COVERAGE DIAGRAMS 441 
The intersections between the path-difference con- 
tours and the distance envelope determine points 
on the coverage diagram. 
The above method should be applied even for 
horizontal polarization when the directivity of the 
antenna is such that F2/F, ~ 1. This follows from 
the concept of generalized reflection coefficients on 
page 385. 
LOBE-ANGLE METHOD 
(HORIZONTAL POLARIZATION) 
Outline of Method 
In this method the angles of lobe maxima are 
determined by modifying the plane earth formula, 
equation (2). In this equation, h; is replaced by hy’, 
which is the equivalent height above a plane tangent 
to the earth’s surface at the reflection point, as 
shown in Figure 8. 
The value of h;’ is given in equations (58) and (60) 
in Chapter 5. The maximum and minimum distances 
from the transmitter base to a point on the lobe 
are calculated by equation (46) in Chapter 5, using a 
modified divergence factor to be described in this sec- 
tion . 
Basic Relations 
Referring to Figure 8 and assuming d, << d@, 
y’ < 10° andy = vy’, the following relations hold. 
mr 
tan 7’ => 7’ = 4h,’ (29) 
1 
, 
tan y’ > 7’ = 5 é (30) 
1 
Hence 
niga 
di Ahy’ 
and 
2hy')? 
a= SRY, 1) 
where, from equation (58) in Chapter 5, 
dy? 
hy’ = h, — —. 
: * oka 
pee kTUNS md 
Gh. 
* 2ka 
and 
2 
oe) 
d, = —. (33) 
md 
Reflection-Point Curves 
The elimination of d; from equations (82) and (33) 
is most conveniently accomplished by graphical aids, 
which may be used in the following way. 
1. From equation (33), a curve may be plotted 
shawing d; as abscissa and n as ordinate for a given 
transmitter height and wavelength. This is illus- 
trated in Figure 9 for tio stations A and B with 
heights equal to 146.5 meters and 302 meters and 
HORIZONTAL POLARIZATION 
ISTATION B 
h,= 302 M 
LOBE NUMBER 7 
STATION A 
hj=146.5M 
REL 
° 10 20 30 40 390 60 
REFLECTION POINT d, IN KILOMETERS 
Figure 9. Location of reflection point d; as a function 
of lobe number 7. 
Tasie 4. Data for station A of Figure 9.* 
| POT y= Nee 
18 range 
eels d (km) 
1 6 
(km) |(meters)| (rad) | (rad) | (rad) D 
50.1 0 |0 0.00789) — 0.00789 0 
28.0 99.6 |0.00362 |0.00440/ — 0.00078 | 0.502} 150.2 
20.2 | 122.5 |0.00590/0.00317) 0.00270}0.740) 26.0 
15.9 | 131.7 |0.00827|.0.00250) 0.00575) 0.817} 181.7 
137.0 |0.01058/ 0.00200) 0.00858} 0.864] 13.6 
10.9 | 139.7 0.01300) 0.00170) 0.00120| 0.910} 191.0 
9.35] 141.4 |0.01540/ 0.00145} 0.01395 |0.930| 7.0 
8.05 | 143.0 |0.01760} 0.00128) 0.01632 |0.943 | 194.3 
7.25 | 148.6 |0.02000} 0.00112) 0.01888/0.960| 4.0 
6.45 | 144.0 |0.02260| 0.00100} 0.02160 |0.964 | 196.4 
10 | 5.80} 144.2 |0.02510} 0.00090; 0.0242 |0.970] 3.0 
11 | 5.32 | 144.7 |0.0275 |0.00083| 0.02667 |0.973 | 197.3 
12 , 4.98 | 145.0 |0.03000/0.00078| 0.03022/0.980} 2.0 
13 | 4.51 | 145.2 |0.03240/0.00071| 0.03169 | 0.982 | 198.2 
14 | 4.19 | 145.7 |0.03480) 0.00066} 0.03414)0.986| 1.4 
15 | 3.87 | 145.7 |0.03730] 0.00061] 0.03669 |0.989 | 198.9 
16 | 3.70 | 145.7 |0.04000 | 0.00058; 0.03942/0.990; 1.0 
17 | 3.48) 146 |0.04220/0.00053) 0.04167 |'0.991 | 199.1 
18 | 3.22/146 |0.04450/0.00050} 0.04400}0.993 | 0.7 
19 | 3.06 | 146.2 |0.04700/0.00048; 0.04652 )0.994 | 199.4 
20 ; 2.90 | 146.2 |0.04960/ 0.00045! 0.04915)0.995 | 0.5 
CHIA®TARwWMWEO |s 
= 
iS 
ey 
* Antenna gain and directivity factors have been omitted from the above 
calculations. 
