SIST EN ISO 13732-3:2006

Ergonomic of the thermal environment - Methods for the assessment of human responses to contact with surfaces - Part 3: Cold surfaces (ISO 13732-3:2005)

This European Standard describes methods for the assessment of the risk of cold injury and other adverse effects when a cold surface is touched by bare hand/finger skin.
This standard provides ergonomics data to establish temperature limit values for cold solid surfaces. The values established can be used in the development of special standards, where surface temperature limit values are required.
The data of this standard will be applicable to all fields where cold solid surfaces cause a risk of acute effects: pain, numbness and frostbite.
The data are not limited to the hands but apply to human skin in general.
The standard is applicable to the healthy skin of adults (females and males). Considerations on the extension of applications are given in Annex B.

Ergonomie der thermischen Umgebung - Bewertungsmethoden für Reaktionen des Menschen bei Kontakt mit Oberflächen - Teil 3: Kalte Oberflächen (ISO 13732-3:2005)

Ergonomie des ambiances thermiques - Méthodes d'évaluation de la réponse humaine au contact avec des surfaces - Partie 3: Surfaces froides (ISO 13732-3:2005)

La présente norme européenne décrit les méthodes permettant d’évaluer le risque de lésion ainsi que d’autres effets indésirables induits par le froid au cours du contact d’une main ou d’un doigt nus avec une surface froide.
Elle fournit des données ergonomiques permettant d’établir les valeurs limites de température pour les surfaces solides froides. Les valeurs établies peuvent etre utilisées au cours de l’élaboration de normes spécifiques lorsque les valeurs limites pour la température de surface sont requises.
Les données de la présente norme sont applicables a tous les domaines dans lesquels des surfaces solides froides sont a l’origine d’un risque d’effets aigus tels que douleur, engourdissement ou gelures.
Les données ne se limitent pas aux mains mais s’appliquent a la peau humaine en général.
La présente norme s’applique a la peau saine des adultes (hommes et femmes). D’autres considérations sur l’extension possible des applications sont indiquées a l’Annexe B.

Ergonomija toplotnega okolja – Metode za ocenjevanje človekovega odziva na dotik s površinami – 3. del: Hladne površine (ISO 13732-3:2005)

General Information

• Status: Withdrawn
• Publication Date: 28-Feb-2006
• Withdrawal Date: 23-Oct-2008
• ICS: 13.180 - Ergonomics
• Technical Committee: VSN - Safety of machinery
• Current Stage: 9900 - Withdrawal (Adopted Project)
• Start Date: 22-Oct-2008
• Due Date: 14-Nov-2008
• Completion Date: 24-Oct-2008
• Directive: 98/37/EC - Machinery
• Mandate: M/BC/CEN/88/13 - Standardization request to CEN/CENELEC relating to machinery
• Ref Project: EN ISO 13732-3:2005 - Ergonomic of the thermal environment - Methods for the assessment of human responses to contact with surfaces - Part 3: Cold surfaces (ISO 13732-3:2005)

Relations

• Replaced By: SIST EN ISO 13732-3:2008 - Ergonomics of the thermal environment - Methods for the assessment of human responses to contact with surfaces - Part 3: Cold surfaces (ISO 13732-3:2005)
• Effective Date: 01-Dec-2008

Standards Content (Sample)

SLOVENSKI STANDARD
SIST EN ISO 13732-3:2006
01-marec-2006
(UJRQRPLMDWRSORWQHJDRNROMD±0HWRGH]DRFHQMHYDQMHþORYHNRYHJDRG]LYDQD
GRWLNVSRYUãLQDPL±GHO+ODGQHSRYUãLQH,62
Ergonomic of the thermal environment - Methods for the assessment of human
responses to contact with surfaces - Part 3: Cold surfaces (ISO 13732-3:2005)
Ergonomie der thermischen Umgebung - Bewertungsmethoden für Reaktionen des
Menschen bei Kontakt mit Oberflächen - Teil 3: Kalte Oberflächen (ISO 13732-3:2005)
Ergonomie des ambiances thermiques - Méthodes d'évaluation de la réponse humaine
au contact avec des surfaces - Partie 3: Surfaces froides (ISO 13732-3:2005)
Ta slovenski standard je istoveten z: EN ISO 13732-3:2005
ICS:
13.180 Ergonomija Ergonomics
SIST EN ISO 13732-3:2006 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 13732-3:2006

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SIST EN ISO 13732-3:2006
EUROPEAN STANDARD
EN ISO 13732-3
NORME EUROPÉENNE
EUROPÄISCHE NORM
December 2005
ICS 13.040.20; 13.180

English Version
Ergonomic of the thermal environment - Methods for the
assessment of human responses to contact with surfaces - Part
3: Cold surfaces (ISO 13732-3:2005)
Ergonomie des ambiances thermiques - Méthodes Ergonomie der thermischen Umgebung -
d'évaluation de la réponse humaine au contact avec les Bewertungsmethoden für Reaktionen des Menschen bei
surfaces - Partie 3: Surfaces froides (ISO 13732-3:2005) Kontakt mit Oberflächen - Teil 3: Kalte Oberflächen (ISO
13732-3:2005)
This European Standard was approved by CEN on 19 May 2005.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European
Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national
standards may be obtained on application to the Central Secretariat or to any CEN member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by translation
under the responsibility of a CEN member into its own language and notified to the Central Secretariat has the same status as the official
versions.
CEN members are the national standards bodies of Austria, Belgium, Cyprus, Czech Republic, Denmark, Estonia, Finland, France,
Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Slovakia,
Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36  B-1050 Brussels
© 2005 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 13732-3:2005: E
worldwide for CEN national Members.

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EN ISO 13732-3:2005 (E)
Contents
page
Foreword.3
Introduction .4
1 Scope .5
2 Normative references .5
3 Terms and definitions .5
4 Principles for risk assessment.6
5 Threshold data .8
6 Risk assessment.13
7 Principles for establishing limit values .14
8 Principles for measures to minimize the risk .15
Annex A (informative)  Scientific background.16
Annex B (informative)  Extension of application.18
Annex C (informative)  Thermal properties of selected materials.19
Annex D (informative)  Examples of cold risk assessment .20
Annex E (informative)  Protective measures .23
Annex ZA (informative)  Relationship between this European Standard and the Essential
Requirements of EU Directive 98/37/EC .24
Bibliography .25

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Foreword
This document (EN ISO 13732-3:2005) has been prepared by Technical Committee CEN/TC 122 “Ergonomics”,
the secretariat of which is held by DIN, in collaboration with Technical Committee ISO/TC 159 “Ergonomics”.
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 June 2006, and conflicting national standards shall be withdrawn at the latest by
June 2006.
This document has been prepared under a mandate given to CEN by the European Commission and the European
Free Trade Association, and supports essential requirements of EU Directives.
For relationship with EU Directives, see informative Annex ZA which is an integral part of this document.
EN ISO 13732 consists of the following parts, under the general title "Ergonomics of the thermal environment -
1)
Methods for the assessment of human responses to contact with surfaces" :
 Part 1: Hot surfaces;
 Part 3: Cold surfaces.
According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following
countries are bound to implement this European Standard: Austria, Belgium, Cyprus, Czech Republic, Denmark,
Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.



1)
Part 2: has been published as ISO Technical specification ISO/TS 13732-2:2001 Human contact with surfaces at moderate

temperature.
3

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Introduction
This European Standard is a type B standard as stated in EN ISO 12100. The provisions of this document may be
supplemented or modified by a type C standard.
NOTE For machines which are covered by the scope of a type C standard and which have been designed and built
according to the provisions of that standard, the provisions of that type C standard take precedence over the provisions of this
type B standard.
Working with unprotected hands is often inevitable in the cold operation when a precision task is demanded.
However the contact of bare skin with cold surfaces reduces skin temperature, causing acute effects such as
discomfort, pain, numbness or frostbite. In addition repeated cold exposures with severe cooling of the skin may
induce non-freezing cold injury (possible damage of nerves or vessels). Although the existing international
standards are at hand for the assessment of the cold hazards involved, no standard concerns the special problems
of contacting cold surfaces so far. Assessment of contact cooling is thus considered necessary.
To assess the risk of the cold injury, it is necessary to know the major factors affecting principally hand/finger
cooling on cold surfaces. These factors involve:
 properties of the object surface;
 temperature of the cold surface and ambience;
 duration of contact between the skin and the surface;
 characteristics of hand/finger skin and the type and nature of the contact.
In practice, these factors are somewhat interacted and complicated. The type of contact material has an impact on
the contact time at various cold temperatures. Thus, the contact time for the critical contact temperature limits on
cold surfaces were empirically correlated with the major factors such as thermal penetration coefficient and surface
temperature of the material, respectively. The statistically non-linear models (empirical models) based on the
database of lower quartile (75 % protected) are able to estimate the finger/hand contact cooling of a large range of
individuals on the cold surfaces.
This European Standard is designed to integrate all results obtained from the experimental research with both
human fingers and an artificial finger. It outlines a guideline document for the specification of safe time limits of
hand/finger contact with various cold surfaces.
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1 Scope
This European Standard describes methods for the assessment of the risk of cold injury and other adverse effects
when a cold surface is touched by bare hand/finger skin.
This standard provides ergonomics data to establish temperature limit values for cold solid surfaces. The values
established can be used in the development of special standards, where surface temperature limit values are
required.
The data of this standard will be applicable to all fields where cold solid surfaces cause a risk of acute effects: pain,
numbness and frostbite.
The data are not limited to the hands but apply to human skin in general.
The standard is applicable to the healthy skin of adults (females and males). Considerations on the extension of
applications are given in Annex B.
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated references,
only the edition cited applies. For undated references the latest edition of the referenced document (including any
amendments) applies.
EN ISO 12100-1:2003, Safety of machinery - Basic concepts, general principles for design - Part 1: Basic
terminology, methodology (ISO 12100-1:2003)
3 Terms and definitions
For the purposes of this document, the terms and definitions given in EN ISO 12100-1:2003 and the following
apply.
3.1
touchable surface
surface of a product, which can be touched by a person
3.2
surface temperature
T
s
temperature of a material surface in °C
3.3
critical contact temperature
T
c
contact temperature at which defined skin response criteria are elicited in °C
3.4
contact period
D
duration during which contact of the skin with the surface takes place in s
3.5
thermal inertia
product of density (ρ), thermal conductivity (K) and specific thermal capacity (c) of a material
5

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3.6
contact factor
F
c
thermal penetration coefficient, computed as square root of the thermal inertia
NOTE The mathematical definition is: F = ρ ⋅ Κ ⋅c .
c
where
ρ is the density of a material;
Κ is the thermal conductivity of a material;
c is the thermal capacity of a material.
3.7
percentile
percentage of population of which specific characteristics fall below or above a given value in a cumulative
distribution
[EN ISO 11064-4]
4 Principles for risk assessment
4.1 General
In order to assess the risk of cold injury and other effects, the following steps (4.2 to 4.8) shall be carried out.
4.2 Identification of cold touchable surfaces
All essential information concerning the cold touchable surfaces of the object shall be gathered. This shall include
the objects attributes:
a) accessibility of the surface;
b) rough estimation of surface temperatures (above or below 0 °C);
c) material and texture of the cold surface;
d) all operating conditions of the object where contact with the cold surface is needed (including the worst case).
4.3 Task observation and analysis
According to the activities and tasks required, all necessary information concerning the contact with the cold
surface shall be collected, by observation or analysis. Particular attention should be paid to possible intentional and
unintentional contact with cold surfaces. The type and nature of the contact shall be identified from the task
observation and analysis:
a) cold surfaces which are or can be touched;
b) intentional or unintentional touching;
c) frequency of intentional touching;
d) probability of unintentional touching;
e) duration of contact with the cold surface;
f) contacting area;
g) contacting force.
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4.4 Classification of contact with a cold surface
4.4.1 General
The type of contact is classified according to the following two categories:
4.4.2 Finger touching
Subjects contact a defined material during a short period (up to 120 s). The contact area is small (only finger pad).
4.4.3 Hand gripping
Subjects grip an object of defined material. Gripping is applied constantly for a longer period (up to 1 200 s).
4.5 Measurement of surface temperature
The surface temperatures shall be measured on those parts of the object where skin contact with the surface can
occur.
The measurement shall be carried out under real operating conditions of the object by thermocouples. The
accuracy of the instrument shall be ± 0,5 °C in a range from – 25 to + 5 °C and ± 1 °C below – 25 °C (see
ISO 7726:2001 and [4]).
NOTE The results of the measurement of the surface temperature can only be compared with the threshold values of
Clause 5, if they are realized using the same physical measurement principle which was used for the determination of the
threshold values of Clause 5. The application of a different measuring principle, e.g. a radiation thermometer, can lead to other
results which are not comparable with the threshold values.
4.6 Period
The contact period of bare skin with a cold surface can be measured or estimated according to values in Table D.1.
4.7 Classification of type of effect on skin during contact
4.7.1 General
Type of effect shall be determined according to the following criteria.
4.7.2 Frostbite
The effect is predicted from a drop in contact temperature to below 0 °C, at which the contacting skin tissue will
freeze.
4.7.3 Numbness
The effect is predicted from a drop in contact temperature to around 7 °C, at which sensory receptors of contacting
skin will be blocked and numbness will occur.
4.7.4 Pain
The effect is predicted from a drop in contact temperature to around 15 °C, at which a subjective sensation of pain
at the contacting skin will be experienced.
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4.8 Risk evaluation
On the basis of this information the data in Clause 5 shall be used for final evaluation to establish if there is a risk
for the selected type of effect to occur. An estimate of the risk is made on the basis of surface temperature and
contact period specified in 5.2 and 5.3.
5 Threshold data
5.1 General
This Clause provides surface temperature data for cooling thresholds from the ergonomics database. Figure 1
shows the principal relation between material, time and temperature for skin in contact with a cold surface. Below
the curve of each material there is a risk of an adverse effect of skin cooling. This figure is presented for guidance
only of the temperature/time relationship and the relative effects of different materials. The quantitative information
is provided in the subsequent Clauses.

Key
1 Aluminium 3 Stone 5 Wood
2 Steel 4 Nylon
D Contact period T Surface temperature
s
Figure 1 — Principal relationship between material, duration and temperature
for skin in contact with a cold surface
The thermal properties of the mentioned materials (Aluminium, Steel, Stone, Nylon, and Wood) and other selected
materials are given in Annex C.
5.2 Finger touching
5.2.1 General
Thresholds for finger skin touching are specified in 5.2.2 (Figures 2 to 4).
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5.2.2 Thresholds for finger contacting cold surfaces
The freezing (frostbite) threshold values of finger touching three cold surfaces (aluminium, steel and stone) are
shown in Figure 2.

Key
1 Aluminium 3 Stone
2 Steel
Figure 2 — Frostbite threshold as function of contact period (finger touching)
The numbness thresholds for finger touching the five materials are indicated in Figure 3.

Key
1 Aluminium 3 Stone 5 Wood
2 Steel 4 Nylon
Figure 3 — Numbness threshold as function of contact period (finger touching)
The pain thresholds for finger touching different materials are indicated in Figure 4.
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Key
1 Aluminium 3 Stone 5 Wood
2 Steel 4 Nylon
Figure 4 — Pain threshold as function of contact period (finger touching)
5.2.3 Thresholds for different materials
Figures 5 to 6 show the three criteria thresholds for contact with metals (aluminium and steel).

Key
1 Pain 3 Frostbite
2 Numbness
Figure 5 — Threshold curves for contact with an aluminium surface (finger touching)

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Key
1 Pain 3 Frostbite
2 Numbness
Figure 6 — Threshold curves for contact with a steel surface (finger touching)
The cooling thresholds for contact with stone are shown in Figure 7. The data was predicted from the model of
finger touching database.

Key
1 Pain 3 Frostbite
2 Numbness
Figure 7 — Threshold curves for contact with a stone surface (finger touching)
The pain and numbness thresholds for the case of contact with nylon or wood are shown in the Figures 8 to 9. The
data did not show any occurrence of freezing for the case of finger touching nylon or wood.
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Key
1 Pain
2 Numbness
Figure 8 — Threshold curves for contact with a nylon surface (finger touching)

Key
1 Pain
2 Numbness
Figure 9 — Threshold curves for contact with a wood surface (finger touching)
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5.3 Hand gripping
The pain thresholds for hand gripping different materials are shown in Figure 10. The limit values are based on the
actually reported perception of pain by subjects.
A difference is observed between the touching and gripping curves due to different types of contact. The pain
thresholds during gripping the material can be lower than that for touching (see Annex A). The main reasons for
this are:
 freedom for small adjustments of the hand grip allowed for better control of the response reaction;
 size and mass of rods gripped were smaller than of blocks touched;
 contact area of the hand grip was larger than for the finger touch;
 during hand gripping blood flow is less obstructed than with finger touching;
 at very low air temperatures radiative or convective heat loss may contribute to pain sensation.

Key
1 Aluminium 3 Stone 5 Wood
2 Steel 4 Nylon
D Time to reach a contact temperature (at the skin of the hand) of 15 ºC
15
Figure 10 — Pain thresholds as function of gripping duration for five materials
6 Risk assessment
6.1 General
Due to large individual variations, the risk level is calculated for the 25 percentile (see EN ISO 11064-4) responses.
The threshold values should be interpreted as safe for ¾ of the exposed population. For the remaining ¼ of a
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minute risk of an adverse cooling effect may still exist. This remaining group comprises people with increased
susceptibility to cooling (see Annex B).
The curves and the suggested risk interpretation therefore, should only serve as guidance for evaluation and
selection of limit values or additional action to minimize the risk.
6.2 Surface temperature higher than thresholds
If the measured surface temperature is higher than the thresholds for defined contact period (up to 10 °C), there is
no risk for the defined effects to occur.
6.3 Surface temperature lower than or equal to thresholds
If the measured surface temperature is below or equal to the thresholds for defined contact period, there is a risk of
pain, numbness or frostbite of the skin to occur.
6.4 Further risk parameter
The risk becomes higher:
 when the measured surface temperature is far below the cooling threshold;
 the longer the contact period exceeds the cooling threshold;
 the smaller the chance is for quick withdrawal;
 the more accessible the cold surface is;
 the higher the probability is for unintended touching;
 the more frequent the contact is likely to occur;
 when less previous knowledge of the contact material is to be expected.
If a risk is detected, measured shall be taken to minimize that risk.
NOTE In addition, national regulations may require the application of protective measures. The particular measures to be
applied depend on the operational context. Examples of protective measures are given in Annex E.
7 Principles for establishing limit values
The information provided in this standard can help to establish:
 limit values of surface temperature, or
 contact periods for use in product standards or for other purposes, or
 contact periods and measures to minimize the risk for use.
A procedure for the determination of surface temperature limit values requires information about:
 materials to be used;
 types of contact (touching or gripping);
 contact periods;
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 types of effect (frostbite, numbness or pain).
A procedure for the determination of contact period limit values requires information about:
 materials to be used;
 surface temperatures;
 types of contact (touching, numbness or pain).
In the Figures 2 to 10 the relations between type of material, temperature and contact period for defined effects are
given. A limit value can be selected from the corresponding figure based on effect and material. Examples are
given in Annex D.
8 Principles for measures to minimize the risk
The following shall be considered to minimize the risk of contact with cold surface:
 risk assessment according to Clause 6;
 types of operations where the contact is required (seldom, often or frequently);
 possibility of surface treatment of the contact area (e.g. painting, plastic coating);
 possibility of protection of area which can be unintentionally touched;
 liquids at temperatures below 0 °C shall not come in contact with skin because of the imminent risk of skin
freezing and development of frostbite. Similarly e.g. solid carbon dioxide gives rise to a risk of frostbite.
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Annex A
(informative)

Scientific background
A.1 General
The contact cooling threshold values specified in 5 are based on the scientific research carried out by Cold
surfaces research group [4]. Firstly, depending on criteria applied, safe contact temperatures have been
investigated for the given materials under cold exposure conditions. Secondly, safe contact time has been
determined for the given combinations of type of material and their surface temperature. The results have been
compiled in a database that can serve as a basis for the development of an ergonomics database in this standard.
The details of the database are presented as follows [4]:
A.2 Database
A.2.1 General
The database, which contains experimental data of finger touching and hand gripping the cold surfaces with human
subjects, was compiled based on the pooled data obtained from all experiments run by five laboratories in the
project. The five partners used a common methodology [6, 7, 8, 9, 11, 12 and 13]. Experiments on various
materials (wood, nylon, stone, steel and aluminium) at surface temperature (T , -40 °C to +5 °C) were performed.
S
Each individual curve of the finger skin-surface contact temperature (T ) versus contact time in the cold was
C
subsequently plotted from all the records. The contact time of critical contact temperature (T = 15 °C, 7 °C and
C
0 °C) for each cooling curve was obtained by inter or extrapolations [5 and 9].
Two databases on touching and gripping experiments were established according to the experimental results. Both
include the essential information from each test:
 characteristics of the subject: age, weight, height, hand surface, hand volume, contact area;
 experimental set-up: surface temperature of the material (T ), exposure hand into a cold box or whole body in
S
a cold climatic chamber;
 parameters such as duration of the resting period in the climatic room, skin temperature before contacting,
temperature, pain and numbness sensation were determined before each test;
 parameters such as criteria used to stop the test (risk of frostbite, pain or time limit reached), duration of the
test, skin temperature, temperature, pain and numbness sensation were determined after each test;
 parameters like time, the temperature, the pain and the numbness sensations were recorded during each test;
 characterisation and evolution of the skin temperature with time (to reach a contact temperature of 15 °C, 7 °C
and 0 °C);
 Characterisation of the material: thermal conductivity, specific heat, density and contact factor.
In addition, the contact time to reach the critical temperature had a large variation among individuals [4 and 14].
The individual variation should be considered when the contact time for the critical temperature is determined. To
avoid the complexity caused by individuals and secure the manual or finger protection on the cold touchable
surfaces, the contact time for the critical T was determined by using the statistical results of the lower quartile. In
C
addition, graphs for threshold lines are only given between –40 °C and +5 °C, because this was the range of
experimental conditions. Mathematical extrapolations beyond these temperatures are not validated.
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A.2.2 Database for touching
The number of touching experiments are 1657 tests for 24 exposure conditions. The results showed that for most
of the experiments with wood and nylon, the limit duration of 120 s could be reached. For steel and aluminium, this
time limits could also be reached at certain surface temperatures. The 120 s were chosen as a longest time for
which people would maintain physical contact with a cold surface. In most practical situations people would
probably release the contact long before that.
From the evolution of the contact temperature with time, the time to reach a temperature of 15 °C (pain threshold t
(15 ºC)) was either interpolated or extrapolated. The times to reach 7 °C (numbness threshold t (7 °C)) and 0 °C
(freezing threshold t (0 °C)) were also extrapolated.
A.2.3 Database for gripping
The database for gripping includes 584 tests for 21 exposure conditions. The fifth material (stone) was also
involved for the studies in addition to wood, nylon, steel and aluminium. The experiments of hands in cold air
(exposure to cold but without gripping) were conducted to obtain the reference values.
The inter and extrapolation of the duration to different temperatures were only possible for 15 °C. For most of the
cases, the contact temperatures at the end of the tests were higher than 15 °C (15,9 °C ± 5,2 °C).
A.3 Empirical modelling
A non-linear regression analysis was used to empirically predict the duration as a function of the surface
temperature (T ) and the contact factor (F ) of the material for various critical contact temperature limits.
S C
The non-linear model obtained has the following form:
B D
Time = (A/Fc ) ⋅ exp(C ⋅Fc ⋅Ts)
where A, B, C and D were constants, which can be estimated by the non-regression iterative procedure. The model
provides specific equations for each material and effect. In some cases the equation was simplified when one or
more of the
...