ISO/TR 22131:2023

ISO/TRDTR 22131:2022(E)
ISO/TC 269/SC 2/WG 1
Date: 2022-08-11
Railway applications — Railway braking — Country specific applications for ISO 20138--1

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Second edition
Date: 2022-10-11

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ISO/DTR 22131:2022(E)
© ISO 2022
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ISO/DTR 22131:2022(E)
Contents
Foreword . iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Slowing or stopping distance calculation using a method implemented in France . 1
4.1 General . 1
4.2 Terms, symbols and abbreviations . 1
4.3 Slowing or stopping distance calculation . 2
4.3.1 French model for “G” position . 2
4.3.2 Calculation using ISO 20138-1:2018, 5.7.5.1 (step model) . 3
4.4 Example of calculation . 4
4.4.1 Test results . 4
4.4.2 Comparison of calculation models with test results . 4
5 Calculation of braking performance implemented in Japan . 5
5.1 General . 5
5.2 Brake ratio for a single vehicle . 5
5.3 Example for brake ratio calculation . 6
5.4 Equivalent response time . 8
6 Stopping or slowing distance calculation methods for some particular rolling stock
in China . 9
6.1 General . 9
6.2 Definitions, symbols and abbreviations . 9
6.3 Train resistance retarding forces. 11
6.3.1 Basic running resistance . 11
6.3.2 Curve resistance . 12
6.4 Train braking force . 14
6.4.1 Total braking force of train . 14
6.4.2 Real friction coefficient . 14
6.4.3 Conversion friction coefficient . 15
6.4.4 Real brake block force . 15
6.4.5 Nominal values of rigging efficiency . 16
6.4.6 Emergency brake cylinder pressure . 17
6.4.7 Conversion brake block force . 17
6.4.8 Conversion braking ratio . 18
6.4.9 Train unit brake ratio . 20
6.4.10 Dynamic brake force . 20
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ISO/DTR 22131:2022(E)
6.4.11 Coefficient of adhesion . 21
6.5 Brake calculation . 21
6.5.1 Braking time . 21
6.5.2 Free running time . 21
6.5.3 Stopping/slowing distance . 22
Bibliography . 23
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ISO/DTR 22131:2022(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
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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
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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 22131:2018), which has been technically
revised.
The main changes are as follows:is: the symbols and terms in Clause 6 have been revised.
— editorial revision of symbols and terms in Clause 6.
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.
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TECHNICAL REPORT ISO/DTR 22131:2022(E)

Railway applications — Railway braking — Country specific
applications for ISO 20138-1
1 Scope
This document provides additional information to assist the understanding and the use of ISO 20138-1.
The calculations in this document follow the same principles but they are slightly different.
This document contains country specific calculation approaches currently in use and represents the
state of knowledge including for calculating:
— stopping and slowing distances;
— equivalent response time;
— brake performance;
— brake ratio.
2 Normative references
There are no normative references in this document.
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 20138-1:2018, Railway applications — Calculation of braking performance (stopping, slowing and
stationary braking) — Part 1: General algorithms utilizing mean value calculation
3 Terms and definitions
NoFor the purposes of this document, the terms and definitions are listedgiven in this
documentISO 20138-1 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/
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ISO/DTR 22131:2022(E)
4 Slowing or stopping distance calculation using a method implemented in
France
4.1 General
This calculation is based on the alternative method of equivalent response time calculation, as used in
the French railway requirements, in particular, for trains operating in “G” position.
4.2 Terms, Symbols and abbreviations
For the purpose of Clause 4, the terms, symbols and abbreviations defined in Table 1 apply.
Table 1 — Symbols, definitions and unitsabbreviations
Term, symbol
Symbol DefinitionDescription Unit
or abbreviation
Point when the brake force, deceleration or pressure has been substantially —
1
achieved, typically 95 %
2
a Equivalent deceleration (on level track, without considering gradient effect) m/s
e
2
g Standard acceleration of gravity m/s
[9]
“G” position Distributor valve and distributor isolating devices (as defined in EN 15355 ) —
i Gradient of the track (positive rising/negative falling) —
sgrad Stopping/slowing distance on a gradient m
stests Stopping distances measured during the tests m
t delay time s
a
t build-up time s
ab
t Equivalent response time s
e
2·t Equivalent response time multiplied by 2 s
e
v0 Initial speed m/s
vfin Final speed (= 0 in the case of a stopping distance) m/s
X Time s
Y Factor of nominal braking force, deceleration or pressure —
4.3 Slowing or stopping distance calculation
4.3.1 French model for “G” position
This model provides a high level of accuracy for the calculation of stopping distances of trains with long
build up time (e.g. “G” position). It is currently used by the infrastructure managers in order to evaluate
the conformance of a train with the train control system and the length of the signalling sections.
For this French model of slowing or stopping distance calculation, Figure 1 maycan be used for trains
operating in “G” position for brake systems with retarding forces acting on rail contact point.
The model uses a linear development of the effort from 0 to 1 during a time of 2· · te.
The equivalent response time, t , can be calculated as set out in Formula (1):
e
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ISO/DTR 22131:2022(E)
t
𝑡𝑡
ab ab
tt+ 𝑡𝑡 =𝑡𝑡 + (1)
e a
ea
2
2
withwhere t and t are in accordance with ISO 20138-1:2018, 5.5.2.
a ab


Key
X time, in s
Y factor of nominal braking force, deceleration or pressure
X time, in s
1 point when the full brake force, deceleration or pressure has been achieved, typically 95 % of maximum value
2 × equivalent response time multiplied by 2, in s
t
e
Figure 1 — Model based on a linear development of the effort from 0 to 1 during a time of 2· · te
The stopping (v = 0) or slowing distance can be calculated as set out in Formula (2):
fin
22 2
2 2
a vv− a ⋅t ⋅ a + 4⋅ gi⋅
( )
𝑎𝑎 𝑣𝑣 −𝑣𝑣
e 0 fin ee e e 0 fin
s = v⋅⋅t + − 𝑠𝑠 =𝑣𝑣 ⋅𝑡𝑡 ⋅ + −
grad 0 e grad 0 e
𝑎𝑎 +𝑔𝑔⋅𝑖𝑖 2⋅(𝑎𝑎 +𝑔𝑔⋅𝑖𝑖)
e e
a +⋅gi 2⋅ a +⋅gi 6⋅ a +⋅g i
( ) ( )
e e e
2
𝑎𝑎 ⋅𝑡𝑡 ⋅(𝑎𝑎 +4⋅𝑔𝑔⋅𝑖𝑖)
e e e
(2)
6⋅(𝑎𝑎 +𝑔𝑔⋅𝑖𝑖)
e
(2)
NOTE 1 The equivalent deceleration, a , does not take the effect of the gradient into account.
e
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ISO/DTR 22131:2022(E)
Formula (2) is valid for calculating the stopping/slowing distance with a fully established brake,
provided that the following condition in Formula (3) is fulfilled:
v − v ≥(a +⋅2 i)⋅t 𝑣𝑣 −𝑣𝑣 ≥ (𝑎𝑎 + 2⋅𝑖𝑖)⋅𝑡𝑡 (3)
0 fin e e 0 fin e e
(3)
where
 sgrad is the stopping/slowing distance on a gradient, in m;
 v is the initial speed, in m/s;
0
 t is the equivalent response time, in s;
e
2
 ae is the equivalent deceleration (on level track, without considering gradient effect), in m/s ;
2
 g is the standard acceleration of gravity, in m/s ;
 i is the gradient of the track (positive rising/negative falling);
 v is the final speed (= 0 in the case of a stopping distance), in m/s.
fin
NOTE 2 The stopping/slowing distance as calculated by applying Formula (2) will beis shorter than calculated
according to the method described in ISO 20138-1:2018, 5.7.4.
4.3.2 Calculation using ISO 20138-1:2018, 5.7.5.1 (step model)
ISO 20138-1:2018, 5.7.5.1 gives Formula (4) for calculations on level track (i = 0) or with gradient.
t 𝑡𝑡
ab ab
It uses the model for theoretical response time tt+ 𝑡𝑡 =𝑡𝑡 + as “step” model.
e a
ea
2
2
2
 
m
st 2
v − ⋅ g⋅⋅i t − v
 
0 e fin
 
m
1 m 1 𝑚𝑚
 dyn  st
st 2 2
s v⋅t− ⋅ g⋅⋅i t+ 𝑠𝑠 =𝑣𝑣 ⋅𝑡𝑡 − ⋅𝑔𝑔⋅𝑖𝑖⋅𝑡𝑡 +
grad 0 e e grad 0 e e
2𝑚𝑚
dyn
2 m 2a
dyn e
2
𝑚𝑚
st 2
�𝑣𝑣 − ⋅𝑔𝑔⋅𝑖𝑖⋅𝑡𝑡 � −𝑣𝑣
0 e
fin
𝑚𝑚
dyn
(4)
2𝑎𝑎
e
(4)
With train resistance and dynamic mass which compensate each other and v = 0, the formula is
fin
simplified as Formula (5):
2
2
gi⋅⋅t (v − gi⋅⋅t )²
𝑔𝑔⋅𝑖𝑖⋅𝑡𝑡 (𝑣𝑣−𝑔𝑔⋅𝑖𝑖⋅𝑡𝑡 )²
e 0 e e 0 e
s = v⋅t− + 𝑠𝑠 =𝑣𝑣 ⋅𝑡𝑡 − + (5)
grad 0 e
grad 0 e
2 2𝑎𝑎
e
22a
e
(5)
where
 s is the stopping/slowing distance on a gradient, in m;
grad
 v is the initial speed, in m/s;
0
 t is the equivalent response time, in s;
e
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ISO/DTR 22131:2022(E)
 mst is the static mass, in kg;
 m is the dynamic mass, in kg;
dyn
2
 g is the standard acceleration of gravity, in m/s ;
 i is the gradient of the track (positive rising/negative falling);
2
 a is the equivalent deceleration (on level track, without considering gradient effect), in m/s ;
e
 v is the final speed (= 0 in the case of a stopping distance), in m/s.
fin
4.4 Example of calculation
4.4.1 Test results
This example is based on a long train of 1 000 m in “G” position.
As a reference for further comparison, the tests realized on the tracks have provided the following
results for the stopping distances s :
tests
Stopping distance on level track 824 m
Stopping distance on a down gradient of 5 ‰ 885 m
Stopping distance on an up gradient of 5 ‰ 776 m
The equivalent response time, t (delay time + 1/2 brake build-up time), derived from the results of the
e
tests is 15,5 s.
The equivalent deceleration without including the effect of the gradient, a , derived from the results of
e
2
the tests is 0,89 m/s .
4.4.2 Comparison of calculation models with test results
The stopping distances, s , calculated using Formula (5) (simplified ISO 20138-1 “step model”) are
tests
given in Table 2:.
Table 2 — Stopping distances calculated using step model
v g i t a s s Difference
0 e e grad tests
       s vs s
grad tests
2 2
 km/h m/s mm/m s m/s m m %
Level track 100 9,81 0 15,5 0,89 864,0 824 5 %
Up gradient 100 9,81 5 15,5 0,89 834,7 776 8 %
Down gradient 100 9,81 −5 15,5 0,89 894,0 885 1 %
The stopping distances, s , calculated using Formula (2) (French alternative method) are given in
tests
Table 3:.
Table 3 — Stopping distances calculated using French alternative method
Condition Difference

Condition Difference
v0 g i te ae sgrad stests
Merged Cells
v0 ≥ (ae + 2g2 g · i) te sgrad vs stests
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ISO/DTR 22131:2022(E)
   v0 (ae + 2 g · i) te
Split Cells
(ae + 2g · i) te
2 2
km/h m/s mm/m s m/s v m/s m m %
0
m/s
   m/s m/s

Level track 100 9,81 0 15,5 0,89 27,8 > 13,8 828,4 824 < 1 %
Up gradient 100 9,81 5 15,5 0,89 27,8 > 15,3 777,7 776 0 %
Down gradient 100 9,81 −5 15,5 0,89 27,8 > 12,3 885,0 885 0 %
The values in the table demonstrate the following:
— The stopping distances calculated with the French alternative method are shorter than the ones of
the simplified “step model” of ISO 20138-1.
— The stopping distances calculated with the French alternative method are more accurate and closer
to the test results on the track.
5 Calculation of braking performance implemented in Japan
5.1 General
[ [3] ]
In Japan, the fundamental law is the Railway Operation Act . . In addition, the Technical Regulatory
Standards on Japanese Railway are published by the Ministry of Land, Infrastructure and Transport and
Tourism (MILT). The technical regulation consists of ministerial ordinances and approved model
specifications. Explanatory documents which complement the ministerial ordinances and approved
model specifications and help users to interpret these correctly have also been published. These
[4][7][8]
documents are generally used as standards as well as Japanese Industrial Standards (JIS) and
[ [5][6] ]
Japan Association of Rolling Stock Industries standards (JRIS) ), , etc. in Japan.
5.2 Brake ratio for a single vehicle
The brake ratio is used to compare the capability of single vehicles and is used for design assessment.
The braking force for a single vehicle can be calculated as set out in Formula (6):
F n⋅ A⋅⋅pi⋅η 𝐹𝐹 =𝑛𝑛 ⋅𝐴𝐴 ⋅𝑝𝑝 ⋅𝑖𝑖 ⋅𝜂𝜂 (6)
tot cyl tot c tot tot
tot cyl tot c tot tot
(6)
where
 F is the braking force, in kN;
tot
 ncyl is the number of brake cylinders;
2
 A is the area of a cylinder, in m ;
tot
 p is the brake cylinder pressure, in kPa;
c
 i is the total rigging ratio;
tot
 ƞ is the mechanical efficiency.
tot
The brake ratio for a single vehicle can be calculated as set out in Formula (7):
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ISO/DTR 22131:2022(E)
F
𝐹𝐹
tot tot
θ ⋅⋅C 100𝜃𝜃 = ⋅𝐶𝐶⋅ 100 (7)
𝑀𝑀 ⋅𝑔𝑔
tot
Mg⋅
tot
with
µ
𝜇𝜇
A A
C= 𝐶𝐶 = (8)
𝜇𝜇
C
µ
C
where
 Ɵ is the brake ratio for a single vehicle, in %;
 F is the braking force, in kN;
tot
 M is the operational mass of the vehicle plus load, in t;
tot
2
 g is the standard acceleration of gravity, in m/s ;
 C is the ratio of friction coefficients;
 µ is the friction coefficient of applied brake block;
A
 µC is the friction coefficient of cast iron block (assumed to be 0,15).
NOTE The friction coefficient of applied brake block, µA, and the acceptance criteria of the brake ratio are
outside the scope of this document.
5.3 Example for brake ratio calculation
In case of a vehicle with a tread brake unit per wheel, as shown in Figure 2, input data are shown in
Table 4.

A
Figure 2 — Vehicle with a tread brake unit per wheel
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ISO/DTR 22131:2022(E)
Table 4 — Input data
Description Symbol Example value Unit
Diameter of brake cylinder d 0,152 m
cyl
2
Standard acceleration of gravity g 9,807 m/s
Total rigging ratio i 3,6 —
tot
Operational mass m 31,4 t
op
Mass per person mp 55 kg/person
Number of brake cylinders n 8 —
cyl
Passenger capacity n 153 —
p
Brake cylinder pressure pc 303 kPa
Mechanical efficiency (including counter —
ƞ 1,0
tot
force)
Friction coefficient of applied brake block —
Split Cells
µ 0,3
A
(composite brake block)
Split Cells
(composite brake block)
Split Cells
The braking force of a vehicle can be calculated as set out in Formula (6):
Fm0,152 ²⋅π / 4⋅⋅8 303⋅3,6⋅1,0
[( ) ]
tot
F = 158,4 kN
tot
[( ) ]
𝐹𝐹 = 0,152𝑚𝑚 ²⋅𝜋𝜋/4 ⋅ 8⋅ 303 kPa⋅ 3,6⋅ 1,0
tot
𝐹𝐹 = 158,4 kN
tot
The mass of a loaded vehicle can be calculated as set out in Formula (9):
M m+ nm⋅
tot op p p
𝑀𝑀 =𝑚𝑚 +𝑛𝑛 ⋅𝑚𝑚 (9)
tot op p p
55

M= 31,4+⋅153
tot

1 000

M = 39,82 t
tot
55
𝑀𝑀 = 31,4t + 153⋅� �⋅ t
tot
1 000
𝑀𝑀 = 39,82t
tot
The ratio of friction coefficients, C, using composite brake blocks can be calculated as set out in
Formula (8):
0,3
C 2,0
0,15

0,3
𝐶𝐶 = = 2,0
0,15
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ISO/DTR 22131:2022(E)
In the end, the brake ratio for a loaded vehicle can be calculated as set out in Formula (7):
158,4
θ ⋅⋅2,0 100
39,82 t⋅9,807
θ= 81 %
158,4 kN
𝜃𝜃 = ⋅ 2,0⋅ 100
39,82t⋅9,807 m/s²
𝜃𝜃 = 81%
5.4 Equivalent response time
5.4.1 General
In Japan, an equivalent response time is determined as below.
5.4.15.4.2 Case 1: Determination based on train speed
The equivalent response time is determined based on train speed. In this case, the brake command and
speed are measured. In the time series chart shown in Figure 3, the horizontal line is extended from the
speed at the starting point of the braking. Moreover, another line is extended from around the speed at
which the deceleration is almost constant. The equivalent response time is decided as the time between
the start of braking and cross point of two extended lines.
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ISO/DTR 22131:2022(E)


Key
X time, in s
Y1 speed
Y2 brake command
X time, in s
1 equivalent response time
a
Extend the horizontal line from the starting point of the braking.
b
Deceleration is almost constant.
Figure 3 — Equivalent response time in case 1 “based on train speed”
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ISO/DTR 22131:2022(E)
5.4.25.4.3 Case 2: Determination based on BC pressure response
The equivalent response time is determined based on BC pressure response. as shown in Figure 4. In
this case, it is the time when the brake cylinder pressure reaches about 60 % to 70 % (typically 63,2 %)
of set point from the starting point of braking.


Key
X time, in s
Y1 brake cylinder pressure
Y2 brake command
X time, in s
1 equivalent response time
Figure 4 — Equivalent response time in case 2 “BC pressure response”
6 Stopping or slowing distance calculation methods for some particular rolling
stock in China
6.1 General
[2]
The following has been taken from a Chinese Railway Industry Standard .
Until now, some traditional calculation methods have been used for conventional predefined units,
e.g.for example, long trains hauled by locomotive. The numerical parameters given in this traditional
method are based on test data and experience and are used for the vehicle design.
6.2 Definitions,Symbols and abbreviations
The symbols and abbreviations used in Clause 6 are detailed in Table 5.
Table 1 — General definitions, symbols and units
Table 5 — Symbols
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ISO/DTR 22131:2022(E)
DefinitionDescription Symbol Unit
Total braking force of train B kN
Dynamic brake force B kN
d
Train unit brake ratio b N/kN
Coefficient independent of speed C1 N/kN
Coefficient dependent on speed C2 N/kN
Coefficient dependent on squared speed C N/kN
3
Diameter of brake cylinder d mm
z
Hauled mass G t
2
Standard acceleration of gravity g m/s
Gradient (positive rising/negative falling) i ‰
Calculation gradient i
‰
j
Single brake block force/braking force K kN
′
Brake pad force of each brake pad ′ kN
K 𝐾𝐾
Conversion brake block force of train Kh kN
′
Conversion brake block force of locomotive
K′𝐾𝐾
kN
h
h
′′
Conversion brake block force of vehicle
′′
K 𝐾𝐾 kN
h h
Total distance along the curve including the transition curve lengths Lr m
Equivalent constant curve length l m
r
Transition length l , l m
yz1 yz2
Train overall length l m
1
Number of vehicles n —
Number of brake blocks n —
k
Number of brake cylinders nz —
Mass of locomotive P t
Cylinder pressure p kPa
z
Brake pipe pressure p kPa
1
Curve radius R m
Wheel radius R mm
c
Brake pipe pressure drop r kPa
Mean swept radius of the brake pad on the disc face rm mm
Effective braking distance s m
e
Free running distance s m
k
Stopping/slowing distance s m
z
Effective braking time t s
e
Free running time t s
k
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ISO/DTR 22131:2022(E)
DefinitionDescription Symbol Unit
Braking time t s
z
Running speed v km/h
Initial speed v km/h
0
Particular speeds v1 … v2 km/h
Angle of constant curve sector α °
Service brake coefficient β —
c
Rigging ratio γ —
z
Rigging efficiency η —
z
Conversion braking ratio of train ϑ
h
Train conversion brake ratio for service brake ϑ
hc
Coefficient of adhesion µz —
Circumference rate π —
Conversion friction coefficient φ —
h
Friction coefficient of each type of brake block φ —
k
Additional curve resistance ω N/kN
r
Basic running resistance for a train ω N/kN
0
Basic running resistance for a single vehicle ω' N/kN
0
6.26.3 Train resistance retarding forces
6.2.16.3.1 Basic running resistance
′
The basic running resistance for a single vehicle, ω′𝜔𝜔 ,, can be calculated as set out in Formula (10).
0 0
2
′ 2
ω′ C+ C⋅+vC⋅v 𝜔𝜔 =𝐶𝐶 +𝐶𝐶 ⋅𝑣𝑣 +𝐶𝐶 ⋅𝑣𝑣 (10)
0 12 3 0 1 2 3
where
 ′
ω
0
is the basic running resistance for a single vehicle, in N/kN;
′
𝜔𝜔
0
 C is the coefficient independent of speed, in N/kN;
1
 C is the coefficient dependent on speed, in N/kN× × h/km;
2
2 2
 C3 is the coefficient dependent on squared speed, in N/kN× × h /km ;
 v is the running speed, in km/h.
Table 6 sets out the characteristic coefficients, C , C , C , for specific Chinese vehicles.
1 2 3
Table 6 — Characteristic coefficients for specific Chinese vehicles
Characteristic coefficient
Vehicle type
C C C
1 2 3
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ISO/DTR 22131:2022(E)
Characteristic coefficient
Vehicle type
C C C
1 2 3
Electric locomotives
SS , SS and SS 2,25 0,019 0 0,000 320
1 3 4
SS7 1,40 0,003 8 0,000 348
SS 1,02 0,003 5 0,000 426
8
6K 1,02 0,003 5 0,000 426
8G 2,55 0,008 3 0,000 212
Diesel locomotives
DF 2,93 0,007 3 0,000 27
DF2 2,98 0,020 2 0,000 33
DF (for freight wagon, for passenger
4
coach)
DF B (for freight wagon, for pa
...

TECHNICAL ISO/TR
REPORT 22131
Second edition
Railway applications — Railway
braking — Country specific
applications for ISO 20138-1
Applications ferroviaires — Freinage ferroviaire — Applications
nationales spécifiques de l'ISO 20138-1
PROOF/ÉPREUVE
Reference number
ISO/TR 22131:2022(E)
© ISO/TR 2022

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ISO/TR 22131:2022(E)
COPYRIGHT PROTECTED DOCUMENT
© ISO 2022
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’s member body in the country of the requester.
ISO copyright office
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Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland
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ISO/TR 22131:2022(E)
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Slowing or stopping distance calculation using a method implemented in France .1
4.1 General . 1
4.2 Symbols and abbreviations . 1
4.3 Slowing or stopping distance calculation . 2
4.3.1 French model for “G” position . 2
4.3.2 Calculation using ISO 20138-1:2018, 5.7.5.1 step model . 3
4.4 Example of calculation. 4
4.4.1 Test results . 4
4.4.2 Comparison of calculation models with test results . 4
5 Calculation of braking performance implemented in Japan . 5
5.1 General . 5
5.2 Brake ratio for a single vehicle . 5
5.3 Example for brake ratio calculation . 6
5.4 Equivalent response time . 7
5.4.1 General . 7
5.4.2 Case 1: Determination based on train speed . 8
5.4.3 Case 2: Determination based on BC pressure response . 8
6 Stopping or slowing distance calculation methods for some particular rolling stock
in China . 9
6.1 General . 9
6.2 Symbols and abbreviations . 9
6.3 Train resistance retarding forces . 10
6.3.1 Basic running resistance . 10
6.3.2 Curve resistance .12
6.4 Train braking force . 14
6.4.1 Total braking force of train . 14
6.4.2 Real friction coefficient . 14
6.4.3 Conversion friction coefficient. 15
6.4.4 Real brake block force . 16
6.4.5 Nominal values of rigging efficiency . 17
6.4.6 Emergency brake cylinder pressure . 17
6.4.7 Conversion brake block force . 17
6.4.8 Conversion braking ratio . 18
6.4.9 Train unit brake ratio .20
6.4.10 Dynamic brake force . 20
6.4.11 Coefficient of adhesion . 21
6.5 Brake calculation . 21
6.5.1 Braking time . 21
6.5.2 Free running time . 22
6.5.3 Stopping/slowing distance . 22
Bibliography .24
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ISO/TR 22131:2022(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 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 22131:2018), which has been technically
revised.
The main changes is: the symbols and terms in Clause 6 have been revised.
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.
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TECHNICAL REPORT ISO/TR 22131:2022(E)
Railway applications — Railway braking — Country
specific applications for ISO 20138-1
1 Scope
This document provides additional information to assist the understanding and the use of ISO 20138-1.
The calculations in this document follow the same principles but they are slightly different.
This document contains country specific calculation approaches currently in use and represents the
state of knowledge including for calculating:
— stopping and slowing distances;
— equivalent response time;
— brake performance;
— brake ratio.
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 20138-1:2018, Railway applications — Calculation of braking performance (stopping, slowing and
stationary braking) — Part 1: General algorithms utilizing mean value calculation
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 20138-1 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 Slowing or stopping distance calculation using a method implemented in
France
4.1 General
This calculation is based on the alternative method of equivalent response time calculation, as used in
the French railway requirements, in particular, for trains operating in “G” position.
4.2 Symbols and abbreviations
For the purpose of Clause 4, the terms, symbols and abbreviations defined in Table 1 apply.
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ISO/TR 22131:2022(E)
Table 1 — Symbols and abbreviations
Symbol
Description Unit
or abbreviation
Point when the brake force, deceleration or pressure has been substantially —
1
achieved, typically 95 %
2
a Equivalent deceleration (on level track, without considering gradient effect) m/s
e
2
g Standard acceleration of gravity m/s
[9]
“G” position Distributor valve and distributor isolating devices (as defined in EN 15355 ) —
i Gradient of the track (positive rising/negative falling) —
s Stopping/slowing distance on a gradient m
grad
s Stopping distances measured during the tests m
tests
t delay time s
a
t build-up time s
ab
t Equivalent response time s
e
2·t Equivalent response time multiplied by 2 s
e
v Initial speed m/s
0
v Final speed (= 0 in the case of a stopping distance) m/s
fin
X Time s
Y Factor of nominal braking force, deceleration or pressure —
4.3 Slowing or stopping distance calculation
4.3.1 French model for “G” position
This model provides a high level of accuracy for the calculation of stopping distances of trains with long
build up time (e.g. “G” position). It is currently used by the infrastructure managers in order to evaluate
the conformance of a train with the train control system and the length of the signalling sections.
For this French model of slowing or stopping distance calculation, Figure 1 can be used for trains
operating in “G” position for brake systems with retarding forces acting on rail contact point.
The model uses a linear development of the effort from 0 to 1 during a time of 2 · t .
e
The equivalent response time, t , can be calculated as set out in Formula (1):
e
t
ab
tt=+ (1)
ea
2
where t and t are in accordance with ISO 20138-1:2018, 5.5.2.
a ab
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ISO/TR 22131:2022(E)
Key
X time, in s
Y factor of nominal braking force, deceleration or pressure
1 point when the full brake force, deceleration or pressure has been achieved, typically 95 % of maximum value
t equivalent response time, in s
e
Figure 1 — Model based on a linear development of the effort from 0 to 1 during a time of 2 · t
e
The stopping (v = 0) or slowing distance can be calculated as set out in Formula (2):
fin
22 2
a vv− at⋅⋅()ag+⋅4 ⋅i
e 0 fin ee e
st=⋅v ⋅ + − (2)
grad 0 e
ag+⋅i 2⋅+ag⋅i 66⋅+ag⋅i
() ()
e e e
NOTE 1 The equivalent deceleration, a , does not take the effect of the gradient into account.
e
Formula (2) is valid for calculating the stopping/slowing distance with a fully established brake,
provided that the condition in Formula (3) is fulfilled:
vv−≥()ai+⋅2 ⋅t (3)
0 fine e
where
s is the stopping/slowing distance on a gradient, in m;
grad
v is the initial speed, in m/s;
0
t is the equivalent response time, in s;
e
2
a is the equivalent deceleration (on level track, without considering gradient effect), in m/s ;
e
2
g is the standard acceleration of gravity, in m/s ;
i is the gradient of the track (positive rising/negative falling);
v is the final speed (= 0 in the case of a stopping distance), in m/s.
fin
NOTE 2 The stopping/slowing distance as calculated by applying Formula (2) is shorter than calculated
according to the method described in ISO 20138-1:2018, 5.7.4.
4.3.2 Calculation using ISO 20138-1:2018, 5.7.5.1 step model
ISO 20138-1:2018, 5.7.5.1 gives Formula (4) for calculations on level track (i = 0) or with gradient.
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ISO/TR 22131:2022(E)
t
ab
It uses the model for theoretical response time tt=+ as “step” model.
ea
2
2
 
m
st 2
v −⋅gi⋅⋅tv−
 
0 e ffin
 
m
m
1 dyn
 
st 2
sv=⋅t −⋅gi⋅⋅t + (4)
grad 0 e e
2 m 2a
dyn e
With train resistance and dynamic mass which compensate each other and v = 0, the formula is
fin
simplified as Formula (5):
2
gi⋅⋅t ()vg−⋅it⋅ ²
e 0 e
sv=⋅t − + (5)
grad 0 e
22a
e
where
s is the stopping/slowing distance on a gradient, in m;
grad
v is the initial speed, in m/s;
0
t is the equivalent response time, in s;
e
m is the static mass, in kg;
st
m is the dynamic mass, in kg;
dyn
2
g is the standard acceleration of gravity, in m/s ;
i is the gradient of the track (positive rising/negative falling);
2
a is the equivalent deceleration (on level track, without considering gradient effect), in m/s ;
e
v is the final speed (= 0 in the case of a stopping distance), in m/s.
fin
4.4 Example of calculation
4.4.1 Test results
This example is based on a long train of 1 000 m in “G” position.
As a reference for further comparison, the tests realized on the tracks have provided the following
results for the stopping distances s :
tests
Stopping distance on level track 824 m
Stopping distance on a down gradient of 5 ‰ 885 m
Stopping distance on an up gradient of 5 ‰ 776 m
The equivalent response time, t (delay time + 1/2 brake build-up time), derived from the results of the
e
tests is 15,5 s.
The equivalent deceleration without including the effect of the gradient, a , derived from the results of
e
2
the tests is 0,89 m/s .
4.4.2 Comparison of calculation models with test results
The stopping distances, s , calculated using Formula (5) (simplified ISO 20138-1 “step model”) are
tests
given in Table 2.
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ISO/TR 22131:2022(E)
Table 2 — Stopping distances calculated using step model
v g i t a s s Difference
0 e e grad tests
    s vs s
grad tests
2 2
km/h m/s mm/m s m/s m m %
Level track 100 9,81 0 15,5 0,89 864,0 824 5 %
Up gradient 100 9,81 5 15,5 0,89 834,7 776 8 %
Down gradient 100 9,81 −5 15,5 0,89 894,0 885 1 %
The stopping distances, s , calculated using Formula (2) (French alternative method) are given in
tests
Table 3.
Table 3 — Stopping distances calculated using French alternative method
Condition Difference
v g i t a s s
0 e e grad tests
v ≥ (a + 2 g · i) t s vs s
0 e e grad tests
v (a + 2 g · i) t
0 e e
2 2
km/h m/s mm/m s m/s m/s m/s m m %
Level track 100 9,81 0 15,5 0,89 27,8 > 13,8 828,4 824 < 1
Up gradient 100 9,81 5 15,5 0,89 27,8 > 15,3 777,7 776 0
Down gradient 100 9,81 −5 15,5 0,89 27,8 > 12,3 885,0 885 0
The values in the table demonstrate the following:
— The stopping distances calculated with the French alternative method are shorter than the ones of
the simplified “step model” of ISO 20138-1.
— The stopping distances calculated with the French alternative method are more accurate and closer
to the test results on the track.
5 Calculation of braking performance implemented in Japan
5.1 General
[3]
In Japan, the fundamental law is the Railway Operation Act. In addition, the Technical Regulatory
Standards on Japanese Railway are published by the Ministry of Land, Infrastructure and Transport
and Tourism (MILT). The technical regulation consists of ministerial ordinances and approved model
specifications. Explanatory documents which complement the ministerial ordinances and approved
model specifications and help users to interpret these correctly have also been published. These
[4][7][8]
documents are generally used as standards as well as Japanese Industrial Standards (JIS) and
[5][6]
Japan Association of Rolling Stock Industries standards (JRIS), etc. in Japan.
5.2 Brake ratio for a single vehicle
The brake ratio is used to compare the capability of single vehicles and is used for design assessment.
The braking force for a single vehicle can be calculated as set out in Formula (6):
Fn=⋅Ap⋅⋅i ⋅η (6)
totcyl totc tottot
where
F is the braking force, in kN;
tot
n is the number of brake cylinders;
cyl
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ISO/TR 22131:2022(E)
2
A is the area of a cylinder, in m ;
tot
p is the brake cylinder pressure, in kPa;
c
i is the total rigging ratio;
tot
ƞ is the mechanical efficiency.
tot
The brake ratio for a single vehicle can be calculated as set out in Formula (7):
F
tot
θ = ⋅⋅C 100 (7)
⋅
Mg
tot
with
μ
A
C = (8)
μ
C
where
Ɵ is the brake ratio for a single vehicle, in %;
F is the braking force, in kN;
tot
M is the operational mass of the vehicle plus load, in t;
tot
2
g is the standard acceleration of gravity, in m/s ;
C is the ratio of friction coefficients;
µ is the friction coefficient of applied brake block;
A
µ is the friction coefficient of cast iron block (assumed to be 0,15).
C
NOTE The friction coefficient of applied brake block, µ , and the acceptance criteria of the brake ratio are
A
outside the scope of this document.
5.3 Example for brake ratio calculation
In case of a vehicle with a tread brake unit per wheel, as shown in Figure 2, input data are shown in
Table 4.
Figure 2 — Vehicle with a tread brake unit per wheel
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ISO/TR 22131:2022(E)
Table 4 — Input data
Description Symbol Example value Unit
Diameter of brake cylinder d 0,152 m
cyl
2
Standard acceleration of gravity g 9,807 m/s
Total rigging ratio i 3,6 —
tot
Operational mass m 31,4 t
op
Mass per person m 55 kg/person
p
Number of brake cylinders n 8 —
cyl
Passenger capacity n 153 —
p
Brake cylinder pressure p 303 kPa
c
Mechanical efficiency (including counter —
ƞ 1,0
tot
force)
Friction coefficient of applied brake block —
µ 0,3
A
(composite brake block)
The braking force of a vehicle can be calculated as set out in Formula (6):
Fm= 0,²152 ⋅π /,48⋅⋅303⋅⋅36 10,
[]()
tot
F =158,4 kN
tot
The mass of a loaded vehicle can be calculated as set out in Formula (9):
Mm=+nm⋅ (9)
totopp p
55
 
M =+31,4 153⋅
tot
 
1000
 
M =39,82 t
tot
The ratio of friction coefficients, C, using composite brake blocks can be calculated as set out in
Formula (8):
03,
C ==20,
01, 5
In the end, the brake ratio for a loaded vehicle can be calculated as set out in Formula (7):
158,4
θ = ⋅⋅20, 100
39,,82t⋅9 807
θ =81 %
5.4 Equivalent response time
5.4.1 General
In Japan, an equivalent response time is determined as below.
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ISO/TR 22131:2022(E)
5.4.2 Case 1: Determination based on train speed
The equivalent response time is determined based on train speed. In this case, the brake command and
speed are measured. In the time series chart shown in Figure 3, the horizontal line is extended from the
speed at the starting point of the braking. Moreover, another line is extended from around the speed at
which the deceleration is almost constant. The equivalent response time is decided as the time between
the start of braking and cross point of two extended lines.
Key
X time, in s
Y1 speed
Y2 brake command
1 equivalent response time
a
Extend the horizontal line from the starting point of the braking.
b
Deceleration is almost constant.
Figure 3 — Equivalent response time in case 1 “based on train speed”
5.4.3 Case 2: Determination based on BC pressure response
The equivalent response time is determined based on BC pressure response as shown in Figure 4. In
this case, it is the time when the brake cylinder pressure reaches about 60 % to 70 % (typically 63,2 %)
of set point from the starting point of braking.
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ISO/TR 22131:2022(E)
Key
X time, in s
Y1 brake cylinder pressure
Y2 brake command
1 equivalent response time
Figure 4 — Equivalent response time in case 2 “BC pressure response”
6 Stopping or slowing distance calculation methods for some particular rolling
stock in China
6.1 General
[2]
The following has been taken from a Chinese Railway Industry Standard .
Until now, some traditional calculation methods have been used for conventional predefined units, for
example, long trains hauled by locomotive. The numerical parameters given in this traditional method
are based on test data and experience and are used for the vehicle design.
6.2 Symbols and abbreviations
The symbols and abbreviations used in Clause 6 are detailed in Table 5.
Table 5 — Symbols
Description Symbol Unit
Total braking force of train B kN
Dynamic brake force B kN
d
Train unit brake ratio b N/kN
Coefficient independent of speed C N/kN
1
Coefficient dependent on speed C N/kN
2
Coefficient dependent on squared speed C N/kN
3
Diameter of brake cylinder d mm
z
Hauled mass G t
2
Standard acceleration of gravity g m/s
Gradient (positive rising/negative falling) i ‰
Calculation gradient i ‰
j
Single brake block force/braking force K kN
Brake pad force of each brake pad ′ kN
K
Conversion brake block force of train K kN
h
Conversion brake block force of locomotive
′
K kN
h
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ISO/TR 22131:2022(E)
TTabablele 5 5 ((ccoonnttiinnueuedd))
Description Symbol Unit
Conversion brake block force of vehicle
′′
K kN
h
Total distance along the curve including the transition curve lengths L m
r
Equivalent constant curve length l m
r
Transition length l , l m
yz1 yz2
Train overall length l m
1
Number of vehicles n —
Number of brake blocks n —
k
Number of brake cylinders n —
z
Mass of locomotive P t
Cylinder pressure p kPa
z
Brake pipe pressure p kPa
1
Curve radius R m
Wheel radius R mm
c
Brake pipe pressure drop r kPa
Mean swept radius of the brake pad on the disc face r mm
m
Effective braking distance s m
e
Free running distance s m
k
Stopping/slowing distance s m
z
Effective braking time t s
e
Free running time t s
k
Braking time t s
z
Running speed v km/h
Initial speed v km/h
0
Particular speeds v … v km/h
1 2
Angle of constant curve sector α °
Service brake coefficient β —
c
Rigging ratio γ —
z
Rigging efficiency η —
z
Conversion braking ratio of train ϑ
h
Train conversion brake ratio for service brake ϑ
hc
Coefficient of adhesion µ —
z
Circumference rate π —
Conversion friction coefficient φ —
h
Friction coefficient of each type of brake block φ —
k
Additional curve resistance ω N/kN
r
Basic running resistance for a train ω N/kN
0
Basic running resistance for a single vehicle ω' N/kN
0
6.3 Train resistance retarding forces
6.3.1 Basic running resistance
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ISO/TR 22131:2022(E)
′
The basic running resistance for a single vehicle, ω , can be calculated as set out in Formula (10).
0
2
′
ω =+CC ⋅+vC ⋅v (10)
01 23
where
ω′ is the basic running resistance for a single vehicle, in N/kN;
0
C is the coefficient independent of speed, in N/kN;
1
C is the coefficient dependent on speed, in N/kN × h/km;
2
2 2
C is the coefficient dependent on squared speed, in N/kN × h /km ;
3
v is the running speed, in km/h.
Table 6 sets out the characteristic coefficients, C , C , C , for specific Chinese vehicles.
1 2 3
Table 6 — Characteristic coefficients for specific Chinese vehicles
Characteristic coefficient
Vehicle type
C C C
1 2 3
Electric locomotives
SS , SS and SS 2,25 0,019 0 0,000 320
1 3 4
SS 1,40 0,003 8 0,000 348
7
SS 1,02 0,003 5 0,000 426
8
6K 1,02 0,003 5 0,000 426
8G 2,55 0,008 3 0,000 212
Diesel locomotives
DF 2,93 0,007 3 0,000 27
DF 2,98 0,020 2 0,000 33
2
DF (for freight wagon, for passenger
4
coach)
DF B (for freight wagon, for passenger 2,28 0,029 3 0,000 178
4
coach)
DF C (for freight wagon)
4
DF 1,31 0,016 7 0,000 391
5
DF D 2,28 0,029 3 0,000 178
7
DF 2,40 0,002 2 0,000 391
8
DF 0,86 0,005 4 0,000 218
11
DFH 1,96 0,010 5 0,000 549
3
Steam locomotives
JS 0,74 0,016 8 0,000 700
QJ 0,70 0,024 3 0,000 673
Passenger coaches
21, 22 (v = 120 km/h) 1,66 0,007 5 0,000 155
max
25B, 25G (v = 140 km/h) 1,82 0,010 0 0,000 145
max
a
Coefficients are used when oil tank wagon is coupled with other freight wagons.
b
If a train consists of one or several oil tank wagons (not an oil tank wagon trainset), then the basic running resistance
for a single oil tank wagon is calculated as rolling bearing wagon.
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ISO/TR 22131:2022(E)
TTabablele 6 6 ((ccoonnttiinnueuedd))
Characteri
...