METEOROLOGICAL ASPECTS OF AIRCRAFT ICING 
ones. By assuming the form of the drop-size distribu- 
tion, it is theoretically possible to determine approxi- 
mately the degree of homogeneity of drop sizes from 
the rotating-cylinder data. In actual practice, how- 
ever, it has been found that determinations of drop- 
size distribution made in flight by this method are not 
reliable [14], although satisfactory results have been 
reported from Mount Washington [7]. Comparisons of 
values of maximum drop-diameter, obtained from the 
width of the area of drop impingement on a stationary 
cylinder, with values of the mean-effective diameter 
simultaneously determined by the rotating-cylinder 
method indicate that most clouds do not contain sig- 
nificant amounts of liquid water in the form of drops 
appreciably larger than the mean-effective diameter. 
For practical purposes, therefore, in the study of icing 
conditions, most clouds may be regarded as composed 
of uniform drops.! 
The Concentration of Liquid Water in Clouds 
In general, the formation of clouds is brought about 
by cooling due to the adiabatic ascent of air. For a 
strictly adiabatic process, without mixing or precipi- 
tation, the concentration of liquid water at an altitude 
2 1s given by the following equation: 
(3) 
where wz is the liquid-water concentration (g¢ m7) at 
altitude 2, p. is the density of dry air (kg m-) at alti- 
tude z, x, is the saturation mixing ratio (g ke) at 
the condensation level, and x, is the saturation mixing 
ratio (¢ ke!) at altitude z. Calculations from this 
equation indicate that the most important factors de- 
termining the liquid-water concentration in adiabat- 
ically lifted air are the temperature at the condensation 
level and the vertical distance above the condensation 
level. The actual altitude of the condensation level is 
of minor importance. Values of w, calculated by equa- 
tion (8), are presented in Table II. These values are 
We = pz (Ge — Lz), 
Tasuy II. Liquip-Watrer ConceNTRATION IN ADIABATICALLY 
Lirtep Atr* 
Vertical distance Temperature at condensation level 
above condensation 
bevel —20F | OF 10F 20F 30F 40F 
ft gms g ms gm gm gm gms 
1000 0.09} 0.18} 0.26) 0.85] 0.44 | 0.53 
2000 0.17 | 0.34] 0.48] 0.65] 0.83 1.01 
3000 0.22 | 0.47] 0.67 | 0.92 1.18 1.44 
4000 0.27 | 0.57) 0.82] 1.138 1.47 1.82 
6000 0.32 | 0.71 1.04 1.46 1.93 2.47 
* Condensation pressure = 850 mb. 
based on a condensation level at a pressure altitude of 
4780 ft. In actual clouds the processes of precipitation 
as well as the entrainment and mixing of drier air both 
act to reduce the liquid-water concentration below the 
values based on adiabatic lifting; hence these values 
1. This conclusion is based on data taken in flight. Observa- 
tions on Mount Washington indicate a considerable frequency 
of nonuniform drop-size distributions [7, 8]. 
1199 
should be regarded as maxima which may be ap- 
proached under certain conditions but are very un- 
likely to be exceeded. 
In a study of the physical factors which influence 
the amount of liquid water in clouds, it is convenient 
to consider three classes of clouds, based on the three 
principal processes by which air may be lifted, namely, 
convection, turbulence, and horizontal convergence of 
the velocity field. 
Clouds Formed Primarily by Convection (Cumulus and 
Cumulonimbus). As long as no precipitation occurs, the 
concentration of liquid water in cumulus clouds is de- 
termined mainly by the temperature of the cloud base, 
the vertical distance above the base, the amount of 
entraiment and mixing, and the humidity of the en- 
vironmental air. Recent studies [2] indicate that the 
lapse rate in cumulus clouds is usually very close to 
that of the environment, and that the amount of en- 
trainment increases as the lapse rate exceeds the moist- 
adiabatic. The conditions for maximum liquid-water 
concentration are, therefore, a lapse rate only slightly 
in excess of moist-adiabatic and high relative humid- 
ity in the environmental air. Under these conditions 
the liquid-water concentration sometimes closely ap- 
proaches the value based on adiabatic lifting. 
In general, the effect of entrainment is to reduce the 
liquid-water concentration below the adiabatic value, 
and this effect increases from the base to the top 
of the cloud. The result is that the greatest values 
of liquid-water concentration occur at a distance above 
the cloud base of from one-half to three-fourths the 
height of the cloud, instead of at the top. The horizon- 
tal distribution of liquid-water concentration across 
cumulus clouds has not been accurately determined 
because instantaneous measurements have not been 
made. However, it would appear reasonable to suppose 
that the central portions of an updraft would be least 
affected by entrainment and would therefore have 
higher liquid-water content than the outer portions. 
The effect of the formation of ice crystals in cumulus 
clouds, as in all other types, is a rapid reduction in the 
liquid-water concentration. The transformation from 
liquid drops to snow usually proceeds quite rapidly 
once it begins, frequently reducing the liquid-water 
concentration from over 1 gm~* to about 0.1 gm 
in twenty minutes or less. The formation of ice crystals 
is one of the most important factors limiting the icing 
hazards in cumulus clouds. Careful observation of cu- 
mulus cloud development indicates that individual cu- 
mulus congestus towers seldom remain in that stage 
longer than ten to fifteen minutes; they generally either 
subside and evaporate or change to ice crystals within 
that time. 
Clouds Formed Primarily by Turbulence (Stratus, Stra- 
tocumulus, and Altocumulus). Clouds of this type are 
formed in the upper portions of certain layers of air 
which are mixed by turbulence. This may be the sur- 
face turbulence layer, as is usually the case with stratus 
or low stratocumulus, or a higher layer which becomes 
unstable as a result of lifting, differential advection, 
or some other process. In the ideal case, in which the 
