278 
TABLE 3 
A, em C1 C2 D.cm 
1 0.109 2.53 0.0656 
11 0.0994 2.60 0.0680 
1.26 0.0862 2.69 0.0713 
1.5 0.0730 — 2.73 0.0774 
2 0.0543 2.64 0.0906 
3 0.0365 2.23 0.121 
4 0.0273 1.85 0.154 
5 0.0217 1.54 0.187 
6 0.0179 1.31 0.222 
8 0.0137 1.01 0.293 
10 0.0110 0.835 0.363 
15 0.00724 0.570 0.534 
20 0.00541 0.427 0.712 
25 0.00437 0.342 0.892 
30 0.00364 0.285 1.07 
50 0.00219 0.171 1.78 
75 0.00146 0.114 2.68 
100 0.00109 0.085 3.57 
wavelength range 1 to 100 cm. The values of ¢, are 
not included, since this coefficient turns out to be 
practically constant, in this range, increasing from the 
value of 1.224 for A = 1 cm to 1.239 for A = 100 em. 
It is evident that for values of p which are not too 
small, equation (48) or (50) has to be used. When 
pis sufficiently close to unity these series cease to give 
any good values of the absorption cross section Q: or 
the attenuation factor a In the K and X bands, Ryde 
and Ryde’ have, therefore, computed the attenuation 
factors exactly. These computations were included 
(without being checked) in Tables 4 and 5, where Q; 
and « have been computed for a series of drops ranging 
in diameter from 0.05 to 0.55 cm. For wavelengths 
\ => 5 cm, the three-term series expansion (48) was 
RADIO WAVE PROPAGATION EXPERIMENTS 
used. It is expected that at these shorter waves, where 
the critical diameters are smaller than the drop diam- 
eters mentioned, the cross sections and attenuation 
factors given in the tables will be but fair approxima- 
tions of the exact values of these quantities. 
The range of values of p covered by these tables ex- 
tends from about p = 0.0016 to p = 1.4. In Figures 
5 and 6 two families of curves are drawn giving 
Q: (A) p and @(A) p/N, the diameter of the drops being 
EMG 
TE 
=3) 
SSSR CO 
?_IKANSS SST ls 
" (ANGE ECB EERS s 
Lo aim arcs 
ei aaa 
(wi lina i 
i sl onl 
100 
Fiaure 5. Absorption cross section, Q;, and attenua- 
tion constant, a, of spherical water drops as a function 
of the wavelength. The abscissa gives the wavelength, 
A, in centimeters. The right-hand ordinate scale gives 
logio (a/N), where a/N, the attenuation constant in a 
rain with 1 drop per cu cm, is expressed i in decibels per 
kilometer. The numbers on the curves give the diameter, 
D, of the drops in centimeters. The left-hand ordinate 
seale gives logio Q, with Q, being expressed in square 
centimeters. 
Taxsie 4. Absorption cross section Q; (em?) of water drops with diameter D (cm). 
Ne D, cm ‘ 
A,em\ _ 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 
1.25 |6.1910-5 9.6010-4 5.661078 1.891072 5.041072 1.13107! 2.15107! 3.66107! 5.6610-! 7.6210 1.01 © 
3 9.1910-§ 1.521074 1.301078 5.5310-8 1.631072 3.731072 6.65107? 1.08107! 1.52107! 2.1510-1 2.72107 
5 2.8410-§ 2.751075 1.2010-4 3.7910-4 9.8510-4 2.24108 4.591078 8.6810°S 1.5410-2 2.591072 4.181072 
8 1.0910-§ 9.4910-§ 3.651075 1.021074 2.40104 4.981074 9.631074 1.741078 2.9710°8 4.851073 7.63 10-S 
10 6.90 10-7 5.8410-§ 2.1610-5 5.7610-5 1.461074 2.591074 4.8110°4 8.441074 1.4010-% 2.251078 3.47 10-3 
15 2.9810-7 2.4510-§ 8.6610-§ 2.181075 4.591075 8.6510-> 1.511074 2.511074 3.981074 6.101074 9.06 10-4 
20 1.6710-7 1.3610-§ 4.7110-@ 1.1510-5 2.3610-5 4.3110-5 7.2910-5 1.1710-4 1.781074 2.6610-4 3.8510-4 
30 7.3610-§ 5.9310-7 2.0210-§ 4.8810-§ 9.741078 1.731075 2.831075 4.381075 6.4810-5 9.291075 1.3010-4 
50 2.6710-§ 2.141077? 7.2710-7 1.7310-§ 3.4110-§ 5.9610-§ 9.57107 1.4510-5 2.0910-5 2.931075 3.97 1075 
75 1.1910-§ 9.4410-8 3.211077 7.631077 1.49107 2.6010-§ 4.15107 6.2310-% 8.941076 1.241075 1.661075 
100 6.7710-® 5.4110-8 1.8310-7 4.341077 8.501077 1.471076 2.3510-§ 3.51107 5.0210-® 6.9210-6 9.27 10-6 
Tasie 5. Attenuation a/N (db/km) in fictitious rains with a concentration of one drop per cubic centimeter of D cm 
diameter. 
D, cm 
Ny ONG 0.05 0.10 0.15 0.20 0.25 0.30 <= 0.35 0.40 0.45 0.50 0.55 
1.25 2.69 10 4.17102 2.46108 8.23108 2.19104 4.90104 9.33104 1.59105 2.46105 3.31105 4.37105 
3 3.99 6.6110 5.63102 2.40108 7.08103 1.62104 2.89104 4.68104 6.61104 9.33104 1.18105 
5 1.23 1.1910 5.2210 1.65102 4.28102 9.72102 1.99108 3.77108 6.69108 1.13104 1.81 104 
8 4.731071 4.12 1.59 10 4.43 10 1.04.102 2.16102 4.18102 7.54102 1.29108 2.10108 3.31103 
10 2.99107! 2.54 9.37 2.5 10 6.35 10 1.12102 2.09102 3.66102 6.09102 9.76102 1.51108 
15 1.30107! 1.07 3.76 9.47 1.9310 3.7610 6.5810 1.09102 1.73102 2.65102 3.93 103 
20 7.2610-2 5.89107! 2.04 5.02 1.03 10 1.87 10 3.1710 5.0710 7.7310 1.1510? 1.67102 
30 3.2010-2 2.57107! 8.79107! 2.12 4,23 7.50 1.2310 1.9010 2.8210 4.0410 5.6310 
50 1.1610-2 9.291072 3.1610-! 7.531071 1.48 2.59 4.16 6.29 9.10 1.2710 1.7210 
75 5.1610-§ 4.1210-2 1.3910-! 3.31107! 6.49107! 1.13 1.80 2.70 3.88 5.37 7.21 
100 2.9410-8 2.3510-2 7.9310-2 1.89107! 3.69107! 6.40107! 1.02 1.53 3.01 4.03 
2.18 
