388 - PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
Substituting for d; and d, from equations (64) and 
(66), 
hy + e(-£) A 
d 1+ 5 Aka 
_h+th/l—c\ da —5) 
a \et 4ka ~ 
Simplifying, 
The procedure for calculating d; when hy, he, and 
d are given is as follows: 
1. Compute c = Lit 
hy + he 
2. Compute m = PRO ORS é 
Hea(ha + In) 
3. Read b from Figure 15. 
d 
nth, 2(c—b) _ bd te Calbia ch (ae 
d 1-0 2ka 
It should be noted that h; may be the height of 
either the transmitter or receiver. The only re- 
strictions are that hi > h, and d; represents the 
distance from hy. 
Another method will now be given for calculating 
@ d,. This method will be particularly useful when 
ae AAG ot) (72) d,/d << 1 and will be applied in Section 5.5.8 on 
generalized coordinates. Let 
Solving for c, 
c=b-+ bm(1 — 8’), (71) 
where 
To determine d;, equation (71) must be solved 
Hee ; d;=sd, s<1. 73 
for b. This is a cubic equation, which is easily solved 4 g (73) 
when 2n is small in comparison to unity. However, Hence 
for m values comparable to unity, or larger, it is d, = (1 — s)d. 
easier to plot a series of curves showing c as a func- 
: From equation (70) 
tion of m for assigned values of b ranging from 
0 to 1. These are straight lines with a slope of hie eisai) ce pe temas (Is) ¢, 
b(1 — 6?) and are given in Figure 15. sd 2ka (1 —=s)d 2ka 
= 100.90 
0 SSS: 
ee SS SS SS SS SS es 
SS SES ee. 
ieee ee Zezez2 
See eeseeeeee= 
Neseesseoesseses 
BEeezeeeeeee ees 
ee ee 22220 
ANIN 
VA 
ne 
‘i 
: 
: 
aa 
: 
it 
v 
Ak 
‘ 
2 
Ere a es al za acl) 
joeoeecesseeceesanese 
eee 
1 Seoaecaesaescnen 
(Bees Se ee eS aes 
Be See oe ae Seo 
Sen Se sene See ono 
(eee 225 
2eeeee eae a= 0.7 1 0.9 i¥o) 
Ficure 15. Graph for obtaining b for given values of cand m. (Marconi, Ltd.) 
