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MOORE AND VONNEGUT 
TaBLe 2—Data on two electrified clouds 
August 13, 1957 
August 16, 1957 
Item Initial echo 
Initial echo Second echo 
09h 58m MST 
10h 00m MST 
10h 12m MST 
10h 15m MST 
11h 14.5m MST 
11h 16.5m MST | 
Potential gradient reversal in cloud 
Time of echo detection overhead 
Estimated threshold median drop diameter 70u 70u 70u 
for reflectivity at detection (for 0.5 gm 
liquid water content) 
Altitude of lowest portion of initial echo, 4.3 km 4.5 km 4.5 km 
MSL 
Altitude of 0°C isotherm within cloud 5.4 km 5.4 km 5.2 km 
Altitude of cloud base, MSL 3.7 km 3.7 km 3.5 km 
Time rain arrived at level of summit (3.1 km 
altitude) 
10h 03m MST 
10h 17m MST 11h 20.3m MST 
Mean diameters of first raindrops collected unknown 3.0mm 3.2mm 
M = drop mass g = gravitational acceleration 
V = drop volume C, = drag coefficient of resistance for 
c = collection efficiency spheres which may vary between 0.30 
L = cloud liquid-water content and 0.21 in the size range between a 
A = drop cross-sectional area 0.5-mm and a 3-mm diameter. 
v = drop velocity 
em For our calculation we take the minimum 
p = density 
To eliminate the effect of updrafts within the 
cloud we use the observed time between the de- 
tection of an echo and the collection of rain at 
the summit, and the fall velocity of the drops 
at the observed altitude. We assume that the 
drops have the shape of an oblate ellipsoid to 
take the case of drops with the largest collection 
cross section. Thus the horizontal cross-sectional 
area for collision is 7a and the drop volume is 
(4/3) za*b, where a and b are the ellipsoid ma- 
jor and minor semiaxes, respectively. (This neg- 
lects the contribution made to the drop col- 
lection area due to the size of cloud droplets 
located at the edge of the raindrop path. This as- 
sumption is discussed below.) For convenience 
we assume also that 6 = ha, where h is a con- 
stant <1, a function of the eccentricity of the 
ellipsoidal drop. 
Therefore 
cLvdt = dowaterhda = dowaterdbd (2) 
From Spilhaus [1948], the terminal velocity v 
of fall for such an ellipsoid is 
dp b 1/2 
jae (3) 
3pa Co (0.9h — 0.01) 
where 
value for C,, which will give the smaller value 
of collection efficiency. 
Substituting for v and clearing we get 
Saune 2 db 
cL di = 2| =**\C,(00h — 001)" ee) 
g pie 
and integrating 
3 mys 1/2 
cL =4 Ee C(0.9h — von | 
g 
(5) 
(bilan — Dinitian) 
At 
Now 1, the radius of the equivalent spherical 
drop, equals bh** by definition. From Magono 
[1954], A for a 3-mm drop is about 0.87; thus 
= 0.91r and b°” = 0.95r'” 
Using 
pwater = 1.0 gm cm™ 
par = 0.79 X 10° gm cm™ at a 4-km altitude 
Ca— 021 
we obtain 
12 
(rfinal 
cL = 2.5 X 1073 
=: rinitial) 
ay (6) 
at a 4-km altitude 
From (3), the fall velocity at 4 km of 3-mm 
