oSIST prEN ISO 7933:2022

SLOVENSKI STANDARD
01-januar-2022
Ergonomija toplotnega okolja - Analitično ugotavljanje in razlaga toplotnega
stresa z izračunom predvidene toplotne obremenitve (ISO/DIS 7933:2021)
Ergonomics of the thermal environment - Analytical determination and interpretation of
heat stress using calculation of the predicted heat strain (ISO/DIS 7933:2021)
Ergonomie der thermischen Umgebung - Analytische Bestimmung und Interpretation der
Wärmebelastung durch Berechnung der vorhergesagten Wärmebeanspruchung
(ISO/DIS 7933:2021)
Ergonomie des ambiances thermiques - Détermination analytique et interprétation de la
contrainte thermique fondées sur le calcul de l'astreinte thermique prévisible (ISO/DIS
7933:2021)
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 7933.2
ISO/TC 159/SC 5 Secretariat: BSI
Voting begins on: Voting terminates on:
2021-11-12 2022-01-07
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
ICS: 13.180
This document is circulated as received from the committee secretariat.
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ISO/DIS 7933.2:2021(E)
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ISO/DIS 7933.2:2021(E)
© ISO 2021
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ii
ISO/DIS 7933.2:2021(E)
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 2
4 Symbols . 2
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 Metabolic rate, M . 5
6.1.2 Effective mechanical power, W . 5
6.1.3 Heat flow by respiratory convection, C . 5
res
6.1.4 Heat flow by respiratory evaporation, E . 5
res
6.1.5 Heat flow by conduction, K . 5
6.1.6 Heat flow by convection, C . 6
6.1.7 Heat flow by radiation, R . 6
6.1.8 Heat flow by evaporation, E . 6
6.1.9 Heat storage for increase of core temperature associated with the
metabolic rate, dS . 6
eq
6.1.10 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 Stress criteria . 7
7.1.2 Strain criteria . 7
7.1.3 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 programme for the computation of the predicted heat
strain model .22
Annex F (normative) Examples of the predicted heat strain model computations .27
Bibliography .28
iii
ISO/DIS 7933.2:2021(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 on 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 the following
URL: 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.
This third edition supersedes the second edition (ISO 7933:2004), which has been technically revised.
The main changes compared to the previous edition are as follows:
— The maximum sweat rate SW described in section B.4 of Annex B is fixed; that is, it is no longer
max
adjusted for metabolic rate.
— As the model has not been extensively validated for conditions with unsteady environmental
parameters, metabolic rate and/or clothing, a caution was added for cases where these parameters
vary substantially with time.
iv
ISO/DIS 7933.2:2021(E)
Introduction
[1]
ISO 15265 describes the assessment strategy for the prevention of discomfort or health effects in
[2]
any thermal working condition, while ISO 16595/WP recommends specific practices concerning
hot working environments. For these hot environments, these standards propose to rely on the wet
[3]
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 desired
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/
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; and 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 in the future 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.
[4]
ISO 9886 describes how physiological parameters are used to monitor the physiological behaviour of
[5]
a particular person and ISO 12894 describes how medical supervision is organized.
v
DRAFT INTERNATIONAL STANDARD ISO/DIS 7933.2:2021(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”, with 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 physiological
strains.
In its present form, this method of assessment is not applicable to cases where special protective
clothing (such as fully reflective clothing, active cooling and ventilation, impermeable coveralls…) is
worn.
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 permit 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.
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 ergonomists, industrial hygienists, etc. as the outcomes may require expert interpretations.
Recommendations about how and when to use this model are given in ISO 16595/WP.
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 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/DIS 7933.2:2021(E)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 13731 apply.
ISO and IEC maintain terminological 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
The symbols and abbreviated terms are listed in Table 1
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 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 age years
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
Corr,i correction factor for the static moisture permeability index —
m
Corr,I correction factor for the static boundary layer thermal insulation —
a
Corr,I correction factor for the static clothing thermal insulation —
cl
Corr,I correction factor for the static total clothing thermal insulation —
T
−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
ISO/DIS 7933.2:2021(E)
Table 1 (continued)
Symbol Term Unit
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 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
incr time increment from time t to time t min
i–1 i
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
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 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 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
ISO/DIS 7933.2:2021(E)
Table 1 (continued)
Symbol Term Unit
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
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
5 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:
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 ; and
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 water 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
ISO/DIS 7933.2:2021(E)
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 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.
6 Main steps of the calculation
6.1 Heat balance equation
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 energy is stored in the body, S.
The different terms of Formula (1) are successively reviewed in 6.1.1 to 6.1.10 in terms of the principles
of calculation (normative expressions for the computations are provided in Annex A).
6.1.1 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.
6.1.2 Effective mechanical power, W
In most industrial situations, the effective mechanical power is small and can be neglected.
6.1.3 Heat flow by respiratory convection, C
res
The heat flow by respiratory convection may be expressed, in principle, by Formula (2):
tt− 
ex a
Cc=×0,000 02 V × (2)
resp ex  
A
 
Du
6.1.4 Heat flow by respiratory evaporation, E
res
The heat flow by respiratory evaporation can be expressed, in principle, by Formula (3):
WW−
 
ex a
Ec=×0,000 02 V × (3)
resee x  
A
 
Du
6.1.5 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 and ignored.
[6]
Note ISO 13732-1 deals specifically with the risks of pain and burns when parts of the body contact hot
surfaces.
ISO/DIS 7933.2:2021(E)
6.1.6 Heat flow by convection, C
The heat flow by convection on the bare skin may be expressed by Formula (4):
C = h × (t – t) (4)
c sk a
For clothed person, 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.
6.1.7 Heat flow by radiation, R
The heat flow by radiation may be 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).
6.1.8 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, 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
6.1.9 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 Formula (1).
6.1.10 Heat storage, S
The heat storage of the body is given by the algebraic sum of the heat flows defined previously.
ISO/DIS 7933.2:2021(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 a 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:
E
req
w = (11)
req
E
max
The calculation of the required sweat rate, SW , is made on the basis of the required evaporative heat
req
flow, but taking account of the evaporative efficiency of the sweating, r as follows in Formula 12:
req
E
req
SW = (12)
req
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
One 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
The interpretation of the values calculated by the recommended analytical method is based on:
— two stress criteria (see 7.1.1):
— the maximum skin wettedness w ;
max
— the maximum sweat rate SW ;
max
— two strain criteria (see 7.1.2):
— the maximum rectal temperature t
re, max
— the maximum water loss D .
max
7.1.1 Stress criteria
The required sweat rate, SW , cannot exceed the maximum sweat rate, SW , achievable by the
req max
person. The required skin wettedness, w , cannot exceed the maximum skin wettedness, w ,
req max
achievable by the person. These two maximum values are a function of the acclimatization of the person.
7.1.2 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
ISO/DIS 7933.2:2021(E)
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
7.1.3 Reference values
Annex B includes reference values for the stress criteria (w and SW ) and the strain criteria (t
max max re,
and D ). w , SW and D values are a function of the acclimatization state of the person.
max max max max 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 current climatic, metabolic rate and clothing conditions during the
i-1
time 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 sweat rate, SW , skin wettedness, w , and evaporative heat flow, E , are
p p p
computed considering the stress criteria (E , w and SW ) as well as the exponential response
max max max
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: and
— from these values, the heat exchanges during the time increment are computed.
The evolutions of SW , t and t are in this way iteratively computed.
p 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.
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 individual physiological supervision of the persons
is recommended. The conditions for carrying out this surveillance and the measuring techniques to be
used are described in ISO 9886.
A computer programme 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) to be used for the validation of any computer
programme developed on the basis of the model presented in Annex A.
ISO/DIS 7933.2:2021(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 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 lab experiments and 366
[12]
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, 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,st
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 = 0,00152 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 = 0,00127 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/DIS 7933.2:2021(E)
— For I ≥ 0,6 clo:
cl
t = 12,17 + 0,02 t + 0,04 t – 0,253 v + 0,194 p + 0,00535 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; and
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)
where tsk
A.6 Determination of the heat accumulation associated with the metabolic rate,
dS
eq
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 = 0,0036·(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. 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
where
k = exp(–1/10) (A.10)
tcr
The heat storage associated with this increase is given by Formula (A.11):
×
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 7933.2:2021(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):
tot,st
I
a
II=+ (A.13)
T cl
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 Corr,I can be estimated with Formulae (A.15) and (A.16):
T
— for a nude person (I = 0):
cl,st
[(0,,047vV−+0 472)(v 0,,117 −0 342)]V
ar ar ww
Corr ,,IC==orrI e (A.15)
Ta
— for a person wearing clothes with I > 0.6 clo:
cl,st
[(0,,043 + 0 066VV−+ 0,)398 (0,094V − 0,)378 V ]
ar ar w w
Corr ,,IC==orrI e (A.16)
Tcl
−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
w
with Formula (A.17):
−1
v = 0,0052 (M – 58) with v ≤ 0,7 m.s (A.17)
w w
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.18) to (A.21):
Corr,I = [(0,6 – I ) × Corr,I + I × Corr,I]/0.6 (A.18)
T cl a cl cl
In any case, this correction factor is limited to 1.
Finally, resultant (or dynamic) thermal insulation values are calculated as:
I = Corr,I × I (A.19)
a,r a a
I = Corr,I × I (A.20)
T,r T T
ISO/DIS 7933.2:2021(E)
I
a,r
(A.21)
II=−
cl,r T,r
f
cl
A.9 Estimation of the heat exchanges through convection and radiation
The dry heat exchanges can be estimated using Formulae (A.22) to (A.26):
C + R = f × [h × (t – t ) + h × (t – t)] (A.22)
cl c 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,r 
which describes the heat exchanges between the skin and the clothing surface.
The convective heat transfer coefficient, h , can be estimated as the greatest value of:
c
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 coefficient, h , can be estimated using Formula (A.27):
r
A ()tt+−273 ()+273
r cl r
h =×εσ×× (A.27)
rclr,
A tt−
Du cl r
where
−8 −2 −4
σ is the Stefan-Boltzmann constant equal to 5,67∙10 W∙m ∙K ; and
A /A is the fraction of surface of the body involved in heat exchange by radiation, equal to 0,67
r Du
for a crouching person, 0,70 for a seated person and 0,77 for a standing person.
ε is the emissivity of the outer clothed surface.
cl,r
ε = ε the emissivity of outer surface of ordinary clothing, when no reflective clothes are used.
cl,r cl
This emissivity is taken to be 0.97.
When a clothing with a reflection coefficient F is worn on a fraction A smaller than 50 % of the body
r p
surface, the emissivity in Formula (A.27) should be calculated as:
ε = (1 – A ) ε + A (1-F) (A.28)
cl,r p cl p r
As stated in Section 1. Scope, this method of assessment is not applicable to cases where special
protective clothing such as fully reflective clothing are worn.
Both Formulae (A.22) and (A.23) should be solved iteratively in order to derive t .
cl
ISO/DIS 7933.2:2021(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 Formula (A.29):
pp−
sk,s a
E = (A.29)
max
R
e,T,r
, , is estimated from
The resultant (or dynamic) clothing total water vapour resistance R Formulae (A.30)
e,T,r
to (A.32):
I
T,r
R = (A.30)
e,T,r
16.7i
m,r
where the dynamic clothing permeability index, i , is equal to the static clothing permeability index,
m,r
i , corrected for the influence of air and body movement.
m
i = i × Corr,i (A.31)
m,r m m
with:
Corr,i = 2,6 Corr,I – 6,5 Corr,I + 4,9 (A.32)
m T T
In this Equation, i is limited to 0,9.
m,r
A.11 Determination of the predicted sweat rate, SW , and the predicted
p
evaporative heat flow at the skin surface, 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.
req
r is then computed from w using the following expressions:
req req
— for w ≤ 1, the efficiency is given by Formula (A.33):
req
r = 1 - w / 2 (A.33)
req req
— for w > 1, the efficiency is given by Formula (A.34):
req
2 w
()
req
r = (A.34)
req
— if r < 0.05, r is set to 0.05
req req
In any case, the required sweat rate SW may not be greater than SW
req max
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 Formulae (A.35) and (A.36):
i
SW = k × SW + (1 – k ) × SW (A.35)
p,i Sw p,i-1 SwW req
where k = exp(−1/10) (A.36)
SW
ISO/DIS 7933.2:2021(E)
3) As explained in item 1), the required skin wettedness, w , is allowed to be theoretically greater
req
than 1 for the computation of the required sweat rate, SW . As the evaporative heat loss is
req
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 effi
...