SIST EN ISO 13370:2017
(Main)Thermal performance of buildings - Heat transfer via the ground - Calculation methods (ISO 13370:2017)
Thermal performance of buildings - Heat transfer via the ground - Calculation methods (ISO 13370:2017)
This document provides methods of calculation of heat transfer coefficients and heat flow rates for
building elements in thermal contact with the ground, including slab‐on‐ground floors, suspended
floors and basements. It applies to building elements, or parts of them, below a horizontal plane in the
bounding walls of the building situated
— at the level of the inside floor surface, for slab‐on‐ground floors, suspended floors and unheated
basements;
In some cases, external dimension systems define the boundary at the lower surface of the floor slab.
— at the level of the external ground surface, for heated basements.
This document includes calculation of the steady‐state part of the heat transfer (the annual average rate
of heat flow) and the part due to annual periodic variations in temperature (the seasonal variations of
the heat flow rate about the annual average). These seasonal variations are obtained on a monthly basis
and, except for the application to dynamic simulation programmes in Annex D, this document does not
apply to shorter periods of time.
Table 1 in the Introduction shows the relative position of this document within the set of EPB
standards in the context of the modular structure as set out in ISO 52000-1.
Wärmetechnisches Verhalten von Gebäuden - Wärmeübertragung über das Erdreich - Berechnungsverfahren (ISO 13370:2017)
Dieses Dokument gibt Verfahren zur Berechnung von Wärmeübertragungskoeffizienten und der Wärmeübertragung durch Bauteile an, die sich in wärmetechnischem Kontakt mit dem Erdreich befinden, einschließlich Bodenplatten auf Erdreich, aufgeständerter Bodenplatten und Kellergeschossen. Es gilt für Bauwerksteile oder Teile dieser, die unterhalb einer waagrechten Ebene der angrenzenden Wände des Gebäudes liegen:
für Bodenplatten auf Erdreich, aufgeständerte Bodenplatten und unbeheizte Kellergeschosse: in Höhe der raumseitigen Bodenplattenoberfläche;
ANMERKUNG In einigen Fällen wird die Grenze der Oberfläche der Bodenplatte von externen Maßsystemen niedriger bestimmt.
für beheizte Kellergeschosse: in Höhe der Oberfläche des umgebenden Erdreichs.
Dieses Dokument schließt die Berechnung der stationären Komponente des Wärmestroms über das Erdreich (Jahresmittel des Wärmestromes über das Erdreich) und der Komponente infolge von jährlichen periodischen Temperaturschwankungen (auf das Jahresmittel bezogene jahreszeitliche Schwankungen des Wärmestromes) ein. Diese jahreszeitlichen Schwankungen werden monatsweise ermittelt, und dieses Dokument gilt nicht für kürzere Zeitabschnitte; ausgenommen ist die Anwendung auf die dynamischen Simulationsprogramme nach Anhang D.
Tabelle 1 zeigt die relative Position dieses Dokuments innerhalb des EPB-Normenpakets im Kontext der in ISO 52000-1 dargelegten modularen Struktur.
ANMERKUNG 1 In ISO/TR 52000-2 befindet sich die gleiche Tabelle, in der für jedes Modul die Nummern der relevanten EPB-Normen und die begleitenden Technischen Berichte aufgeführt sind, die veröffentlicht oder in Bearbeitung sind.
ANMERKUNG 2 Die Module stehen grundsätzlich für EPB-Normen, auch wenn eine EPB-Norm mehr als ein Modul abdecken kann bzw. ein Modul von mehr als einer EPB-Norm abgedeckt werden kann, etwa im Falle eines vereinfachten und eines ausführlichen Verfahrens. Siehe auch Abschnitt 2 und Tabellen A.1 und B.1.
Performance thermique des bâtiments - Transfert de chaleur par le sol - Méthodes de calcul (ISO 13370:2017)
L'ISO 13370:2017 décrit des méthodes de calcul des coefficients de transfert thermique et des flux thermiques des parois de bâtiments en contact avec le sol, comprenant les planchers sur terre-plein, les planchers sur vide sanitaire et les sous-sols. Il s'applique aux parois, ou portions de parois, se trouvant en dessous d'un plan horizontal dans l'enveloppe extérieure du bâtiment, qui est situé:
- au niveau de la surface du plancher intérieur, dans le cas de planchers sur terre-plein, de planchers sur vide sanitaire et de sous-sols non chauffés;
NOTE Pour certains cas, les dimensions extérieures définissent la limite à la surface inférieure de la dalle de plancher.
- au niveau de la surface du sol extérieur, dans le cas de sous-sols chauffés.
L'ISO 13370:2017 comprend le calcul de la partie du transfert thermique correspondant au régime stationnaire (flux thermique moyen annuel), ainsi que de la partie du transfert thermique résultant des variations périodiques annuelles de la température (variations saisonnières du flux thermique autour de la moyenne annuelle). Ces variations saisonnières sont déterminées sur une base mensuelle. L'ISO 13370:2017 n'est pas applicable à des périodes de temps plus courtes, sauf pour l'application aux programmes de simulation dynamique de l'Annexe D.
NOTE Le Tableau 1 de l'Introduction indique la position relative de l'ISO 13370:2017 dans la série de normes PEB dans le contexte de la structure modulaire définie dans l'ISO 52000‑1.
Toplotne značilnosti stavb - Prenos toplote skozi zemljo - Računske metode (ISO 13370:2017)
Ta dokument določa metode za izračun koeficientov prenosa toplote in stopnje toplotnega toka za stavbne elemente v toplotnem stiku s tlemi, vključno s podi iz plošč, spuščenimi podi in kletmi. Uporablja se za stavbne elemente (ali njihove dele) pod vodoravno ravnino v veznih stenah stavbe:
– na ravni notranje talne površine (za pode iz plošč, spuščene pode in neogrevane kleti);
V nekaterih primerih sistemi zunanjih dimenzij določajo mejo na spodnji površini talne plošče.
– na ravni zunanje talne površine (za ogrevane kleti).
Ta dokument vključuje izračun ustaljenega dela prenosa toplote (povprečna letna stopnja toplotnega toka) in dela, ki je posledica rednih letnih sprememb temperature (sezonske spremembe stopnje toplotnega toka v bližini letnega povprečja). Podatki o teh sezonskih spremembah se pridobijo vsak mesec in ta dokument se ne uporablja za krajša časovna obdobja, razen za namene uporabe za programe dinamične simulacije iz dodatka D.
Preglednica 1 v uvodu prikazuje relativno mesto tega dokumenta znotraj skupine standardov EPB v kontekstu modularne strukture, kot je opredeljeno v standardu ISO 52000-1.
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
SIST EN ISO 13370:2017
01-september-2017
1DGRPHãþD
SIST EN ISO 13370:2008
7RSORWQH]QDþLOQRVWLVWDYE3UHQRVWRSORWHVNR]L]HPOMR5DþXQVNHPHWRGH ,62
Thermal performance of buildings - Heat transfer via the ground - Calculation methods
(ISO 13370:2017)
Wärmetechnisches Verhalten von Gebäuden - Wärmeübertragung über das Erdreich -
Berechnungsverfahren (ISO 13370:2017)
Performance thermique des bâtiments - Transfert de chaleur par le sol - Méthodes de
calcul (ISO 13370:2017)
Ta slovenski standard je istoveten z: EN ISO 13370:2017
ICS:
91.120.10 Toplotna izolacija stavb Thermal insulation of
buildings
SIST EN ISO 13370:2017 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST EN ISO 13370:2017
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SIST EN ISO 13370:2017
EN ISO 13370
EUROPEAN STANDARD
NORME EUROPÉENNE
July 2017
EUROPÄISCHE NORM
ICS 91.120.10 Supersedes EN ISO 13370:2007
English Version
Thermal performance of buildings - Heat transfer via the
ground - Calculation methods (ISO 13370:2017)
Performance thermique des bâtiments - Transfert de Wärmetechnisches Verhalten von Gebäuden -
chaleur par le sol - Méthodes de calcul (ISO Wärmeübertragung über das Erdreich -
13370:2017) Berechnungsverfahren (ISO 13370:2017)
This European Standard was approved by CEN on 27 February 2017.
CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this
European Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references
concerning such national standards may be obtained on application to the CEN-CENELEC Management Centre or to any CEN
member.
This European Standard exists in three official versions (English, French, German). A version in any other language made by
translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC Management
Centre has the same status as the official versions.
CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,
Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania,
Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Avenue Marnix 17, B-1000 Brussels
© 2017 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 13370:2017 E
worldwide for CEN national Members.
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SIST EN ISO 13370:2017
EN ISO 13370:2017 (E)
Contents Page
European foreword . 3
2
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SIST EN ISO 13370:2017
EN ISO 13370:2017 (E)
European foreword
This document (EN ISO 13370:2017) has been prepared by Technical Committee ISO/TC 163 "Thermal
performance and energy use in the built environment" in collaboration with Technical Committee
CEN/TC 89 “Thermal performance of buildings and building components” the secretariat of which is
held by SIS.
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 January 2018 and conflicting national standards shall
be withdrawn at the latest by January 2018.
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. CEN shall not be held responsible for identifying any or all such patent rights.
This document has been prepared under a mandate given to CEN by the European Commission and the
European Free Trade Association.
This document is part of the set of standards and accompanying technical reports on the energy
performance of buildings and has been prepared under a mandate given to CEN by the European
Commission and the European Free Trade Association (Mandate M/480, see reference [EF3] below).
Directive 2010/31/EU recasting the Directive 2002/91/EC on energy performance of buildings (EPBD,
[EF4]) promotes the improvement of the energy performance of buildings within the European Union,
taking into account all types of energy uses (heating, lighting, cooling, air conditioning, ventilation) and
outdoor climatic and local conditions, as well as indoor climate requirements and cost effectiveness
(Article 1).
The directive requires Member States to adopt measures and tools to achieve the prudent and rational
use of energy resources. In order to achieve those goals, the EPBD requires increasing energy efficiency
and the enhanced use of renewable energies in both new and existing buildings. One tool for this is the
application by Member States of minimum requirements on the energy performance of new buildings
and for existing buildings that are subject to major renovation, as well as for minimum performance
requirements for the building envelope if energy-relevant parts are replaced or retrofitted. Other tools
are energy certification of buildings, inspection of boilers and air-conditioning systems.
The use of European standards increases the accessibility, transparency and objectivity of the energy
performance assessment in the Member States facilitating the comparison of best practices and
supporting the internal market for construction products. The use of EPB standards for calculating
energy performance, as well as for energy performance certification and the inspection of heating
systems and boilers, ventilation and air-conditioning systems will reduce costs compared to developing
different standards at national level.
The first mandate to CEN to develop a set of CEN EPBD standards (M/343, [EF1]), to support the first
edition of the EPBD ([EF2]) resulted in the successful publication of all EPBD related CEN standards in
2007-2008.
Mandate M/480 was issued to review the mandate M/343 as the recast of the EPBD raised the need to
revisit the standards and reformulate and add standards so that they become on the one hand
unambiguous and compatible, and on the other hand a clear and explicit overview of the choices,
boundary conditions and input data that need to be defined at national or regional level. Such national
or regional choices remain necessary, due to differences in climate, culture and building tradition,
3
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SIST EN ISO 13370:2017
EN ISO 13370:2017 (E)
policy and legal frameworks. Consequently, the set of CEN EPBD standards published in 2007-2008 had
to be improved and expanded on the basis of the recast of the EPBD.
The EPB standards are flexible enough to allow for necessary national and regional differentiation and
facilitate Member States implementation and the setting of requirements by the Member States.
Further target groups are users of the voluntary common European Union certification scheme for the
energy performance of non-residential buildings (EPBD article 11.9) and any other regional (e.g. pan
European) parties wanting to motivate their assumptions by classifying the building energy
performance for a dedicated building stock.
This document supersedes EN ISO 13370:2007.
According to the CEN-CENELEC Internal Regulations, the national standards organizations of the
following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria,
Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia,
France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta,
Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland,
Turkey and the United Kingdom.
References:
[EF1] EPBD, Directive 2002/91/EC of the European Parliament and of the Council of 16 December
2002 on the energy performance of buildings
[EF2] EPBD Mandate M/343, Mandate to CEN, CENELEC and ETSI for the elaboration and adoption of
standards for a methodology calculating the integrated energy performance of buildings and estimating
the environmental impact, in accordance with the terms set forth in Directive 2002/91/EC , 30 January
2004
[EF3] Mandate M/480, Mandate to CEN, CENELEC and ETSI for the elaboration and adoption of
standards for a methodology calculating the integrated energy performance of buildings and promoting
the energy efficiency of buildings, in accordance with the terms set in the recast of the Directive on the
energy performance of buildings (2010/31/EU), 14 December 2010
[EF4] EPBD, Recast of the Directive on the energy performance of buildings (2010/31/EU). 14
December 2010
Endorsement notice
The text of ISO 13370:2017 has been approved by CEN as EN ISO 13370:2017 without any modification.
4
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SIST EN ISO 13370:2017
INTERNATIONAL ISO
STANDARD 13370
Third edition
2017-06
Thermal performance of buildings —
Heat transfer via the ground —
Calculation methods
Performance thermique des bâtiments — Transfert de chaleur par le
sol — Méthodes de calcul
Reference number
ISO 13370:2017(E)
©
ISO 2017
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SIST EN ISO 13370:2017
ISO 13370:2017(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2017, Published in Switzerland
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized otherwise in any form
or by any means, electronic or mechanical, including photocopying, or posting on the internet or an intranet, without prior
written permission. Permission can be requested from either ISO at the address below or ISO’s member body in the country of
the requester.
ISO copyright office
Ch. de Blandonnet 8 • CP 401
CH-1214 Vernier, Geneva, Switzerland
Tel. +41 22 749 01 11
Fax +41 22 749 09 47
copyright@iso.org
www.iso.org
ii © ISO 2017 – All rights reserved
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SIST EN ISO 13370:2017
ISO 13370:2017(E)
Contents Page
Foreword .v
Introduction .vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 2
4 Symbols and subscripts . 3
4.1 Symbols . 3
4.2 Subscripts . 3
5 Description of the method . 4
5.1 Output . 4
5.2 General description . 4
5.3 Periodic coefficients . 5
6 Calculation of heat transfer via the ground . 5
6.1 Output data . 5
6.2 Calculation time intervals . 6
6.3 Input data . 7
6.4 Thermal properties . 7
6.4.1 Thermal properties of the ground . 7
6.4.2 Thermal properties of building materials . 8
6.4.3 Surface resistances . . 8
6.5 Internal temperature and climatic data . 8
6.5.1 Internal temperature. 8
6.5.2 Climatic data . 8
6.6 Thermal transmittance and heat flow rate . 9
6.6.1 Thermal transmittance . . 9
6.6.2 Thermal bridges at edge of floor . 9
6.6.3 Calculation of heat flow rate . 9
6.6.4 Effect of ground water . . 9
6.6.5 Special cases .10
6.7 Parameters used in the calculations .10
6.7.1 Characteristic dimension of floor .10
6.7.2 Equivalent thickness .11
7 Calculation of thermal transmittances .11
7.1 Slab-on-ground floor .11
7.2 Suspended floor .13
7.3 Heated basement .15
7.3.1 General.15
7.3.2 Basement floor .17
7.3.3 Basement walls .17
7.3.4 Heat transfer from whole basement .18
7.4 Unheated basement .18
7.5 Partly heated basement .19
7.6 Effective thermal resistance of floor construction .19
Annex A (normative) Input and method selection data sheet — Template .20
Annex B (informative) Input and method selection data sheet — Default choices .23
Annex C (normative) Calculation of ground heat flow rate .26
Annex D (normative) Slab-on-ground with edge insulation .32
Annex E (informative) Heat flow rates for edge and central regions of a building .37
Annex F (normative) Application to dynamic calculation programmes .38
© ISO 2017 – All rights reserved iii
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SIST EN ISO 13370:2017
ISO 13370:2017(E)
Annex G (normative) Ventilation below suspended floors .40
Annex H (normative) Periodic heat transfer coefficients .43
Bibliography .49
iv © ISO 2017 – All rights reserved
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SIST EN ISO 13370:2017
ISO 13370:2017(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/d irectives).
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/p atents).
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: ww w .iso. org/iso / foreword. html.
ISO 13370 was prepared by ISO Technical Committee ISO/TC 163, Thermal performance and energy use
in the built environment, Subcommittee SC 2, Calculation methods, in collaboration with the European
Committee for Standardization (CEN) Technical Committee CEN/TC 89, Thermal performance of
buildings and building components, in accordance with the Agreement on technical cooperation between
ISO and CEN (Vienna Agreement).
This third edition cancels and replaces the second edition (ISO 13370:2007), which has been technically
revised.
The changes in this third edition are mostly editorial. This document has been re-drafted according to
CEN/TS 16629:2014. Some additional output variables have been introduced to facilitate the linkages
between this document and ISO 52016-1.
© ISO 2017 – All rights reserved v
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SIST EN ISO 13370:2017
ISO 13370:2017(E)
Introduction
This document is part of a series aimed at the international harmonization of the methodology for
assessing the energy performance of buildings. Throughout, this series is referred to as a “set of EPB
standards”.
All EPB standards follow specific rules to ensure overall consistency, unambiguity and transparency.
All EPB standards provide a certain flexibility with regard to the methods, the required input data and
references to other EPB standards, by the introduction of a normative template in Annex A and Annex B
with informative default choices.
For the correct use of this document, a normative template is given in Annex A to specify these choices.
Informative default choices are provided in Annex B.
The main target groups for this document are architects, engineers and regulators.
Use by or for regulators: In case the document is used in the context of national or regional legal
requirements, mandatory choices may be given at national or regional level for such specific
applications. These choices (either the informative default choices from Annex B or choices adapted to
national/regional needs, but in any case following the template of Annex A) can be made available as
national annex or as separate (e.g. legal) document (national data sheet).
NOTE 1 So in this case:
— the regulators will specify the choices;
— the individual user will apply the document to assess the energy performance of a building, and thereby use
the choices made by the regulators.
Topics addressed in this document can be subject to public regulation. Public regulation on the same
topics can override the default values in Annex B. Public regulation on the same topics can even, for
certain applications, override the use of this document. Legal requirements and choices are in general
not published in standards but in legal documents. In order to avoid double publications and difficult
updating of double documents, a national annex may refer to the legal texts where national choices
have been made by public authorities. Different national annexes or national data sheets are possible,
for different applications.
It is expected, if the default values, choices and references to other EPB standards in Annex B are not
followed due to national regulations, policy or traditions, that:
— national or regional authorities prepare data sheets containing the choices and national or regional
values, according to the model in Annex A. In this case a national annex (e.g. NA) is recommended,
containing a reference to these data sheets;
— or, by default, the national standards body will consider the possibility to add or include a national
annex in agreement with the template of Annex A, in accordance to the legal documents that give
national or regional values and choices.
Further target groups are parties wanting to motivate their assumptions by classifying the building
energy performance for a dedicated building stock.
More information is provided in the Technical Report (ISO/TR 52019-2) accompanying this document.
The subset of EPB standards prepared under the responsibility of ISO/TC 163/SC 2 cover inter alia:
— calculation procedures on the overall energy use and energy performance of buildings;
— calculation procedures on the internal temperature in buildings (e.g. in case of no space heating or
cooling);
— indicators for partial EPB requirements related to thermal energy balance and fabric features;
vi © ISO 2017 – All rights reserved
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SIST EN ISO 13370:2017
ISO 13370:2017(E)
— calculation methods covering the performance and thermal, hygrothermal, solar and visual
characteristics of specific parts of the building and specific building elements and components, such
as opaque envelope elements, ground floor, windows and facades.
ISO/TC 163/SC 2 cooperates with other technical committees for the details on appliances, technical
building systems, indoor environment, etc.
This document provides the means (in part) to assess the contribution that building products and
services make to energy conservation and to the overall energy performance of buildings.
In contrast with ISO 6946, which gives the method of calculation of the thermal transmittance of
building elements in contact with the external air, this document deals with elements in thermal
contact with the ground. The division between these two International Standards is at the level of the
inside floor surface for slab-on-ground floors, suspended floors and unheated basements, and at the
level of the external ground surface for heated basements. In general, a term to allow for a thermal
bridge associated with the wall/floor junction is included when assessing the total heat loss from a
building using methods such as ISO 13789.
The calculation of heat transfer through the ground can be done by numerical calculations, which also
allow analysis of thermal bridges, including wall/floor junctions, for assessment of minimum internal
surface temperatures.
In this document, methods are provided which take account of the three-dimensional nature of the heat
flow in the ground below buildings.
Thermal transmittances of floors give useful comparative values of the insulation properties of
different floor constructions and are used in building regulations in some countries for the limitation of
heat losses through floors.
Thermal transmittance, although defined for steady-state conditions, also relates average heat flow to
average temperature difference. In the case of walls and roofs exposed to the external air, there are
daily periodic variations in heat flow into and out of storage related to daily temperature variations,
but this averages out, and the daily average heat loss can be found from the thermal transmittance
and daily average inside-to-outside temperature difference. For floors and basement walls in contact
with the ground, however, the large thermal inertia of the ground results in periodic heat flows related
to the annual cycle of internal and external temperatures. The steady-state heat flow is often a good
approximation to the average heat flow over the heating season.
In addition to the steady-state part, a detailed assessment of floor losses is obtained from annual
periodic heat transfer coefficients related to the thermal capacity of the soil, as well as its thermal
conductivity, together with the amplitude of annual variations in monthly mean temperature.
Annex F provides a method for incorporating heat transfers to and from the ground into calculations
undertaken at short time intervals (e.g. 1 h).
ISO/TR 52019-2 provides information on
— t
...
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