Radar System Engineering

62 THE RADAR EQUATION [SEC.215
per kilometer, with precipitation rate in millimeters per hour. The
most extensive analysis of this sort has been carried out by J. W. and
D. Ryde, upon \vhose~\,ork'thecurves of Fig. 2.17 are based. The direct
measurements of attenuation and rainfall which ha~’e been made confirm
these predictions satisfactorily. The chief difficulty in such experiments
is connected with the measurement of the rainfall, which is homogeneous
in neither time nor space.
The dashed curves of Fig. 2.17 show the attenuation in fog or clouds
which, as we have said, does not depend on the drop diameter. According
to Ryde a certain limit of optical visibility can be, at least loosely,
associated with each of the dashed curves. For the conditions to which
Curve f applies, for example, the optical range is limited to about 400 ft.
At a wavelength of 3 mm the radar range could be 50 to 100 times as
long,
It would be easy, but not very instructive, to introduce an exponential
factor into the radar equation to take account of the attenuation that
we have been discussing. }Ve leave this task to the reader, \rho will
find no difficulty in calculating, for any given case, the reduction in range
caused by a specified strength of attenuation, which is effective, of
course, on both the outgoing and return path. One general observation
should be made, however, which is that the effect of an exponential term
in the radar equation is insignificant at very short ranges but overwhelming
at very long ranges. What we mean by short and long is
determined by the rate of attenuation. An entirely arbitrary criterion,
\rhich will serve as well as any other for discussion, is the range for \vhich
the presence of the atmospheric attenuation just doubles the normal rate
of decrease of signal intensity with range. If a is the rate of attenuation
in db/km, the range RO so defined is given by Ro = 8.68/a km. At
shorter ranges than this the inverse-square la~v is the more important
factor; at ranges greater than R, the exponential factor controls the
situation and any slight improvement in range must be bought at enormous
price. In other words, once attenuation takes hold, it is of little
avail to struggle against it.
1J. IV. Ryde and D Ryde, Report 8670 of ‘~hc ResearchLaboratory of Cxeneral
Electric Company,Ltd. ‘~hisis a Britishpublication.