frequencies (200, 3,000, and 10,000 me) and super- 
standard conditions corresponding to ranges of 1 to 
100 M units in M deficit and 10 to 1,000 ft in duct 
thickness. 
The solid curves are contours of constant decibel 
attenuation (of the first mode) per thousand yards. 
One enters the diagram with given values of duct 
thickness and M deficit and interpolates between these 
contours to obtain the corresponding attenuation. 
The dashed curves are contours of constant “‘trap- 
ping index” (number of classically trapped modes). 
In terms of the standard notation their equation is 
[as a2) 
Their significance lies in that they furnish an indica- 
tion of the number of modes other than the first that 
must be taken into account. If, for example, the 
bilinear M curve in question corresponds to a point 
midway between the m = 1 and m = 2 contours, 
the first mode is strongly trapped and the second 
mode attenuation is reduced considerably below 
standard. Which mode is dominant then depends 
critically upon the heights of transmitter and 
receiver, and the simple first mode picture becomes 
incomplete except at great distances and sae 
heights. 
Tf one attempts to apply these results to simple 
surface ducts differing from the idealized bilinear 
9A? 
M deficit = T6h2 
