442, : PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
REFLECTION POINT IN KILOMETERS (STATION 8) 
16 32 a0 6a 80 96 
o 
VARIATION OF EFFECTIVE HEIGHT h, 
WITH REFLECTION POINT d, 
FOR A: h,=146.5 M ALS 
FOR Bs hs302M DeL42M 
HORIZONTAL POLARIZATION 
le 
STATION A 
STATION B 
ucttas GTATION®) 
o 
° 
EFFECTIVE HEIGHT IN 
EFFECTIVE HEIGHT IN METERS (STATION A) 
y 
° 
rs 
° 
@ ry 2 a 
REFLECTION POINT IN KILOMETERS (STATION A) 
Ficure 10. Variation in effective height hy’ with 
reflection point di. 
wavelengths } = 1.50 meters and \ = 1.42 meters 
respectively. 
2. From equation (58) in Chapter 5, a second curve 
may be plotted with d, as abscissa and the equivalent 
height h,’ as ordinate as shown in Figure 10. To illus- 
trate, computed data for station A are given in 
Table 4, for a free-space range of dp = 100 km. d is 
calculated from equations (16) and (17). 
3. For any n, including integral and fractional 
values, d,; may be found from Figure 9 and the 
corresponding h,’ from Figure 10. The angles y’ 
corresponding to lobe maxima may then be calculated 
from equation (32). 
Lobe Angles with Horizontal 
The angle y’ given by equation (32) is measured 
with respect to the tangent plane through the reflec- 
tion point shown in Figure 8. This plane is inclined 
at an angle @ with the horizontal at the base of the 
transmitter. The true angle 7 which the lobe-center 
line makes with the horizontal is 
y=7 —-4, (34) 
where 
A= =e (35) 
Hence by equation (82) 
nr 
yg cet ONT ah 
s(n - #) ka? (36) 
2ka 
where odd values of n give maxima and even values 
minima, provided the reflection phase shift is 7 
radians. The angle may be either positive or nega- 
tive, as shown by equation (86). 
Use of Modified Divergence Factor 
The value of the divergence factor must be de- 
termined in order to calculate the maximum and 
minimum lobe lengths by equation (46) in Chapter 5. 
A convenient formula for the divergence factor at 
the angles of lobe maxima is obtained by substitut- 
ing y’ for y in equation (92) in Chapter 5. The 
errors involved in this assumption have been given 
previously .Substitution of y’ = yin equation (92) 
in Chapter 5 yields 
2hi’ 
1 
\ ‘ ka(y’)? 
For lobe maxima 
Xr 
hy ee 38 
YF (38) 
Hence 
ON 
iets ee 
\ - 2ka(y')3 
Contours of constant y’ are shown in Figures 11 
and 12 where y’ is a function of D and ni. 
Construction of Lobes 
For horizontal polarization, the distance dmax 
from the base of the transmitter to the lobe max- 
imum is calculated from equation (46) in Chapter 5 
by substituting K = (F2/F;)pD and sin? (Q/2) = 1. 
For horizontal polarization p = 1. Thus, 
— F,.. -? F. 
dmax = VG. E = * |] 4—D 40 
ido] 7, = F, (40) 
or 
dimnax = VGido E a. He D| 5 (41) 
Py 
Here F, and F; arecomputed from theangles yz and v 
given by equations (62) and (63) in Chapter 5. Thedis- 
tance dpi, from the transmitter base to the minimum 
point is obtained by substituting sin? (Q@/2) = 0 and 
K = (F./F;)D in equation (46) in Chapter 5. Thus 
