54 j TECHNICAL SURVEY 
nate all but he and S, defining our coverage diagram. 
We may substitute the approximate value for D 
into equation (5) and also use equation (4) to elimi- 
nate S from the equation 
10-4/20 — 
al 1 _ de | x 
mt Lv/2rh; (1 — a) 4thia? 
4 
[: i ( = = la a5 sin2® ‘ (6) 
4 
We may now set 
o=(n-5)n; = i ey oom (7) 
which correspond to the maxima of the lobes. We 
may alternatively take 
’=n7, (7b) 
corresponding to lobe minima or, more generally 
@ = (n+b)7 (7c) 
to represent any specific position on the lobe. 
With A, hi, \¢, and @ as variables, we may throw 
equation (6) into the form of a nomogram, from 
which we determine a, first for the lobe tips, second 
for the minima, and third for as many intermediate 
points as are necessary. 
With the a’s so determined, proceed to equation 
(4), also in nomographic form, to get S. Finally, use 
equation (2), to determine h:. This equation can also 
be thrown into nomographic form if we set 
82 
ae he = h’s (8) 
where h’s is measured vertically from the line tangent 
to the base of the transmitter. 
Another somewhat simpler type of coverage dia- 
gram is possible. If we take 
10° 
4nS? 
10-4*/10 = 
(9) 
as defining the intensity for a transmitter in free 
space, we get for the ratio of the two 
72 
—(4—A*)/10 — 1()B/10 — i @ 
10 10 E G = x) | ar 
4 
4(7*5) sinr?S, (10) 
where B is the number of decibels by which the 
actual field exceeds the free space value. Coverage 
diagrams of this type consist of lines radiating from 
the transmitter, rather than contours. For non- 
standard propagation the drawings have some com- 
plications, but the procedures are clear. This method 
has the additional advantage of fitting in with the 
theory used for surface targets, for which it is simpler 
to use free space intensities and lump the field 
strength integrated over the target area as an 
“effective” target area in a uniform field. 
