EN ISO 7933:2023

SLOVENSKI STANDARD
01-december-2023
Nadomešča:
SIST EN ISO 7933:2004
Ergonomija toplotnega okolja - Analitično ugotavljanje in razlaga toplotnega
stresa z izračunom predvidene toplotne obremenitve (ISO 7933:2023)
Ergonomics of the thermal environment - Analytical determination and interpretation of
heat stress using calculation of the predicted heat strain (ISO 7933:2023)
Ergonomie der thermischen Umgebung - Analytische Bestimmung und Interpretation der
Wärmebelastung durch Berechnung der vorhergesagten Wärmebeanspruchung (ISO
7933:2023)
Ergonomie des ambiances thermiques - Détermination analytique et interprétation de la
contrainte thermique fondées sur le calcul de l'astreinte thermique prévisible (ISO
7933:2023)
Ta slovenski standard je istoveten z: EN ISO 7933:2023
ICS:
13.180 Ergonomija Ergonomics
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

EN ISO 7933
EUROPEAN STANDARD
NORME EUROPÉENNE
August 2023
EUROPÄISCHE NORM
ICS 13.180 Supersedes EN ISO 7933:2004
English Version
Ergonomics of the thermal environment - Analytical
determination and interpretation of heat stress using
calculation of the predicted heat strain (ISO 7933:2023)
Ergonomie des ambiances thermiques - Détermination Ergonomie der thermischen Umgebung - Analytische
analytique et interprétation de la contrainte thermique Bestimmung und Interpretation der Wärmebelastung
fondées sur le calcul de l'astreinte thermique prévisible durch Berechnung der vorhergesagten
(ISO 7933:2023) Wärmebeanspruchung (ISO 7933:2023)
This European Standard was approved by CEN on 13 June 2023.

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 CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
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EUROPÄISCHES KOMITEE FÜR NORMUNG

CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels
© 2023 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 7933:2023 E
worldwide for CEN national Members.

Contents Page
European foreword . 3

European foreword
This document (EN ISO 7933:2023) 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 2024, and conflicting national standards
shall be withdrawn at the latest by February 2024.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document supersedes EN ISO 7933:2004.
Any feedback and questions on this document should be directed to the users’ national standards
body/national committee. A complete listing of these bodies can be found on the CEN website.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland,
Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Republic of
North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Türkiye and the
United Kingdom.
Endorsement notice
The text of ISO 7933:2023 has been approved by CEN as EN ISO 7933:2023 without any modification.

INTERNATIONAL ISO
STANDARD 7933
Third edition
2023-07
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 7933:2023(E)
ISO 7933:2023(E)
© ISO 2023
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
or ISO’s member body in the country of the requester.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
ii
ISO 7933:2023(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 1
5 Principles of the predicted heat strain (PHS) model . 4
6 Main steps of the calculation .5
6.1 Heat balance equation . 5
6.1.1 General . 5
6.1.2 Metabolic rate, M . 5
6.1.3 Effective mechanical power, W . 5
6.1.4 Heat flow by respiratory convection, C . 5
res
6.1.5 Heat flow by respiratory evaporation, E . 5
res
6.1.6 Heat flow by conduction, K . 5
6.1.7 Heat flow by convection, C . 6
6.1.8 Heat flow by radiation, R . 6
6.1.9 Heat flow by evaporation, E . 6
6.1.10 Heat storage for increase of core temperature associated with the
metabolic rate, Q . 6
eqi
6.1.11 Heat storage, S . 6
6.2 Calculation of the required evaporative heat flow, the required skin wettedness
and the required sweat rate . 7
7 Interpretation of required sweat rate . 7
7.1 Basis of the method of interpretation . 7
7.1.1 General . 7
7.1.2 Stress criteria . 7
7.1.3 Strain criteria . 8
7.1.4 Reference values . 8
7.2 Analysis of the work situation . 8
7.3 Determination of allowable exposure time, D . 8
lim
Annex A (normative) Data necessary for the computation of thermal balance .9
Annex B (informative) Criteria for estimating acceptable exposure time in a hot work
environment .17
Annex C (informative) Metabolic rate .19
Annex D (informative) Clothing thermal characteristics .20
Annex E (informative) Computer program for the computation of the predicted heat strain
model .22
Annex F (informative) Examples of the predicted heat strain model computations .27
Bibliography .28
iii
ISO 7933:2023(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.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2 (see www.iso.org/directives).
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. Details of
any patent rights identified during the development of the document will be in the Introduction and/or
on the ISO list of patent declarations received (see www.iso.org/patents).
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see
www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 159, Ergonomics, Subcommittee
SC 5, Ergonomics of the physical environment, in collaboration with the European Committee for
Standardization (CEN) Technical Committee CEN/TC 122, Ergonomics, in accordance with the
Agreement on technical cooperation between ISO and CEN (Vienna Agreement).
This third edition cancels and replaces the second edition (ISO 7933:2004), which has been technically
revised.
The main changes are as follows:
— The maximum sweat rate S described in B.4 has been corrected, i.e. it is no longer adjusted for
Wmax
metabolic rate.
— As the model has not been extensively validated for conditions with unsteady environmental
parameters, metabolic rate and/or clothing, a caution has been added for cases where these
parameters vary substantially with time.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
iv
ISO 7933:2023(E)
Introduction
ISO 15265 describes the assessment strategy for the prevention of discomfort or health effects in any
1)
thermal working condition, while ISO 8025 recommends specific practices concerning hot working
environments. For these hot environments, these standards propose relying on the wet bulb globe
temperature (WBGT) heat stress index described in ISO 7243 as a screening method for establishing
the presence or absence of heat stress, and on the more elaborate method presented in this document,
to make a more accurate estimation of stress, to determine the allowable durations of work in these
conditions and to optimize the methods of protection. This method, based on an analysis of the heat
exchange between a person and the environment, is intended to be used directly when it is desirable to
carry out a detailed analysis of working conditions in heat.
This document makes it possible to predict the evolution of a few physiological parameters (skin and
rectal temperatures, as well as sweat rate) over time for a person working in a hot environment. This
prediction is made according to the climatic parameters, the energy expenditure of the person and his
or her clothing. This prediction is made for an average person and should be used to assess the risk of
heat stress for a group of people; it cannot predict a particular person’s responses.
This document 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.
Occupational health specialists are responsible for evaluating the risk encountered by a given individual,
taking into consideration their specific characteristics that can differ from those of a standard person.
ISO 9886 describes how physiological parameters are used to monitor the physiological behaviour of a
particular person and ISO 12894 describes how medical supervision is organized.
1) Under preparation. Stage at the time of publication: ISO/DIS 8025:2023.
v
INTERNATIONAL STANDARD ISO 7933:2023(E)
Ergonomics of the thermal environment — Analytical
determination and interpretation of heat stress using
calculation of the predicted heat strain
1 Scope
This document describes a model [the predicted heat strain (PHS) model] for the analytical
determination and interpretation of the thermal stress (in terms of water loss and rectal temperature)
experienced by an average person in a hot environment and determines the maximum allowable
exposure times within which the physiological strain is acceptable for 95 % of the exposed population
(the maximum tolerable rectal temperature and the maximum tolerable water loss are not exceeded by
95 % of the exposed people).
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 average person. In this way, this document makes it possible to determine which parameter
or group of parameters can be changed, and to what extent, in order to reduce the risk of excessive
physiological strain.
In its present form, this method of assessment is not applicable to cases where special protective
clothing (e.g. fully reflective clothing, active cooling and ventilation, impermeable coveralls) is worn.
This document does not predict the physiological response of an individual person, but only considers
average persons in good health and fit for the work they perform. It is therefore intended to be
used by, among others, ergonomists and industrial hygienists, as the outcomes can require expert
interpretations. Recommendations about how and when to use this model are given in ISO 8025.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements 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 13731, Ergonomics of the thermal environment — Vocabulary and symbols
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 13731 apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
4 Symbols
For the purposes of this document, the symbols and units listed in Table 1 apply.
ISO 7933:2023(E)
Table 1 — Symbols and units
Symbol Term Unit
α fraction of the body mass at the skin temperature —
α fraction of the body mass at the skin temperature at time t —
i i
α fraction of the body mass at the skin temperature at time t —
i–1 i–1
β correction factor for the static moisture permeability index —
im
β correction factor for the static boundary layer thermal insulation —
Ia
β correction factor for the static clothing thermal insulation —
Icl
β correction factor for the static total clothing thermal insulation —
IT
ε emissivity of outer clothing surface, assuming this is non-reflective —
cl
ε emissivity of outer clothing surface —
cl,r
θ angle between walking direction and wind direction —
A DuBois body area surface m
Du
A fraction of the body surface covered by the reflective clothing —
p
A effective radiating area of a body m
r
−2
C convective heat flow W⋅m
−1
c water latent heat of vaporization J⋅kg
e
−1 −1
c specific heat of dry air at constant pressure J⋅kg ⋅K
p
−1 −1
c specific heat of the body J⋅kg ⋅K
p,b
−2
C respiratory convective heat flow W⋅m
res
D allowable exposure time min
lim
D allowable exposure time for heat storage min
lim,tcr
D allowable exposure time for water loss, 95 % of the working population min
lim,loss
D maximum water loss g
max
−2
E maximum evaporative heat flow at the skin surface W⋅m
max
−2
E predicted evaporative heat flow at the skin surface W⋅m
p
−2
E required evaporative heat flow at the skin surface W⋅m
req
−2
E respiratory evaporative heat flow W⋅m
res
f clothing area factor —
cl
F reflection coefficients for different special materials —
r
−2 −1
h convective heat transfer coefficient W⋅m ⋅K
c
−2 −1
h radiative heat transfer coefficient W⋅m ⋅K
r
2 −1
I resultant boundary layer thermal insulation m ⋅K⋅W
a,r
2 −1
I static (or basic) boundary layer thermal insulation m ⋅K⋅W
a
2 −1
I resultant clothing thermal insulation m ⋅K⋅W
cl,r
2 −1
I static (or basic) clothing thermal insulation m ⋅K⋅W
cl
i resultant moisture permeability index —
m,r
i static (or basic) moisture permeability index —
m
2 −1
I resultant total clothing thermal insulation m ⋅K⋅W
T,r
2 −1
I static (or basic) total clothing thermal insulation m ⋅K⋅W
T
−2
K conductive heat flow W⋅m
k time constant of the increase of the sweat rate min
Sw
time constant of the variation of the core temperature as function of the met-
k min
tcr
abolic rate
k time constant of the variation of the skin temperature min
tsk
−2
M metabolic rate W⋅m
ISO 7933:2023(E)
TTabablele 1 1 ((ccoonnttiinnueuedd))
Symbol Term Unit
p water vapour partial pressure at air temperature kPa
a
−2
Q heat storage during the last time increment at time t W⋅m
tot,i i
heat storage during the last time increment at time t , due to the increase of
i
−2
Q W⋅m
eq,i
core temperature associated with the metabolic rate
−2
R radiative heat flow W⋅m
2 −1
R resultant clothing total water vapour resistance m ⋅Pa⋅W
e,T,r
r required evaporative efficiency of sweating —
req
−2
S body heat storage rate W⋅m
body heat storage for increase of core temperature associated with the met-
−2
S W⋅m
eq
abolic rate
−2
S maximum sweat rate capacity W⋅m
Wmax
−2
S predicted sweat rate W⋅m
Wp
−2
S predicted sweat rate at time t W⋅m
Wp,i i
−2
S predicted sweat rate at time t W⋅m
Wp,i–1 i–1
−2
S required sweat rate W⋅m
Wreq
t time min
t air temperature °C
a
t clothing surface temperature °C
cl
t core temperature °C
cr
t core temperature as a function of the metabolic rate at time t °C
cr,eq i i
t core temperature as a function of the metabolic rate at time t °C
cr,eq i–1 i–1
t steady-state value of core temperature as a function of the metabolic rate °C
cr,eqm
t core temperature at time t °C
cr,i i
t core temperature at time t °C
cr,i-1 i–1
t expired air temperature °C
ex
t mean radiant temperature °C
r
t rectal temperature °C
re
t maximum rectal temperature °C
re,max
t rectal temperature at time t °C
re,i i
t rectal temperature at time t °C
re,i–1 i–1
t skin temperature °C
sk
t steady-state mean skin temperature °C
sk,eq
t steady-state mean skin temperature for clothed person °C
sk,eq,cl
t steady-state mean skin temperature for nude person °C
sk,eq,nu
t mean skin temperature at time t °C
sk,i i
t mean skin temperature at time t °C
sk,i–1 i–1
−1
V expired volume flow rate L⋅min
ex
−1
v air velocity m⋅s
a
−1
v relative air velocity m⋅s
ar
−1
v walking speed m⋅s
w
−2
W effective mechanical power W⋅m
W humidity ratio of inhaled air kg /kg
a water air
W body mass kg
b
W humidity ratio of expired air kg /kg
ex water air
ISO 7933:2023(E)
TTabablele 1 1 ((ccoonnttiinnueuedd))
Symbol Term Unit
w skin wettedness —
w maximum skin wettedness —
max
w predicted skin wettedness —
p
w required skin wettedness —
req
5 Principles of the predicted heat strain (PHS) model
WARNING — The model has not been extensively validated for conditions with unsteady
environmental parameters, metabolic rate and/or clothing and therefore must be used
cautiously in cases where these parameters vary substantially with time. It does not enable
users to determine validly the duration of time needed for an average person whose rectal
temperature has risen to 38 °C or more to recover a rectal temperature of 36,8 °C.
The PHS model is based on the thermal energy balance of the body, which requires the values of the
following parameters:
a) the parameters of the thermal environment as measured or estimated according to ISO 7726:
— air temperature, t ;
a
— mean radiant temperature, t ;
r
— water vapour partial pressure, p ;
a
— air velocity, v .
a
b) the metabolic rate, M, as measured or estimated using ISO 8996 or other methods of equal or
greater accuracy;
c) the static clothing thermal characteristics, as measured or estimated using ISO 9920 or other
methods of equal or greater accuracy.
Clause 6 describes the principles of the calculation of the different heat exchanges occurring in the
heat balance equation, as well as those of the sweat loss necessary for the maintenance of the thermal
equilibrium of the body. The mathematical expressions given in Annex A shall be used for these
calculations.
Clause 7 describes the method for interpreting the results from Clause 6, which leads to the
determination of the predicted sweat rate, the predicted rectal temperature and the allowable exposure
times. The determination of the allowable exposure times is based on two strain criteria: maximum
allowable rectal temperature and maximum allowable body water loss, given in Annex B.
The accuracy with which the predicted sweat rate and the exposure times are estimated is a function
of the model (i.e. of the expressions in Annex A) and the maximum allowable values which are adopted.
It is also a function of the accuracy of estimation and measurement of physical parameters, metabolic
rate and thermal insulation of the clothing.
ISO 7933:2023(E)
6 Main steps of the calculation
6.1 Heat balance equation
6.1.1 General
The thermal energy balance of the human body can be written as Formula (1):
M − W = C + 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, are 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
res res
by conduction, K, convection, C, radiation, R, and evaporation, E.
If the balance is not satisfied, some excess energy is stored in the body, S.
The different terms of Formula (1) are successively reviewed in 6.1.2 to 6.1.11 in terms of the principles
of calculation (normative expressions for the computations are provided in Annex A).
6.1.2 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.
6.1.3 Effective mechanical power, W
In most industrial situations, the effective mechanical power is small and can be ignored, i.e. W = 0.
6.1.4 Heat flow by respiratory convection, C
res
The heat flow by respiratory convection is expressed, in principle, by Formula (2):
tt− 
ex a
Cc=×0,000 02 V × (2)
 
resp ex
A
 
Du
6.1.5 Heat flow by respiratory evaporation, E
res
The heat flow by respiratory evaporation is expressed, in principle, by Formula (3):
WW−
 
ex a
Ec=×0,000 02 V × (3)
resee x  
A
 
Du
6.1.6 Heat flow by conduction, K
Heat flow by thermal conduction occurs on the body surfaces in contact with solid objects. It is usually
quite small and ignored.
NOTE ISO 13732-1 deals specifically with the risks of pain and burns when parts of the body come into
contact with hot surfaces.
ISO 7933:2023(E)
6.1.7 Heat flow by convection, C
The heat flow by convection on the bare skin is expressed by Formula (4):
C = h × (t – t ) (4)
c sk a
For clothed people, the heat flow by convection occurs at the surface of the clothing and is expressed by
Formula (5):
C = h × f × (t – t) (5)
c cl cl a
Annex D provides some indications for the evaluation of the clothing thermal characteristics.
6.1.8 Heat flow by radiation, R
The heat flow by radiation is expressed by Formula (6):
R = h × f × (t – t) (6)
r cl cl a
where h is the radiative heat transfer coefficient and takes into account the clothing characteristics
r
(e.g. emissivity and the presence of reflective clothing) and the effective radiating area of the person
related to the posture (e.g. standing, seated, crouching person).
6.1.9 Heat flow by evaporation, E
The maximum evaporative heat flow, E , is that which can be achieved in the hypothetical case of the
max
skin being completely wetted. In these conditions, Formula (7) applies:
pp−
sk,s a
E = (7)
max
R
e,T,r
where the dynamic clothing total water vapour resistance, R , takes into account the clothing
e,T,r
characteristics as well as the movements of the person and the air.
The actual evaporation heat flow, E, depends upon the fraction, w, of the skin surface wetted by sweat
and is given by Formula (8):
E = w × E (8)
max
6.1.10 Heat storage for increase of core temperature associated with the metabolic rate, Q
eqi
Even in a neutral environment, the core temperature rises towards a steady-state value, t , as a
cr,eq
function of the metabolic rate.
The core temperature reaches this steady-state temperature exponentially with time. The heat storage
associated with the increase from time t to time t , Q does not contribute to the onset of sweating
i–1 i eqi
and should therefore be deducted from Formula (1).
6.1.11 Heat storage, S
The heat storage of the body is given by the algebraic sum of the heat flows defined previously.
ISO 7933:2023(E)
6.2 Calculation of the required evaporative heat flow, the required skin wettedness and
the required sweat rate
Because conduction (K) is ignored as it is a non-significant avenue of heat exchange, the general
Formula (1) can be written as Formula (9):
E + S = M – W – C – E – C – R (9)
res res
The required evaporative heat flow, E , is the evaporation heat flow required for the maintenance of
req
the thermal equilibrium of the body and, therefore, for the body heat storage rate to be equal to zero. It
is given by Formula (10):
E = M – W – C – E – C – R (10)
req res res
The required skin wettedness, w , is the ratio between the required evaporative heat flow and the
req
maximum evaporative heat flow at the skin surface, as in Formula (11):
E
req
w = (11)
req
E
max
The calculation of the required sweat rate, S , is made on the basis of the required evaporative heat
Wreq
flow, but taking account of the evaporative efficiency of the sweating, r , as in Formula (12):
req
E
req
S = (12)
Wreq
r
req
−2 −2 −1
NOTE The sweat rate in W⋅m represents the equivalent in heat of the sweat rate expressed in g⋅m h .
−2 −2 −1 −1 2
1 W⋅m corresponds to a flow of sweat of 1,47 g⋅m h or 2,67 g⋅h for a standard person (1,8 m of body
surface).
7 Interpretation of required sweat rate
7.1 Basis of the method of interpretation
7.1.1 General
The interpretation of the values calculated by the recommended analytical method is based on:
— two stress criteria (see 7.1.2):
— the maximum skin wettedness, w ;
max
— the maximum sweat rate, S ;
Wmax
— two strain criteria (see 7.1.3):
— the maximum rectal temperature, t ;
re, max
— the maximum water loss, D .
max
7.1.2 Stress criteria
The required sweat rate, S , cannot exceed the maximum sweat rate, S , achievable by the person.
Wreq Wmax
The required skin wettedness, w , cannot exceed the maximum skin wettedness, w , achievable by
req max
the person. These two maximum values are a function of the acclimatization of the person.
ISO 7933:2023(E)
7.1.3 Strain criteria
In the case of non-equilibrium of the thermal balance, the rectal temperature increase should be limited
at a maximum value, t , such that the probability of any acute pathological effect due to heat stress
re,max
is extremely limited. Finally, whatever the thermal balance, the water loss should be restricted to a
value, D , compatible with fluid and electrolyte maintenance by the body.
max
7.1.4 Reference values
Annex B includes reference values for the stress criteria (w and S ) and the strain criteria (t
max Wmax re, max
and D ). w , S and D values are a function of the acclimatization state of the person.
max max Wmax max
7.2 Analysis of the work situation
Heat exchanges are computed at time t , from the body conditions existing at the previous computation
i
time, t , and as a function of the climatic parameters, the metabolic rate and clothing conditions during
i-1
the time increment.
The steps are:
— the required evaporative heat flow, E , skin wettedness, w , and sweat rate, S , are first
req req Wreq
computed;
— from these, the predicted sweat rate, S , skin wettedness, w , and evaporative heat flow, E , are
Wp p p
computed considering the stress criteria (E , w and S ) as well as the exponential response
max max Wmax
of the sweating system;
— the rate of heat storage is estimated by the difference between the required and predicted
evaporative heat flow;
— the stored heat contributes to the increase or decrease in skin and core temperatures and these are
estimated;
— from these values, the heat exchanges during the time increment are computed.
The evolutions of S , t and t are in this way iteratively computed.
Wp cr re
7.3 Determination of allowable exposure time, D
lim
The allowable exposure time, D , is reached when either the predicted rectal temperature (t ) or the
lim re
predicted cumulated water loss reaches the corresponding maximum values.
Special precautionary measures need to be taken and individual physiological supervision of the
persons is recommended in work situations in which:
— the maximum evaporative heat flow at the skin surface, E , is negative, leading to condensation of
max
water vapour on the skin; or
— the estimated allowable exposure time is less than 30 min.
The conditions for carrying out this surveillance and the measuring techniques to be used are described
in ISO 9886.
A computer program in BASIC is given in Annex E, which allows for the calculation and the interpretation
of any condition where the metabolic rate, the clothing thermal characteristics and the climatic
parameters are known.
Annex F provides some data (input data and results) that shall be used for the validation of any computer
program developed on the basis of the model presented in Annex A.
ISO 7933:2023(E)
Annex A
(normative)
Data necessary for the computation of thermal balance
A.1 Ranges of validity
The numerical values and the formulae given in this annex conform to the state of knowledge at the
time of publication. Some are likely to be amended in the light of increased knowledge.
The algorithms described in this annex were validated on a database of 747 laboratory experiments
[15]
and 366 field experiments from eight European research institutions. Table A.1 gives the ranges of
conditions for which the PHS model can be considered to be validated. When one or more parameters
are outside this range, this model should be used with care and special attention given to the people
exposed.
Table A.1 — Ranges of validity of the PHS model
Parameters Units Minimum Maximum
t °C 15 50
a
p kPa 0,5 4,5
a
t – t °C 0 60
r a
–1
v ms 0 3
a
−2
M W⋅m 56 250
I clo 0,1 1,0
cl
The time increment used during this validation study was equal to 1 min. The model has not been
validated for times in excess of 480 min.
A.2 Determination of the heat flow by respiratory convection, C
res
The heat flow by respiratory convection can be estimated by Formula (A.1):
C = 0,001 52 M (28,56 – 0,885 t + 0,641 p ) (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 Formula (A.2):
E = 0,001 27 M (59,34 + 0,53 t – 11,63 p) (A.2)
res a a
A.4 Determination of the steady-state mean skin temperature
In climatic conditions for which this document is applicable, the steady-state mean skin temperature
can be estimated as a function of the parameters of the working situation, using Formulae (A.3) and
(A.4).
— For I ≤ 0,2 clo:
cl
t = 7,19 + 0,064 t + 0,061 t – 0,348 v + 0,198 p + 0,616 t (A.3)
sk,eq,nu a r a a re
ISO 7933:2023(E)
— For I ≥ 0,6 clo:
cl
t = 12,17 + 0,02 t + 0,04 t – 0,253 v + 0,194 p + 0,005 35 M + 0,513 t (A.4)
sk,eq,cl a r a a re
For I values between 0,2 and 0,6, the steady-state skin temperature is interpolated between these two
cl
values using Formula (A.5):
t = t + 2,5 × (t – t ) × (I – 0,2) (A.5)
sk,eq sk,eq,nu sk,eq,cl sk,eq,nu cl,st
A.5 Determination of the instantaneous value of skin temperature
The skin temperature, t , at time t can be estimated from:
sk,i i
— the skin temperature, t , at time t one minute earlier;
sk,i–1 i-1
— the steady-state skin temperature, t , predicted from the conditions existing during the last
sk,eq
minute by Formula (A.5).
The time constant of the response of the skin temperature being equal to 3 min, Formulae (A.6) and
(A.7) are used:
t = k × t + (1 – k ) × t (A.6)
sk,i tsk sk,i–1 tsk sk,eq
k = exp(–1/3) (A.7)
tsk
A.6 Determination of the heat accumulation associated with the metabolic rate,
Q
eqi
In a neutral environment, the core temperature increases as a function of metabolic rate. For an average
person, equilibrium core temperature is related to metabolic rate according to Formula (A.8):
t = 0,003 6(M – 55) + 36,8 (A.8)
cr,eq
The core temperature reaches this equilibrium core temperature following a first-order system with a
time constant equal to 10 min. At time i, it is estimated using Formulae (A.9) and (A.10):
t = k × t + (1 – k ) × t (A.9)
cr,eq,i tcr cr,eq,i-1 tcr cr,eq
k = exp(–1/10) (A.10)
tcr
The heat storage associated with this increase is given by Formula (A.11):
Q = c × W / (A × 60) × (t – t ) × (1 – α ) (A.11)
eqi p,b b Du cr,eq,i cr,eq,i-1 i-1
ISO 7933:2023(E)
A.7 Determination of the static insulation characteristics of clothing
−1
For a nude person and in static conditions without movements either of the air (<0,2 m⋅s ) or of the
person, the sensible heat exchanges (C + R) can be estimated by Formula (A.12):
tt−
sk a
CR+= (A.12)
I
T
For a clothed person, this static heat resistance, I , can be estimated using Formula (A.13):
T
I
a
II=+ (A.13)
Tcl
f
cl
where
2 −1
— I can be estimated as 0,111 m K⋅W ;
a
— the clothing area factor, f , is given by Formula (A.14):
cl
f = 1 + 1,97·I (A.14)
cl cl
A.8 Determination of the resultant (or 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, this needs to be corrected. The correction
factor β can be estimated with Formulae (A.15) and (A.16):
IT
— for a nude person (I = 0):
cl,st
0,,047vv−0 472 +−0,,117vv0342
[]() ()
ar ar ww
ββ==e (A.15)
IT Ia
— for a person wearing clothes with I > 0,6 clo:
cl,st
0,,043 +−()0 066vv0,,398 +−()0 094vv0,378
[]
ar ar ww
ββ==e (A.16)
IT cl
When the walking speed is undefined or the person is stationary, the value for v can be calculated
w
with Formula (A.17):
v = 0,005 2 (M – 58) (A.17)
w
−1
where v ≤ 0,7 m⋅s .
w
When the walking speed v is known, but the direction varies, the relative air velocity is taken as the
w
largest of the two velocities v and v .
a w
When a walking direction θ is kept relative to the air velocity, the relative air velocity is given by
Formula (A.18):
v = |v +v cos(πθ/180)| (A.18)
ar a w
−1
In all cases, the relative air velocity, v , is limited to 3 m⋅s and the walking speed, v , limited to
ar w
−1
1,5 m⋅s .
ISO 7933:2023(E)
For conditions with I between 0 and 0,6 clo, the correction factor is estimated by interpolation
cl
between these two values by Formulae (A.19) to (A.22):
β = [(0,6 – I ) × β + I × β ]/0,6 (A.19)
IT cl Ia cl cl
In any case, this correction factor is limited to 1.
Finally, resultant (or dynamic) thermal insulation values are calculated as:
I = β × I (A.20)
a,r Ia a
I = β × I (A.21)
T,r IT T
I
a,r
II=− (A.22)
cl,rT,r
f
cl
A.9 Estimation of the heat exchanges through convection and radiation
The dry heat exchanges can be estimated using Formulae (A.23) to (A.27). Formulae (A.23) describes
the heat exchanges between the clothing and the environment:
C + R = f × [h × (t – t ) + h × (t – t )] (A.23)
cl c cl a r cl r
Formulae (A.24) describes the heat exchanges between the skin and the clothing surface:
 
tt−
sk cl
CR+= (A.24)
 
I
cl,r
 
The convective heat transfer coefficient, h , can be estimated as the greatest value of:
c
0,25
2,38|t – t | (A.25)
cl a
3,5 + 5,2v (A.26)
ar
0,6
8,7v (A.27)
ar
The radiative heat exchange coefficient, h , can be estimated using Formula (A.28):
r
A ()tt+−273 (
...