44.6 4 PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
TABLE 7 
dmin(HP)  dmin (VP) dmin (VP) 
n K (km) (km) dmin (HP) 
2 0.835 26.0 38.2 1.47 
4 0.725 13.6 37.4 2.75 
6 0.625 7.0 41.9 5.98 
8 0.548 4.0 44.8 11.2 
10 0.486 3.0 52.9 17.6 
12 0.436 2.0 57.3 28.6 
14 0.40 1.40 60.6 43.3 
16 0.375 1.0 62.9 62.9 
18 0.360 0.70 64.3 91.9 
20 0.355 0.50 64.7 129.4 
Tables 6 and 7 show the effect of a reflection 
coefficient which is less than unity. upon the max- 
imum and minimum ranges of station A in the last 
section.The first table gives odd values of n and 
maximum ranges; the second table gives even values 
of n and minimum ranges. The free-space range is 
100 km. 
GENERALIZED COVERAGE DIAGRAMS 
(HORIZONTAL POLARIZATION) 
Basic Parameters 
The u-v method applied to generalized coordi- 
nates which was given in previous text may be 
extended to all transmitter heights and wavelengths. 
In this method, points on the lobe are located by the 
intersection of the path-difference locus with the 
normalized distance envelope. The basic parameters 
are do and R. 
ln constructing a coverage diagram for a doublet 
transmitter, the transmitter height, the wavelength 
and the radio gain are known. It will be shown in 
later text that the normalized free-space distance, 
do = do/dz, is related to the gain factor A by 
L885 A, (49) 
The path-difference parameter FR has been expressed 
in equation (114) in Chapter 5 in terms of a height- 
wavelength factor r which is defined by 
R =m, (50) 
where ian 
pes (51) 
2N 29 73? 
The first maximum, which for horizontal polariza- 
tion occurs when A = }/2, corresponds to n = 1, 
the second minimum to n = 2, etc. Recalling the 
discussion on pp- 438 ff-, it follows that it is pos- 
sible to construct coverage diagrams in generalized 
coordinates with r the pattern or chart parameter 
and do the curve parameter on a chart for which r 
is fixed. 
Determination. of do 
It is possible to express do = d)/d7 in terms of 
E/E,, the ratio of the field strength H corresponding 
to the lobe, to the free-space field H, at unit distance 
from the transmitter. Since 
E 
dy = ae 
it follows that 
dy = — = ——., (52) 
The ratio HE may be expressed in terms of the 
gain factor A through the following relationships. 
By equation (16) in Chapter 2 
By = SE 
45 
When d = 1, this gives 
E? 
Pj =—. 53 
Nareae (53) 
For a doublet receiver with matched load and ad- 
justed for maximum power transfer, equation (17) 
in Chapter 2 gives 
ees 
‘ 1207 8x 
Hence 
Sel pe = (54) 
E 82 *P, 872A 
Substituting the value of E/E from equation (54) 
into equation (52): 
a=+(2), (55) 
dr \8rA 
and 1 8r\h — (8r\x 
a (® A V2ka 3 Tae (56) 
Equation (56) shows that if log h: is plotted against 
log A for fixed values of dy and X, a straight line 
results. These straight lines are shown in Figure 14. 
If h; and E/E, or hy, \, and A are known, do may 
be calculated from equations (52) or (55). The 
value of do determines the range of the lobe tor 
specified values of r. In Figure 14, the various 
values of do used in constructing the charts are 
specified as A, B, C,--- , M, N, and are shown as 
functions of h; as ordinate and 20 log A — 20 log X 
as abscissa. 
Determination of r 
Figure 15 shows r for various values of transmitter 
height h; and wavelength \ where 
2hidr hy3/2 V2ka 2he” 2 k 
= = =. (57) 
Aka dka oN ka 
a 
r 
The values of , determine how the path-difference 
curves intersect the envelopes corresponding to 
assigned values of sin? (9/2) in the equation 
d = 3 @ 
1 =ae = av Va — D)? + 4D sin? a (58) 
The generalized coverage charts are designated as 
