BS EN 13803:2017
BSI Standards Publication
Railway applications  Track  Track alignment design parameters  Track gauges 1 435 mm and wider
BRITISH STANDARD
BS EN 13803:2017
National foreword This British Standard is the UK implementation of EN 13803:2017. It supersedes BS EN 138031:2010 and BS EN 138032:2006+A1:2009, which are withdrawn. The UK participation in its preparation was entrusted to Technical Committee RAE/2, Railway Applications  Track. A list of organizations represented on this committee can be obtained on request to its secretar y. This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. © The British Standards Institution 2017 Published by BSI Standards Limited 2017 ISBN 978 0 580 82260 5 ICS 93.100 Compliance with a British Standard c annot confer immunity from Compliance legal obligations. This British Standard was published under the authority of the Standards Policy and Strategy Committee on 30 June 2017. Amendments/corrigenda issued since si nce publication Date
Text affec ted
BRITISH STANDARD
BS EN 13803:2017
National foreword This British Standard is the UK implementation of EN 13803:2017. It supersedes BS EN 138031:2010 and BS EN 138032:2006+A1:2009, which are withdrawn. The UK participation in its preparation was entrusted to Technical Committee RAE/2, Railway Applications  Track. A list of organizations represented on this committee can be obtained on request to its secretar y. This publication does not purport to include all the necessary provisions of a contract. Users are responsible for its correct application. © The British Standards Institution 2017 Published by BSI Standards Limited 2017 ISBN 978 0 580 82260 5 ICS 93.100 Compliance with a British Standard c annot confer immunity from Compliance legal obligations. This British Standard was published under the authority of the Standards Policy and Strategy Committee on 30 June 2017. Amendments/corrigenda issued since si nce publication Date
Text affec ted
BS EN 13803:2017
EN 13803
EUROPEAN STANDARD NORME EUROPÉENNE EUROPÄISCHE NORM
April 2017
ICS 93.100
Supersedes EN 138031:2010, EN 138032:2006+A1:2009
English Version
Railway applications  Track  Track alignment design parameters  Track gauges 1 435 mm and wider Applications ferroviaires  Voie  Paramètres de conception du tracé de la voie  Écartement 1 435 mm et plus large
Bahnanwendungen  Oberbau  Trassierungsparameter Trassierungsparameter  Spurweiten 1 435 mm und größer
This European Standard was approved by CEN on 21 December 2016. 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. Uptodate lists and bibliographical references concerning such national standards may be obtained on application to the CENCENELEC Management Management Centre or to any CEN member. This European Standard exists in three official versions (English, French, German). A version in any other language made by translation under the responsibility of a CEN member into its own language and notified to the CENCENELEC CENCENELEC Management Centre has the same status as the official versions. CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION STANDARDIZATION COMITÉ EUROPÉEN DE NORMALISATION EUROPÄISCHES KOMITEE FÜR NORMUNG CENCENELEC Management Centre: Avenue Marnix 17, B1000 Brussels
© 2017 CEN
All rights rights of exploitation in any form and by any means reserved reserved worldwide for CEN national Members.
Ref. No. EN 13803:2017 E
BS EN 13803:2017
EN 13803:2017 (E)
Contents
Page
European foreword .............................................................................. ......................................................................... 6 1
Scope ................................................................................ .................................................................................... 7
2
Normative references .................................................................................. .................................................. 7
3
Terms and definitions ................................................................................................................................... 7
4
Symbols and abbreviations ...................................................................................................................... 10
5 5.1 5.2
General ............................................................................................................................................................. 11 Background .................................................................................................................................................... 11 Alignment characteristics .................................................................................... ..................................... 11
6 Limits for 1 435 mm gauge ....................................................................................................................... 13 6.1 Radius of horizontal curve R .................................................................................................................... 13 6.2 Cant D......................................................................................... ....................................................................... 13 6.3 Cant deficiency I ............................................................................ ............................................................................ ................................................................ 14 6.4 Cant excess E .................................................................................................................................................. .................................................................................................................................................. 16 6.5 Length of cant transitions LD and transition curves in the horizontal plane LK ..................... ..................... 17 6.5.1 General ............................................................................................................................................................. 17 6.5.2 Lengths of linear cant transitions and clothoids .............................................................................. 17 6.5.3 Lengths of transition curves with nonconstant n onconstant gradient of curvature and cant ................. 18 6.6 Cant gradient dD/d s .................................................................................................................................... 19 6.7 Rate of change of cant dD/dt .................................................................................................................... .................................................................................................................... 19 6.8 Rate of change of cant deficiency dI /d /dt ................................................................................................ ................................................................................................ 20 6.9 Length of constant cant between two linear cant transitions transiti ons Li .................................................. .................................................. 21 6.10 Abrupt change of horizontal curvature curvature .................................................................................. .............. 22 6.11 Abrupt change of cant deficiency ΔI ...................................................................................................... ...................................................................................................... 22 6.12 Length between two abrupt changes of horizontal curvature Lc ................................................ ................................................ 22 6.13 Length between two abrupt changes of cant deficiency L s ............................................................ 23 6.14 Track gradients p ......................................................................................................................................... 24 6.15 Vertical radius Rv ................................................................................ .......................................................... 25 6.16 Length of vertical curves Lv ................................................................................... ................................................................................... .................................... 25 6.17 Abrupt change of track gradient Δ p ...................................................................................................... 26 Annex A (normative) Rules for converting parameter values for track gauges wider than 1 435 mm .................................................................................... ..................................................................... 27 A.1 Scope ................................................................................................................................................................. 27 A.2 Symbols and abbreviations ...................................................................................................................... 27 A.3 Basic assumptions and equivalence rules ............................................................................... ............ 29 A.3.1 General ............................................................................................................................................................. 29 A.3.2 Basic formulae ........................................................................... .................................................................... 29 A.3.3 Basic data ........................................................................................................................................................ 30 A.4 Detailed conversion rules ......................................................................................................................... 30 A.4.1 General .................................................................................. ........................................................................... 30 A.4.2 Cant D1 (Subclause 6.2 of the main m ain body of the standard) ............................................................ 30 A.4.3 Cant deficiency I 1 (Subclause 6.3 of the main body of the standard) ........................................ 32 A.4.4 Cant excess E 1 (Subclause 6.4 of the main body of the standard) ............................................... 33 A.4.5 Lengths of cant transitions LD and transition curves in the horizontal plane LK (Subclause 6.5 of the main body of the standard) ............................................................................ 33
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A.4.6 A.4.7 A.4.8
Cant gradient dD1/d s (Subclause 6.6 of the main body of the standard) ................................. 34 Rate of change of cant dD1/dt (Subclause (Subclause 6.7 of the main m ain body of the standard) ................. 34 Rate of change of cant deficiency dI 1/dt (Subclause (Subclause 6.8 of the main body of the standard) ............................................................................................................................................. ............ 35 35 A.4.9 Abrupt change of curvature and abrupt change of cant deficiency ΔI 1 (Subclauses 6.10 and 6.11 of the main body of the standard)...................................................... 36 A.4.10 Other parameters (Subclauses 6.1, 6.9, 6.12, 6.13, 6.14, 6.15, 6.16 and 6.17 of the main body of the standard) .................................................................................. ..................................... 36 Annex B (normative) Track alignment design parameter limits for track gauges wider than 1 435 mm .................................................................................................................. ....................................... 37 B.1 Scope ................................................................................................................................................................. 37 B.2 Requirements for a gauge of 1 520 mm and 1 524 mm .................................................................. 37 B.2.1 General ............................................................................................................................................................. 37 B.2.2 Radius of horizontal curve R1 ................................................................................................................... 37 B.2.3 Cant D1............................................................................................................................................................... 37 B.2.4 Cant deficiency I 1............................................................................. .............................................................. 38 B.2.5 Cant excess E 1 ................................................................................................................................................. 39 B.2.6 Length of cant transitions LD1 and transition curves in the horizontal plane LK 1 .................. 39 B.2.7 Cant gradient dD1/d s ................................................................................................................................... 40 B.2.8 Rate of change of cant dD1/dt ................................................................................................................... ................................................................................................................... 41 B.2.9 Rate of change of cant deficiency dI 1/dt ............................................................................................... ............................................................................................... 41 B.2.10 Length of constant cant between two linear cant transitions transiti ons Li1 ................ ................................ 42 B.2.11 Abrupt change of horizontal curvature curvature .................................................................................. .............. 43 B.2.12 Abrupt change of cant deficiency ΔI 1 ..................................................................................................... 43 B.2.13 Length between two abrupt changes of horizontal curvature LC 1 ............................................... 43 B.2.14 Length between two abrupt changes of cant deficiency L s1 ........................................................... 43 B.2.15 Track gradients p1 ..................................................................................................................................... ... 44 44 B.2.16 Vertical radius Rv 1 ........................................................................... .............................................................. 44 B.2.17 Length vertical curves Lv 1 .......................................................................................................................... 44 B.2.18 Abrupt change of track gradient Δ p1 ...................................................................................... ............... 44 44 B.3 Requirements for a gauge of 1 668 mm .................................................................................. .............. 44 B.3.1 General ............................................................................................................................................................. 44 B.3.2 Radius of horizontal curve R1 ................................................................................................................... 44 B.3.3 Cant D1............................................................................................................................................................... 44 B.3.4 Cant deficiency I 1............................................................................. .............................................................. 45 B.3.5 Cant excess E 1 ................................................................................................................................................. 46 B.3.6 Length of cant transitions LD1 and transition curves in the horizontal plane LK 1 .................. 46 B.3.7 Cant gradient dD1/d s ................................................................................................................................... 47 B.3.8 Rate of change of cant dD1/dt ................................................................................................................... ................................................................................................................... 48 B.3.9 Rate of change of cant deficiency dI 1/dt ............................................................................................... ............................................................................................... 49 B.3.10 Length of constant cant between two linear cant transitions transiti ons Li1 ................ ................................ 50 B.3.11 Abrupt change of horizontal curvature .................................................................................. .............. 50 B.3.12 Abrupt change of cant deficiency ΔI 1 ..................................................................................................... 50 B.3.13 Length between two abrupt changes of horizontal curvature LC 1 ............................................... 51 B.3.14 Length between two abrupt changes of cant deficiency L s1 ........................................................... 51 B.3.15 Track gradients p1 ..................................................................................................................................... ... 51 51 B.3.16 Vertical radius Rv 1 ........................................................................... .............................................................. 51 B.3.17 Length vertical curves Lv 1 .......................................................................................................................... 52 B.3.18 Abrupt change of track gradient Δ p1 ...................................................................................... ............... 52 52 Annex C (informative) Supplementary information about shape and length of transition transition curves ............................................................................ .................................................................................... 53 C.1 General ............................................................................................................................................................. 53
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C.2 C.2.1 C.2.2 C.3 C.3.1 C.3.2
Definitions and properties of different transition curves and cant transitions.................... 53 Definitions ...................................................................................................................................................... 53 Properties ....................................................................................................................................................... 54 Further aspects that may be considered for a progressive track alignment design ........... 59 Background .................................................................................................................................................... 59 Progressive track alignment design ............................................................................... ....................... 59
Annex D (informative) Constraints and risks associated with the use of exceptional limits ........ 62 Annex E (informative) Evaluation of conditions at the toe of a switch .................................................. 63 E.1 General ............................................................................................................................................................. 63 E.2 Method based on effective radius .......................................................................................................... 63 Annex F (informative) Design considerations for switch and crossing units ...................................... 65 F.1 Examples of common switch and crossing units .............................................................................. 65 F.2 Use of diamond crossings, diamond crossings with slips and tandem turnouts .................. 67 F.3 Switch and crossing units on, or near, underbridges .................................................................... 67 F.4 Abutting switch and crossing units................................................................................ ........................ 67 F.5 Switch and crossing units on horizontal curves................................................................................ 67 F.6 Switch and crossing units on canted track ......................................................................................... . 68 F.7 Vertical alignments and switch and crossing units ......................................................................... 68 Annex G (informative) Examples of applications .......................................................................................... 71 G.1 General ............................................................................................................................................................. 71 G.2 Example of crossover on horizontal curve.......................................................................................... 71 G.3 Example of bilinear cant transition ..................................................................................................... 72 G.4 Example where a cant transition is designed without a coinciding transition curve ......... 73 G.5 Example of substandard transition curve ............................................................................... ............ 74 G.6 Example where several alignment elements forms an intermediate length.......................... 75 Annex H (informative) Examples of local limits for cant deficiency ....................................................... 76 Annex I (informative) Considerations regarding cant deficiency and cant excess ........................... 77 I.1 Introduction ................................................................................................................................................... 77 I.2 Cant deficiency .............................................................................................................................................. 77 I.3 Cant excess ............................................................................... ....................................................................... 77 I.4 Wheel climb criterion ................................................................................................................................. 77 I.5 Vehicle overturning .................................................................................... ................................................. 78 I.6 The lateral strength of a track under loading (Prud'homme ( Prud'homme limit ) ............................................ 78 I.7 Cant deficiency at switch and crossing layouts on curves ............................................................. 78 Annex J (informative) Passenger comfort on curves .............................................................................. ...... 79 J.1 General ...................................................................................... ....................................................................... 79 J.2 Lateral acceleration .................................................................................................................................... 79 J.3 Lateral jerk ..................................................................................................................................................... 79 J.3.1 Lateral jerk as a function of rate of change of cant deficiency ..................................................... 79 J.3.2 Lateral jerk as a function of an abrupt change of cant deficiency .............................................. 80 J.4 Roll motions ................................................................................................................................................... 80 Annex K (normative) Sign rules for calculation of ΔD, ΔI ΔI and and Δ p ............................................................ p ............................................................ 81 K.1 General regarding the sign rules ............................................................................................................ 81 K.2 Sign rules for calculation of ΔD Δ D ............................................................................................................... 81 K.3 Sign rules for calculation of ΔI Δ I ....................................................................................... ....................................................................................... .......................... 81 K.4 Sign rules for calculation of Δ p...................................................................................... p ...................................................................................... .......................... 82 Annex L (informative) Length of constant cant between two linear cant transitions Li.................. 84 Annex M (informative) The principle of virtual transition ........................................................................ 85
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M.1 M.2
Virtual transition at an abrupt change of cant deficiency.............................................................. 85 Virtual transition at a short intermediate length between two abrupt changes of cant deficiency ................................................................................ ......................................................................... 86 M.3 Limits based on the principle of the virtual transition ................................................................... 87 M.3.1 General ............................................................................................................................................................. 87 M.3.2 Characteristic vehicle with a distance of 20 m between bogie centres..................................... 87 M.3.3 Characteristic vehicle with a distance of 12,2 m and 10,06 m between bogie centres ....... 87 Annex N (normative) Lengths of intermediate elements Lc to prevent buffer locking ..................... 89 N.1 General ............................................................................................................................................................. 89 N.2 Basic vehicles and running conditions ................................................................................................. 89 N.3 Lengths Lc of an intermediate straight track between two long circular curves in the opposite directions .................................................................................................................. .................... 89 N.4 General cases for end throw differences ............................................................................. ................. 90 Annex O (informative) Considerations for track gradients........................................................................ 93 O.1 Uphill gradients ............................................................................................................................................. 93 O.2 Downhill gradients ....................................................................................................................................... 93 O.3 Gradients for stabling tracks and at platforms .................................................................................. 93 Annex ZA (informative) Relationship between this European Standard and the Essential Requirements of EU Directive 2008/57/EC .................................................................................... .... 94 Bibliography ........................................................................................................................................ ......................... 97
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European foreword This document (EN 13803:2017) has been prepared by Technical Committee CEN/TC 256 “Railway applications”, the secretariat of which is held by DIN. This European Standard shall be given the status of a national standard, either by publication of an identical text or by endorsement, at the latest by October 2017, and conflicting national standards shall be withdrawn at the latest by October 2017. Attention is drawn to the possibility that some of the elements of this document may be the subject of patent rights. CEN shall not be held responsible for identifying any or all such patent rights. This document supersedes EN 138031:2010 and EN 138032:2006+A1:2009. This document has been prepared under a mandate given to CEN by the European Commission and the European Free Trade Association, and supports essential requirements of EU Directive 2008/57/EC. For relationship with EU Directive 2008/57/EC, see informative Annex ZA, which is an integral part of this document. According to the CENCENELEC Internal Regulations, the national standards organizations of the following countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Croatia, Cyprus, Czech Republic, Denmark, Estonia, Finland, Former Yugoslav Republic of Macedonia, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Serbia, Slovakia, Slovenia, Spain, Sweden, Switzerland, Turkey and the United Kingdom.
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1
Scope
The purpose of this European Standard is to specify 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. This European Standard applies to nominal track gauges 1 435 mm and wider with speeds up to 360 km/h. Normative Annex A describes the conversion rules which shall be applied for tracks with nominal gauges wider than 1 435 mm. Normative Annex B is applied for nominal track gauges 1 520 mm, 1 524 mm and 1 668 mm. This European Standard is also applicable where track alignment takes into account vehicles that have been approved for high cant deficiencies (including tilting trains). More restrictive requirements of Technical specifications for interoperability relating to the ‘infrastructure’ subsystem of the rail system in the European Union (TSI INF) and other (national, company, etc.) rules will apply. This European Standard need not be applicable to lines, or dedicated parts of railway infrastructure that are not interoperable with railway vehicles tested and approved according to EN 14363.
2
Normative references
The following documents, in whole or in part, are normatively referenced in this document and are indispensable for its application. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. EN 138485, Railway applications — Track — Track geometry quality — Part 5: Geometric quality levels — Plain line EN 14363, Railway applications  Testing and Simulation for the acceptance of running characteristics of railway vehicles  Running Behaviour and stationary tests EN 152731, Railway applications — Gauges — Part 1: General — Common rules for infrastructure and rolling stock EN 152732, Railway applications — Gauges — Part 2: Rolling stock gauge EN ISO 800003, Quantities and units  Part 3: Space and time (ISO 800003)
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 European Standard specifies both a normal limit and an exceptional limit. The exceptional limits represent the least restrictive limits applied by any European railway, and are intended for use only under special circumstances and can require an associated maintenance regime.
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 righthand curve and negative on a lefthand 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. Note 2 to entry: It is possible to use other forms of transition curve, which show a nonlinear variation of curvature. Informative Annex C 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.
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.
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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 cant amount by which one running rail is raised above the other running rail, in a track cross section 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. Informative Annex C gives a detailed account of certain alternative types of transitions that may be used in track alignment design.
3.16 cant gradient absolute value of the derivative (with respect to chainage) of cant 3.17 rate of change of cant absolute value of the time derivative of cant
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3.18 rate of change of cant deficiency absolute value of the time derivative of cant deficiency (and/or cant excess) 3.19 track distance lateral distance between two tracks, measured at the horizontal projection of the track centre lines Note 1 to entry:
4
Other standards can define track distance as the sloping length parallel to a canted track plane.
Symbols and abbreviations
No.
Symbol
Designation
Unit
1
dD/ds
cant gradient
mm/m
2
dD/dt
rate of change of cant
mm/s
3
dI /dt
rate of change of cant deficiency (and/or cant excess)
mm/s
4
D
cant
mm
5
DEQ
equilibrium cant
mm
6
E
cant excess
mm
7
g
acceleration due to gravity according to EN ISO 800003
m/s2
8
I
cant deficiency
mm
9
Lc
length between two abrupt changes of curvature
m
10
LD
length of cant transition
m
11
L g
length of constant gradient
m
12
LK
length of transition curve
m
13
Li
length of alignment elements between two linear cant transitions
m
14
Ls
length between two abrupt changes of cant deficiency
m
15
Lv
length of vertical radius
m
16
p
gradient

17
qE
factor for calculation of equilibrium cant: 11,8
mm∙m∙(h/km)2
18
qN
factor for calculation of length of cant transition or transition curve with nonconstant gradient of cant and curvature, respectively
19
qR
factor for calculation of vertical radius
m∙h2/km2
20
qs
factor for calculation of lengths between abrupt changes of cant deficiency

21
qV
factor for conversion of the units for vehicle speed: 3,6
(km/h)/(m/s)
22
R
radius of horizontal curve
m
23
Rv
radius of vertical curve
m
24
s
longitudinal distance
m
25
t
time
s
26
V
speed
km/h
27
CE, lim
limit applicable at fixed crossings and expansion devices (index)

28
lim
general limit (index)

29
R, lim
limit applicable at small radius curves (index)

30
u, lim
upper limit for a parameter which also have a lower limit (index)

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5
General
5.1 Background This European Standard 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 inservice tolerances are not specified in this standard). Engineering requirements specific to the mechanical behaviour of switch and crossing components and subsystems are to be found in the relevant standards. Certain design considerations for switches and crossings layouts are presented in informative annexes. This European Standard 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 s tated in this European Standard. Limits in this European Standard are based on practical experience of European railways. Limits are applied where it is necessary to compromise between train performance, comfort levels, maintenance of the vehicle and track, and construction cos ts. 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 European Standard also specifies exceptional limits less restrictive than normal limits, which represent the least restrictive limits applied by any European railway. Such limits are intended for use only under special circumstances and can require an associated maintenance regime. In particular, use of exceptional limits (instead of normal limits) for several parameters at the same location shall be avoided. Informative Annex D describes the constraints and risks associated with the use of design values in the range between a limit and corresponding exceptional limit. Operational limits for speed and cant deficiency shall be applied to specific vehicles according to their approval parameters. Due to lack of experience among the European railways, no limits are specified for higher speeds than 360 km/h. 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 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.
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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
Transition curves, other types a
Horizontal curvature varies nonlinearly with chainage
a
Informative Annex C 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. Possible design criteria for the alignment before the switch, taking the entry angle in account, are described in informative Annex E. When a turnout is placed on a track gradient other than zero, a vertical curve and/or cant, the horizontal geometry of the diverging track will deviate s lightly 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 predefined relationship raising one rail and lowering the other rail. The cant can be considered as a sequence of elements connected at tangent points where two elements have the same magnitude of applied cant. (At a tangent point with cant, the same rail is the high rail before and after the tangent point.) Elements for cant are specified in Table 3. Table 3 — Elements for cant Alignment element
Characteristics
Constant cant
Cant is constant along the entire element
Cant transition, linear
Cant varies linearly with chainage
Cant transition, nonlinear a
Cant varies nonlinearly with chainage
Informative Annex C gives a detailed account of certain alternative types of cant transitions that may be used in track alignment design. a
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Cant transitions should normally coincide with transition curves, but exceptions are possible. The geometrical consequences of placing a turnout on track gradients, vertical curves and/or applying cant in a turnout are described in informative Annex F. The alignment of a ballasted track is normally maintained by Track Construction and Maintenance Machines. The maintenance with such machines is simplified if there is no more than one tangent point within the measuring chord of the machine (typically 10 m to 20 m). All limits and exceptional limits in Clause 6 apply, hence the permissible range for one parameter, for example horizontal radius R, can be further restricted due to the chosen values of other parameters. For example, at a certain location in an alignment sequence, the permissible range for horizontal radius R can be limited due to applied cant D, limit for cant deficiency I and/or characteristics of adjacent elements. Informative Annex G presents certain applications of the limits.
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Limits for 1 435 mm gauge
6.1 Radius of horizontal curve R In this European Standard, radius is positive on both righthand and lefthand curves. Speed independent lower limit for horizontal radii Rlim is specified in Table 4. Table 4 — Lower limit for horizontal curves Rlim Normal limit a
Exceptional limit a 150 m
a
Further requirements for the radius along platforms are defined in TSI INF.
NOTE Not all vehicles are designed and approved for horizontal radii smaller than 150 m (for example, see EN 15273–2).
There is no upper limit for horizontal radius in this European Standard. However, local standards can have such an upper limit, related to capabilities of the alignment software to handle very large numbers or to other practical aspects.
6.2 Cant D In this European Standard, cant on a horizontal curve is positive if the outer rail is higher than the inner rail. NOTE 1 Negative cant is unavoidable at switches and crossings on a canted main line where the turnout is curving in the opposite direction to the main line and, in certain cases, on the plain line immediately adjoining a canted turnout. Negative cant can also be used on temporary tracks.
Upper limits for cant Dlim, independent of horizontal radius R, are specified in Table 5.
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Table 5 — Upper limits for cant Dlim Normal limits
Exceptional limits
General a
160 mm
180 mm b
Switches and crossings a
120 mm
160 mm
Further requirements for the cant along platforms are defined in TSI INF.
a b
Cant exceeding 160 mm can cause freight load displacement and deterioration of passenger comfort when a train stops or runs with low speed (high value of cant excess). Ontrack machines and vehicles with special loads with a high centre of gravity can become unstable. Therefore, an associated maintenance regime and other measures may be necessary (for example exclude certain types of freight traffic, avoid trains regularly stopping on such a curve, etc.).
Upper limit for cant DR,lim, as a function of horizontal radius R, is specified in Table 6. Table 6 — Upper limit for cant DR,lim as a function of horizontal radius R Normal limit a
Exceptional limit a D R ,lim
R 50 m −
=
1,5 m / mm
a
This limit may be relaxed provided that measures are taken to ensure safety, see EN 13848–5 or in the case of the diverging track of a turnout with an element of least 10 m length with constant cant on both sides of the curve with small radius. NOTE 2 High cant on smallradius curves increases the risk of derailing when vehicles are running at low speed. Under these conditions, vertical wheel forces applied to the outer rail are much reduced, especially where track twist (see EN 13848–1 and EN 13848–5) causes additional force reductions. NOTE 3 Track twist limits are defined in EN 13848–5 as a function of applied cant. Using high cant values will impose lower twist values or other measures to ensure safety.
6.3 Cant deficiency I For given values of local radius R and cant Formula (1): I
=
DEQ
−
D
=
qE
V 2 −
R
D,
and speed V , the cant deficiency I is defined according to
D
where DEQ
qE NOTE 1
is equilibrium cant (mm) and = 11,8 mm∙m∙h2/km2. With negative cant, the cant deficiency will be higher than equilibrium cant.
General upper limits for cant deficiency I lim are specified in Table 7.
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Table 7 — Upper limits for cant deficiency I lim Normal limits a
Exceptional limits a
153 mm
180 mm b
Nontilting trains V ≤
220 km/h
220 km/h < V ≤ 300 km/h
153 mm b
300 km/h < V ≤ 360 km/h
100 mm b Tilting trains
80 km/h ≤ V ≤ 260 km/h c
275 mm
300 mm
It is common practice to apply different limits for cant deficiency to different categories of trains. It is assumed that every vehicle has been tested and approved according to the procedures in EN 14363 in conditions covering its own range of operating cant deficiency (denoted I adm in EN 14363). Examples of local limits are shown in informative Annex H. a
b
Trains complying with EN 14363, equipped with a cant deficiency compensation system other than tilt, may be permitted by the Infrastructure Manager to run with higher cant deficiency values. Currently, there are no lines in Europe used or planned where maximum speed for tilting trains exceeds 260 km/h. c
NOTE 2 For a given vehicle, increased cant deficiency generates increasing forces between the wheel and the rail; see informative Annex I. NOTE 3 Depending on the characteristics of specific features in track, such as bridges carrying directlaid ballastless track, tracks with jointed rails, sections of line exposed to very strong cross winds, etc., it can be necessary to restrict the permissible cant deficiency. Rules in respect of these restrictions cannot be formulated beforehand since they will be dictated by the design of these features. NOTE 4
High values of cant deficiency are related to passenger (dis)comfort, see informative Annex J.
For tracks with crossings in the outer rail and for expansion devices, there are more restrictive upper limits I CE ,lim, dependent on speed V , specified in Table 8.
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Table 8 — Upper limits for cant deficiency for tracks with crossings in the outer rail and for expansion devices I CE,lim Normal limits
Exceptional limits
Fixed common crossings V ≤ 230
km/h
230 km/h < V ≤ 360 km/h
110 mm
Same as the normal limit in Table 7
Not permitted
Not permitted
Fixed obtuse crossings V ≤ 160
km/h
100 mm
Same as the normal limit in Table 7
160 km/h < V ≤ 230 km/h
75 mm
Same as the normal limit in Table 7
230 km/h < V ≤ 360 km/h
Not permitted
Not permitted
Crossings with movable parts V ≤ 230
km/h
130 mm
Same as the normal limit in Table 7
80 mm
Same as the normal limit in Table 7
230 km/h < V ≤ 360 km/h
Expansion devices V ≤ 160
km/h
100 mm
Same as the normal limit in Table 7
160 km/h < V ≤ 230 km/h
80 mm
Same as the normal limit in Table 7
230 km/h < V ≤ 360 km/h
60 mm
Same as the normal limit in Table 7
6.4 Cant excess E On a horizontal curve where cant deficiency (defined in Formula (2)) is negative, there is cant excess E defined by Formula (3). E
= −
I
(2)
On canted turnouts, and on plain tracks in close conjunction to canted switch and crossing units, there may be applied cant also on straight track. Cant may also be applied on temporary straight tracks. On a canted straight track, there is cant excess E defined by Formula (3): E
=
D
(3)
General upper limits for cant excess speed of the slowest train on the line.
E lim are
specified in Table 9. These limits apply for the regular
Table 9 — Upper limits for cant excess E lim Normal limit
Exceptional limit
110 mm
150 mm
NOTE The value of E affects innerrail stresses induced by slow trains, since the quasistatic vertical wheel/rail force on the inner rail is increased; see informative Annex I.
For tracks with crossings in the low rail and for expansion devices, there are more restrictive upper limits E CE ,lim, defined by Formula (4) and Table 8: E CE ,lim
=
I CE ,lim
(4)
Requirements regarding changes in cant deficiency (6.5, 6.8, 6.11 and 6.13) apply also for changes in cant excess.
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6.5 Length of cant transitions LD and transition curves in the horizontal plane LK 6.5.1 General Cant transitions should normally coincide with transition curves. However, it can be necessary to provide cant transitions in circular curves and straights. For cant transitions and transition curves the limits are as fo llows: — speed independent lower limits for lengths of transition curves LK ,lim are specified in Table 10;
dD are specified in 6.6; ds lim
— upper limits for cant gradient
dD are specified in 6.7; and dt lim
— upper limits for rate of change of cant
dI are specified in 6.8. dt lim
— upper limits for rate of change of cant deficiency
Table 10 — Lower limits for lengths of transition curves LK ,lim Normal limit
Exceptional limit
20 m
0
6.5.2 Lengths of linear cant transitions and clothoids
dD dD , rate of change of cant and rate of ds dt
For linear cant transitions and clothoids, cant gradient
dI can be calculated according to Formulae (5) to (7): dt
change of cant deficiency dD ds
dD dt dI dt
=
=
=
∆D
LD V
(5)
⋅
∆D
⋅
∆I
qV L D
V
qV LK
(6)
(7)
where ΔD
is the change of cant over the length LD, as defined in normative Annex K,
ΔI
is the change of cant deficiency over the length LK , as defined in normative Annex K,
V
is the speed in km/h and
qV
= 3,6 (km/h)/(m/s).
Formula (7) assumes that any cant transition coincides with a transition curve, LK = LD, and Formulae (5) to (7) assume that the mathematical properties are constant over this length. Otherwise,
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the transition curve and the cant transition shall be divided in parts (with constant properties) which are evaluated separately. 6.5.3 Lengths of transition curves with nonconstant gradient of curvature and cant
dD , rate of ds
For transition curves with nonconstant gradient of curvature and cant, cant gradient
dI dD and rate of change of cant deficiency can be calculated according dt dt
change of cant
Formulae (8) to (10): dD ds dD
dt dI dt
= q N ⋅
= q N ⋅ = q N ⋅
∆D LD
V
(8)
⋅
∆D
⋅
∆I
q v LD V
q v LK
(9)
(10)
where ΔD
is the change of cant over the length LD, as defined in normative Annex K,
ΔI
is the change of cant deficiency over the length LK , as defined in normative Annex K,
V
is the speed in km/h,
qV
= 3,6 (km/h)/(m/s), and
the factor qN
is defined in Table 11.
For certain types of transitions with nonconstant gradient of curvature and cant, the value of the factor q N is specified in Table 11. Table 11 — Factor qN for transitions with nonconstant gradient of curvature and cant Bloss
Cosine
Helmert (Schramm)
Sine (Klein)
1,5
π/2
2
2
Formula (10) assumes that any cant transition coincides with a transition curve, LK = LD, and Formulae (8)(10) assume that the mathematical properties are constant over this length. Otherwise, the transition curve and the cant transition shall be divided in parts (with constant properties) which are evaluated separately.
dD may be replaced with a criterion for the second derivative dt
The criterion for rate of change of cant
d 2D , as defined in 6.7. dt 2
of cant with respect to time
NOTE Informative Annex C gives further information on clothoids with linear cant transitions and alternative types of transition curves and cant transitions.
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6.6 Cant gradient dD/d s dD are specified in Table 12. ds lim
Upper limits for cant gradients
dD ds lim
Table 12 — Upper limits for cant gradients
V ≤ 50 km/h
Normal limits
Exceptional limits
2,50 mm/m
3,33 mm/ma
V > 50 km/h a
2,50 mm/m
According to EN 13848–5, a more restrictive limit for cant than the limit in Table 6 can apply.
6.7 Rate of change of cant dD/dt dD for linear and nonlinear cant transitions are specified in dt lim
Upper limits for rate of change of cant Table 13 and Table 14, respectively.
dD for linear cant transitions dt lim
Table 13 — Upper limits for rate of change of cant
Normal limits
Exceptional limits
Nontilting trains V ≤ 200 km/h I ≤ 160 mm
50 mm/s
70 mm/s a
160 mm < I ≤ 180 mm
50 mm/s
60 mm/s
Nontilting trains 200 km/h < V ≤ 360 km/h 50 mm/s
60 mm/s
Tilting trains V ≤ 200 km/h 75 mm/s
95 mm/s
Tilting trains 200 km/h < V ≤ 260 km/h b 60 mm/s a
70 mm/s
Where I ≤ 153 mm and d I/ dt ≤ 70 mm/s, the exceptional limit for d D/ dt may be raised to 85 mm/s.
b
Currently, there are no lines in Europe used or planned where maximum speed for tilting trains exceeds 260 km/h.
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dD for nonlinear cant transitions dt lim
Table 14 — Upper limits for rate of change of cant Normal limit
Exceptional limit V ≤ 300
km/h a 76 mm/s b
55 mm/s a
Currently, there are no lines in Europe used or planned where maximum speed on nonlinear cant transitions exceeds 300 km/h. b
Where the absolute value of second derivative of cant with respect to time (d2D/dt 2) is less than 150 mm/s2 this limit may be raised.
6.8 Rate of change of cant deficiency dI /dt dI for clothoids and for transition curves with dt lim
Upper limits for rate of change of cant deficiency
nonconstant gradients are specified in Table 15 and Table 16, respectively.
dI for clothoids dt lim
Table 15 — Upper limits for rate of change of cant deficiency
Normal limits
Exceptional limits
Nontilting trains V ≤ 220 km/h I ≤
160 mm
160 mm < I ≤ 180 mm
55 mm/s
100 mm/s
55 mm/s
90 mm/s
Nontilting trains 220 km/h < V ≤ 300 km/h 55 mm/s
75 mm/s
Nontilting trains 300 km/h < V ≤ 360 km/h 30 mm/s
55 mm/s
Tilting trains V ≤ 225 km/h 100 mm/s
180 mm/s
Tilting trains 225 km/h < V ≤ 260 km/h a 80 mm/s a
Currently, there are no lines in Europe used or planned where maximum speed for tilting trains exceeds 260 km/h
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dI for transition curves with dt lim
Table 16 — Upper limits for rate of change of cant deficiency nonconstant gradients
Exceptional limits
Normal limits Nontilting trains V ≤ 300 km/h 95 mm/s
120 mm/s
Nontilting trains 300 km/h < V ≤ 360 km/h 30 mm/s
55 mm/s
Tilting trains V ≤ 225 km/h 100 mm/s
180 mm/s
Tilting trains 225 km/h < V ≤ 260 km/h a 95 mm/s
120 mm/s
a
Currently, there are no lines in Europe used or planned where maximum speed for tilting trains exceeds 260 km/h
Where a transition curve is of substandard length with respect to the
dI dt
criterion, this criterion shall
be replaced with the criterion that the change of cant deficiency over its length shall be less than the upper limit for abrupt change of cant deficiency Δ I , as defined in 6.11. NOTE High values for rate of change of cant deficiency are related to passenger (dis)comfort; see informative Annex J.
For tilting trains, both active and passive tilt systems need time to adapt the angle of tilt to the curve radius and it is for this reason that horizontal curves shall include transition curves of sufficient length. The transition curves should coincide with the cant transitions. If they do not, special running tests are recommended to determine whether permissible speed needs to be reduced. On lines with tilting trains, the clothoid is normally used for transition curves, giving a linear variation of curvature. Where using transition curves with nonconstant gradients, the function of the tilt system shall be taken into account for the analysis of the complex interaction between the vehicle and the track.
6.9 Length of constant cant between two linear cant transitions Li Lower limits for length of constant cant placed between two linear cant transitions Li,lim are specified in Table 17. Table 17 — Lower limits for lengths of constant cant between two linear cant transitions Li ,lim Normal limit
Exceptional limit a
20 m
0
a
The use of the exceptional limit between two linear cant transitions with a total change of cant gradient more than the upper limits in Table 12 should be avoided.
For an alternative method to define the minimum lengths, see i nformative Annex L.
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6.10 Abrupt change of horizontal curvature An abrupt change of curvature may occur in close conjunction to switches and crossings, at alignment for low speeds (sidings etc.) or at small deviations in alignment within a limited length. It is unavoidable on at least one track of a turnout. In most other cases, transition curves should be u sed. For abrupt changes of curvature there are limits as follows: — upper limits for abrupt change of cant deficiency ΔI lim are specified in 6.11; — lower limits for length between two abrupt changes of curvature Lc,lim in 6.12; — lower limits for length between two abrupt changes of cant deficiency Ls,lim in 6.13.
6.11 Abrupt change of cant deficiency ΔI An abrupt change of cant deficiency ΔI occurs where there is an abrupt change of curvature. A tangent point with an abrupt change of cant deficiency generates disturbed vehicle dynamics. The magnitude of the abrupt change of cant deficiency is defined by the sign rules given in normative Annex K. Upper limits for abrupt change of cant deficiency ΔI lim are specified in Table 18. Table 18 — Upper limits of abrupt change of cant deficiency (ΔI lim) Normal limits
Exceptional limits
V ≤ 60 km/h
110 mm
130 mm a
60 km/h < V ≤ 200 km/h
100 mm
125 mm
200 km/h < V ≤ 230 km/h
85 mm
230 km/h < V ≤ 360 km/h
25 mm b
a
Where V ≤ 40 km/h and I  ≤ 75 mm both before and after an abrupt change of curvature, the exceptional limit for ΔI may be raised to 150 mm. b
The limit is aimed to be applicable for plain track. Currently, no turnouts are designed for higher speeds in the diverging track than 230 km/h.
Outside zones with switches and crossings, design values for abrupt changes of cant deficiency (if used) should be much lower than the upper limits in Table 18. Where there is an abrupt change of cant deficiency, some European railways use the principle of virtual transition described in informative Annex M. The values for abrupt change of cant deficiency, when based on the principle of virtual transition, shall also conform to the upper limits specified in Table 18.
6.12 Length between two abrupt changes of horizontal curvature Lc There are limits on how much end throws may differ between two adjacent vehicles. The criterion is related to buffer locking, but also vehicles with central couplers can have similar limits. The end throw is the geometrical overthrow d ga for the end of the vehicle, as defined in EN 152731. This European Standard bases on the criterion on the static end throw differences. The limit refers to a long circular curve of 190 m radius to be connected to a long circular curve, also of 190 m radius, in the opposite direction, with an intermediate straight of 6,00 m length. This leads to a maximum for the end throw difference of 395 mm for two 26,4 m long passenger coaches with a bogie distance of 19,0 m and allows a long circular curve of 213 m radius to be directly connected to a long circular curve, also of
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213 m radius, in the opposite direction. It also allows for any combination of circular curves where the change of curvature is less than 1/106,5 m −1. NOTE The EUROFIMA coach with the following characteristics (length: 26,4 m, bogie distance: 19,0 m, buffer width: 635 mm, transversal play of the vehicle: ± 60 mm) fulfils the requirements concerning buffer recovery for the above mentioned reference situation.
For dedicated freight tracks, the criterion is based on the static end throw differences for two 18,0 m long freight vehicles with a bogie distance of 12,0 m, which shall be limited to a maximum of 225 mm. This criterion allows a long circular curve of 200 m radius to be directly connected to a long circular curve, also of 200 m radius, in the opposite direction. It also allows for any combination of circular curves where the change of curvature is less than 1/100 m−1. Where the horizontal curves have curvatures that differ more than 1/106,5 m−1 or 1/100 m−1, respectively, an intermediate element shall be inserted to reduce the differences in end throw, using the static method in EN 152731, down to less than or equal to 395 mm or 225 mm, respectively. This intermediate element may be a straight line, a transition curve, or a circular curve. The required length of the intermediate element depends on the radii of the small radius curves as well as the type of intermediate element. For vehicles with other characteristics, it is assumed that running gear, couplers and buffers are designed for the minimum length of the intermediate element LC . Infrastructure managers can specify more restrictive, longer lengths on (dedicated parts of) their network in order to prevent buffer locking for existing vehi cles that do not fulfil these assumptions. Table 19 specifies certain lower limits for the lengths of a straight intermediate element for certain combinations of long circular curves in opposite directions. The track has a maximum inservice gauge value of 1 470 mm (nominal gauge 1 435 mm plus 35 mm, see EN 138485). Normative Annex N specifies more details and more examples. Table 19 — Certain lower limits for the length between two abrupt changes of curvature Lc ,lim Alignment sequence
Limits for tracks for Limits for dedicated passenger coaches freight tracks
R =
150 m – straight – R = 150 m
10,78 m
6,79 m
R =
160 m – straight – R = 160 m
9,48 m
6,01 m
R =
170 m – straight – R = 170 m
8,30 m
5,20 m
R =
180 m – straight – R = 180 m
7,20 m
4,25 m
R =
190 m – straight – R = 190 m
6,00 m
3,01 m
R =
200 m – straight – R = 200 m
4,50 m
0
R =
210 m – straight – R = 210 m
2,11 m
0
R =
213 m – straight – R = 213 m
0
0
6.13 Length between two abrupt changes of cant deficiency L s The disturbed vehicle dynamics created by an abrupt change of cant deficiency are damped as a function of time. Speeddependent lower limits for length of intermediate element(s) between two abrupt changes of cant deficiency Ls,lim are specified in Formula (11) and Table 20:
Ls lim q s lim V =
,
⋅
,
(11)
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where qs,lim
is a factor (m·h/km) defined in Table 20 and
V
is the train speed (km/h).
Table 20 — Lower limits of the factor q s,lim defining the minimum length between two tangent points with abrupt changes of cant deficiency (L s,lim) Normal limits
Exceptional limits
V ≤ 70 km/h
0,20
0,10 a
70 km/h < V ≤ 100 km/h
0,20
0,15 b
100 km/h < V ≤ 360 km/h
0,25
0,19
a
Where ΔI ≤ 110 mm and V ≤ 50 km/h, qs,lim may be reduced to 0,08 m∙h/km.
b
Where ΔI ≤ 100 mm and V ≤ 90 km/h, qs,lim may be reduced to 0,10 m∙h/km.
NOTE For switches and crossings placed on transition curves, the length between two abrupt changes of cant deficiency may involve more than one intermediate element.
The intermediate element is normally an element with constant cant deficiency (or constant cant excess). Where cant deficiency is not constant, rate of change of cant deficiency shall not be higher than the upper limit in 6.8. The lower limit Ls,lim does not apply where the total change of cant deficiency over the two (or more) tangent points does not exceed the upper limit in 6.11. The magnitude of total change of cant deficiency is defined by the sign rules given in normative Annex K. Where there is an abrupt change of cant deficiency, some European railways use the principle of virtual transition described in informative Annex M. The length between two tangent points with abrupt changes of cant deficiency, when based on the principle of virtual transition, shall also conform to the lower limits specified in Table 20.
6.14 Track gradients p The absolute magnitudes of track gradients p shall be limited due to available traction in relation to train mass, as well as braking performances of the trains. No upper limits for the magnitudes of gradients are specified in this European Standard. For certain design considerations, see informative Annex O. NOTE 1
Upper limits for the track gradients are defined in TSI INF.
Lower limits for lengths of constant track gradients L g,lim are specified in Table 21. Table 21 — Lower limits for lengths of constant track gradients L g,l im Normal limit
Exceptional limit
20 m
0
For lines for certain rolling stock with secondary air suspension, between a convex vertical curve and a concave vertical curve which both have vertical radii close to the lower exceptional limits as defined in 6.15, it is recommended to apply a lower limit of 0,5 m/(km/h)∙V for the length of an intermediate constant gradient. No upper limits for lengths of constant track gradients L g,u,lim are specified in this European Standard.
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NOTE 2
Certain upper limits for the lengths of track gradients are defined in the TSI INF.
6.15 Vertical radius Rv Vertical curves are normally designed as parabolas (2nd degree polynomials) or as circular curves. They may be designed without transition curves. NOTE A vertical curve in the diverging track of canted switches and crossings unit can be of a higher order polynomial than a parabola.
Switch and crossing units should be installed where the tracks are level, on a constant gradient, or at large vertical radius. Speed independent lower limits for vertical radii Rv,lim are specified in Table 22. Table 22 — Lower limits for vertical radii Rv,lim Normal limits
Exceptional limits
General
2 000 m
500 m a
Switches and Crossings, Convex curves
5 000 m
2 000 m
Switches and Crossings, Concave curves
3 000 m
2 000 m
Marshalling humps, convex curves
250 m a
Marshalling humps, concave curves
300 m a
a
Not all vehicles are designed and approved for vertical radii less than 500 m (see EN 15273–2).
The vertical radius for both plain track and switches and crossing units shall also comply with the speeddependent lower limits specified in Formula (12) and Table 23. 2 R v ≥ q R , lim ⋅V
(12)
Table 23 — Lower limits for the factor for vertical radius qR,lim Normal limits Exceptional limits Convex curves 0,35 m·h2/km2
0,15 m·h2/km2
Concave curves 0,35 m·h2/km2
0,13 m·h2/km2
There is no upper limit for vertical radius in this European Standard. However, local standards may have such an upper limit, related to capabilities of the alignment software to handle very large numbers or to other practical aspects.
6.16 Length of vertical curves Lv Lower limits for the lengths for vertical curves Lv,lim are specified in Table 24. Table 24 — Lower limits for the lengths for vertical curves Lv,lim Normal limit Exceptional limit 20 m
0
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6.17 Abrupt change of track gradient Δ p Two constant track gradients shall normally not be connected to each other without an intermediate vertical curve. In exceptional cases, there may be an abrupt change of track gradient Δ p. The magnitude of the abrupt change of track gradient Δ p is defined by the sign rules given in normative Annex K. Upper limits for an abrupt change of track gradient Δ plim are specified Table 25. Table 25 — Upper limits for an abrupt change of track gradient in plain track Δ plim Normal limits Exceptional limits 0 < V ≤ 230 km/h
1 mm/m
2 mm/m
230 km/h < V ≤ 360 km/h
0,5 mm/m
1 mm/m
For sidings, with a permissible speed not exceeding 40 km/h, the exceptional limit may be raised to 4,5 mm/m, provided that the abrupt change of gradient occurs outside switches and crossings. Inside a switch and crossing unit placed over a tangent point where there is an abrupt change of cant gradient, there will be an associated abrupt change of track gradient for the diverging track. This effect may be neglected since it is taken into account by the upper limit for the cant gradient. NOTE
For ferry ramps, limits for abrupt change of track gradient are specified in EN 15273–3.
Two abrupt changes of track gradients should not be arranged in close conjunction. However, the arrangement can be justified in the diverging track between two switch and crossing units. The distance between two such abrupt changes of track gradients should exceed the length of a vertical curve, with a radius according to 6.15, which generates the same total change of track gradient.
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Annex A (normative) Rules for converting parameter values for track gauges wider than 1 435 mm
A.1 Scope This annex describes the rules, which shall be applied for converting the values and limits in the standard for gauges wider than 1 435 mm. Normative Annex B specifies the limits of the track alignment parameters, based on the following rules, which shall be applied to tracks with a gau ge of 1 520 mm, 1 524 mm and 1 668 mm.
A.2 Symbols and abbreviations Unless otherwise indicated, the symbols and abbreviations of Table A.1 apply to Annex A.
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Table A.1 — Symbols and abbreviations No.
Symbol
Designation
31
ai, ai1
quasistatic lateral acceleration, at track level, but parallel to the m/s2 vehicle floor
32
aq, aq1
noncompensated lateral acceleration in the running plane
m/s 2
33
b
vehicle wheelbase
m
34
B, B1
distance between the spring suspension points on a wheelset
mm
35
dai/dt , dai1/dt
rate of change of quasistatic lateral acceleration at track level m/s3 but parallel to the vehicle floor
36
dD/ds, dD1/ds
cant gradient
mm/m
37
dD/dt , dD1/dt
rate of change of cant
mm/s
38
dI /dt , dI 1/dt rate of change of cant deficiency
mm/s
39
D, D1
Cant
mm
40
e, e1
distance between the nominal centre points of the two contact mm patches of a wheelset (e.g. about 1500 mm for nominal track gauge 1435 mm)
41
E , E 1
cant excess
mm
42
H s
quasistatic lateral force applied by a wheelset to the track
N
43
h g
height above the top of the rails for the mass centre of a vehicle
m
44
I , I 1
cant deficiency
mm
45
K , K 1
suspension stiffness coefficient
N/m
46
qE , qE 1
factor for calculation of equilibrium cant
mm∙m∙h2/km2
47
QN
nominal vertical wheel/rail force
N
48
sr
roll flexibility coefficient, equivalent to flexibility coefficient s in EN 15273–1
49
st
tilt compensation factor of a tilt system
50
u
cross level variation between wheelsets linked by the m suspension system
51
W
ratio e1/e (e1/1500 mm)

52
Δa i, Δai1
abrupt change of quasistatic lateral acceleration Δai
m/s2
53
ΔD, ΔD1
overall track cant variation along a cant transition
mm
54
ΔI , ΔI 1
overall cant deficiency (and/or cant excess) variation over a mm transition, or abrupt change of cant deficiency at a tangent point
55
ΔQ, ΔQ1
quasistatic vertical wheel/rail force increment
N
56
φ , φ 1
roll velocity
rad/s
28
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EN 13803:2017 (E)
Parameters quoted with the index 1 relate to the values converted for nominal track gauges wider than 1 435 mm, as opposed to the original 1 435 mm gauge values, which are not indexed.
A.3 Basic assumptions and equivalence rules A.3.1 General The conditions are based on the same criteria for the following concepts: — track forces and safety; — economic aspects of track maintenance; — ride comfort and roll flexibility coefficient. It is assumed that: — the track system and track quality are similar for the wider gauges; — the composition of the vehicles and their wheel arrangements are similar; the masses, the positions of the centres of gravity, rigidity and dampers are similar; the same safety limits apply with regard
Y ; Q lim
to derailment,
— the same levels of safety with regard to track shift limit will be obtained using the same levels for H S and, in the case of derailment and overturning, by using the same values of reduced vertical forces, ΔQ, on the wheels (the guiding wheels in the case of derailment); — the same degree of track fatigue will be obtained if the H S and Q values are maintained; — the same ride passenger comfort for passenger will be obtained if the values of ai,
da i dt
and Δai are
kept unchanged.
A.3.2 Basic formulae Formula (A.1) quantifies the influence of cant deficiency I on the quasistatic lateral force between a wheelset and the track H s: Hs
= 2⋅ Q N ⋅
I e
(A.1)
Formula (A.2) quantifies the influence of cant deficiency I on the quasistatic vertical wheel/rail force increment ΔQ: ∆Q = 2 ⋅ Q N ⋅ I ⋅
h g e2
(A.2)
In the case of cant excess, I is replaced by E in Formulae (A.1) and (A.2) (see 6.4). Formula (A.3) quantifies the influence of cross level variation u on the quasistatic vertical wheel/rail force increment ΔQ:
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u B
2
∆Q = K ⋅ ⋅ 4 e
(A.3)
For normal railway vehicles, the distance B may be assumed to be 500 mm longer than distance e. For 1 435 mm gauge, B may be assumed to be 2 000 mm. Formulae (A.4) and (A.5) quantifies the influence of cant deficiency I on noncompensated lateral acceleration on the track plane and inside the vehicle body (of a nontilting vehicle), respectively: I aq = g ⋅ e ai
=
(A.4)
( 1 + s r ) ⋅ aq
(A.5)
A.3.3 Basic data The value of the parameters for nominal track gauges wider than 1 435 mm will be designated with the index 1. Each network system shall take into account the values of e1 and B1. If not available, e1 may be obtained by adding 65 mm to the gauge and B1 may be assumed to be 500 mm longer than distance e1. A commonly used conversion factor W is defined by Formula (A.6): W =
e1 e
=
e1 1500mm
(A.6)
For nominal track gauges wider than 1 435 mm Formulae (A.7) and (A.8) apply: W > 1 B1
>
(A.7)
B
(A.8)
A.4 Detailed conversion rules A.4.1 General The following subclauses define, for each of the track alignment design parameters, the conversion rule to be applied.
A.4.2 Cant D1 (Subclause 6.2 of the main body of the standard) The horizontal radius may be derived from the values of cant Formula (A.9): R = C ⋅
V
D and
cant deficiency I according to
2
D + I
(A.9)
The factor for calculation of equilibrium cant C can be derived by Formulae (A.10) and (A.11): C 1 =
C =
30
e1 2
( qv ) ⋅ g e
( qv )
2
⋅g
(A.10)
(A.11)
BS EN 13803:2017
EN 13803:2017 (E)
where qV
= 3,6 (km/h)/(m/s) and
g
= 9,81 m/s2
Combining Formulae (A.10)(A.11) gives Formula (A.12) which shall be used in conjunction with the corresponding values for cant and cant deficiency for the modified gauge value, D1 and I 1: C1
a)
=
r C
(A.12)
⋅
Safety: 1) Track shift limit: Not relevant. 2) Derailment and overturning: Reduced vertical forces ΔQ on the high rail (in the case of a train which is stopped or travelling at low speed) can be estimated with Formulae (A.13)(A.14): ∆Q1 = 2 ⋅ Q N ⋅ D1 ⋅
∆Q = 2 ⋅ Q N ⋅ D ⋅
hg e
2
hg e1
2
(A.13)
(A.14)
Assuming the same reduction in vertical wheel/rail force, ΔQ1 = ΔQ, Formula (A.15) applies:
D1 = W 2 ⋅ D
(A.15)
Limit cant as a function of horizontal radius is specified by Formula (A.16): D1R ,lim
=
W
2
⋅
DR ,lim
=
W
2
R 50 m 1,5m/mm −
⋅
(A.16)
b) Track fatigue criteria: 1) Additional vertical forces on the low rail (low speed) ΔQ can be estimated with Formulae (A.13)(A.14). Hence, Formula (A.15) applies for this criterion. 2) Quasistatic lateral force applied by a wheelset to the track (low speed) H s can be estimated with Formulae (A.17)(A.18): 2 Q N
Hs
=
Hs
= 2 ⋅ Q N ⋅
⋅
⋅
D1 e1
D e
(A.17)
(A.18)
Assuming the same quasistatic lateral force, H s1 = H s, Formula (A.19) applies: D1
=
W D ⋅
(A.19)
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c)
Ride comfort for passengers: Lateral acceleration in the vehicle body (low speed) ai can be estimated with Formulae (A.20) and (A.21): ai1
ai
=
=
(1 + s r 1 ) ⋅ aq1 = (1 + s r 1 ) ⋅ g ⋅
(1 + s r ) ⋅ aq = (1 + s r ) ⋅ g ⋅
D e
D1 e1
(A.20)
(A.21)
Assuming the same lateral acceleration in the vehicle body, ai1 = ai, Formula (A.22) applies: 1 + s r
D1 =
1 + s r 1
⋅
W ⋅D
(A.22)
For sr 1 = sr , Formula (A.22) may be simplified to Formula (A.23): D1
=
W ⋅D
(A.23)
d) Rule for converting values: Normal limits and exceptional limits for cant, independent of horizontal radius, Dlim in 6.2 shall be multiplied by W . Normal limit for cant as a function of horizontal radius, DR,lim in 6.2 shall be multiplied by W 2. For tracks alongside passenger platforms, a cant restriction will be
1 + s r 1 + s r 1
⋅
W ⋅ D . If sr = sr 1, this
restriction will be W ⋅ D .
A.4.3 Cant deficiency I 1 (Subclause 6.3 of the main body of the standard) Cant deficiency for gauges wider than 1 435 mm I 1 may be estimated with Formula (A.24): I1 =
a)
C 1 ⋅ V 2 R
−
D1 = W ⋅ I
(A.24)
Safety: 1) Quasistatic lateral force applied by a wheelset to the track H s can be estimated with Formulae (A.25)(A.26): I 1
Hs
= 2⋅
Q N ⋅
Hs
= 2⋅
I Q N ⋅ e
e1
(A.25)
(A.26)
Assuming the same quasistatic lateral force, H s1 = H s, Formula (A.27a) applies: I1
32
=
W ⋅ I
(A.27a)
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2) Derailment and overturning: The risk for derailment and overturning is assumed to be eliminated by the same criteria as for quasistatic lateral forces, therefore Formulae (A.24) to (A.26) apply for these crit eria. b) Track fatigue criteria: The same degree of fatigue applies to the same values of Hs, therefore Formulae (A.24)(A.26) apply for this criterion. c)
Ride comfort for passengers: Lateral acceleration in the vehicle body ai can be estimated with Formulae (A.27b)(A.28): ai 1
ai
=
=
(1 + s r 1 ) ⋅ aq1 = (1 + sr 1 ) ⋅ g ⋅
(1 + s r ) ⋅ aq = (1 + s r ) ⋅ g ⋅
I e
I 1 e1
(A.27b)
(A.28)
Assuming the same lateral acceleration in the vehicle body, ai1 = ai, Formula (A.29) applies: I1
=
1 + s r 1 + s r 1
⋅ W ⋅ I
(A.29)
For sr 1 = sr , Formula (A.29) may be simplified to Formula (A.30): I1
= W ⋅ I
(A.30)
d) Rule for converting values: Limits and exceptional limits for cant deficiency in 6.3, including the values governed by the footnotes, shall be multiplied by W .
A.4.4 Cant excess E 1 (Subclause 6.4 of the main body of the standard) Cant excess is defined by Formula (A.31) on horizontal curves and Formula (A.32) on straight track: E1
= − I 1
E1
=D 1
(A.31) (A.32)
This parameter mainly affects track fatigue and specifically the increase in vertical forces on the lower rail ΔQ. However, it does also affect lateral forces H s and lateral acceleration in the vehicle body ai. Rule for converting values: Limits and exceptional limits for cant excess in 6 .4 shall be multiplied by W .
A.4.5 Lengths of cant transitions LD and transition curves in the horizontal plane LK (Subclause 6.5 of the main body of the standard) (This subclause is valid only for the linear transition curves.) The lower limit for the length cant transitions and transition curves is 20 m, exceptional limit is zero.
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The length of transition curves shall comply with Formulae (A.33), (A.34) and (A.35), and Subclauses A.4.6, A.4.7 and A.4.8: −1
dD LD ≥ ∆D1 ⋅ 1 ds lim LD ≥
V max
LK ≥
V max
q v
q v
(A.33) −1
dD ⋅ ∆D1 ⋅ 1 dt lim
(A.34)
−1
dI ⋅ ∆I 1 ⋅ 1 dt lim
(A.35)
Formula (A.35) assumes that any cant transition curve coincides with a transition curve, LK = LD, and Formulae (A.33)(A.35) assume that the mathematical properties are constant over this length. Otherwise, the transition curves and the cant transitions shall be divided in parts (with constant properties) which are evaluated separately.
A.4.6 Cant gradient dD1/d s (Subclause 6.6 of the main body of the standard) The limits for this parameter are associated with safety from the point of view of derailment of slow trains as a result of flange climbing. The same degree of safety with regard to derailment will be obtained with the same reduction in vertical force on the guiding wheel. The ratio
dD ds
represents the
average cant variation corresponding to the wheelbase b (which is the distance between axles for twoaxle wagons, and separately as the bogie axle distance and the distance between bogie pivots for bogie vehicles). The reduction in vertical wheel/rail force Δ Q corresponding to
u
=
b
dD ⋅
ds
may be calculated
with Formulae (A.36) and (A.37): 2
B ∆Q1 = K 1 ⋅ ⋅ ⋅ 1 4 ds e1 b
dD1
(A.36)
2
B ∆Q = K ⋅ ⋅ ⋅ 4 ds e b
dD
(A.37)
Assuming the same reduction in vertical wheel/rail force, ΔQ1 = ΔQ, Formula (A.38) applies: 2
B dD = W ⋅ ⋅ ds B 1 ds
dD1
2
(A.38)
Rule for converting limits: 2
B Limits and exceptional limits for cant gradient in 6.6 shall be multiplied by W ⋅ . B 1 2
A.4.7 Rate of change of cant d D1/dt (Subclause 6.7 of the main body of the standard) The conversion rule for the limits for rate of change of cant is based on ride comfort for passengers.
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Roll velocity of the vehicle body φ , due to rate of change of cant, may be calculated with Formulae (A.39) and (A.40):
dD1 dt φ 1 =
(A.39)
dD dt φ =
(A.40)
e1
e
NOTE
Rate of change of cant deficiency
dI dt
, roll flexibility coefficient
sr and
tilt compensation factor of a tilt
system st (if used) also affect the roll velocity. This contribution is taken into account by the limits for rate of change of cant deficiency.
Assuming the same roll velocity, φ1 = φ , Formula (A.41) applies: dD1
= W ⋅
dt
dD dt
(A.41)
Rule for converting values: Limits and exceptional limits for rate of change of cant in 6.7, including the values governed by the footnotes, shall be multiplied by W .
A.4.8 Rate of change of cant deficiency dI 1/dt (Subclause 6.8 of the main body of the standard) The conversion rule for the limits for rate of change of cant deficiency is based on passenger comfort. Lateral jerk in the vehicle body may be calculated with Formulae (A.42) and (A.43):
da i1 dt
= (1 + s r1 ) ⋅
da q1 dt
dI1 dt ⋅g = ( 1 + s r1 ) ⋅ e1
dI dt da q da i = (1 + s r ) ⋅ = (1 + s r ) ⋅ ⋅ g dt
dt
dI 1 dt
=
1 + sr
⋅W⋅
1 + s r1
dI dt
(A.43)
e1
Assuming the same lateral jerk,
da i 1 dt
=
da i dt
(A.42)
, Formula (A.44) applies:
(A.44)
For sr1 = sr , Formula (A.44) may be simplified to Formula (A.45):
dI 1 dt
= W⋅
dI dt
(A.45)
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Where a transition curve is of substandard length with respect to the
dI 1 dt
criterion, this criterion may
be replaced with the criterion that the change of cant deficiency over its length shall be less than the upper limit for abrupt change of cant deficiency ΔI 1, as defined in A.4.9. Rule for converting values: Limits and exceptional limits for rate of change of cant deficiency in 6.8 shall be multiplied by W .
A.4.9 Abrupt change of curvature and abrupt change of cant deficiency ΔI 1 (Subclauses 6.10 and 6.11 of the main body of the standard) The conversion rule for the limits for abrupt change of cant deficiency is based on passenger comfort. The passenger comfort will be the same for the same values of abrupt changes of acceleration Δai. Hence: ∆I 1 =
1 + s r 1 + s r 1
⋅ W ⋅ ∆I
(A.46)
For sr 1 = sr , Formula (A.46) may be simplified to Formula (A.47): ∆I 1 = W ⋅ ∆I
(A.47)
Rule for converting values: Limits and exceptional limits for abrupt change of cant deficiency in 6.11, including the values governed by the footnotes, shall be multiplied by W .
A.4.10Other parameters (Subclauses 6.1, 6.9, 6.12, 6.13, 6.14, 6.15, 6.16 and 6.17 of the main body of the standard) The limits of these parameters are not gaugedependent. Limits and exceptional limits given i n the main part of the standard, Subclauses 6.1, 6.9, 6.12, 6.13, 6.14, 6.15, 6.16 and 6.17, are applicable also to a track gauge wider than 1 435 mm.
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Annex B (normative) Track alignment design parameter limits for track gauges wider than 1 435 mm
B.1 Scope This Annex defines the relevant limits for the track alignment design parameters to be applied for tracks laid with nominal track gauges wider than 1 435 mm. The limits have been derived, for the parameters covered in the main body of the standard, by application of the conversion rules specified in informative Annex A, rounded (to the more conservative side) to multiples of 5 mm. Some of the limits converted from the 1435 mm network have not been used in broad gauge applications. Hence, other more restrictive values can be applied by Infrastructure managers according to the network features, the rolling stock running on it, etc.
B.2 Requirements for a gauge of 1 520 mm and 1 524 mm B.2.1 General The limits defined in Subclauses B.2.2 to B.2.18 apply for tracks with a track gauge of 1 520 mm or 1 524 mm. Base values are: e1 = 1 585 mm; B1 = 2 085 mm.
B.2.2 Radius of horizontal curve R1 The lower limit for horizontal radius is not gaugedependent. The lower limit in 6.1 applies also for 1 520 mm and 1 524 mm gauges.
B.2.3 Cant D1 Upper limits for cant D1,lim, independent of horizontal radius R1, are specified in Table B.1. Table B.1 — Upper limits for cant D1,lim Normal limits
Exceptional limits
General
165 mm
190 mm a
Switches and crossings
125 mm
165 mm
a
Cant exceeding 165 mm can cause freight load displacement and deterioration of passenger comfort when a train stops or runs with low speed (high value of cant excess). Ontrack machines and vehicles with special loads with a high centre of gravity can become unstable. Therefore, an associated maintenance regime and other measures may be necessary (for example exclude certain types of freight traffic, avoid trains regularly stopping on such a curve, etc).
Upper limit for cant D1R,lim, as a function of horizontal radius R1, is specified in Table B.2.
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Table B.2 — Upper limit for cant D1R,lim as a function of horizontal radius R1 Normal limit a
Exceptional limit a D1R ,lim
( R 50m) 0,74mm/m
=
−
⋅
a
This limit may be relaxed provided that measures are taken to ensure safety, see EN 13848–5 or in the case of the diverging track of a turnout with an element of least 10 m length with constant cant on both side of the curve with small radius.
B.2.4 Cant deficiency I 1 General upper limits for cant deficiency I 1,lim are specified in Table B.3. Table B.3 — Upper limits for deficiency I 1,lim Normal limits a
Exceptional limits a
Nontilting trains V ≤
220 km/h
190 mm b
160 mm
220 km/h < V ≤ 300 km/h
160 mm b
300 km/h < V ≤ 360 km/h
105 mm b Tilting trains
80 km/h ≤ V ≤ 260 km/h c
290 mm
315 mm
a
It is common practice to apply different limits for cant deficiency to different categories of trains. It is assumed that every vehicle has been tested and approved according to the procedures in EN 14363 in conditions covering its own range of operating cant deficiency (denoted I adm in EN 14363). Examples of local limits are shown in informative Annex H. b
Trains complying with EN 14363, equipped with a cant deficiency compensation system other than tilt, may be permitted by the Infrastructure Manager to run with higher cant deficiency values. c
Currently, there are no lines in Europe used or planned where maximum speed for tilting trains exceeds 260 km/h.
For tracks with crossings in the outer rail and for expansion devices, there are more restrictive upper limits I 1CE ,lim, dependent on speed V , specified in Table B.4.
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Table B.4 — Upper limits for cant deficiency for tracks with crossings in the outer rail and for expansion devices I 1CE,lim Normal limits
Exceptional limits
Fixed common crossings V ≤
230 km/h
230 km/h < V ≤ 360 km/h
115 mm
Same as the normal limit in Table B.3
Not permitted
Not permitted
Fixed obtuse crossings 105 mm
Same as the normal limit in Table B.3
160 km/h < V ≤ 230 km/h
75 mm
Same as the normal limit in Table B.3
230 km/h < V ≤ 360 km/h
Not permitted
Not permitted
V ≤
160 km/h
Crossings with movable parts V ≤
230 km/h
230 km/h < V ≤ 360 km/h
135 mm
Same as the normal limit in Table B.3
80 mm
Same as the normal limit in Table B.3
Expansion devices 105 mm
Same as the normal limit in Table B.3
160 km/h < V ≤ 230 km/h
80 mm
Same as the normal limit in Table B.3
230 km/h < V ≤ 360 km/h
60 mm
Same as the normal limit in Table B.3
V ≤
160 km/h
B.2.5 Cant excess E 1 General upper limits for cant excess E 1,lim are specified in Table B.5. These limits apply for the regular speed of the slowest train on the line. Table B.5 — Upper limits for cant excess E 1,lim Normal limit
Exceptional limit
115 mm
155 mm
For tracks with crossings in the low rail and for expansion devices, there are more restrictive upper limits E 1CE ,lim, defined by Formula (B.1) and Table B.4: E 1CE ,lim
=
I 1CE ,lim
(B.1)
Requirements regarding changes in cant deficiency (B.2.6, B.2.9, B.2.12 and B.2.14) apply also for changes in cant excess.
B.2.6 Length of cant transitions LD1 and transition curves in the horizontal plane LK 1 Cant transitions should normally coincide with transition curves. However, it can be necessary to provide cant transitions in circular curves and straights. For cant transitions and transition curves the limits are as fo llows: — speed independent lower limits for lengths of transition curves LK 1,lim are specified in Table B.6;
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dD1 are specified in B.2.7; ds lim
— upper limits for cant gradient
dD1 are specified in B.2.8; and dt lim
— upper limits for rate of change of cant
dI 1 are specified in B.2.9. dt lim
— upper limits for rate of change of cant deficiency
Table B.6 — Lower limits for lengths of transition curves LK 1,lim Normal limit
Exceptional limit
20 m
0
dD1 dD1 , rate of change of cant and rate ds dt
For linear cant transitions and clothoids, cant gradient
dI 1 can be calculated according to Formulae (B.2)(B.4): dt
of change of cant deficiency dD1 ds dD1 dt
dI 1 dt
=
∆D1 LD
=
(B.2)
V ∆D1
⋅
qV
=
V ∆I 1
⋅
qV
LD
LK
(B.3)
(B.4)
where ΔD1
is the change of cant over the length LD, as defined in normative Annex K,
ΔI 1
is the change of cant deficiency over the length LK , as defined in normative Annex K,
V
is the speed in km/h and
qV
= 3,6 (km/h)/(m/s).
Formula (B.4) assumes that any cant transition curve coincides with a transition curve, LK = LD, and Formulae (B.2)(B.4) assume that the mathematical properties are constant over this length. Otherwise, the transition curves and the cant transitions shall be divided in parts (with constant properties) which are evaluated separately.
B.2.7 Cant gradient dD1/d s
dD1 are specified in Table B.7. ds
Upper limits for cant gradients
d D1 ds lim
Table B.7 — Upper limits for cant gradients
V ≤ 50 km/h V > 50 km/h a
40
Normal limits
Exceptional limits
2,55 mm/m
3,40 mm/m a 2,55 mm/m
According to EN 13848–5, a more restrictive limit for cant than the limit in Table B.2 can apply.
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EN 13803:2017 (E)
B.2.8 Rate of change of cant dD1/dt dD1 for linear and nonlinear cant transitions are specified dt lim
Upper limits for rate of change of cant in Table B.8 and Table B.9, respectively.
d D1 for constant cant gradients dt lim
Table B.8 — Upper limits for rate of change of cant Normal limits
Exceptional limits
Nontilting trains V ≤ 200 km/h I ≤ 169 mm
50 mm/s
70 mm/s a
169 mm < I ≤ 190 mm
50 mm/s
60 mm/s
Nontilting trains 200 km/h < V ≤ 360 km/h 50 mm/s
60 mm/s
Tilting trains V ≤ 200 km/h 75 mm/s
100 mm/s
Tilting trains 200 km/h < V ≤ 260 km/h b 60 mm/s a
70 mm/s
Where I < 160 mm and d I/ dt ≤ 70 mm/s, the exceptional limit for d D/dt may be raised to 85 mm/s.
b
Currently, there are no lines in Europe used or planned where maximum speed for tilting trains exceeds 260 km/h.
d D1 for nonlinear cant transitions dt lim
Table B.9 — Upper limits for rate of change of cant Normal limit
Exceptional limit V ≤ 300
km/h a 80 mm/s b
55 mm/s a
Currently, there are no lines in Europe used or planned where maximum speed on nonlinear cant transitions exceeds 300 km/h. b
Where the absolute value of second derivative of cant with respect to time (d2D/dt 2) is less than 155 mm/s 2 this limit may be raised.
B.2.9 Rate of change of cant deficiency dI 1/dt dI 1 for clothoids and for transition curves with dt lim
Upper limits for rate of change of cant deficiency
nonconstant gradients are specified in Table B10 and Table B.11, respectively.
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d I 1 for clothoids dt lim
Table B.10 — Upper limits for rate of change of cant deficiency Normal limits
Exceptional limits
Nontilting trains V ≤ 220 km/h I ≤
165 mm
165 mm < I ≤ 190 mm
55 mm/s
105 mm/s
55 mm/s
95 mm/s
Nontilting trains 220 km/h < V ≤ 300 km/h 55 mm/s
75 mm/s
Nontilting trains 300 km/h < V ≤ 360 km/h 30 mm/s
55 mm/s
Tilting trains V ≤ 225 km/h (WG15–4) 105 mm/s
190 mm/s
Tilting trains 225 km/h < V ≤ 260 km/h a 80 mm/s a
Currently, there are no lines in Europe used or planned where maximum speed for tilting trains exceeds 260 km/h.
d I 1 for transition curves dt lim
Table B.11 — Upper limits for rate of change of cant deficiency with nonconstant gradients Normal limits
Exceptional limits
Nontilting trains V ≤ 300 km/h 100 mm/s
125 mm/s
Nontilting trains 300 km/h < V ≤ 360 km/h 30 mm/s
55 mm/s Tilting trains V ≤ 225 km/h
105 mm/s
190 mm/s
Tilting trains 225 km/h < V ≤ 260 km/h a 100 mm/s
125 mm/s
a
Currently, there are no lines in Europe used or planned where maximum speed for tilting trains exceeds 260 km/h. Where a transition curve is of substandard length with respect to the
dI 1 dt
criterion, this criterion may
be replaced with the criterion that the change of cant deficiency over its length shall be less than the upper limit for abrupt change of cant deficiency Δ I 1, as defined in B.2.12.
B.2.10Length of constant cant between two linear cant transitions Li1 The lower limits for the length alignment elements Li1,lim are not gaugedependent.
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All limits in 6.9 apply also for 1 520 mm and 1 524 mm gauges.
B.2.11 Abrupt change of horizontal curvature An abrupt change of curvature may occur in close conjunction to switches and crossings, at alignment for low speeds (sidings etc.) or at small deviations in alignment within a limited length. It is unavoidable on at least one track of a turnout. In most other cases, transition curves should be used. For abrupt changes of curvature there are limits as follows: — upper limits for abrupt change of cant deficiency ΔI 1,lim are specified in B.2.12; — lower limits for length between two abrupt changes of curvature Lc1,lim in B.2.13; — lower limits for length between two abrupt changes of cant deficiency Ls1,lim in B.2.14.
B.2.12 Abrupt change of cant deficiency ΔI 1 An abrupt change of cant deficiency Δ I 1 occurs where there is an abrupt change of curvature. A tangent point with an abrupt change of cant deficiency generates disturbed vehicle dynamics. The magnitude of the abrupt change of cant deficiency is defined by the sign rules given in normative Annex K. Upper limits for abrupt change of cant deficiency Δ I 1,lim are specified in Table B.12. Table B.12 — Upper limits of abrupt change of cant deficiency (ΔI 1,lim)
V ≤
60 km/h
60 km/h < V ≤ 200 km/h
Normal limits
Exceptional limits
115 mm
135 mm a
105 mm
130 mm
200 km/h < V ≤ 230 km/h
85 mm
230 km/h < V ≤ 360 km/h
25 mm b
a
Where V ≤ 40 km/h and I  ≤ 75 mm both before and after an abrupt change of curvature, the exceptional limit for ΔI may be raised to 150 mm. b
The limit is aimed to be applicable for plain track. Currently, no turnouts are designed for higher speeds in the diverging track than 230 km/h.
Where there is an abrupt change of cant deficiency, some European railways use the principle of virtual transition described in informative Annex M. The values for abrupt change of cant deficiency, when based on the principle of virtual transition, shall also conform to the upper limits specified in Table B.12.
B.2.13 Length between two abrupt changes of horizontal curvature LC 1 The lower limits for the length alignment elements LC1,lim are not gaugedependent. All limits in 6.12 apply also for 1 520 mm and 1 524 mm gauge.
B.2.14 Length between two abrupt changes of cant deficiency L s1 The lower limits for the length alignment elements Ls1,lim are not gaugedependent. All limits in 6.13 apply also for 1524 mm gauge and are the same of Table B.13, however the conditions with ΔI values, inside Table 20, are changed because ΔI values are gaugedependent.
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Speeddependent limits for the factor qs,lim (m·h/km) are specified in Table B.13. Table B.13 — Lower limits of the factor q s,lim defining the minimum length between two tangent points with abrupt changes of cant deficiency (L s1,lim) Normal limits
Exceptional limits
V ≤ 70 km/h
0,20
0,10 a
70 km/h < V ≤ 100 km/h
0,20
0,15 b
100 km/h < V ≤ 360 km/h
0,25
0,19
a
Where ΔI ≤ 115 mm and V ≤ 50 km/h, qs,lim may be reduced to 0,08 m∙h/km.
b
Where ΔI ≤ 105 mm and V ≤ 90 km/h, qs,lim may be reduced to 0,10 m∙h/km.
B.2.15Track gradients p1 The limits for track gradients are not gaugedependent. All limits in 6.14 apply also for 1 520mm and 1 524 mm gauge.
B.2.16Vertical radius Rv 1 The lower limits for vertical radius are not gaugedependent. All limits in 6.15 apply also for 1 520 mm and 1 524 mm gauge.
B.2.17Length vertical curves Lv 1 The lower limits for length of vertical curves radius are not gaugedependent. All limits in 6.16 apply also for 1 520 mm and 1 524 mm gauge.
B.2.18 Abrupt change of track gradient Δ p1 The upper limits for abrupt change of track gradient are not gaugedependent. All limits in 6.17 apply also for 1 520 mm and 1 524 mm gauge.
B.3 Requirements for a gauge of 1 668 mm B.3.1 General The limits defined in the following Subclauses B.3.2 to B.3.18 apply for tracks with a track gauge of 1 668 mm. Base values are: e1 = 1 733 mm; B1 = 2 233 mm.
B.3.2 Radius of horizontal curve R1 The lower limit for horizontal radius is not gaugedependent. The lower limit in 6.1 applies also for 1 668 mm gauge.
B.3.3 Cant D1 Upper limits for cant D1,lim, independent of horizontal radius R1, are specified in Table B.14.
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Table B.14 — Upper limits for cant D1,lim Normal limits
Exceptional limits
General a
180 mm
205 mm b
Switches and crossings a
135 mm
185 mm
a
Further requirements for the cant along platforms are defined in TSI INF.
b
Cant exceeding 180 mm can cause freight load displacement and deterioration of passenger comfort when a train stops or runs with low speed (high value of cant excess). Ontrack machines and vehicles with special loads with a high centre of gravity can become unstable. Therefore, an associated maintenance regime and other measures may be necessary (for example exclude certain types of freight traffic, avoid trains regularly stopping on such a curve, etc).
Upper limit for cant D1R,lim, as a function of horizontal radius R1, is specified in Table B.15. Table B.15 — Upper limit for cant D1R,lim as a function of horizontal radius R1 Normal limit a
Exceptional limit a D1R ,lim
( R 50m) 0,9mm/m
=
−
⋅
a
This limit may be relaxed provided that measures are taken to ensure safety, see EN 13848–5 or in the case of the d iverging track of a turnout with an element of least 10m length with constant cant on both side of the curve with small radius.
B.3.4 Cant deficiency I 1 General upper limits for cant deficiency I 1,lim are specified in Table B.16. Table B.16 — Upper limits for cant deficiency I 1,lim Normal limits a
Exceptional limits a
Nontilting trains V ≤
220 km/h
175 mm
205 mm b
220 km/h < V ≤ 300 km/h
175 mm b
300 km/h < V ≤ 360 km/h
115 mm b
Tilting trains 80 km/h ≤ V ≤ 260 km/h c
315 mm
345 mm
a
It is common practice to apply different limits for cant deficiency to different categories of trains. It is assumed that every vehicle has been tested and approved according to the procedures in EN 14363 in conditions covering its own range of operating cant deficiency (denoted I adm in EN 14363). Examples of local limits are shown in informative Annex H. b
Trains complying with EN 14363, equipped with a cant deficiency compensation system other than tilt, may be permitted by the Infrastructure Manager to run with higher cant deficiency values. c
Currently, there are no lines in Europe used or planned where maximum speed for tilting trains exceeds 260 km/h.
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For tracks with crossings in the outer rail and for expansion devices, there are more restrictive upper limits I 1CE ,lim, dependent on speed V , specified in Table B.17. Table B.17 — Upper limits for cant deficien cy for tracks with crossings in the outer rail and for expansion devices I 1CE,lim Normal limits
Exceptional limits
Fixed common crossings V ≤
230 km/h
230 km/h < V ≤ 360 km/h
125 mm
Same as the normal limit in Table B.16
Not permitted
Not permitted
Fixed obtuse crossings 115 mm
Same as the normal limit in Table B.16
160 km/h < V ≤ 230 km/h
85 mm
Same as the normal limit in Table B.16
230 km/h < V ≤ 360 km/h
Not permitted
Not permitted
V ≤
160 km/h
Crossings with movable parts V ≤
230 km/h
230 km/h < V ≤ 360 km/h
150 mm
Same as the normal limit in Table B.16
90 mm
Same as the normal limit in Table B.16
Expansion devices 115 mm
Same as the normal limit in Table B.16
160 km/h < V ≤ 230 km/h
90 mm
Same as the normal limit in Table B.16
230 km/h < V ≤ 360 km/h
65 mm
Same as the normal limit in Table B.16
V ≤
160 km/h
B.3.5 Cant excess E 1 General upper limits for cant excess E 1,lim are specified in Table B.18. These limits apply for the regular speed of the slowest train on the line. Table B.18 — Upper limits for cant excess E 1,lim Normal limit
Exceptional limit
125 mm
170 mm
For tracks with crossings in the low rail and for expansion devices, there are more restrictive upper limits E 1CE ,lim, defined by Formula (B.5) and Table B.16: E 1CE ,lim
=
I 1CE ,lim
(B.5)
Requirements regarding changes in cant deficiency (B.3.6, B.3.9, B.3.12 and B.3.14) apply also for changes in cant excess.
B.3.6 Length of cant transitions LD1 and transition curves in the horizontal plane LK 1 Cant transitions should normally coincide with transition curves. However, it can be necessary to provide cant transitions in circular curves and straights. For cant transitions and transition curves the limits are as fo llows: — speed independent lower limits for lengths of transition curves LK 1,lim are specified in Table B.19;
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dD1 are specified in B.3.7; ds lim
— upper limits for cant gradient
dD1 are specified in B.3.8; and dt lim
— upper limits for rate of change of cant
dI 1 are specified in B.3.9. dt lim
— upper limits for rate of change of cant deficiency
Table B.19 — Lower limits for lengths of transition curves LK 1,lim Normal limit
Exceptional limit
20 m
0
dD1 dD1 , rate of change of cant and rate ds dt
For linear cant transitions and clothoids, cant gradient
dI 1 can be calculated according Formulae (B.6)(B.8). dt
of change of cant deficiency dD1 ds dD1 dt
dI 1 dt
=
∆D1 LD
=
(B.6)
V ∆D1
⋅
qV
=
LD
V ∆I 1
⋅
qV
LK
(B.7)
(B.8)
where ΔD1
is the change of cant over the length LD, as defined in normative Annex K,
ΔI 1
is the change of cant deficiency over the length LK , as defined in normative Annex K,
V
is the speed in km/h and
qV
= 3,6 (km/h)/(m/s).
Formula (B.8) assumes that any cant transition curve coincides with a transition curve, LK = LD, and Formulae (B.6)(B.8) assume that the mathematical properties are constant over this length. Otherwise, the transition curves and the cant transitions shall be divided in parts (with constant properties) which are evaluated separately.
B.3.7 Cant gradient dD1/d s dD1 are specified in Table B.20. ds lim
Upper limits for cant gradients
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d D1 ds lim
Table B.20 — Upper limits for cant gradients Normal limits
Exceptional limits a
2,65 mm/m
3,55 mm/m
V ≤ 50 km/h V > 50 km/h a
2,65 mm/m
According to EN 13848–5, a more restrictive limit for cant than the limit in Table B.15 can apply.
B.3.8 Rate of change of cant d D1/dt dD1 for linear and nonlinear cant transitions are specified dt lim
Upper limits for rate of change of cant
in Table B.21 and Table B.22, respectively.
d D1 for constant cant gradients dt lim
Table B.21 — Upper limits for rate of change of cant
Normal limits
Exceptional limits
Nontilting trains V ≤ 200 km/h I ≤ 185 mm
55 mm/s
80 mm/s a
185 mm < I ≤ 208 mm
55 mm/s
65 mm/s
Nontilting trains 200 km/h < V ≤ 360 km/h 55 mm/s
65 mm/s
Tilting trains V ≤ 200 km/h 85 mm/s
105 mm/s
Tilting trains 200 km/h < V ≤ 260 km/h b 65 mm/s a
80 mm/s
Where I < 175 mm and dI/ dt ≤ 80 mm/s, the exceptional limit for d D/dt may be raised to 95 mm/s.
b
Currently, there are no lines in Europe used or planned where maximum speed for tilting trains exceeds 260 km/h.
d D1 for nonlinear cant transitions dt lim
Table B.22 — Upper limits for rate of change of cant Normal limit
Exceptional limit V ≤ 300
60 mm/s
km/h a 85 mm/s b
a
Currently, there are no lines in Europe used or planned where maximum speed on nonlinear cant transitions exceeds 300 km/h. b
Where the absolute value of second derivative of cant with respect to time is less than 170 mm/s2 this limit may be raised.
(d2D/dt 2)
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B.3.9 Rate of change of cant deficiency dI 1/dt dI 1 for clothoids and for transition curves with dt lim
Upper limits for rate of change of cant deficiency
nonconstant gradients are specified in Table B.23 and Table B.24, respectively.
d I 1 for clothoids dt lim
Table B.23 — Upper limits for rate of change of cant deficiency Normal limits
Exceptional limits
Nontilting trains V ≤ 220 km/h I ≤
184 mm
184 mm < I ≤ 208 mm
60 mm/s
115 mm/s
60 mm/s
100 mm/s
Nontilting trains 220 km/h < V ≤ 300 km/h 60 mm/s
85 mm/s
Nontilting trains 300 km/h < V ≤ 360 km/h 30 mm/s
60 mm/s
Tilting trains V ≤ 225 km/h 115 mm/s
205 mm/s
Tilting trains 225 km/h < V ≤ 260 km/h a 90 mm/s a
Currently, there are no lines in Europe used or planned where maximum speed for tilting trains exceeds 260 km/h.
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d I 1 for transition curves dt lim
Table B.24 — Upper limits for rate of change of cant deficiency with nonconstant gradients Normal limits
Exceptional limits
Nontilting trains V ≤ 300 km/h 105 mm/s
135 mm/s
Nontilting trains 300 km/h < V ≤ 360 km/h 30 mm/s
60 mm/s
Tilting trains V ≤ 225 km/h 115 mm/s
205 mm/s
Tilting trains 225 km/h < V ≤ 260 km/h a 105 mm/s
135 mm/s
a
Currently, there are no lines in Europe used or planned where maximum speed for tilting trains exceeds 260 km/h.
Where a transition curve is of substandard length with respect to the
dI 1 dt
criterion, this criterion may
be replaced with the criterion that the change of cant deficiency over its length shall be less than the upper limit for abrupt change of cant deficiency ΔI, as defined in B.3.12.
B.3.10Length of constant cant between two linear cant transitions Li1 The lower limits for the length alignment elements Li1 are not gaugedependent. All limits in 6.9 apply also for 1 668 mm gauge.
B.3.11 Abrupt change of horizontal curvature An abrupt change of curvature may occur in close conjunction to switches and crossings, at alignment for low speeds (sidings, etc.) or at small deviations in alignment within a limited length. It is unavoidable on at least one track of a turnout. In most other cases, transition curves should be used. For abrupt changes of curvature there are limits as follows: — upper limits for abrupt change of cant deficiency ΔI 1,lim are specified in B.3.13; — lower limits for length between two abrupt changes of curvature Lc1,lim in B.3.14; — lower limits for length between two abrupt changes of cant deficiency Ls1,lim in B.3.15.
B.3.12 Abrupt change of cant deficiency ΔI 1 An abrupt change of cant deficiency Δ I 1 occurs where there is an abrupt change of curvature. A tangent point with an abrupt change of cant deficiency generates disturbed vehicle dynamics. The magnitude of the abrupt change of cant deficiency is defined by the sign rules given in normative Annex K. Upper limits for abrupt change of cant deficiency Δ I 1,lim are specified in Table B.25.
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Table B.25 — Upper limits of abrupt change of cant deficiency (ΔI 1,lim) Normal limits
Exceptional limits
V ≤ 60 km/h
125 mm
150 mm a
60 km/h < V ≤ 200 km/h
115 mm
140 mm
200 km/h < V ≤ 230 km/h
95 mm
230 km/h < V ≤ 360 km/h
25 mm b
a
Where V ≤ 40 km/h and I  ≤ 85 mm both before and after an abrupt change of curvature, the exceptional limit for ΔI may be raised to 170 mm. b
The limit is aimed to be applicable for plain track. Currently, no turnouts are designed for higher speeds in the diverging track than 230 km/h.
Where there is an abrupt change of cant deficiency, some European railways use the principle of virtual transition described in informative Annex M. The values for abrupt change of cant deficiency, when based on the principle of virtual transition, shall also conform to the upper limits specified in Table B.25.
B.3.13 Length between two abrupt changes of horizontal curvature LC 1 The lower limits for the length alignment elements LC1,lim are not gaugedependent. All limits in 6.12 apply also for 1 668 mm gauge.
B.3.14 Length between two abrupt changes of cant deficiency L s1 The lower limits for the length alignment elements Ls1,lim are not gaugedependent. All limits in 6.13 apply also for 1668 mm gauge, however the conditions with Δ I values, inside Table 19, are changed because ΔI values are gaugedependent. Speeddependent limits for the factor qs,lim (m·h/km) are specified in Table B.26. Table B.26 — Lower limits of the factor q s,lim defining the minimum length between two tangent points with abrupt changes of cant deficiency (L s1,lim) Normal limits
Exceptional limits
V ≤ 70 km/h
0,20
0,10 a
70 km/h < V ≤ 100 km/h
0,20
0,15 b
100 km/h < V ≤ 360 km/h
0,25
0,19
a
Where ΔI ≤ 125 mm and V ≤ 50 km/h, qs,lim may be reduced to 0,08 m∙h/km.
b
Where ΔI ≤ 115 mm and V ≤ 90 km/h, qs,lim may be reduced to 0,10 m∙h/km.
B.3.15 Track gradients p1 The limits for track gradients are not gaugedependent. All limits in 6.14 apply also for 1 668 mm gauge.
B.3.16 Vertical radius Rv 1 The lower limits for vertical radius are not gaugedependent. All limits in 6.15 apply also for 1 668 mm gauge.
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B.3.17Length vertical curves Lv 1 The lower limits for length of vertical curves radius are not gaugedependent. All limits in 6.16 apply also for 1 668 mm gauge.
B.3.18 Abrupt change of track gradient Δ p1 The lower limits for abrupt change of track gradient are not gauged ependent. All limits in 6.17 apply also for 1 668 mm gauge.
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Annex C (informative) Supplementary information about shape and length of transition curves
C.1 General The most common type of transition curve is the clothoid (sometimes approximated as a third degree polynomial, a “cubic parabola”), where curvature changes linearly with chainage. If it coincides with a cant transition, applied cant changes linearly with chainage. Hence, the cant gradient is constant along the transition curve, but changes abruptly at the beginning and end of the transition curve. However, there exist also other types of transition curves and cant transitions. The common characteristic is that the abrupt change of cant gradient at a tangent point is eliminated. Hence, the derivative of cant is continuous over a tangent point, but the second derivative of cant may change abruptly. For one of the transition curves/cant transitions, the Sine curve, also the second derivative of cant is continuous over a tangent point, but the third derivative of cant changes abruptly. Clause C.2 defines and presents some properties of the following transition curves and cant transitions: — Clothoid; —
Helmert curve, also known as Schramm curve;
—
Bloss curve;
— Cosine curve; — Sine curve, also known as Klein curve. Clause C.3 describes further analysis of the behaviour of a rigid vehicle on cant transitions – a track alignment taking into account the mass centre and the roll motion of a vehicle.
C.2 Definitions and properties of different transition curves and cant transitions C.2.1 Definitions In this clause, it is assumed that transition curve and the cant transition are of the same type and coincide. Hence, length of the cant transition ( LD ) equals the length of the transition curve ( LK ). Cant and curvature follow the same type of mathematical function, hence only the formula for cant is presented in Table C.1.
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Table C.1 — Definitions of cant transitions (and transition curves) Type of cant transition (and transition curve) Linear (Clothoid)
Helmert curve (Schramm curve)
Mathematical function for cant
( ) = D1 +
D s
s
⋅ ∆D
LD 2
s First half: D ( s ) = D1 + 2⋅ ⋅ ∆D L D 2 s Second half: D ( s ) = D1 + 1 − 2⋅ 1 − ⋅ ∆D L D
Bloss curve
Cosine curve
2
s s D ( s ) = D1 + 3 − 2 ⋅ ⋅ ⋅ ∆D L L D D 1 ⋅s ( ) = D1 + ⋅ 1 − cos ⋅ ∆D 2 L π
D s
Sine curve (Klein curve)
( ) = D1 +
D s
s
LD
D
−
1 2 ⋅ π
⋅ sin
2 ⋅ π ⋅ s LD
⋅ ∆D
C.2.2 Properties Peak values for first, second and third derivatives of cant (with respect to chainage), are presented in Table C.2. Cant and curvature follow the same type of mathematical function, hence only the derivatives for cant is presented in Table C.2. To calculate derivatives with respect to time, the first derivate shall be multiplied with speed (in metre per second), the second derivative shall be multiplied with speed in the power of two and the third derivative shall be multiplied with speed in the power of three. Table C.2 also presents approximate values (based on the small angle approximation) for the lateral shift which is created when a transition curve is inserted between two elements of constant curvature.
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Table C.2 — Certain properties for cant transitions and transition curves Type of cant transition First derivate Second derivate Third derivate Lateral shift (and transition curve) of cant of cant of cant (approximate) Linear (Clothoid)
∆D
Infinite
Infinite
LK
LD
Helmert curve (Schramm curve)
2⋅
Bloss curve
3 2
Cosine curve
π
2
Sine curve (Klein curve)
⋅
⋅
2⋅
∆D LD
∆D
LD ∆D LD
∆D LD
2
24
4⋅
LD
6⋅
2
2
⋅
2 ⋅ π ⋅
LK
2
Infinite
LK
2
LD
LK
2
∆D LD
Infinite
2
1
⋅
R1
2
40
∆D
R1
2
48
∆D LD
π
Infinite
∆D
1
⋅
1
⋅
R1
2
⋅
1
42,23 R1 2
4 ⋅ π ⋅
∆D LD
3
LK
2
⋅
1
61,21 R1
−
−
−
1 R2
1 R2
1 R2
−
−
1 R2
1 R2
The shape of the function for cant and curvature, and their derivatives are illustrated in Figures C.1C.7 (where l is either LD or LK ).
Key 1
cant and curvature
2
first derivative
3
second derivative (infinite)
Figure C.1 — Clothoid with linear cant transition — Normalized cant and curvature in the horizontal plane, normalized derivatives
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Key 1
cant and curvature
2
first derivative
3
second derivative
4
third derivative (infinite)
Figure C.2 — Helmert (Schramm) transition — Normalized cant and curvature in the horizontal plane, normalized derivative
Key 1
cant and curvature
2
first derivative
3
second derivative
4
third derivative (infinite)
Figure C.3 — Bloss transition — Normalized cant and curvature in the horizontal plane, normalized derivatives
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Key 1
cant and curvature
2
first derivative
3
second derivative
4
third derivative (infinite)
Figure C.4 — Cosine transition — Normalized cant and curvature in the horizontal plane, normalized derivatives
Key 1
cant and curvature
2
first derivative
3
second derivative
4
third derivative
5
fourth derivative (infinite)
Figure C.5 — Sine (Klein) transition — Normalized cant and curvature in the horizontal plane, normalized derivatives
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Key 1
clothoid with linear cant transition
2
Helmert (Schramm) transition
3
Bloss transition
4
cosine transition
5
sine (Klein) transition
Figure C.6 — Dimensionless first derivatives
Key 1
clothoid with linear cant transition (infinite)
2
Helmert (Schramm) transition
3
Bloss transition
4
cosine transition
5
sine (Klein) transition
Figure C.7 — Dimensionless second derivatives
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C.3 Further aspects that may be considered for a progressive track alignment design C.3.1 Background In conventional track alignment, lateral acceleration and lateral jerk is taken into account for a point at track level (proportional to cant deficiency and rate of change of cant deficiency). When the vehicle body is exposed to roll motions generated by cant gradients, lateral acceleration and lateral jerk for the mass centre of the vehicle is slightly different. If cant is 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, there will also be a minor influence on the vertical acceleration of the mass centre of the vehicle. This effect can be eliminated by raising one rail and lowering the other rail in the same proportion.
C.3.2 Progressive track alignment design C.3.2.1
General
Lateral acceleration and lateral jerk are here described for a rigid vehicle travelling along a track without flexibility. Roll motions generated by cant gradients can be quantified, and also their influence on lateral motions of the mass centre at the assumed height h above track level. Therefore, the transition curve in the horizontal projection acquires a shape to compensate for the lateral displacement of the mass centre due to roll motions. A continuous function can be achieved for the noncompensated lateral acceleration at the height h . Track alignment starts with a specified function for the total noncompensated lateral acceleration at the alignment design height h . The total noncompensated lateral acceleration at the height h , the Froudeangle β Q (see C.3.2.4) and the equilibrium cant follow the same function as the cant, which has an influence on the shape in the horizontal projection of the track centre line. The method remains the same for “outswinging” transition curves, which start with a sli ght reverse curvature. Where cant is constant, all geometric criteria remain unchanged relative to the normative part of the text. C.3.2.2 Angular acceleration around roll axis
Angular acceleration α around roll axis is proportional to the second derivative (with respect to time) of cant. If expressed in the unit radians/s 2, it can be calculated by dividing the second derivative of cant with the distance between the nominal centre points of the two contact patches of a wheelset ( e ). In Formula (C.1), e 1500 mm for 1435 mm gauge. For other gauges, see normative Annex B. =
2
d D ds
2
α =
e qV ⋅
2
(C.1)
where qV
= 3,6 km/h/(m/s)
As a limit for roll acceleration
α
lim
≈
0,1 rad/s2 can be chosen. Together with limited noncompensated
lateral and vertical acceleration, this limits acceleration field everywhere within t he vehicle. C.3.2.3 Angular jerk around roll axis
Angular jerk α around roll axis is proportional to the third derivative (with respect to time) of cant. If expressed in the unit radians/s3, it can be calculated by dividing the third derivative of cant with the
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distance between the nominal centre points of the two contact patches of a wheelset ( e ). In Formula (C.2), e = 1 500 mm for 1 435 mm gauge. For other gauges, see normative Annex B. d
3
ds
D
=
3
α e ⋅ qV 3
(C.2)
where = 3,6 km/h/(m/s)
qV
This condition does not permit jumps in the second local derivative of cant, nor, if proportionality between horizontal curvature and cant, in the second local derivative of curvature either. As a limit for lim 0,2 rad/s3 can be chosen. roll jerk α ≈
C.3.2.4
Noncompensated lateral acceleration
An additional term for lateral acceleration for a mass centre of a rigid vehicle can be calculated by multiplying the angular acceleration around roll axis with the assumed height h of the mass centre above track level. The angle β Q between the normal to the track plane and the resultant noncompensated lateral acceleration in the car body ( aQ ) represents a dimensionless W. Froude number defined for all track guided systems and shall be limited everywhere along the track. In Formula (C.3), e = 1 500 mm for 1 435 mm gauge. For other gauges, see normative Annex B. β Q
2 h d 2D V D a Q lim I lim = = ⋅ κ H + ⋅ ⋅ − ≤ = g g e ds 2 qV e g e
aQ
1
(C.3)
where qV
= 3,6 km/h/(m/s) and
κ H
is horizontal curvature (1/m)
The limit for cant deficiency is specified i n 6.3, Tables 7 and 8. Outside a cant transition, e.g. if cant is constant as normally in a circular curve, the second derivative of cant in Formula (C.3) disappear. Hence, equation and condition are reduced to the formulae in the main body of this European Standard. C.3.2.5
Noncompensated lateral jerk
An additional term for lateral jerk for a mass centre of a rigid vehicle, can be calculated by multiplying the angular jerk around roll axis with the assumed height h of the mass centre above track level. In Formula (C.4), e = 1 500 mm for 1 435 mm gauge. For other gauges, see normative Annex B. 2 d 3 da κ 1 d 1 dD h D V H ⋅ V ≤ 1 ⋅ Q = ⋅ = ⋅ + ⋅ ⋅ − ⋅ g ds e ds 3 qV e ds qV g dt dt g dt
d β Q
1
daQ
where qV
60
= 3,6 km/h/(m/s) and
1 dI = ⋅ lim e dt lim
(C.4)
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d κ H
is the derivate of horizontal curvature with respect to chainage (1/m2)
ds
The limit for rate of change of cant deficiency is specified in 6.8, Table 16. C.3.2.6
Vertical acceleration and vertical jerk
The local vertical acceleration normal to the horizontal plane is the only kinematic criterion identical to that of the normative part of this European Standard. Limits for vertical acceleration may be derived from 6.15, Table 23. For improved comfort, especially if high vertical accelerations are permitted at certain locations, the vertical jerk normal to the horizontal plane can be limited by using vertical transition curves. Then jerk field is limited everywhere within the vehicle.
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Annex D (informative) Constraints and risks associated with the use of exceptional limits
For certain parameters, this European Standard also specifies exceptional limits less restrictive than normal limits, which represent the least restrictive limits applied by any European railway. For those parameters, the use of values above limits up to the exceptional limits results in a reduced level of comfort for the passengers and can lead to higher track maintenance costs. Therefore, unnecessary use of those values should be avoided. It is permissible to use the exceptional limits specified in this standard if use of the limits incurs unacceptable costs in achieving the desired speed. However, every effort should be made to design the alignment with substantial margin to the limits. The exceptional limits for cant deficiency are only acceptable for certain designs of vehicles and even then, it will lead to lower comfort levels for the passengers and almost certainly higher maintenance costs. Switches and crossings are more susceptible to the dynamic influences at higher speeds especially within curved layouts and, therefore, the consequences of using values close to exceptional limits are greater than in comparable conditions of the plain track. Due to the constructional complexity of switch and crossing units, the economic consequences of using high dynamic values or not optimizing the design become very important. Increased wear on track components causes more rapid deterioration of track quality, increases track maintenance, and could result in poor reliability of track installations. The constraints and risks associated with the use of design values close to the exceptional limits are dependent upon the types of vehicles using the t rack and the traffic density. The interaction between the vehicles and switch and crossing layouts, or other alignment configurations with abrupt change of cant deficiency is complex. Currently there are no international specifications for the homologation of vehicles for such conditions and for very small horizontal radii. In horizontal curves with very small radii, the following factors could also have an increased influence on the derailment risk for different vehicles: — lubrication conditions at the wheelrail interface; — stiffness of primary and secondary suspension; — longitudinal forces within the train consist; — entry angle at the switch toe.
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Annex E (informative) Evaluation of conditions at the toe of a switch
E.1 General EN 132323 specifies speeddependent upper limits for the angle of attack α (angle between the wheel and the rail). For plain track in front of a switch, EN 132323 defines the angle of attack as a sum of three terms: — ψ1 which is due to the play in the roller bearings and primary suspension (vehicle dependent); — ψ2 which is due to the play between the wheels and the rails (depending on gauge widening, wheel profiles and wheel base); — ψ3 which is due to the horizontal alignment (depending on wheel base and horizontal curvature). For switches, there is an entry angle θ at the tip of the switch. The entry angle is especially large for intersecting switches. EN 132323 specifies upper limits for the entry angle. Where there is a horizontal curve in front of a switch, in the same direction as the switch radius, Formula (E.1) applies: a = θ +ψ 1 +ψ 2 +ψ 3
(E.1)
Consequently, the horizontal alignment in front of a switch tip should generate an angle ψ3 according to Formula (E.2): ψ 3 ≤ a lim − θ −ψ 1 − ψ 2
(E.2)
E.2 Method based on effective radius The cant deficiency for the effective radius at the switch toe (Rs may be used as to define permissible speed over the diverging track in an intersecting switch. The effective radius at a switch toe, when the switch is placed on a straight track, is obtained by considering the offset between the toe and chord equal to the distance between bogie centres (Lb) as a versine (v ), see Figure E.1. The effective radius at the switch toe is defined according to Formula (E.3): Rs
Lb =
2
8 v
(E.3)
⋅
where Rs, Lb and v
are in metres.
The length of chord Lb is usually equal to the shortest distance between the bogie centres of passenger coaches operating over a route or railway (see informative Annex M). If the switch is placed in a curved track of radius defined according to Formula (E.4) or (E.5):
RI,
then the effective radius at the switch toe (R' s) is
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—
when the switch toe is of type inside curved switch; R'S
—
=
RS ⋅ R I RS
+R
(E.4)
I
when the switch toe is of the type outside curved switch; R' S
RS R I ⋅
=
RS
−
RI
(E.5)
NOTE 1 An inside curved switch is always of similar flexure, while an outside curved switch may be considered of similar flexure (Rs > RI), contra flexure (Rs < RI), or straight ( Rs = RI).
The equivalent cant deficiency I s can be calculated according to Formula (E.6) or (E.7): — for a switch placed on a straight IS
=
C
V
2
RS
−
D
(E.6)
— for a switch placed on a curve IS
=
C
V
2
R' S
−
D
(E.7)
where C D
NOTE 2
= 11,8 mm∙m∙h2/km2 and is the cant (mm), which can be either positive or negative. Negative values for I s can occur, indicating cant excess.
With this method an upper limit of 125 mm is used for the absolute value of I s. The virtual rate of change of cant deficiency for the effective radius at the switch toe is not taken into consideration when determining the maximum permissible speed over the diverging track in switch and crossing layouts.
Key 1
switch toe
Figure E.1 — Parameters for calculating the effectiv e radius at a switch toe
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Annex F (informative) Design considerations for switch and crossing units
F.1Examples of common switch and crossing units Certain common types of turnouts are shown in Figures F.1 to F.4.
Key X chainage Y curvature
Figure F.1 — Rails and horizontal curvature for the diverging track of a natural turnout with curved common crossing
Key X chainage Y curvature
Figure F.2 — Rails and horizontal curvature for the diverging track of a natural turnout with straight common crossing Characteristic for a natural turnout is the constant radius through the switch panel and the closure panel.
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Key X chainage Y curvature
Figure F.3 — Rails and horizontal curvature for the diverging track of a circular curve turnout (composite turnout) with straight common crossing Characteristics for a circular curve turnout are a constant radius through the switch panel and another constant radius (smaller or larger) through the closure panel.
Key X chainage Y curvature
Figure F.4 — Rails and horizontal curvature for the diverging track of a transitioned turnout with straight common crossing Characteristic for a transitioned turnout is the use of transition curves with increasing and/or decreasing curvature. Due to geometrical constraints, there will always be an abrupt change of curvature at the tip of the switch blades. Certain transitioned turnouts also have an abrupt change of curvature at the end of the turnout. The length of the circular portion of the curve may be zero. Also the length of the straight at the end of the turnout may be zero, in that case the common crossing will be curved. In a turnout with a curved diverging track through the crossing panel, as in Figure F.1, the crossing, check rail, and other components are subjected to higher forces due the cant deficiency on the diverging track. The alignment of the diverging track through the crossing panel of a turnout should, wherever
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possible without introducing additional abrupt changes of curvature, be straight, as shown in Figures F.2 to F.4. The criteria for abrupt change of curvature, abrupt change of cant deficiency and rate of change of cant deficiency are defined in Clause 6.
F.2Use of diamond crossings, diamond crossings with slips and tandem turnouts The use of diamond crossings, diamond crossings with slips, and tandem turnouts in tracks with high speeds, or high axle loads should be avoided. The accumulation of discontinuities in the running plane increases the dynamic wheel/rail forces and, consequently, higher maintenance costs are incurred.
F.3Switch and crossing units on, or near, underbridges When the expandable length of a bridge deck is greater than 30 m to 40 m, switch and crossing units should not be installed in lengths of track affected by movements at the expansion joint in the bridge deck. If this is unavoidable, a detailed analysis of the interaction between the bridge structure and the switch and crossing unit should be carried out. The use of switch and crossing units across expansion joints in bridge decks is normally not possible. Over massive viaducts, without moveable bearings, no such restrictions have to be taken into consideration.
F.4 Abutting switch and crossing units When switch and crossing units are to follow each other, the distance between units should be such that: —
the switch and crossing units are of nominal lengths, and a practical length of rail can be installed between the two switch and crossing units;
—
the bearers of the first switch and crossing unit do not interfere with bearers of the next switch and crossing unit;
—
distances between the bearers and sleepers (where used) are within the tolerances in the appropriate track design standard.
The criteria for distances between abrupt change of curvature and abrupt change of cant deficiency are defined in Clause 6.
F.5Switch and crossing units on horizontal curves Ideally, switch and crossing units should be placed on straight through tracks. Where a switch and crossing unit is placed on a horizontal curve, the bending of the components to 1 1 match the curvature of the firstly designed track ( ), the curvature of the second track ( ) is RI
affected. The exact value the curvature of the second track (
R II
1 R II
) depends on the principles for
lengthening and shortening the rails on the closure panel. An approximate estimation of the curvature of the second track (
1 R II
) is based on the superposition of curvatures (according to the small angle
approximation). Formula (F.1) is applicable for an inside curved switch and crossing unit and Formula (F.2) is applicable for an outside curved switch and crossing unit:
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1
R II
≈
1 R II
1
RI
+
1 ≈
RI
1
R0 1
−
R0
(F.1)
(F.2)
where 1
R0
is the curvature (m −1) of the diverging track of the switch and crossing unit in the version for straight track 1
NOTE 2
An inside curved switch and crossing unit is of similar flexure. An outside curved switch and crossing
unit can be of similar flexure (
RI
1
RI
and
1
For transition curves,
R0
,
1
NOTE 1
>
R II
1
R0
are the magnitudes of the local curvatures.
), straight (
1
RI
=
1
R0
) and/or contra flexure (
1
RI
<
1
R0
).
(See also EN 13232–1 for definitions.)
The approximate estimation of the magnitude of the curvature
1
R II
is useful for checking the criteria for
horizontal radius, cant deficiency, cant excess, and distances between abrupt changes of curvature and distances between abrupt changes of cant deficiency according to Clause 6. It should not be used in the alignment calculation for settingout data.
F.6Switch and crossing units on canted track Where a switch and crossing unit is used on a canted track, the influence of the cant on track distance and deflection angle at the last bearer (as quantified in the horizontal plane) may be taken into consideration. A correction factor f D, applicable both to track distance and tangent for deflection angle at the last bearer is defined by Formula (F.3):
D e
f D = cos arcsin
(F.3)
where D
is cant at the last bearer and
e
is the distance between the nominal centre points of the two contact patches of a wheelset (e.g. about 1 500 mm for track gauge 1 435 mm).
The use of switch and crossing units in tracks with cant gradients should be avoided. The torsional stiffness of a turnout depends upon characteristics such as rail profile and type of crossing. Furthermore, there is a considerable variation between the torsional stiffness of a switch panel and a crossing panel. The situation is more complex if the start and/or end of a cant gradient is within the length of the switch and crossing unit. A detailed analysis should be carried out to establish the feasibility of using a switch and crossing unit on a cant gradient.
F.7Vertical alignments and switch and crossing units Where a switch and crossing unit is used on a track gradient, the influence of the gradient on the length of the unit and deflection angle at the last bearer (as quantified in the horizontal plane) may be taken
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into consideration. A correction factor f L, applicable to longitudinal distance, and a correction factor f p, applicable to tangent for deflection angle at the last bearer are defined by Formulae (F.4)(F.5). f L
=
f p
=
(
cos arctan
( p))
1
(
cos arctan
( p ) )
(F.4)
(F.5)
where p
is the track gradient
Within the central area of a crossover, the vertical alignments of all tracks shall enable the rails to be in the same running plane. For a canted common crossing, there will be a significant correction term for the track levels at the last bearer, defined by Formula (F.6) for an outside curved switch and crossing unit and Formula (F.7) for an inside curved switch and crossing unit: ∆ z = ∆y ⋅
D e
∆ z = −∆y ⋅
D e
(F.6)
(F.7)
where Δ z
is the correction term for track levels (m),
Δ y
is the track distance for a noncanted last bearer (m),
D
is cant at the last bearer (mm) and
e
is the distance between the nominal centre points of the two contact patches of a wheelset (e.g. about 1 500 mm for track gauge 1 435 mm).
For a canted common crossing, there will also be a significant correction term for the track gradients at the last bearer, defined by Formulae (F.8)(F.11): ∆ p =
∆ p =
∆ p =
∆ p =
D dy ⋅
e ds D dy ⋅
e ds D dy ⋅
e ds D dy ⋅
e ds
+
−
+
+
∆y
e ∆y
e ∆y
e ∆y
e
⋅
⋅
⋅
⋅
dD ds dD ds dD ds dD ds
(F.8)
(F.9)
(F.10)
(F.11)
where Δ p
is the correction term for track gradients (),
Δ y
is the track distance for a noncanted last bearer (m),
D
is cant at the last bearer (mm),
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is tangent for the deflection angle (for an noncanted last bearer),
dy ds
is cant gradient (), and
dD ds
= 1 500 mm Formula (F.8) is applicable for a facing outside curved turnout and a trailing inside curved turnout, on a cant transition with increasing cant. e
Formula (F.9) is applicable for a facing outside curved turnout and a trailing inside curved turnout, on a cant transition with decreasing cant. Formula (F.10) is applicable for a facing inside curved turnout and a trailing outside curved turnout, on a cant transition with decreasing cant. Formula (F.11) is applicable for a facing inside curved turnout and a trailing outside curved turnout, on a cant transition with increasing cant. Due to the cone effect, the vertical bending of the track components does not correspond to the vertical curvature in the profiles of the two tracks. To calculate the bending curvature, perpendicular to the track plane a correction term is defined by Formula (F.12): ∆
1 R v
=
D e
⋅
1 R
(F.12)
where ∆
1
is the correction term for vertical bending curvature (m −1),
R v
D
is cant (mm),
R
is the horizontal radius (m), and
e
is the distance between the nominal centre points of the two contact patches of a wheelset (e.g. about 1 500 mm for track gauge 1 435 mm)
For a concave vertical curve, the correction term
∆
1 R v
is added to vertical curvature
profile of the track, while for a convex vertical curve, the correction term vertical curvature
1
R v
1 R v
Rv
of the vertical
is subtracted from
of the vertical profile of the track. The correction may be taken into account
when applying the criteria for vertical radius in 6.15.
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Annex G (informative) Examples of applications
G.1 General This annex presents examples of applications of rules and limits in this standard. The purpose of the examples is to clarify the application of certain normative rules. However, all rules and limits in Clause 6 apply.
G.2 Example of crossover on horizontal curve Figure G.1 illustrates the rails and the curvature of a crossover between two through tracks.
Key X
chainage
Y
curvature
1
curvature function for the diverging track
2
tangent point with abrupt change of curvature
3
tangent point with abrupt change of curvature
4
intermediate element
5
tangent point with abrupt change of curvature
6
tangent point with abrupt change of curvature
7
fixed common crossing, noncontinuous rail in the through track
8
fixed common crossing, noncontinuous rail in the diverging track
9
fixed common crossing, noncontinuous rail in the diverging track
10
fixed common crossing, noncontinuous rail in the through track
Figure G.1 — Rails in the horizontal plane and curvature function for the diverging track in the crossover, turnouts with originally curved common crossings Requirements for abrupt change of cant deficiency ΔI apply for tangent point 2, 3, 5 and 6. Requirements for intermediate element Ls apply for the length of element 4.
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The requirements regarding cant deficiency for noncontinuous rails I CE apply for fixed common crossings at locations 7 and 9. The requirements regarding cant excess for noncontinuous rails E CE apply for a fixed common crossing at location 10. For a fixed crossing at location 8, the sign of the curvature decides whether I CE,lim or E CE,lim applies: — if the crossing is on the outer rail of the diverging track, I CE,lim applies; and — the diverging track is straight, or the crossing is on the inner rail of the diverging track, E CE,lim applies. If at least one radius is less than 213 m, the buffer locking criterion according to normative Annex N shall be checked.
G.3 Example of bilinear cant transition Figure G.2 illustrates a bilinear cant transition. The dotted lines represent the level of the left rail compared to the level of the right rail. (A common type of bilinear cant transition is the cant transition on a reverse curve.)
Key X
chainage
Y
level of left rail compared to right rail
1
constant cant
2
tangent point for cant
3
constant cant gradient
4
tangent point for cant
5
constant cant gradient
6
tangent point for cant
7
constant cant
Figure G.2 — Level of left rail compared to right rail on a bilinear cant transition Since the cant gradient on the first part of the transition (3), is not the same as on the second part (5), the two different parts shall be evaluated separately. The first part includes the change of cant Δ D from tangent point 2 to tangent point 4, and the corresponding length LD between those two points. The second part includes the change of cant ΔD from tangent point 4 to tangent point 6, and the corresponding length LD between those two points.
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The same principle also applies where tangent point 4 has a cant value other than zero. The change of cant ΔD and the length change of cant
dD dt
LD are
used in the calculation of cant gradient
dD ds
and rate of
.
The same principle applies for the evaluation of rate of change of cant d eficiency
dI dt
.
G.4 Example where a cant transition is designed without a coinciding transition curve Figure G.3 illustrates an example where a cant transition is designed without a coinciding transition curve. The solid lines represent cant, and the dotted lines represent curvature. (The layout may be arranged after a canted turnout where there is not space for a transition curve in the diverging track after the last bearer, which can be assumed to be placed at tangent point 3 in the figure).
Key X
chainage
Y
cant and curvature, respectively
1
constant cant
2
constant curvature
3
tangent point with abrupt change of curvature
4
tangent point for cant
5
constant curvature
6
tangent point with abrupt change of curvature
7
constant curvature
8
constant cant gradient
9
tangent point for cant
10
constant cant
Figure G.3 —Cant and curvature for a layout where a cant transition is not coinciding with a transition curve The cant transition has constant properties from tangent point 4 to tangent point 9. Therefore, change of cant ΔD can be calculated from tangent point 4 to tangent point 9, and the corresponding length LD between those two points.
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The change of cant ΔD and the length change of cant
dD dt
LD are
used in the calculation of cant gradient
dD ds
and rate of
.
The requirements regarding abrupt change of cant deficiency ΔI apply for tangent points 3 and 6. Cant excess and cant deficiency shall be checked at all local maxima, i.e. along the constant curvature 2, at tangent point 4, immediately before and after tangent point 6 and immediately after tangent point 9.
G.5 Example of substandard transition curve Figure G.4 illustrates the curvature of a transition curve located near an abrupt change of curvature.
Key X
chainage
Y
curvature
1
constant curvature
2
tangent point for transition curve
3
tangent point for transition curve
4
tangent point with abrupt change of curvature
5
constant curvature
Figure G.4 —Curvature function where a transition curve is located near an abrupt change of curvature If the transition curve from tangent point 2 to tangent point 3 fulfils the requirement with respect to rate of change of cant deficiency
dI dt
, there is no requirement for the length
Ls for
the intermediate
element from tangent point 3 to tangent point 4. (For a turnout partly or fully placed on a transition curve, tangent point 4 may be located even between tangent point 2 and tangent point 3.) However, if the transition curve does not fulfil the requirement with respect to rate of change of cant deficiency
dI dt
, the upper limit for abrupt change of cant deficiency ΔI lim applies for the change of cant
deficiency from tangent point 2 to tangent point 3. Furthermore, the requirements for the length between abrupt changes of curvature Ls apply for the length of the intermediate element from tangent point 3 to tangent point 4. Alternatively, the total change of cant deficiency from curvature 1 to curvature 5 shall be less than the limit for abrupt change of cant deficiency ΔI lim. In all cases, the upper limit for abrupt change of cant deficiency ΔI lim applies for the change of cant deficiency at tangent point 4.
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If at least one radius is less than 213 m, the buffer locking criterion according to normative Annex N shall be checked. The principles apply also for cases where the alignment element from tangent point 3 to tangent point 4 is a circular curve.
G.6 Example where several alignment elements forms an intermediate length Figure G.5 illustrates the curvature where the two intermediate elements together fulfil the length requirement of an intermediate element. The situation is common for crossovers where one or both turnouts are placed on horizontal curves.
Key X
chainage
Y
curvature
1
constant curvature
2
tangent point with abrupt change of curvature
3
constant curvature
4
tangent point with abrupt change of curvature
5
constant curvature
6
tangent point with abrupt change of curvature
7
constant curvature
Figure G.5 —Curvature function where a two short elements together fulfils the requirement for an intermediate element The total length from tangent point 2 to tangent point 6 may be used for the evaluation of the requirement, provided that:
Ls
— the change of cant deficiency from curvature 1 to curvature 5 does not exceed the upper limit for abrupt change of cant deficiency ΔI lim; and — the change of cant deficiency from curvature 3 to curvature 7 does not exceed the upper limit for abrupt change of cant deficiency ΔI lim. If at least one radius is less than 213 m, the buffer locking criterion according to normative Annex N shall be checked. The principles apply also for cases where an intermediate alignment elements is a transition curve, provided that rate of change of cant deficiency
dI dt
does not exceed the upper limit.
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Annex H (informative) Examples of local limits for cant deficiency
In Europe, it is common practice to apply different limits for cant deficiency to different categories of trains. It is assumed that every vehicle has been tested and approved according to the procedures in EN 14363 in conditions covering its own range of operating cant deficiency. Table H.1 shows certain examples of local limits for cant deficiency. Table H.1 — Certain examples of limits for cant deficiency for 1435 mm gauge Train categories / line categories
Limits
France and Belgium (for speed above 300 km/h)
80 mm
Category A vehicles in Italy
92 mm
Austria, Czech Republic, Sweden and Spain (freight vehicles, old passenger coaches)
100 mm
Freight vehicles in UK
110 mm
Category B vehicles in Italy. Freight vehicles in Switzerland
122 mm
Passenger vehicles in Austria and Czech Republic. Freight vehicles in Germany and France. Passenger and freight vehicles in Belgium. Freight vehicles and certain passenger vehicles in Denmark
130 mm
Norway and Spain a. Passenger vehicles in Czech Republic, Denmark, Germany, Switzerland and UK
150 mm
Category C vehicles in Italy. Passenger and certain freight vehicles in Sweden
153 mm
Passenger vehicles in Portugal a
155 mm
Normal passenger trains and light freight trains in France. Certain passenger vehicles in Denmark and Norway.
160 mm
Certain vehicles in France
180 mm
Tilting trains in Sweden
245 mm
Tilting trains in Czech Republic
270 mm
Tilting trains in Italy, Norway, Portugal a and Switzerland
275 mm
Tilting trains in Germany and UK
300 mm
a
For Portugal and Spain, the limits here are expressed as an equivalent limit for 1 435 mm gauge.
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Annex I (informative) Considerations regarding cant deficiency and cant excess
I.1 Introduction The correct contact between wheels and rails is necessary to maintain safe operation (see EN 14363). Three main causes of failure are: —
wheel climb;
—
vehicle overturning; and
—
exceeding the lateral strength limit of a track under loading (Prud'homme limit),
These causes are related to cant deficiency and cant excess, as well as curve radius and twist (see EN 138481 and EN 138485).
I.2 Cant deficiency The lateral forces in the wheel/rail interface may be divided into two components: — the quasistatic forces, which are related to horizontal radius, cant deficiency and axle load; — the dynamic forces, which are related to track quality, stiffness variations, vehicle characteristics and speed. Vehicles with special mechanical characteristics (low axle load, reduced unsprung masses, low roll coefficient), may be allowed to operate over higher cant deficiencies than conventional rolling stock. For considerations regarding comfort for passengers, see informative Annex J.
I.3 Cant excess Cant excess results in higher quasistatic vertical forces on the low rail. Lateral wheel/rail forces on the low rail increase with vertical wheel/rail forces. At high value of cant excess, wheelsets are displaced closer to the inner rail. The rolling radius difference will not fit the difference in rolling distance for left and right wheel, which leads to rail corrugation. Consequently, rail wear and forces on the fastening system can increase. Cant excess also influence the wheel climb criterion.
I.4 Wheel climb criterion Wheel climb is a derailment caused by the fact that a wheel, usually the wheel tread on the outer rail of a curve, leaves the rail head and rises above it. The wheel/rail interface is governed by friction forces, and the derailment mode is characterized by the
Y Q
ratio, where Y is the lateral wheel/rail force and Q
the vertical wheel/rail force on the wheel.
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Small radius, high cant (high cant excess), track twist and high friction in the wheel/rail interface increase the risk for wheel climb.
I.5 Vehicle overturning Overturning conditions result when a vehicle at high cant deficiency initiates a rotation around the outer rail. The determining criterion for this risk is the vertical wheel/rail force on the inner rail. The likelihood of this type of event occurring with nontilting vehicles is small since the upper limits for cant deficiency is small, due to the fact that the limit of the lateral track shift forces is usually reached at lower cant deficiency values. However, for tilting train operation, the combination of lateral inertia forces and the forces generated from cross wind can result in zero vertical forces of the inner wheels. EN 14363 describes the necessary procedure and the limits for the defined socalled “Overturning criterion”. Specifications for the influence of cross wind are in EN 140676 and in the TSI INF, and characteristic wind curves are defined in the HighSpeed Rolling Stock TSI.
I.6 The lateral strength of a track under loading (Prud'homme limit ) If lateral (quasistatic and dynamic) wheel/rail forces are too high, the forces will cause permanent lateral displacements of the track. These track geometrical defects will grow with traffic. This process can lead to the derailment of a vehicle. This limit of the lateral track strength is expressed in the form of the corresponds to the upper limit for the various types of track tested.
Prud'homme
limit which
Since the Prud'homme limit applies to freshlytamped track, temporary speed restrictions can be applied during the track consolidation period. Track components (rail profile, type of sleeper, type of fastening, ballast characteristics) and other factors as track consolidation after tamping, thermal forces in rails, proximity of two wheelsets, dynamic vertical wheel/rail forces) influence the resistance to lateral track displacement.
I.7 Cant deficiency at switch and crossing layouts on curves Because of the constructional discontinuities in the running edge at the switches and the influences of the check rails or wing rails at the crossing nose, the dynamic behaviour and the peak values of the lateral wheel/rail forces are higher than in the plain track. These situations can be critical when the switch and crossing layouts are installed in tracks with high cant deficiencies. Despite the lower axle loads of tilting t rains, the level of such peak forces can be higher, since the speed is higher than for conventional trains. In order to avoid damage to either track or wheel, the upper limit for cant deficiency for tilting trains on curves with switches and crossings or other similar features, such as expansion devices, should be lower than the general limit for cant deficiency. For the verification of the maximum permissible speed and by respecting the diversity of the running properties of different tilting trains, the reactions should be measured directly on the elements of track and wheel. It should also be taken into account, that the conventional measurements on wheel, according to EN 14363, are influenced by the lowpass filtering cutoff frequencies of about 20 Hz to 40 Hz. Hence, it can be necessary to use measurement systems with higher lowpass filtering cutoff frequencies and/or complement the measuring system on the wheels by taking direct measurements on track components such as stock rail, check rail, and/or wing rail. It can also be necessary to evaluate the situation at the check rails when there is maximum lateral wheel flange wear, since the peak lateral forces can be higher than when the wheel flanges are unworn.
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Annex J (informative) Passenger comfort on curves
J.1 General Methods for measurement and evaluation of ride comfort for passengers are defined in EN 12299. The standard quantifies ride comfort through indirect measurements, i.e. measuring and postprocessing relevant motion quantities. Certain procedures in the standard are based on bandpass filtered acceleration measurements and are excluding the effects of the designed track geometry. They are quantifying the combined effects of track irregularities and dynamic vehicle behaviour. Comfort on Curve Transitions (P CT method) is a method to quantify ride comfort (discomfort) on transition curves. Comfort on Discrete Method (P DE method) is a method to quantify ride comfort (discomfort) on large track irregularities on horizontal curves and straight tracks. Comfort on Curve Transitions (P CT method) and Comfort on Discrete Events (P DE method) include evaluation of lowpass filtered lateral acceleration, lowpass filtered lateral jerk and lowpass filtered roll velocity. These motion measurements shall be made at the floor for the vehicle. Hence, the designed track geometry, as well as the vehicle roll flexibility (and tilt system if used), will affect the comfort quantification. The methods in EN 12299 are applicable both for measurements of motions and to simulations of motions.
J.2 Lateral acceleration Lowpass filtered lateral acceleration, parallel to the vehicle floor, is a major component on both Comfort on Curve Transitions (P CT method) and Comfort on Discrete Events (P DE method). The lowpass filtering reduces the influence of track irregularities. The major contributor is noncompensated lateral acceleration in the track plane, which is proportional to cant deficiency. For a nontilting vehicle, the lateral acceleration at the floor may be estimated by multiplying the noncompensated lateral acceleration in the track plane with a factor (1+sr ), where sr is the roll flexibility coefficient. For a tilting vehicle, the lateral acceleration at the floor may be estimated by multiplying the noncompensated lateral acceleration in the track plane with a factor ((1+ sr )·(1st )), where sr is the roll flexibility coefficient and st is the compensation factor in the tilt system.
J.3 Lateral jerk J.3.1 Lateral jerk as a function of rate of change of cant deficiency Lowpass filtered lateral jerk is a major component on Comfort on Curve Transitions ( P CT method). The lowpass filtering reduces the influence of track irregularities. The major contributor is noncompensated lateral jerk in the track plane, which is proportional to the rate of change of cant deficiency. For a nontilting vehicle, the lateral jerk at the floor may be estimated by multiplying the noncompensated lateral jerk in the track plane with a factor (1+ sr ), where sr is the roll flexibility coefficient.
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For a tilting vehicle, the lateral jerk at the floor may be estimated by multiplying the noncompensated lateral jerk in the track plane with a factor ((1+sr )·(1)·(1st )), )), where sr is is the roll flexibility coefficient and st is the compensation factor in the tilt system. s ystem. The P CT CT method has been validated for clothoids with a duration of at least 2 s. There is no validated method for shorter transition curves or transition curves with nonlinear change of cant deficiency.
J.3.2 Lateral jerk as a function of an abrupt change of cant deficiency The lateral jerk is high at abrupt changes of cant deficiency. The lateral jerk for a given abrupt change of cant deficiency increases (but less than proportionally) with speed. Since there is no validated method to quantify transition curves with a shorter duration than 2 seconds, there is no generally accepted method to quantify discomfort at an abrupt change of cant deficiency. However, it is obvious that an abrupt change of cant deficiency generates more discomfort than a transition curve with the same magnitude of the c hange of cant deficiency.
J.4 Roll motions Lowpass filtered roll velocity is a minor component in Comfort on Curve Transitions (P CT CT method). The lowpass filtering reduces the influence of track irregularities. The roll motion of the vehicle body is i s affected by rate of change of cant on cant transitions. The roll motion is also affected by the rate of change of cant deficiency. If both cant and cant deficiency increase on a transition curve, the effect of rate of change cant deficiency reduces the roll velocity of a nontilting vehicle (due to the roll coefficient), but increases the roll velocity of a tilting vehicle.
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Annex K (normative) Sign rules for calculation of ΔD, ΔI and Δ p
K.1 General regarding the sign rules In most standards for track alignment design parameters, rules and limits are given without sign rules which distinguish between right hand and left hand curves, as well as uphill and downhill gradients. The same approach has been used in this European Standard. This normative annex defines the rules for calculating differences for such parameters.
K.2 Sign rules for calculation of ΔD ΔD is the change of cant over the length of the cant transition LD. For the most usual case of a cant transition where left rail is either the high rail or the low rail, change of cant Δ D is calculated according to Formula (K.1). For the more unusual case of a cant transition where left rail is the high rail in one end and the low rail in the other o ther end, change of cant ΔD is calculated according to Formula (K.2):
∆D = D2 − D1
∆D = D2 + D1
(K.1) (K.2)
where D1
is the applied cant (mm) in the beginning of the cant transition, and
D2
is the applied cant (mm) in the end of the cant transition.
The application of Formulae (K.1) and (K.2) assumes that the mathematical properties are constant over the whole length of the cant transition. Otherwise, the cant transition shall be divided in parts, where ΔD is calculated for each part, and where the requirements in Clause 6 shall be fulfilled for each part of the cant transition. For example, a reverse transition with two different constant cant gradients shall be evaluated as two cant transitions.
K.3 Sign rules for calculation of ΔI ΔI is either a continuous change of cant deficiency I (and/or cant excess E ) over a certain length (a transition curve or a cant transition on straight track or a circular curve), or an abrupt change of cant deficiency (and/or cant excess E ) at an abrupt change of curvature. ΔI is defined according to Formulae (K.3) or (K.4). NOTE
By definition, I = = E .
Formula (K.3) applies to transitions with condition A in both ends or condition B in both ends, according to Table K.1. Formula (K.3) also applies for abrupt changes of cant deficiency where the conditions immediately before and immediately after the abrupt change of curvature are the same (either A or B in Table K.1). Formula (K.4) applies to transitions with condition A in one end and condition B in the other end, according to Table K.1. Formula (K.4) also applies for abrupt changes of cant deficiency where the
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conditions, according to Table K.1, immediately before and immediately after the abrupt change c hange of curvature are different. ∆I = I 2 − I 1
∆I =
I2
+
(K.3)
I 1
(K.4)
where I 1
is the cant deficiency (mm) in the beginning of the transition, or immediately before the abrupt change of curvature, and
I 2
is the cant deficiency (mm) in the end of the cant cant transition, or immediately immediately after the abrupt abrupt change of curvature. Table K.1 — Conditions at the tangent points Condition Text a Right hand curve with positive cant deficiency
A
Right hand curve with negative cant deficiency (cant excess)
B
Left hand curve with positive cant deficiency
B
Left hand curve with negative cant deficiency (cant excess)
A
Straight track with cant, left rail is low
A
Straight track with cant, left rail is high
B
Text a The perceived lateral acceleration acceleration in the track plan plan is towards left under Condition A, and towards right under Condition B. The application of Formulae (K.3) and (K.4) assumes that the mathematical properties are constant over the whole length of the transition. Otherwise, the transition shall be divided in parts, where Δ I is calculated for each part, and where the requirements in Clause 6 shall be fulfilled for each part of the transition. For example, a reverse transition with different mathematical properties before and after the inflexion point shall be evaluated as two transition curves. Clause 6 allows two (or more) abrupt changes of curvature to be separated with a length which is substandard according to 6.13, provided that the total change of cant deficiency does not exceed the upper limit for abrupt change of cant deficiency. The total change of cant deficiency is calculated with Formulae (K.3) and (K.4) (depending on the conditions in i n Table K.1), using the cant deficiency immediately before the first abrupt change of curvature as I 1 and the cant deficiency immediately after the last abrupt change of curvature as I 2.
K.4 Sign rules for calculation of Δ p The abrupt change of gradient is normally defined according to Formula (K.5), but where a downhill gradient is connected to an uphill gradient i t is defined according to Formula (K.6). ∆ p =
82
p2
−
p1
(K.5)
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∆ p = p2 + p1
(K.6)
where p1
is the gradient of the first element and
p2
is the gradient of the second element.
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Annex L (informative) Length of constant cant between two linear cant transitions Li
In certain applications, the actual length of any alignment element (other than transition curves) should be set equal to or above a lower limit given in Table L.1, taking into account the actual alignment design parameters of the neighbouring cant elements; longer elements should be used for higher values of these parameters. It is desirable where possible to join two reverse circular curves by a continuous transition curve instead of placing a straight line element between the two transitions curves. Hence, in this case, the length of straight line element is zero. Table L.1 — Lower limit for length of constant cant between two linear cant transitions Li Normal limits a
a
Exceptional limits
0 < V ≤ 70 km/h
V /3
m/(km/h)
V /10
m/(km/h)
70 km/h < V ≤ 200 km/h
V /2
m/(km/h)
V /5,2
m/(km/h)
200 km/h < V ≤ 360 km/h
V /1,5
V /2,5
m/(km/h)
m/(km/h)
Without going under 20 m.
A rapid succession of curves and straights may induce a reduction in comfort, particularly when the length of individual alignment elements are such that the passengers are subjected to changing accelerations at a rate which corresponds to the natural frequencies of the vehicles.
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Annex M (informative) The principle of virtual transition
M.1 Virtual transition at an abrupt change of cant deficiency This principle is based upon the assumption that a characteristic vehicle travelling over an abrupt change of cant deficiency gains, or loses, cant deficiency (and/or cant excess) over a length equal to the distance between the bogie centres of the characteristic vehicle ( Lb). This distance is also denoted L virtual transition and is assumed to extend a distance b each side of the abrupt change in cant 2
deficiency. The virtual rate of change of cant deficiency ∆I ∆t
=
∆I
V
Lb q v
∆I ∆t
is defined according to Formula (M.1).
(M.1)
where qV
= 3,6 km∙s/(h∙m),
∆I
= abrupt change of cant deficiency (mm),
V
is the vehicle speed (km/h), and
Lb
= distance between the bogie centres of the characteristic vehicle (m).
The calculated virtual rate of change of cant deficiency bogie centres of the vehicle. Consequently, values of cant deficiency (
dI dt
∆I ∆t
∆I ∆t
is dependent upon the distance between the
are not comparable with the rates of change of
) on transition curves specified in 6.8.
Upper limits for the virtual rate of change o f cant deficiency
∆I ∆t
are given in M.3.
The corresponding value for ΔI (see 6.11) for a given speed V , a given length Lb and a given value of ∆I virtual rate of change of cant deficiency can be calculated according to Formula (M.2). ∆t ∆I =
q v ∆I V
∆t
Lb
(M.2)
where qV
= 3,6 km∙s/(h∙m),
V
is the vehicle speed (km/h),
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∆I ∆t
= virtual rate of change of cant deficiency (mm/s), and
Lb
= distance between the bogie centres of the characteristic vehicle (m).
The values for the abrupt change of cant deficiency, when based on the principle of the virtual transition, shall also conform to the upper limits specified in 6.11.
M.2 Virtual transition at a short intermediate length between two abrupt changes of cant deficiency Where two abrupt changes of cant deficiency are separated by a length ( Ls) which is shorter than the distance between the bogie centres of the characteristic vehicle ( Lb), and the second abrupt change of cant deficiency interacts with the first abrupt change of cant deficiency in a way that the total change of cant deficiency over the two tangent points is increased, the length (Ls) of the intermediate element(s) is assessed by calculating a virtual rate of change of cant deficiency
∆I defined according to ∆t
Formula (M.3).
∆I ∆I 1 + ∆I 1 V = Lb + Ls qv ∆t
(M.3)
where qV
= 3,6 km∙s/(h∙m),
∆I
= abrupt change of cant deficiency (mm),
V
is the vehicle speed (km/h),
Lb
= distance between the bogie centres of the characteristic vehicle (m), and
Ls
= distance between the two abrupt changes of cant deficiency (m).
NOTE
Clause M.1 applies to each of the two changes of cant deficiency.
∆I is dependent upon the distance between the ∆t ∆I bogie centres of the vehicle. Consequently, the values of are not comparable with the rates of ∆t The calculated virtual rate of change of cant deficiency
change of cant deficiency
dI dt
on transition curves specified in 6.8.
Upper limits for the virtual rate of change of cant deficiency
∆I are given in M.3. ∆t
The lower limit for Ls for a given speed V , a given combination of ΔI 1 and ΔI 2, and a given value of ∆I ∆t is expressed by Formula (M.4). lim
L s lim =
86
∆I 1 + ∆I 2 V − Lb q v ∆I ∆t lim
(M.4)
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where qV
= 3,6 km∙s/(h∙m),
∆I
= abrupt change of cant deficiency (mm),
V
is the vehicle speed (km/h),
Lb
= distance between the bogie centres of the characteristic vehicle (m), and
Ls
= distance between the two abrupt changes of cant deficiency (m).
Negative values for Ls,lim mean that an intermediate element is not required and consequently may have any length according to the principle of virtual transition. The value for the intermediate length L s , when based on the principle of the virtual transition, shall also conform to the lower limits specified in 6.12 and 6.13. The compliance with this requirement shall always be checked, i.e. also for cases where L s > Lb .
M.3 Limits based on the principle of the virtual transition M.3.1 General The principle of the virtual transition is defined i n M.1 and M.2. European railway companies that use the principle of the virtual transition usually have different characteristic vehicles and, consequently, there is a variation in the distance between the bogie centres. Also, the upper limits for the virtual rate of change of cant deficiency
∆I ∆t
are different for these railway
companies. Some of these railway companies restrict their use of the principle of virtual transition to speeds below 160 km/h. Examples of limits are given in M.3.2 and M.3.3.
M.3.2 Characteristic vehicle with a distance of 20 m between bogie centres Upper limits for virtual rate of change of cant deficiency
∆I ∆t
for a characteristic vehicle with a distance
of 20 m between bogie centres are specified in Table M.1. Table M.1 — Upper limits for the virtual rate of change of cant deficiency (
Normal limits General Switches and crossings
∆ I ∆t
)
Exceptional limits
55 mm/s 125 mm/s
150 mm/s
M.3.3 Characteristic vehicle with a distance of 12,2 m and 10,06 m between bogie centres Upper limits for virtual rate of change of cant deficiency
∆I ∆t
for characteristic vehicles with distances of
12,2 m and 10,06 m between bogie centres are specified in Table M.2.
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Table M.2 — Upper limits for the virtual rate of change of cant deficiency (
88
Normal limits
Exceptional limits
General
35 mm/s
55 mm/s
Switches and crossings
35 mm/s
80 mm/s
∆ I ∆t
)
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Annex N (normative) Lengths of intermediate elements Lc to prevent buffer locking
N.1 General There are limits on how much end throws may differ between two adjacent vehicles. The criterion is related to buffer locking, but also vehicles with central couplers can have similar limits. The end throw is the geometrical overthrow d ga for the end of the vehicle, as defined in EN 152731. The criterion is relevant for horizontal alignments with small radius curves in opposite directions. For horizontal curves with substandard radius, the criterion can also be relevant for a curve connected to a straight track or within compound curves.
N.2 Basic vehicles and running conditions The requirements for lengths of intermediate elements are derived to allow interoperability for two types of basic vehicles. The basic passenger coach has certain characteristics as follows: — distance between bogie pivots: 19,0 m — distance between buffer face and the bogie pivot: 3,7 m The basic freight vehicle has certain characteristics as follows: — distance between wheelsets, or bogie pivots:12,0 m — distance between buffer face and the wheelset or bogie pivot: 3,0 m For mixed traffic tracks and dedicated passenger tracks, the limits for the horizontal alignment defined in this annex result in end throw differences of 395 mm for two adjacent basic passenger coaches. For dedicated freight tracks, the limits for the horizontal alignment defined in this annex result in end throw differences of 225 mm for two adjacent basic freight vehicles. For vehicles with other characteristics, it is assumed that running gear, couplers and buffers are designed for the minimum length of the intermediate element LC. Infrastructure managers can specify more restrictive, longer lengths on (dedicated parts of) their network in order to prevent buffer locking for existing vehi cles that do not fulfil these assumptions.
N.3 Lengths Lc of an intermediate straight track between two long circular curves in the opposite directions The tables in this clause are based on cases where the horizontal alignment contain a long circular curve, an intermediate straight track and long circular curve in the opposite direction of the first curve. The track has a maximum inservice gauge value of 1 470 mm (nominal gauge 1 435 mm plus 35 mm, see EN 138485). The first vehicle has the first wheelset (or bogie pivot) on the first circular curve and the second vehicle has the last wheelset (or bogie pivot) on the second circular curve. The two intermediate wheelsets (or bogie pivots) are placed either on the curves or on the intermediate straight track. For other cases, see N.4.
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This European Standard bases on the criterion on the static end throw differences. The limit refers to a long circular curve of 190 m radius to be connected to a long circular curve, also of 190 m radius, in the opposite direction, with an intermediate straight of 6,00 m length. This leads to a maximum for the end throw difference of 395 mm for two basic passenger coaches and allows a long circular curve of 213 m radius to be directly connected to a long circular curve, also of 213 m radius, in the opposite direction. It also allows for any combination of circular curves where the change of curvature is less than 1/106,5 m−1. Where the horizontal curves have curvatures that differ more than 1/113 m−1, an intermediate element shall be inserted to reduce the differences in end throw, using the static method in EN 152731, down to less than or equal to 395 mm for the basic passenger coaches. This element may be a straight track, a transition curve, or a circular curve. The required length of the intermediate element depends on the radii of the small radius curves as well as the type of intermediate element. Table N.1 specifies lower limits for the length of a straight intermediate element for certain combinations of long circular curves for the passenger coach defined above. The criterion for dedicated freight lines allows a long circular curve of 200 m radius to be directly connected to a long circular curve, also of 200 m radius, in the opposite direction. It also allows for any combination of circular curves where the change of curvature is less than 1/100 m −1. Where the horizontal curves have curvatures that differ more than 1/100 m−1, an intermediate element shall be inserted to reduce the differences in end throw, using the static method in EN 152731, down to less than or equal to 225 mm for the basic freight vehicles. This element may be a straight track, a transition curve, or a circular curve. The required length of the intermediate element depends on the radii of the small radius curves as well as the type of intermediate element. Table N.2 specifies lower limits for the length of a straight intermediate element for certain combinations of long circular curves for dedicated freight lines for the basic freight vehicle defined above.
N.4 General cases for end throw differences Where an intermediate track element is required, and it is not a straight track, a detailed calculation shall be made to check the magnitude of the end throw differences. Where the two small radius curves are short and the adjoining elements before the first curve and/or after the second curve have larger radius, the length of the intermediate element may, after special investigation, be shorter. This criterion is also applicable for horizontal curves with substandard radius less than 150 m. A special investigation is necessary to ensure that static end throw differences are less than or equal to 395 mm for basic passenger coaches on mixedtraffic lines and dedicated passenger lines, or 225 mm for basic freight vehicles on dedicated freight lines.
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Table N.1 — Lower limits for the length Lc (m) of a straight intermediate element between two long circular curves in the opposite directions R1
150
155
160
165
170
175
180
185
190
195
200
205
210
215
220
150
10,78
10,53
10,29
10,06
9,83
9,60
9,38
9,16
8,94
8,73
8,52
8,31
8,11
7,91
7,71
160
10,29
9,86
9,48
9,22
8,97
8,73
8,49
8,25
8,02
7,79
7,56
7,34
7,12
6,91
6,69
170
9,83
9,37
8,97
8,62
8,30
8,04
7,78
7,73
7,28
7,04
6,80
6,55
6,31
6,06
5,81
180
9,38
8,91
8,49
8,12
7,78
7,48
7,20
6,93
6,65
6,37
6,08
5,79
5,49
5,18
4,86
190
8,94
8,45
8,02
7,63
7,28
6,96
6,65
6,33
6,00
5,67
5,33
4,97
4,59
4,19
3,76
200
8,52
8,01
7,56
7,16
6,80
6,44
6,08
5,71
5,33
4,93
4,50
4,04
3,54
2,97
2,28
210
8,11
7,59
7,12
6,70
6,31
5,91
5,49
5,06
4,59
4,09
3,54
2,91
2,11
0,73
0
220
7,71
7,17
6,69
6,25
5,81
5,35
4,86
4,34
3,76
3,10
2,28
0,95
0
0
0
230
7,32
6,77
6,27
5,79
5,29
4,76
4,18
3,52
2,74
1,67
0
0
0
0
0
240
6,95
6,38
5,85
5,32
4,74
4,11
3,38
2,50
1,07
0
0
0
0
0
0
250
6,54
5,99
5,42
4,81
4,14
3,36
2,39
0,51
0
0
0
0
0
0
0
260
6,22
5,60
4,97
4,26
3,46
2,44
0,36
0
0
0
0
0
0
0
0
270
5,86
5,20
4,48
3,66
2,64
0,86
0
0
0
0
0
0
0
0
0
280
5,51
4,78
3,96
2,96
1,45
0
0
0
0
0
0
0
0
0
0
290
5,15
4,33
3,37
2,06
0
0
0
0
0
0
0
0
0
0
0
300
4,77
3,85
2,68
0
0
0
0
0
0
0
0
0
0
0
0
310
4,37
3,31
1,75
0
0
0
0
0
0
0
0
0
0
0
0
320
3,95
2,67
0
0
0
0
0
0
0
0
0
0
0
0
0
330
3,47
1,85
0
0
0
0
0
0
0
0
0
0
0
0
0
340
2,94
0
0
0
0
0
0
0
0
0
0
0
0
0
0
350
2,30
0
0
0
0
0
0
0
0
0
0
0
0
0
0
360
1,41
0
0
0
0
0
0
0
0
0
0
0
0
0
0
370
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
R2
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Table N.2 — Lower limits, for dedicated freight lines, for the length Lc (m) of a straight intermediate element between two long circular curves in the opposite directions R1
150
155
160
165
170
175
180
185
190
195
200
150
6,79
6,61
6,43
6,25
6,09
5,92
5,76
5,60
5,44
5,28
5,13
160
6,43
6,20
6,01
5,82
5,63
5,45
5,26
5,07
4,89
4,70
4,51
170
6,09
5,85
5,63
5,42
5,20
4,98
4,76
4,54
4,31
4,08
3,84
180
5,76
5,51
5,26
5,01
4,76
4,51
4,25
3,98
3,70
3,40
3,09
190
5,44
5,16
4,89
4,60
4,31
4,01
3,70
3,36
3,01
2,61
2,15
200
5,13
4,82
4,51
4,18
3,84
3,48
3,09
2,65
2,15
1,51
0
210
4,82
4,47
4,11
3,73
3,32
2,88
2,37
1,73
0,68
0
0
220
4,50
4,11
3,69
3,25
2,75
2,15
1,35
0
0
0
0
230
4,17
3,73
3,24
2,70
2,04
1,07
0
0
0
0
0
240
3,83
3,32
2,74
2,04
0,96
0
0
0
0
0
0
250
3,47
2,87
2,15
1,07
0
0
0
0
0
0
0
260
3,08
2,36
1,35
0
0
0
0
0
0
0
0
270
2,65
1,73
0
0
0
0
0
0
0
0
0
280
2,16
0,68
0
0
0
0
0
0
0
0
0
290
1,51
0
0
0
0
0
0
0
0
0
0
300
0
0
0
0
0
0
0
0
0
0
R2
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Annex O (informative) Considerations for track gradients
O.1 Uphill gradients For the line between stations, a long uphill gradient should be limited with regards to train mass and available traction. Also the coupler strength can define a binding limitation for train mass and/or uphill gradients. Horizontal curves generate increased resistance against the train motion. The magnitude of this increment depends on horizontal radius, curve length and vehicle characteristics. Track gradients shorter than the train length for the heaviest train on the line may have a less restrictive limit for the gradient. Where trains are expected to accelerate from a stop or from a lower speed, the upper limit for the track gradient should be more restrictive than for locations where trains are expected to run at constant speed. It is recommended that in projects of new lines, the gradient is evaluated through simulation running, considering the characteristics of the freight train defined by the infrastructure manager.
O.2 Downhill gradients Downhill gradients should be limited, taking the braking capability of the vehicles into account.
O.3 Gradients for stabling tracks and at platforms Gradients at stations should take into account that a train will be accelerating from a stop at the station. Stabling tracks should ideally be horizontal. National or company rules may specify limits on gradient through station platforms. For stopping positions along platforms and stabling positions, the relevant gradient is the average gradient over the train length, not the local maximum. A more restrictive limit for track gradient can be justified where vehicles will be regularly attached to or detached from a trainset.
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Annex ZA (informative) Relationship between this European Standard and the Essential Requirements of EU Directive 2008/57/EC
This European Standard has been prepared under a mandate given to CEN/CENELEC/ETSI by the European Commission and the European Free Trade Association to provide a means of conforming to Essential Requirements of the Directive 2008/57/EC1). Once this standard is cited in the Official Journal of the European Union under that Directive and has been implemented as a national standard in at least one Member State, compliance with the clauses of this standard given in Tables ZA.1 till ZA.3 confers, within the limits of the scope of this standard, a presumption of conformity with the corresponding Essential Requirements of that Directive and associated EFTA regulations. Table ZA.1 — Correspondence between this European Standard, Commission Regulation (EU) No 1299/2014 of 18 November 2014 on the technical specifications for interoperability relating to the ‘infrastructure’ subsystem of the rail system in the European Union, and Directive 2008/57/EC Clause(s)/subclause(s) of this European Standard
Chapter/§/annexes of the TSI
Corresponding text, articles/§/annexes of the Directive 2008/57/EC
Comments
5 General
4. Description of the infrastructure subsystem
Annex III, Essential requirements
4.2. Functional and technical specifications of subsystem
1.1. Safety
According to 4.2.4.3 (2) – Cant deficiency – of the merged TSI INF it is permissible for trains specifically designed to travel with higher cant deficiency (for example multiple units with axle loads lower than set out in Table 2; vehicles with special equipment for the negotiation of curves) to run with higher cant deficiency values, subject to a demonstration that this can be achieved safely.
5.2 Alignment characteristics 6 Limits for 1 435 mm gauge 6.1 Radius of horizontal curve 6.2 Cant 6.3 Cant deficiency
4.2.3. Line layout 4.2.3.3. Maximum gradients
1 General requirements Clauses 1.1.1, 1.1.2 1.5 Technical compatibility 2. Requirements specific to each subsystem
4.2.3.3.(1) Gradients of 6.11 Abrupt change of cant 2.1. Infrastructure tracks through deficiency passenger platforms 2.1.1. Safety 6.14 Track gradients 4.2.3.3. (3) Gradients 6.15Vertical radius for main tracks Annex A 4.2.3.4. Minimum radius of horizontal (normative) curve Rules for converting parameter values for track 4.2.3.5 Minimum radius of vertical curve gauges wider than 1 435 mm. 4.2.4. Track parameters
According to 6.2.4.4.  Assessment of track layout  of the merged TSI INF following track design parameters shall be assessed against the local design speed at design review: curvature, cant, cant deficiency and abrupt change of cant deficiency. According to Appendix R of the merged TSI INF requirements for the design of track, including switches and crossings, which are compatible with the use of eddy current braking systems (4.2.6.2.2) remain an open point.
1) This Directive 2008/57/EC adopted on 17 th June 2008 is a recast of the previous Directives 96/48/EC ‘Interoperability of the transEuropean highspeed rail system’ and 2001/16/EC ‘Interoperability of the transEuropean conventional rail system’ and revisions thereof by 2004/50/EC ‘Corrigendum to Directive 2004/50/EC of the European Parliament and of the Council of 29 April 2004 amending Council Directive 96/48/EC on the interoperability of the transEuropean highspeed rail system and Direct ive 2001/16/EC of the European Parliament and of the Council on the interoperability of the transEuropean conventional rail system’.
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Clause(s)/subclause(s) of this European Standard
Chapter/§/annexes of the TSI
Annex B
4.2.4.2 (1). Design cant for lines
(normative) Track alignment design parameter limits for track gauges wider than 1 435 mm. Annex N (normative) Lengths of intermediate elements Lc to prevent buffer locking
4.2.4.2 (2). Design cant in platforms 4.2.4.3. Cant deficiency 4.2.4.4. Abrupt change of cant deficiency. 4.2.5. Switches and crossings 4.2.5.2. Use of swing nose crossings 4.2.9. Platforms 4.2.9.4. Track layout alongside platforms. 6. Assessment of conformity of interoperability constituents and EC verification of the subsystems 6.2. Infrastructure subsystem 6.2.4. Particular assessments procedures for subsystems 6.2.4.4. Assessment of track layout 6.2.4.8. Assessment of switches and crossings 7.7. Special cases Appendix I  Reverse curves with radii in the range from 150 m up to 300 m – Tables 43 and 44
Corresponding text, articles/§/annexes of the Directive 2008/57/EC
Comments
According to the scope of EN 13803:2017 more restrictive requirements of Technical Specifications for Interoperability relating to the ‘infrastructure’ subsystem of the rail system in the European Union (TSI INF) and other (national, company, etc.) rules will apply. According to the scope of EN 13803:2017 this European Standard need not be applicable to lines, or dedicated parts of railway infrastructure that are not interoperable with railway vehicles tested and approved according to the European Standard EN 14363. EN 13803:2017 refers to the merged TSI INF for maximum gradients of tracks through passenger platforms, upper limits for main track gradients, minimum horizontal radius along platforms and design cant along platforms According to Table 7 –Table Footnote b of EN 13803:2017, trains complying with EN 14363, equipped with a cant deficiency compensation system other than tilt, may be permitted by the Infrastructure Manager to run with higher cant deficiency values. There exists no compatibility on limit values for following common track design parameters between the merged TSI INF and EN 13803:2017. Track gauge 1 435 mm Minimum radius of vertical curve  Design cant for freight and mixed traffic lines  Cant deficiency (see references merged TSI INF and EN 13803:2017 here before for cant deficiency) Track gauge 1 520 mm in the merged TSI INF compared to 1 520 mm and 1 524 mm in EN 13803:2017 Straight intermediate track elements between reverse curves  Minimum radius of vertical curve  Design cant for lines  Cant deficiency  Abrupt change of cant deficiency Track gauge 1 668 mm Minimum radius of vertical curve  Design cant for lines  Cant deficiency  Abrupt change of cant deficiency Track gauge 1 600 mm Normative Annex B of EN 13803:2017 contains no limits for design parameters for track gauge 1 600 mm. The limits can be calculated based on the rules for converting parameter values for track gauges wider than 1 435 mm in normative Annex A.
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Table ZA.2 — Correspondence between this European Standard, the Commission Regulation (EU) No 1302/2014 of 18 November 2014 concerning a technical specification for interoperability relating to the ‘rolling stock — locomotives and passenger rolling stock’ subsystem of the rail system in the European Union and Directive 2008/57/EC Clause(s)/subclause(s) of this European Standard
Chapter/§/annexes of the TSI
6 Limits for 1 435 mm gauge
4. Characterization of the rolling stock Annex III, Essential requirements system 1. General requirements 4.2. Functional and technical 1.1. Safety specification of the subsystem Clauses 1.1.1, 1.1.2 4.2.3. Track interaction and gauging 2. Requirements specific to each 4.2.3.1. Gauging subsystem 4.2.3.4. Rolling stock dynamic 2.4. Rolling stock behaviour 2.4.3. Technical compatibility 4.2.3.4.2. Running dynamic behaviour
6.1 Radius of horizontal curve 6.3 Cant deficiency 6.15 Vertical radius
Corresponding text, articles/§/annexes of the Directive 2008/57/EC
Comments
4.2.3.6. Minimum curve radius Annex A, A.1 Buffers
Table ZA.3 — Correspondence between this European Standard, the Draft Commission Regulation (EU) No 321/2013 of 13 March 2013 concerning the technical specification for interoperability relating to the subsystem ‘rolling stock — freight wagons’ of the rail system in the European Union repealing Decision 2006/861/EC and Directive 2008/57/EC Clause(s)/subclause(s) of this European Standard
Chapter/§/annexes of the TSI
Corresponding text, articles/§/annexes of the Directive 2008/57/EC
6 Limits for 1.435 mm gauge
4. Description of the infrastructure system
Annex III, Essential requirements
4.2. Functional and technical specifications of subsystem
1.1. Safety
6.1 Radius of horizontal curve 6.15 Vertical radius
4.2.2. Structures and mechanical parts 4.2.2.1. Mechanical interface 4.2.3. Gauging and track interaction 4.2.3.1. Gauging
Comments
1. General requirements Clauses 1.1.1, 1.1.2 2. Requirements specific to each subsystem 2.4. Rolling stock 2.4.3. Technical compatibility
WARNING — Other requirements and other EU Directives may be applicable to the product(s) falling within the scope of this standard.
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Bibliography
[1]
EN 12299, Railway applications  Ride comfort for passengers  Measurement and evaluation
[2]
EN 132321, Railway applications  Track  Switches and crossings  Part 1: Definitions
[3]
EN 132323, Railway applications —Track — Switches and crossings for Vignole rails — Part 3: Requirements for wheel/rail interaction
[4]
EN 138481, Railway applications — Track — Track geometry quality — Part 1: Characterisation of track geometry
[5]
EN 140676, Railway applications  Aerodynamics  Part 6: Requirements and test procedures for cross wind assessment
[6]
EN 152733, Railway applications — Gauges — Part 3: Structure gauges
[7]
Commission Regulation N° 1299/2014 of 18 November 2014 on the technical specifications for interoperability relating to the ‘infrastructure’ subsystem of the rail system in the European Union published in the Official Journal L 356, 12.12.2014, p.1.(TSI INF)
[8]
Commission Decision of 21 February 2008 concerning a technical specification for interoperability relating to the ‘rolling stock’ subsystem of the transEuropean highspeed rail system published in the Official Journal L 84  26.03.2008 p. 132 (HighSpeed Rolling Stock TSI)
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