prEN ISO 7933

SLOVENSKI STANDARD
01-junij-2018
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Ergonomics of the thermal environment - Analytical determination and interpretation of
heat stress using the predicted heat strain model (ISO/DIS 7933:2018)
Ergonomie der thermischen Umgebung - Analytische Bestimmung und Interpretation der
Wärmebelastung mit dem Modell der vorhergesagten Wärmebeanspruchung (ISO/DIS
7933:2018)
Ergonomie des ambiances thermiques - Détermination analytique et interprétation de la
contrainte thermique fondées sur le calcul de l'astreinte thermique prévisible (ISO/DIS
7933:2018)
Ta slovenski standard je istoveten z: prEN ISO 7933
ICS:
13.180 Ergonomija Ergonomics
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

DRAFT INTERNATIONAL STANDARD
ISO/DIS 7933
ISO/TC 159/SC 5 Secretariat: BSI
Voting begins on: Voting terminates on:
2018-04-13 2018-07-06
Ergonomics of the thermal environment — Analytical
determination and interpretation of heat stress using the
predicted heat strain model
Ergonomie des ambiances thermiques — Détermination analytique et interprétation de la contrainte
thermique fondées sur le calcul de l'astreinte thermique prévisible
ICS: 13.180
THIS DOCUMENT IS A DRAFT CIRCULATED
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STANDARD UNTIL PUBLISHED AS SUCH.
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NATIONAL REGULATIONS.
ISO/DIS 7933:2018(E)
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TO SUBMIT, WITH THEIR COMMENTS,
NOTIFICATION OF ANY RELEVANT PATENT
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©
PROVIDE SUPPORTING DOCUMENTATION. ISO 2018

ISO/DIS 7933:2018(E)
© ISO 2018
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ii © ISO 2018 – All rights reserved

ISO/DIS 7933:2018(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Symbols . 1
4 Principles of the predicted heat strain (PHS) model . 4
5 Main steps of the calculation . 5
5.1 Heat balance equation . 5
5.1.1 Metabolic rate, M .5
5.1.2 Effective mechanical power, W .5
5.1.3 Heat flow by respiratory convection, C .
res 5
5.1.4 Heat flow by respiratory evaporation, E .
res 5
5.1.5 Heat flow by conduction, K .5
5.1.6 Heat flow by convection, C .6
5.1.7 Heat flow by radiation, R .6
5.1.8 Heat flow by evaporation, E.6
5.1.9 Heat storage for increase of core temperature associated with the
metabolic rate, dS .
eq 6
5.1.10 Heat storage, S .6
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 . 7
6.1 Basis of the method of interpretation . 7
6.1.1 Stress criteria . 7
6.1.2 Strain criteria . 8
6.1.3 Reference values . 8
6.2 Analysis of the work situation . 8
6.3 Determination of allowable exposure time, D .
lim 8
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 .17
Annex C (informative) Metabolic rate .19
Annex D (informative) Clothing thermal characteristics .21
Annex E (informative) Computer programme for the computation of the predicted heat
strain model .23
Annex F (normative) Examples of the predicted heat strain model computations .31
Bibliography .32
ISO/DIS 7933:2018(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 third edition cancels and replaces the second edition (ISO 7933:2004).
iv © ISO 2018 – All rights reserved

ISO/DIS 7933:2018(E)
Introduction
This series of International Standards describe a coordinated set of methods for the evaluation of
[1]
working conditions as a function of the thermal environment. ISO 15265 describes the assessment
strategy for the prevention of discomfort or health in any thermal working condition, while
[2]
ISO 16595/WP recommends specific practices concerning hot working environments. For these hot
environments, these standards propose to rely on the wet bulb globe temperature (WBGT) heat stress
index described in ISO 7243 [3] as a screening method - for establishing the presence or absence of heat
stress and on the more elaborate method presented in this International standard, 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 desired to carry out an intensive
analysis of working conditions in heat.
This International Standard standardizes the method that occupational health specialists are expected
to use to approach a given problem and progressively collect the information needed to control or
prevent the problem.
This third edition of the standard 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
still be taken into account in the future 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. It does not either account for transients in environmental conditions, metabolic rate and/or
clothing and therefore makes possible to predict the evolution of the core temperature and the water
loss in conditions where these parameters remain steady. In addition, occupational health specialists
are responsible for evaluating the risk encountered by a given individual, taking into consideration
[4]
their specific characteristics that might differ from those of a standard subject. ISO 9886 describes
how physiological parameters are used to monitor the physiological behaviour of a particular subject
[5]
and ISO 12894 describes how medical supervision is organized.
DRAFT INTERNATIONAL STANDARD ISO/DIS 7933:2018(E)
Ergonomics of the thermal environment — Analytical
determination and interpretation of heat stress using the
predicted heat strain model
1 Scope
The main objective of this International Standard is to describe a mathematical model (the predicted
heat strain model) for the analytical determination and interpretation of the thermal stress (in terms
of water loss and core temperature) experienced by a subject in a hot environment and to determine
the “maximum allowable exposure times”, with which the physiological strain is acceptable for 95% of
the exposed population. (the maximum tolerable core 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 subject. In this way, this International Standard 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 physiological
strains.
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. Recommendations about how and when to use this
model are given in ISO 15265, Ergonomics of the thermal environment -- Risk assessment strategy for
the prevention of stress or discomfort in thermal working conditions
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 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 thermal insulation and water vapour
resistance of a clothing ensemble
ISO 13731, Ergonomics of the thermal environment — Vocabulary and symbols
ISO 13732-1, Ergonomics of the thermal environment — Methods for the assessment of human responses to
contact with surfaces — Part 1: Hot surfaces
ISO 15265, Ergonomics of the thermal environment — Risk assessment strategy for the prevention of stress
or discomfort in thermal working conditions
ISO 16595/WP, Ergonomics of the thermal environment: Working practices in hot environments
3 Symbols
For the purposes of this document, the symbols and abbreviated terms, designated in Table 1 as
“symbols” with their units, are in accordance with ISO 13731.
ISO/DIS 7933:2018(E)
However, additional symbols are used for the presentation of the predicted heat strain index. A complete
list of symbols used in this International standard is presented in Table 2.
Table 1 — Symbols and units conforming to ISO 13731
Symbol Term Unit
α fraction of the body mass at the skin temperature ‒
α skin-core weighting at time t ‒
i i
α
skin-core weighting at time t ‒
i–1 i–1
ε skin emissivity ‒
ε emissivity of clothing ‒
cl
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 2
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
C correction factor for the static moisture permeability index ‒
orr,im
C correction factor for the static boundary layer thermal insulation ‒
orr,Ia,st
C correction factor for the static clothing thermal insulation ‒
orr,Icl,st
C correction factor for the static total clothing thermal insulation ‒
orr,Itot,st
-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
D maximum water loss to protect 95 % of the working population g
max,95
-2
dS body heat storage at the time i W⋅m
i
body heat storage rate due to increase of core temperature associated with the
-2
dS W⋅m
eq
metabolic rate
-2
E evaporative heat flow at the skin surface W⋅m
-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 reduction factor for radiation heat exchange due to wearing reflective clothes ‒
cl,R
F Reflection coefficients for different special materials ‒
r
H body height m
b
-2 -1
h dynamic convective heat transfer coefficient W⋅m ⋅K
c,dyn
-2 -1
h radiative heat transfer coefficient W⋅m ⋅K
r
2 -1
I dynamic boundary layer thermal insulation m ⋅K⋅W
a,dyn
2 -1
I static boundary layer thermal insulation m ⋅K⋅W
a,st
2 -1
I dynamic clothing thermal insulation m ⋅K⋅W
cl,dyn
2 -1
I static clothing thermal insulation m ⋅K⋅W
cl,st
2 © ISO 2018 – All rights reserved

ISO/DIS 7933:2018(E)
Table 1 (continued)
Symbol Term Unit
i dynamic moisture permeability index ‒
m,dyn
i static moisture permeability index ‒
m,st
incr time increment from time t to time t min
i–1 i
2 -1
i dynamic total clothing thermal insulation m ⋅K⋅W
T,dyn
2 -1
i static total clothing thermal insulation m ⋅K⋅W
T,st
-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
tcreq
abolic rate
k time constant of the variation of the skin temperature min
tsk
-2
M metabolic rate W⋅m
p water vapour partial pressure at air temperature kPa
a
p
saturated water vapour pressure at skin temperature kPa
sk,s
-2
R radiative heat flow W⋅m
2 -1
R dynamic clothing total water vapour resistance m ⋅Pa⋅W
e,T,dyn
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 meta-
-2
S W⋅m
eq
bolic rate
-2
Sw maximum sweat rate capacity W⋅m
max
-2
Sw predicted sweat rate W⋅m
p
-2
Sw predicted sweat rate at time t W⋅m
p,i i
-2
Sw predicted sweat rate at time t W⋅m
p,i–1 i–1
-2
Sw required sweat rate W⋅m
req
t time min
t air temperature °C
a
t clothing surface temperature °C
cl
t core temperature °C
cr
t steady state core temperature as a function of the metabolic rate °C
cr,eq
t
t core temperature as a function of the metabolic rate at time °C
cr,eq i i
t
t core temperature as a function of the metabolic rate at time °C
cr,eq i–1 i–1
t steady state value of core temperature as a function of the metabolic rate °C
cr,eq,m
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 acceptable core temperature °C
cr,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 subjects °C
sk,eq,cl
t steady state mean skin temperature for nude subjects °C
sk,eq,nu
ISO/DIS 7933:2018(E)
Table 1 (continued)
Symbol Term Unit
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
w skin wettedness ‒
-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
w maximum skin wettedness ‒
max
w predicted skin wettedness ‒
p
w required skin wettedness ‒
req
4 Principles of the predicted heat strain (PHS) model
The PHS model is based on the thermal energy balance of the body which requires the values of the
following parameters, which are estimated or measured according to ISO 7726:
a) the parameters of the thermal environment:
— air temperature, t ;
a
— mean radiant temperature, t ;
r
— partial vapour pressure, p ; and
a
— air velocity, v ;
a
b) the mean characteristics of the subjects exposed to this working situation:
— the metabolic rate, M, estimated on the basis of ISO 8996; and
— 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 water 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 for interpreting the results from Clause 5, which leads to the
determination of the predicted sweat rate, the predicted core temperature and the allowable exposure
times. The determination of the allowable exposure times is based on two strain criteria: maximum
core temperature increase and maximum body water loss, 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 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.
4 © ISO 2018 – All rights reserved

ISO/DIS 7933:2018(E)
5 Main steps of the calculation
5.1 Heat balance equation
The thermal energy balance of the human body may be written as:
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 energy is stored in the body, S.
The different terms of Equation (1) are successively reviewed in 5.1.1 to 5.1.10 in terms of the principles
of calculation (detailed expressions are shown in Annex A).
5.1.1 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.
5.1.2 Effective mechanical power, W
In most industrial situations, the effective mechanical power is small and can be neglected.
5.1.3 Heat flow by respiratory convection, C
res
The heat flow by respiratory convection may be expressed, in principle, by the following equation:
tt− 
ex a
Cc=×0,00002 V × (2)
 
resp ex
A
 Du 
5.1.4 Heat flow by respiratory evaporation, E
res
The heat flow by respiratory evaporation can be expressed, in principle, by the following equation:
 
WW−
ex a
Ec=×0,00002 V × (3)
 
resee x
A
 Du 
5.1.5 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, not directly taken into account and quantitatively assimilated to the heat losses by convection
and radiation which would occur on these surfaces if they were not in contact with any solid body.
[6]
ISO 13732-1 deals specifically with the risks of pain and burns when parts of the body contact hot
surfaces.
ISO/DIS 7933:2018(E)
5.1.6 Heat flow by convection, C
The heat flow by convection on the bare skin may be expressed by the following equation:
C = h × (t – t) (4)
c,dyn sk a
For clothed person, the heat flow by convection occurs at the surface of the clothing and is expressed by
the following equation:
C = h × f × (t – t) (5)
c,dyn cl cl a
Annex D provides some indications for the evaluation of the clothing thermal characteristics.
5.1.7 Heat flow by radiation, R
The heat flow by radiation may be expressed by the following equation:
R = h × f × (t – t) (6)
r cl cl a
where the radiative heat transfer coefficient, h , takes into account the clothing characteristics, (e.g.
r
emissivity and the presence of reflective clothing) and the effective radiating area of the subject related
to the position (e.g. standing, seated, crouching subject)”.
5.1.8 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:
pp−
sk,s a
E = (7)
max
R
e,T,dyn
where the dynamic clothing total water vapour resistance, R , takes into account the clothing
e,T,dyn
characteristics as well as the movements of the subject 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:
E = w × E (8)
max
5.1.9 Heat storage for increase of core temperature associated with the metabolic rate, dS
eq
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
t t
associated with the increase from time to time , dS does not contribute to the onset of sweating
i–1 i eq,
and should therefore be deducted from the heat balance equation.
5.1.10 Heat storage, S
The heat storage of the body is given by the algebraic sum of the heat flows defined previously.
6 © ISO 2018 – All rights reserved

ISO/DIS 7933:2018(E)
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 + 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:
E = M – W – C – E – C – R – dS (10)
req res res eq
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.
The calculation of the required sweat rate is made as follows on the basis of the required evaporative
heat flow, but taking account of the evaporative efficiency of the sweating, r
req:
E
req
w = (11)
req
E
max
The required sweat rate is then given by:
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 subject (1,8 m of body
surface).
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 (see 6.1.1):
— the maximum skin wettedness, w ; and
max
— the maximum sweat rate: Sw ,
max
and on two strain criteria (see 6.1.2):
— the maximum core temperature: t ; and
cr, max
— the maximum water loss: D .
max
6.1.1 Stress criteria
The required sweat rate, Sw , cannot exceed the maximum sweat rate, Sw , achievable by the
req max
subject. The required skin wettedness, w , cannot exceed the maximum skin wettedness, w ,
req max
achievable by the subject. These two maximum values are a function of the acclimatization of the
subject.
ISO/DIS 7933:2018(E)
6.1.2 Strain criteria
In the case of non-equilibrium of the thermal balance, the core temperature increase should be limited
at a maximum value, t , such that the probability of any pathological effect is extremely limited.
cr,max
Finally, whatever the thermal balance, the water loss should be restricted to a value, D , compatible
max
with the maintenance of the hydromineral equilibrium of the body.
6.1.3 Reference values
Annex B includes reference values for the stress criteria (w and Sw ) and the strain criteria (t
max max cr,
and D ). Different values are presented for acclimatized and non-acclimatized subjects.
max max
6.2 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 current climatic, metabolic and clothing conditions during the time
i-1
increment.
The steps are:
— the required evaporative heat flow, E , skin wettedness, w , and sweat rate, Sw , are first
req req req
computed;
— from these, the predicted evaporative heat flow, E , skin wettedness, w , and sweat rate, Sw , are
p p p
then computed considering the stress criteria (E , w and Sw ) as well as the exponential
max max max
response 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 the skin and body temperatures;
— body and core temperature are estimated; and
— 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 cr
In the present state of the standard, this procedure makes it possible to take into account only constant
working conditions.
6.3 Determination of allowable exposure time, D
lim
The allowable exposure time, D , is reached when either the core temperature or the cumulated water
lim
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 of
max
water vapour on the skin; or
— the estimated allowable exposure time is less than 30 min,
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.
A computer programme in Quick 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.
8 © ISO 2018 – All rights reserved

ISO/DIS 7933:2018(E)
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/DIS 7933:2018(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 are likely to be amended in the light of increased knowledge.
The algorithms described in this annex were validated on a database of 747 lab experiments and 366
field experiments from 8 European 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, the present 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 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,st
The time increment used during this validation study was equal to 1 min.
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:
C – 0,885t p) (A.1)
res = 0,001 52M(28,56 a + 0,641 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 0,53t – p) (A.2)
res = 0,001 27M(59,34 + a 11,63 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.
— For nude subjects (I ≤ 0,2):
cl,st
t = 7,19 + 0,064t + 0,061t – 0,348v + 0,198p + 0,616t (A.3)
sk,eq,nu a r a a re
10 © ISO 2018 – All rights reserved

ISO/DIS 7933:2018(E)
— For clothed subjects ( ≥ 0,6):
Icl.st
t = 12,17 + 0,02t + 0,04t – 0,253v + 0,194p + 0,00535M + 0,513t (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 extrapolated between these
cl,st
two values using:
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; and
sk,i–1 i-1
— the steady state skin temperature, t , predicted from the conditions existing during the last
sk,eq
minute by equation (A.5).
The time constant of the response of the skin temperature being equal to 3 min, the following equation
is used:
t = k × t + (1 – k ) × t (A.6)
sk,i tsk sk,i–1 tsk sk,eq
k = exp(–1/3) (A.7)
where tsk
A.6 Determination of the heat accumulation associated with the metabolic
rate, dS
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:
t = 0,0036·(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:
t = k × t + (1 – k ) × t (A.9)
cr,eq,i tcr cr,eq,i-1 tcr cr,eq
where
k = exp(–1/10) (A.10)
tcr
The heat storage associated with this increase is:
×
dS = c W /(A × 60) × (t – t × (1 – α) (A.11)
eq p,b b Du cr,eq,i cr,eq,i-1) i-1
ISO/DIS 7933:2018(E)
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 the following:
tt−
sk a
CR+=
(A.12)
I
totst
For a clothed subject, this static heat resistance, can be estimated using:
I ,
tot,st
I
a,st
II=+ (A.13)
tot,st cl,st
f
cl
where
2 -1
— , I , can be estimated equal to 0.111 m K⋅W ;
a,st
— the clothing area factor, f , is given by:
cl
f = 1 + 1.97·I (A.14)
cl cl,st
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, this needs to be corrected. The correction
factor C can be estimated as follows:
orr,tot
— for a nude person (I = 0):
cl,st
[(0,,047vV−+0 472)(v 0,,117 −03342)]V
ar ar w w
CC== e (A.15)
orr,Itot,storr,Ia,st
— for a person wearing clothes with I > 0.6 clo:
cl,st
[(0,,043 + 0 066VV−+ 0,)398 (0,,,094VV − 0 378)]
ar ar ww
CC==e (A.16)
orr,Itot,storr ,Icl,st
-1 -1
with the relative air velocity, v , limited to 3 m s and the walking speed, v , limited to 1.5 m s .
ar w
When the walking speed is undefined or the person is stationary, the value for v can be calculated as:
w
-1
v = 0,0052v(M – 58) with v ≤ 0,7 m.s (A.17)
w w
-2
with M expressed in W m
For conditions with I between 0 and 0.6 clo, the correction factor is estimated by interpolation
cl
between these two values, by the following expressions:
C = [(0,6 – I ) × C + I × C]/0.6 (A.18)
orr,Itot,st cl,st orr,Ia,st cl,st orr,Icl,st
In any case, this correction factor is limited to 1.
Finally:
I = C × I (A.19)
a,dyn orr,Ia,st a,st
I = C × I (A.20)
T,dyn orr,Itot,st T,st
12 © ISO 2018 – All rights reserved

ISO/DIS 7933:2018(E)
I
a,dyn
(A.21)
II=−
cldynT,dyn
f
cl
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.22)
cl c,dyn cl a r cl r
which describes the heat exchanges between the clothing and the environment, and:
 
tt−
sk cl
CR+= (A.23)
 
 
I
cl,dyn
 
which describes the heat exchanges between the skin and the clothing surface.
The dynamic convective heat transfer coefficient, h , can be estimated as the greatest value of:
c,dyn
0,25
2.38|t – t | (A.24)
cl a
3.5 + 5,2v (A.25)
ar
0.6
8.7v (A.26)
ar
The radiative heat exchange, h , can be estimated using the following equation:
r
A ()tt+−273 ()+273
r cl r
h =×εσ×× (A.27)
r
A tt−
Du cl r
where
-8 -2 -4
σ is the Stefan-Boltzmann constant equal to 5,67∙10 W∙m ∙K ; and
ε is the emissivity of the skin equal to 0,97.
The fraction of skin surface involved in heat exchange by radiation, A /A is equal to 0,67 for a
r Du,
crouching subject, 0,70 for a seated subject and 0,77 for a standing subject.
When a clothing with a reflection coefficient F is worn on a fraction A of the body surface, h should be
r p r
corrected by a factor, F , given by:
cl,R
F = (1 – A )ε + A × F (A.28)
cl,R p cl p r
Both expressions A.22 and A.23 should be solved iteratively in order to derive t .
cl
ISO/DIS 7933:2018(E)
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:
pp−
sk,s a
E = (A.29)
max
R
e,T,dyn
, , is estimated from the following equation:
The dynamic clothing total water vapour resistance R
e,T,dyn
I
T,dyn
R = (A.30)
e,T,dyn
16.7i
m,dyn
where the dynamic clothing permeability index, i , is equal to the static clothing permeability
m,dyn
index, i , corrected for the influence of air and body movement.
mst
i = i × C (A.31)
m,dyn m,st orr,im
with:
C = 2,6 C – 6,5 C + 4,9 (A.32)
orr,im orr,Itot,st orr,Itot,st
In this expression, i is limited to 0,9.
m,dyn
A.11 Determination of the predicted sweat rate, S , and predicted evaporative
wp
heat flow, E
p
The flow chart in Figure A.1 shows how the evaluations are performed. It requires the following
explanations.
1) A greater skin wettedness is associated with (in fact, the result of) a lower evaporative efficiency.
The required evaporative efficiency decreases from 100 % to 50 % as the skin wettedness increases
to 100 %. When the required evaporative heat flow, E , is greater than the maximum evaporative
req
heat flow at the skin surface, the required wettedness, w , estimated from expression (11) is
req
greater than 1, and the evaporation efficiency, r , is expected to become lower than 0,5. r is
req req
computed from w using the following expressions:
req
1 −w
req
for w ≤1, the efficiency is given by: r =  (A.33)
req
req
2 −w
req
for w >1, the efficiency is given by: r = (A.34)
req
req
r
, however, is at the minimum 5 %, reached for a theoretical required wettedness value of 1.684.
req
2) 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 is given by the following expression:
i
Sw = k × Sw + (1 – k ) × Sw (A.35)
p,i Sw p,i-1 Sw req
where k = exp(-1/10) (A.36)
Sw
3) As explained in item 1), the required skin wettedness, w , is allowed to be
req
theoretically greater than 1 for the computation of the required sweat rate, Sw .
req
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, w , cannot be greater than one. The evaporative efficiency is then equal
p
to 0,5 and the predicted sweat rate, Sw , is equal to twice the maximum evaporation heat flow, E .
p max
14 © ISO 2018 – All rights reserved

ISO/DIS 7933:2018(E)
Figure A.1 — – Flow chart for the determination of the predicted sweat rate, Sw , and the
p
predicted evaporative heat flow rate E
p
A.12 Evaluation of the rectal temperature
The heat storage during the last time increment at time, t , is given by:
i
dS = E – E + dS (A.37)
i req p eqi
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.38)
cr
This fraction is limited to:
— 0.7 for t 36.8 °C;
cr ≤
— 0.9 for t ≥ 39.0 °C.
cr
ISO/DIS 7933:2018(E)
Figure A.2 illustrates the distribution of the temperature in the body at time, t , and time t . From this
i-1 i
it can be computed that:
 
tt−
dS ××A 60 α
cr,-ii1sk, -1
i du i
t =  +−t α −tt  (A.39)
cr,i cr,i−1 i-1 sk,i
α
cW× 2 2
i
 sp b 
 
1−
The rectal temperature is estimated according to the following expression:
21tt−− .,926 131
cr,I re,-
...