250 RADIO WAVE PROPAGATION EXPERIMENTS 
2. Unstable equilibrium (resulting when the initial 
surface air temperature is less than the sea surface 
temperature). In this case the moisture content of the 
air is always less than that corresponding to satura- 
tion at the sea surface temperature, so that the lower 
layers of air suffer an increase in humidity as well as 
in temperature. Owing to the greater sensitivity of 
M to humidity than to temperature this tends to bring 
about a decrease of M with height in a layer of air 
adjacent to the sea surface, while the unstable condi- 
tions give rise to vertical mixing which keeps the M 
distribution close to standard above this layer so that 
the duct is confined to lower levels than in the case of 
neutral equilibrium. 
3. Stable equilibriwm (resulting when the initial 
surface air temperature is greater than the sea sur- 
face temperature). If, in addition, the air is initially 
quite dry, ie., has a moisture content less than that 
corresponding to saturation at the sea surface tempera- 
ture, then the resulting rapid decrease of moisture with 
height plus the stable temperature distribution leads 
to a tendency to surface duct formation. On the other 
hand, if the initial moisture content of the air is rela- 
tively large, moisture may be condensed out of the 
surface layers of air thus tending to give rise to’ an 
increase in humidity with elevation which when suffi- 
ciently marked may counteract the effect of the stable 
temperature distribution and so prevent the forma- 
tion of a duct or even produce substandard conditions. 
‘In either case, the stable structure of the air tends to 
hinder vertical mixing so that modification from the 
surface upward proceeds slowly and hence is highly 
dependent on the distance traveled by the air over 
the water. 
Necessary Calculations. To determine quantitatively 
the possibilities of duct formation, the following items 
can be readily calculated from any particular observed 
set of initial conditions. 
1. Temperature excess, which is merely the repre- 
sentative surface air temperature (before modifica- 
tion) minus the sea surface temperature. 
2. M deficit, defined as the value of M correspond- 
ing to the sea surface temperature minus the value 
of M determined from the representative surface air 
temperature and humidity (before modification) ; 
values of M can be ascertained from nomograms," 
tables,’ or directly from the formula.) In the case of 
M corresponding to the sea temperature, a 98 per cent 
saturation is assumed; the 2 per cent vapor pressure 
correction is subtracted to take into account the salin- 
ity of the sea water. 
3. Ratio of duct width to M deficit, determined 
from the chart in Figure 19 for a given temperature 
hNomograms are included and explained on pages 256 - 257. 
!Tables for computing M can be found in references 8 and 9. 
iThe formula expressing M in terms of pressure, temper- 
ature, humidity, and elevation is given on pages 256-257. 
excess and wind speed as measured at the 1,000-ft 
level. 
4. Duct width, found by multiplying the above 
ratio (3) by the M deficit. 
Applicability of the Method. Since the procedure 
is designed to take into account only the surface modi- 
fication of air over water, its application is restricted 
to the prediction of the first four types of M curves 
described on pages 245-248: standard, substandard, 
simple surface trapping, and transitional. The causes 
of S-shaped M curves are not considered in this 
method. Standard conditions can be presumed to 
occur when the calculations indicate a duct width of 
zero, which is the case when the M deficit is zero. Jf 
the M deficit is negative, then the calculated duct 
width will be negative, and substandard conditions are 
to be inferred. A positive M deficit indicates duct 
formation (simple surface trapping), and the calcula- 
tions of the duct width given an estimate of the height 
to which the duct extends. If this height is small, 
conditions may be inferred to correspond to the tran- 
sitional case. Once the duct width is calculated, a 
complete picture of the distribution of M with height 
LIMITED TO OVER-WATER NO TRAVEL 
TRAVEL 10-30 MILES LIMITATION 
WIND SPEED IN MPH AT 1000 FT 
TEMPERATURE EXCESS IN DEGREES F 
5 fo) “5 
TEMPERATURE EXCESS IN DEGREES © 
Figure 19. Graphs showing the value of the ratio of 
duct width d to the M deficit, AM for values of temper- 
ature excess and wind speed at the 1,000-ft level. 
(Typical values are given in Table 2.) 
