1192 
surface increases, the percentage of the droplets caught 
in the swept-out volume decreases and the percentage 
of the total body area wetted decreases. Increases in 
the radius of the leading edge also have the effect of 
limiting the impingement area to the region near the 
forward stagnation pressure point. 
Conditions for Ice Formation. When supercooled drop- 
lets impinge upon the surface of an airplane component, 
the formation of ice follows at a rate determined by the 
temperature gradient in the immediate environment 
and the thermal conduction through the gaseous and 
solid boundaries. It is apparent that the average en- 
vironmental temperature must be below the melting 
point of ice. If the droplet freezes quickly upon impact, 
the shape of the formation will be determined by the 
droplet impingement pattern; however, if freezing is 
delayed somewhat after impact, part of the droplet 
will flow along the solid surface and freeze at a point 
farther in the rear. The time required for the droplet 
to freeze therefore determines the shape and the loca- 
tion of the ice, both of which are significant factors 
in determining the effect of ice on airplane performance. 
The temperature of the air particle on the surface of 
an airplane differs from that of the ambient region 
because of the velocity of the stream; this departure is 
a function of the second power of the velocity in addi- 
tion to other factors. Factors in the boundary layer 
that determine the temperature of the air particle 
on the surface include the conversion of the kinetic en- 
ergy of the gas particle to thermal energy, the con- 
version of mechanical energy or work to thermal energy 
in the viscous boundary layer, and the conduction of 
heat through the gaseous boundary layer. The combined 
action of these factors determines the recovery tem- 
perature of an air particle on the surface of a body in 
an air stream; however, it should be noted that the 
heat involved in the phase changes of the water droplet 
on the surface and conduction through the solid boun- 
dary have thus far not been considered. 
When the supercooled water droplet strikes the solid 
boundary, the mechanical disturbance to the droplet 
causes the phase change to ice. If it is assumed that 
there is no exchange of heat with the environment and 
that the droplet temperature rises to 32F during the 
freezing process, the percentage of the droplet under- 
gomg the phase change will be proportional to the 
ratio between the degrees of supercooling of the droplet 
when it struck the surface and the latent heat of fusion. 
After impingement, evaporation from the droplet 
starts. The rate of evaporation is determined by the 
difference between the vapor pressures at the droplet- 
air interface and in the ambient region. The evapora- 
tion of water from the droplet after impact absorbs 
heat. (It is to be noted that the temperature and vapor 
pressure at the droplet-air interface are interrelated 
and that calculations for one must start with an as- 
sumed value for the other from which increasingly ac- 
curate evaluations may follow by successive approxi- 
mations.) 
The flow conditions that may exist along the surface 
of an airplane component such as a wing include the 
CLOUDS, FOG, AND AIRCRAFT ICING 
stagnation region at the leading edge, a laminar region 
also near the leading edge, a turbulent region following 
the laminar one, and in some cases, a turbulent sepa- 
rated-flow region. It may be concluded from the fore- 
going discussion that the temperature on the air-water 
interface of a droplet is affected by frictional heating, 
by conduction through the boundary layer, and by 
heat absorbed in evaporation. These effects differ in 
magnitude and in relation to each other in the different 
flow regions. It therefore follows that the temperature 
of the air-water interface differs for various points on 
the surface of a component along a line parallel to 
the stream flow, because the only other factor arising 
from the moving stream—the conversion of kinetic en- 
ergy to thermal energy—remains constant at all points 
on the body. It may be further concluded, therefore, 
that the rapidity with which the water is converted to 
ice varies for various locations on the surface of an 
airplane. Inasmuch as all the factors involved in these 
variations are functions of the velocity, increasing the 
velocity increases the variations. It is further apparent 
that if different points on a component move at different 
velocities (e.g., the points along the radius of a pro- 
peller or helicopter blade), still another factor exists 
that causes surface-temperature variations and there- 
fore variations of freezing conditions. 
The discussion has been presented without a con- 
sideration of the flow of heat through the solid bound- 
ary. Obviously, if heat is applied or taken away 
through the solid boundary, the conditions for icing 
will be affected. When the solid boundary is a thermal 
conductor, which it usually is, variations in the de- 
parture from ambient temperature on the air-water 
interface or on a component surface produce thermal 
gradients in the solid boundary layer and a flow of 
heat from the hottest region to the coldest. Thus 
heat flows from the tip of a metal propeller blade to 
the hub region. Likewise, because the recovery tem- 
perature on the leading edge of an airfoil at the stag- 
nation point 1s higher than in the laminar region, heat 
will flow rearward in a metal skin, and icing will be 
more rapid at the leading edge than would be explain- 
able by the conditions of that local region. 
Although of minor importance, the heat from the 
sun and other sources of radiant thermal energy and 
the kinetic energy of the impinging water droplet when 
converted to thermal energy also affect the conditions 
for icing on the surface of an airplane. 
Because not all of the droplet will freeze immediately 
in most encounters with icing, the liquid water will be 
subject to abrasion by the air stream, which may blow 
away in the boundary layer a part of the droplet re- 
maining in the liquid phase or move some of the liquid 
along the airfoil surface in the direction of the moving 
stream. The smoothness of the surface will affect this 
factor. Also, part of a droplet, particularly if it is a 
large droplet, may bounce away from the solid bound- 
ary (in part or entirely) upon impact and re-enter the 
boundary air. It is possible that droplets contained in 
the laminar streamlines of the boundary layer and 
near the leading edge which have zero or negative 
