Radar System Engineering

SEC. 4.1] RANGE, PRF, AND SPEED OF SCAN 119
chapters. This number will be denoted by N- and defined, where exact
specification is required, by the relation
(1)
In Eq. (1), v, is the pulse-repetition frequent y, e is the width in radians
of the radar beam, between half-gain points as usual, and u~ is the angular
velocity of scanning in radians per second. Of course NM is closely
related. to the more general and more loosely defined quantity ni introduced
in Sec. 2.11. If N* is required to be, for example, 10, the rate of
rotation of the antenna in the previous example must be restricted to
0.14 rps or about 9 rpm.1
The numbers arrived at in this example are typical of long-range
ground-based microwave radar. Any considerable improvement in all
three characteristics—range, scanning speed, and angular resolution—
will be blocked by irreconcilable requirements as long as a single radar
set is relied upon for the entire coverage. But the restriction falls
even more severely on radar systems designed to search rapidly iri two
angular coordinates rather than in one.
Suppose that it is our ambition to design a radar system which will
locate in azimuth, elevation, and range any aircraft within 20 miles
with the angular accuracy that can be achieved through the use of a
beam 2° wide in both azimuth and elevation. The solid angle which
the beam itself includes is roughly 0.001 steradlans whereas the hemisphere
to be searched represents a solid angle of 27r. Some 6000” patches”
in the sky must therefore be covered. The number of radar pulses
needed during a complete scanning operation, regardless of the order
in which it is carried out, cannot be less than 6000 N... The maximum
pulse-recurrence frequency consistent with a 20-mile rangez is about
45OO pps. Hence the minimum time for completion of the scanning
operation is 6000 N,~/4500 or 1.3N.C sec. Even if N- is permitted to
be as small as 3, for a complete picture a scanning time of 4 sec is required,
which for many purposes is uncomfortably long.
The only physical constant which has been invoked in the foregoing
discussion is the velocity of light. The only assumption which has
been made about the radar system amounts to this: There is only one
channel, through which elements of information in the form of echoes
I It should be noted that imposing this restrictionincidentally insuresthat the
antennawill not turn too far away from the direction of the target before the echo
returns.
*Certain practical considerationswhich prevent the use of the entire interval
between pulsesfor receptionof signals and which thereforeset the limit on P,even
lowerthan c/2R (seeChap. 12) arehereignored.