prEN 17636

Railway applications - Infrastructure - Track alignment design parameters for urban rail

This document specifies rules and limits for track alignment design parameters, including alignments within switches and crossings. Several of these limits are functions of speed. Alternatively, for a given track alignment, it specifies rules and limits that determine permissible speed with regards to track alignment.
This document applies to urban or suburban rail networks for passenger services not integrated with the national network.
Sections of urban or suburban rail networks integrated in the national rail networks are not covered by this document. They are covered by EN 13803 (or for nominal track gauges smaller than 1 435 mm by national alignment rules).
For the purpose of this document, urban or suburban rail networks include:
-   Networks designed for own right of way and segregated from general road and pedestrian traffic,
and
-   Networks (partly) not segregated from general road and pedestrian traffic, with shared lanes.
This document applies to rail systems with steel wheels running on steel vignole or grooved rails. Rail systems with specific construction issues (e.g. rack railways, funicular railways and other types of cable drawn rail systems) are not covered by this document.
This document defines the parameters, rules and limits for nominal track gauges of 1 435 mm and 1 000 mm with permissible speeds up to 120 km/h. For other nominal track gauges, this document defines conversion rules which shall be used to define the limits.

Bahnanwendungen - Oberbau - Streckentrassierungsparameter für den städtischen Schienenverkehr

Dieses Dokument legt Regeln und Grenzwerte für die Linienführung in Gleisen fest, einschließlich der Trassierung in Weichen und Kreuzungen. Verschiedene dieser Grenzwerte sind Funktionen der Geschwindigkeit. Alternativ legt das Dokument für eine vorhandene Trassierung die Regeln und Grenzwerte fest, die die zulässige Geschwindigkeit bestimmen.
Dieses Dokument gilt für städtische oder regionale Schienennetze für Personenbeförderungsdienste, die nicht in das nationale Netz integriert sind.
Abschnitte von städtischen oder regionalen Schienennetzen, die in die nationalen Schienennetze integriert sind, werden in diesem Dokument nicht behandelt. Sie werden durch EN 13803 abgedeckt (oder für nominale Spurweiten kleiner als 1 435 mm durch nationale Trassierungsregeln).
Für die Anwendung dieses Dokuments sind städtische oder regionale Eisenbahnnetze:
-   Schienennetze, die mit eigenen Fahrrechten und getrennt vom allgemeinen Straßen- und Fußgängerverkehr betrieben werden,
und
-   (teilweise) nicht vom allgemeinen Straßen- und Fußgängerverkehr getrennte Netze mit gemeinsamen Fahrspuren.
Dieses Dokument gilt für Schienensysteme mit Stahlrädern, die auf Vignol- oder Rillenschienen aus Stahl laufen. Schienensysteme mit besonderen baulichen Eigenheiten (z. B. Zahnradbahnen, Standseilbahnen und andere Arten von seilgezogenen Schienensystemen) werden in diesem Dokument nicht behandelt.
Dieses Dokument legt die Parameter, Regeln und Grenzwerte für Nennspurweiten von 1 435 mm und 1 000 mm mit zulässigen Geschwindigkeiten bis zu 120 km/h fest. Für andere Nennspurweiten legt dieses Dokument Umrechnungsregeln fest, die zur Definition der Grenzwerte verwendet werden müssen.

Applications ferroviaires - Infrastructure - Paramètres de conception du tracé de la voie pour le rail urbain

Le présent document spécifie les règles et limites pour les paramètres de tracé de voie, y compris dans les appareils de voie. Plusieurs de ces limites dépendent de la vitesse. En outre, le présent document spécifie les règles et limites qui déterminent la vitesse maximale autorisée pour un tracé de voie spécifique.
Le présent document s'applique aux réseaux ferroviaires urbains ou suburbains destinés au transport de voyageurs, qui ne sont pas intégrés au réseau national.
Le présent document ne couvre pas les tronçons des réseaux ferroviaires urbains ou suburbains qui sont intégrés au réseau national. Ceux-ci sont couverts par l'EN 13803 (ou par les règlements nationaux dans le cas des écartements de voie nominaux inférieurs à 1 435 mm).
Pour les besoins du présent document, les réseaux ferroviaires urbains ou suburbains incluent :
- les réseaux en site propre intégral séparés de la circulation routière et piétonne générale ;
et
- les réseaux (partiellement) en site partagé/banalisé non séparés de la circulation routière et piétonne générale.
Le présent document s'applique aux systèmes ferroviaires équipés de roues en acier circulant sur rails Vignole ou rails à gorge en acier. Les systèmes ferroviaires présentant des problématiques de construction spécifiques (trains à crémaillère, funiculaires et autres types de systèmes ferroviaires tirés par des câbles, par exemple) ne sont pas couverts par le présent document.
Le présent document définit les paramètres, règles et limites applicables aux écartements de voie nominaux de 1 435 mm et de 1 000 mm, où la vitesse maximale de circulation est limitée à 120 km/h. Pour les autres écartements de voie nominaux, le présent document définit les règles de conversion à utiliser pour définir les limites applicables.

Železniške naprave - Infrastruktura - Parametri za načrtovanje trase proge za mestno železnico

General Information

• Status: Not Published
• ICS: 93.100 - Construction of railways
• Technical Committee: CEN/TC 256 - Railway applications
• Drafting Committee: CEN/TC 256/SC 1/WG 15 - Track alignment design parameters
• Current Stage: 4599 - Dispatch of FV draft to CMC - Finalization for Vote
• Start Date: 02-Feb-2023
• Due Date: 22-Apr-2022
• Completion Date: 02-Feb-2023
• Mandate: M/486 - Mandate for programming and standardisation addressed to the European standardisation bodies in the field of urban rail
• Ref Project: oSIST prEN 17636:2021 - Railway applications - Infrastructure - Track alignment design parameters for urban rail

Standards Content (Sample)

SLOVENSKI STANDARD
oSIST prEN 17636:2021
01-marec-2021
Železniške naprave - Infrastruktura - Parametri za načrtovanje trase proge za
mestno železnico

Railway applications - Infrastructure - Track alignment design parameters for urban rail

Bahnanwendungen - Oberbau - Streckentrassierungsparameter für den städtischen
Schienenverkehr

Applications ferroviaires - Infrastructure - Paramètres de conception du tracé de la voie

pour le rail urbain
Ta slovenski standard je istoveten z: prEN 17636
ICS:
93.100 Gradnja železnic Construction of railways
oSIST prEN 17636:2021 en,fr,de

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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oSIST prEN 17636:2021
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oSIST prEN 17636:2021
DRAFT
EUROPEAN STANDARD
prEN 17636
NORME EUROPÉENNE
EUROPÄISCHE NORM
January 2021
ICS 93.100
English Version
Railway applications - Infrastructure - Track alignment
design parameters for urban rail
Bahnanwendungen - Oberbau -
Streckentrassierungsparameter für den städtischen
Schienenverkehr

This draft European Standard is submitted to CEN members for enquiry. It has been drawn up by the Technical Committee

CEN/TC 256.

If this draft becomes a European Standard, CEN members are bound to comply with the CEN/CENELEC Internal Regulations

which stipulate the conditions for giving this European Standard the status of a national standard without any alteration.

This draft European Standard was established by CEN in three official versions (English, French, German). A version in any other

language made by translation under the responsibility of a CEN member into its own language and notified to the CEN-CENELEC

Management Centre has the same status as the official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia,

Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway,

Poland, Portugal, Republic of North Macedonia, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and

United Kingdom.

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 supporting documentation.

Warning : This document is not a European Standard. It is distributed for review and comments. It is subject to change without

notice and shall not be referred to as a European Standard.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
CEN-CENELEC Management Centre: Rue de la Science 23, B-1040 Brussels

© 2021 CEN All rights of exploitation in any form and by any means reserved Ref. No. prEN 17636:2021 E

worldwide for CEN national Members.
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oSIST prEN 17636:2021
prEN 17636:2021 (E)
Contents Page

European foreword ....................................................................................................................................................... 4

1 Scope .................................................................................................................................................................... 5

2 Normative references .................................................................................................................................... 5

3 Terms and definitions ................................................................................................................................... 5

4 Symbols and abbreviations ......................................................................................................................... 8

5 General ................................................................................................................................................................ 9

5.1 Background ....................................................................................................................................................... 9

5.2 Line categories .............................................................................................................................................. 10

5.3 Alignment characteristics ......................................................................................................................... 10

6 Limits for 1 435 mm and 1 000 mm nominal track gauge ............................................................. 12

6.1 Horizontal radius R .................................................................................................................................... 12

6.2 Applied cant D .............................................................................................................................................. 12

6.3 Cant deficiency I .......................................................................................................................................... 13

6.4 Cant excess ................................................................................................................................................ 14

6.5 Length of cant transition L and transition curve in the horizontal plane L .................... 14

D K

6.5.1 General ............................................................................................................................................................. 14

6.5.2 Length of linear cant transition and clothoid .................................................................................... 15

ddD / s

6.6 Cant gradient .................................................................................................................................. 15

6.7 Rate of change of cant ddD / t .................................................................................................................. 16

6.8 Rate of change of cant deficiency ddIt/ .............................................................................................. 16

6.9 Length of constant cant between two linear cant transitions L ................................................ 16

6.10 Abrupt change of horizontal curvature ................................................................................................ 17

6.11 Abrupt change of cant deficiency ∆I ..................................................................................................... 17

6.12 Length between two abrupt changes of horizontal curvature L ............................................... 17

6.13 Length between two abrupt changes of cant deficiency L .......................................................... 18

6.14 Track gradient p .......................................................................................................................................... 19

6.15 Length of constant gradient L ............................................................................................................... 19

6.16 Vertical radius R ........................................................................................................................................ 19

6.17 Length of vertical curve L ....................................................................................................................... 20

6.18 Abrupt change of track gradient ∆p ...................................................................................................... 21

Annex A (normative) Rules for converting parameter values for nominal track gauges

other than 1 435 mm or 1 000 mm ........................................................................................................ 22

A.1 Scope ................................................................................................................................................................. 22

A.2 Symbols and abbreviations ...................................................................................................................... 22

A.3 Basic assumptions and equivalence rules ........................................................................................... 23

A.3.1 General ............................................................................................................................................................. 23

A.3.2 Basic formulae ............................................................................................................................................... 24

A.3.3 Basic data ........................................................................................................................................................ 24

A.4 Detailed conversion rules ......................................................................................................................... 25

A.4.1 General ............................................................................................................................................................. 25

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A.4.2 Cant (6.2) .................................................................................................................................................. 25

A.4.3 Cant deficiency I (6.3) .............................................................................................................................. 27

A.4.4 Cant excess E (6.4) .................................................................................................................................... 28

A.4.5 Length of cant transition L and transition curve in the horizontal plane L (6.5) ......... 29

D K

A.4.6 Cant gradient ddDs/ (6.6) ..................................................................................................................... 29

A.4.7 Rate of change of cant ddDt/ (6.7) ..................................................................................................... 30

A.4.8 Rate of change of cant deficiency ddIt/ (6.8)................................................................................. 30

A.4.9 Abrupt change of curvature and abrupt change of cant deficiency ∆I (6.10 and

6.11) ................................................................................................................................................................... 31

A.4.10 Other parameters (6.1, 6.9, 6.12, 6.13, 6.14, 6.15, 6.16, 6.17 and 6.18) .................................... 31

Annex B (normative) Three-dimensional track geometry with regards to resulting cant

gradient and resulting vertical radius .................................................................................................. 32

B.1 General considerations regarding three-dimensional track geometry .................................... 32

B.2 Angular twist T and resulting cant gradient ddDs/ ............................................................... 32

( )

B.2.1 Calculation of resulting cant gradient ddDs/ where cant is applied by lifting one

( )

rail D / 2 and lowering the other rail D / 2 ......................................................................................... 32

B.2.2 Calculation of resulting cant gradient ddDs/ when cant is applied by lifting one

( )

rail D .................................................................................................................................................................. 33

B.3 Resulting vertical radius R ............................................................................................................... 34

( )

Annex C (normative) Sign rules for calculation of ∆D , ∆I and ∆p .......................................................... 35

C.1 General regarding the sign rules ............................................................................................................. 35

C.2 Sign rules for calculation of ∆D ............................................................................................................... 35

C.3 Sign rules for calculation of ∆I ................................................................................................................ 35

C.4 Sign rules for calculation of ∆p ................................................................................................................ 37

Annex D (normative) Lengths of intermediate elements L between small radius curves in

opposite directions ...................................................................................................................................... 38

D.1 General ............................................................................................................................................................. 38

D.2 Lengths of intermediate elements L for Line Category A1435 .................................................... 38

D.3 Lengths of intermediate elements L for Line Category B1435 .................................................... 39

D.4 Lengths of intermediate elements L for Line Category C1000 .................................................... 41

Bibliography ................................................................................................................................................................. 42

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oSIST prEN 17636:2021
prEN 17636:2021 (E)
European foreword

This document (prEN 17636:2021) has been prepared by Technical Committee CEN/TC 256 “Railway

applications”, the secretariat of which is held by DIN.
This document is currently submitted to the CEN Enquiry.

This document has been prepared under a mandate given to CEN by the European Commission and the

European Free Trade Association.
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oSIST prEN 17636:2021
prEN 17636:2021 (E)
1 Scope

This document specifies rules and limits for track alignment design parameters, including alignments

within switches and crossings. Several of these limits are functions of speed. Alternatively, for a given

track alignment, it specifies rules and limits that determine permissible speed with regards to track

alignment.

This document applies to urban or suburban rail networks for passenger services not integrated with the

national network.

Sections of urban or suburban rail networks integrated in the national rail networks are not covered by

this document. They are covered by EN 13803 (or for nominal track gauges smaller than 1 435 mm by

national alignment rules).
For the purpose of this document, urban or suburban rail networks include:

— Networks designed for own right of way and segregated from general road and pedestrian traffic,

and

— Networks (partly) not segregated from general road and pedestrian traffic, with shared lanes.

This document applies to rail systems with steel wheels running on steel vignole or grooved rails. Rail

systems with specific construction issues (e.g. rack railways, funicular railways and other types of cable

drawn rail systems) are not covered by this document.

This document defines the parameters, rules and limits for nominal track gauges of 1 435 mm and

1 000 mm with permissible speeds up to 120 km/h. For other nominal track gauges, this document

defines conversion rules which shall be used to define the limits.
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.

EN 15273-1, Railway applications — Gauges — Part 1: General — Common rules for infrastructure and

rolling stock
3 Terms and definitions
For the purposes of this document, the following terms and definitions apply.
3.1
track gauge
distance between the corresponding running edges of the two rails
3.2
nominal track gauge

single value which identifies the track gauge but may differ from the design track gauge, e.g. the most

widely used track gauge in Europe that has a nominal value of 1 435 mm although this is not the design

track gauge normally specified
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3.3
limit
design value not to be exceeded

Note 1 to entry: These values ensure maintenance costs of the track are kept at a reasonable level, except where

particular conditions of poor track stability can occur, without compromising passenger comfort. However, the

actual design values for new lines should normally have substantial margins to the limits.

Note 2 to entry: For certain parameters, this document specifies both a normal limit and an exceptional limit.

Exceptional limits are intended for use only under special circumstances and can require an associated maintenance

regime as well as requiring to be verified against the local rolling stock.
3.4
alignment element

segment of the track with either vertical direction, horizontal direction or cant obeying a unique

mathematical description as a function of chainage

Note 1 to entry: Unless otherwise stated, the appertaining track alignment design parameters are defined for the

track centre line and the longitudinal distance for the track centre line is defined in a projection in a horizontal

plane.
3.5
chainage
longitudinal distance along the horizontal projection of the track centre line
3.6
curvature

derivative of the horizontal direction of the track centre line with respect to chainage

Note 1 to entry: In the direction of the chainage, curvature is positive in a right-hand curve and negative on a left-

hand curve. The magnitude of the curvature corresponds to the inverse of the horizontal radius.

3.7
circular curve
curved alignment element of constant curvature
3.8
transition curve
alignment element where curvature changes with respect to chainage

Note 1 to entry: The clothoid (sometimes approximated as a 3rd degree polynomial, “cubic parabola”) is

normally used for transition curves, giving a linear variation of curvature. In some cases, curvature is smoothed at

the ends of the transition. A transition can also be created by a sequence of short circular curves with radii which

changes stepwise.

Note 2 to entry: It is possible to use other forms of transition curve, which show a nonlinear variation of

curvature. EN 13803 gives a detailed account of certain alternative types of transitions that may be used in track

alignment design.

Note 3 to entry: Normally, a transition curve is not used for the vertical alignment.

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3.9
compound curve

sequence of curved alignment elements, including two or more circular curves in the same direction

Note 1 to entry: The compound curve can include transition curves between the circular curves and/or the

circular curves and the straight tracks.
3.10
reverse curve

sequence of curved alignment elements, containing alignment elements which curve in the opposite

directions

Note 1 to entry: A sequence of curved alignment elements can be both a compound curve and a reverse curve.

3.11
applied cant

amount by which one running rail is raised above the other running rail, at base measurement for applied

cant
3.12
equilibrium cant

cant at a particular speed at which the vehicle will have a resultant force perpendicular to the running

plane
3.13
cant deficiency
difference between applied cant and a higher equilibrium cant

Note 1 to entry: When there is cant deficiency, there will be an unbalanced lateral force in the running plane. The

resultant force will move towards the outer rail of the curve.
3.14
cant excess
difference between applied cant and a lower equilibrium cant

Note 1 to entry: When there is cant excess, there will be an unbalanced lateral force in the running plane. The

resultant force will move towards the inner rail of the curve.

Note 2 to entry: Cant on a straight track results in cant excess, generating a lateral force towards the low rail.

3.15
cant transition
alignment element where cant changes with respect to chainage
Note 1 to entry: Normally, a cant transition coincides with a transition curve.

Note 2 to entry: Cant transitions giving a linear variation of cant are usually used. In some cases, cant is smoothed

at the ends of the transition.

Note 3 to entry: It is possible to use other forms of cant transition, which show a nonlinear variation of cant.

EN 13803 gives a detailed account of certain alternative types of transitions that may be used in track alignment

design.
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3.16
cant gradient
absolute value of the derivative (with respect to chainage) of cant
3.17
resulting cant gradient

derived gradient of cant on a track gradient which results in the same angular twist as a cant gradient on

a level track
3.18
angular twist

the derivative of roll angle (rotation around the longitudinal axis) with respect to longitudinal distance

measured in coordinate system which has the same direction as the sloping track on a track gradient

3.19
rate of change of cant
absolute value of the time derivative of cant
3.20
rate of change of cant deficiency
absolute value of the time derivative of cant deficiency (and/or cant excess)
4 Symbols and abbreviations
No. Symbol Designation Unit
1 dD/ds cant gradient mm/m
2 (dD/ds) resulting cant gradient mm/m
3 dD/dt rate of change of cant mm/s
4 dI/dt rate of change of cant deficiency (and/or cant excess) mm/s
5 D applied cant mm
6 D equilibrium cant mm
7 E base measurement for applied cant, 1500mm for 1435mm gauge, mm
1060mm for 1000mm gauge
8 E cant excess mm
9 G acceleration due to gravity according to EN ISO 80000-3 m/s
10 I cant deficiency mm
11 L length between two abrupt changes of curvature m
12 L length of cant transition m
13 L length of constant gradient m
14 L length of transition curve m
15 L length of alignment elements between two linear cant transitions m
16 L length between two abrupt changes of cant deficiency m
17 Lv length of vertical radius m
18 P track gradient -
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No. Symbol Designation Unit
19 q factor for calculation of equilibrium cant: 11,8 for 1435mm mm∙m∙(h/km)
gauge, 8,3 for 1000mm gauge
20 q factor for calculation of length of cant transition or transition -
curve with non-constant gradient of cant and curvature,
respectively
2 2
21 qR factor for calculation of vertical radius m∙h /km
22 q factor for calculation of lengths between abrupt changes of cant -
deficiency
23 q factor for conversion of the units for vehicle speed: 3,6 km∙s/(h∙m)
24 R radius of horizontal curve m
25 R radius of vertical curve m
26 (R ) resulting vertical radius m
v r
27 s longitudinal distance m
28 t Time s
29 T angular twist Rad/m
30 V Speed km/h
lim
31 limit (index) -
32 index for resulting parameters in three-dimensional calculations -
R, lim
33 additional limit applicable at small radius curves (index) -
5 General
5.1 Background

This document specifies rules and limits for track alignment design. These limits assume that standards

for acceptance of vehicle, track construction and maintenance are fulfilled (construction and in-service

tolerances are not specified in this document). Engineering requirements specific to the mechanical

behaviour of switch and crossing components and subsystems are to be found in the relevant standards.

This document is not a design manual. The limits are not intended to be imposed as usual design values.

However, design values shall be within the limits stated in this document.

Limits in this document are based on practical experiences of European Urban Rail networks. Limits are

applied where it is necessary to compromise between train performance, comfort levels, maintenance of

the vehicle and track, and construction costs.

Unnecessary use of design values close to limits should be avoided, substantial margins to them should

be provided. There are often conflicts between the desire for margins to one parameter and another,

these should be distributed over all design parameters, possibly by applying a margin with respect to

speed.

For certain parameters, this document also specifies exceptional limits less restrictive than normal limits.

Such limits are intended for use only under special circumstances and can require an associated

maintenance regime as well as requiring to be verified against the local rolling stock. In particular, use of

exceptional limits (instead of normal limits) for several parameters at the same location shall be avoided.

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Operational limits for speed and cant deficiency shall be applied to specific vehicles according to their

approval parameters. Speed may also be restricted for other reasons than track alignment, for example

reduced visibility and operational rules.

The limits are defined for normal service operations. If and when running trials are conducted, for

example to ascertain the vehicle dynamic behaviour (by continually monitoring of the vehicle responses),

exceeding the limits (particularly in terms of cant deficiency) should be permitted and it is up to the

infrastructure manager to decide any appropriate arrangement. In this context, safety margins are

generally reinforced by taking additional steps such as ballast consolidation, monitoring of track

geometric quality, etc.
5.2 Line categories

Urban and suburban rail systems are local systems of different character. The requirements on the

infrastructure are related to the vehicle types to be used on the network. Three line categories are

defined, including systems for nominal track gauge 1 435 mm and 1 000 mm:

— Category A1435, lines for medium size rail vehicles with nominal track gauge 1 435 mm

— Category B1435, lines for small rail vehicles with nominal track gauge 1 435 mm

— Category C1000, lines for small rail vehicles with nominal track gauge 1 000 mm

For other nominal track gauges, limits can be defined using conversion rules specified in normative

Annex A.

It is assumed that all vehicles have been tested and approved according to the relevant standards in

conditions for the line category.
5.3 Alignment characteristics

The alignment defines the geometrical position of the track. It is divided into horizontal alignment and

vertical alignment.

The horizontal alignment is the projection of the track centre line on a horizontal plane. The horizontal

alignment consists of a sequence of alignment elements, each obeying a unique mathematical description

as a function of longitudinal distance along the horizontal projection (chainage). The elements for

horizontal alignment are connected at tangent points, where two connected elements have the same

coordinates and the same directions. Elements for horizontal alignment are specified in Table 1.

Table 1 — Elements for horizontal alignment
Alignment element Characteristics
Straight line No horizontal curvature
Circular curve Constant horizontal curvature

Transition curve, Clothoid type Horizontal curvature varies linearly with chainage

Compound transition A sequence of short circular curves where curvature
increases or decreases stepwise

EN 13803 gives a detailed account of certain alternative types of transition curves that may be used

in track alignment design

Most modern switches have a tangential geometry, where the diverging track starts with an alignment

that is tangential with the through track. However, switch designs may start with an abrupt change of

horizontal direction at the beginning of the switch. When a turnout is placed on a track gradient other

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than zero, a vertical curve and/or cant, the horizontal geometry of the diverging track will deviate slightly

from the element types in Table 1.

The vertical alignment defines the level of the track as a function of chainage (the longitudinal position

along the horizontal projection of the track centre line). The elements for vertical alignment are

connected at tangent points, where two connected elements have the same level and the same track

gradient p (with certain exceptions). Elements for vertical alignment are specified in Table 2.

Table 2 — Elements for vertical alignment
Alignment element Characteristics
Constant gradient No vertical curvature

Vertical curve, parabola Derivative of gradient with respect to chainage is constant

Vertical curve, circular Derivative of vertical angle with respect to sloping length along the track is

constant

NOTE A vertical curve in track that starts or ends in canted switches and crossings can be of a higher order

polynomial than a parabola.

The applied cant D in the track is the difference in level of two running rails. Cant can be applied by

raising one rail above the level of the vertical profile and keeping the other rail on the same level as the

vertical profile, or by a pre-defined relation raising one rail and lowering the other rail (a common

relation is 50 %/50 %). The cant can be considered as a sequence of elements connecte

...