EN ISO 7933:2004

SLOVENSKI STANDARD
01-november-2004
1DGRPHãþD
SIST EN 12515:2001
SIST ENV 26385:2001
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Ergonomics of the thermal environment - Analytical determination and interpretation of
heat stress using calculation of the predicted heat strain (ISO 7933:2004)
Ergonomie der thermischen Umgebung - Analytische Bestimmung und Interpretation der
Wärmebelastung durch Berechnung der vorhergesagten Wärmebeanspruchung (ISO
7933:2004)
Ergonomie des ambiances thermiques - Détermination analytique et interprétation de la
contrainte thermique fondées sur le calcul de l'astreinte thermique prévisible (ISO
7933:2004)
Ta slovenski standard je istoveten z: EN ISO 7933:2004
ICS:
13.180 Ergonomija Ergonomics
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EUROPEAN STANDARD
EN ISO 7933
NORME EUROPÉENNE
EUROPÄISCHE NORM
August 2004
ICS 13.180 Supersedes EN 12515:1997
English version
Ergonomics of the thermal environment - Analytical
determination and interpretation of heat stress using calculation
of the predicted heat strain (ISO 7933:2004)
Ergonomie des ambiances thermiques - Détermination Ergonomie der thermischen Umgebung - Analytische
analytique et interprétation de la contrainte thermique Bestimmung und Interpretation der Wärmebelastung durch
fondées sur le calcul de l'astreinte thermique prévisible Berechnung der vorhergesagten Wärmebeanspruchung
(ISO 7933:2004) (ISO 7933:2004)
This European Standard was approved by CEN on 8 August 2004.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the Central Secretariat or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the official
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CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
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Slovenia, Spain, Sweden, Switzerland and United Kingdom.
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© 2004 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 7933:2004: E
worldwide for CEN national Members.

Foreword
This document (EN ISO 7933:2004) has been prepared by Technical Committee ISO/TC 159
"Ergonomics" in collaboration with Technical Committee CEN/TC 122 "Ergonomics", the
secretariat of which is held by DIN.

This European Standard shall be given the status of a national standard, either by publication of
an identical text or by endorsement, at the latest by February 2005, and conflicting national
standards shall be withdrawn at the latest by February 2005.

This document supersedes EN 12515:1997.

According to the CEN/CENELEC Internal Regulations, the national standards organizations of
the following countries are bound to implement this European Standard: Austria, Belgium,
Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary,
Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland,
Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.

Endorsement notice
The text of ISO 7933:2004 has been approved by CEN as EN ISO 7933:2004 without any
modifications.
INTERNATIONAL ISO
STANDARD 7933
Second edition
2004-08-15
Ergonomics of the thermal
environment — Analytical determination
and interpretation of heat stress using
calculation of the predicted heat strain
Ergonomie des ambiances thermiques — Détermination analytique et
interprétation de la contrainte thermique fondées sur le calcul de
l'astreinte thermique prévisible

Reference number
ISO 7933:2004(E)
©
ISO 2004
ISO 7933:2004(E)
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ii © ISO 2004 – All rights reserved

ISO 7933:2004(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope. 1
2 Normative references . 1
3 Symbols . 2
4 Principles of the method of evaluation. 5
5 Main steps of the calculation. 5
5.1 General heat balance equation. 5
5.2 Calculation of the required evaporative heat flow, the required skin wettedness and the
required sweat rate . 7
6 Interpretation of required sweat rate . 8
6.1 Basis of the method of interpretation . 8
6.2 Analysis of the work situation . 8
6.3 Determination of maximum allowable exposure time (D ) . 9
lim
6.4 Organization of work in the heat . 9
Annex A (normative) Data necessary for the computation of thermal balance. 10
Annex B (informative) Criteria for estimating acceptable exposure time in a hot work environment. 18
Annex C (informative) Metabolic rate . 20
Annex D (informative) Clothing thermal characteristics . 22
Annex E (informative) Computer programme for the computation of the Predicted Heat Strain
Model. 24
Annex F (normative) Examples of the Predicted Heat Strain Model computations . 33
Bibliography . 34

ISO 7933:2004(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies
(ISO member bodies). The work of preparing International Standards is normally carried out through ISO
technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 7933 was prepared by Technical Committee ISO/TC 159, Ergonomics, Subcommittee SC 5, Ergonomics
of the physical environment.
This second edition cancels and replaces the first edition (ISO 7933:1989), which was based on the Required
Sweat Rate index. In order to avoid any confusion and, as extensive modifications are brought to the
prediction model, the name of the index has been changed to Predicted Heat Strain (PHS).
iv © ISO 2004 – All rights reserved

ISO 7933:2004(E)
Introduction
Other International Standards of this series describe how the parameters influencing the human
thermoregulation in a given environment must be estimated or quantified. Others specify how these
parameters must be integrated in order to predict the degree of discomfort or the health risk in these
environments. The present document was prepared to standardize the methods that occupational health
specialists should use to approach a given problem and progressively collect the information needed to
control or prevent the problem.
The method of computation and interpretation of thermal balance is based on the latest scientific information.
Future improvements concerning the calculation of the different terms of the heat balance equation, or its
interpretation, will be taken into account when they become available. In its present form, this method of
assessment is not applicable to cases where special protective clothing (reflective clothing, active cooling and
ventilation, impermeable, with personal protective equipment) is worn.
In addition, occupational health specialists are responsible for evaluating the risk encountered by a given
individual, taking into consideration his specific characteristics that might differ from those of a standard
subject. ISO 9886 describes how physiological parameters must be used to monitor the physiological
behaviour of a particular subject and ISO 12894 describes how medical supervision must be organized.

INTERNATIONAL STANDARD ISO 7933:2004(E)

Ergonomics of the thermal environment — Analytical
determination and interpretation of heat stress using
calculation of the predicted heat strain
1 Scope
This International Standard specifies a method for the analytical evaluation and interpretation of the thermal
stress experienced by a subject in a hot environment. It describes a method for predicting the sweat rate and
the internal core temperature that the human body will develop in response to the working conditions.
The various terms used in this prediction model, and in particular in the heat balance, show the influence of
the different physical parameters of the environment on the thermal stress experienced by the subject. In this
way, this International Standard makes it possible to determine which parameter or group of parameters
should be modified, and to what extent, in order to reduce the risk of physiological strains.
The main objectives of this International Standard are the following:
a) the evaluation of the thermal stress in conditions likely to lead to excessive core temperature increase or
water loss for the standard subject;
b) the determination of exposure times with which the physiological strain is acceptable (no physical
damage is to be expected). In the context of this prediction mode, these exposure times are called
“maximum allowable exposure times”.
This International Standard does not predict the physiological response of individual subjects, but only
considers standard subjects in good health and fit for the work they perform. It is therefore intended to be
used by ergonomists, industrial hygienists, etc., to evaluate working conditions.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 7726, Ergonomics of the thermal environment — Instruments for measuring physical quantities
ISO 8996, Ergonomics of the thermal environment — Determination of metabolic rate
ISO 9886, Ergonomics — Evaluation of thermal strain by physiological measurements
ISO 9920, Ergonomics of the thermal environment — Estimation of the thermal insulation and evaporative
resistance of a clothing ensemble
ISO 7933:2004(E)
3 Symbols
For the purposes of this document, the symbols and abbreviated terms, designated below as “symbols” with
their units, are in accordance with ISO 7726.
However, additional symbols are used to for the presentation of the Predicted Heat Strain index.
A complete list of symbols is presented in Table 1.
Table 1 — Symbols and units
Symbol Term Unit
–
–
code = 1 if walking speed entered, 0 otherwise
–
–
code = 1 if walking direction entered, 0 otherwise
α
fraction of the body mass at the skin temperature dimensionless
α
skin-core weighting at time t dimensionless
i
i
α
skin-core weighting at time t dimensionless
i–1
i–1
ε
emissivity dimensionless
θ
angle between walking direction and wind direction degrees
A
DuBois body surface area square metre
Du
A
fraction of the body surface covered by the reflective clothing dimensionless
p
A
effective radiating area of a body dimensionless
r
C
convective heat flow watts per square metre
c
water latent heat of vaporization joules per kilogram
e
C
correction for the dynamic total dry thermal insulation at or above dimensionless
orr,cl
0,6 clo
C
correction for the dynamic total dry thermal insulation at 0 clo dimensionless
orr,Ia
C
correction for the dynamic clothing insulation as a function of the dimensionless
orr,tot
actual clothing
C
correction for the dynamic permeability index dimensionless
orr,E
c
specific heat of dry air at constant pressure joules per kilogram of dry air
p
kelvin
C
respiratory convective heat flow watts per square metre
res
c
specific heat of the body watts per square meter per
sp
kelvin
D
maximum allowable exposure time minutes
lim
D
maximum allowable exposure time for heat storage minutes
lim tre
D
maximum allowable exposure time for water loss, mean subject minutes
limloss50
D
maximum allowable exposure time for water loss, 95 % of the minutes
limloss95
working population
D
maximum water loss grams
max
D
maximum water loss to protect a mean subject grams
max50
D
maximum water loss to protect 95 % of the working population grams
max95
DRINK
1 if workers can drink freely, 0 otherwise dimensionless
2 © ISO 2004 – All rights reserved

ISO 7933:2004(E)
Symbol Term Unit
dS
body heat storage during the last time increment watts per square metre
i
dS
body heat storage rate for increase of core temperature watts per square meter
eq
associated with the metabolic rate
E
evaporative heat flow at the skin watts per square metre
E
maximum evaporative heat flow at the skin surface watts per square metre
max
E
predicted evaporative heat flow watts per square metre
p
E
required evaporative heat flow watts per square metre
req
E
respiratory evaporative heat flow watts per square metre
res
f
clothing area factor dimensionless
cl
F
reduction factor for radiation heat exchange due to wearing dimensionless
cl,R
clothes
F
emissivity of the reflective clothing dimensionless
r
H
body height meters
b
h
dynamic convective heat transfer coefficient watts per square metre kelvin
cdyn
h
radiative heat transfer coefficient watts per square metre kelvin
r
I
static boundary layer thermal insulation square meters kelvin per watt
a st
I
static clothing insulation square meters kelvin per watt
cl st
I
clothing insulation clo
cl
I
total static clothing insulation square meters kelvin per watt
tot st
I
dynamic boundary layer thermal insulation square meters kelvin per watt
a dyn
I
dynamic clothing insulation square meters kelvin per watt
cl dyn
I
total dynamic clothing insulation square meters kelvin per watt
tot dyn
i
static moisture permeability index dimensionless
mst
i
dynamic moisture permeability index dimensionless
mdyn
incr
time increment from time t to time t minutes
i–1 i
k fraction k of predicted sweat rate dimensionless
Sw
K conductive heat flow watts per square metre
M metabolic rate watts per square meter
p water vapour partial pressure kilopascals
a
p saturated water vapour pressure at skin temperature kilopascals
sk,s
R radiative heat flow watts per square metre
r
required evaporative efficiency of sweating dimensionless
req
R
dynamic total evaporative resistance of clothing and boundary square metres kilopascals per
tdyn
air layer watt
S
body heat storage rate watts per square metre
S
body heat storage for increase of core temperature associated watts per square metre
eq
with the metabolic rate
Sw
maximum sweat rate watts per square metre
max
Sw
predicted sweat rate watts per square metre
p
Sw
predicted sweat rate at time t watts per square metre
p,i
i
ISO 7933:2004(E)
Symbol Term Unit
Sw
predicted sweat rate at time t watts per square metre
p,i–1
i–1
Sw
required sweat rate watts per square metre
req
t
time minutes
t
air temperature degrees celsius
a
t
clothing surface temperature degrees celsius
cl
t
core temperature degrees celsius
cr
t
steady state value of core temperature as a function of the degrees celsius
cr,eqm
metabolic rate
t
core temperature as a function of the metabolic rate degrees celsius
cr,eq
t
core temperature as a function of the metabolic rate at time t degrees celsius
cr,eq i
i
t
core temperature as a function of the metabolic rate at time t degrees celsius
cr,eq i–1
i–1
t
core temperature at time t degrees celsius
cr,i
i
t
core temperature at time t degrees celsius
cr,i-1
i–1
t
expired air temperature degrees celsius
ex
t
mean radiant temperature degrees celsius
r
t
rectal temperature degrees celsius
re
t
maximum acceptable rectal temperature degrees celsius
re, max
t
rectal temperature at time t degrees celsius
re,i
i
t
rectal temperature at time t degrees celsius
re,i–1
i–1
t
steady state mean skin temperature degrees celsius
sk,eq
t
steady state mean skin temperature for nude subjects degrees celsius
sk,eq nu
t
steady state mean skin temperature for clothed subjects degrees celsius
sk,eq cl
t
mean skin temperature at time t degrees celsius
sk,i
i
t
mean skin temperature at time t degrees celsius
sk,i–1
i–1
V
respiratory ventilation rate litres per minute
v
air velocity metres per second
a
v
relative air velocity metres per second
ar
v
walking speed metres per second
w
w
skin wettedness dimensionless
W
effective mechanical power watts per square metre
W
humidity ratio kilograms of water per
a
kilogram of dry air
W
body mass kilograms
b
W
humidity ratio for the expired air kilograms of water per
ex
kilogram of dry air
w
maximum skin wettedness dimensionless
max
w
predicted skin wettedness dimensionless
p
w
required skin wettedness dimensionless
req
4 © ISO 2004 – All rights reserved

ISO 7933:2004(E)
4 Principles of the method of evaluation
The method of evaluation and interpretation calculates the thermal balance of the body from
a) the parameters of the thermal environment:
 air temperature, t ;
a
 mean radiant temperature, t ;
r
 partial vapour pressure, p ;
a
 air velocity, v ;
a
(These parameters are estimated or measured according to ISO 7726.)
b) the mean characteristics of the subjects exposed to this working situation:
 the metabolic rate, M, estimated on the basis of ISO 8996;
 the clothing thermal characteristics estimated on the basis of ISO 9920.
Clause 5 describes the principles of the calculation of the different heat exchanges occurring in the thermal
balance equation, as well as those of the sweat loss necessary for the maintenance of the thermal equilibrium
of the body. The mathematical expressions for these calculations are given in Annex A.
Clause 6 describes the method of interpretation which leads to the determination of the predicted sweat rate,
the predicted rectal temperature, and the maximum allowable exposure times and work-rest regimens to
achieve the predicted sweat rate. This determination is based on two criteria: maximum body core
temperature increase and maximum body water loss. Maximum values for these criteria are given in Annex B.
The precision with which the predicted sweat rate and the exposure times are estimated is a function of the
model (i.e. of the expressions proposed in Annex A) and the maximum values, which are adopted. It is also a
function of the accuracy of estimation and measurement of the physical parameters and of the precision with
which the metabolic rate and the thermal insulation of the clothing are estimated.
5 Main steps of the calculation
5.1 General heat balance equation
5.1.1 General
The thermal balance equation of the body may be written as:
M−WC= +E +K++C R++E S (1)
res res
This equation expresses that the internal heat production of the body, which corresponds to the metabolic rate
(M) minus the effective mechanical power (W), is balanced by the heat exchanges in the respiratory tract by
convection (C ) and evaporation (E ), as well as by the heat exchanges on the skin by conduction (K),
res res
convection (C), radiation (R), and evaporation (E), and by the eventual balance, heat storage (S), accumulating
in the body.
The different terms of Equation (1) are successively reviewed in terms of the principles of calculation (detailed
expressions are shown in Annex A).
ISO 7933:2004(E)
5.1.2 Metabolic rate, M
The estimation or measurement of the metabolic rate is described in ISO 8996.
Indications for the evaluation of the metabolic rate are given in Annex C.
5.1.3 Effective mechanical power, W
In most industrial situations, the effective mechanical power is small and can be neglected.
5.1.4 Heat flow by respiratory convection, C
res
The heat flow by respiratory convection may be expressed, in principle, by the equation
tt−
ex a
Cc=×0,072V× (2)
res p
A
Du
5.1.5 Heat flow by respiratory evaporation, E
res
The heat flow by respiratory evaporation may be expressed, in principle, by the equation
WW−
ex a
Ec=×0,072V× (3)
res e
A
Du
5.1.6 Heat flow by conduction: K
As this International Standard deals with the risk of whole-body dehydration and hyperthermia, the heat flow
by thermal conduction at the body surfaces in contact with solid objects may be quantitatively assimilated to
the heat losses by convection and radiation, which would occur if these surfaces were not in contact with any
solid body. In this way, the heat flow by conduction is not directly taken into account.
ISO 13732-1 deals specifically with the risks of pain and burns when parts of the body contact hot surfaces.
5.1.7 Heat flow by convection at the skin surface, C
The heat flow by convection at the skin surface may be expressed by the equation
Ch=×f×t−t (4)
( )
cdyn cl sk a
where the dynamic convective heat transfer coefficient between the clothing and the outside air, h , takes
cdyn
into account the clothing characteristics, the movements of the subject and the air movements.
Annex D provides some indications for the evaluation of the clothing thermal characteristics.
5.1.8 Heat flow by radiation at the surface of the skin, R
The heat flow by radiation may be expressed by the equation
R=×hf ×t −t (5)
( )
rcl sk r
where the radiative heat transfer coefficient between the clothing and the outside air, h , takes into account the
r
clothing characteristics, the movements of the subject and the air movements.
6 © ISO 2004 – All rights reserved

ISO 7933:2004(E)
5.1.9 Heat flow by evaporation at the skin surface, E
The maximum evaporative heat flow at the skin surface, E , is that which can be achieved in the
max
hypothetical case of the skin being completely wetted. In these conditions
p − p
sk,s a
E = (6)
max
R
tdyn
where the total evaporative resistance of the limiting layer of air and clothing, R takes into account the
,
tdyn
clothing characteristics, the movements of the subject and the air movements.
In the case of a partially wetted skin, the evaporation heat flow, E, in watts per square metre, is given by
Ew=×E (7)
max
5.1.10 Heat storage for increase of core temperature associated with the metabolic rate, dS
eq
Even in neutral environment, the core temperature rises towards a steady state value t as a function of the
cr,eq
metabolic rate relative to the individual's maximal aerobic power.
The core temperature reaches this steady state temperature exponentially with time. The heat storage
associated with this increase, dS does not contribute to the onset of sweating and must therefore be
eq,
deducted from the heat balance equation.
5.1.11 Heat storage, S
The heat storage of the body is given by the algebraic sum of the heat flows defined previously.
5.2 Calculation of the required evaporative heat flow, the required skin wettedness and the
required sweat rate
Taking into account the hypotheses made concerning the heat flow by conduction, the general heat balance
Equation (1) can be written as
E+SM= −W−−−C E C−R (8)
res res
The required evaporative heat flow, E , is the evaporation heat flow required for the maintenance of the
req
thermal equilibrium of the body and, therefore, for the heat storage to be equal to zero. It is given by
E =MW−−−−C E C−R−dS (9)
req res res eq
The required skin wettedness, w , is the ratio between the required evaporative heat flow and the maximum
req
evaporative heat flow at the skin surface:
E
req
w = (10)
req
E
max
The calculation of the required sweat rate is made on the basis of the required evaporative heat flow, but
taking account of the fraction of sweat that trickles away because of the large variations in local skin
wettedness. The required sweat rate is given by
E
req
(11)
Sw =
req
r
req
NOTE The sweat rate in watts per square meter represents the equivalent in heat of the sweat rate expressed in grams
–2 –2 –1 –1
of sweat per square metre of skin surface and per hour. 1 W⋅m corresponds to a flow of 1,47 g⋅m h or 2,67 g⋅h for
a standard subject (1,8 m of body surface).
ISO 7933:2004(E)
6 Interpretation of required sweat rate
6.1 Basis of the method of interpretation
The interpretation of the values calculated by the recommended analytical method is based on two stress
criteria:
 the maximum skin wettedness, w
max
 the maximum sweat rate: Sw
max
and on two strain criteria
 the maximum rectal temperature: t
re, max
 the maximum water loss: D .
max
The required sweat rate, Sw , cannot exceed the maximum sweat rate, Sw , achievable by the subject.
req max
The required skin wettedness, w , cannot exceed the maximum skin wettedness, w , achievable by the
req max
subject. These two maximum values are a function of the acclimatization of the subject.
In the case of non-equilibrium of the thermal balance, the rectal temperature increase must be limited at a
maximum value, t such that the probability of any pathological effect is extremely limited.

re,max
Finally, whatever the thermal balance, the water loss should be restricted to a value, D , compatible with
max
the maintenance of the hydromineral equilibrium of the body.
Annex B includes reference values for the stress criteria (w and Sw ) and the strain criteria (t and
max max re,max
D ). Different values are presented for acclimatized and non-acclimatized subjects, and according to the
max
degree of protection that is desired [mean level or 95 % (alarm) level].
6.2 Analysis of the work situation
Heat exchanges are computed at time, t , from the body conditions existing at the previous computation time
i
and as a function of the climatic and metabolic conditions prevailing during the time increment.
 The required evaporative heat flow (E ), skin wettedness (w ) and sweat rate (Sw ) are first
req req req
computed.
 Then the predicted evaporative heat flow (E ), skin wettedness (w ) and sweat rate (Sw ) are computed,
p p p
considering the limitations of the body (w and Sw ) as well as the exponential response of the
max max
sweating system.
 The rate of heat storage is estimated by the difference between the required and predicted evaporation
heat flow. This heat contributes to increase or decrease the skin and body temperatures. These two
parameters are then estimated, as well as the rectal temperature.
 From these values, the heat exchanges during the next time increment are computed.
The evolutions of Sw and t are in this way iteratively computed.
p re
This procedure makes possible to take into account not only constant working conditions, but also any
conditions with climatic parameters or work load characteristics varying in time.
8 © ISO 2004 – All rights reserved

ISO 7933:2004(E)
6.3 Determination of maximum allowable exposure time (D )
lim
The maximum allowable exposure time, D , is reached when either the rectal temperature or the cumulated
lim
water loss reaches the corresponding maximum values.
In work situations for which
 either the maximum evaporative heat flow at the skin surface, E , is negative, leading to condensation
max
of water vapour on the skin,
 or the estimated allowable exposure time is less than 30 min, so that the phenomenon of sweating onset
plays a major role in the estimation of the evaporation loss of the subject,
special precautionary measures need to be taken and direct and individual physiological supervision of the
workers is particularly necessary. The conditions for carrying out this surveillance and the measuring
techniques to be used are described in ISO 9886.
6.4 Organization of work in the heat
This International Standard makes it possible to compare different ways of organizing work and scheduling
rest periods if it is necessary.
A computer programme in Quick Basic is given in Annex E. It allows for the calculation and the interpretation
of any combination of sequences where the metabolic rate, the clothing thermal characteristics and climatic
parameters are known.
Annex F provides some data (input data and results) to be used for the validation of any computer programme
developed on the basis of the model presented in Annex A.

ISO 7933:2004(E)
Annex A
(normative)
Data necessary for the computation of thermal balance
A.1 Ranges of validity
The numerical values and the equations given in this annex conform to the present state of knowledge. Some
of them are likely to be amended in the light of increased knowledge.
The algorithms described in this annex were validated on a database including 747 lab experiments and
366 field experiments, from 8 research institutions. Table A.1 gives the ranges of conditions for which the
Predicted Heat Strain (PHS) model can be considered to be validated. When one or more parameters are
outside this range, it is recommended to use the present model with care and to bring special attention to the
people exposed.
Table A.1 — Ranges of validity of the PHS model
Parameters Minimum Maximum
t °C 15 50
a
p kPa 0 4,5
a
t – t °C 0 60
r a
–1
v ms 0 3
a
M W 100 450
I clo 0,1 1,0
cl
A.2 Determination of the heat flow by respiratory convection, C
res
The heat flow by respiratory convection can be estimated by the following empirical expression:
CM=+0,00152 (28,56 0,885t+ 0,641p ) (A.1)
res a a
A.3 Determination of the heat flow by respiratory evaporation, E
res
The heat flow by respiratory evaporation can be estimated by the following empirical expression:
E=+0,00127Mt(59,34 0,53−11,63p ) (A.2)
res a a
A.4 Determination of the steady state mean skin temperature
In climatic conditions for which this International Standard is applicable, the steady state mean skin
temperature can be estimated as a function of the parameters of the working situation, using the following
empirical expressions.
10 © ISO 2004 – All rights reserved

ISO 7933:2004(E)
For nude subjects (I u 0,2) For clothed subjects (I W 0,6)
cl cl
t = 7,19 + 0,064 t + 0,020 t
t = 12,17
sk,eq nu a a
sk,eq cl
+ 0,061 t + 0,044 t
r r
– 0,348 v – 0,253 v
a a
+ 0,198 p + 0,194 p
a a
+ 0,000 M + 0,005 346 M
+ 0,616 t + 0,512 74 t
re re
For I values between 0,2 and 0,6, the steady state skin temperature is extrapolated between these
cl
two values using:
tt=+ 2,5× (t −t )× (l− 0,2) (A.3)
sk,eq sk,eq nu sk,eq cl sk,eq nu cl
A.5 Determination of the instantaneous value of skin temperature
The skin temperature t at time t can be estimated
sk,i
i
 from the skin temperature t at time t one time increment earlier, and
sk,i-1
i–1
 from the steady state skin temperature t predicted from the conditions prevailing during the last time
sk,eq
increment by the equations described in (A.4).
The time constant of the response of the skin temperature being equal to 3 min, the following equation is used.
tt=+0,716 5 0,283 5t (A.4)
sk,iisk, –1 sk,eq
A.6 Determination of the heat accumulation associated with the metabolic rate, S
eq
In a neutral environment, the core temperature increases with time during exercise, as a function of the
metabolism rate relative to the individual's maximum aerobic power.
For an average subject, it can be assumed that this equilibrium core temperature increases as a function of
the metabolic rate, according to the following expression:
tM=−0,003 6 ( 55)+ 36,8 (A.5)
cr,eq
The core temperature reaches this equilibrium core temperature following a first order system with a time
constant equal to 10 min:
−t
tt=+36,8 ( − 36,8)× 1− exp (A.6)
cr cr,eq 

This expression can be translated in the following
tt=×k+t × (1−k) (A.7)
cr,eqiicr,eq −1 cr,eq
−incr

where k = exp


ISO 7933:2004(E)
The heat storage associated with this increase is
dS = c × (t − t ) × (1 − α) (A.8)
eq sp cr,eq i cr,eq i–1
A.7 Determination of the static insulation characteristics of clothing
For a nude subject and in static conditions without movements either of the air or of the person, the sensible
heat exchanges (C + R) can be estimated by
tt−
sk a
CR+=  (A.9)
I
tot st
2 −1
where the static heat resistance for nude subjects can be estimated equal to 0,111 m ⋅K⋅W .
For a clothed subject, this static heat resistance, I can be estimated using
,
tot st
I
a st
II= + (A.10)
tot st cl st
f
cl
where the ratio of the subject’s clothed to unclothed surface areas, f , is given by
cl
f = 1 + 1,97 I (A.11)
cl st
cl
A.8 Determination of the dynamic insulation characteristics of clothing
Activity and ventilation modify the insulation characteristics of the clothing and the adjacent air layer. Because
both wind and movement reduce the insulation, it therefore needs to be corrected. The correction factor for
the static clothing insulation and the external air layer insulation can be estimated with the following equations
I
= C × I (A.12)
tot dyn orr,tot tot st
I = C × I (A.13)
a dyn orr,Ia a st
(0,043 −+ 0,398vv  0,066 − 0,378v + 0,094v )
ww
ar ar
CC== e (A.14)
orr,tot orr,cl
For I W 0,6 clo for nude persons or the adjacent air layer, by
cl
(−+0,472vv 0,047 − 0,342v + 0,117v )
ar arw w
CC== e (A.15)
orr,tot orr, I
a
and for 0 clo u I u 0,6 clo, by
cl
C = (0,6 − I ) C + I × C
(A.16)
orr,tot cl orr,Ia cl orr,cl
−1 −1
with v limited to 3 m⋅sec and v limited to 1,5 m⋅sec .
ar w
When the walking speed is undefined or the person is stationary, the value for v can be calculated as
w
−1
vM=−0,0052 ( 58)     with v u 0,7 m⋅ s (A.17)

ww
Finally, I can be derived as
cl dyn
I
adyn
I = I − (A.18)
cl dyn tot dyn
f
cl
12 © ISO 2004 – All rights reserved

ISO 7933:2004(E)
A.9 Estimation of the heat exchanges through convection and radiation
The dry heat exchanges can be estimated using the following equations:
C + R = f × [h × (t − t ) + h × (t − t )] (A.19)

cl cdyn cl a r cl r
which describes the heat exchanges between the clothing and the environment, and

tt−
sk cl
CR+= (A.20)

I
cl dyn

which describes the heat exchanges between the skin and the clothing surface.
The dynamic convective heat exchange, h , can be estimated as the greatest value of
cdyn
0,25
2,38 t − t  (A.21)
sk a
3,5 + 5,2 v (A.22)
ar
0,6
8,7 v (A.23)
ar
The radiative heat exchange, h , can be estimated using the equation
r
tt+−273 (+ 273)
A()
−8 cl r
r
h=×5,67 10 ε× × (A.24)
r
At −t
Du cl r
A
r
The fraction of skin surface involved in heat exchange by radiation, , is equal to 0,67 for a crouching
A
Du
subject, 0,70 for a seated subject and 0,77 for a standing subject.
When reflective clothing is being worn, h must be corrected by a factor F given by
r cl,R
F = (1 − A ) 0,97 + A × F (A.25)

cl,R p p
r
Both expressions computing C + R must be solved iteratively in order to derive t .
cl
A.10 Estimation of the maximum evaporative heat flow at the skin surface, E
max
The maximum evaporative heat flow at the skin surface is given by
p − p
sk,s a
E = (A.26)
max
R
tdyn
The evaporative resistance, R , is estimated from the following equation:
tdyn
I
tot dyn
R = (A.27)
tdyn
i
mdyn
16,7
where the dynamic clothing permeability index, i , is equal to the static clothing permeability index i
mdyn mst
corrected for the influence of air and body movement.
i = i × C (A.28)
mdyn mst orr, E
ISO 7933:2004(E)
with
C = 2,6 C − 6,5 C + 4,9 (A.29)

orr, E orr,tot orr,tot
In this expression, i is limited to 0,9.
mdyn
A.11 Determination of the predicted sweat rate (Sw ) and predicted evaporative heat
p
flow (E )
p
The flow chart in Figure A.1 shows how the evaluations are performed.
This flow chart requires the following explanations:
R1: when the required evaporative heat flow E is greater than the maximum evaporation rate, the skin is
req
expected to be fully wetted: w greater than 1. w implies then the thickness of the water layer on the skin,
req req
rather than the equivalent fraction of the skin, which is covered with sweat. As the theoretical w is greater
req
than 1, the evaporation efficiency is expected to become lower.
1− w
req
For w u 1, the efficiency is given by r =
req
req
2 − w
req
For w W 1, it is given by r =
req req
This value, however, is at the minimum 5 %. This is reached for a theoretical wettedness of 1,684.
R2: the sweat rate response can be described by a first order system with a time constant of 10 min.
Therefore, the predicted sweat rate at time, t , (Sw ) is equal to a fraction k of the predicted sweat rate at
p,i Sw
i
time (t ) (Sw ) one time increment earlier plus the fraction (1– k ) of the sweat rate required by the
p,i–1 Sw
i–1
conditions prevailing during the last time increment (Sw ), and k is given by.
req Sw
k = exp(−incr / 10)
Sw
R3: as explained above, the required skin wettedness is allowed to be theoretically greater than 1 for the
computation of the predicted sweat rate. As the evaporative heat loss is restricted to the surface of the water
layer, that is, the surface of the body, the predicted skin wettedness cannot be greater than one. This occurs
as soon as the predicted sweat rate is more than twice the maximum evaporation heat flow.
A.12 Evaluation of the rectal temperature
The heat storage during the last time increment at time, t , is given by
i
S = E − E + S (A.30)
req p eq
This heat storage leads to an increase in core temperature, taking into account the increase in skin
temperature. The fraction of the body mass at the mean core temperature is given by
(1 − α ) = 0,7 + 0,09 (t − 36,8) (A.31)
cr
14 © ISO 2004 – All rights reserved

ISO 7933:2004(E)
This fraction is limited to
0,7 for t < 36,8 °C
cr
0,9 for t > 39,0 °C
cr
Figure A.2 illustrates the distribution of the temperature in the body at time (t ) and time t . From this it can
i–1 i
be computed that

tt−
1 dS α
cr,1ii−−sk,1
ii
tt=+− α−t (A.32)

cr,iicr,−−1 i 1 sk,i
α
cW 22
pb
1 −
The rectal temperature is estimated according to the following expres
...