PRECIPITATION ELECTRICITY 
Before integration of this expression is possible, the 
distributions and the velocities of fall must be ex- 
pressed as a function of the gravitational forces and 
electric field. Under most conditions, the velocity of 
fall may be determined from the terminal velocity of 
fall of a spherical body im the earth’s gravitational 
field together with known values for the electric field 
and the mobility of the particle. The terminal velocity 
of fall, V, for droplets of various sizes has been accu- 
rately determined and may be read from tables [6]. 
The mobility w is defined as the velocity of the particle 
in unit electric field, whence one may write approxi- 
mately 
v= V+ u#. (6) 
Thus, droplets carrying charges of one sign move faster 
than their normal terminal velocity, while those of op- 
posite sign move slower. Substituting this approxima- 
tion in (5), assuming that the droplets are all the same, 
and integrating, one finds that the electric field in- 
creases with the time ¢ in accordance with the following 
relation, 
GW — 
N4Q4V 4 E + aan 
M+Q4V + 
gee nga 1 aL pact | (7) 
N_QU_ 
E= 
—4r[o—n_q_u_(1+(n1,¢4u4)/(n_q_u_))]t 
[le ae h 
whence, approximating, the maximum equilibriwm field 
is given nearly enough by 
_ Bole = Vo 
ee GF WG (8) 
where all quantities are now expressed as positive num- 
bers. Attention is drawn to the fact that the selection 
of signs given above is arbitrary, and that in nature a 
negative instead of a positive charge frequently comes 
down on rain. 
In interpreting equation (7), it is noted that when 
the positive carriers are small and have very low ter- 
minal velocities of fall, their actual velocities closely 
approximate the velocities of the carriers of negative 
charges. Thus the difference mm terminal velocities be- 
comes small, and the electric field approaches zero. In 
nonprecipitating clouds, therefore, one would expect 
that the measured electric fields would be very small; 
this is in accordance with direct observation [16]. When 
the rain droplets become reasonably large, the electric 
fields increase to large values. In fact, according to 
equation (7), the electric field is proportional to the 
rainfall intensity and to the free electric charge carried 
by the larger droplets. Since the negative carriers are 
very small compared to a raimdrop, one may ignore 
their velocity and calculate Table II from equations 
(1) and (8), using the best available data [13, p. 94] to 
show how the equilibrium electric field increases with 
the size of the raindrop. It is interesting to note in 
Table II that, while cloud droplets produce a negligible 
field, the equilibrium field for large droplets is great 
133 
enough to produce a discharge in air and thus initiate 
lightning. Equation (8) is therefore consistent with 
observation. 
Using balloons, Simpson and Robinson [26] made 
measurements purporting to show that the electric 
fields inside active electrical storm clouds are “of the 
order of 100 volts/em.” This conclusion is seriously in 
error, for actual measurements in aircraft show that 
fields of 1000 v em commonly occur in such clouds 
without producing a lightning stroke [16]. The electric 
field on the belly of a B-25 aircraft at the beginning of 
an energetic lightning stroke has been measured as 
3400 v em [14]. 
Tasue II. Evecrric Fizrup anp Dropiet Size 
Electric field to 
support droplet, 
Maximum 
Droplet radius equilibrium electric 
(mu) (v cm-) field (v cm) 
Noy wep core en Ganda 5 X10 1,500 0.5 
IDMBA®s oocococece il $< 1WO-% 24,000* 10.8 
Medium rain...... & X< 102 24, 000* 1,930 
Excessive rain....| 1X 107 24,000* 24,300* 
* Because the effective dielectric strength for long discharge 
paths in air approximates only 3000 v cm™, active lightning 
strokes would prevent such high values of electric field from 
maturing. 
From equation (7) it can correctly be inferred that 
an increase in the conductivity of the atmosphere will 
reduce the generated electric field. It is not impossible 
that sudden localized increases in the electrical conduc- 
tivity of the air, due to a lightning discharge or local- 
ized radioactivity, would so increase the conductivity 
that the generated electric fields would be small even 
with large droplets and big free charges. Thus, light- 
ning would be suppressed. This matter requires further 
investigation and may be of importance in the artificial 
suppression of lightning discharges by localized dissi- 
pation of radioactive material into the atmosphere. 
The analysis presented above properly emphasizes 
the dual and interrelated character of thunderstorm 
electricity as compared with charge production and 
separation. Electric storm fields would not exist if 
charges were not actively separated. The analysis shows 
that separation cannot take place unless the forces 
acting on the positive charges are different from the 
forces acting on the negative charges. This implies, in 
turn, the necessity for a selective deposit of a charge of 
definite sign on rain particles and a deposit of a charge 
of opposite sign on lighter cloud particles or air mole- 
cules. 
Electrification of Aircraft Flying through Precipitation 
It was found during World War II that aircraft fly- 
ing in cold areas systematically lost all radio commu- 
nication and navigational facilities whenever they en- 
countered dry ice-crystal clouds or snow. Pilots flying 
through such precipitation in mountainous areas with- 
out usable radio navigational facilities continually faced 
dangerous situations that adversely affected the deliv- 
ery of urgent war goods to Alaska. 
Hundreds of flights made by the Army-Navy Pre- 
cipitation-Static Research Team near Minneapolis, 
