122 TECHNICAL SURVEY 
reflected energy is considered to be of random phase 
and magnitude. The magnitude of the reradiated 
field (microvolts per meter at a distance of 1 mile 
from the target) is found by using a coefficient of 
reradiation, pr, which varies with the target and 
aspect. 
The received field intensity is by the reciprocity 
theorem: 
\E|= iol Sk a. (106) 
Substituting from equation (105) 
Pr fi EB, 2 
|B |= "oS A 
For a particular coverage contour, such as the 
threshold of detection, usually taken as a signal-to- 
noise ratio of unity, a minimum received field inten- 
sity | Hy | may be assumed. This is related to receiver 
noise voltages, antenna -gain, and other factors of 
design. Using | Ey | for | Z| and solving for d 
[ead ee eae (107) 
Because of the way in which: £; and pz are defined, 
do, the maximum free space range, has the dimen- 
sions of length (in miles). It depends on the design 
of the transmitter and receiver and on the target. 
A may be considered a coverage factor which depends 
DPz 
RIGHT SCALE 
PHASE LAG IN DEGREES 
—0.0) 0.00 0.01 0.02 0.03 
ees eae ee 7 
HONS aye a 
RGM 
on y and terrain effects. 
Because of the implicit character of the parameters 
of A in equation (103), a general solution of A as a 
function of y is not feasible. However, examination 
of typical problems discloses that the range of varia- 
tion of some of the factors is limited, and a method 
of successive approximations may be readily applied. 
In most cases $ and ¢ will vary slowly (about. % as 
fast) compared to 6 below 2° or 3°. At higher angles 
the rate of change may be faster, but contribution 
of the reflected wave at these angles is likely to be 
unimportant. 
The method described here consists in computing 
the lobe angles, diffraction, and divergence as though 
the only phase shift involved was that due to path 
difference as given on pages 102-104, 111-114, 119. 
The phase shifts from the apparent lobe angles thus 
computed are then determined. The diffraction phase 
shift is ¢, and the reflection phase shift is 
¢’ = ¢ — 180°, (108) 
where ¢ is obtained from Figure 70. If horizontal 
polarization is used ¢ may be taken as 180°, and 
¢’ is then zero. With curves of the phase shift 
“+ ¢ and the product f(y — 26)Dpz plotted 
against vy the apparent lobe angles.«and lengths 
computed above may be corrected to obtain the 
actual values. The details of this method will be 
given in the example below. 
RELATIVE STRENGTH OF REFLECTED RAY 
$IN RADIANS 
FicurE 72. Relative magnitude and phase of the reflected ray. 
