TMERMitL S4LANS1 Qr TME BODY 108829 
Thermal Balance of the Human Body and its 
Application as an Index of Climatic Stress 
Climatology and Environmental 
Protection Section 
Military Planning Division 
Office of The Quartermaster General 
20 August 19A5 
Authors: 
Jesse H. Plummer, Ph. D. 
Margaret lonides 
Paul A. Siple, Major, QHC THE THERMAL BALANCE OF THE hUlAN BODY AND ITS Ai'PLICATION 
AS AN INDEX 01' CLliiATIC STRESS 
The study of the effects of climatic stress upon the individual has 
occupied the attention of physiologists for the last hundred years. Since 
the outbreak of the present war the problem has become much more pertinent 
owing to the military necessity of maintaining large bodies of men in 
different climatic zones. Furthermore, it is frequently necessary to trans- 
port the same group from one climate to another, in which case accurate 
estimates of the new clothing requirements are essential. 
One means of attacking the problem of developing such an index is 
through an analysis of the heat transfer from the body to the surrounding 
environment. This has been studied experimentally at the Pierce Laboratory 
(l) and the results extrapolated to a wider range of environmental conditions 
by the Research and Development Branch of the OQMG. (2) The latter report 
outlines* the basic principles of the problem but leaves many of the details 
to the imagination of the reader. It is the purpose of this paper to fill 
in some of the omissions and to illustrate means of simplifying the cal- 
culations so that the utility of this type of index may be fully realized. 
The fundamental equation for the heat balance is: 
1. m*C=E*C+H in which 
M is the metabolic rate, 
D is the change in the stored heat, 
E is the evaporative heat transfer, 
C is the convective heat transfer, and 
R is the transfer by radiation. 
This equation simply states that the quantity of heat transferred is 
equal to the sum of the quantities transferred through each of the avenues 
of heat loss. Caution must be exercised in the application of the equation 
as M and E are the only terms which are always positive. D, C, and R may 
be either positive or negative, depending upon the direction of flow. Con- 
duction through the clothing is neglected since its inclusion would lead to 
counting the same quantity twice. 
To clarify this point further Fig. 1, which is a diagram of a cross 
section of an insulated pipe, may be considered to represent a man. The 
interior of the pipe corresponds to the deep body tissues, the pipe wall to 
the surface tissues, and the insulation clothing. Surrounding the whole is 
a mass of moving air. 
If the temperatures within the system are not changing with respect to 
time there is no change in the stored heat and if M represents the steady 
heat loss from the interior of the pipe. t3 
*2 
r2 T3 
I 
P 
P 
I 
N 
I 
INTERIOR 
I 
w 
a 
r 
P 
S 
u 
E 
E 
U 
L 
of 
AIK 
A 
If 
V« 
A AIR 
T 
A 
A 
T 
I 
L 
PIPE 
L 
I 
0 
L 
L 
0 
N 
N 
FIGUhE 1. 
2. U = TX - T2 s T? - T3 : (T3 - (_l + in which 
lint Ic la lr 
T-j_ is Ihe temperature of the interior, 
T2 is the temperature of the outer surface of the pipe, (skin 
temperature), 
T3 is the temperature of the outer surface of the insulation, 
(clothing layer), 
is the temperature of the atmosphere, 
lint 1® t*le thermal resistance of the pipe wall, (Surface tissues), 
10 is the thermal resistance of the insulation, (clothing layer), 
Ia is the thermal resistance to the flow of heat by convection from 
the surface of the insulation, and 
Ir is the resistance to the flow of heat by radiation from the 
surface of the insulation. 
The te peratures T]_ and may be accurately measured regardless of 
whether the figure represents a pipe or an approximation to a man. T3 may 
be measured, but less accurately, while To is not readily obtained. Ia 
and Ic may also be measured, but Ir must be obtained from other data. * 
Eliminating T3 from eq. 2 results in: 
3. - = Ie_zJa 
Ic * 1 
li L 
!a Ir Now, Ia, Ir and are environmental factors for their values may be 
determined when the air temperature, wind velocity, atmospheric pressure, 
and the .temperature of the surroundings are known. M and ?2 are internal 
variables whose values are set by the conditions of the problem, and Ic 
is a variable which may be increased or decreased to provide the necessary 
protection. For instance, if the environment together with the rate of 
heat production are specified and T2 must remain above some limiting 
temperature, the value of Ic may be found from eq. 3 which will maintain 
T2 at the limiting value. The value of Ic necessary to establish equili- 
brium becomes a measure of the severity of the environment and as such is an 
index of climatic strain. 
Consider the situation in which Ic is either zero or possesses some 
definite value. Consider also that T2 has a fixed upper limit which cannot 
be safely exceeded. Then, for any environment there will be a maximum value 
for M which cannot be exceeded without increasing T2 above its safe limit. 
This maximum value of N is also an index for defining the severity of 
climatic strain. 
Either of these indices could be used but the heat transfer from human 
beings, while it is analogous to the loss of heat' from pipes, also takes 
place through other channels. These other factors which must be considered 
are: 
1. The evaporation loss Es from the skin. 
2. The evaporation loss E]_ from the lungs 
3. The heat A transferred by warming or cooling inspired air. 
Items 2 and 3 represent direct transfer from the interior of the body and 
may be accounted for in eq. 2 by replacing M by M - El * A. 
The loss of heat through evaporation from the skin is more difficult 
to handle because of the need for specifying where the evaporation occurs. 
If the clothing is dry and the evaporation proceeds at the skin surface 
eq. 2 must be replaced by* 
A. M - El ♦ A = Ti - T2 = E ♦ T2 - . e + (l_ ♦ JL) 
lint Ic !a Ir 
If, on the other hand, the clothing is saturated and the evaporation takes 
place at the outer surface eq. 2 becomes: 
5. U - E-l * A » Tx - T2 = T2 - T3 = E ♦ (T3 - (1. ♦ _1_) 
Tvr u r in which the brackets have been placed around Ic to indicate that its 
value has been changed because of the saturation with sweat. 
In the preceding discussion the units have not been mentioned, but 
the equations hold for any consistent set of units. If a mixed system is 
used appropriate numerical factors must be inserted where necessary. 
The temperature of the clothing surface Ts may be eliminated from 
eq. 4 with the result: 
4a. B - EX ♦ A * E ♦ 3.09 (T2 - T^) 
* 1 
_1_ - _i_ 
la Ir 
in which Ic has been replaced by Ido and all resistances should be expressed 
in do units, temperatures in degrees F., and energies in Kg. Cals, per 
square meter per hour. The factor 3.09 is a conversion constant brought in 
by the nixed units. 
The same may be done with eq. 5 resulting in: 
- £i - *: ,-4=—. ♦ *■<» - tt) 
Ici° Uoio) * _i 
uIr u. * a. 
la lr 
in which the units are the same as in eq. 4a and the brackets have been 
?laced around Ic]_0 to indicate that the resistance of wet clothing is 
o be used. 
Frequently it is convenient to express these equations in terms of 
thermal conductances in which case equations 4a and 5a become: 
4b. U - % ♦ A = B * T2 - Ta 
+ JL 
cclo 0a ♦ Cr 
5b. k - E]_ * A s F ♦ T2 - T^ 
1 * Ca + Cr Cdo + -I— — 
Cdo °a * r 
2 
in which Cclo is the thermal conductance of the clothing in Kg. Cals/m/°F/hr., 
CQ and Cr are the surface conductances due to convection and eradiation 
respectively in the same units, temperatures are expressed in °F., and 
energies in Kg. Cals/m2/hr. Conductances in these units are related to resistances in do by the relation; 
6. Conductance : 3.09 
resistance in do 
Upon conparing equation 4b with 5b, it is apparent that the values 
assigned to E are not necessarily the same/ The letter E merely represents 
the quantity of heat lost through evaporation and nay have any value con- 
sistent with the assumptions that in eq. 4b the evaporation is proceeding at 
the skin surface and in eq. 5b the evaporation occurs at the surface of the 
clothing. For that reason the factor 1 multiplying E in eq. 
5b should not be interpreted as an 1 ♦ Ca ♦ Cr evaporative efficiency 
factor. Instead this term is actually qc1q a measure of the change 
in heat transfer by radiation and convection caused by 
the change in T3. 
Figure 2 illustrates the point. If the clothing 
layer between T2 and T- is considered to be sat- 
urated, but no evaporation is taking place, the 
temperature gradient will be as shown by the 
solid line. Suppose now that evaporation occurs 
at +he clothing surface, because of the increased 
hekt flow through the clothing, the temperature 
gradient must increase, and, if Tj and 1/ are 
constant. Ta must fall and reduce the value of 
('Ij - Tj. decrease in t he differential 
decreases the convective and radiative transfer. 
Equation 5 shows, however, that it is possible to compute the total 
loss by evaluating the effect of convec+ion, conduction, and radiation exactly 
as though evaporation were neglected and then compensate for this neglect by 
multiplying E by the term 1 E must be evaluated as the evap- 
oration from a surface 1 » Ca * Gr at the temperature Tj. T, can 
only be expressed in Gci0 terms of E or tl, but its value 
together with that of E may be found from equation 5 
by trial and error. 
So far these equations are quite general, the only assumptions that 
have been made concern the location of the area from which evaporation occurs 
and that the effect of radiation can be expressed in terms of conductances or 
resistances. The latter is equivalent to assuming that there is no solar 
or sky radiation and that surrounding temperatures are approximately air 
temperature. For conditions in which radiation must be considered separately 
equations 4b and 5b become: 
4c. w - Ei 1 A = E + To - T, ♦ _R 
jrrt a_ 
Ca cclo 5c. u - Ei * a = a * -■ ♦ Iz.. * h- 
1 _ia_ -1_ ♦' I . 
t<clo Cclo Ca 
in which R is considered positive if its net effect results in a transfer 
of heat from the body to the surroundings and negative if the reverse is 
true. In these equations the factor 1 which multiplies R in 
equation Ac and K * E in equation 1 * Ca 5c enters for precisely the same 
reasons as the factor 1 Ccl0 multiolying E in eq. 5b. 
1 * Ca * Or 
Equations Ac and 5c may also be used with equation 2 to eliminate T2 
or skin temperature.- V/hen this is done we have the followings 
Ad. U - Ei t A = 3.09 (Tj - TL) * E (Iclo * Ia) Ma 
Int * Icio ♦ la 
5d. M - E]_ t A = 3-09 (Tj - TA) + (E ♦ R) Ia 
Int Iclo + 
Equations Ad and 5d express the thermal balance of the body as a function of 
the temperature differential between the interior of the body and the atmos- 
phere, the various resistances of the system, and evaporation and radiation. 
If each of these individual factors may be measured, equations Ad and 5d 
may be used to determine an index of climatic strain. Exactly which terra is 
used to define an index may depend upon the particular problem. For cold 
weather conditions Ido appears to be the most logical choice, which is 
equivalent to describing the environment in terms of the protection req\iired 
to sustain a given metabolic rate. For hot weather conditions there appear 
to be two choices, either of which would be satisfactory. For given atmos- 
pheric conditions, E may be found and the maximum value of the metabolic 
rate used as an index of the severity of the climate, or if the metabolic 
rate is fixed the required value for evaporation may serve as an index of 
climatic strain. 
burton (3) lias discussed these possibilities and has shown tnat there 
is no simple relationship existing between the two except at limiting 
metabolic rates. 
The primary reason for the complexity found by Burton arises from the 
attempt to evaluate evaporation in terms of comfort or wetted area and also 
the effect of clothing on evaporative heat loss, furthermore, the evapora- 
tive loss and the metabolic rate are closely related since in a given en- 
vironment an increase in metabolic rate will cause an increase in internal 
temperature which will be followed by an increase in skin temperature and 
an increase in evaporation. The Evaluation of Ca and la 
The basic deteminations of these factors for the human body both clothed 
and unclothed were made by Winslow, Herrington, and Sagge (U) for wind veloci- 
ties between 8 and 100 feet per minute and in a relatively restricted tempera- 
ture range. Burton (5) extended these values and calculated Ia for various 
altitudes or atmospheric pressures and showed that the effect of temperature 
was small. 
The Research and Development Branch of the 0QM3 developed the relation 
for Car 
7. CaD 1 / 0.U07 /DVR\£ / ,00123 /DVR\in which 
T= 
Ca is the surface conductance 
k is the thermal conductivity of air at the interfacial temperature 
R is the density of air at the interfaolal temperature 
u is the viscosity of air at the interfaoial temperature 
Q is the cylinder diameter 
V is the wind velocity 
and any consistent system of units may be used to evaluate each of the terms. 
Cylinders ware used for this derivation for their shapes more closely 
approximates that of the human body than either spiieres or flat planes which 
are the only other f orms for which convective constants are known over a wide 
range of wind velocities. Comparison of this equation with physiological data 
indicates that the convective heat loss from the body is very close to that 
of a three inch cylinder within the limits of the experimental conditions. 
For this diameter the expression deviates from experimental results of cylinders 
ty less than for wind velocities between one tenth and fifty miles per hour. 
Equation 7 in spite of its complexity possesses the advantage that the 
effect of pressure and temperature variations can he calculated for any cylinder 
diameter, and both are functions of the diameter of the cylinder under test. 
Variations in the moisture content of the atmosphere will also cause small 
changes in the surface conductance. The available data is insufficient to 
provide an accurate estimate of these changes but they are probably of the 
order of 1$ or less. The density of the atmosphere increases with an increase 
in moisture content, but this is offset by an increase in viscosity. The 
thermal conductivity of water vapor at 212°F is approximately "}Q% less than 
that of dry air so that in the concentrations usually found in the atmosphere 
its effect must be very small. Fig. 3 shows the relation between the convective heat loss and wind vel- 
ocity for a three inch diameter cylinder with surface temperatures of 0°F, 
60°F, and 120°F. The factors used in this calculation are given In Table I 
and have been taken from McAdan (6) and International Critical Tables. 
Altitude 
Ft, 
Tgmp. 
Table I 
FACTORS USED IN CALCULATION CF SURFACE 
HEAT TRANSFER COEFFICIENTS 
Thermal Conductivity of Air Density of Air 
B.t.u.Ar./ft./°F/ft. lb,/ft. 
Viscosity of Air 
lb./hr./ft. 
0 
0 
.0132 
.0863 
.0392 
0 
60 
.011*7 
.0763 
.01*33 
0 
120 
.0161 
.0681* 
.01*72 
5,000 
1*2.2 
.011*3 
.0656 
.01*21 
10,000 
2l*.3 
.0138 
.0561 
.01*09 
15,000 
6.5 
.0131* 
.01*79 
.0397 
20,000 
-10.6 
.0129 
.01*01 
.0385 
The same figure also shorn a plot of the equation used ty the Pierce Laboratories 
as a solid line within the region covered by experimental conditions and as a 
dotted line for extrapolation. The R.D.B. value for C« is appreciably higher at 
wind velocities above 10 miles per hour, and there are reasons to suspect that 
even this figure may be low. 
It is difficult to realise that the body loses heat at the Sanaa rate as a 
three inch diameter cylinder when both are at the same temperature and exposed 
to the same conditions. However, a man may be considered to be an assemblage 
of cylinders of various sites and, as shown in Fig. U, the surface conductance 
per unit area for small cylinders is greater than that for large ones. Further* 
more the effect of surface resistance may be considered as a motionless film 
between the body surface and the moving air stream. For low wind velocities 
this resistance will be equivalent to that of a dead air layer about two milli- 
meters thick, so that very small diameters such as the fingers effectively will 
merge together to form a single larger cylinder. With increased wind velocity 
the insulating air film will decrease in thickness so that it may well be that 
the body loses heat at the same rate as a cylinder but that there is a decrease 
in the effective diameter as the wind velocity increases. 
This reasoning is very much simplified and should not be taken too seriously. 
Nevertheless it does point to the desirability of obtaining surface conductances 
from the body when exposed to high wind velocities. 
The influence of altitude up on surface conductance may be found ty insert- 
ing the values from Table I in equation. A change in altitude also implies a 
change in temperature and the values in the Table have been calculated ty 
assuming a lapse rate of 3.56°F per thousand feet. The other factors have 
been corrected for both pressure and temperature change. The relation between conductance and wind velocity is shown in Fig. 5. These curves are quite 
similar to the ernes published by Burton (5), but are expressed as conductances 
instead of resistances. 
In fact, the surface conductance or resistances calculated from equation 
7 merely substantiate the accuracy of Burton’s figures since the difference 
between t he two sets of values is of the order of 0.1 do or less. 
The Evaluation of Iclo and Cc^Q 
These terms may be either the unknowns for which the equations are being 
solved or constants which are inserted in the equations. If they are being 
used as constants, their values for specific outfits may be found ty actual 
test following the methods outlined by Balding et al. (7) 
Another way of determining the insulating power of clothing has been pro- 
posed by Siple et al (2) who has shown that remarkably close agreement with 
experiment can be secured by careful measurement of clothing thickness and fit. 
This method is based upon the assumptions! 
1, Clothing resistance is proportional to the thickness of the cloth 
and is the same for all conventional fabrics. 
2, The effective thermal resistance of an air space within the cloth- 
ing is proportional to the thickness if the space is less than one 
fourth of an inch thick, Air spaces greater than one fourth of an 
inch are considered to have the resistance of a quarter inch space. 
3, The outer layer of clothing is either a good windbreak or the wind 
velocity is so low that its penetration into the clothing is 
negllgable. 
The first two assumptions are in good agreement with experiment and the 
third is merely a limitation of the conditions for which the method may be 
applied. Clothing resistances calculated in this way appear to be particularly 
usefvil for the following purposes. 
1, To make an estimate of the Insulating value of an outfit in the 
absence of any specific data. 
2, To make an estimate of the insulation which any garment contributes 
to a given assembly. 
3, To determine the thermal balance of an assembly for the purpose of 
correcting points which are too tight or too loose to give optimum 
protection• 
h. To indicate where additional thickness may be added to improve 
Insulation with a minimum increase in weight. 
5. To evaluate the loss of local insulation at pressure points. 6. To evaluate the component parts of linen garments. 
This method has recently been tested ty Li bet (8) mho concluded that the 
results are probably accurate within 5 or 10$. He also discusses the limita- 
tions of the method, but finds that these are not serious and that the errors 
are small and tend to cancel. Again, however, the results are based on re- 
latively few experiments and it mould be desirable to have more data so that 
the limitations of the method may be accurately determined. 
An easy may of calculating the value of the ten* 3*09 (T2 “ Tji) 
¥7 
and 3*1 (T2 - is through the use of line charts shewn in Figs. 6 and 7. 
iSo'/V" 
These charts are quite similar as the only difference is in the mind velocity 
scale which has been altered in Fig. 7 to take into account the radiation con- 
ductance of 2.6 or a resistance of 1.19 clo. If other values of radiation 
conductance are used they may be combined with the convective conductance and 
the surface resistance calculated. In this case, either chart may be used. 
The Evaluation of Terms Involving Radiation 
In attempting to calculate the radiant transfer between the body and its 
three cases must be sharply distinguished. These depend upon the 
presence of solar radiation and if this is absent upon whether or not the 
radiation to the surrounding surface must be treated s eparately from the 
radiation to the surrounding atmosphere. 
Case 1. The surrounding surfaces may be considered as black bodies 
at air temperature* 
This is the only case for which the radiant interchange may be accurately 
calculated for Hardy (9) has demonstrated that the human skin either black or 
white has an emnlssivlty of .97 or 97$ of that of a black body. Fabrics of 
wool, silk, or cotton also have high emmlssivltles which have been shown ty 
Hutte (10) to be .80 or higher. Furthermore the surrounding surfaces Indoors 
are generally covered with paint films or paper which have emmisslvlties of 
.80 to .95. Even aluminum paints have emmlssivlties between .3 and .7. These 
figures seem high but it must be remembered that they have been measured at 
approximately body temperature and that the marl man radiation intensity from 
an object at this temperature occurs at a wave length of 9 microns—well beyond 
the visible spectrum. 
In any case the emnlssivlty of the surroundings is not greatly important 
because the radiant interchange between an object and a surface which completely 
encloses it is given byj 
8. R.v[(T3)l‘-(ilt)l|]/ a, in which Is the emmissivity of the enclosed surface 
is the area of the enclosed surface 
B2 is the emmissivity of the enclosing surface 
&2 Is the area of the enclosing surface 
T3 is the surface temperature of the clothing 
is the temperature of the surrounding air and surfaces 
S is the Stefan Boltzman constant 
R is the net radiant interchange 
When B]_ and fl£ are unity this reduces to the customary form of the Stefan 
Boltzman law. Also when Dg is much larger than D3 the second term in the 
denominator approaches 0 and may be neglected. Consequently the net radiant 
transfer is controlled primarily by the emmissivity of the smaller surface. 
The numerator of equation. U may be readily evaluated from Fig. 8, which is 
a graph of the value of D], S r when Di it, equal to 1 sq. meter. This is the 
quantity of heat radiated from a black body at the temperature T to surround- 
ings at absolute 0. The quantity of heat received from the surroundings at the 
temperature is and this value may be taken from the same curve. 
The net interchange is equal to the difference between these values. 
R so obtained is measured in and is the quantity of heat 
radiated from a black body to black surroundings. Corrections for the 
emalssivlties for the two surfaces can easily be made by dividing this result 
by the denominator of equation 8. 
Radiation values obtained in this way may be substituted for R in equations 
I40 and 5c. This method depends upon a knowledge of the value of Tt. When T, is 
unknown C_ may be approximated from Fig. 6 by drawing a straight line through 
that portion of the curve which will Include both T3 and The dotted lines 
in Fig. 6 sheer three such approximations. The slope of the upper line gives a 
value of 3.5 far C*. and the error involved in using this value will be less 
than 5 Kg.Cal. per square meter per hour when both T3 and Tj, are between 30°F 
and luO°r • The use of the middle lino indicating a conductance of 2.6 will 
cause an error not greater than 10 Kg.Cal/k/hr. over the temperature range 
5°F to 100°F and the lower line with a conductance of 1.7 will be accurate to 
5 Kg.Cal/lr/hr. or less between 20°F and -ltO°F. 
The radiation conductance of 2.6 will be used throughout the balance of 
this report although more precise values may be obtained for any particular 
case by drawing a straight line from the curve at the temperature and the 
curve at an estimated value of T3 from the approximate relation. 9. T3 " T2 T2 T4) / 
" 
The slope of this line is the radiation conductance from the clothing surface 
and may be substituted without change in eq. 4b and 5b or converted to Ir by 
means of eq. 6 and used in eq. 4& and 5a. 
Case II Radiation to surrouhding surfaces must be treated 
separately from radiation to the atmosphere 
The complexity of this situation is so great that only approximate 
solutions may be obtained. The difficulty is caused by the atmospheric absorp- 
tion of radiation from surfaces at body temperatures. The amount of absorption 
depends upon the path length of the beam and on the concentration of water vapor 
in the atmosphere. A ten foot air column at a temperature of 100°F and with a 
vapor pressure of 20mm. would have an emnissivity of 0.2. If the vapor pressure 
were reduced by one-half or the length of the column by one-half, the emmissivity 
would be only 0.1. 
Since the emmissivity of the atmosphere changes greatly with change in 
vapor pressure, general expressions for the value of the radiant interoliange 
cannot be given. Approximate values can be obtained by numerically integrating 
the interchange along all possible paths. 
Qase 2 - polar PaWilga 
Solar radiation has been discussed theoretically by Elum (11), Schickele 
(2), and Burton (3), and some experimental data has been secured by Robinson (12). 
Unfortunately, these results provide only estimates of the magnitude of the 
radiation factor. In fact, Dr. Blum has expressed the situation perfectly when 
he said, "It seems to me what we need is a lot of measurements that we do not 
have", and present information is based almost wholly upon the value of the 
solar constant, together with a few measurements of atmospheric transmission, 
albedo, reflecting power of clothing, etc. Such measurements as are available 
are not sufficient for general evaluation of radiation over different parts of 
the globe. 
The effect of the radiation term can be quiu« appreciable. Blum ana 
Schickele have evaluated the radiation iactor as being approximately 5<J to 
250 kg. calories per square meter per hour. 
Burton (3) has shown that radiation may be expressed as an increment in 
temperature and algebraicly added to the temperature differential, figure 2 
in his report (3) illustrates the values that may be found. For the present, 
this is one of the easiest ways of handling the radiation problem and is prob- 
ably as accurate as any other. 
The most practical approach to the radiation problem appears to be from 
the experimental side in developing an instrument which would give, directly, the integrated effects of all radiation and such an instrument might then be 
used by the Weather Bureau and radiation factors measured in many places. 
Evaluation of Internal Conductance 
The internal conductance of the body has been measured by Dubois (13), 
Hardy (lU), Hardy and Uittleman (15), Winslow, Herrington and Gagge (16), The 
measurements of these investigators were obtained in conditions of comfort, 
vaso constriction, and slight vaso dilation. Robinson provided the data from 
which conductances may be obtained a limiting conditions of heat stress. 
Robinson's data has been plotted in Figure 9 to show the relationship between 
conductance and internal temperature. It is interesting to note that the 
conductance changes only slightly in the range of comfort, but a large increase 
occurs as the internal temperature approaches maximum safe figures. This rise 
indicates a great Increase in the rate of heat transfer which must be caused 
by an increased volume of blood flow. 
Internal conductances must be based upon the measurement of internal 
temperatures, skin temperatures, and metabolic rate. At conditions of thermal 
strain the temperature differential is quite small and any error in the measure- 
ment of skin temperatures will cause an appreciable change in the value found 
for conductance. However, under these same conditions skin temperatures will 
be much more uniform so the probability of error is somewhat minimised. It 
would be desirable to have many more measurements of this factor, particularly 
for different types of individuals under conditions of high thermal stress. 
Evaluation of Evaporation from the Lungs and Wanning Inspired Air 
These two terms represent direct beat losses from the interior of the body 
and are probably closely associated with the metabolic rate. Burton (5) assumed 
that the value of these two terms is 2B% of the total heat production. Balding 
at al (7) have provided a line chart for the determination of these factors 
when the pulmonary ventilation is known. Unfortunately, the writer has been 
unable to find any figures correlating pulmonary ventilation with metabolic 
rate so that it seems necessary to find some other means of evaluating these 
factors. It will be shown later that Burton's estimate was very close to the 
value which may be obtained from Robinson's (22) data. 
Basic studies of the evaporative constants of the human body have been made 
by Gagge (17) and by Winslow, Herrington, and Gagge (18). They found that at 
wind velocities of 17 feet per minute the maximum rate of evaporative transfer 
was 2.99 Kg.Cal/lT/hr/nsn. This figure was then extended to higher velocities by 
means of the equationt 
10. E-2.99 (1 / V ) in which 
HT" 
E equals the evaporative transfer in Kg.Cal/i^/hr./imB 
V is the wind velocity in cm/sec 
The value of the term (1 / V ) was t aken from the work of Carrier 
nr (19) and while this is in good agreement with experiment for small changes in 
wind velocity it does not provide accurate results over a wide range of veloci- 
ties. The most accurate data on the evaporation from wet cylinders exposed to 
a transverse air flow was obtained by Powell (20) in a very carefully executed 
series of experiments. He found that the rate of evaporation could be expressed 
asr 
11. E = 1.72xlO"7 (pw - Pa) V°-6/D°*U 
in which E is the evaporation in gms/cm2/sec 
Pw is the vapor pressure of the water surface in mm. hg. 
Pa is the vapor pressure of the water in the atmosphere 
V is the wind velocity in cm/sec 
D is the diamtter of the cylinder in cm. 
Qy a suitable choice of diameter this expression may be made to coincide with 
the physiological data with the result* 
12. B- 8.1 V0*6 
in which E is the evaporative heat transfer in and V is the 
wind velocity in miles per hour. 
This equation agrees with the physiological experiments and also coincides 
with the physical experiments on the effect of wind velocity upon rate of 
evaporation. 
The diameter required is about Uj inches which seems large when it is 
remembered that the body behaves as a three inch diameter cylinder for convective 
transfer. It must be realised, however, that the convective resistance to heat 
flow in still air is equivalent to a motionless film approximately 2 millimeters 
in thickness. The resistance to evaporative transfer is equivalent to a similar 
film 2 centimeters in thickness. If the radius of all parts of the body were to 
be increased by 2 cm., many parts would merge and the body would tend to approach the 
shape of a single large cylinder. Consequently, it is expected that the body 
will behave as a cylinder of large diameter for evaporative transfer and as a 
cylinder of smaller diameter for convective transfer. 
Nevertheless, it would be desirable to have measurements made at higher 
velocities for as the thickness of the resistive film decreases with increased 
velocities a change in effective diamter may also be found. 
As a first approximation eq. 12 may be used to evaluate the evaporation 
from nude men or from clothed men when the clothing is saturated. The situation 
becomes more complicated when the clothing is dry and the evaporation proceeds 
from the skin surface for then the clothing and entrapped air then interpose an 
additional barrier to the rate of flow. Fourt (2) has shown that the rate of evaporation is related to the air 
permeability of the fabric and to the air space beneath it. Some of his re- 
sults for a series of different types of cloth are shown in Fig. 10. These 
data may be approximated within experimental error by multiplying the evapora- 
tion from a bare surface by (air permeability of fabric) 0.8. This term may 
J5oo 
be used to modify Powells equation to obtain one expression which relates 
evaporation to fabric permeability and to wind velocity. Powell's equation 
then becomes: 
13. E - 8.1 (Air permeability of fabric 
2000 
in which the air permeability is measured In cubic with a pressure 
drop across the fabric of 0.5 inch water. The figure 2800 used in this 
expression is simply the value found in the permeability test equipment when 
the resistance of the cloth approaches zero. 
The value of S in equation 13 may be readily found from Fig. II by drawing 
a straight line between the appropriate point on the wind velocity scale 0 and 
the point on the vapor pressure differential scale C corresponding to the 
existing conditions. The point at which this line intersects scale F gives 
the evaporative loss from a bare surface. The effect of covering the surface 
may then be found by drawing a line between the loss from a bare surface and 
the point on the fabric permeability scale C corresponding to the type of fabric 
used. The Intersection of this line with scale E gives the evaporative loss 
from beneath a dry fabric. 
The evaporative loss so found assumes a wetted area of 100$ and that the 
dry fabric covering is 1 cm. away from the wet surface. These conditions are 
probably never realized in practice for when the wetted area approaches 100$ 
the clothing is wetted and some of the evaporation occurs within the cloth or 
from its surface. Nevertheless, these equations and the chart furnish a first 
approximation to the rate of evaporation and the accuracy will improve as the 
wetted area is diminished. 
The effect of wetted area and comfort upon rates of evaporation may be 
easily obtained by first finding the transfer from the completely wetted sur- 
face and multiplying these values by the % wetted area. Also the same chart 
may be used to find any of the variables if the others are known or even to 
find the relation between any two if the balance are given. 
Scale A and B on this figure are provided to ahow roughly the relation 
between the vapor pressure of saturated air and the temperature of the air. 
Discussion 
In attempting to use equations U or 5 or one of their variations, it must 
be remembered that they only state the relations that must exist for equilibrium 
conditions. For instance. Burton (3) has shown that the evaporation from a wet 
surface covered with wet clothing must be greater than from a bare wet surface. This does not mean that adding a layer of wet clothing over a bare wet surface 
will increase the evaporative cooling. Instead, it means that the evaporation 
has become less effective since it occurs at the surface of the clothing and, 
consequently, a greater amount must be lost to maintain equilibrium. As used 
in these equations E and R are almost independent of the balance of the system. 
Their values are determined by other factors such as wind velocity, vapor 
pressure, cloudiness, etc. which do not appear explicitly. 
To clarify this point further consider eq. Ud. If U is changed and the 
temperatures, resistances and evaporations remain constant then R must also 
change. But K can only vary if the reflecting power of the clothing, its 
temperature, or the intensity of the solar radiation is altered. Under the 
conditions mentioned, the equation simply states that if U is varied R must also 
; be varied or equilibrium conditions will cease to exist. In this case, the 
temperatures within the system will change in the direction to restore equilibrium. 
1 Alterations of temperature within the system will also make a change in the 
quantity of beat stored. 
E. On the other hand the temperatures of the system are definite functions of 
M, 6, R, and the different resistances. Change any one of these terms and un- 
less some other compensating change is made the temperatures at all points within 
the system will assume new values. Eq. lid shows that there is a fixed relation 
between internal temperature, metabolic rate and environmental conditions. 
Vary either of the latter and the internal temperature will show a corresponding 
change. The effect is masked by the large increase in Internal conductance which 
takes place when the environment becomes severe. Nielsen (21) has shown that the 
internal temperature is strongly Influenced by the performance of work, but his 
experiments were not sufficiently complete to establish the variation of internal 
temperature for different external conditions. The working periods were generally 
one hour in duration and the temperature changes during this period are greatly 
influenced by heat storage. 
The storage factor has not been considered but allowance may be easily made 
for it by adding the hourly rate of increase or decrease to U in the equations 
prior to l*d and 5d. The latter are suitable only for equilibrium and altering 
them to allow for changes in storage is much more complicated. 
Exactly which of these equations is used in developing an index is dependent 
upon the conditions of the problem, the Information available, and the Information 
desired. The limiting metabolism may be chosen and this shows the maximum work 
rate which can be sustained, but gives little or no information concerning 
relative comfort or effeclency. The simplest way of solving the equations con- 
sists in finding E for various fixed values of the other variables. However, E 
is not easily related to comfort or efficiency. 
Neither of these methods is wholly satisfactory but there is still another 
, way of approaching the problem. An instrument is being developed by this 
section which can measure the total quantity of heat which may be accepted 
by the atmosphere. Thile there are some practical problems to be solved it 
is by no means impossible or even impractical. Such an instrument would give a direct measure of the value of C + E -I R for a bare surface maintained at some 
fixed temperature. Suppose then that the thermal acceptance of the atmosphere 
is defined as the quantity of heat which would be lost through the skin of a 
nude nan whose skin temperature was maintained at 97°F. If in addition, w;e 
define the thermal acceptance ratio as the thermal acceptance of the atmosphere 
divided by the rate of heat Production a number is obtained which seems to be 
definitely related to the physiological variables. Fig. 12 shows the relation 
between the skin temperature from Robinson's data for men clothed in shorts and 
the thermal acceptance ratio. This data appears to be linear and when statistic- 
ally analyzed forms a series of three straight lines which intersect near 96,6°F 
and a ratio of 1.30. This would imply that perhaps two errors had been made. 
First, that no account had been taken of the heat loss through the lungs, and, 
secondly, that the heat loss from the bare surface was in error by an amount 
equivalent to a change in skin temperature of .4, degree Fahrenheit. If allowance 
were to be made for the heat transfer from the lungs, we would expect the line to 
intersect at 97°F and a ratio of unity. Since no allowance was made for * A, 
it is to be expected that the intersection would occur at pr-e point on the 
ratio axis greater than 1. The actual intersection at 1.30 implies that the 
heat transfer from the lungs is equivalent to 23$ of the metabolic rate. 
Statistically, this is not highly significant because the scatter of the 
experimental points about the lines in such that we could legitimately choose 
almost every point likely within the cross-hatched area of Figure 13. This 
area is bbunded by lines which have been drawn two standard deviations away from 
the skin temperature line and represents the area which is common to all three 
sets of lines. If the same procedure is repeated for men wearing clothing, it 
is found that the lines relating skin temperature to thermal acceptance ratio 
differ only slightly in position from the lines draw.n for men wearing shorts, 
and this difference is, in general, within two standard deviations. The area 
which is within two standard deviations of the three lines for clothed men is 
somewhat smaller in a different position than that shown in ligure 13. Both 
lie in common area shown in the heavily cross-hatched area in the same figure, 
and its center lies at temperature of 97.1°F and a ratio of 1.35. This implies 
that the heat loss through the lungs is 26$ of the metabolic rate, so if Burton's 
estimate of 25$ is accepted it is well within the experimental error of the data 
taken from Robinson, (22) 
The thermal acceptance ratio as has been defined herein is an empirical 
arrangement. 'The equations could be set up to derive it by theoretical means, 
but the equations are so complicated that it is difficult to draw; any conclusions 
from them. The real test of such a system is whether or not it may be used 
easily and simply to give an index of climatic strain, and it should show a 
definite relation to the physiological variables within the system. 
The relation between the thermal acceptance ratio and deep body temperature 
as taken from Robinson is data shown in Figure 15. then it is realized that this 
chart includes all of the data for men clothed and men wearing shorts and working 
at three different rates of activity in a number of different environmental con- 
ditions, the relation seems to be very good indeed. A sharp rise in internal 
temperature is observed when the body is under severe climatic stress. Figure 16 shows the relationship between the heart rate and thermal accept- 
ance ration, and again the scatter is no more than that usually found for heart 
rates. 
Figure 17 shows the relationship between the internal conductance and the 
thermal acceptance ratio, and the scatter here is no more than is observed when 
a conductance is plotted against internal temperature. 
The thermal acceptance of the atmosphere is something which may be measured 
on an instrument or which could be calculated accurately in the absence of out- 
door radiation. Ihen such r adiatlon is present, it will be necessary to use 
Burton's (3) data for a rough estimate. The ratio for any activity may then be 
readily found by dividing the atmospheric acceptance by the metabolic rate. 
The relation between the acceptance ratio and comfort may be found from 
the data on skin temperatures since the comfort range of skin temperature is 
known for low activity. No information is available, however, as to the range 
of comfortable temperatures for higher activities. It is possible to relate 
comfort to the conductance through the tissues and use this means of evaluating 
comfort in terms of thermal acceptance ratio. This and the correlation with 
other laboratories will be the subject of another report. tfPS8P» 
EQUATION FOE SKIN TEilPEEATUKE AS A FUNCTION OF THEE11AL ACCEPTANCE EATIO 
Based on the data of Robinson's (22) 
Clothing 
.Activity 
Kg. Cals. 
Equation 
for Ts 
Standard 
deviation of 
points about 
line 
Tfl at R« 1 
Standard 
Deviation 
of line 
at R - 1 
Jungle Suits 
189 
Ts = 101.3-3.OiR 
l.i 
98.3 
.35 
Jungle Suite 
125 
Xs : 98.9-l.i9R 
1.5 
97.i 
.51 
Jungle Suits 
i9 
Ts » 98.3- .51R 
1.1 
$7.8 
.50 
Shorts 
188 
T8 - 99.i-2.25R 
2.0 
97.2 
.52 
Shorts 
130 
Te ■ 98.2-l.25R 
1.3 
97.0 
.39 
Shorts 
i6 
XB = 97.1- .UR 
1.7 
96.7 
.70 REFERENCES 
1. Amer. Jour. Physiol. 116:669 1936 
120:1 1937 
120:288 1937 
124:30 1938 
124:51 1938 
1938 
127:505 1939 
131: 79 1940 
134:664 1941 
2. Conference Report OQMG 8/25/44 Principles of Environmental Stress. 
3. Associate Committee on Aviation Medical Research Report #C2754 
4. Amer. Jour. Physiol. 116:669 1936 
5. A.C.M.R. Report $2035 
6. Heat Transmission and Ed. Mcgraw Hill 1944 
7. Clothing Test Methods (National Research Council Report 1945) 
8. Air Force Report #T£EAL - SH - S - 241 
9. Jour. Clin. Investigation 13: 817 1934 
10. Hutte, 25th ed. Vol. I., If. Ernst P. Sohn, Berlin 
11. Included in ref. ffb 
12. Interim R§port #11, Dept, of Physiol. Indiana Univ. Medical School 5/14/44 
13. The Mechanism of Heat Loss and Temperature Regulation 
Stanford University Press 1937 
.14. J. Nutrition 16; 493, 1938 
15. Amer. Jour. Physiol. 120:1 1937 
16. " " " ' 120:277 1937 
17. " " " 120:288 1937 
18. A.H.S.V.E. Guide 1937 
19. Trans. Inst. Chem. Eng. 18:36 1940 
20. Skand. Archiv. for Physiol. 79:13 1938 
21. Interim Report #12, Indiana University Medical School CLIMATOLOGY 8. ENVIRONMENTAL PROTECTION SEC 
RESEARCH & DEVELOPMENT BRMMCH O Q.M.C, 
tmrniimilHllllllllil‘HMJHUUlUHifaaU.iafatH.t!H±ltl« 
CONVECTIVE HEAT TRANSFER FROM 
3" DIAMETER CYLINDER TO AIR FOR 
DIFFERENT SURFACE TEMPERATURES 
COMPARED WITH THE FORMULA DE- 
VELOPED AT THE PIERCE LABORATORIES 
PIERCE FORMULA: C=LQ4NV 
C=KG CAL/VVSEC 
V=WINO VELOCITY IN CM/SEC 
IF* 3 I CLIMATOLOGY & ENVIRONMENTAL PROTECTION SEC 
RESEARCH A DEVELOPMENT BRANCH OQM.G 
CONDUCTIVE HEAT TRANSFER 
FROM CYLINDERS IN AIR AS A 
FUNCTION OF WIND VELOCITY 
AND CYLINDER DIAMETER. 
SURFACE TEMP OF CYLINDERS 60*F_ 
Figt No 4 CLIMATOLOGY & ENVIRONMENTAL PROTECTION SEC 
RESEARCH ft DEVELOPMENT BRANCH OO MG 
LJ ■ ii:;;n;;n-n-rr»rMn--n-;"t vl:;;! 
I SURFACE CONDUCTANCE 
H AS A FUNCTION OF WIND 
VELOCITY & ALTITUDE 
r* mo. » NOMOGRAM FOR CALCULATION OF CONDUCTIVE AND CONVECTIVE HEAT 
TRANSFER TO OR FROM THE HUMAN BODY 
EXAMPLE: GIVEN: SKIN TEMPERATURE 90*F 
AIR TEMPERATURE 20*F 
WIND VELOCITY 5M.RH. 
CLOTHING 3 CLD 
PROBLEM: TO FIND HEAT LOSS. 
L DRAW A STRAIGHT LINE FROM 5 ON THE WIND VELOCITY 
SCALE B TO 3 ON THE CLOTHING RESISTANCE SCALE D. THIS 
LINE CROSSES THE TOTAL RESISTANCE SCALE C AT 3.32. 
2. DRAW A STRAIGHT LINE FROM 3.32 ON THE TOTAL RESISTANCE 
SCALE TO 70 ON THE TEMPERATURE DIFFERENTIAL SCALE A. 
3. THE TOTAL HEAT LOSS IS FOUND AT THE POINT WHERE THIS 
LAST LINE INTERSECTS THE HEAT TRANSFER SCALE E. 
4. THE DIRECTION OF HEAT FLOW IS FROM THE HCHER TO THE 
LOWER TEMPERATURE. 
Comp. *4,by CKmatotofy Saclwn ftaiaarch and Davaloo 
mant Branch of I ha Offica of tha Quartarmaslar Canaral 
Fig. No. 6 NOMOGRAM FOR THE CALCULATION OF HEAT TRANSFER FROM THE HUMAN 
BOO BY CONDUCTION, CONVECTION, AND RADIATION WHEN THESE FACTORS 
CAN BE EXPRESSED AS RESISTANCES 
EXAMPLE: GIVEN: SKIN TEMPERATURE 90*F. 
AIR 8. SURROUNDING 
TEMPERATURE 2CfF. 
WIND VELOCITY 5 M.P.K 
CLOTHING 3 CLD 
PROBLEM: TO FIND HEAT LOSS. 
1 DRAW A STRAIGHT LINE FROM 5 ON THE WIND VELOCITY 
SCALE B TO 3 ON THE CLOTHING RESISTANCE SCALE 0. THIS 
LINE CROSSES THE TOTAL RESISTANCE SCALE C AT 
2 DRAW A STRAIGHT LINE FROM ON THE TOTAL RESISTANCE 
SCALE TO 70 ON THE TEMPERATURE DIFFERENTIAL SCALE A 
3 THE TOTAL HEAT LOSS IS FOUND AT THE POINT WHERE THIS 
LAST LINE INTERSECTS THE HEAT TRANSFER SCALE E. 
4 THE DIRECTION OF HEAT FLOW IS FROM THE HIGHER TO THE 
LOWER TEMPERATURE. 
Comp.l»d by Climatology Section Research and Develop 
ment Branch of the Office of the Quarter matter General 
Fig. No. T RADIATION 
” HEAT IN W . 'HR[wHteH ; 
ERASURE. HEgTwrT?R*N|^R' 
if5|wCEIV'EDUt° 
RCU PW SS :T 
tot ~te f Tjisuu y :3ip ifecto WwiE.; j; ~ NDLiC.T.ANCE JEMPERATURE , 
iTprof1 atuf: pffiiSHglpppfp 
H I f¥* tt . t A HO «R C '•ftt Relationship of evaporation rate to wind velocity, for fabrics having the 
air permeabilities shown at the ends of the lines. S/P - Kg.eal/Mr per ml 
vapor pressure difference. Air permeability = ft?/ft? min at pressure ■ 0.5 inch 
water. 
Compiled by Climatology Section. Research and Develop- 
ment Branch of the Office of the Quartermaster General. 
Fig. No. 10 NOMOGRAM FOR CALCULATION OF EVAPORATIVE HEAT TRANSFER 
FROM THE HUMAN BODY 
BASED ON THE EQUATION E V*-* C A 
Compiled by Cl.mploloty SaclKyi, InllrtH and Davalop. 
Fig. No.. II f ROBINSON REPORT 
NO. 12 
MEN WEARING SHORTS 
Metabolic Rote* 
Trr A • 190 K*. Cel*. / m2 / hr. 
g±, X • 125 K«. Cole /M2/JK* 
Q • 50 k» coie / *2/ 
” ’ Rweercfc ft 0«vt!apm*r flnancn, cc ft C 
ENVIRONMENTAL UNITS 
.. TEWPERATV.M. ;RAN«|;>. g4':F; jgPE. 
.VAPOR PRESSURE RANGE, 4mmHo-4£nhH9. 
Ijiigp 4|j||  
MEN WEARINGSHORTfe' 
: 1 J. .j X&3END ■ • 
a v crags 
thiHtt ,8AN0 ;iri Twj:.. „ 
0€ptAT;tOMfe 
I ,j.; I 
Aft£A CDfctMON TC ERROR 
bauds yTw:s»PTv»Tfe 
A Re A COMMON It) ERROR 
BANDS qf ALjL pjpCRIMEKI 
JNCUUDW CLOT RED MEN) 
-•nlllii: -lUiJ 
II ROBINSON REPORT I If 
NO. 12 
i|j|' • CLOTHED MEN 
0 * MEN WEARING SHORTS |B8 
1; IS 
, ’' j, ’. TSaTTpIallpTj™: ijir 
TEMPERATURE RANGE, 64 »E - 
VAPOR PRESSURE RANGE, 4mmHfl-42tm,H, 
mun&.« Eiggmy.: £.:.3.!j|3.siH.8.K»r.:__ 
..{:;i 6ct Ki.Di|hi/kpy'il*!:i. f J.JVJ r H EAR^s P --: :---TTT 
:T:HE R MAI. A COER T AN CF R A T I 0 
-i-|r- ilv j■■iA_.i ,l">" i....L-|. 
-- 1 i-H !"-:--i" ft 
j m-ms'W • i ; i i ! 
—pwrwri—b' t"T'”i“i—!—~ 
-||si|fjr| i r mi : :i 
i i -r-r-l ■ ■!: ■ i i 1 : : : “i i : I-  i I:!.'... 
M ROBINSON REPORT S 
NO.I2 
j A • CLOTHED MEN 
O - MEN WEARING SHORTS 
Bn, . iiTT 
TEMPERATURE: RKN0E, B4 ,F - |22;*r 
;•:■:: VAPf>h■ PR£9&bfe SANte€,4mmllg 4g^mllq 
....:.wiI... 
I|p activities i 
190 Kg. Cols /MV hr 
125Kg. Cal*/MV hr 
—:f— r-—f-- 50Kg Calsy MVhr t"T"T'"