298 
T 
———s— 4 
1.0 2.0 3.0 
RAIN DROP DIAMETER, mm 
Fic. 6—Experimentally determined collection 
efficiencies for raindrop falling through artificial 
cloud of 5- to 10-micron-diameter droplets [after 
Kinzer and Cobb, 1956] 
range overhead), the computed collection ef- 
ficiency of unity required would still be greater 
by a factor of 2 than the collection efficiencies 
observed in the laboratory. Kinzer and Cobb 
[1956] made laboratory observations of the col- 
lection efficiency of water drops supported by an 
upward flow of a cloud of known properties, in 
the absence of any external applied electric field. 
The collection efficiencies they reported are 
shown in Figure 6. It can be seen that for drops 
0.1 mm to 3.0 mm in diameter falling through a 
cloud of small droplets, the mean collection ef- 
ficiency is less than 50%. 
To a first approximation, a raindrop falling 
through a cloud of water droplets has the op- 
portunity of coalescing only with those cloud 
droplets lying at least partly within the vol- 
ume that it sweeps out. If, however, we consider 
the finite size of the small droplets it is apparent 
that the rain drop might coalesce with small 
drops just tangent to its path. Accordingly to be 
rigorous the effective radius for collision should 
be that of the raindrop plus that of the cloud 
droplet. For simplicity this consideration has 
not been included in (2); instead, a solution 
was made for the apparent collection efficiency 
in natural clouds as a coefficient for comparison 
with collection efficiencies determined in a labo- 
ratory cloud by Kinzer and Cobb [1956] who 
used the same simplifying assumption for 
When the growing drop becomes much larger 
than the droplets that are captured, the correc- 
tion for the size of the droplets becomes very 
MOORE AND VONNEGUT 
small, much less than the high collection ‘coef- 
ficients’ indicated. 
Discussion OF COALESCENCE 
An observer of the convective clouds in New 
Mexico soon notices that rain falls abruptly 
from these clouds as though a valve had just 
been opened or some trigger mechanism had been 
activated. Here the initial rainfall does not start 
slowly indicating slow droplet growth or an or- 
derly process of rain formation. A cloud may 
float around producing no rain for an hour (or 
for as little as 15 min); then, closely associated 
with a burst of convection, there is an abrupt 
change in the cloud, with vigorous production of 
rain in a transient gush. 
The calculations above were an effort to de- 
termine the collection coefficients necessary for 
initial raindrops in these clouds to fit the ob- 
served time sequence. The effective values found 
for the collection of actual raindrops are ap- 
preciably greater than collection efficiencies ex- 
perimentally determined in a laboratory. There 
are several possible explanations for the sur- 
prising fact that our observations give collection 
efficiencies greater than unity. It may be that 
unwarranted assumptions have been made in the 
model of drop growth that we and others have 
used. 
This model probably is a fairly good deserip- 
tion of the growth process when a large drop 
falls through a cloud of small droplets. When 
large numbers of big drops have formed and 
the precipitation process is well underway, more 
rapid drop growth can also occur by interactions 
between large drops. These interactions are more 
complicated and probably not well described by 
the model. 
It is possible that the high collection effi- 
ciencies we obtain may arise from large drop 
interactions that are not properly accounted for 
by the model. We discount this possibility, how- 
ever, for our observations concern the first drops 
to fall from the cloud during the beginning of 
the precipitation process. At the time of our ob- 
servations the concentration of raindrops was 
quite low (possibly 0.3 drops m™), and the con- 
centration of rain water was but 0.005 that of 
the cloud-hquid water content. It is doubtful 
that interactions between big drops are im- 
portant during this period and it appears to us 
that the assumptions of the model are justified. 
We believe that the high collection efficiencies 
indicated by our observations may arise from the 
