164 ; TECHNICAL SURVEY 
was 50 to 60 db below free space near the limit of 
sensitivity; the observed maximum was 13 db above 
free space, and the minimum could not be observed. 
In this case the effects of superrefraction were quite 
pronounced. In January the signal was less than 40 
db below free space during 6.5 per cent of the time; 
the corresponding figure for July is as high as 33 
per cent. 
The reliability of these transmission circuits is 
shown in Figure 38. Here, both for the optical and 
nonoptical paths, the percentage of time during 
which the signal strength was below specified values 
is plotted for the various frequencies used. The 
specified values of signal strength, for each frequency 
and path, are measured relative to the corresponding 
undisturbed value. The results, which give averages 
of the performance during July 1943 and January 
1944, indicate that the reliability increases appreci- 
ably with decreasing frequency. 
It must be said that the New York area where 
these experiments were made is not particularly 
affected by blackout situations, and the results are 
probably not typical for locations where blackouts 
are a frequent occurrence. The general nature of 
these data is confirmed by results of extensive 
experiments in England and in Massachusetts Bay. 
Scattering and Absorption 
by Water Drops 
As microwave sets have come into general use in 
recent years the ‘‘rain echoes” frequently seen on 
the scope have attracted attention. The possibility 
of using microwave radar as an aid to meteorological 
forecasting and for aerial navigation was early recog- 
nized and is now being put to operational use. 
At first sight, ground clutter resulting from trap- 
ping of radiation in a ground-based duct and rain 
reflections look somewhat alike on the scope of a 
radar set. At closer inspection differences appear; 
the cloud pictures are usually more fuzzy and less 
sharply defined than the echoes received from ground 
targets. An experienced operator usually has little 
difficulty in distinguishing rain echoes from echoes 
of targets or objects at the ground, but occasional 
mistakes have been reported, especially from the 
tropics. 
Rain echoes are a result of the scattering of micro- 
waves by the raindrops. Electromagnetic theory 
shows that the amount of scattering increases very 
rapidly as the wavelength is decreased. It also 
increases rapidly with increasing drop diameter. On 
account of this sharp variation the scattering effects 
become appreciabie only when the wavelength is 
below a certain maximum value and when the drops 
exceed a certain critical size. Rain echoes are rarely 
observed at longer waves than S band, but they are 
common at S band and become very important at 
the shorter microwaves. 
For a time it was thought that clouds could 
produce microwave echoes, but more thorough inves- 
tigations have now established the fact that the 
droplets in clouds are too small to produce appreci- 
able scattering. Only drops that are large enough to 
constitute genuine rain are seen by a radar, and, 
especially at S band, light rains will often escape 
detection. The term “‘storm echo,” invented at a 
time when the origin of these echoes was not yet 
clearly understood, should be avoided, and the terms 
“vain echo” or “precipitation echo’’ should be used 
instead. A rain seen by the radar is not necessarily 
recorded by an observer at the ground, as the rain 
may be confined to the free atmosphere and never 
reach the earth. This occurs either when the rain 
falls in an ascending stratum of air where the air 
rises more rapidly than the drops fall or when the 
raindrops evaporate again before reaching the 
ground. Both cases occur quite commonly in the 
atmosphere, especially under convective conditions 
such as are indicated by cumulus clouds and thunder- 
storms. Snow may also be seen on microwave scopes 
provided the snowfall is sufficiently heavy. 
While clouds themselves do not produce microwave 
echoes, they may contain falling rain of one of the 
forms just indicated. Visual appearances are deceiv- 
ing, and an imposing looking cumulus cloud might be 
entirely invisible on the scope, whereas a cloud that 
is inconspicuous to the eye but contains falling 
raindrops might give a pronounced echo. 
The question of “shadow” cast by a storm echo 
is of some operational interest. A shadow is formed 
when the absorption that accompanies scattering by 
the raindrops becomes so strong that the remaining 
radiation no longer suffices to produce visible echoes 
from targets behind the rain area. This effect is 
pronounced on X band, and even more on K band, 
and is often quite conspicuous with airborne equip- 
ment where it may happen that a rain storm blanks 
out a sector of the sweep. On S band the absorption 
is usually much weaker and targets can often be seen 
behind a rain echo. 
The usefulness of rain echoes for aerial navigation, 
particularly in the tropics, is now so generally known 
that the subject need not be discussed further. 
SNELL’S LAW 
The ordinary law of refraction known as Snell’s 
law may be expressed as 
No sin Bo = m Sin f; , 
where {o and (; are the angles which the ray makes 
with the perpendicular to the boundary. Here it is 
more convenient to take the angle a between the 
ray and the boundary surface. Snell’s }aw then reads 
No COS ao = NM COS a. 
.The refraction at a sharp boundary is shown in 
