PHYSICAL BIOCLIMATOLOGY 
where k is the thermal conductivity of the air; U = 
ved/u, Reynolds number; u is the viscosity of the air, 
and d is the diameter of the cylinder or sphere, or the 
trunk width of the human body. The exponent n de- 
pends on the structure of the air flow. For the range 
which is of interest to us (10? < U < 10°) the following 
values have been found: 
G n References 
Cylinder, normal to axis.. 0.35 0.56 [72] 
SLOINEIES Gog o Oe A Ores ene arene O70 O.5% [13, 16, 19] }(1a) 
Human body, supine, nude. 1.0 0.54 [18, 16, 19] 
Under normal conditions, for the supine adult, we 
find approximately [13]: 
ha = 6.3 ~/v Cal m “hr * (deg C) +, (2) 
where v is expressed in kilometers per hour and is 
greater than 2 km hr. In these measurements [13], 
the exposed surface is taken as fifty per cent of the 
geometrical surface. More recent measurements made 
for sitting persons [84] and standing persons [63] showed 
values of 5.5+/v and 3.9+/», respectively. The scatter 
in the factors (6.3, 5.5, and 3.9) is caused by differences 
in the methods used for determining the area from 
which heat is lost. 
Siple [27, 79] used the heat of fusion of water to 
determine the ‘wind chill” which, actually, is the 
cooling power at sub-zero temperatures. In his ant- 
arctic experiments he found the formula, 
h = 10.9./v + 9.0 — v. (2a) 
He used sas a measuring device a cylindrical vessel 
which contained the water to be frozen. The plastic 
wall, one-eighth of an inch thick, has to be considered 
as a thermal insulator, or the whole instrument may be 
thought of as a clothed cooling device. Therefore, equa- 
tion (15) (see below) should be applied with S = 0 
and h, = 5 Cal m~ hr’. Best agreement with the 
measurements [27, 79] can be found by writing equation 
(15) in the form: 
1 
We Fy + He 
where h, = 5, ha = 9.0./v, and h. = 80, all in Cal 
m hr (deg C)* (v in km hr). The values of Aa 
and h, thus extracted from the experiments fit the 
data to be expected for a cylinder of this size and a 
plastic wall of this thickness. 
According to equation (1), the local value of hy 
is large for highly curved surfaces such as the fingers. 
Moreover, ha decreases with decreasing atmospheric 
pressure. 
In the absence of forced flow, the higher surface 
temperature in itself produces convection. From the 
law of similarity and from experiments we obtain 
food _ OG, 3) 
k 
G = d'gp (3s = dh) lige Ti 
Ute Onis On) / 25 
g = acceleration of gravity, 
3; = skin temperature, 
Ja = air temperature. 
(2b) 
ll 
1113 
Values measured in calm air give 
c = 0.37 for cylinders [72], 
ec = 0.44 for spheres [13]. 
Because of body motion and other sources of air 
flow, the human body is rarely surrounded by com- 
pletely calm air, and hence equation (3) is rarely 
applicable. Actually, in rooms of normal size and in 
calm air, a value of ha = 3.3 Calm” hr’ (deg C) 
was found for recumbent adults and h, = 3.9 Cal 
m hr (deg C)* was found for recumbent children 
[13, 16]. A value of ha = 2.0 Cal m™~ hr * (deg C)* 
was found for seated persons, on the basis of the 
geometric instead of the projected surface [84]. In 
narrow containers, such as calorimeters designed for 
human subjects, even smaller values have been ob- 
served [64]. 
Heat Transfer by Evaporation. Analogous laws are 
applicable to the evaporation of moisture from the skin 
to the air. The numerical values for boundary layer 
and austausch may be applied here. For the vapor 
transfer coefficient 
Ig = V/(@s — ea), 
where V is the heat loss (m Cal m~” hr‘) by evapo- 
ration, and e, and e, are the vapor pressures of skin and 
air, respectively, theory and measurements [10, 11] 
yield the value: 
lin = 108 fh, Cell ta lore > sal) (4) 
Experiments reveal that either the skin becomes wet, 
owing to active secretion of sweat glands, or water 
diffuses through a slightly permeable membrane at the 
surface (presumably the stratum granulosum). The 
second process, the so-called perspiratio insensibilis, 
is almost independent of wind, since the diffusion re- 
sistance is considerably greater in the skin than in the 
boundary layer of the air [19]. On the other hand, this 
portion of heat transfer by evaporation apparently in- 
creases with increasing #,, the saturation vapor pres- 
sure at skin temperature. If f denotes the wet portion 
of the total surface, and ¢ is a constant, then 
V = [fhw + c(1 — f)] is — @a). (5) 
Equation (4) applies only at sea-level pressure. Ac- 
cording to equations (1) and (1a), ha is nearly propor- 
tional to 7p and thus decreases with altitude. How- 
ever, since equation (4) contains the diffusion constant, 
which increases as 1/p, we find h, < 1//p. We thus 
find an increase of the vapor transfer coefficient with 
height. In view of the fact that the perspzratio insens?- 
bilds is independent of h,, the well-known desiccation 
at high altitudes must be attributed less to this factor 
than to the decrease in ég. 
Heat Transfer by Radiation. Radiation from the 
sun and sky, and solar radiation reflected from the sur- 
roundings (S) cover the spectral range between 0.3 u 
and 3 yw; radiation of the skin and terrestrial objects 
(R), that between 3 » and 50 uw. The optical constants 
for the skin differ widely for S and R: the mean energy 
albedos are 0.35 and 0.04, respectively [16, 42]. The 
mean absorption coefficients for incident solar and ter- 
restrial radiation are 7 cm‘ and 100 em “, respectively, 
