ISO/FDIS 24675-2

Railway applications - Running time calculation for timetabling - Part 2: Distance-speed diagrams and speed curves

In order to create punctual timetables, it is necessary to accurately calculate and plan out running time between stopping or passing points, headway between trains, train scheduling, rolling stock scheduling, driver and crew scheduling, operation scheduling in stations and depots and line / infrastructure capacity. Among these values, shortest running time between stopping or passing points must be calculated first, as this is the basis of timetabling. This document describes a practical procedure to create and verify distance-speed diagrams and speed curves using the parameters specified in ISO 24675-1. Shortest running time is obtained by numerically integrating the speed curves. This enables railway infrastructure managers, railway operators and related organizations to calculate accurate running time at the stage of setting up feasible and punctual daily timetables, seasonal timetables, annual timetables, strategic timetables for long-term perspective, and other timetables of a railway system. This document excludes running time calculation used for purposes other than timetabling.

Applications ferroviaires — Calcul des temps de parcours pour la construction des horaires — Partie 2: Diagrammes distance-vitesse et courbes de vitesse

General Information

• Status: Not Published
• ICS: 03.220.30 - Transport by rail
• ICS: 45.020 - Railway engineering in general
• Technical Committee: ISO/TC 269/SC 3 - Operations and services
• Drafting Committee: ISO/TC 269/SC 3 - Operations and services
• Current Stage: 5000 - FDIS registered for formal approval
• Start Date: 29-Aug-2025
• Completion Date: 15-Aug-2025

Overview

ISO/FDIS 24675-2 specifies a practical procedure for creating and verifying distance‑speed diagrams and speed curves used to calculate the shortest running time for railway timetabling. Built to work with the input parameters defined in ISO 24675-1, the standard focuses on the physical motion of trains, describing how to derive a position‑based speed curve and obtain running time by numerical integration of that curve. The document targets railway infrastructure managers, operators and related organizations responsible for producing punctual, feasible daily, seasonal and strategic timetables.

Key Topics

• Distance‑speed diagrams and speed curves: Methods to represent train speed as a function of position along the infrastructure and to ensure the speed curve does not exceed the most restrictive speed profile at any location.
• Calculation principles: Emphasis on Newtonian motion applied to traction, resistance and braking forces to prepare realistic speed curves (as a precursor to time computation).
• Numerical integration: Shortest running time is obtained by integrating the prepared speed curve over the route.
• Verification and accuracy: Procedures to verify calculation results and check conformity with mandatory parameters and the most restrictive speed profiles.
• Input and dependencies: Uses the mandatory parameters and verifications defined in ISO 24675-1 and references related vocabularies such as ISO 24478 and IEC 60050-811.

Practical features covered in the standard include distance‑speed diagram presentation, bounding by restrictive speed profiles, and documented verification steps to ensure calculated values are reliable for timetabling.

Applications

ISO/FDIS 24675-2 is applicable where accurate running time forms the basis for scheduling and operations planning, including:

• Train timetabling (daily, seasonal, annual and strategic)
• Headway and line capacity assessment
• Rolling stock and crew scheduling
• Station and depot operation planning

By standardizing the creation and verification of speed curves and distance‑speed diagrams, the document helps improve punctuality, support consistent timetable production, and enable fair, repeatable calculations across infrastructure managers and operators.

Related Standards

• ISO 24675-1 - Requirements and mandatory input parameters for running time calculation (normative companion to Part 2).
• ISO 24478:2023 - Braking vocabulary used for defining braking terms.
• IEC 60050-811:2017 - Electrotechnical vocabulary relevant to traction and rolling stock.

Notes

• ISO/FDIS 24675-2 excludes running time calculations for purposes other than timetabling.
• Annexes in the document include illustrative examples of distance‑speed diagrams and calculation procedures for speed curves to assist implementation and verification.

Keywords: running time calculation, distance-speed diagrams, speed curves, shortest running time, timetabling, railway operators, infrastructure managers, numerical integration.

Standards Content (Sample)

FINAL DRAFT
International
Standard
ISO/TC 269/SC 3
Railway applications — Running
Secretariat: JISC
time calculation for timetabling —
Voting begins on:
2026-01-01
Part 2:
Distance-speed diagrams and speed
Voting terminates on:
2026-02-26
curves
Applications ferroviaires — Calcul des temps de parcours pour la
construction des horaires —
Partie 2: Diagrammes distance-vitesse et courbes de vitesse
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 3
Railway applications — Running
Secretariat: JISC
time calculation for timetabling —
Voting begins on:
Part 2:
Distance-speed diagrams and speed
Voting terminates on:
curves
Applications ferroviaires — Calcul des temps de parcours pour la
construction des horaires —
Partie 2: Diagrammes distance-vitesse et courbes de vitesse
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 2026
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
3.1 General terms .1
3.2 Terms related to infrastructure . .2
3.3 Terms related to rolling stock .2
4 Relation between shortest running time and timetabling . 3
5 Running time calculation with a speed curve . 4
6 Calculation . 4
6.1 Basic principles .4
6.2 Calculation of a speed curve .5
6.3 Calculation of running time with a speed curve .6
7 Verification of accuracy of the calculation results . 7
Annex A (informative) Examples of distance-speed diagrams . 14
Annex B (informative) Calculation procedures for a speed curve .20

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 document 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 3,
Operations and services.
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
Introduction
The purpose of this document is to help many railway-related organizations around the world, regardless of
their experience, to calculate accurate train running time between two points such as stations for all rolling
stock types and its speed, helping to improve the punctuality of railways around the world.
Improving railway punctuality can increase the competitiveness of railway transportation against other
modes of transportation such as planes, buses and cars. More customers using railway means more
income for railway infrastructure managers, railway operators and related organizations. It also means
the promotion of national economic growth, increased social efficiency and the use of environmentally
friendly energy leading to increased global sustainability. Overall, an increased use of railways leads to an
improvement of quality of life (QOL) for customers.
In order to create punctual timetables, it is necessary to accurately calculate and plan out running time
between stopping or passing points, headway between trains, train scheduling, rolling stock scheduling,
driver and crew scheduling, operation scheduling in stations and depots and both line and infrastructure
capacities. Among these values, shortest running time between stopping or passing points is calculated
first, as this is the basis of timetabling.
This enables railway stakeholders to calculate the time accurately at the stage of setting up timetables of
a railway system, such as daily timetables, seasonal timetables, annual timetables, strategic timetables for
long-term perspective, and other timetables of a railway system. These timetables are created not only with
the shortest running time shown in this document but also with other factors for safety and punctuality
during commercial operations.
In many cases, running time calculation is realized using many detailed factors of practical real railway
operations. However, it is almost impossible to verify the appropriateness of the running time calculation
from the viewpoint of all such factors. On the other hand, suitable and practical verification procedures
for running time calculation need to be identified to ensure the quality and validity of the running time
calculation for punctual timetabling.
A practical running time calculation involves many factors of real railway operations. In order to establish
clear verification procedures of running time calculation, this document mainly focuses on physical
movements of a train.
ISO 24675-1 specifies the requirements with input parameters for running time calculation and with
verification of the usage of those parameters. Figure 1 shows the relation between this document and
ISO 24675-1.
v
Figure 1 — Relation between this document and ISO 24675-1
In addition to this document, further documents will complete the ISO 24675 series on railway timetabling.
All parts together form a specific and comprehensive guidance for railway timetabling. Figure 2 shows a
roadmap of the target for railway timetabling. It involves important elements of railway timetabling to be
standardized in the future.
Figure 2 — Roadmap for railway timetabling

vi
FINAL DRAFT International Standard ISO/FDIS 24675-2:2026(en)
Railway applications — Running time calculation for
timetabling —
Part 2:
Distance-speed diagrams and speed curves
1 Scope
This document specifies a practical procedure to create and verify distance-speed diagrams and speed
curves using the parameters specified in ISO 24675-1, from which the shortest running time for railway
timetabling is obtained by numerically integrating the speed curves.
This document excludes running time calculation used for purposes other than timetabling.
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 24675-1:2022, Railway Applications — Running time calculation for timetabling — Part 1: Requirements
ISO 24478:2023, Railway applications — Braking — General vocabulary
IEC 60050-811:2017, International Electrotechnical Vocabulary (IEV) — Part 811: Electric traction
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 24675-1, ISO 24478, IEC 60050-811,
and the following 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/
3.1 General terms
3.1.1
position
distance from a specific reference point on a defined path on the infrastructure
[SOURCE: ISO 24675-1:2022, 3.1.3]
3.1.2
stopping point
point where a train stops or starts
[SOURCE: ISO 24675-1:2022, 3.1.4]

3.1.3
passing point
pre-defined point where the passing time of the train is recorded
3.1.4
starting point
point where a running time calculation starts
3.1.5
ending point
point where a running time calculation ends
3.1.6
speed curve
function from a position (3.1.1) value to a speed value showing speed changing of a train according to its
position (3.1.1)
3.1.7
timetabling
defining a set of train schedules for a railway system to provide a service considering conditions such as the
interaction between trains, infrastructure capacity, rolling stock, personnel, stations and depots scheduling,
shunting, commercial requirements, etc. according to its validity period or application
[SOURCE: ISO 24675-1:2022, 3.1.7]
3.1.8
running time
amount of time, on a defined path on the infrastructure, for the head of a train to pass from one stopping
point (3.1.2) or passing point (3.1.3) to another without making any stops in between
[SOURCE: ISO 24675-1:2022, 3.1.1]
3.1.9
shortest running time
running time (3.1.8) when a train is driven in the quickest way while conforming with predetermined
operating restrictions
[SOURCE: ISO 24675-1:2022, 3.1.2]
3.1.10
unit time
minimum time that constitutes the timetable
3.2 Terms related to infrastructure
3.2.1
gradient resistance force
force derived from track gradient
[SOURCE: ISO 24675-1:2022, 3.2.1]
3.3 Terms related to rolling stock
3.3.1
static mass
mass of the rail vehicle/unit/train in a stationary condition
[SOURCE: ISO 24478:2023, 3.5.5]

3.3.2
running resistance force
resistance to motion of a vehicle or train
[SOURCE: ISO 24675-1:2022, 3.3.2]
3.3.3
tractive force
force in direction of travel exerted by traction motors, engines or other means of propulsion
[SOURCE: ISO 24675-1:2022, 3.3.3]
3.3.4
braking deceleration
deceleration throughout the distance travelled from the commencement of the brake application until
achieving standstill or the final speed
Note 1 to entry: The braking distance represents the distance travelled from the commencement of the brake
application until achieving standstill or the final speed.
[SOURCE: ISO 24478:2023, 3.6.30, modified — "braking distance" has been replaced with the text after
"throughout" in the definition.]
3.3.5
inertia ratio
factor greater than unity applied to the mass of a train or vehicle to make allowance for the inertia of the
revolving masses inseparable from the movement of the train
[SOURCE: IEC 60050-811:2017, 811-05-07, modified — the text "same as allowance for rotating parts " has
been deleted from the end of the definition.]
4 Relation between shortest running time and timetabling
A running time used for timetabling is not always equal to the shortest running time. Adding additional time
is necessary to consider actual driving conditions for increasing safe operations and punctuality. This clause
shows four elements of a running time used for timetabling.
Figure 3 shows the following elements in a running time structure used for timetabling with the shortest
running time.
a) Shortest running time: The shortest running time is calculated using at least all the mandatory
parameters specified in ISO 24675-1.
b) Slack time: The slack time is calculated by rounding up to the unit time of the corresponding railway
line such as five-seconds, ten-seconds, fifteen-seconds or a half-minute.
c) Supplemental time: In the process of timetabling, feasible driving operations, vehicle variation, track
conditions and driving guidance should be considered. Given those factors differ according to the
conditions and features of the railway lines, based on these factors, the addition of supplemental time
to the shortest running time is necessary to appropriately prepare a running time for real railway
operation conditions. The supplemental time also serves in order to ensure punctuality, considering the
potential slight delays occurring in real railway operation conditions.
d) Running time used for timetabling: The running time used for timetabling is the sum of the shortest
running time, slack time and supplemental time.

Key
a shortest running time (target of this document)
b slack time
c supplemental time
d running time used for timetabling
Figure 3 — Running time structure used for timetabling
5 Running time calculation with a speed curve
Running time calculation generally consists of two steps.
— The first step is to determine a speed curve based on Newton’s laws. In practice, the speed curve
calculation needs railway operation field-related information. A speed curve is shown as a graph
expressing the train speed on each train position along its route. Although there are various ways of
drawing such graphs, examples of typical distance-speed diagrams are shown in Annex A.
— The second step is to calculate the time by numerically integrating the given speed curve and is based
on general calculation procedures, i.e. that are not specific to the railway field. This means that railway
domain knowledge is used in the calculation at the first step.
Once the speed curve is determined, running time can be obtained at the second step using the speed curve
as follows.
a) Create a speed curve.
b) Calculate the running time with the speed curve.
Clause 6 shows running time calculation with basic principles based on Newton’s laws and specific
information on railways.
6 Calculation
6.1 Basic principles
Speed curve involves the information on the speed of a train according to its position. For any point between
the starting point and ending point, a speed value is determined.
The calculation is based on Newton’s first law of dynamics stating that an object stays at rest or at constant
speed unless it is acted upon by an external force. It is also based on Newton’s second law that says when
a force acts on an object, the force accelerates the object in the same direction and the acceleration of the
object is proportional to the force. It represents the relation between acceleration and all the forces applied.
The purpose of the calculation is to find a relation between the position and time. Acceleration is the second
derivative of position with respect to time. It can be integrated to find a relation between the speed and
time.
Although train movement is a continuous phenomenon, it is calculated discretely as a uniform acceleration
motion for each calculation step.

Details for an efficient implementation of calculation algorithms are not part of this document. Hence,
specific examples of calculation procedures are described in Annex B.
a) Newton’s second law:
FM (1)
where
F is the force applied to the train, expressed in N;
M is the static mass of the train, expressed in kg;
α is the acceleration, expressed in m/s .
By deforming Formula (1), the acceleration is calculated as set out in Formula (2):
TvRvRx
rg
  (2)
 M
where
α is the acceleration, expressed in m/s ;
T is the tractive force, expressed in N;
R is the running resistance force, expressed in N;
r
R is the gradient resistance force, expressed in N;
g
γ is the inertia ratio;
M is the static mass of the train, expressed in kg;
v is the speed of the train, expressed in m/s;
x is the position of the train, expressed in m.
There are various calculation algorithms during braking phases, but at a minimum, whether the gradient
and running resistance forces are to be taken into account during braking phases or not shall be decided.
b) uniformly accelerated motion:
vvt (3)
t
svt (4)
2 2
2 svv (5)
1 0
where
v is the initial speed of the train before acceleration, expressed in m/s;
v is the speed of the train after acceleration, expressed in m/s;
α is the acceleration, expressed in m/s ;
s is the distance of train movement, expressed in m;
t is the time duration, expressed in s.
6.2 Calculation of a speed curve
The main assumptions for the speed curve calculation are as follows:
— the train is considered as a point mass;
— the requirements for train control systems [e.g. European Train Control System (ETCS),
Linienzugbeeinflussung (LZB), Chinese Train Control System (CTCS)] are not specified in this document.
...

ISO/DIS FDIS 24675-2:2025(en)
ISO/TC 269/SC 3/WG 3
Secretariat: JISC
Date: 2025-08-0812-17
Railway applications — Running time calculation for
timetabling— —
Part 2:
Distance-speed diagrams and speed curves

DISApplications ferroviaires — Calcul des temps de parcours pour la construction des horaires —
Partie 2: Diagrammes distance-vitesse et courbes de vitesse
FDIS stage
A model document of an International Standard (the Model International Standard) is available at:

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
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: + 41 22 749 01 11
EmailE-mail: [e-mail]
Website: www.iso.orgwww.iso.org
Published in Switzerland
ISO #####-#:####(X/FDIS 24675-2:2025(en)
Contents
Foreword . v
Introduction . vi
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
3.1 General terms . 1
3.2 Terms related to infrastructure . 3
3.3 Terms related to rolling stock . 3
4 Relation between shortest running time and timetabling . 3
5 Running time calculation with a speed curve . 4
6 Calculation . 5
6.1 Basic principles . 5
6.2 Calculation of a speed curve. 7
6.3 Calculation of running time with a speed curve . 9
7 Verification of accuracy of the calculation results . 9
Annex A (informative) Examples of distance-speed diagrams . 19
Annex B (informative) Calculation procedures for a speed curve . 27

© ISO #### 2025 – All rights reserved
iv
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 document 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 3,
Operations and services.
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.
v
ISO #####-#:####(X/FDIS 24675-2:2025(en)
Introduction
The purpose of this document is to help many railway-related organizations around the world, regardless of
their experience, to calculate accurate train running time between two points such as stations for all rolling
stock types and its speed, helping to improve the punctuality of railways around the world.
Improving railway punctuality can increase the competitiveness of railway transportation against other
modes of transportation such as planes, buses and cars. More customers using railway means more income
for railway infrastructure managers, railway operators and related organizations. It also means the promotion
of national economic growth, increased social efficiency, and the use of environmentally friendly energy
leading to increased global sustainability. Overall, an increased use of railwayrailways leads to an
improvement of “Qualityquality of Life (QoL)”life (QOL) for customers.
This document describes the requirements for shortestIn order to create punctual timetables, it is necessary
to accurately calculate and plan out running time calculation when setting upbetween stopping or passing
points, headway between trains, train scheduling, rolling stock scheduling, driver and crew scheduling,
operation scheduling in stations and depots and both line and infrastructure capacities. Among these values,
shortest running time between stopping or passing points is calculated first, as this is the basis of timetabling.
This enables railway stakeholders to calculate the time accurately at the stage of setting up timetables of a
railway system, such as daily timetables, seasonal timetables, annual timetables, strategic timetables for long-
term perspective, and other timetables of a railway system. It is necessary to note that theseThese timetables
are created not only with the shortest running time shown in this document but also with other factors for
safety and punctuality during commercial operations.
In many cases, running time calculation is realized using many detailed factors of practical real railway
operations. However, it is almost impossible to verify the appropriateness of the running time calculation from
the viewpoint of all such factors. realised using many detailed factors of practical real railway operations.
However, it is almost impossible to verify the appropriateness of the running time calculation from the
viewpoint of all such factors. On the other hand, suitable and practical verification procedures for running
time calculation areneed to be identified to ensure the quality and validity of the running time calculation for
punctual timetabling.
Running time calculation consists of two steps in general. The first step is to determine a speed curve based
on Newton’s laws. A speed curve is shown as a graph expressing the train speed on each train position along
its route. In practice, a speed curve involves much information on distinctive characteristics of the railway
operation field. The second step is to calculate the time by numerically integrating the given speed curve and
is based on general calculation procedures not only for the railway operation field. In other words, railway-
domain knowledge is reflected into the calculation at the first step. Once the speed curve is prepared, running
time can be obtained at the second step using the speed curve.
As it is described above, aA practical running time calculation involves many factors of real railway operations.
But inIn order to establish clear verification procedures of running time calculation, this document mainly
focuses on physical movements of a train.
ISO 24675-1 specifies the requirements with input parameters for running time calculation and with
verification of the usage of those parameters. 0Figure 1 shows the relation between this document and ISO
24675-1.
© ISO #### 2025 – All rights reserved
vi
Requirements of this document
Calculation of a speed curve (shown in Subclause 6.2)
Verification (shown in Clause 7)
✓Most restrictive speed profile at each position
✓Presenting distance-speed diagrams
✓Not exceed the most restrictive speed profile
✓Compare the calculated values
✓Mandatory parameters in ISO 24675-1
Shortest running time calculation
Calculation Calculation Shortest
parameters running time
method
Selected parameters
General principles
✓ Infrastructure parameters
of physics
(shown in Subclause 5.2)
✓ Rolling stock condition parameters
(shown in Subclause 5.3)
✓ Operational condition parameters
(shown in Subclause 5.4)
Verification(shown in Clause 6)
✓Increase of shortest running time
✓Decrease of shortest running time
Requirements of ISO 24675-1
Figure 1 — Relation between this document and ISO 24675-1
vii
ISO #####-#:####(X/FDIS 24675-2:2025(en)
In addition to this document, further documents will complete the standardISO 24675 series ofon railway
timetabling. All parts together form a specific and comprehensive guidance for railway timetabling. 0Figure 2
shows a roadmap of the target of our working groupfor railway timetabling. It involves important elements of
railway timetabling to be standardized in the future.

Figure 2 — Roadmap of our working groupfor railway timetabling
© ISO #### 2025 – All rights reserved
viii
ISO/DISFDIS 24675-2:2025(en)
Railway applications — Running time calculation for timetabling — —
Part 2:
Distance-speed diagrams and speed curves
1 Scope
In order to create punctual timetables, it is necessary to accurately calculate and plan out running time
between stopping or passing points, headway between trains, train scheduling, rolling stock scheduling, driver
and crew scheduling, operation scheduling in stations and depots and line / infrastructure capacity.
Among these values, shortest running time between stopping or passing points must be calculated first, as this
is the basis of timetabling.
This document specifies a practical procedure to create and verify distance-speed diagrams and speed curves
using the parameters specified in ISO 24675-1. Shortest, from which the shortest running time for railway
timetabling is obtained by numerically integrating the speed curves.
This enables railway infrastructure managers, railway operators and related organizations to calculate
accurate running time at the stage of setting up feasible and punctual daily timetables, seasonal timetables,
annual timetables, strategic timetables for long-term perspective, and other timetables of a railway system.
This document excludes running time calculation used for purposes other than timetabling.
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 24675--1:2022, Railway Applications — Running time calculation for timetabling — Part 1: Requirements
ISO 24478:2023, Railway applications — Braking — General vocabulary
IEC 60050-811:2017, International Electrotechnical Vocabulary (IEV) — Part 811: Electric traction
3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 24675-1, ISO 24478:2023, IEC
60050-811:2017, and the following 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/
3.1 General terms
3.1.1 3.1.1
position
distance from a specific reference point on a defined path on the infrastructure
[SOURCE: ISO 24675-1:2022, 3.1.3]
3.1.2 3.1.2
stopping point
point where a train stops or starts
[SOURCE: ISO 24675-1:2022, 3.1.4]
3.1.3 3.1.3
passing point
pre-defined point where the passing time of the train is recorded
3.1.4 3.1.4
starting point
point where a running time calculation starts
3.1.5 3.1.5
ending point
point where a running time calculation ends
3.1.6 3.1.6
speed curve
function from a position (3.1.1(3.1.1)) value to a speed value showing speed changing of a train according to
its position (3.1.1(3.1.1))
3.1.7 3.1.7
timetabling
defining a set of train schedules for a railway system to provide a service considering conditions such as the
interaction between trains, infrastructure capacity, rolling stock, personnel, stations and depots scheduling,
shunting, commercial requirements, etc. according to its validity period or application
[SOURCE: ISO 24675-1:2022, 3.1.7]
3.1.8 3.1.8
running time
amount of time, on a defined path on the infrastructure, for the head of a train to pass from one stopping point
(3.1.2(3.1.2)) or passing point (3.1.3(3.1.3)) to another without making any stops in between
[SOURCE: ISO 24675-1:2022, 3.1.1]
3.1.9 3.1.9
shortest running time
running time (3.1.8(3.1.8)) when a train is driven in the quickest way while conforming with predetermined
operating restrictions
3.1.10
[SOURCE: ISO 24675-1:2022, 3.1.2]
3.1.10
unit time
minimum time that constitutes the timetable
ISO/DISFDIS 24675-2:2025(en)
3.2 Infrastructure
3.2.1
3.2 Terms related to infrastructure
3.2.1
gradient resistance force
force derived from track gradient
[SOURCE: ISO 24675-1:2022, 3.2.1]
3.3 RollingTerms related to rolling stock
3.3.1 3.3.1
static mass
mass of the rail vehicle/unit/train in a stationary condition
[SOURCE: ISO 24478:2023, 3.5.5]
3.3.2 3.3.2
running resistance force
resistance to motion of a vehicle or train
[SOURCE: ISO 24675-1:2022, 3.3.2]
3.3.3 3.3.3
tractive force
force in direction of travel exerted by traction motors, engines or other means of propulsion
[SOURCE: ISO 24675-1:2022, 3.3.3]
3.3.4 3.3.4
braking deceleration
deceleration throughout the braking distance travelled from the commencement of the brake application until
achieving standstill or the final speed
Note 1 to entry: The braking distance represents the distance travelled from the commencement of the brake application
until achieving standstill or the final speed.
[SOURCE: ISO 24478:2023, 3.6.30], modified — "braking distance" has been replaced with the text after
"throughout" in the definition.]
3.3.5 3.3.5
inertia ratio
factor greater than unity applied to the mass of a train or vehicle to make allowance for the inertia of the
revolving masses inseparable from the movement of the train same as allowance for rotating parts
[SOURCE: IEC 60050-811:2017, 811-05-07], modified — the text "same as allowance for rotating parts " has
been deleted from the end of the definition.]
4 Relation between shortest running time and timetabling
A running time used for timetabling is not always equal to the shortest running time. Adding additional time
is necessary to consider actual driving conditions for increasing safe operations and punctuality. This clause
shows four elements of a running time used for timetabling.
0Figure 3 shows the following elements and a structure ofin a running time structure used for timetabling
with the shortest running time.
a) a) Shortest running time: The shortest running time is calculated using at least all the mandatory
parameters specified in ISO 24675-1.
b) b) Slack time: The slack time causedis calculated by rounding up to the unit time of the
corresponding railway line such as five-seconds, ten-seconds, fifteen-seconds or a half-minute.
c) c) SupplementSupplemental time: In the process of timetabling, feasible driving operations,
vehicle variation, track conditions, and driving guidance areshould be considered. BecauseGiven those
factors differ according to the conditions and features of the railway lines, based on these factors, the
addition of supplementsupplemental time to the shortest running time is necessary to appropriately
prepare a running time for real railway operation conditions. The supplementsupplemental time also
serves in order to ensure punctuality, considering the potential slight delays occurring in real railway
operation conditions.
d) d) Running time used for timetabling: The running time used for timetabling is the sum of the
shortest running time, slack time and supplementsupplemental time.
Considering these elements, accurate and appropriate calculation of the

Key
a shortest running time is indispensable for punctual railway operations.(target of this document)
(a) (b) (c)
(d)
Key
(a) Shortest running time (target of this document)
(b) Slack time
(c) Supplement time
(d) Running time used for timetabling

Figure 3 — Elements and structure of a b slack time
c supplemental time
d running time used for timetabling
Figure 3 — Running time structure used for timetabling
5 Running time calculation with a speed curve
Running time calculation generally consists of two steps.
— The first step is to determine a speed curve based on Newton’s laws. In practice, the speed curve
calculation needs railway operation field-related information. Here, aA speed curve is shown as a graph
expressing the train speed on each train position along its route. Although there are various ways of
drawing such graphs, examples of typical distance-speed diagrams are shown in Annex AAnnex A.
ISO/DISFDIS 24675-2:2025(en)
— The second step is to calculate the time by numerically integrating the given speed curve and is based on
general calculation procedures, i.e. that are not specific to the railway field. In other words,This means that
railway -domain knowledge is reflected intoused in the calculation at the first step.
Once the speed curve is determined, running time can be obtained at the second step using the speed curve as
follows.
a) a) Create a speed curve.
b) b) Calculate the running time with the speed curve.
6Clause 6 shows running time calculation with basic principles based on Newton’s laws and specific
information on railways.
6 Calculation
6.1 Basic principles
Speed curve involves the information on the speed of a train according to its position. For any point between
the starting point and ending point, a speed value is determined.
The calculation is based on Newton’s first law of dynamics stating that an object stays at rest or at constant
speed unless it is acted upon by an external force. It is also based on Newton’s second law that says when a
force acts on an object, the force accelerates the object in the same direction and the acceleration value of the
object is proportional to the force. It represents the relation between acceleration and all the forces applied.
The purpose of the calculation is to find a relation between the position and time. Acceleration is the second
derivative of position with respect to time. It can be integrated to find a relation between the speed and time.
Although train movement is a continuous phenomenon, it is calculated discretely as a uniformlyuniform
acceleration motion for each calculation step.
Details for an efficient implementation of calculation algorithms are not part of this document. Hence, specific
examples of calculation procedures are described in 0Annex B.
a) a) Newton’s second law:
𝐹=𝑀×𝛼 (1)
where
F is the force applied to the train, expressed in N;
M is the static mass of the train, expressed in kg;
α is the acceleration value, expressed in m/s .
F is the force applied to the train, expressed in N;
M is the static mass of the train, expressed in kg;
α is the acceleration, expressed in m/s .
By deforming 0Formula (1),, the acceleration value is calculated as set out in 0Formula (2).:
(2)
𝑇(𝑣)−𝑅 (𝑣)−𝑅 (𝑥)
r g
𝛼= (2)
𝛾×𝑀
where
α is acceleration value, expressed in m/s ;
T is tractive force, expressed in N;
R is running resistance force, expressed in N;
r
R is gradient resistance force, expressed in N;
g
γ is inertia ratio;
M is static mass of the train, expressed in kg;
v is speed of train, expressed in m/s;
x is position of train, expressed in m.
α is the acceleration, expressed in m/s ;
T is the tractive force, expressed in N;
Rr is the running resistance force, expressed in N;
Rg is the gradient resistance force, expressed in N;
γ is the inertia ratio;
M is the static mass of the train, expressed in kg;
v is the speed of the train, expressed in m/s;
x is the position of the train, expressed in m.
There are various calculation algorithms during braking phases, but at a minimum it is necessary to decide,
whether the gradient and running resistance forces are to be taken into account during braking phases or not
shall be decided.
b) b) Uniformlyuniformly accelerated motion:
v  v t
(3)


 t
(4)
s v t




2 s v  v (5)
𝑣 =𝑣 +𝛼×𝑡 (3)
1 0
𝛼×𝑡
𝑠=𝑣 ×𝑡+ (4)
2 2
2×𝛼×𝑠=𝑣 −𝑣 (5)
1 0
where
v is initial speed of train before acceleration, expressed in m/s;
v is speed of train after acceleration, expressed in m/s;
α is acceleration value, expressed in m/s ;
ISO/DISFDIS 24675-2:2025(en)
s is distance of train movement, expressed in m;
t is time duration, expressed in s.

v0 is the initial speed of the train before acceleration, expressed in m/s;
v1 is the speed of the train after acceleration, expressed in m/s;
α is the acceleration, expressed in m/s ;
s is the distance of train movement, expressed in m;
t is the time duration, expressed in s.
6.2 Calculation of a speed curve
The main assumptions for the speed curve calculation are as follows.:
— — the train is considered as a point mass;
— — the requirements offor train control systems ([e.g., . European Train Control System (ETCS, ),
Linienzugbeeinflussung (LZB, ), Chinese Train Control System (CTCS))] are not specified in this document.
NOTE A length of a train is an important parameter especially when considering long trains. However, noting
the accuracy of calculation needed in this document, it is not mandatory.
Based on the different speed limitations depending on the infrastructure condition, the train characteristics
and operational condition restrictions, etc., the resulting and most restrictive speed profile at each position
shall be defined. 0Figure 4 shows an example of the most restrictive speed profile (bold dash-dot line). The
speed curve of the train shall not exceed the most restrictive speed profile.
y
x
Key
x  position, expressed in m
y  speed, expressed in km/h
most restrictive speed profile
maximum speed depending on the infrastructure condition
maximum operational speed of rolling stock
maximum operational speed on operational condition
temporary speed restriction
Key
X position, expressed in m
Y speed, expressed in km/h
1 most restrictive speed profile
2 maximum speed depending on the infrastructure condition
3 maximum operational speed of rolling stock
4 maximum operational speed on operational condition
5 temporary speed restriction
Figure 4 — Example of the most restrictive speed profile
All the requirements in ISO 24675-1 shall be adopted when speed curve is calculated in this document.
ISO/DISFDIS 24675-2:2025(en)
The calculation of speed curve is based on Newton’s laws (see 6.16.1).). The sum of forces in the formula for
traction, running resistance and other influences depends on specified parameters which need to be included
into the calculation.
6.3 Calculation of running time with a speed curve
Running time is calculated with a given speed curve. This is because the running time can be obtained by
numerically integrating the speed. In some cases, speed curve and running time are calculated simultaneously.
See Annex BAnnex B. .
For different calculations, the running time of a specific section should always be the same if the restriction
conditions within that section are the same on both calculations, regardless of different calculation starting
and ending points, origins, or destinations, outside that specific section. For example, the running time for
section C to D in 0 should be the same for two calculations, routes,
a) a) A to C to D to E, and
b) b) B to C to D to F
if the applicable conditions (such as speed restrictions, infrastructure restrictions, train composition, etc).)
are the same in sectionssection C to D in both calculations.

Key
X position, expressed in m
Y speed, expressed in km/h
1 railway line
2 speed curve
A candidate for eith
...