400 PROPAGATION THROUGH THE STANDARD ATMOSPHERE 
Taste 2. 10 log G, = 13.5 db; 10 log G-=0.0db; \ = 1.5 meters; h; = 30 meters; hk: = 1,000 meters; >=10 m*, 
RadioGain Radar Gain 
2 Ps P, 
Dp v d(km) R n D 2 2 20 log Ap 20logA 10 log P, 10 log P, 
0.12 3.098 70.49 7.78 0.83 0.97 1.30 5.6 —112 —106.4 —93 —172 
0.11 2.934 66.75 8.54 0.91 0.98 1.43 6 —111 —105 —92.5 —170 
0.10 2.755 62.68 9.45 1.005 0.98 1.58 6 —110 —104 —91.5 —169 
0.09 2.561 58.25 10.55 1.22 0.98 1.76 6 —110 —104 —91.5 —169 
0.08 2.349 53.45 11.92 1.27 0.99 1.99 5.2 —109 —104 —90 —167 
0.07 2.119 48.21 13.68 1.45 0.99 2.29 3.5 —109 —105.5 —92 —170 
0.06 1.870 42.54 16.02 1.70 0.99 2.68 —1 —107 —108 —94.5 —175 
0.055 1.738 39.22 17.50 1.86 0.99 2.92 —7.5 —106 —113.5 —100 —186 
0.05 1.600 36.4 19.28 2.05 1.00 3.22 —16 —106 —122 —108.5 —203 
0.045 1.457 32.89 21.45 2.28 1.00 3.58 —1.5 —105 —106.5 —93 —172 
0.04 1.311 29.59 24.16 2.57 1.00 4.04 +3.8 —104 —100 —87 —159 
0.035 1.158 26.14 27.64 2.94 1.00 4.62 6 —103 — 97 —79.5 —153 
0.03 1.002 22.62 32.28 3.43 1.00 5.39 +2 —102 —100 —86.5 —159 
0.025 0.841 18.98 38.67 4.12 1.00 6.48 —8 —100 —108 —94.5 —165 
0.02 0.678 15.30 48.49 5.16 1.00 8.10 5.7 — 98 —104 —91.5 —167 
0.01 0.345 7.79 97.08 10.33 1.00 16.22 0 — 92 — 92 —78.5 —143 
* Lobe pattern factor = 20 log Va —D)* + 4D sin? (0/2). 
7. To find A, we need first the free-space value Ao, 
which is given in Figure 3 in Chapter 2 as a function 
of d. Since dp = 4.12 V30 = 22.6 km, the value of 
d corresponding to v = 2.76 is d = udp = 62.3 km, 
and 20 log Ap = — 111. 
8. To find the value of 
Q 
10 log 4) ( — D)??+ 4D sin’ >> 
we need D. Since n is practically unity, correspond- 
ing to the first maximum, sin? (2/2) may be taken as 
unity. Hence the radical reduces to 1 + D. Calcula- 
tion using equation (103) and Figure 17 gives 
D = 0.98, and hence 
1+D =1.98, 
20 log (1 + D) = 6. 
Since the transmitting antenna gain G; is 13.5 db, 
and assuming the receiving antenna gain to be 0 db, 
10 log (P2/P1) has the value 20 log A + 13.5 or 
P, 
10 log Ba 
= he Na — D)+ 4D sin? 5 GiG2 + 0.0db 
— 111 db + 6-db + 13.5 db 
= — 105-+ 13.5 = — 91.5 db. 
Repeating the process for other values of p, a 
table of 10 log (Ps/P;) versus d is obtained. These 
points have been plotted in Figure 26, together with 
the points in the diffraction region obtained with the 
data given on pp.413- 416. For sketching in the 
optical part, the value of n is kept in mind, since 
this indicates on which lobe and where on the lobe 
the point lies. 
Rapar Gain: Two-Way TRANSMISSION 
To change from 20 log A = — 105 to 10log (P2/P;) 
at the radar receiver, using equation (5) and G; = G2 
= 13.5 db, 
10 log (P2/P1) = 27 + 7.5 + 10 log « — 20log 1.5 
+ 40 log A, 
= 27+ 7.5 +10 —3.5+ 40log A, 
= 41+ 40log A = — 169db. 
Type IV. Determination of Con- 
tours Along which the Gain Factor 4 
Has a Given Value, the Transmitter 
Height and Wavelength Being Given 
This is the so-called coverage problem which is 
treated in greater detail in Chapter 6. While the 
usual coverage diagram is derived on the basis of 
one-way or communication formulas, the diagram is 
still useful for radar since a target wil! return more or 
less energy to the receiver according to its position 
on the coverage diagram. The contour gain factor A 
is readily converted to P2/P, for either one-way 
or radar by means of equations (8) and (5). 
The method described here is more accurate than 
the graphical methods given in Chapter 6. It is best 
suited for finding maximum lobe ranges correspond- 
ing to a given radar gain. If A is given, and hz for a 
given distance d is wanted, a curve can be drawn as 
that for Type Iland then fz: found for the given 
value of A. 
PROBLEMS 
A radar set operating over the sea has a trans- 
mitter with antenna height of 30 meters and a wave- 
length of 1.5 meters. As in the previous problems, a 
receiver with an antenna of 0 db gain is assumed in 
place of a target and the gain of the transmitter is 
again assumed as 13.5 db. The polarization is hori- 
zontal. The gain factor A, for illustration, is chosen 
as —130db. Positions of the receiver are to be 
found at which the gain factor takes that value. 
