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TRITA - FKT Report 2001:54ISSN 1103 - 470XISRN KTH/FKT/EX--01/54--SE

Stockholm2001 Railway TechnologyDepartment of Vehicle EngineeringRoyal Institute of Technology

Track geometry forhigh-speed railways

A literature surveyand

simulation of dynamic vehicle responce

by

Martin Lindahl


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TRITA-FKT Report 2001:54ISSN 1103-470XISRN KTH/FKT/EX--01/54--SE

Track geometry for

high-speed railways

A literature surveyand

simulation of dynamic vehicle responce

by

Martin Lindahl

Postal AddressRoyal Institute of TechnologyRailway TechnologyS-100 44 Stockholm

Visiting addressTeknikringen 8Stockholm

Telephone+46 8 790 76 28Fax+46 8 790 76 29

[email protected]


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Abstract

The present work consists of two main parts. The first part (Chapter 2 and 3) deals with aliterature survey where a short introduction is given for track geometry and track/vehicleinteraction. After the introduction, a survey over the present standard in Europe and

Japan is made. In particular the recent proposals for a common European Standard(CEN) and TSI (Technical Specification for Interoperability) are reviewed.

The second part (Chapter 4, 5 and 6) starts with an attempt to foresee the performance ofa train that would be available from the industry around 2010. Furthermore, the secondpart deals with simulations. Firstly, hunting stability is simulated to establish a vehicleconfiguration that could deal with higher speeds. Secondly, track shift forces aresimulated with Prudhommes criteria as boundary condition. Thirdly, a risk factor forvehicle overturning was calculated in the most adverse case where the train was runningon a curve and the wind was directed outwards. In the simulations, two sets of trackirregularities were used.

Some consequences of different kinds of freight train operations are discussed in Chapter7.

In short terms, the following conclusions have been drawn:

- A cant up to 200 mm is possible if the track is built for dedicated high-speed traffic; infreight train operations some 20-50 mm lower.

- A cant deficiency of 225-250 mm could be allowed when using carbody tilt andsuitable bogie technology. The tilt is a basic requirement when using such high valuesof cant deficiency.

- The transition curves should be long, i.e. the duration in the transition curve should bein the order of around 4-5 sec, if carbody tilt is anticipated.

- It could be concluded that hunting stability can be achieved.- The track quality has too be improved relative to current standards for 200 km/h in

order to meet requirements on lateral track shift forces. The degree of improvementshould be further investigated.

- It is concluded that safety criteria for side-wind exposure can be met, if the trains havefavourable, although, realistic, aerodynamic performance.

- The maximum gradient shall be chosen according to the type of freight trafficforeseen in the future.

Keywords: track, geometry, high-speed, train, railway, cant, cant deficiency, cant excess, tangent track,transition curve, horizontal curve radius, gradient, vertical curve radius, simulation, hunting stability, trackshift force, vehicle overturning, track irregularity, freight trains


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Sammanfattning

I Sverige finns behov av sprgeometri fr hghastighetsbanor. Bl.a. har frganaktualiserats i samband med studier av den s.k. Europakorridoren (Stockholm -Jnkping - Kpenhamn/Gteborg). I dessa sammanhang har det framfrts nskeml om

en hastighetsstandard fr 350 km/h, vilket r den standard som tminstone delvisprojekteras och byggs i Mellan- och Sydeuropa. Fr Sveriges del, som r ett land medlnga transportavstnd, finns det behov av korta restider p lnga avstnd, vilket talar frhg hastighet. Detta stller krav p stora kurvradier. Samtidigt finns ett starkt behov avatt bygga banorna med relativt lga investeringskostnader samt sm intrng i natur ochbebyggelse. Detta stller krav p att inte gra kurvradierna strre n absolut ndvndigtoch ven att kunna tillta relativt strre lutningar i banan.

En litteraturgenomgng har utfrts dr frslagen till europastandard fr sprgeometristuderats (CEN och TSI). Dessa frslag till europastandard skapar flera mjligheter attminimera bde horisontella och vertikala kurvradier. Det fresls ven vara mjligt atttillta tg med korglutning efter srskilt tillstnd av banhllaren. Lutningar i banan uppemot 35 fresls ven vara tilltet.Rapporten tar ven upp den framtida tgteknologin om vad som r tekniskt mjligt vilkethar diskuterats med tekniska experter inom industrin. Optimerad passiv hjulparsstyrningr en del som diskuterats. I detta sammanhang har utvecklingen av aktivsekundrfjdring nmnts som ett alternativ men dock inte studerats ingende. Denaerodynamiska utformningen har frfinats och senast knd teknologi har anvnds.

Simuleringarna har utfrts i tre olika steg. Frst grs en gngstabilitetssimulering fr attfaststlla att anvnd teknik klarar av hastigheterna som efterstrvas. Nsta steg var attberkna sprfrskjutningskrafter med Prudhommes kriterium som grnsvrde. I dennadel simulerades olika fall dr sprlget varierades fr att ge en uppfattning om vad somkrvdes fr att klara grnsvrdet. Slutligen simulerades skerheten mot vltning vidkraftig sidvind enligt freslagna riktvrden fr vilka vindhastigheter som br klaras.

Bland annat har fljande slutsatser dragits:

- Rlsfrhjning upp mot 200 mm r mjligt vid antagandet av enbart hghastighets-trafik (V 200 km/h).

- Rlsfrhjningsbrist upp mot 250 mm kan tilltas frutsatt att korglutningsteknik ochlmpliga boggier anvnds.

- Lnga vergngskurvor rekommenderas (en varaktighet om minst ca 4-5 s).- Uppstllda gngstabilitetsvillkor uppns.

- Sprlget mste frbttras fr att grnsvrdet fr de laterala sprfrskjutnings-krafterna ska klaras. Graden av frbttring mste studeras vidare.

- Villkoren fr sidvindsstabilitet klaras om tget fr en god aerodynamisk utformning.- Banans lutningsfrhllanden br vljas med hnsyn till den godstrafik som frutses.

Nyckelord: Sprgeometri, hghastighetsbana, tg, hghastighetstg, godstg rlsfrhjning,rlsfrhjningsbrist, rlsfrhjningsverskott, rakspr, vergngskurva, horisontalkurva, lutning, vertikal-kurva, simulering, gngstabilitet, sprfrskjutningskraft, vltning, sprlgesfel.


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Preface and acknowledgements

This study has been carried out at the Division of Railway Technology, Department ofVehicle Engineering, Royal Institute of Technology (KTH, Kungliga TekniskaHgskolan), Stockholm, in close cooperation with the Swedish National Rail

Administration (Banverket), Europakorridoren AB, Helsingborg, BombardierTransportation, Vsters, and the Swedish National Road and Transport ResearchInstitute (VTI), Linkping. The bulk of this study constitutes my Master of Sciencethesis.

The financial support from Banverket, Bombardier Transportation and Europakorridorenfor the present work is gratefully acknowledged. Thereby it was possible to give anextra-ordinary support and supervision from KTH senior staff.

I would like to thank my supervisor Sebastian Stichel and my examiner Professor EvertAndersson for their knowledge and support during the course of this work.

There have been four reference group meetings. This reference group consisted ofpersons from Banverket, Europakorridoren, Bombardier Transportation, VTI and KTH. Iwould like to state my kind regards to Bertil Eriksson and Per Hurtig from Banverket,Mikael Stamming from Europakorridoren, Olle Ek and Jan gren from BombardierTransportation and Bjrn Kufver from VTI.

The vehicle model used in the simulations have been provided by courtesy ofBombardier Transportation.

Thanks are also delivered to Ingemar Persson from DEsolver AB for his support andhelp during the simulations.

Due to the great extent of this work, some contributions have been delivered fromSebastian Stichel and Evert Andersson. Part of Chapter 4 has been written by SebastianStichel and the bulk of Chapter 7 has been written by Evert Andersson.

Friends, Brothers, Mum and Dad, thank you for patience.

At last but not least I would like to thank my girlfriend for her support andencouragement. I should not managed this without you.

Stockholm, December 2001

Martin Lindahl


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Table of contents

Abstract .............................................................................................................................i

Sammanfattning ............................................................................................................ iii

Preface and acknowledgements......................................................................................v

1 Introduction.................................................................................................................11.1 Background to the present study ....................................................................11.2 Objective and approach of the present study..................................................11.3 Thesis contribution .........................................................................................2

2 Track geometry and track/vehicle interaction .........................................................3

2.1 Design track geometry....................................................................................32.1.1 Track gauge................................................................................................32.1.2 Track cant...................................................................................................32.1.3 Horizontal curve.........................................................................................42.1.4 Transition curve and superelevation ramp.................................................52.1.5 Gradient......................................................................................................62.1.6 Vertical curve.............................................................................................6

2.2 Track/vehicle interaction ................................................................................82.2.1 Track plane acceleration............................................................................82.2.2 Equilibrium cant and balanced speed ........................................................92.2.3 Cant deficiency and cant excess ..............................................................102.2.4 Permissible speed with respect to radius, cant and cant deficiency.........122.2.5 Rate of cant and rate of cant deficiency...................................................13

3 Standards, practices and TSI...................................................................................15

3.1 Track gauge ..................................................................................................153.2 National standards in Sweden.......................................................................15

3.2.1 Track cant and track distance...................................................................153.2.2 Cant deficiency and cant excess ..............................................................153.2.3 Horizontal curve radius............................................................................163.2.4 Transition curve and superelevation ramp...............................................183.2.5 Gradient....................................................................................................193.2.6 Vertical curve radius ................................................................................20

3.3 National standards in Germany ....................................................................223.3.1 Track cant.................................................................................................233.3.2 Cant deficiency ........................................................................................23

3.3.3 Horizontal curve radius............................................................................243.3.4 Transition curve and superelevation ramp...............................................263.3.5 Gradient....................................................................................................263.3.6 Vertical curve radius ................................................................................27

3.4 Practices in France........................................................................................283.4.1 Cant, cant deficiency and cant excess......................................................28

3.5 Practices in Japan..........................................................................................293.6 Technical Specifications of Interoperability and CEN proposal ..................30

3.6.1 Track cant and track distance...................................................................303.6.2 Cant deficiency and cant excess ..............................................................31


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3.6.3 Horizontal curve radius............................................................................343.6.4 Transition curve and superelevation ramp...............................................353.6.5 Gradient....................................................................................................373.6.6 Vertical curve radius ................................................................................37

3.7 Comparison between different projects and standards.................................393.7.1 Horizontal curve radius............................................................................39

3.8 Recent resarch on nominal track geometry ..................................................413.8.1 Optimisation of horizontal alignments for railways ................................413.8.2 Ride comfort and motion sickness in tilting trains ..................................41

3.9 Summary and conclusions............................................................................43

4 High-speed train technology year 2010...................................................................45

4.1 Maximum train speed ...................................................................................454.2 Train configuration.......................................................................................454.3 Tilt technology..............................................................................................46

4.3.1 General.....................................................................................................464.3.2 Possible overspeed with tilt technology...................................................46

4.4 Running gear design .....................................................................................474.5 Aerodynamic shape ......................................................................................484.6 Track irregularities .......................................................................................48

5 Track/vehicle dynamic simulations - models, conditions and criteria .................49

5.1 Simulation strategy .......................................................................................495.2 Simulation software......................................................................................495.3 Test speed .....................................................................................................495.4 Hunting stability ...........................................................................................505.5 Track shift forces ..........................................................................................515.6 Vehicle overturning at strongly side-wind ...................................................52

5.6.1 General.....................................................................................................525.6.2 Tolerable wind velocities.........................................................................525.6.3 Intercept method risk factor.....................................................................535.6.4 Disadvantages with intercept method......................................................555.6.5 Aerodynamic train design........................................................................55

5.7 Rails, wheels and equivalent conicity...........................................................565.8 Track irregularities .......................................................................................57

5.8.1 Classification of track irregularities.........................................................575.8.2 Track irregularities for dynamics analysis...............................................585.8.3 Peak values of track irregularities............................................................62

5.9 Model of the EMU coach .............................................................................655.9.1 Three different vehicle configurations.....................................................655.9.2 Hold-off-device........................................................................................68

6 Dynamic analysis of simulated vehicle response ....................................................69

6.1 Hunting stability on tangent track and on curve...........................................696.1.1 Conditions................................................................................................696.1.2 Track irregularities...................................................................................706.1.3 Criteria for hunting stability.....................................................................706.1.4 Hunting stability on tangent track............................................................706.1.5 Hunting stability on large radius curves ..................................................72


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6.2 Evaluation of track shift forces.....................................................................746.2.1 Conditions................................................................................................746.2.2 Track irregularities...................................................................................756.2.3 Track shift forces variation along the track .............................................766.2.4 Track shift forces for different cant .........................................................766.2.5 Comparisons between different track irregularities.................................78

6.2.6 Improvements of track irregularities........................................................806.3 Evaluation of vehicle overturning ................................................................846.3.1 Conditions................................................................................................846.3.2 Track irregularities...................................................................................856.3.3 Safety against vehicle overturning at different conditions ......................856.3.4 Conclusions..............................................................................................88

7 Consequences of freight trains operations..............................................................89

7.1 Different categories of freight trains ............................................................897.2 Permissible axle load and track loadings......................................................917.3 Track cant and cant excess ...........................................................................93

7.4 Gradients versus train mass ..........................................................................967.4.1 Freight trains category I - heavy freight trains.........................................977.4.2 Freight trains category II - fast trains for unit-loads and heavy express..977.4.3 Freight trains category III - high-speed for light express or mail............99

8 Possible track geometry..........................................................................................101

8.1 Horizontal curve radius ..............................................................................1018.2 Vertical curve radius...................................................................................108

9 Conclusions and further research .........................................................................109

9.1 Conclusions on the literature study ............................................................109

9.2 Conclusions on dynamic analysis of simulated vehicle response ..............1099.3 Conclusions on horizontal and vertical curve radii ....................................1109.4 Conclusions on freight train operations......................................................1119.5 Further research ..........................................................................................111

References..................................................................................................................... 113

Appendix A - Notations...............................................................................................117

Appendix B - Abbreviations .......................................................................................121

Appendix C - Further diagrams on track shift forces..............................................123

Appendix D - Further diagrams on vehicle overturning .........................................131

Appendix E - Overturning due to side-wind.............................................................133

Appendix F - Train mass versus gradient .................................................................139

Appendix G - General Description of the GENSYS Software Package .................145


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Track geometry for high-speed railways

1

1 Introduction

1.1 Background to the present study

In Sweden the high-speed line Botniabanan (250 km/h) is currently in the design phase.There are also feasibility studies concerning Europabanan and Gtalandsbanan, ahigh-speed line intended to connect Stockholm with Gothenburg and Copenhagen. Theobjective for these railways is to manage speeds above 300 km/h, maybe up to 350 km/h.These railways require a high standard and high performance.

With conventional (non-tilting) passenger trains running at 350 km/h, horizontal curveradii tend to be large (6000 m according to Banverket). In some cases it is alsorecommended to have a margin for future improvement in speed and passenger comfort,which will further increase required radii. In such a case the radius tend to be 10000 m.In addition, heavy freight trains require modest gradients (10 12 ) if ordinary

locomotives are to be used.Altogether, this would cause a very rigid and non-flexible alignment, both horizontallyand vertically. There would be a substantial need for bridges, high embankments andtunnels, depending on the topography of the landscape. The cost may increase so muchthat the project would be unprofitable from the social-economics point of view. Due tothe rigid alignment the project would also run the risk to cause excessively largeinfringements in nature and culture environments. The project could therefore bepolitically questioned.

The present Swedish standards and recommendations are principally the same as forlower speeds. A separate standard for high-speed railways in Sweden does not exist atthe moment. The standard for higher speeds have the same margin for future higherspeed as for the lower speeds, i.e. speeds less than or equal to 200 km/h. In somefeasibility studies there have been attempts to copy standards prepared for the firstgeneration German high-speed railways, which give very large curve radii and modestgradients.

1.2 Objective and approach of the present study

The aim with this work is to investigate what track standards could be allowed in order toachieve high-speed performance. One important boundary condition is the use of latestknown train technology, which can be assumed to be a standard within about 10 years.

The study has the following approaches:

- Make a literature survey of approved and forthcoming standards and practises forhigh-speed railways in Japan and Europe including the TSI (Technical Specificationfor Interoperability). It covers horizontal curve radius, transition curve length,appropriate cant, gradient, vertical curve radius etc.


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Introduction

- Describe a possible train vehicle which might run on the designed high-speed lines.What is today known technology, which could be commercially available within 10years? The problem should especially focus on tilting technology and modern runninggear, track forces, aerodynamics, on side-wind stability etc. Among other thingsresults from present research and experience at Bombardier Transportation, KTH andVTI will be used.

- Vehicle dynamic simulations will be performed to investigate possible limits withinwhich modern technology probably can be possible to accomplish.

Three kinds of different conditions will be looked at:

1. Track for all types of trains, including heavy freight trains

2. Track for high-speed trains and light freight trains (unit-loads and heavy mail)

3. Track for high-speed trains only (passenger, light express goods and light mail)

High-speed trains and heavy freight trains have different demands on track standardconcerning horizontal alignment, cant, gradients and vertical curves.

1.3 Thesis contribution

This thesis is believed to make contributions to the following areas:

- Give examples of what track geometry parameters that could be managed when takendifferent train categories into account.

- In particular, give examples of horizontal curve radius and cant deficiency that couldbe allowed for high-speed trains when safety related factors like hunting stability,

track shift forces and vehicle overturning are taken into consideration.- Foresee, and discuss the performance of a train that would be available from the

industry around 2010.


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3

2 Track geometry and track/vehicle interaction

2.1 Design track geometry

Track geometry is very important for the behaviour of vehicles. In this section anintroduction to the most common quantities of track geometry will be presented. Thesequantities are

- Track gauge

- Track cant

- Transition curve and superelevation ramp

- Horizontal curve radius

- Vertical curve radius and gradient

2.1.1 Track gauge

The definition of track gauge is shown in Figure 2-1. Standard track gauge is 1435 mm.

Figure 2-1 The definition of track gauge.

2.1.2 Track cant

The difference between the level of the two rails in a curve is called cant ht(also calledsuperelevation) and is arranged to compensate part of the lateral acceleration, see Figure2-2. A cant angle arise where a cant is arranged. The angle can be determined by

(2-1)

where 2bo = 1.500 m on standard track gauge.

tht

2bo--------asin=


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Track geometry and track/vehicle interaction

The cant is maximized with respect to stationary conditions and slowly running trains. Amaximum value is set for cant because of the following problems which arise if a train isforced to stop or run slowly in a curve:

- passenger discomfortat standstill or low speed;

- risk ofderailment of freight trains in sharp curves due to the combined effect of high

lateral and low vertical load on the outer wheel at low speed;- possible displacement of wagon loads;

Figure 2-2 Cant ht and cant angle t.

2.1.3 Horizontal curve

The most distinguished parameter for a circular curve is the radius, R = constant, whichis inverse proportional to curvature, . The radius is related to the centre of thetrack. Esveld says [11]: it is a known fact that a vehicle running at a speed v in a curvewith a radius R undergoes a centrifugal lateral acceleration a = v2/R which results in anumber of undesirable effects. These effects can be:

- possible passenger discomfort;

- possible displacement of wagon loads,

- risk of vehicle overturning in combination with strong side winds;- risk of derailment caused by flange climbing of a wheel on the outer rail or by

loosening of rail fastenings;

- high lateral forces on the track.

k 1 R=


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5

Figure 2-3 The definition of horizontal circular curve radius R.

2.1.4 Transition curve and superelevation ramp

A transition curve with a linear variation of curvature is called clothoid. Transitioncurves are used between tangent track and circular curves or between two adjacentcurves to allow a gradual change in curvature and lateral acceleration. The centre line ofa transition curve has the same tangent at the connecting points as the adjacent part,whereas the curvature changes gradually from the value of one connection point to thevalue of the other [11].

Transition curves also introduce cant via superelevation ramps. Asuperelevation ramp isa section of the track where the cant changes gradually.

The clothoid type of transition curve has a linear function of chainages, i.e. of the

longitudinal coordinate [16]

(2-2)

ifs = s0 = 0 at the start of the transition curve

where

kis the curvature and A is the clothoid parameter.

If the clothoid starts from a straight line (k0 = 0), has the length Lt and ends at a circlewith the radius R, we obtain the following relation:

(2-3)

k s( ) k0s

A2

------+=

A2

Lt R=


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2.1.5 Gradient

The topographical conditions usually require some kind of vertical-longitudinalgradients, along the way. Building bridges and tunnels is a very expensive way tomanage the topography constraints. In particular heavy railway traffic has problems toovercome large longitudinal gradients. Therefore restrictions for the amount of gradient

are needed. The following requirements need to be considered because they have anaffect on railway traffic:

- The power supply and energy consumption will increase with large gradients.

- Heavy freight trains with an ordinary locomotive may have problems to climb up thegradient.

- Braking distances increase for high-speed and freight trains in an ascending gradient

Thus, large gradients result, principally, in heavier locomotives, increased locomotivepower, and/or less freight train weight, and/or reduced speed and line capacity, and/orrequirement of higher braking capacity, and/or larger signalling distances.

2.1.6 Vertical curve

A vertical curve provides a smooth transition between successive tangent gradients in therailway profile. In changes of gradients a suitable radius must be used. If the verticalacceleration on a crest is too great, the loads on the vehicle wheels can cause the wheelsto climb the rail and thus cause a derailment. Furthermore, the resistance against vehicleoverturning at side-winds will be lower It is also important that passenger comfort isbeing ensured. How two adjacent gradients are related to the vertical curve radius and the

profile elevation is shown in Figure 2-4.


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7

Figure 2-4 Conditions for vertical geometry between two adjacent gradients

With the simple parabola in Figure 2-4, using small-angle approximations, the verticaloffset at any given longitudinal coordinate x, is given by:

(2-4)

where A is the algebraic difference between two gradients with gradesa and b (expressedin , positive uphill) and L is the length of the curve between the tangent points ta andtb. (Note that negative z coordinates are measured downwards from the tangents for acrest and positive z coordinates are measured upwards for a hallow). The maximum z forx = L/2, is given by

(2-5)

Given values ofa, b and Rv gives the following condition

(2-6)

(2-7)

z x( )a b( )

2000L---------------- x

2 Ax

22000L---------------= =

z L2---

e a b( ) L8000------------= =

L

Rv a b( )

1000-----------------------=

zL2---

Rva b( )2

8 106-------------------=


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2.2 Track/vehicle interaction

This section is believed to present quantities that are significant in track/vehicleinteraction.

2.2.1 Track plane acceleration

In case of quasistatic curving (i.e. curving at constant speed, radius and cant on perfecttrack geometry) the vehicle is exposed to two accelerations: horizontal centrifugalacceleration and gravitational acceleration, see Figure 2-5(a). The resultant of theacceleration vector can be split up into two composants; is parallel to the track plane

and is perpendicular to the track plane, see Figure 2-5(b).

Figure 2-5 Definition of track plane acceleration ay and lateral force angle .

The acceleration is called track plane acceleration or, simply, lateral acceleration.

The equations can be written as follows [1]:

(2-8)

(2-9)

ayaz

ay

ayv

2

R----- t g t

v2

R----- t g

ht2bo--------cos=sincos=

azv

2

R----- t g tcos+sin=


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9

Assuming small angels (t 0.15 rad) the equations can be approximated by:

(2-10)

(2-11)The lateral force angle in Figure 2-5 are related to the acceleration ay and az inaccordance to the following equation

(2-12)

2.2.2 Equilibrium cant and balanced speed

The cant which gives ay = 0. for a given radius and given vehicle speed is calledequilibrium cant, heq. The equilibrium cant is thus

(2-13)

Equation (2-13) are based on SI-units. In practice it is useful to express speed V in[km/h] and cant in [mm] shown in Equation (2-14)

(2-14)

The equation can be simplified further if the values 2bo for standard track gauge and thegravitational acceleration g are used

(2-15)

It is very common to write the formula in the way shown in Equation (2-15), but it isimportant to be careful with the units.

The vehicle speed giving ay = 0 for a given radius and a given cant is called the

equilibrium speedor balanced speed, veq and is defined as

. (2-16)

Thus, at equilibrium speed the lateral acceleration in the track plane, ay, is zero. Withspeed expressed in [km/h] and cant in [mm] this equation transforms to (for standardgauge):

ayv

2

R----- g tsin

v2

R----- g

ht2bo--------=

az g

ayaz-----atan=

heq2b0

g-------- v

2

R-----

heq mm,2bo mm,

g----------------- V

2

3.62 R------------------

heq mm,15009.81------------ V

2

3.62

R------------------ 11.8

V2

R------

veqR g ht

2bo--------------------=


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(2-17)

2.2.3 Cant deficiency and cant excess

For several reasons, fully compensated track plane acceleration can not be achieved in allcases according to [3]:

- It is a possibility that a train stops or runs slowly in a curve. Therefore, the maximumcant has to be limited. Other reasons to limit the cant have been discussed earlier inSection 2.1.2. It is then desirable to allow a cant deficiency, i.e. a certain amount ofuncompensated lateral acceleration ay remains in the track plane.

- Not all trains have the same speed. Therefore, it would not be possible to achieve fullycompensated lateral acceleration for all trains anyway.

Cant deficiency

When the cant is less than the equilibrium cant a so called cant deficiency arises. Thecant deficiency is the additional cant that is needed to achieve equilibrium cant. Cantdeficiency hdis the difference between equilibrium cant heq and actual cant htand is thusdetermined by the following equation:

(2-18)

With Equation (2-13) substituted into (2-18) we get in SI-units:

(2-19)

A common way to write the formula is shown in Equation (2-20). The speed V isexpressed in km/h and cant and cant deficiency is expressed in [mm].

(2-20)

An additional way to express cant deficiency is to solve Equation (2-10) for v2/R andsubstitute the expression into Equation (2-19) and relate cant deficiency to the track

plane acceleration which gives (in SI-units) [1]

(2-21)

where ay > 0

VeqR ht mm,

11.8---------------------=

hd heq ht=

hd2b0

g-------- v

2

R----- ht=

hd mm, 11,8V

2

R------ ht mm,=

hd2bo

g-------- ay=


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11

In Table 2-1 some examples of the relationship between track plane acceleration, sideforce angle and cant deficiency are given.

The cant deficiency allowed in real train operations is determined by the followingfactors according to [3], [11]:

- track construction (with respect to its ability to resist high forces);

- state of track components;

- track alignment (i.e. magnitude and shape of geometrical irregularities);- type of vehicle and running gear1;

- axle loads and unsprung masses;

- state of maintenance of the rolling stock;

- passenger comfort.

If high values are allowed for cant deficiency (track plane acceleration) the trackcomponents must be designed accordingly and there must be no risk of exceeding thelateral track resistance immediately after tamping.

Table 2-1 The relationship between track plane acceleration, side force angle andcant deficiency

Track plane accelerationay (m/s2) Lateral force angle () Cant deficiencyhd(m)

0.654 3.81 0.100

0.981 5.71 0.150

1.176 6.84 0.180

1.307 7.61 0.200

1.471 8.53 0.225

1.634 9.51 0.2501.797 10.46 0.275

1. In particular suspension, centre of gravity and side-wind sensitivity.


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Cant excess

If the actual cant is higher than the equilibrium cant something calledcant excess will beintroduced. Cant excess is the difference between actual cant and equilibrium cant and isdefined as:

(2-22)Cant excess is achieved when the vehicle is running at a lower speed than the designspeed of the track. Cant excess can be related to lateral acceleration in the same way ascant deficiency shown in Equation (2-21)

(2-23)

where ay < 0 and he > 0.

2.2.4 Permissible speed with respect to radius, cant and cant deficiency

With a given horizontal curve radius and permissible lateral acceleration, ay,lim, orpermissible cant deficiency, hd,lim, an expression for permissible speed, vlim, can beexpressed in many different ways [1]:

(2-24)

SI-units is used in Equation (2-24). Alternatively, in Equation (2-25) permissible speed,Vlim, is given in [km/h] while cant ht and permissible cant deficiency hd,lim are given in[mm]. Radius is always given in metres. Standard gauge is assumed.

(2-25)

he ht heq=

he2bo

g-------- ay=

vlim R ay li m, ght

2bo--------+

R g2bo----------- hd lim, ht+( )= =

Vli m R hd l im, ht+( )12.96g

2bo-----------------=

R hd l im, ht+( )

11.8---------------------------------


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2.2.5 Rate of cant and rate of cant deficiency

Rate of cant (cant gradient) as a function of time

The following relationship are used for cant gradients with linear superelevation ramps,

where htis the cant variation over the transition length Lt: [3], [7]

(2-26)

Rate of cant deficiency as a function of time

Rate of cant deficiency describes the change of lateral acceleration (in the track plane) asa function of time. Another word for rate of cant deficiency is lateral jerk.

For transition curves with a linear change of curvature and superelevation ramps withlinear variation of cant, the following relationship is derived, where hd is the cantdeficiency variation: [3], [7]

(2-27)

dh tdt

-------ht vmax

Lt-----------------------=

dhddt

--------hd vmax

Lt------------------------=


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15

3 Standards, practices and TSI

In this Chapter standards and practices according to Sweden, Germany, France and Japanare being presented. The proposal from the European Association for RailwayInteroperability (AEIF), Technical Specifications of Interoperability (TSI) [12] is also

demonstrated. TSI do often refer to the European (CEN) provisional standard [7]. Thisreport will also refer to the European provisional standard.

3.1 Track gauge

Every high-speed rail system in the world have 1435 mm in designed track gauge. Allcontent in the following Sections and Chapters refers to this standard gauge.

3.2 National standards in Sweden

In Sweden does exists a regulation BVF 586.41 [5] and a handbook, BVH 586.40 [4]concerning track geometry parameters. The regulations is mandatory while the handbookis informative. In the following text the regulation is called BVF while the handbook iscalled BVH.

3.2.1 Track cant and track distance

According to Banverket cant shall not exceed 150 mm. Track distance most frequentlyused in Sweden is 4.5 metres, although there are exceptions in both directions.

3.2.2 Cant deficiency and cant excess

Cant deficiency

The uncompensated lateral acceleration, which is proportional to cant deficiency, should

not be too large. Table 3-1 shows the permissible cant deficiency and its correspondinglateral acceleration for three different categories of rolling stock according to Banverket.


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Standards, practices and TSI

The different train categories in Table 3-1 have the following meaning:

- Category A conventional vehicles with older running gear and freight trains;

- Category B vehicles with improved running gear, according to approval;

- Category S vehicles with improved running gear and carbody tilt system.

Cant excess

According to Banverket cant excess should not be larger than 100 mm on tracks withradius larger than 1000 m. On tracks with radius less than 1000 m cant excess should notexceed 70 mm.

3.2.3 Horizontal curve radius

The recommended horizontal curve radius in Banverket handbook BVH 586.40 is avalue calculated with cant ht= 150 mm and cant deficiency hd= 100 mm in the formulafor equilibrium cant, i.e. Category A trains. For new lines it is recommended that thedimensional speed is multiplied with a speed factor = 1.3 This factor is used to get amargin with respect to ride comfort and increased speed in the future.

(3-1)

Table 3-1 Permissible cant deficiency and the corresponding lateral acceleration.Track without turnouts. Source: Banverket[4].

Train categoryPermissible cant

deficiency (mm)

Lateral acceleration, ay

(m/s2)A 100 0.65

B 150 0.98

S 245 1.60

Table 3-2 Recommended horizontal curve radius.Source: Banverket[4].

200km/h

250km/h

280km/h

300km/h

330km/h

350km/h

Recommendedradius [m]

3200 5000 6300 7200 8700 9800

Rrec min,1.3 Vdim( )

211.8

250----------------------------------------------=


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Minimum value of the horizontal radius according to Banverket can be expressed as

(3-2)

Corresponding radii, as a function of target speed, are shown in Table 3-3. There is an

inherent assumption that trains of category A will be used.

Limit values of horizontal curve radius according to Swedish standard is presented in

Figure 3-1 below.

Figure 3-1 Recommended and minimum horizontal curve radius as a function of

speed. Source: Banverket[4].

In reality, however, it is often difficult to meet these recommendations. On several newlybuilt lines compromises have been made, of economic and other reasons. For example,this is the case for many sections on the West Coast Main Line (Gteborg - Malm) andthe Mlar Line (Stockholm - rebro), where no margin exists for future improvement inspeed or comfort, if trains Category A are used. On the newly started project Botnia-banan ((Sundsvall -) Nyland - Ume) the target speed is 250 km/h. For large sections ofthis line such a speed will only be achieved by using tilting trains (Category S).

Table 3-3 Minimum horizontal curve radius.Source: Banverket[4], [5].

200km/h

250km/h

280km/h

300km/h

330km/h

350km/h

Minimum radius [m] 1888 2950 3700 4248 5140 5782

RminVdim

2 11.8

250-----------------------------=

0

1000

2000

30004000

5000

6000

7000

8000

9000

10000

11000

100 150 200 250 300 350

Speed [km/h]

Horizontalc

urveradius[m]

Recommended radius according to BVH 586.40

Minimum radius according to BVF 586.41 and

BVH 586.40


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3.2.4 Transition curve and superelevation ramp

According to Banverket [4] transition curves should be arranged with linear curvaturechanges (clothoids) and superelevation ramps should be arranged with linear changes ofcant. The transition curve shall coincide with the superelevation ramp in both shape andposition. Generally, the length of transition curves depends, among others, on the

permitted gradient of cant, which is an important safety aspects because of wheelunloading and thus the risk of derailment. However, in long transition curves, which isthe case in high-speed operations, ride comfort aspects usually determine the minimumlength of transition curves.

The change of lateral acceleration with respect to time is called jerk. The jerk can also bedescribed as a change of cant deficiency with respect to time, as mentioned in Chapter 2.Thus, the length of transition curve is dependent of the allowed amount of jerk. Theallowed rate of cant deficiency is a question of comfort. In Sweden used values formaximum rate of cant and rate of cant deficiency is shown in Table 3-4.

In a superelevation ramp the cant changes linearly. The twist1:n states the change of rate

of cant per unit length. n is called ramp number.

(3-3)

whereLt = length of linear superelevation ramp in metres.ht,mm = cant difference in [mm].

It is normally the S-train requirements that determines the length of the transition curve.The length of the transition curve should be adjusted to the maximum speed of trainscategory S that the curve radius allows. The recommended transition curve lengthaccording to Banverket [4] is:

(3-4)

for R Rrec and

(3-5)

for R > Rrec.

Table 3-4 Maximum rate of cant and rate of cant deficiencySource: Banverket[4].

Train category Maximum rate of cant Maximum rate of cant deficiency

A 46 mm/s 46 mm/s

B 55 mm/s 55 mm/s

S 70 mm/s 79 mm/s

1n---

ht mm,1000 Lt---------------------=

Lt 5 R=

LtVdim

3

9 R-----------=


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There are other formulas used by Banverket that state the permitted speed in transitioncurves. According to Banverket BVF 586.41 [5] the length of superelevation ramp, Lt[m], and permissible speed, Vlim [km/h], should be calculated with the followingstatements:

(3-6)

(3-7)

(3-8)

Here ht and hd are the changes of cant and cant deficiency, respectively, over thetransition curve. The constants qtand qdcan be found in Table 3-5 and are depending ontrain category.

3.2.5 Gradient

Banverket prescribes in their handbook BVH 586.40 [4] a largest permissible gradient of10 on track with heavy freight trains. 12.5 can be permitted if the mean value doesnot exceed 10 over each kilometre. On tracks with only passenger trains and lightfreight trains higher values may be allowed.

Table 3-5 Constants qt and qdfor each train category.Source: Banverket[5].

Train category qt qd

A 6 6

B 5 5

S 4 3.5

Lt 0.4 ht mm,

Vdi mLt 1000

qt ht mm,--------------------------

VdimLt 1000

qd hd mm,----------------------------


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3.2.6 Vertical curve radius

In Banverket regulation BVF 586.41 [5] the vertical curve radius shall be in accordanceto permissible speed as shown in Equation (3-9):

(3-9)

Equation (3-9) leads to vertical curve radii shown in Table 3-6.

Banverket prescribes in their handbook BVH 586.40 [4] a recommended vertical curveradius:

(3-10)

Some recommended vertical curve radii are shown in Table 3-7.

The minimum vertical curve radius is calculated according to BVH 586.40 [4] with

respect to the overspeed of 25% of category S-train (1.252 = 1.5625; 0.16*1.5625 =

0.25).(3-11)

Table 3-6 Minimum vertical curve radius.Source: Banverket[5].

200km/h

250km/h

280km/h

300km/h

330km/h

350km/h

Minimum vertical radius [m] 6400 10000 12544 14400 17424 19600

Table 3-7 Recommended vertical curve radius.Source: Banverket[4].

200km/h

250km/h

280km/h

300km/h

330km/h

350km/h

Recommended vertical curveradius [m]

16900 26500 33200 38100 46100 51800

Rv min,

Vdim2

6.25----------- 0.16 Vdim2

=

Rv rec min,, 0.25 1.3 Vdi m( )2

Rv min, 0.25 Vdim2


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Minimum values of vertical curve radius are shown in Table 3-8.

In Figure 3-2 shows the relations between recommended and minimum vertical curveradius according to Banverket.

Figure 3-2 Limit value of vertical curve radius as a function of speed.Source: Banverket[4], [5].

Table 3-8 Minimum vertical curve radius.Source: Banverket[4].

Vertical curve radius 200

km/h

250

km/h

280

km/h

300

km/h

330

km/h

350

km/hMinimum vertical radius [m] 10000 15625 16900 22500 27225 30625

0

10000

20000

30000

40000

50000

60000

100 150 200 250 300 350

Speed [km/h]

Verticalcurveradius[m

]Minimum vertical radius according to BVF 586.41

Minimum vertical radius according to BVH 586.40

Recommended vertical radius according to BVH 586.40


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3.3 National standards in Germany

In Germany different train categories are not used in the same manner as in Sweden. Aclassification is used where values are prescribed with or without permission. Designvalues for equilibrium cant according to German standards, 800.0110 [9], are shown inTable 3-9.

Table 3-9 Design values of equilibrium cant.Source: Deutsche Bahn [9].

Without permission Equilibrium cant

Recommended heq = 170 mm

Limit heq = 290 mm

Permission necessary

Permission heq = ht+ hd(values are shown inTable 3-10 and Table 3-11)

Exception heq = ht+ hd(values are shown inTable 3-10 and Table 3-11)


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3.3.1 Track cant

Values for cant according to [9] are shown in Table 3-10. The recommended value forcant is 100 mm and the maximum value with permission is 180 mm.

There is a recommended value of cant depending on the speed of the fastest trains andthe horizontal curve radius.

(3-12)

There is also a minimum value of cant which has to be arranged according to Equation(3-13)

(3-13)

hd,lim, See 3.3.2 Cant deficiency

Examples of horizontal curve radius according to German standard are shown in section3.3.3.

3.3.2 Cant deficiency

Table 3-11 shows values for permitted cant deficiency on plain track according to [9].

Table 3-10 Design values of cant.

Source: Deutsche Bahn [9]Without permission

Recommended ht= 100 mm

Limit ht= 160 mm (Ballast track)ht= 170 mm (Ballastless track)

Permission necessary

Permission mm (Ballast track)

mm (Ballastless track)

Exception ht> 180 mm

160 ht 180

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