ISO/FDIS 20138-2

Railway applications — Calculation of braking performance (stopping, slowing and stationary braking) — Part 2: General algorithms utilizing step by step calculation

This document specifies the methodologies for calculation of braking performance for railway rolling stock. This document describes the general algorithms/formulae using instantaneous value inputs to perform calculations of brake equipment and braking performance, in terms of stopping/slowing distances, braking power and energy for all types of rolling stock, either as vehicles or units. The calculations can be performed at any stage of the assessment process (design, manufacture, testing, verification, investigation, etc.) of railway rolling stock. This document does not set out specific acceptance criteria (pass/fail). This document is not intended to be used as a design guide for the selection of brake systems and does not specify performance requirements. This document does not provide a method to calculate the extension of stopping distances when the level of demanded adhesion exceeds the available adhesion (wheel slide activity). This document contains examples of the calculation of brake forces for different brake equipment types and examples of the calculation of stopping distance for vehicles or units.

Applications ferroviaires — Calcul des performances de freinage (freinage d'arrêt, de ralentissement et d'immobilisation) — Partie 2: Algorithmes généraux utilisant le calcul pas à pas

Le présent document décrit les méthodologies de calcul des performances de freinage du matériel roulant ferroviaire. Le présent document décrit les algorithmes et formules généraux qui utilisent des valeurs instantanées comme valeurs d'entrée pour effectuer les calculs de dimensionnement des équipements de frein et les performances de freinage, en termes de distances d'arrêt et de ralentissement, de puissance et d'énergie de freinage pour tous les types de matériels roulants, qu'il s'agisse de véhicules ou de rames. Les calculs peuvent être effectués à n'importe quelle étape du processus d'évaluation (conception, fabrication, essais, vérification, investigation, etc.) du matériel roulant ferroviaire. Le présent document ne spécifie pas les critères d'acceptation spécifiques (réussite/échec). Le présent document n'est pas destiné à servir de guide de conception pour le choix des systèmes de freinage et ne spécifie pas les exigences de performances. Le présent document ne spécifie pas de méthode pour calculer l'allongement des distances d'arrêt en cas de dégradation du niveau d'adhérence disponible (phénomène d'enrayage). Le présent document donne des exemples de calcul des efforts de freinage pour les différents types d'équipements de frein, ainsi que des exemples de la distance d'arrêt propre à un véhicule isolé ou à une composition de train.

General Information

• Status: Not Published
• ICS: 45.020 - Railway engineering in general
• Technical Committee: ISO/TC 269/SC 2 - Rolling stock
• Drafting Committee: ISO/TC 269/SC 2/WG 1 - Railway braking
• Current Stage: 5000 - FDIS registered for formal approval
• Start Date: 09-Jul-2025
• Completion Date: 06-Jun-2025

Relations

• Revises: ISO 20138-2:2019 - Railway applications — Calculation of braking performance (stopping, slowing and stationary braking) — Part 2: General algorithms utilizing step by step calculation
• Effective Date: 23-Sep-2023

Standards Content (Sample)

FINAL DRAFT
International
Standard
ISO/TC 269/SC 2
Railway applications — Calculation
Secretariat: AFNOR
of braking performance (stopping,
Voting begins on:
slowing and stationary braking) —
2025-09-24
Part 2:
Voting terminates on:
2025-11-19
General algorithms utilizing step by
step calculation
Applications ferroviaires — Calcul des performances de freinage
(freinage d'arrêt, de ralentissement et d'immobilisation) —
Partie 2: Algorithmes généraux utilisant le calcul pas à pas
RECIPIENTS OF THIS DRAFT ARE INVITED TO SUBMIT,
WITH THEIR COMMENTS, NOTIFICATION OF ANY
RELEVANT PATENT RIGHTS OF WHICH THEY ARE AWARE
AND TO PROVIDE SUPPOR TING DOCUMENTATION.
IN ADDITION TO THEIR EVALUATION AS
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO-
LOGICAL, COMMERCIAL AND USER PURPOSES, DRAFT
INTERNATIONAL STANDARDS MAY ON OCCASION HAVE
TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL
TO BECOME STAN DARDS TO WHICH REFERENCE MAY BE
MADE IN NATIONAL REGULATIONS.
Reference number
FINAL DRAFT
International
Standard
ISO/TC 269/SC 2
Railway applications — Calculation
Secretariat: AFNOR
of braking performance (stopping,
Voting begins on:
slowing and stationary braking) —
Part 2:
Voting terminates on:
General algorithms utilizing step by
step calculation
Applications ferroviaires — Calcul des performances de freinage
(freinage d'arrêt, de ralentissement et d'immobilisation) —
Partie 2: Algorithmes généraux utilisant le calcul pas à pas
RECIPIENTS OF THIS DRAFT ARE INVITED TO SUBMIT,
WITH THEIR COMMENTS, NOTIFICATION OF ANY
RELEVANT PATENT RIGHTS OF WHICH THEY ARE AWARE
AND TO PROVIDE SUPPOR TING DOCUMENTATION.
© ISO 2025
IN ADDITION TO THEIR EVALUATION AS
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO-
LOGICAL, COMMERCIAL AND USER PURPOSES, DRAFT
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
INTERNATIONAL STANDARDS MAY ON OCCASION HAVE
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL
or ISO’s member body in the country of the requester.
TO BECOME STAN DARDS TO WHICH REFERENCE MAY BE
MADE IN NATIONAL REGULATIONS.
ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: [phone]
Email: [e-mail]
Website: www.iso.org
Published in Switzerland Reference number
ii
Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 2
5 General explanation of step by step calculation . 4
5.1 Method .4
5.2 Braking force models .4
5.3 Algorithm .5
5.3.1 General description .5
5.3.2 Time integration .5
5.3.3 Determination of time step by checking relative distance deviation,ξ .6
5.3.4 Equivalent system response time,t .7
a,e
5.3.5 Equivalent brake deceleration, a .7
f,e
5.4 Supplementary dynamic calculations .7
5.4.1 Energy dissipated by each brake equipment type, W .7
B,n
5.4.2 Value of the required wheel/rail adhesion for the braked wheelset, τ .7
ax
5.4.3 Maximum braking power of each brake equipment type,P .8
max,n
6 Considerations for stopping or slowing distances and deceleration calculations . 8
6.1 Accuracy of input values .8
6.2 Distance calculations .8
6.3 General characteristics .8
6.4 Brake equipment type characteristics .8
6.4.1 General .8
6.4.2 Input data .9
6.5 Initial and operating characteristics .9
6.5.1 Nominal conditions .9
6.5.2 Wheel diameter .9
6.5.3 Initial speed .9
6.5.4 Gradient .9
6.5.5 Level of the brake demand .9
6.5.6 Degraded mode .9
6.5.7 Degraded condition . .9
6.5.8 Available coefficient of wheel/rail adhesion .10
6.6 Other deceleration calculations .10
6.6.1 General .10
6.6.2 Decelerations resulting from the force generated by each brake equipment
type, a .10
j,n
6.6.3 Mean deceleration over a specific speed range, a , based on distance .10
f(v1, v2)
7 Immobilization brake calculation .10
Annex A (informative) Workflow of kinetic calculations .11
Annex B (informative) Calculation of braking forces (non-stationary) .12
Annex C (informative) Examples for brake calculation .16
Bibliography .26

iii
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).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 269, Railway applications, Subcommittee SC 2,
Rolling stock.
This second edition cancels and replaces the first edition (ISO 20138-2:2019), which has been technically
revised.
The main changes are as follows:
— ISO 24478 has been added to Clause 2;
— the former terms 3.1 “slowing distance” and 3.2 “slowing time” have been deleted and this document
now refers to ISO 24478 and ISO 20138-1 only in Clause 3;
— Clause 4 “Symbols" has been revised;
— Clause 5 “General explanation of step by step calculation” has been revised;
— Clause 6 “Considerations for stopping or slowing distances and deceleration calculations” has been
revised;
— Annex A “Workflow of kinetic calculations” has been revised;
— Annex B has been revised and renamed in “Calculation of retarding forces (non-stationary)”;
— Annex C “Examples for brake calculation” has been revised;
— the Bibliography has been revised.
A list of all parts in the ISO 20138 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.

iv
...

ISO/TC 269/SC 02/WG 1 2
Secretariat: AFNOR
Date: 2025-09-10
Railway applications — Calculation of braking performance
(stopping, slowing and stationary braking) — Part 2: General
algorithms utilizing step by step calculation
Second edition
Date: 2025-05-20
ISO #####-#:####(X)
Part 2:
General algorithms utilizing step by step calculation
Applications ferroviaires — Calcul des performances de freinage (freinage d'arrêt, de ralentissement et
d'immobilisation) —
Partie 2: Algorithmes généraux utilisant le calcul pas à pas
FDIS stage
2 © ISO #### – All rights reserved

All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication
may be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying,
or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO
at the address below or ISO'sISO’s member body in the country of the requester.
ISO Copyright Office copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: + 41 22 749 01 11
Email: E-mail: [e-mail]
Website: www.iso.org
Published in Switzerland.
iii
Content
iv
Contents
Foreword . vi
Introduction . viii
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Symbols . 2
5 General explanation of step by step calculation . 5
5.1 Method . 5
5.2 Braking force models . 5
5.3 Algorithm . 5
5.4 Supplementary dynamic calculations . 8
6 Considerations for stopping or slowing distances and deceleration calculations . 8
6.1 Accuracy of input values. 8
6.2 Distance calculations . 9
6.3 General characteristics . 9
6.4 Brake equipment type characteristics . 9
6.5 Initial and operating characteristics . 9
6.6 Other deceleration calculations . 10
7 Immobilization brake calculation . 11
Annex A (informative) Workflow of kinetic calculations . 12
Annex B (informative) Calculation of braking forces (non-stationary) . 15
Annex C (informative) Examples for brake calculation . 19
Bibliography . 34

v
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).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent rights
in respect thereof. As of the date of publication of this document, ISO had not received notice of (a) patent(s)
which may be required to implement this document. However, implementers are cautioned that this may not
represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 269, Railway applications, Subcommittee SC 2,
Rolling stock.
This second edition cancels and replaces the first edition (ISO 20138-2:2019), which has been technically
revised.
The main changes are as follows:
— — normative reference to ISO 24478 has been added;
— — to Clause 3 “Terms and definitions” has been revised ( 2;
— the former terms 3.1 “slowing distance” and 3.2 “slowing time” have been deleted and thethis document
now refers to ISO 24478 and ISO 20138-1 only);
— — in Clause 4 3;
— 4 “Symbols" and Table 1 havehas been revised;
— 5— Clause 5 “General explanation of step by step calculation” has been revised;
— 6— Clause 6 “Considerations for stopping or slowing distances and deceleration calculations” has been
revised;
— Annex A— Annex A “Workflow of kinetic calculations” has been revised;
— Annex B— Annex B has been revised and renamed in “Calculation of retarding forces (non-stationary)”;
vi
— Annex C— Annex C “Examples for brake calculation” has been revised;
— — the Bibliography has been revised.
A list of all parts in the ISO 20138 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
vii
Introduction
The objective of this document is to enable the railway industry and operators to work with common
calculation methods.
The methodology of step by step calculation is based on numerical time integration.
The step by step calculation method cannot be used for stationary braking. This document considers an
example for stationary braking of a multiple unit according to ISO 20138-1.
When calculating stopping and slowing distances using the step by step calculation method, it is intended that
both ISO 20138-1 and this document be considered.
viii
Railway applications — Calculation of braking performance
(stopping, slowing and stationary braking) —
Part 2:
General algorithms utilizing step by step calculation
1 Scope
This document specifies the methodologies for the calculation of braking performance for railway rolling
stock.
This document describes the step by step calculation methods for railway applications. In addition, the
algorithms provide a means of comparing the results of other braking performance calculation methods.
This document describes the general algorithms and formulae using instantaneous value inputs to perform
the calculations of brake equipment and braking performance, in terms of stopping and slowing distances, and
braking power and energy for all types of rolling stock, either as vehicles or units. The calculations can be
performed at any stage of the assessment process (design, manufacture, testing, verification, investigation,
etc.) of railway rolling stock.
This document does not set out specific acceptance criteria (pass or fail).
This document is not intended to be used as a design guide for the selection of brake subsystems and does not
specify performance requirements. This document does not provide a method to calculate the extension of
stopping distances when the level of demanded wheel/rail adhesion exceeds the available wheel/rail adhesion
(wheel slide activity).
This document contains examples of the calculation of braking forces for different brake subsystems and
examples of the calculation of stopping distance for vehicles or units.
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 20138--1, Railway applications — Calculation of braking performance (stopping, slowing and stationary
braking) — Part 1: General algorithms utilizing mean value calculation
ISO 24478, Railway applications — Braking — General vocabulary
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 20138-1 and ISO 24478 apply.
ISO and IEC maintain terminology databases for use in standardization at the following addresses:
— — ISO Online browsing platform: available at https://www.iso.org/obp
— — IEC Electropedia: available at https://www.electropedia.org/
4 Symbols
For the purposes of this document, the general symbols given in Table 1Table 1 and ISO/FDIS 20138-1:2025,
1)
Table 1 apply.
Table 1 — Symbols
Symbol Description Unit
a Instantaneous deceleration m/s
af,e Equivalent (mean) deceleration m/s
af(v1, v2) Mean deceleration over the speed range v2≤ v ≤ v1 m/s
aj Constant deceleration during iteration step j m/s
D Maximum wheel diameter m
max
Dmin Minimum wheel diameter m
FB Braking force N
FB,ECB Braking force of the linear eddy current brake N
F Maximum braking force of the linear eddy current brake N
B,ECB,max
F Braking force of an electro-dynamic brake N
B,ED
FB,ED,max Maximum braking force of an electro-dynamic brake N
FB,FR Braking force of a fluid retarder N
F Maximum braking force of a fluid retarder N
B,FR,max
F Wheel/rail adhesion independent retention force, e.g. force of permanent magnetic track
B,ind
N
brake
F Braking force of a wheel/rail adhesion independent brake system type z N
B,ind,z
FB,Mg,A Attraction force of one magnet assembly acting on a single rail N
FB,τ,i Wheel/rail adhesion dependent retarding force generated by applied parking brake N
FB,τ,req Wheel/rail adhesion dependent retention force N
𝐹
Remaining force of static mass N
B,𝜏,req,rem
Fb Instantaneous braking force acting at the rail generated by the brake equipment N
Fb,n Instantaneous braking force of brake subsystem n N
F Braking force for brake subsystem n during iteration step j N
B,n,j
F Instantaneous braking force for brake subsystem n during iteration step j N
b,n,j
FB,nom Nominal braking force N
FD Downhill force due to gravity N
F Downhill force due to gravity for a given slope i N
D (i)
F Proportion of downhill force to be resisted per wheelset with applied parking brakes N
d,ax
Fext External force N
Fg Weight force N
FH Retention force N
1)
Under preparation. Stage at the time of publication: ISO/FDIS 20138-1:2025.
Symbol Description Unit
F Static axle load perpendicular to the rail per wheelset with applied parking brake for a
N,ax
N
specific wheelset
F Static axle load perpendicular to the rail per wheelset with applied parking brake (i is an
N,i
N
index used for sorting wheelsets)
F Parking brake force per wheelset acting at the rail N
PB,ax
FPerp Perpendicular force N
FPerp,ax Perpendicular force N
Fpad,i Brake pad force (i is an index used for sorting) N
F Static axle load perpendicular to the rail per w
...