The Mechanism of Hail Formation 
RAYMUND SANGER 
Swiss Federal Institute of Technology, Zurich, Switzerland 
Abstract—Critical considerations of the Ludlam model for producing large hailstones 
are presented. In connection with the results of the work on turbulence by Kolmogoroy, 
von Karman and Heisenberg, it is questionable whether the procedure of how the water 
content of supercooled droplets is transported onto neighboring ice particles occurs ac- 
cording to the laws of molecular diffusion. The significance of the Bergeron-Findeisen 
mechanism for producing precipitation 1s mentioned and referred to the newest ex- 
perimental finding on the structure of hailstones. 
In a recent article Ludlam [1958] goes very 
thoroughly into the problem of hail formation 
and comes to the conclusion that the formation 
of large hailstones is due exclusively to droplets 
present near the base of Cumulus clouds and 
having a radius of 20-30 », particularly when 
these are very sparsely scattered with an inci- 
dence of less than 10°/em*. These particles, 
which lie at the large end of the drop spectrum, 
are therefore to be regarded as the initial par- 
ticle or embryo of the large hailstones. Ludlam 
bases his observation on a model of the way 
showers are produced, which in all essentials cor- 
responds to the all-water precipitation process 
of the kind most recently employed to explain 
the origin of warm rain where the solid phase of 
the water does not appear at all. Since the 
fundamental features of all such models are de- 
rived from theoretical considerations, idealizing 
isolated aspects of a natural process and there- 
fore representing only an approximation to re- 
ality, there is always the danger that conclusions 
may be drawn on which too much reliance is 
placed. And precisely the inference already re- 
ferred to, namely, that large hailstones owe 
their origin entirely and only to the sparse pres- 
ence of relatively large droplets around the 
cloud base, should properly be treated with some 
scepticism. 
By introducing thermals into the pattern of 
air currents, Ludlam has overcome the difficul- 
ties which arise in explaining the production of 
showers by means of the air-parcel theory and 
the related concept of air columns existing in- 
side Cumulus clouds in the form of a steady up- 
draft. At the same time it also becomes possi- 
ble to understand the discrepancy between the 
values for temperature and liquid-water con- 
tent measured inside the clouds, and the values 
30 
calculated in accordance with the parcel theory 
as an adiabatie process. (The origin of these 
vortex motions Ludlam sees principally in lo- 
cally conditioned increases in temperature or in 
instability accompanying an atmospheric front.) 
Cloud particles of initial radius 20-30 p, may, 
if they are favorably placed at the start, grow 
to such an extent while they are within the 
thermal (reaching a radius perhaps of 150 ,) 
and gather such a speed of fall (1-2 m/sec), 
that they escape the general erosion of the ther- 
mal which sets in when it reaches the top of the 
cloud; and they are then caught up in the 
course of falling by the following thermal, and 
continue to grow into precipitation particles or 
drops of water. In this way the particles of pre- 
cipitation have time to pick up the necessary 
amount of water despite the usual deficiency 
(in fact) in the fluid-water content by contrast 
with the adiabatic values, yet without having to 
climb to any considerable height and thereby 
run the risk of reaching the —40°C level where 
spontaneous glaciation prevents any further 
growth. 
In the mechanism of shower formation which 
has just been described, the initial particles are 
already of such a size that growth can in prac- 
tice only take place through coalescence with 
other particles, while the condensation of water 
vapor on the particle is only of secondary im- 
portance. (We shall return later to the diffu- 
sion of water vapor in the Bergeron-Findeisen 
process.) For this mechanism of shower forma- 
tion it is unimportant whether and where the 
particle, during its growth into a particle of 
precipitation, undergoes freezing, which may be 
initiated by the presence of some foreign ice 
particles or ice-forming nuclei. Nor is it of any 
consequence in this connection whether the 
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