track geometry for high-speed railways

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

Stockholm2001

Railway TechnologyDepartment of Vehicle Engineering

Royal Institute of Technology

Track geometry forhigh-speed railways

A literature surveyand

simulation of dynamic vehicle responce

by

Martin Lindahl

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

Track geometry forhigh-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]

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 andJapan 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 Prud´hommes 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 inorder 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

i

Sammanfattning

I Sverige finns behov av spårgeometri för höghastighetsbanor. Bl.a. har fråganaktualiserats i samband med studier av den s.k. Europakorridoren (Stockholm -Jönköping - Köpenhamn/Göteborg). I dessa sammanhang har det framförts önskemål omen hastighetsstandard för 350 km/h, vilket är den standard som åtminstone delvisprojekteras och byggs i Mellan- och Sydeuropa. För Sveriges del, som är ett land medlånga transportavstånd, finns det behov av korta restider på långa avstånd, vilket talar förhög hastighet. Detta ställer krav på stora kurvradier. Samtidigt finns ett starkt behov avatt bygga banorna med relativt låga investeringskostnader samt små intrång i natur ochbebyggelse. Detta ställer krav på att inte göra kurvradierna större än absolut nödvändigtoch även att kunna tillåta relativt större lutningar i banan.

En litteraturgenomgång har utförts där förslagen till europastandard för spårgeometristuderats (CEN och TSI). Dessa förslag till europastandard skapar flera möjligheter attminimera både horisontella och vertikala kurvradier. Det föreslås även vara möjligt atttillåta tåg med korglutning efter särskilt tillstånd av banhållaren. Lutningar i banan uppemot 35 ‰ föreslås även vara tillåtet.

Rapporten tar även upp den framtida tågteknologin om vad som är tekniskt möjligt vilkethar diskuterats med tekniska experter inom industrin. Optimerad passiv hjulparsstyrningär en del som diskuterats. I detta sammanhang har utvecklingen av aktivsekundärfjädring nämnts som ett alternativ men dock inte studerats ingående. Denaerodynamiska utformningen har förfinats och senast känd teknologi har används.

Simuleringarna har utförts i tre olika steg. Först görs en gångstabilitetssimulering för attfastställa att använd teknik klarar av hastigheterna som eftersträvas. Nästa steg var attberäkna spårförskjutningskrafter med Prud´hommes kriterium som gränsvärde. I dennadel simulerades olika fall där spårläget varierades för att ge en uppfattning om vad somkrävdes för att klara gränsvärdet. Slutligen simulerades säkerheten mot vältning vidkraftig sidvind enligt föreslagna riktvärden för vilka vindhastigheter som bör klaras.

Bland annat har följande slutsatser dragits:

- Rälsförhöjning upp mot 200 mm är möjligt vid antagandet av enbart höghastighets-trafik (V ≥ 200 km/h).

- Rälsförhöjningsbrist upp mot 250 mm kan tillåtas förutsatt att korglutningsteknik ochlämpliga boggier används.

- Långa övergångskurvor rekommenderas (en varaktighet om minst ca 4-5 s).

- Uppställda gångstabilitetsvillkor uppnås.

- Spårläget måste förbättras för att gränsvärdet för de laterala spårförskjutnings-krafterna ska klaras. Graden av förbättring måste studeras vidare.

- Villkoren för sidvindsstabilitet klaras om tåget får en god aerodynamisk utformning.

- Banans lutningsförhållanden bör väljas med hänsyn till den godstrafik som förutses.

Nyckelord: Spårgeometri, höghastighetsbana, tåg, höghastighetståg, godståg rälsförhöjning,rälsförhöjningsbrist, rälsförhöjningsöverskott, rakspår, övergångskurva, horisontalkurva, lutning, vertikal-kurva, simulering, gångstabilitet, spårförskjutningskraft, vältning, spårlägesfel.

iii

Preface and acknowledgements

This study has been carried out at the Division of Railway Technology, Department ofVehicle Engineering, Royal Institute of Technology (KTH, Kungliga TekniskaHögskolan), Stockholm, in close cooperation with the Swedish National RailAdministration (Banverket), Europakorridoren AB, Helsingborg, BombardierTransportation, Västerås, and the Swedish National Road and Transport ResearchInstitute (VTI), Linköping. 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 Ågren from BombardierTransportation and Björn 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

v

Table of contentsAbstract .............................................................................................................................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 .........................................................32.1 Design track geometry....................................................................................3

2.1.1 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...................................................................................153.1 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 ........................................................................................233.3.3 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

vii

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...................................................................454.1 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 .................495.1 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....................................................696.1 Hunting stability on tangent track and on curve...........................................69

6.1.1 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

viii

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.................................786.2.6 Improvements of track irregularities........................................................80

6.3 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..............................................................897.1 Different categories of freight trains ............................................................897.2 Permissible axle load and track loadings......................................................917.3 Track cant and cant excess ...........................................................................937.4 Gradients versus train mass ..........................................................................96

7.4.1 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..........................................................................................1018.1 Horizontal curve radius ..............................................................................1018.2 Vertical curve radius...................................................................................108

9 Conclusions and further research .........................................................................1099.1 Conclusions on the literature study ............................................................1099.2 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

ix

Track geometry for high-speed railways

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 ‘Götalandsbanan’, 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 à 12 ‰) if ordinarylocomotives 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.

1

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 theindustry around 2010.

2


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.

ϕt

ht

2bo

--------asin=

3

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 discomfort at standstill or low speed;

- risk of derailment of freight trains in sharp curves due to the combined effect of highlateral and low vertical load on the outer wheel at low speed;

- possible displacement of wagon loads;

Figure 2-2 Cant ht and cant angle ϕt.

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 curve

with 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 byloosening of rail fastenings;

- high lateral forces on the track.

k 1 R⁄=

4


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. A superelevation 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 thelongitudinal coordinate [16]

(2-2)

if s = s0 = 0 at the start of the transition curve

where

k is 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⋅=

5


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 gradientare 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 theprofile elevation is shown in Figure 2-4.

6


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 grades a 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 of a, b and Rv gives the following condition

(2-6)

(2-7)

z x( ) a b–( )2000L---------------- x

2– Ax

2–

2000L---------------= =

zL2---

� �� e a b–( ) L

8000------------–= =

LRv a b–( )

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

zL2---

� �� Rv

a b–( )2

8 106⋅

-------------------⋅–=

7


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 Φ.

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

The equations can be written as follows [1]:

(2-8)

(2-9)

ay

az

ay

ayv

2

R----- ϕt g ϕt

v2

R----- ϕt g

ht

2bo

--------⋅–cos⋅=sin⋅–cos⋅=

azv

2

R----- ϕt g ϕtcos⋅+sin⋅=

8


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

(2-10)

(2-11)

The lateral force angle Φ 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 theequilibrium speed or 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 ϕtsin⋅–≈ v

2

R----- g

ht

2bo

--------⋅–=

az g≈

Φay

az

-----atan=

heq

2b0

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≈ V

2

R------⋅≈

veq

R g ht⋅ ⋅2bo

--------------------=

9


(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 hd is the difference between equilibrium cant heq and actual cant ht and 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 trackplane acceleration which gives (in SI-units) [1]

(2-21)

where ay > 0

Veq

R ht mm,⋅11.8

---------------------=

hd heq ht–=

hd

2b0

g-------- v

2

R-----⋅ ht–=

hd mm, 11,8V

2

R------⋅ ht mm,–=

hd

2bo

g-------- ay⋅=

10


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 acceleration

ay (m/s2)Lateral force angle

Φ (°)Cant deficiency

hd (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 0.250

1.797 10.46 0.275

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

11


Cant excess

If the actual cant is higher than the equilibrium cant something called cant 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–=

he

2bo

g--------– ay⋅=

vlim R ay lim, ght

2bo

--------⋅+� �� R g⋅

2bo

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

Vlim R hd lim, ht+( ) 12.96g2bo

-----------------⋅=R hd lim, ht+( )

11.8---------------------------------≈

12


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 ∆ht is 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)

dht

dt-------

∆ht vmax⋅Lt

-----------------------=

dhd

dt--------

∆hd vmax⋅Lt

------------------------=

13


14


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 alsodemonstrated. 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.


Cant deficiency

The uncompensated lateral acceleration, which is proportional to cant deficiency, shouldnot 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.

15

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 γ = 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 cantdeficiency (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⋅( )2

11.8⋅250

----------------------------------------------=

16


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 aninherent assumption that trains of category A will be used.

Limit values of horizontal curve radius according to Swedish standard is presented inFigure 3-1 below.

Figure 3-1 Recommended and minimum horizontal curve radius as a function ofspeed. 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 (Göteborg - Malmö) andthe Mälar Line (Stockholm - Örebro), 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 - Umeå) 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

Rmin

Vdim2

11.8⋅250

-----------------------------=

0100020003000400050006000700080009000

1000011000

100 150 200 250 300 350

Speed [km/h]

Ho

rizo

nta

lcu

rve

rad

ius

[m]

Recommended radius according to BVH 586.40

Minimum radius according to BVF 586.41 andBVH 586.40

17



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 thepermitted 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 twist 1:n states the change of rateof 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⋅=

Lt

Vdim3

9 R⋅-----------=

18


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 qt and qd can 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 qd for 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,⋅≥

Vdim

Lt 1000⋅qt ∆⋅ ht mm,--------------------------≤

Vdim

Lt 1000⋅qd ∆⋅ hd mm,----------------------------≤

19


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,Vdim

2

6.25----------- 0.16 Vdim

2⋅=≥

Rv rec min,, 0.25 1.3 Vdim⋅( )2⋅≥

Rv min, 0.25 Vdim2⋅≥

20


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 200km/h

250km/h

280km/h

300km/h

330km/h

350km/h

Minimum 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]

Ver

tica

lcu

rve

rad

ius

[m]

Minimum vertical radius according to BVF 586.41Minimum vertical radius according to BVH 586.40Recommended vertical radius according to BVH 586.40

21


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)

22


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 mm (Ballast track)

mm (Ballastless track)

Exception ht > 180 mm

160 ht 180≤<

170 h< t 180≤

ht rec,7.1 Vdim

2⋅R

-----------------------=

ht min,11.8 Vdim

2⋅R

-------------------------- hd lim,–=

23



The recommended horizontal curve radius according to DB is derived from thefollowing formula and some examples are shown in Table 3-12.

(3-14)

This recommendation is based on an equilibrium cant of 170 mm, i.e. 100 mm of cantand 70 mm of cant deficiency.

The limit of horizontal curve radius (without permission) can be described of Equation(3-15) and some examples are shown in Table 3-13.

(3-15)

This limit value is based on an equilibrium cant of 290 mm.

Table 3-11 Design value of cant deficiencySource: Deutsche Bahn [9]

Without permission

Recommended hd = 70 mm

Limit hd = 130 mm


Permission hd = 150 mm

Table 3-12 Recommended horizontal curve radius.Source: Deutsche Bahn [9].

200km/h

250km/h

280km/h

300km/h

330km/h

350km/h

Recommended radius [m] 2776 4338 5542 6247 7559 8503

Table 3-13 Limit value of horizontal curve radius.Source: Deutsche Bahn [9].

200km/h

250km/h

280km/h

300km/h

330km/h

350km/h

Limit radius [m] 1628 2543 3190 3662 4431 4984

Rrec

Vdim2

11.8⋅heq

-----------------------------Vdim

211.8⋅

170-----------------------------= =

Rlim

Vdim2

11.8⋅290

-----------------------------=

24


A value of horizontal curve radius were permission is needed can be described byEquation (3-16) according to DB.

(3-16)

This permission value is based on an equilibrium cant of 330 mm with a cant of 180 mmand a cant deficiency of 150 mm.

Some examples are shown in Table 3-14.

Figure 3-3 shows the horizontal curve radius as a function of speed for three differentlevels according to German standard. Table 3-9 to 3-11 described the levels whichGerman standard is based upon.

Figure 3-3 Horizontal curve radius as a function of speed.Source: Deutsche Bahn [9].

Table 3-14 Permission value of horizontal curve radius.Source: Deutsche Bahn [9].

Horizontal curve radius 200km/h

250km/h

280km/h

300km/h

330km/h

350km/h

Permission value [m] 1430 2234 2803 3218 3894 4380

Rpermission

Vdim2

11.8⋅330

-----------------------------=

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

100 150 200 250 300 350

Speed [km/h]

Ho

rizo

nta

lcu

rve

rad

ius

[m] Recommended minimum value according to DB

Limit value (without permission) according to DB

Permission value according to DB

25



Transition curvature shall coincide with superelevation ramps in both shape and position.The regulations for the design of transition curves, due to maximum cant gradient, arethe same as Equation (3-6) [10], [15]:

(3-17)

The lower permissible limit of Lt according to this formula is applied on low speed trackonly; for high-speed lines the transition length is determined by the rate of change in cantdeficiency according to Equation (3-20).

The permitted speed in transition curves with linear change of cant, however, is partlydifferent from Sweden. In Germany the maximum speed for non-tilting trains isaccording to [10], [15]

(3-18)

(3-19)

The minimum length of clothoid type of transition curves is according to DB [9] inaccordance with Equation (3-19) which after rewriting can be obtained as follows

(3-20)

For tilting trains the following formula is valid for transition curves with linear change ofcurvature and cant, respectively [10] [15]:

(3-21)

3.3.5 Gradient

DB have prescribed [10] a largest permissible gradient of 12.5 ‰ for mixed traffic mainlines (Hauptbahnen). For commuter lines (S-Bahnen) and secondary lines(Nebenbahnen) the maximum gradient is 40 ‰. Also, in the new-build high-speed linesthe higher gradient (40 ‰) is used.

Lt 0.4 ∆ht mm,⋅≥

Vdim

Lt 1000⋅8 ∆⋅ ht mm,-------------------------≤

Vdim

Lt 1000⋅4 ∆⋅ hd mm,--------------------------≤

Lt min,4 Vdim ∆hd⋅ ⋅

1000--------------------------------≥

Vdim

Lt 1000⋅6 ∆⋅ ht mm,-------------------------≤

26



Minimum permissible vertical curve radius is shown in Table 3-15.

Some examples are shown in the following table.

Table 3-15 Design value for vertical curve radius

Without permission

Recommendedminimum value

Limit value


Permissionon a crest

in a hallow

Exception value -

Table 3-16 Recommended minimum value for vertical curve radiusSource: Deutsche Bahn [9].

Vertical curve radius 200km/h

250km/h

280km/h

300km/h

330km/h

350km/h

Recommended minimum 16000 25000 31360 36000 43560 49000

Limit 10000 15625 16900 22500 27225 30625

Permission value on a crest 6400 10000 12544 14400 17424 19600

Permission value in a hallow 5200 8125 10192 11700 14157 15925

Rv 0.4 Vdim2⋅=

Rv 0.25 Vdim2⋅=

Rv 0.16 Vdim2⋅=

Rv 0.13 Vdim2⋅=

Rv 2000m≥

27


3.4 Practices in France

3.4.1 Cant, cant deficiency and cant excess

Recent information regarding France is scarce. The following was found in [18].

Experiment shows that the non compensated lateral acceleration should not exceed 0.10

à 0.15 g (1.0 à 1.5 m/s2) according to comfort requirements. SNCF allows a cant

deficiency of 150 mm (exceptional value 160 mm)1 and a cant excess of 70 to 100 mm(exceptional values between 105 and 135 mm, in dedicated high-speed operations,without freight trains).

At SNCF the limiting value of cant is about 160 mm and exceptionally 180 mm. A cantof 180 mm was utilized as limiting value at the high-speed line Paris-Sud Est. The cant isgiven to respect the limiting values of cant deficiency (150 mm) and cant excess (100mm).

1. The ‘Grande Vitesse Paris-Sud-Est’ line limited the value of cant deficiency to 100 mm [15].

28


3.5 Practices in Japan

A specified track geometry standard for the Japan railway has not been found in Englishbut a Data Book 2000 for the Central Japan Railway Company [19] was found. In thebook a compilation over the structural specifications was arranged, see Table 3-17

Table 3-17 Structural specifications for the Central Japan Railway Company.

TokaidoShinkansen

SanyoShinkansen

Tohoku-JoetsuShinkansen

Start of operations 1964 1972 1982

Maximum operating speed [km/h] 270 300a

a. Planned speed

275

Maximum gradient [‰] 20 15 15

Minimum curve radius [m] 2500 4000 4000

Minimum vertical curve radius [m] 10000 15000 15000

Cant [mm] 200 180 180

Distance between track centres 4.24 4.3 4.3

29


3.6 Technical Specifications of Interoperability and CEN proposal

The purposes of the Technical Specifications of Interoperability (TSI) [12] are accordingto Article 5(3) of Directive 96/48/EC (among other things):

- specify the essential requirements for the subsystems and their interfaces;

- establish the basic parameters that are necessary to meet essential requirements;

- establish the conditions to be compiled with, to achieve the specified performancesfor each of the following categories:

- lines specially built for high-speed,

- lines specially upgraded for high-speed,

- lines specially built or upgraded for high-speed, which have specialfeatures as a result of topographical, relief or town-planning constraints;

- establish possible implementing provisions in certain specific cases;

- determine the interoperability constituents and interfaces which must be covered byEuropean specifications, including European standards which are needed to achieveinteroperability within the trans-European high-speed rail system while meeting theessential requirements;

Furthermore, according to TSI, the performance levels of high-speed trains can also beenhanced by adopting specific systems, such as vehicle body tilting.

The TSI is yet not completed; the above mentioned version [12] is a draft.

3.6.1 Track cant and track distance

According to the draft TSI the cant for new high-speed lines in the design phase shall belimited to 180 mm to agree with the specifications set out by CEN/TC 256/WG15, Trackalignment design parameters, a provisional European norm, prENV 13803-1 [7]. Furtherthe TSI says that for tracks in operation, a maintenance tolerance of 20 mm is allowed,without trespassing a maximum cant of 190 mm. This value may be raised to 200 mmmaximum on tracks reserved for passenger traffic alone in accordance with thespecifications in the CEN provisional standard on maximum limiting values.

The minimum track distance between main track centres on lines specially built for high-speed is 4.5 m according to TSI. This value could be decreased and adapted according tothe performance levels and could be 4.20 m if 250 < V ≤ 300 km/h and 4.0 m if speed V≤ 250 km/h.

30


Table 3-18 shows values of cant according to CEN provisional standard, currentlyprENV 13803-1, final draft, February 2001.


Cant deficiency

Table 3-19 to Table 3-21 show the limit values of cant deficiency on plain trackaccording to TSI.

Higher values of cant deficiency than shown in Table 3-19 may be allowed for lineswhose construction involves very tough topographical constraints, see Table 3-20.

Table 3-18 Limiting values of cantSource: CEN provisional standard, prENV 13803-1 [7].

Traffic categories

Mixed traffic linesdesigned for

passenger train

Mixed traffic lineswith passenger

train(or 250

on upgraded lines)with vehiclesincorporating

special technicaldesign

characteristics

High-speed lineswith dedicated

passenger traffic

Recommendedlimiting value [mm]

160 160 160

Maximumlimiting value [mm]

180 180 200

Table 3-19 Cant deficiency for lines specially built for high-speed.Conventional trains without tilt. Source: TSI [12].

Speed range (km/h) Limiting value (mm)

100

80

200 V 300≤<

V 230≤

250 V 300≤ ≤

250 V 300≤ ≤

V 300>

31


Higher values of cant deficiency than shown in Table 3-20 may be allowed for lineswhose construction involves very strict topographical constraints, see Table 3-21.

However, on lines the radii of which have been defined on the basis of the cantdeficiency values in the above tables, interoperable high-speed trains equipped with tilttechnology may be admitted to run with higher cant deficiency values, provided thatadopting such values for those trains does not bring about restrictions for otherinteroperable trains [12].

Table 3-20 Cant deficiency for lines specially upgraded for high-speed andconnecting lines.Lines whose construction involves very tough topographical constraints.Conventional trains without tilt. Source: TSI [12].

Speed range (km/h) Limiting value (mm)

160

150

140

130

Table 3-21 Cant deficiency for lines specially built or upgraded for high-speedhaving special features.Lines whose construction involves very strict topographical constraints.Conventional trains without tilt. Source: TSI [12].

Speed range (km/h)Maximum limiting

value (mm)

Cant deficiency range forwhich the length of curves islimited to 20% of the total

curve length (mm)

180

165

150

130

V 160≤

160 V< 200≤

200 V< 230≤

230 V< 250≤

V 160≤ 160 hd< 180≤

160 V< 230≤ 150 hd< 165≤

230 V< 250≤ 130 hd< 150≤

250 V< 300≤ 100 hd< 130≤

32


According to the CEN provisional standard the values of cant deficiency and itscorresponding lateral acceleration are based on the following considerations:

- Track forces and safety;

- Economic aspects of track maintenance;

- Ride comfort and roll flexibility coefficients of the vehicles.

Table 3-22 below lists the limiting values of cant deficiency in accordance to CENprovisional standard [7].

Cant excess

The TSI does not discuss cant excess. However, CEN provisional standard gives asguidance, the following limiting values for cant excess:

- 110 mm as recommended limiting value;

- 130 mm is a maximum limiting value.

Table 3-22 Limiting values of cant deficiency.Conventional trains without tilt. Source: CEN provisional standard, [7].

Traffic categories

Recommendedlimiting value [mm]

Maximum limitingvalue [mm]

Freight Passenger Freight Passenger

Mixed traffic linesdesigned for passenger

trains

100 100 150 150

80 80 130 130

Mixed traffic lineswith passenger train

(or 250 km/ onupgraded lines)

with vehicles incorpo-rating special techni-

cal designcharacteristics

110 160 160 180

x 140 x 160

x 120 x 160

x 100 x 150

High-speed lines withdedicated passenger

traffic

x 100 x 150

x 80 x 130

200 V 300≤<

200 V 250≤<

250 V 300≤<

V 230≤

V 160≤

160 V 200≤<

200 V 230≤<

230 V 250≤<

250 V 300≤ ≤

V 250=

V 250>

33



The parameters that shall be considered in the determination of the minimum curveradius according to CEN provisional standard [7] are:

- The maximum and minimum operating speeds;

- The applied cant;

- The limiting values for cant deficiency and cant excess.

The minimum allowable curve radius for the maximum operating speed shall becalculated using the following equation:

(3-22)

The minimum allowable curve radius for the minimum operating speed shall becalculated using the following equation:

(3-23)

The minimum curve radius should be optimised so that the values of cant, cantdeficiency and cant excess comply with the limits specified in [7] and satisfy thefollowing condition:

(3-24)

Table 3-23 gives some examples of the usage of Equation (3-22) - (3-24).

Table 3-23 Examples of optimised cant and optimised horizontal curve radius.Calculations are made with both high-speed trains (conventional trainswithout tilt) and slowly running freight trains. Values of cant deficiencyand cant excess are recommended values according to TSI [12].

Vmax

[km/h]Vmin

[km/h]hd

[mm]he

[mm]ht

[mm]R

[m]

300 80 100 110 126 4696

300 120 100 110 150 4247

300 160 100 110 193 3618

350 80 80 110 120 7209

350 120 80 110 135 6713

350 160 80 110 160 6017

R11.8

ht hd+---------------- Vmax

2⋅=

R11.8

ht he–--------------- Vmin

2⋅=

11.8 Vmin2⋅

ht he–-------------------------- R

11.8 Vmax2⋅

ht hd+---------------------------≥ ≥

34


For lines specially built or upgraded for high-speed having special features a cantdeficiency of 130 mm can be applied for speed up to 300 km/h. Still no tilt system is inuse. Table 3-24 give some examples.


Rate of cant

For cant gradients with uniform slope, the following relationship with ∆ht being the cantvariation is desired according to CEN provisional standard [7]:

(3-25)

The limiting value of rate of cant as a function of time (dht/dt)lim is shown in Table 3-25.

Table 3-24 Examples of horizontal curve radius with a cant deficiency of 130 mmfor 250 km/h and 300 km/h with different values of cant.Conventional trains without tilt.

Vmax[km/h]

hd[mm]

ht[mm]

R[m]

250 130 160 2543

300 130 160 3662

250 130 180 2379

300 130 180 3425

250 130 200 2235

300 130 200 3218

Table 3-25 Limiting values of rate of cant as a function of time (dht/dt)lim.The values apply to cant gradient with uniform slope.Conventional trains without tilt. Source: CEN provisional standard, [7].

Traffic categories


passenger trains


train speeds


passenger traffic

Recommendedlimiting values

[mm/s]

50 50 50

Maximum limitingvalues [mm/s]

60 60 60

dht

dt-------

∆ht Vmax⋅3.6 Lt⋅

------------------------dht

dt-------

� ��

lim≤=

200 v 300≤< v 230≤ 250 v 300≤<

35


Limiting values of rate of cant as a function of length (dht/dx)lim shall apply to thefollowing values, although not critical at high-speed operations:

Recommended limiting value: 2.25 mm/mMaximum limiting value: 2.5 mm/m

Rate of cant deficiency

For transition curves with a uniform variation of curvature and a uniform variation ofcant, the following relationship is derived, ∆hd is the variation of cant deficiency:

(3-26)

The limiting value of rate of cant deficiency as a function of time (dhd/dt)lim is shown inTable 3-26.

Length of transition curves in the horizontal plane

The length of transition curves in the horizontal plane should, according to Europeanprovisional standard [7], be determined by the limiting values of rate of cant deficiencyas a function of time, dhd/dt and rate of cant as a function of length, dht/dx.

(3-27)

(3-28)

The length of transition curve shall be the longest value derived from the above formulafor the selected values of dhd/dt and dht/dx.

Table 3-26 Limiting values of rate of cant deficiency as a function of time(dhd/dt)lim.The values shown apply to all forms of transition curves.Conventional trains without tilt. Source: CEN provisional standard, [7].

Traffic categories


passenger trains


train speeds


passenger traffic


[mm/s]

50 50 50

Maximum limitingvalues [mm/s]

75 90 75

dhd

dt--------

∆hd Vmax⋅3.6 Lt⋅

-------------------------dhd

dt--------

� ��

lim≤=

200 V 300≤< V 230≤ 250 V 300≤<

Lt

Vmax

3.6----------- ∆hd

dhd

dt--------

� ��

lim

1–

⋅≥

Lt ∆ht

dht

dx-------

� ��

lim

1–

⋅≥

36


3.6.5 Gradient

According to TSI, gradients as steep as 35 ‰ shall be allowed for main tracks at thedesign phase, provided the following requirements are met:

- The slope of the sliding average profile over 10 km is less than or equal to 25 ‰;

- The maximum length of continuous 35 ‰ gradient does not exceed 6 km.

Those recommended limiting values shown above apply only to high-speed linesdedicated to passenger traffic. Exceptions are made for France, which already hasgradients up to 40 ‰ on one line (Paris-Sud-Est). Furthermore, the new line betweenCologne and Frankfurt is also using gradients as high as 40 ‰. Other restrictions arevalid for freight trains.


The vertical curve radius shall be designed using the following formula

(3-29)

The vertical acceleration, av, used in Equation (3-29) shall be selected taking intoconsideration ride comfort where there is a possibility of a non optimal track bed. Inaddition, consideration shall be given to safety to guard against derailment due to wheelunloading when running over humps (crests). However, this safety limit is notconsidered unless the maximum limiting values for av are exceeded. The limit values ofvertical acceleration are shown in Table 3-27.

Table 3-27 Limit values of vertical acceleration, av,lim.Source: CEN provisional standard [7].

Traffic categories


passenger trains


train


passenger traffic


[m/s2]

0.22 0.22 0.22

Maximum limiting

values [m/s2]0.44a

a. With a tolerance of +10% on a crest, +30% in a hallow

0.31 0.44a

Rv

Vmax2

12.96 av⋅----------------------- Rv lim,≥=

200 V 300≤< V 230≤ 250 V 300≤<

37


Equation (3-29) and the limit values of vertical accelerations in Table 3-27 yield limitingvalues of vertical curve radius.

Table 3-28 Limit values of vertical curve radius, Rv,lim.Source: CEN provisional standard [7].

Traffic categories


passenger train


train


passenger traffic

Recommendedlimiting values [m]

Minimum limitingvalues [m]

200 V 300≤< V 230≤ 250 V 300≤<

0.35Vmax2

0.35Vmax2

0.35Vmax2

0.175Vmax2

0.25Vmax2

0.175Vmax2

38


3.7 Comparison between different projects and standards


Table 3-29 “Planned alignment and track parameters of new lines of the secondgeneration high-speed railways.”Source: Compilation made of E. Hohnecker [20].

Line Vlim

[km/h]Rmin

[m]ht,max

[mm]hd,max

[mm]ay

[m/s2]

DBa

a. Ballast track

300 3200 200 130 0.85

JRb

b. Ballastless track

350 4000 200 160 1.05

SNCFa 350 4000 200 160 1.05

39


Tabl

e3-

30C

ompa

riso

nbe

twee

ndi

ffer

entq

uant

ities

ondi

ffer

entr

ailw

ayco

mpa

nies

thro

ugho

utth

ew

orld

.E

xcep

tiona

lval

ues

notc

onsi

dere

d.

Org

anis

atio

nT

SI/

CE

NJR

JRJR

DB

DB

SN

CF

SN

CF

BV

Item

Toka

ido

Shi

nkan

sen

Sany

oS

hink

anse

n

Toky

o-Jo

etsu

Shi

nkan

sen

Han

nove

r-W

ürzb

urg

Köl

n-R

hein

/M

ann

TG

VP

aris

-S

udE

stT

GV

Atl

anti

que

Bot

niab

anan

(par

tly)

Max

imum

desi

gnsp

eed

[km

/h]

280

300

300

350

250

Max

imum

serv

ice

spee

d[k

m/h

]27

030

027

525

027

030

020

0a /

250b

a.C

ateg

ory

Atr

ains

b.C

ateg

ory

Str

ains

(til

ttec

hnol

ogy)

Can

t[m

m]

180

200

180

180

6516

018

018

015

0

Can

tdef

icie

ncy

[mm

]10

010

010

010

080

150

8560

100/

220

Can

texc

ess

[mm

]11

050

100

Min

imum

curv

era

dius

[m]

2500

4000

4000

7000

3350

4000

6250

3200

Min

imum

radi

usof

desi

gnsp

eed

[m]

5100

3425

4000

6020

2950

/20

00

Tra

ckdi

stan

ce[m

]4.

54.

244.

34.

34.

24.

24.

5

Min

imum

vert

ical

curv

era

dius

[m]

1000

015

000

1500

022

000

1200

014

000

1100

0

Max

imum

grad

ient

[‰]

3520

1515

12.5

4035

2510

40


3.8 Recent resarch on nominal track geometry

3.8.1 Optimisation of horizontal alignments for railways

In Kufvers doctoral thesis [16] the focus was on optimal alignment and cant on singlehorizontal curves. He made, for example, studies on the following track quantities:radius, cant and lenghts of transition curves and corresponding superelevation ramps.

The objective of his study was to develop methods for comparing and optimising ofhorizontal alignments when building new lines and improving existing ones.

In short terms some of Kufvers conclusions will now be presented.

A single curve consists of a transition curve, a circular curve and transition curve, placedbetween two tangent tracks. If a lengthening of the transition curves is wanted then itwill require a reduction of the radius in the circular part of the curve. This is valid for asingle curve between two fixed straight lines.

The present study does not bring up passenger comfort as an object function. Accordingto Kufver the PCT functions are the most reasonable overall comfort functions becausePCT includes the lateral acceleration, lateral jerk and roll velocity. These physicalquantities are the most basic ones when calculating alignment and cant.

Kufver came to the conclusion that S-shaped ramps and corresponding types oftransition curves have no substantial advantages compared to transition curves withlinear change of curvature (clothoids).

The optimal lenghts of the clothoids depend on the limit for cant, the roll coefficient ofthe vehicle and the degree of compensation in the body tilt system. One of the mostimportant findings is that a tilt system with a large degree of compensation for lateralacceleration favours long transition curves (clothoids). Thereby the roll velocities arereduced. Within an alignment restricted by existing obstacles longer transition curveswill in many cases lead to less radius in the circular curve and thus a higher lateralacceleration. However, the latter problem will to a large extent be compensated by meansof the carbody tilt, which reduces the lateral acceleration on passengers. However, thecurve radius must always be sufficiently large in order to cope with the desired speed forconventional (non-tilting) trains.

For more detailed descriptions, see Kufver [16].

3.8.2 Ride comfort and motion sickness in tilting trains

Förstberg [14] made two kinds of tests when determining ride comfort and motionsickness. Firstly, in the tilting tests, the concept of symptoms of motion sicknessincidence (SMSI) was used. Those tests utilised different strategies for active tilt of thecarbody to reduce lateral acceleration during curving. For example, when using a lowerratio of tilt compensation a reduction of reported symptoms of motion sickness wasfound.

41


Secondly, when evaluating the simulator tests, the evaluation variable nausea rating(NR) was used. Förstberg found that it was likely that lower compensation and limitedtilt velocity are favourable in a everyday population of passengers. The main conclusionsdrawn by Förstberg are:

- Roll motions presented alone are not very nauseogenic and only small differenceswere found between gender.

- Lateral accelerations alone seem to be medium challenging.

- Combinations of high roll and high lateral accelerations seem to be highlyprovocative for motion sickness. However, it is necessarily not nauseogenic with highcompensation ratios alone. For example, low roll velocity and low lateral accelerationwith a compensation rate of 75%, show low nausea ratings.

- Both high lateral acceleration and high roll velocity have negative effects on theability to work and/or read as well as the ride comfort.

One consequence of Förstberg’s research is that long transition curves would bedesirable from a motion point of view. This is essentially the same conclusions as madeby Kufver described in the previous Section.

For more detailed descriptions, see Förstberg [14].

42


3.9 Summary and conclusions

In Europe it is a clear trend to make specifications for high-speed track geometry lessstrict, i.e. to allow tighter horizontal curves and steeper gradients for a given speed. Themost obvious case may be Germany, where the first generation of ‘Neubau-Strecken’(for example Hannover - Würzburg) was built with curve radii of 5100 - 7000 m and agradient of 12 ‰ at 250 - 280 km/h. The second generation ‘Neubau-Strecken’ (Köln -Frankfurt for example) allows a curve radius of 3350 m and a gradient of 40 ‰ foroperation at 300 km/h. The CEN provisional standard and the newly drafted TSI confirmthis trend. This is along the same line as part of the Japanese Shinkansen, where ahorizontal curve radius of 2500 m is allowed at 270 km/h.

Partly this trend is due to the fact that most of the new lines are built exclusively forhigh-speed passenger trains, not mixed traffic including heavy freight trains. Quite lightpassenger trains with high traction forces and power (per tonne of train) are able to climbmuch steeper grades than locomotive-hauled heavy freight trains. Also, for passengertrains a higher track cant can be arranged, in some cases up to 200 mm, because there isno risk of danger if a passenger train stops at a section with high cant - in an ordinaryfreight train there is risk for load displacement in wagons. The higher cant on high-speedlines allows somewhat reduced horizontal curve radius for the same cant deficiency andspeed.

However, this seems not to be the main reason for the smaller horizontal curve radius. Inthe new practice and proposed European standards a quite high cant is allowed also onlines with mixed traffic (normally 160 mm, exceptionally 180 mm). The earlierrequirements on (a low) cant excess for slowly running freight trains had typical limitvalues of just 50 - 70 mm in, for example, Germany and Sweden. This, in turn, requiredlow cant to be arranged on high-speed lines with mixed traffic and slowly running freighttrains. In the final draft of the CEN proposal (prENV 13803-1) it is now recommended tohave a limit value of 110 mm (maximum 130 mm) for cant excess. The suitability ofsuch a change is also confirmed by recent Swedish research [25]. This produces muchbetter conditions for increasing the cant while reducing curve radius on high-speed lines.

Similar trends are obvious also for the maximum allowed cant deficiency (lateralacceleration in the track plane). For conventional trains (without carbody tilt) on linesspecially built for high-speed a limit value of 100 mm is recommended (80 mm forspeeds above 300 km/h). However, in cases of very strict topological constraints a limitvalue of 130 mm is allowed.

Another important feature of the drafted TSI is the allowance for rising speeds by usingtilt technology, or inversely, to reduce the necessary horizontal curve radius for a givenspeed. Such measures are allowed as long as operations of conventional (non-tilting)high-speed trains are not restricted. It is left to the Infrastructure Manager to takedecisions on tilting trains running at a higher cant deficiency than conventional trains.

Regarding length of transition curves, recent Swedish research [16] allows optimisationof transition lengths within a defined terrain corridor with a number of obstacles. Theoptimisation has passenger comfort as an object function. According to this research theoptimum transitions lengths are depending on (among others) the position of obstaclesand also on whether carbody tilt is applied or not. There is a clear tendency that the

43


introduction of carbody tilt favours longer transition curves in relation to cases where tiltis not applied. This is mainly due to the additional roll velocity introduced on tiltingtrains. Longer transition curves reduce the roll velocity, which is favourable from acomfort point of view. In this context, recent Swedish research [14] also shows thatlower roll velocity is very favourable also with respect to the provocation of motionsickness, which is shown to be a certain problem on tilting trains. All this is inaccordance with CEN proposed standard, which limit the rate of change in cant and cantdeficiency. It should be pointed out, however, that for tilting trains the optimum rate ofchange in cant and cant deficiency are normally lower than the limit values in CEN,transition curves and superelevation ramps are longer.

Finally, the recommended values for vertical curve radius are normally 2 – 3 times largerthan the minimum limiting radius. This is the case in most standards. The minimumrequirements are quite similar to each other, including Banverket standard. Normally, therequired vertical radius is somewhat larger on crests than in hallows. This is due to therisk of wheel unloading on crests.

Some of the above mentioned design parameters are believed to have significantinfluence in the average construction cost of newly built high-speed railways, namelyhorizontal curve radius, vertical curve radius and gradient.

The technical feasibility of using tilting trains in very high-speed operations isinvestigated in Chapter 4 - 6 in the present study. This would reduce the necessaryhorizontal curve radius. In Chapter 7 a brief investigation is made on the permissiblegradient and cant for various types of freight trains.

44


4 High-speed train technology year 2010

To be able to make realistic suggestions regarding track lay-out for high-speed lines, it isimportant to reflect upon the trains which are going to run on these lines. Possiblemaximum train speed without hunting problems or possible cant deficiency in curveswithout exceeding limits for track shift forces, are strongly depending on design andperformance of the running gear. The aerodynamic shape of the train plays an importantrole not only for running resistance but also for side-wind stability of trains.

The aim of this chapter is to foresee the performance of a train, which would be availablefrom industry around 2010, i.e. at the earliest time regular traffic on e.g. The EuropeanCorridor (Europakorridoren) or other high-speed lines in Sweden is about to start. This isimportant for the investigation and proposal of an optimum track geometry for the future,which is the main object of this study.

The assumptions on the technology and performance of future high-speed trains aremade in close co-operation between the author and a number of experts from KTH andindustry (Bombardier Transportation, Västerås, Sweden). Among these experts are Mr.Jan Ågren (Lead engineer, Centre of Competence Vehicle Dynamics, Bombardier), Mr.Mikael Sima (Expert in Aerodynamics, Bombardier) and Prof. Evert Andersson (KTHRailway Technology, as well as Company Senior Specialist in Vehicle Technology,Bombardier).

It is aimed that assumptions on possible future vehicle technology should not be toooptimistic, but rather be at the safe side. The assumed future technology should beknown today, although not always implemented in commercial high-speed trains oftoday. It should be noted that the technology is judged as possible to implement,although there is yet no decision to fully make these implementations in commercialtrains. It is mainly a question whether such trains will be demanded on the Europeanmarket.

4.1 Maximum train speed

To our opinion it is realistic to achieve maximum train speeds of 350 km/h within tenyears. Today there are already trains operating with a design speed of 300 - 330 km/h(France, Germany). In Spain there are trains ordered for a maximum speed of 350 km/h.

4.2 Train configuration

Future high-speed trains will probably mostly be electrical multiple units (EMU) wheremany axles in the train are driven. Advantages compared to loco-hauled trains are mainlyhigher possible acceleration and lower maximum axle load. Therefore an EMU unit waschosen for the simulations.

45

High-speed train technology year 2010

4.3 Tilt technology

4.3.1 General

Several trains with tilt technology are today operating in large scale at maximum speeds200 - 250 km/h (Italy, Sweden, Finland, Germany and also in the UK in the near future).Up to now there are no tilting trains operating at speeds above 250 km/h. The hypothesisis that it may be possible to operate tilting trains also at speeds of 300-350 km/h in thefuture. This study is an attempt to test this hypothesis.

4.3.2 Possible overspeed with tilt technology

Trains with tilt technology have the opportunity to operate at a higher cant deficiencyand hence at higher speeds in curves. The possible percentage of overspeed is, amongother things, limited by:

- Possible lateral accelerations and roll motions with respect to passenger comfort. Thisis an issue of suspension and carbody tilt control

- Possible tilt angle within the vehicle (in particular between bogie and carbody.

- Permissible track forces. This is mainly an issue of track design and maintenance, aswell as suspension in the running gear. For vertical track forces also the unsprungmass, axle load and the location of centre of gravity are important factors.

Examples of permitted overspeed in circular curves as a function of cant are shown is thefollowing figure.

46


Figure 4-1 Permitted overspeed in a circular curve as a function of cant.The permitted overspeed in relation to conventional trains with anallowed cant deficiency of 100 mm (recommended value according to TSIfor the speed range up to 300 km/h). Note: For a cant deficiency of 150mm is no tilt needed.

Note that length of transition curves and superelevation ramps may also limit the (over-)speed.

4.4 Running gear design

Maximum train speed and maximum overspeed in curves are strongly depending on thedesign of the running gear, especially the suspension. A train with a maximum speed of350 km/h on tangent track and with up to 250 mm of cant deficiency in curves has to beequipped with well designed running gear. Using the experience from the Swedishrunning gear design, this study will test if this is possible or not.

In principle, an optimised combination of wheelset guidance and damping has to beapplied. A very flexible wheelset steering will likely lead to problems with the huntingstability, while a very stiff guidance would produce high lateral track forces.

In the future, active technology might be introduced to even better solve this problem.There are, however, still many uncertainties combined with active technology forsteering wheelsets. Therefore a decision was made not to take such possibilities intoconsideration in the present study.

One of the developments which will likely be introduced on a larger scale during thenext 5-10 year is the so-called Hold-of-device (HOD). It is added in order to center the

0%

10%

20%

30%

40%

50%

60%

70%

0 50 100 150 200

Cant [mm]

Per

mit

ted

ove

rsp

eed

[%]

Cant deficiency hd=150mm

Cant deficiency hd=250 mm

47

High-speed train technology year 2010

carbody in curves. This will make it possible to negotiate curves with high cantdeficiency without worsening passenger comfort by hitting the lateral bump stops in thesuspension, thus producing less dynamic forces on track and passengers. Also, if thecarbody were cantered by means of the HOD, the risk of overturning in strong side-winds would be reduced

State of the art technology has been supplied by Bombardier Transportation (Sweden)although this is partly proprietary information. This technology has been furtherinvestigated and developed in this study.

4.5 Aerodynamic shape

The aerodynamic shape of a high-speed train is important for the running resistance andenergy consumption of the train. Furthermore, side-wind stability (i.e. the ability to besafe against overturning in strong side winds) has become a more and more importantissue to study in combination with high-speed train operation. There are at least threereasons for this: Speeds are getting higher, vehicles are getting lighter and high-speedlines are often exposed to wind because of frequent use of high embankments andbridges.

In this study an aerodynamic shape representative for the best trains existing today isassumed. The aerodynamic coefficients for the used vehicle model are revealed inAppendix E. In comparison, such a train would generate about 20% less overturningmoment than the present Swedish X 2000 (at the same roof height).

4.6 Track irregularities

A track which is suitable for trains at a speed of 350 km/h must have a good standardregarding track irregularities. It should be possible on future built high-speed lines toachieve and maintain a track quality better than current Swedish main lines standards,without increasing maintenance costs to an unrealistic level. This assumption has beenconfirmed by personal communications with specialists from Banverket. One of the aimswith this study is to estimate the amount of improvements which would be necessary.

These issues will be further investigated and discussed in Sections 5.8, 6.2.5 and 6.2.6.

48


5 Track/vehicle dynamic simulations - models, conditionsand criteria

5.1 Simulation strategy

The simulations have been carried out in three different parts. Firstly, simulations ofhunting stability is performed to appoint that used technology can be managed in suchhigh speed as 350 km/h. Secondly, the track shift forces will be calculated according toPrud´hommes criteria. Thirdly, vehicle overturning was simulated.

5.2 Simulation software

GENSYS multibody computer code was used in the track/vehicle dynamic simulations.GENSYS calculates the behaviour of a railway vehicle accurately and is one of theoldest and largest packages currently in use. There are more than a few options regardingthe number of degrees of freedom for the individual bodies such as wheels, bogies,carbody etc. For further information about the simulation tool, please see Appendix G.

5.3 Test speed

In simulations is it easy to control the speed of the train, compared with full scaletestings where the actual train speed might be difficult to control.

According to CEN TC 256 WG 10 [8] and UIC 518 [24], safety-related quantities mustbe evaluated at a slightly higher speed then the intended permissible speed. CEN statedthat the test speed should be the lower of 110% of permissible speed and the speed whichcorresponds to 110% of permissible cant deficiency.

Kufver [16] says that it would be relevant in certain studies to compare alignments withdifferent radii. Kufver suggested that it would be reasonable to use the same test speed inall alternatives and hence a different cant deficiency.

In simulations concerning hunting stability a test speed of 385 km/h was chosen. Thisspeed corresponds to 110% of the intended permissible speed (350km/h).

When evaluating track shift forces a test speed of 360 km/h was regarded toapproximately fulfil the condition of 110% of permissible cant deficiency. The horizontalcurve radius at a cant of 180 mm, cant deficiency of 250 mm and speed of 350 km/h isequal to the horizontal curve radius at a cant of 180 mm, cant deficiency of 275 mm andspeed of 360 km/h (R=3361m in both cases). 110% of 250 mm is equal to 275 mm. Acant deficiency of 275 mm was chosen as boundary condition.

In the simulations concerning vehicle overturning it was judged to be adequate to choosea test speed of 350 km/h (100% of permissible speed) and radii that correspond to cant

49

Track/vehicle dynamic simulations - models, conditions and criteria

deficiencies of 100% of permissible cant deficiency. This is because very strong side-winds and the risk of overturning is a very unlikely event, two unlikely events - too highcant deficiency and strong side-winds - is still more unlikely to happen and shouldtherefore not be considered as a realistic case.

5.4 Hunting stability

Two types of instabilities will be studied in the present work. High frequency instabilityoccurs at high-speeds and high equivalent conicity. Low frequency instability tends tooccur if the wheelset hunting frequency and a natural frequency of the vehicle on itssuspension are rather similar. Thus, low frequency instability is more or less similar to aresonance phenomenon. The matter of equivalent conicity is explained in detail in thecourse books [2], Chapter 4, and [3], Chapter 7 and 8.

Two requirements must be fulfilled in the simulations:

- The hunting frequency should not exceed 10 Hz because of the risk of resonance withthe lateral bending mode of the carbody. Wheelset steering will be chosen to fulfillthis requirement.

- The decay of the hunting amplitude must be at least 60% in two cycles after a suddendisturbance. In addition, no significant sustained vibration shall be visible after 200-400 metres.

The hunting stability is tested by simulation on both tangent and curved track, at speedaccording to Section 5.3. The equivalent conicity is varied according to Section 5.7.

50


5.5 Track shift forces

The track shift force is represented by ΣY in Figure 5-1.

Figure 5-1 Track forces where Ql and Qr are the vertical forces and Yl and Yr arethe lateral forces.The track shift force is represented by ΣY.

The safety-critical limit for track shifting according to Prud’homme criterion is

[kN] (5-1)

where ks = 0.85 in the simplified statistical analysis in this study. 2Q0 is the static verticalaxle load and k1 is a factor usually set to 1 for passenger vehicles, according to CEN andUIC 518 [8], [24]. The value of ks = 0.85 was chosen because track shift forces usuallyare evaluated statistically. This usually results in a spread of track shift forces of about±15% around the mean value. Therefore we decided to apply the safety margin to “be onthe conservative side”. Further, the track shift forces are filtered before evaluation. Themean value over 2 metres is compared with Prud’hommes limit. The limit refers to 46kg/metre rails in ballasted track with a maximum timber sleepers spacing of 650 mm.Today’s track with concrete sleepers, 60 kg/metre rails with welded joints and ballastedtrack gives also a certain safety margin, see further CEN [8].

ΣYlim Slim k= s k1⋅= 102Q0

3----------+� �

� �⋅

51


5.6 Vehicle overturning at strongly side-wind

5.6.1 General

For trains, which are exposed to strong side-winds pointing outwards in the curve thereexists a risk for vehicle overturning around the outer rail. This is particularly true if theyare running through curves at high-speed, high cant deficiency and track irregularities.

The overturning risk is increased if the centre of gravity is moved outwards in the curve.Thus, large lateral spring travels due to suspension flexibility usually increase the risk ofoverturning. A tight lateral bump stop, or a Hold-off-Device (HOD), both limiting thelateral offset of the centre of gravity, will help to reduce the risk of overturning.

In this Section a method to quantify the risk of vehicle overturning is presented.

5.6.2 Tolerable wind velocities

The environment in which a train operates may be very different from place to place,especially regarding the probability of being exposed to strong side winds. In Sweden,side winds velocities up to 30 à 40 m/s may be found on selected open locations withoutany shielding trees, buildings, hills or similar. The strongest winds usually occur invicinity of the sea, especially at the West Coast. The wind velocity increases at higherheight above ground. The wind velocity also increases above high embankments,because the wind hitting the embankment side is usually forced to run over it. Also, thewind varies over time and occurs as “wind gales”. It is usually very difficult tosummarise these complex phenomena into a limited number of simple load cases foreach newly built train.

Furthermore, different types of trains can also be more or less sensitive to side winds.The aerodynamic properties, especially the cross section shape and height are decisivefor the aerodynamic forces acting on the train. In particular, the lateral force and the rollmoment are important aerodynamic characteristics with respect to overturning; forexample a higher roof height of the train will usually increase the risk. Also the height ofcentre of gravity is important for the risk of overturning. See further Appendix E andLippert [21] for details.

Another factor increasing the risk of overturning is the lateral deflection of the centre ofgravity, i.e. how much the c.g. is moved outwards in the curve under influence of thecentrifugal forces and the side wind forces. Thus a large lateral spring travel due tosuspension flexibility is not desirable from this point of view (although improving theride quality). Therefore, a tight lateral bump stop or a so-called Hold-off-Device (HOD),both limiting the lateral offset of the c.g., will help to reduce the risk of overturning.

Several procedures have been used to cope with the side wind issue. In Sweden acomprehensive effort was made in the 1980´s, related to the design of X 2000. Largeefforts have recently been made in Germany and France.

52


The European standard for evaluating safety against vehicle overturning at strong sidewinds is under development within the framework of TSI [12] [13]. In this study thepreliminary requirements according to a “Working proposal”, June 2001, [26] are used.

The idea is firstly that the train must have a basic resistance against overturning at strongside winds. Although the exact level of side wind velocity is yet not settled, a levelaround 23 m/s of tolerable side wind from the most adverse direction is discussed. Thislevel is related to the “Vector intercept” criterion presented in the next Section 5.6.3. Thelevel 23 m/s is quite equivalent to the safety level set down for X 2000, although theoverturning risk criteria were formulated in another way [28].

Secondly, if there is an unacceptable risk that the wind velocity on specific locations willbe higher than the basic level mentioned above, the infrastructure manager is responsiblefor taking adequate measures to maintain the level of traffic safety [12]. This can bemade by temporary speed restrictions at strong side winds (which requires anappropriate wind reporting system and traffic management). The infrastructure managermay also install protective equipment such as wind barriers.

In this study the strategy is to investigate whether the high-speed train meets theappropriate overturning criteria (see Section 5.6.3), with a constant side wind velocity of23 m/s applied to the train from the most adverse direction, when the train is running atits maximum admissible cant deficiency at the maximum operating speed.

5.6.3 Intercept method risk factor

The method for determining the risk of vehicle overturning used in the present study isthe intercept method, which is based on the vertical track forces of the vehicle. Theintercept method calculates a resulting force as a result of all wheel forces. Figure 5-2and Table 5-1 show the definition of quantities for calculation of the risk of vehicleoverturn with the intercept method.

Figure 5-2 Definition of quantities for calculation of risk of vehicle overturn withthe intercept method.

53


bt is a measure for the risk of the vehicle turn-over and describes the distance betweenthe centre of the track plane and the point where the resultant force is acting. bt can becalculated by replacing the wheel forces with a resultant force under the restriction thatthe resultant force causes the same forces and moments as the wheel forces.

The forces in the left and right parts of Figure 5-2 are equivalent to each other, the twoforce components in the right figure are the vector sums of the Y- and Q-forces in the leftfigure. The resultant R of the two forces in the right figure cuts the track plane at adistance bt from the track centre line. The roll moments in the two parts of Figure 5-2 arethe same if the following is valid:

(5-2)

The absolute value in the nominator is needed to consider overturning to both the left andright side. When the wheels on one side are totally unloaded, bt has got the value bo andstays constant. The permissible value for bt can be defined as

(5-3)

Put Equation (5-3) into Equation (5-2) and solve E in the new equation. We get a ratio ofbt and bo that defines a risk factor according to Equation (5-4):

(5-4)

Typical values for E are between 0.8-1. In the present study a limit value of 0.9 has beenused.

With the intercept method risk factor, E can be calculated for one wheelset, one bogie orthe whole vehicle. In this study, E is calculated for the whole vehicle, considering theforces of all wheels.

Table 5-1 Quantities for the calculation of the overturning risk according to theintercept method

ΣQl Sum of the vertical wheel forces, left wheel [kN]

ΣQr Sum of the vertical wheel forces, right wheel [kN]

R Resulting force [kN]

bt See Figure 5-2 [m]

bo Half lateral distance between the contact points ofleft and right wheel

[m]

bt

ΣQl ΣQr–

ΣQl ΣQr+--------------------------------- bo⋅=

bt bt lim, E bo⋅= =

Ebt

bo

-----

ΣQl ΣQr–

ΣQl ΣQr+--------------------------------- bo⋅

bo

-------------------------------------------ΣQl ΣQr–

ΣQl ΣQr+---------------------------------= = =

54


The quantity E from the simulations has been low-pass filtered with the frequency f = 1.5Hz (the reason is given below).

5.6.4 Disadvantages with intercept method

According to Lippert [21] the intercept method has two disadvantages. Firstly, the vectorintercept is calculated by using the wheel forces which are - due to fast dynamicvariations - a conservative criterion to show side-wind stability, especially when realtrack with track irregularities is simulated. As commented above, the signals must below-pass filtered to be appropriate to a quite slow process like overturning. Secondly, btof the intercept method can not become larger than bo. This means that as soon as allwheels on one side loose contact, bt stays constant, independent from changes in theforce acting on the train. Although losing contact with all wheels at the same time is acritical situation, it must not necessarily immediately overturn the vehicle due to thevehicle’s inertia.

A low-pass filtering of 1.5 Hz is considered as slightly conservative. It has been used foroverturning investigations of the Swedish X 2000 train and has been used in thepreliminary outline of the future Rolling stock TSI [13]. However, it is yet (Dec. 2001)not finally decided exactly how to make a realistic specification of safety against vehicleoverturning.

5.6.5 Aerodynamic train design

A good aerodynamic shape, according to Section 4.5 is assumed. In combination with aroof height limited to 3.6 m the lateral forces and the overturning moments due to side-wind is on the low side, although considered to be realistic.

55


5.7 Rails, wheels and equivalent conicity

Equivalent conicity is a geometrical property between wheels and rails, describing themagnitude of rolling radius difference (between right and left wheel) when the wheelsetis displaced laterally relative to a tangent track (where the wheelset is nominally at itscentre position). For exact definitions and many other details, see course books [2],Chapter 4, and [3], Chapter 7 and 8.

The equivalent conicity is very dependent on the actual wheel and rail profiles (at the railhead) as well as on the rail inclination in the track and on the track gauge. It is alsodependent on built-in geometrical tolerances and on the actual wear shapes of bothwheels and rails.

In the TSI and CEN specifications the maximum equivalent conicity shall apply fordifferent maximum speeds V (km/h) corresponding to Table 5-2:

Thus, on tracks and vehicles for these speeds the rails and wheels shall be obtained andmaintained that the above shown equivalent conicity can be achieved. As one of severalmeasures to meet these conicity requirements, the track gauge must be in the range of1434 - 1440 mm in all speeds above 250 km/h, according to TSI [12].

The strategy in this study is to select a suitable combination of rail and wheel profiles inorder to arrive at the desired equivalent conicity on tangent track. Variations of conicity(for given rail and wheel profiles) are made by varying the track gauge within certainlimits.

Two kinds of rail profiles have been used in the present study; UIC 60 rail profile and aBV 50 rail profile, both with the Swedish rail inclination of 1:30. The UIC 60 rail profileis standardised by the UIC and is used on many lines and new-built lines in Europe. Thisrail profile has been used in the simulations of track forces and vehicle overturn. A wornBV 50 rail has been used for stability simulations on tangent track thus leading to ahigher value of equivalent conicity than new nominal rail head shapes. For stabilitysimulations on curves the UIC 60 rail profile is used.

The above-mentioned rail profiles are combined with wheel profiles type UIC/ORES1002, see Section 5.9. In this procedure the equivalent conicity can be varied up to avalue of at least 0.40, which can be used in the stability simulations.

Table 5-2 Maximum equivalent conicity at different maximum speed.All according to CEN and TSI.

Speed (km/h)Design value(maximum)

In service, taking intoaccount wheel and rail wear

230 < V ≤ 250 0.25 0.30

250 < V ≤ 280 0.20 0.25

V > 280 0.10 0.15

56


5.8 Track irregularities

5.8.1 Classification of track irregularities

Most railway companies classify their tracks with regard to the level of permissible trackirregularities. On main lines, in particular on high-speed lines, less irregularities arepermitted than on lines for lower speeds. This section refers to the classification in theCEN/TC 256 WG 10 [8] as well as Banverket BVF 587.02 [6]. Three classes of trackqualities are defined with regard to the necessity of maintenance and to the applicabilityfor acceptance of vehicles. The three levels used by the CEN are described below.

- QN1 refers to the value which necessitates observing the condition of the track ortaking maintenance measures as part of regularly planned maintenance operations.

- QN2 refers to the value which requires short term maintenance action.

- QN3 refers to the value which, if exceeded, leads to the track section being excludedfrom the analysis because the track quality encountered is not representative of usualquality standards.

Banverket uses the following levels:

- A. New-built or recently adjusted track.

- B. Lower quality limit. States target value of maintenance actions. The trackirregularities should normally be adjusted before this level attains. This limit is oftenrelated to comfort aspects.

- C. This limit should not be exceeded. The track irregularity must be corrected as soonas possible. Reduced speed limits should be taken into consideration until theirregularities have been corrected.

Each level refer to a certain quality class, K0 - K5, depending on the permitted speed onthat particular track [6].

57


5.8.2 Track irregularities for dynamics analysis

As input data for analysis of vehicle dynamics the absolute irregularities as function ofdistance have to be known or assumed. Track irregularities can be represented by thefollowing description:

- Vertical irregularity, deviation from the designed vertical alignment (centre line).

- Lateral irregularity, deviation from the designed lateral alignment (centre line).

- Gauge irregularity, deviation from nominal gauge.

- Cant irregularity, deviation from designed cant.

The four different irregularity types are illustrated in Figure 5-3.

Figure 5-3 Track irregularities described by four different quantities

In the present study two sets of track irregularities with quite different characteristicswere used. The first set of irregularities originals from a curve between Simonstorp and

Katrineholm recorded by a Mauzin track recording coach. The track is denoted S221.The other track irregularity is measured on a tangent track between Åby and Nyköping.Both tracks are regarded as “median standard” track.

The aim of the simulations performed in this study is to find out what amplitude ofirregularities can be permitted, without exceeding the safety-critical limit of track shiftforces at 275 mm cant deficiency (i.e. 110% of the cant deficiency 250 mm. Theamplitude of the described track irregularities are varied by multiplication with differentfactors. The other characteristics (wavelengths etc.) remain the same.

1. S22: BV50 rails, continuous welded rails (CWR) and concrete sleepers spacing of 650 mm. It was orig-inally defined for the specification of the track forces and ride qualities for the high-speed tilting trainX 2000.

58


To make a quality control of the track irregularities a methodology was set out in thisstudy. The so-called Q-values [6] of the reference irregularities were calculated. The Q-value is a measure of the average standard deviations with respect to the comfort limitsof Banverket’s standard classification. A Q-value of 80 means the standard deviationsare 0.7 times the limit. A Q-value of 100 means that the standard deviations are 0.5 timesthe limit value of the current quality class. Thus, the aim of this part of the study was tofind the Q-value and relative amplitude that meets the regarded levels of track forces.

To get a track classified in a special quality class a Q-value of 80 is necessary to beachieved. If the Q-value is equal to 80 it meets the quality requirements stated for Ban-verket quality classification level B.

The Q-values in this study refer to Banverket quality class K0. This is the quality classdefined for speeds in the range of 200 km/h (above 145 km/h for conventional trains andabove 185 km/h for tilting high-speed trains). The different combinations of track irregu-larities are shown in Table 5-3 and Table 5-4.

The characteristics of Track 5 and Track 10 are shown in Figure 5-4 and Figure 5-5,respectively.

Table 5-3 Track irregularities based on the irregularity S22 (curved track).

TrackQ-value

(class K0)Lateralfactor

Verticalfactor

Gaugefactor

Cantfactor

Multiplicationfactor

Track 2 (S22) 65 0.650 0.800 0.650 0.800 1.0

Track 3 82 0.520 0.640 0.520 0.640 0.8

Track 4 90 0.455 0.560 0.455 0.560 0.7

Track 5 99 0.390 0.480 0.390 0.480 0.6

Track 6 107 0.325 0.400 0.325 0.400 0.5

Table 5-4 Track irregularities based on the irregularity between Åby andNyköping (tangent track).

TrackQ-value

(class K0)Lateralfactor

Verticalfactor

Gaugefactor

Cantfactor

Multiplicationfactor

Track 7 89 0.650 0.800 0.650 0.800 1.0

Track 8 107 0.455 0.560 0.455 0.560 0.7

Track 9 114 0.390 0.480 0.390 0.480 0.6

Track 10 99 0.533 0.680 0.533 0.680 0.85

59


Figure 5-4 Track irregularity characteristics of Track 5.

-15

-10

-5

0

5

10

15

600 700 800 900 1000 1100Distance [m]

Ver

tical

[mm

]

-15

-10

-5

0

5

10

15

600 700 800 900 1000 1100Distance [m]

Late

ral[

mm

]

1425

1430

1435

1440

1445

600 700 800 900 1000 1100Distance [m]

Gau

ge[m

m]

-15

-10

-5

0

5

10

15

600 700 800 900 1000 1100Distance [m]

Can

t[m

m]

60


Figure 5-5 Track irregularity characteristics of Track 10.

-15

-10

-5

0

5

10

15

600 800 1000 1200 1400Distance [m]

Ver

tical

[mm

]

-15

-10

-5

0

5

10

15

600 800 1000 1200 1400Distance [m]

Late

ral[

mm

]

1425

1430

1435

1440

1445

600 800 1000 1200 1400Distance [m]

Gau

ge[m

m]

-15

-10

-5

0

510

15

600 800 1000 1200 1400Distance [m]

Can

t[m

m]

61


5.8.3 Peak values of track irregularities

Another check of track irregularities is to look at peak values.

The quality standard according to Banverket is measured with the testing and trackrecording coach called STRIX [6] and are shown in Table 5-5.

The track quality values according to CEN/TC 256 WG 10 [8] have been obtained frommeasurements with the NS measuring vehicle and are shown in Table 5-7.CEN/TC 256 WG 10 says among others that a transfer function of the measuring systemmay be used to obtain absolute values of measured track geometry.

Note that quantities in Table 5-7 are not directly comparable with quantities in Table 5-5and Table 5-6, as the measuring system has different transfer functions from real torecorded irregularities.

Table 5-5 Track geometry quality of longitudinal level (vertical irregularity).Peak values according to Banverket [6].

Deviation from base value [mm]

QualityClass

Speed limitconventional

train(km/h)

Speed limithigh-speed

train(km/h)

Longitudinal level Cant

Short wavefault 1-25 m

Longwavefault

Deviation

A B C A B A B C

K0 145 - 185 - 2 6 9 7 15 2 4 6

Table 5-6 Track geometry quality of alignment (lateral irregularity).Peak values according to Banverket [6].

Deviation from base value [mm]

Qualityclass

Speed limitconventional

train(km/h)

Speed limithigh-speed

train(km/h)

Alignment Gauge

Short wavefaultwavelength1-25 m

Longwavefault

Deviation

A B C A B A B C

K0 145 - 185 - 2 3 5 5 10 ±2 ±5 +15,-5

62


The STRIX values of Track 5 are plotted against distance along the track and areillustrated in Figure 5-6. The maximum peak value of vertical irregularity of left andright rail for Track 5 are 3.64 mm and 3.6 mm, respectively. The maximum peak value oflateral irregularity for the left rail is 1.21 mm.

Figure 5-6 Track irregularities as a function of distance.Longitudinal level (vertical irregularity) and alignment (lateralirregularity) of Track 5.

Table 5-7 Track geometry quality values.Source: CEN/TC 256 WG 10 [8].

Permissiblelocal speed in

km/h

Alignment Longitudinal level

Values of quality level in mm

QN1 QN2 QN1 QN2

Absolute maximum value of lateral and vertical irregularity (mean to peak)

200 < v ≤ 300 4 6 4 8

-5

0

5

600 700 800 900 1000 1100distance [m]

late

rali

rreg

ular

ity,

left

rail,

peak

valu

e[m

m]

-5

0

5

600 700 800 900 1000 1100distance [m]

vert

ical

irreg

ular

ity,

left

rail,

peak

valu

e[m

m]

-5

0

5

600 700 800 900 1000 1100distance [m]

vert

ical

irreg

ular

ity,

right

rail,

peak

valu

e[m

m]

63


In Figure 5-7 the STRIX values of Track 10 are shown. The maximum peak values ofvertical irregularity for left and right rail for Track 10 are 3.91 mm and 4.13 mm,respectively. The maximum peak value of lateral irregularity for the left (outer rail in thecurve) rail is 2.25 mm.

Figure 5-7 Track irregularities as a function of distance.Longitudinal level (vertical irregularity) and alignment (lateralirregularity) of Track 10.

In Section 6.2.4 - 6.2.6 further studies on the effect of different track irregularities will bepresented.

-5

0

5

600 800 1000 1200 1400distance [m]

late

rali

rre

gu

lari

ty,l

eftr

ail,

pea

kva

lue

[mm

]

-5

0

5

600 800 1000 1200 1400distance [m]

vert

ica

lirr

eg

ula

rity

,le

ftra

il,pe

ak

valu

e[m

m]

-5

0

5

600 800 1000 1200 1400distance [m]

vert

ica

lirr

eg

ula

rity

,rig

htr

ail,

pea

kva

lue

[mm

]

64


5.9 Model of the EMU coach

One electric multiple unit (EMU), a four-axled bogie vehicle (axle arrangement Bo’Bo’),will be used in the simulations. This is a simplification, because the different vehicles ina train will interact. However, the results will most likely be on the conservative and safeside, because the interaction between coaches rather improves the running behaviourthan worsens it. Especially, this is true with respect to low-frequency dynamics (0.5-2Hz) due to long-waved track irregularities, low frequency instability and vehicleoverturning.

As mentioned in Section 5.7, in the stability simulations a worn UIC/ORE S1002 wheelprofile have been used in order to achieve the desired equivalent conicity of at least 0.15,preferably up to 0.3 á 0.4. In the simulations of track shift forces and vehicle overturn atheoretical UIC/ORE S1002 wheel profile have been used.

5.9.1 Three different vehicle configurations

A baseline vehicle (vehicle configuration A) was firstly defined. This vehicle has thefollowing data:

Table 5-8 Data of the vehicle configuration A.

Carbody length [m] 25

Carbody height [m] 3.6

Bogie centre distance [m] 18

Bogie wheelbase [m] 2.7

Total vehicle mass [t] 51.4

Mass distribution See Table 5-9

65


The static axle loads are 126 kN for all wheelsets, which is a very low axle load for amotored coach of full length. The vehicle data used for the simulations are not takenfrom any real rail vehicle, but are reasonable extracts from today´s vehicle technology.Despite of this, detailed suspension data are proprietary.

When evaluating the risk of vehicle overturning also two other configurations were used,in order to investigate the sensitivity for vehicle mass and the location of the centre ofgravity (c.g.). The first simulations on side-wind stability showed that vehicleconfiguration A was not stable enough. Therefore a vehicle configuration B was defined,having an extra mass of 4000 kg, with its centre located 3 metres behind the leadingbogie centre and 0.4 m above the track plane. This was judged to be a realistic approachto be used in the leading vehicle (and in the vehicle at the opposite end if necessary).Normally just the leading vehicle is being critical with respect to side-wind stability [21][2]. Apart from the additional mass, vehicle configuration B is the same as configurationA. Mass distribution data for vehicle configuration B are shown in Table 5-10.

Table 5-9 Rigid bodies in the model of the EMU, vehicle configuration A

Mass Mass moments of inertiaHeight of mass centre

above track plane

M(kg)

Jxx

(kgm2)

Jyy

(kgm2)

Jzz

(kgm2)(m)

Carbody 33 000 50 600 1 800 300 1 800 300 1.55

Bogie framea

a. Including frame-mounted traction motors.

6 000 1 590 5 300 8 500 0.70

Wheelsetb

b. Including traction gear and bearings.

1 600 960 300 960 0.42

Table 5-10 Rigid bodies in the model of the EMU, vehicle configuration B


above track plane

M(kg)

Jxx

(kgm2)

Jyy

(kgm2)

Jzz

(kgm2)(m)

Carbody 37 000 55 800 1 950 000 1 950 000 1.426

Bogie framea

a. Including frame mounted traction motors.

6 000 1 590 5 300 8 500 0.70

Wheelsetb


1 600 960 300 960 0.42

66


The static axle loads for vehicle configuration B (in empty condition) are 142.4 kN forthe wheelsets in the leading bogie and 129.3 kN for the trailing bogie. The higher axleloads (142.4 kN) in the leading bogie is believed to meet the requirements of TSI [13],specifying a maximum axle load of 167 kN in fully loaded condition.

Finally, to further investigate the influence of the centre of gravity with respect to strongside-winds a third vehicle configuration C was defined. This vehicle has the carbodycentre of gravity located 0.10 m above that of configuration B. Otherwise, configurationC is identical to configuration B. See Table 5-11.

Vehicle configurations B and C are considered as being realistic for future high-speedEMUs. It should be pointed out that the “extra mass” located behind the leading bogie inreality may be part of ordinary vehicle equipment, such as heavy electrical transformersor similar. It may not be necessary to put in additional “ballast mass”, but rather toconsider the desired mass and mass distribution when the ordinary equipment is locatedin future vehicles. The resulting total mass and axle loads of configurations B and C arequite normal according to recent vehicle technology; compare for example with theGerman ICE 3 and the Swedish Öresund Train.

As said above, configurations B and C have been used only for side-wind stabilityevaluations, although they are considered as the most realistic for future high-speedtrains. Only configuration A has been used in the hunting stability and track shiftanalysis. The reason is that the investigations started with hunting stability and track shiftforces, while the problem related to side-wind stability was experienced on a later stage.It was not judged as necessary to rework hunting stability and track shift forces with thenew configurations B and C. The carbody mass and centre of gravity normally have nosignificant influence on hunting stability or the risk of exceeding the track shift forcelimit, all this according to Prof. Andersson´s experience.

Table 5-11 Rigid bodies in the model of the EMU, vehicle configuration C


above track plane

M(kg)

Jxx

(kgm2)

Jyy

(kgm2)

Jzz

(kgm2)(m)

Carbody 37 000 55 800 1 950 000 1 950 000 1.526

Bogie framea

a. Including frame mounted traction motors.

6 000 1 590 5 300 8 500 0.70

Wheelsetb


1 600 960 300 960 0.42

67


5.9.2 Hold-off-device

A future train designed for a high-speed line like in the present study would be equippedwith a so-called hold-off-device (HOD) as described before. The HOD is not taken intofull consideration in the present simulation model. This leads to hits in the bumpstops incurves with high cant deficiencies. This can be regarded as the “worst case”corresponding to a malfunction of the HOD. The dynamic performance would be betterif the HOD is used and is working properly. Thus the conditions investigated in thisstudy are conservative. Therefore we judged to make this simplification. However, oneaspect of HOD is considered, namely that the lateral suspension travel in the secondarysuspension is limited to ± 30 mm. This assumption will reduce the risk of vehicleoverturning at strong winds, compared to the case with an ordinary passive suspensionhaving 60 - 90 mm of lateral travel.

68


6 Dynamic analysis of simulated vehicle response

This chapter deals with the simulation results. Firstly, an exposition of the simulationresults from the hunting stability point of view is made. Secondly a presentation is madeof the track shift forces simulations. Finally the evaluation of vehicle overturning ispresented.

6.1 Hunting stability on tangent track and on curve

6.1.1 Conditions

Hunting stability was evaluated on tangent track and in curves with different radius, inthe latter cant deficiency was varied in order to use the same test speed. A test speed of385 km/h was chosen to fulfil the condition of 110% of the desirable top speed 350 km/h,in accordance with UIC 518 requirements. In order to use the same test speed on tangenttrack and in different curve combinations this condition satisfies the intention. This alsocorresponds to the other condition stated of CEN and UIC. This condition says that thetest speed must be evaluated at 110% of permissible cant deficiency. For example: SpeedV = 350 km/h, cant ht = 180 mm and cant deficiency hd = 250 mm give a radius of R =3361 m. Speed V = 385 km/h, cant ht = 180 mm and radius R = 3361 give a cantdeficiency hd = 340 mm. This results in 136% of permissible cant deficiency. This ismore than 110% of permissible cant deficiency and the condition is fulfilled.

Table 6-1 and 6-2 show the simulation conditions for hunting stability in curves.

Table 6-1 Simulation conditions for hunting stability in curves.Speed V = 385 km/h and cant ht = 180 mm.

Train speed[km/h]

Cant[mm]

Cant deficiency[mm]

Horizontal curve radius[m]

385 180 50 7604

385 180 100 6246

385 180 150 5299

385 180 200 4602

385 180 250 4067

385 180 300 3643

69

Dynamic analysis of simulated vehicle response

6.1.2 Track irregularities

In the hunting stability simulations the track is without irregularities except a singlelateral disturbance (i.e about the same amplitude as the lateral wheel/rail clearance) havebeen used in the stability simulations. The irregularity used will excite a lateral motion ofthe wheelsets and bogies. The wheel flanges will hit the rails. Thus also high wheel/railcontact angles are taken into account, not limiting the hunting investigations to smallmotions around the centre position. The wavelength and the amplitude of the singlelateral disturbance is 20 m and ± 3 mm, respectively.

6.1.3 Criteria for hunting stability

To be considered as “fully stable” without undesired “hunting”, the lateral accelerationsin the carbody shall have a decay of at least 60% in the first two cycles from the highestpeak. I addition, no sustained vibration shall be visible after 200 – 400 m. Finally, thefrequency of vibration should not be higher than 10 Hz, in order to limit the risk ofexciting the carbody vibration modes in lateral bending.

6.1.4 Hunting stability on tangent track

With the wheel and rail profiles chosen according to Section 5.7 equivalent conicity upto about 0.3 has been investigated. This is very much above the required conicityaccording to TSI, which is 0.15 including tolerances for wheel and rail wear.

A minor and brief optimisation was firstly made on suitable parameters in the bogie,such as wheelset guidance stiffness (longitudinal and lateral), primary damping (betweenwheelsets and bogie frame) and yaw damping (between bogie frame and carbody). It wasfound that an intermediate stiffness in the wheelset guidance was near optimum with

Table 6-2 Simulation conditions for hunting stability in curves.Speed V = 385 km/h and cant ht = 200 mm.

Train speed[km/h]

Cant[mm]

Cant deficiency[mm]


385 200 50 6995

385 200 100 5829

385 200 150 4997

385 200 200 4372

385 200 250 3886

385 200 300 3498

70


respect to hunting stability. This intermediate stiffness is something in between the quiteflexible guidance stiffness on X 2000 (for 200 - 210 km/h) and the traditional stiffguidance normally used in Continental Europe. It is believed (although not proved in thisstudy) that certain flexibility is favourable also with respect to lateral track shift forces.

With the “optimised” parameters as mentioned above, stability on tangent track – at 385km/h - can be achieved at an equivalent conicity of 0.20 – 0.25, according to thesimulations. This is above the required value of 0.15, but it should be noted that stabilityshould also be achieved with some adverse change in stiffness or damping in the bogie.That matter has not been further investigated in this study.

For evaluation of the stability, the lateral acceleration in the carbody was calculated atthree different locations in the simulations. The three locations on the floor was aboveeach bogie and in the middle of the carbody. In Figure 6-1 to 6-3 an example of thelateral accelerations is shown for these three locations. In this case the vehicle is fullystable without any hunting motion, according to the criteria defined in Section 6.1.3. Alot of other cases, with different equivalent conicity, have been simulated, but are notshown in detail.

Figure 6-1 Lateral acceleration (m/s2) in the carbody above 1st bogie.Tangent track with initial disturbance. Speed V = 385 km/h.

Figure 6-2 Lateral acceleration (m/s2) in the middle of the carbody.Tangent track with initial disturbance. Speed V = 385 km/h.

Lateral acceleration in the carbody above 1st bogie

-2,00-1,000,001,002,00

500 600 700 800 900 1000

Distance [m]

ayc

[m/s

2 ]

Lateral acceleration in the middle of the carbody

-2,00-1,000,001,002,00

500 600 700 800 900 1000

Distance [m]

ayc

[m/s

2 ]

71


Figure 6-3 Lateral acceleration (m/s2) in the carbody above 2nd bogie.Tangent track with initial disturbance. Speed V = 385 km/h.

6.1.5 Hunting stability on large radius curves

In curves the lateral acceleration is much larger. There is not only a contribution from thedynamic behaviour but also a quasi-static contribution which occurs when a vehicle runswith constant speed on ideal track with a constant curve radius, cant and wheel-railfriction. The quasistatic contribution to the carbody lateral acceleration in a curve with a

cant deficiency of 250 mm is in the order of 2 m/s2. This is under assumption that thecarbody is not tilted. The lateral accelerations in the carbody for a case where the radiusis 4067, cant is 180 mm and cant deficiency is 250 mm are presented in Figure 6-4 to 6-6

Figure 6-4 Lateral acceleration (m/s2) in the carbody above 1st bogie.A curve with initial disturbance where radius is 4067 m, cant is 180 mmand cant deficiency is 250 mm. Speed V = 385 km/h.

Lateral acceleration in the carbody above 2nd bogie

-2,00-1,000,001,002,00

500 600 700 800 900 1000

Distance [m]

ayc

[m/s

2 ]

Lateral acceleration in the carbody above 1st bogie

-1.000.001.002.003.004.005.00

500 600 700 800 900 1000

distance [m]

ayc

[m/s

2 ]

72


Figure 6-5 Lateral acceleration (m/s2) in the middle of the carbody.A curve with initial disturbance where radius is 4067 m, cant is 180 mmand cant deficiency is 250 mm. Speed V = 385 km/h.

Figure 6-6 Lateral acceleration (m/s2) in the carbody above 2nd bogie.A curve with initial disturbance where radius is 4067 m, cant is 180 mmand cant deficiency is 250 mm. Speed V = 385 km/h.

From the figures it is concluded that the vehicle is stable without hunting. This is thecase also for all the other cases according to Table 6-1 and 6-2.

The criteria of reducing the oscillation within two cycles is also fulfilled in the largehorizontal curves with a high cant deficiency. The hunting frequency is much lower thanthe stated condition of 10 Hz.

Lateral acceleration in the middle of the carbody

-1.000.001.002.003.004.005.00

500 600 700 800 900 1000

distance [m]

ayc

[m/s

2 ]

Lateral acceleration in the carbody above 2nd bogie

-1.000.001.002.003.004.005.00

500 600 700 800 900 1000

distance [m]

ayc

[m/s

2 ]

73


6.2 Evaluation of track shift forces

6.2.1 Conditions

Track shift forces can be critical when high lateral forces shift the track, which might, asa final consequence, lead to a derailment of the following vehicle. The limit valueaccording to CEN/TC 256 WG 10 depends on axle load and is calculated using thePrud’homme formula (see Section 5.5). The limit value for the used vehicleconfiguration A in the present study is 44.2 kN which allows an extra margin of 15% forstatistical scatter.

According to CEN TC 256 WG 10 and UIC 518, track shift forces must be evaluated at aslightly higher speed then the intended permissible speed. CEN stated that the vehiclemust be evaluated at 110% of permissible cant deficiency in curves. Kufver [16] came tothe conclusion that it may be reasonable to modify this condition slightly whenalignment alternatives with different radii are being evaluated, in order to use the sametest speed in all alternatives. This principle will be used here.

The investigations has been performed for cant deficiencies of adequately 100, 150, 200,250, 275 and 300 mm and the curve radii will be varied in accordance. Note that thesecant deficiencies correspond to 110% of admissible cant deficiency, as earlier discussedin Section 5.3. These relations are shown in shown in Table 6-3. The corresponding testspeed is 360 km/h in these investigations.

Table 6-4 to 6-6 show simulation conditions for the evaluation of track shift forces.

Table 6-3 Used values of cant deficiency and admissible cant deficiency accordingto European standards.

Cant deficiency used in simulation [mm] 100 150 200 250 275 300

Admissible cant deficiency [mm] 91 136 182 227 250 273

Table 6-4 Simulation conditions for track shift forces.Cant ht = 160 mm, speed V = 360 km/h.

Train speed[km/h]

Cant[mm]

Cant deficiency[mm]


360 160 100 5881

360 160 150 4933

360 160 200 4248

360 160 250 3730

360 160 275 3516

360 160 300 3325

74



Nine sets of track irregularities were used in the present study for simulations of trackshift forces, denoted Track 2 to Track 10, c.f. Section 5.8.

Table 6-5 Simulation conditions for track shift forces.Cant ht = 180 mm, speed V = 360 km/h

Train speed[km/h]

Cant[mm]

Cant deficiency[mm]


360 180 100 5462

360 180 150 4634

360 180 200 4024

360 180 250 3556

360 180 275 3361

360 180 300 3186

Table 6-6 Simulation conditions for track shift forces.Cant ht = 200 mm, speed V = 360 km/h.

Train speed[km/h]

Cant[mm]

Cant deficiency[mm]


360 200 100 5098

360 200 150 4369

360 200 200 3823

360 200 250 3398

360 200 275 3220

360 200 300 3059

75


6.2.3 Track shift forces variation along the track

A study of the track shift forces as a function of distance confirm the substantial dynamiccontribution of track irregularities which starts at 600 metres. Figure 6-7 shows thewhole simulated track including the transition curve. Note that these simulations aremade under the conditions of a lateral bumpstop between carbody and bogie. With asmother suspension, i.e. a Hold-off-Device (HOD) or a tilting bogie bolster below thesecondary suspension, the dynamic peaks of the track shift forces would have beenreduced. The peak values of the track shift forces would have been much less with aHold-off-device in operation.

Figure 6-7 Example of track shift force S as a function of distance on Track 5.Transition curve have a length of 360 m, radius is 3361 m, cant is 180 mmand cant deficiency is 275 mm. Speed V = 360 km/h.The slight disturbance from the transition curve is almost damped outwhen the track irregularity starts (at the distance of 600 m).

6.2.4 Track shift forces for different cant

An example of the resulting track shift force for Track 5 and Track 10, where cant isvaried from 160 mm to 200 mm at a vehicle speed of 360 km/h, are shown in Figure 6-8to Figure 6-9. The simulation results for other tracks are shown in Appendix C. Nosignificant differences between different cant values can be observed. The limit value isreached at a cant deficiency of 275 mm on both tracks.

Note that the track shift forces are evaluated as the average over 2 m, denoted S2m.

Track shift force 1st bogie, 2nd wheelset

0

10000

20000

30000

40000

50000

0 200 400 600 800 1000 1200 1400

Distance [m]

S[N

]

Start of the horizontalcurve radius (360 m)

76


Figure 6-8 Track shift force S as a function of cant deficiency hd on Track 5.Three different values of cant are shown. 1st bogie, 2nd wheelset.

Figure 6-9 Track shift force S as a function of cant deficiency hd on Track 10.Three different values of cant are shown. 1st bogie, 2nd wheelset.

20

25

30

35

40

45

50

55

50 75 100 125 150 175 200 225 250 275 300 325 350

Cant deficiency [mm]

Sm

ax[k

N]

S2m (ht=160mm) S2m (ht=180mm)S2m (ht=200mm) S2m,lim

15

20

25

30

35

40

45

50

50 75 100 125 150 175 200 225 250 275 300 325 350


Sm

ax[k

N]

S2m (ht=160mm) S2m (ht=180mm)

S2m (ht=200mm) S2m,lim

77


6.2.5 Comparisons between different track irregularities

In this section comparisons between different track irregularities are presented. In Figure6-10 and Figure 6-11 the track shift forces in relation to limit value (Smax/Slim) areshown for cant ht = 180 mm. A comparison with a simulation without irregularitiesshows the dynamic contribution.

It can be observed in Figure 6-11 that the maximum peak forces Smax in relation to thelimit Slim are not always increasing monotonously with increasing cant deficiency orincreasing magnitude of track irregularities. This is mainly due to non-linearity in thewheel-rail contact or in the lateral bump-stop suspension. It is quite typical for caseswhere just an occasional peak is registered and evaluated for each simulated case, whichleads to results with a limited statistical significance. Within the scope of this study it hasnot been judged as possible to perform a full set of simulation on different tracks to gaina full statistical significance. Instead, we have chosen the approximate approach to havea margin of 15% in the limit value of track-shift forces, to allow for typical statisticalscatter; c.f. Section 5.5.

Figure 6-10 Track shift force S (in relation to limit value) as a function of cantdeficiency hd for Track 2 - Track 6, as well as track with noirregularities.Cant ht = 180 mm. 1st bogie, 2nd wheelset.

0

0,5

1

1,5

50 75 100 125 150 175 200 225 250 275 300 325 350


Sm

ax/S

lim

Track 2 Track 3 Track 4

Track 5 Track 6 No irregularities

ht=180 mm

78


Figure 6-11 Track shift force S (in relation to limit) as a function of cant deficiencyhd for Track 7 - Track 10, as well as track with no irregularities.Cant ht = 180 mm. 1st bogie, 2nd wheelset.

It is interesting to note that the two cases in Figure 6-10 and 6-11, differing in the sourcesof track irregularities, produce approximately the same results if the Q-values are thesame. Both Track 5 and Track 10 has Q-values of 99 and they both produce Smax = Slim

at a cant deficiency of 275 mm. However, these results should not be generalised,because just two different tracks irregularities have been investigated.

0

0,5

1

1,5

50 75 100 125 150 175 200 225 250 275 300 325 350


Sm

ax/S

lim

Track 7 Track 8 Track 9

Track 10 No irregularities

ht=180 mm

79


6.2.6 Improvements of track irregularities

As mentioned earlier, a full study on the effect of track irregularities for differentoperational cases, including sets of different high-speed rail vehicle configurations invarious conditions, is outside the scope and possibilities of this study. Therefore asimplified procedure has been applied, just to give an indication whether lateral trackforces and track quality would be in the right order of magnitude.

As described in Section 5.8 the simulated tracks are evaluated according to Banverket Q-number definition, taking the standard deviations of vertical, lateral and cantirregularities into account. There is no statistical analysis on different types andamplitudes of occasional irregularities, to be evaluated according to quality level C (c.f.Section 5.8). This is to be done in further investigations. From this point of view thisstudy would produce somewhat optimistic results.

Also from the vehicle point of view there are simplifications, mainly due to theassumption of a lateral bump stop in the suspension between bogie and carbody, insteadof having a Hold-off-Device (HOD) or a tilting bolster below the secondary suspension,both cases allowing a more flexible suspension. Such implementations would produce abetter ride and likely somewhat reduced peak lateral track forces. From this point of viewthis study would produce somewhat conservative results.

With the above mentioned in mind some preliminary results and indications will beshown and discussed below.

80


Figure 6-12 shows necessary improvement of the relative magnitude of the trackirregularities, compared to a track with Q-number of 80 for class K0 according toBanverket. Preliminary, this improvement of track irregularities is needed to get asuitable track quality for high-speed operations. The necessary improvement of the trackbed to allow a cant deficiency of 275 mm is approximately 25% in relation to a trackwith quality class K0 according to Banverket. In this context it should be repeated that acant deficiency of 275 mm is necessary at tests, in order to have an admissible cantdeficiency of 250 mm in operation.

Figure 6-12 Necessary improvements of track irregularities as a function of cantdeficiency. Track 2 - 6.The results are presented relative quality class K0 according to Banverketbased on the track irregularities measured on a curve betweenSimonstorp and Katrineholm.

0

25

50

75

100

125

150

100 125 150 175 200 225 250 275 300 325 350


Tra

ckir

reg

ula

rity

rela

tive

K0

[%]

ht = 180 mm

81


The corresponding necessary improvement with respect to quality class K0 according toBanverket for track irregularity measured between Åby and Nyköping to be allowed fora cant deficiency of 275 mm are shown in Figure 6-13. Also in this track the necessaryimprovements would be approximately 25% in relation to current quality class K0.

Figure 6-13 Necessary improvements of track irregularities as a function of cantdeficiency. Track 7 - 10.The results are presented relative quality class K0 according to Banverketbased on the track irregularities measured on tangent track between Åbyand Nyköping.

0

25

50

75

100

200 225 250 275 300 325 350


Tra

ckir

reg

ula

rity

rela

tive

K0

[%]

ht = 180 mm

82


Figure 6-14 gives a hint of the necessary improvement of track irregularities to get asuitable track for high-speed operations at different cant deficiencies.

Figure 6-14 Comparison of the track shift forces between different tracks.The figure gives a indication of the necessary improvements of trackirregularities.

Cant = 180 mm, 1st bogie, 2nd wheelset

05

1015202530354045505560

50 100 150 200 250 300 350


Tra

cksh

ift

forc

e[k

N]

S2m,till

Track 3(K0)

Track 5

No trackirregularities

83


6.3 Evaluation of vehicle overturning

6.3.1 Conditions

In Section 5.6.3 a description of the intercept method was given. As mentioned before,the intercept method evaluates the risk of overturning by calculating a so-called vectorintercept of all wheel forces. The distance of the intercept vector from the middle of thetrack plane can be determined by only knowing the vertical wheel forces. This distancein relation to half the distance between contact points (bo) will lead to the intercept riskfactor E. The vehicle will run safe for E < 1 and begin to turn over for the value of 1. Itwill become 1, when all windward wheels are unloaded. The value of E can not exceedthe value 1. In this study the intercept method risk factor E is calculated for the wholevehicle, i.e all vertical forces for one side of the vehicle are summarized. Beforeevaluation, E is filtered by a low pass filter at 1.5 Hz limit frequency.

Cant deficiency was adequately chosen to 150, 200, 250 and 275 mm, and the curve radiiwere varied in accordance. After a few preliminary simulations where both a cant of 180mm and 200 mm were used, a difference between these two values of cant were hard todiscern when evaluating the risk of vehicle overturning. As a result, only simulationswith a cant of 180 mm are presented here.

In such a case the vector intercept E must not exceed 0.9, i.e. the vector intercept bt shallnot reach more than 0.9 x 0.75 m from the track centre towards the outer rail. In thiscriterion there is a margin before the train really turns over. According to simulations thismargin is typically 3 – 5 m/s of wind velocity above the stated wind velocity of 23 m/s.

84


According to the above mentioned requirements the simulated speed is 350 km/h, i.e. thetested maximum speed of the trains. Cant deficiency is varied in intervals up to 275 mm.Because the cant itself has obviously just an insignificant influence, a “standard” cant of180 mm is chosen. The horizontal curve radius is chosen to suit speed and cantdeficiency, according to Table 6-7 below.


The track irregularities that were used in the present study for simulations of vehicleoverturning are Track 5 and Track 10. The reason for not using other tracks in thesimulations were that it is important to have a suitable and adapted track standard whenevaluating vehicle overturning. If several very unlikely events are combined the resultingworst case would be too unrealistic.

6.3.3 Safety against vehicle overturning at different conditions

In Figure 6-15 the maximum value of the intercept method risk factor E is shown as afunction of wind velocity for vehicle configuration B. Vehicle speed V = 350 km/h andcant ht = 180 mm. The results are shown at four different values of cant deficiencies andtheir corresponding radius.

Table 6-7 Simulation conditions for vehicle overturning.Speed V = 350 km/h and cant ht = 180 mm

Train speed[km/h]

Cant[mm]

Cant deficiency[mm]


350 180 150 4380

350 180 200 3804

350 180 250 3362

350 180 275 3177

85


Figure 6-15 Maximum value of the intercept method risk factor E at different windvelocities for vehicle configuration B.Speed V = 350 km/h and cant ht = 180 mm. Values are shown at fourdifferent values of cant deficiencies from 150 mm to 275 mm.

Permissible wind velocity from the most unfavourable direction for three different trainconfigurations are presented in Figure 6-16. Train configuration B has 4000 kg moreweight in the carbody behind the leading bogie. This condition must be taken intoconsideration when evaluating safety against vehicle overturning.

The permissible wind velocity according to the intercept method risk factor for vehicleconfiguration B at a cant deficiency of 250 mm is 23.4 m/s. In vehicle configuration Cthe permissible wind velocity is calculated to 22.5 m/s. The difference betweenconfiguration B and C is the height of c.g. for the carbody, c.f. Section 5.9.1. These

Intercept method risk factor,R=3804 m, hd=200 mm

0,50

0,60

0,70

0,80

0,90

1,00

20 22 24 26 28 30Wind velocity [m/s]

Ein

t[-]


0,50

0,60

0,70

0,80

0,90

1,00

20 22 24 26 28 30Wind velocity [m/s]

Ein

t[-]


0,50

0,60

0,70

0,80

0,90

1,00

20 22 24 26 28 30Wind velocity [m/s]

Ein

t[-]


0,50

0,60

0,70

0,80

0,90

1,00

20 22 24 26 28 30Wind velocity [m/s]

Ein

t[-]

86


vehicle configurations are considered to be technically achieveable and realistic forfuture high-speed EMUs.

Figure 6-16 Permissible wind velocity as a function of cant deficiency according tointercept method risk factor.Speed V = 350 km/h and cant ht = 180 mm.

Permissible wind speed according to intercept method risk factor

18

1920

2122

23

2425

2627

28

125 150 175 200 225 250 275 300Cant deficiency [mm]

Win

dve

loci

ty,v

win

d[m

/s] Train configuration A

Train configuration BTrain configuration C

ht = 180 mm

87


The significant difference between allowed wind velocity with respect to E = 0.9 andcritical wind velocity at simulated vehicle overturning is presented in Figure 6-17. Thelines are not parallel and the cap of wind velocity is diverted at higher value of cantdeficiency.

Figure 6-17 Allowed wind velocity as a function of cant deficiency.According to intercept method risk factor at simulated vehicleoverturning. Speed V = 350 km/h and cant ht = 180 mm.

6.3.4 Conclusions

As a result of simulations on vehicle overturning it seems to be realistic to run at about350 km/h at cant deficiencies around 250 mm with state-of-the-art vehicle technology.However, the final TSI criteria for evaluation of overturning was not laid down at thetime of this study. Therefore, there is some incertainty on this matter.

20

22

24

26

28

30

125 150 175 200 225 250 275 300


Win

dve

loci

ty,v

win

d[m

/s]

Intercept method risk factor Vehicle overturning

ht = 180 mm

88


7 Consequences of freight trains operations

This chapter will discuss some consequences of different kinds of freight train operationsfrom a track geometry point of view. In order to do this, it is initially necessary toidentify the different categories of future freight trains that are likely to occur, withspeeds, total train mass, axle loads and other characteristics.

The main issue is how steep gradients that can be allowed with respect to possible trainmass hauled by different sizes of locomotives. Also other aspects will be discussed, suchas the influence of gradients with respect to braking performance, as well as possibletrack cant and cant excess. Very briefly also the issue of permissible axle load will bediscussed.

7.1 Different categories of freight trains

Principally three principal categories of freight trains, I, II and III according to below,have been identified and considered for future rail operations in general:

I. Freight trains for heavy mass goods, such as bulk, steel, paper, timber, chemicals,heavy machinery and other finished heavy goods in large quantities.

Trains for unit-load carriers such as containers and swap bodies, with open flatwagons, also containing a various amount of road vehicle semitrailers are includedin this category. The unit-loads are loaded and unloaded at large-scale terminals onnon-electrified track, with cranes or heavy mobile lifts. Sometimes the wagons ofsuch trains have long-stroke end buffers to limit the impact on sensible goods atwagon shunting operations. It is quite common that wagons for heavy mass goodsare mixed with container and swap bodies in the same train.

This category of trains is typical for today's rail freight traffic. They have usually anaxle load of up to 22.5 tonnes and a maximum speed of 90 - 100 km/h, in somespecial cases up to 120 km/h. Freight wagons have a traditional design withstandardised components and subsystems for international cross-border exchange.

In the future a great part of these trains are assumed to have an axle load of 25tonnes, in some cases likely up to 28 - 30 tons. In some cases they will have a widerand higher loading gauge (height 4.8 m), at least in Swedish domestic traffic, thantoday's internationally exchangeable wagons (maximum height 4.3 - 4.6 m). Trainlength is believed to stay within the internationally standardised 750 m, althoughlonger trains may be considered in special cases. Train mass may in most cases staywithin about 2000 - 2500 tonnes, which is 30 - 50% higher than today's ordinarytrains. If high-strength automatic couplers are introduced in the future, train massmay be further increased on certain trains.

Speeds will be maintained in the present range: around 90 - 120 km/h, possibly withan increased amount of traffic in the higher range. However, the use of tarpaulincovers on many loads, semi-trailers and swap bodies may prevent higher speeds thanabout 100 km/h. A possible trend is that transport of containers and swap bodies

89

Consequences of freight trains operations

may - to a large extent - be transferred to lighter and faster trains according tocategory II.

II. Fast freight trains for unit-loads, heavy express goods and heavy mail.

This is a fairly new category of freight trains, which may be an important category inthe future. The Swedish trains for heavy mail (called B-mail), in service from 2001,is an example of such trains. Such operations are run also in France and Germany. Inthe future, transport of containers and swap bodies (with stiff covers) may betransferred from category I trains to category II trains.

The characteristics of category II trains are:

- Maximum speed 160 - 180 km/h, average speed in the range 120 - 150 km/h, onsuitable track.

- Trains just make short underway stops for fast loading and unloading (5 - 15 min)at small-scale terminals, on electrified track sidings, with small-scale orautomatic load transfer equipment.

- Goods and pallets are in many cases loaded directly on the floor, thus goods is inmany cases not secured from sliding on the floor or ‘moving around’ to someextent in the wagon or in the container.

- Trains are believed to be hauled by ordinary locomotives in most cases,principally similar to modern passenger train locomotives. Another option maybe self-propelled multiple-unit freight trains, with traction equipment in thewagons.

- Locomotives and loaded wagons have a total centre of gravity lower than 2 mabove rail level, in most cases lower than 1.8 m.

- Brake systems have high performance disc brakes with 2 - 4 brake discs per axle.Brake control and actuation is of the electro-pneumatic type, with a properelectronic wheel skid protection.

- Trains have a limited mass and length, for quick acceleration, short stops andsuitability for fast loading/unloading at small-scale terminals.

- Due to the high average speed and short stops this type of trains will be able tofollow - or almost follow - the speed pattern of fast regional and inter-regionalpassenger trains. This will increase the capacity on lines with a great share of fastpassenger traffic. It will also enhance the productivity of such trains, making itpossible to run 1000 - 1500 km per day, also under day-time, with an averageannual performance of at least 200 - 300 kkm.

90


III. Freight trains for light express goods or mail, with high punctuality and servicelevel.

In principal, category III is made up by trains which are, technically similar to high-speed passenger trains. They also have similar speed and braking performance assuch trains. The French TGV trains for ordinary mail are of this category. It has beendiscussed also to introduce similar fast mail trains in Sweden, but limited linecapacity in mixed heavy freight operation makes it inconvenient. The possibleintroduction of future dedicated high-speed lines would make such trains moreconvenient.

The characteristics of category III trains are:

- Maximum speed 200 - 300 km/h, average speed in the range 160 - 250 km/h, onsuitable track. Due to a good traction performance these trains will also be able toclimb the same gradients as high-speed trains.

- Trains just make very short underway stops for fast loading and unloading (3 - 10min), on electrified track sidings with loading platforms.

- Goods are loaded in small containers or ‘baskets’ on board the train, thuspreventing the goods to slip on the floor and move around.

- Due to the high average speed and short stops this type of trains will be able tofollow approximately the same speed pattern as high-speed passenger trains.They will be able to run at night- or daytime, likely without special restrictionsdue to limited capacity. They will have a high productivity, in most cases in theorder of 300 - 500 kkm per year.

7.2 Permissible axle load and track loadings

Most high-speed lines in Europe and Japan are dedicated high-speed lines for high-speedpassenger (or mail) trains only. As far as known there are two exceptions: (1) the firstgeneration of the German high-speed lines (Neubaustrecken) and (2) the North EastCorridor (New York - Washington DC) in the USA, in both cases with heavy freightmixed with high-speed passenger operations. It is reported that some extra wear andtrack maintenance has occurred. In Germany, axle loads up to 22.5 tonnes are allowed; inthe USA freight train axle loads up to at least 30 tonnes is usual.

There are at least two problems associated with mixed operations with heavy freighttrains on the same track as lighter high-speed passenger trains:

1. Line capacity. Due to the different average speeds the two types of trains reduces theline capacity, although these problems can be reduced with proper infrastructurefacilities (possibilities of quick overtaking) and a high time precision.

2. Dynamic track loadings and track maintenance. Freight trains with heavy axle loadsand simple suspensions may likely cause high dynamic track loadings and a quitehigh rate of track deterioration. A poor track standard with significant geometrical

91


irregularities would then cause problems for the lighter high-speed trains.Alternatively, the track maintenance and renewal would be excessive and expensive.

It is anticipated that future high-speed lines for speeds above 250 km/h would normallynot allow heavy freight trains, i.e. trains of category I. In most cases other parallel linesare available, otherwise it is anticipated either that speed is kept at 250 km/h as amaximum, or that special measures are taken to maintain the track properly. As a thirdalternative it would be possible to improve the rail vehicles in order to reduce theirsensitivity to track irregularities (active suspensions etc.).

For trains of category II a maximum axle load in the range of 20 - 22.5 tonnes isforeseen. This is the range which is used for passenger trains on modern track in somecountries. In Germany, France and USA such passenger trains are run with ordinarymodern locomotives at axle loads between 20 and 23 tonnes. In the latter case - 23tonnes in the USA, with a maximum speed of 200 km/h - the track is built up by 68 kg/mrails. In Germany and France axle loads of locomotives in passenger trains are 20 - 21tonnes at speeds around 200 km/h. In this case the track is built up by 60 kg/m rails,normally with a sleeper spacing of 0.6 m. In Sweden and the UK axle loads of about 18tonnes is used on locomotives in speeds around 200 km/h. In Sweden this track loadingwas originally accepted for the older 50 kg/m rails and quite weak concrete sleepers(types 101 and S2) at a spacing of 0.65 m.

In Sweden, modern high-performance track is built up by UIC 60 kg/m rails on elasticrubber pads laid on concrete sleepers (type S3) with a spacing of 0.6 - 0.65 m. The elasticrubber pads (thickness ca 10 mm) are believed to reduce the dynamic vertical high-frequency forces (30 - 150 Hz) compared to stiffer pads which has earlier being used andis still used on several railways. To further increase the resistance against trackdeterioration concrete sleepers with a larger support area may be considered in thefuture [25] [27].

All the three major European rail vehicle suppliers - Alstom, Bombardier (formerAdtranz) and Siemens - offer passenger locomotives for around 200 km/h with an axleload of 20 - 21 tonnes. They typically have a maximum tractive power of 6000 - 6500kW (at the wheel periphery) and would be suitable for category II freight operations.

It is assumed that the Swedish authorities (mainly Banverket) will put relevantrequirements on freight wagons for speeds in the range of 160 - 180 km/h, i.e. not onlyaccepting the poor dynamic performance of ordinary freight wagons at these speeds. Itwould at least be possible to apply the minimum requirements according to UIC 518[24]. A further possibility may be to give incentives for improved dynamic performance(low dynamic track forces) by differentiated track fees. This possibility is also applicableto the locomotives.

For freight trains of category III, i.e. high-speed trains, axle loads are assumed to bewithin the range as defined in TSI; i.e. generally a maximum of 167 kN, although drivenaxles are allowed to have static axle loads up to 177 kN at speeds not exceding 250 km/h.

92


In any case the general requirements according to CEN and UIC must be considered, i.e.the dynamic maximum vertical wheel loads should meet the following limit values:

for speeds up to 160 km/h Qmax,lim ≤ 200 kN160 km/h < Vlim ≤ 200 km/h Qmax,lim ≤ 190 kN200 km/h < Vlim ≤ 250 km/h Qmax,lim ≤ 180 kN250 km/h < Vlim ≤ 300 km/h Qmax,lim ≤ 170 kN300 km/h and above Qmax,lim ≤ 160 kN

Note that it would be possible - also in this case - to give incentives for a good dynamicperformance by differentiated track fees.

7.3 Track cant and cant excess

Track cant - or superelevation - is currently limited to 150 mm in Sweden. This is anormal cant on lines with ordinary freight traffic. Similar cant is used in many othercountries, although up to 160 mm is applied in a few cases. There are at least two reasonsfor limiting track cant:

1. A very high track cant leads to high lateral accelerations parallel to the wagon floor,if the train is running very slowly. In ordinary freight wagons where goods andpallets may be loaded directly on the floor and is secured from moving around justby friction, it seems important not to have too large track cant if the trains arestopped or is moving slowly on a canted curve. Because of the generally good trackstandard on high-speed tracks, with small anticipated dynamic lateral accelerationsat low speeds, it would be possible to increase the track cant without infringing thesafety against ‘moving around’. From this point of view it would likely be possibleto increase the maximum cant to 160 or 170 mm. This is also the limit values of cantin the newly proposed CEN provisional standard on track for mixed freight andpassenger traffic [7].

2. Cant excess should not be too high for slow trains. On high cant, the low wheels andrails would be highly loaded, possibly causing track deterioration. In the popularrailway engineering traditions it is also said that high cant excess leads to excessivewear and damage on the low rail, due to the higher vertical force. According toinvestigations made by KTH in co-operation with Banverket [25] the latter problemis obviously overstated, at least in larger curve radii (R > 800 m). In larger curves (R> 2000 m) the wear problem is negligible, because the attack angles between wheelsand rail are very small. Also from the track deterioration point of view it is verylikely that a cant excess of 110 - 130 mm is acceptable occasionally, at least forvehicles with an axle load limited to 22 tonnes and a centre of gravity at maximum 2m above rail level (1.8 m for locomotives); i.e. freight trains category II. At a cantexcess of 120 mm the quasistatic vertical wheel-rail force is calculated to approx.140 kN in this case, which is below the permissible vertical quasistatic forceaccording to UIC 518.

93


These principles and conclusions are also reflected in the newly proposed CENprovisional standard [7], which states that a cant excess of 110 mm would be acceptable,with 130 mm as a maximum limit value.

In case of freight trains without goods and pallets loaded directly on the floor, forexample mail trains, it may be possible to have a larger track cant, i.e 180 - 200 mm. Thisis also in line with the newly proposed CEN and TSI standards.

Example: A freight train of category II runs at 120 km/h in a curve radius of 3525 m anda track cant of 160 mm. The cant excess at this speed is 112 mm. At 140 km/h the cantexcess is 94 mm.

More examples: Let us consider a case were heavy freight train (category I) is allowed torun at 90 km/h. This is combined with conventional high-speed trains where thepermissible cant deficiency is maximised to 80 mm according to TSI for speeds over 300km/h. At a top speed of 350 km/h for the high-speed train the corresponding cant is 123mm and the smallest possible horizontal curve radius is 7120 m. This pertains to a cantexcess of 110 mm for a heavy freight train at 90 km/h, which is in accordance to TSI.With a tilting train the possible cant deficiency would be as much as 250 mm accordingto the preliminary conclusions of this study. Thus, the permissible cant is 135 mm andthe horizontal curve radius is 3755 m. Even this would be valid with a cant excess of110 mm. This reduces the horizontal curve radius with 47%. The results are presented inTable 7-1.

Table 7-1 Optimised horizontal curve radius and optimised cant for all kind ofoperations, trains for heavy mass goods, category I, are included.Vmin = 90 km/h.

Conventionaltrain

Train with tilttechnology

Speed of high-speed trains km/h 350 350

Speed of heavy freight trains km/h 90 90

Cant deficiencya

a. Valid for high-speed passenger train

mm 80b

b. Recommended value according to CEN and TSI

However, as pointed out earlier it is questionable whether heavy freight trains ofcategory I should be allowed on high-speed lines with maximum speeds above 250 km/h.

250

Cant excess mm 110b 110b

Cant (optimised) mm 123 135

Horizontal curve radius (optimised) m 7121 3755

94


In Table 7-2 further results are presented with speed of 120 km/h for freight trains ofcategory II.

Table 7-2 Optimised horizontal curve radius and optimised cant for high-speedtrains and freight trains of category II.Vmin = 120 km/h.

Conventionaltrain

Train with tilttechnology

Speed of high-speed trains km/h 350 350

Speed of freight train of category II km/h 120 120

Cant deficiencya

a. Valid for high-speed passenger train

mm 80b


250

Cant excess mm 110b 110b

Cant (optimised) mm 135 158


95


If the permissible speed for freight trains of category II increases to 160 km/h theconditions become more favourable concerning maximised cant and optimisedhorizontal curve radius. According to TSI a cant of 160 mm is allowed for mixed trafficlines. For a conventional high-speed train the permissible cant deficiency is 80 mm atspeeds above 300 km/h. The optimised horizontal curve radius in this case is 6023 m.The cant excess becomes exactly 110 mm. With a cant deficiency of 250 mm for thetilting train a calculation gives a horizontal curve radius of 3526 m. The cant excess isfor this case only 74 mm, which is significantly lower than the permissible value. Theresults are shown in Figure 7-3.

7.4 Gradients versus train mass

In this section we will investigate the ability to run freight trains as function of gradients.Firstly the locomotive must be able to bring the train in motion also on an uphillgradient, if the train has been stopped.

Secondly the train must be able to accelerate after it has been brought into motion. Thedesired amount of acceleration, however, is dependent on the performance requirementsof the trains and on the desired capacity of the line - a slow acceleration of a freight trainwill block the line for a long time, thus reducing the line capacity.

Thirdly the trains must be able to brake on the prescribed braking distance also ondownhill gradients. This is a question of braking capacity of the trains and also ofsignalling distances.

We will briefly investigate these issues for the three train categories defined in 7.1.

Table 7-3 Optimised horizontal curve radius for high-speed lines with fast freighttrains of category II.Vmin = 160 km/h.

Conventionaltrain

Train with tilting

technologya

a. High-speed passenger train

Speed of high-speed passenger trains km/h 350 350

Speed of freight trains of category II km/h 160 160

Cant deficiency mm 80b


250

Cant excess mm 110b 74

Cant mm 160 160


96


7.4.1 Freight trains category I - heavy freight trains

If ordinary heavy freight trains are to be run on the high-speed line, the gradients must bebuilt to the usual national standard. In Sweden this means a gradient of maximum 10 ‰.This is the standard for main lines in southern Sweden and will also be built on the new‘Botniabanan’ Sundsvall - Umeå, where a maximum speed of 250 km/h is foreseen forhigh-speed passenger trains.

With the current four-axled locomotives, class Rc (mass 78 tonnes), a maximumtrainload of 1400 tonnes can be hauled in gradients of 10 ‰. With this train load thelocomotive is able to bring the train in motion, with an available adhesion α = 0.25 andrunning resistance as defined in Appendix F in a 400 m radius curve.

The acceleration of such heavy trains in the above mentioned gradients will, however, bevery slow. In cases where the adhesion is just 0.25 all the time, it will not be able to reachthe normal maximum speed of the train (usually 90 - 100 km/h) in that gradient. In shortgradients, however, this limitation may not be severe, because the train will accelerate assoon as the train has left the steep gradient.

The required signalling distance is dependent on the gradient: a long downhill gradientwill usually increase the required signalling distance in order to stop the train withnormal brakes. In some cases the maximum speed will be reduced.

As briefly discussed in Section 7.2 it is believed that heavy freight trains will normallynot be allowed on high-speed lines with a maximum speed of more than 250 km/h. It isalso believed that many lines for the speed range 200 - 250 km/h will not either bedesigned for heavy freight trains, if gradients are considered. In many cases there areparallel lines for heavy freight traffic. A limited number of lighter category I freighttrains are able to run on steeper gradients at suitable speed anyway.

7.4.2 Freight trains category II - fast trains for unit-loads and heavy express

This category of trains would, under certain conditions, be allowed on high-speed linesfor speeds above 250 km/h. Some of these technical conditions have been brieflydiscussed in Section 7.2 (axle load) and 7.3 (cant and cant excess). In this section, thegradients will be discussed.

The first requirement is that the gradient is limited in order to assure that the train can bebrought in motion with the available tractive force of the locomotive and the availablewheel-rail adhesion. Or inversely: the train mass must be limited depending on thegradient.

As for trains in category I the tractive force with an available adhesion of 0.25 mustbalance the running resistance at starting, according to the equations in Appendix F.However, in the case of high-speed lines the curves radii are much larger - in the order of3000 - 5000 m instead of down to 300 á 400 m. Therefore, in this case the curve radius isassumed to be 3000 m. This will reduce the running resistance at starting, thus allowingsome more train mass in the same gradient.

97


Using the equations and assumptions in Appendix F the permissible train mass fordifferent gradients is calculated and shown in Table 7-4.

The trains are assumed to contain 50 axles in the case of one locomotive and 100 axles inthe case of two locomotives. This is simple stepwise assumptions. However, a sensitivityanalysis has been made, showing that variation of the number of axles with 40% in thecase of one locomotive, changes the permissible train mass by just approx. 6 tonnes in a25 ‰ gradient, which is not considered as significant. Thus, the number of axles in thetrain is not critical as long as the total train mass is the same.

The calculations shown in Table 7-4 are just considering what is required in order tobring the train in motion, according to traditional rules for conventional freight trains.The acceleration of the freight train will be very slow as long as the whole train remainsin the gradient. This may not be acceptable in long gradients, if high train performanceand/or capacity of the line are required. As a rough limit of what is considered as a longgradient, the maximum train length may be used, say in the order of 400 - 750 m.

Therefore, in long gradients it is recommended that the gradients be reduced below whatis indicated in Table 7-4. This is particularly important if the uphill gradient is locatedimmediately after a station or a signal, where freight trains stop frequently. These issueshave not been investigated in detail in this study. However, it is recommended to makeproper investigations in each real case of a high-speed line, provided that category IIfreight trains are planned to be run on the actual line. Traffic simulations must be donewith a proper simulation model.

It should be noted that the braking performance of category II freight trains must behigher than for ordinary category I freight trains, due to the higher speeds. The gradients,the signalling distances and the maximum axle load has to be considered. It is believed

Table 7-4 Permissible train mass in order to bring the train in motion ongradients.One or two locomotives á 84 tonnes.Container train, 50 axles (one loco), 100 axles (two locos)Curve radius: min 3000 m

Gradient(‰)

Numberof locos

Train mass(tonnes)

Wagon mass(tonnes)

15 1 1242 1158

20 1 950 866

25 1 770 686

30 1 647 563

20 2 1900 1732

25 2 1540 1372

30 2 1294 1126

40 2 980 812

98


that electro-pneumatic disc brakes will be used, with two or three discs per axle. Thesemechanical brakes will be supplemented by regenerative electrical brakes on thelocomotive, which is used as the first option for braking in normal operation. Inprincipal, this is the same braking technology as on passenger trains.

Figure 7-1 Possible train mass due to starting in gradients

7.4.3 Freight trains category III - high-speed for light express or mail

As category III freight trains are intended to have similar performance as the high-speedpassenger trains, i.e. with good traction performance, these trains will also be able toclimb the same gradients as passenger high-speed trains. Also the braking performancemust be equipped accordingly, to match the signalling system. Hence, if only category IIIfreight trains will be allowed on the line, the gradients are in this case not restricted bythe freight trains. The gradients may be as high as 35 ‰ according to TSI.

0

500

1000

1500

2000

2500

0 10 20 30 40 50

Gradient [‰]

Po

ssib

letr

ain

mas

s[t

on

ne]

Wagon mass, one locoWagon mass, two locosTrain mass, one locoTrain mass, two locos

2 locos á 84 ton

1 loco á 84 ton

99


100


8 Possible track geometry

In this chapter possible track geometry is presented. Tables and figures show a proposalof possible values of cant and cant deficiency and their corresponding horizontal curveradius at different target speeds. Examples of possible vertical curve radius are given aswell.

8.1 Horizontal curve radius

Examples of possible horizontal curve radius are given in the following tables andfigures. Tables 8-1 to 8-4 show examples of horizontal curve radius at different values ofcant deficiencies. The applied cant will be varied from 150 mm to 200 mm at differentspeeds from 200 km/h to 350 km/h. the relations are also shown in Figures 8-1 to 8-4.

Further, the same relations are shown in Figures 8-5 to 8-8 changing the independentvariables and parameters.

Note that the cant, and consequently also the curve radius, may be limited if freight trainsof category I or II are to be run on the high-speed track. This issue has been dealt with inSection 7.3.

101

Possible track geometry

Figure 8-1 Horizontal curve radius R as a function of cant deficiency hd.Curves are shown at speeds of 200, 280 and 350 km/h. Cant ht = 150 mm.

Table 8-1 Examples of horizontal curve radius at four different values of cantdeficiencies.Speeds varied from 200 km/h to 350 km/h. Cant ht = 150 mm.

Speed [km/h]Cant deficiency [mm]

200 250 280 300 330 350

100 1888 2950 3700 4248 5140 5782

150 1573 2458 3084 3540 4283 4818

200 1349 2107 2643 3034 3671 4130

250 1180 1844 2313 2655 3213 3614

0

1000

2000

3000

4000

5000

6000

100 125 150 175 200 225 250 275 300


Ho

rizo

nta

lcu

rve

rad

ius

[m]

V=200 km/h V=280 km/h V=350 km/h

ht = 150 mm

102





200 250 280 300 330 350

100 1816 2837 3558 4085 4942 5560

150 1523 2379 2984 3426 4145 4663

200 1312 2049 2570 2950 3570 4015

250 1152 1799 2257 2590 3134 3526

0

1000

2000

3000

4000

5000

6000

100 125 150 175 200 225 250 275 300Cant deficiency [mm]

Ho

rizo

nta

lcu

rve

rad

ius

[m]

V=200 km/h V=280 km/h V=350 km/h

ht = 160 mm

103





200 250 280 300 330 350

100 1686 2634 3304 3793 4589 5162

150 1431 2236 2803 3218 3894 4380

200 1242 1941 2435 2795 3382 3804

250 1098 1715 2152 2740 2988 3362

0

1000

2000

3000

4000

5000

6000

100 125 150 175 200 225 250 275 300


Ho

rizo

nta

lcu

rve

rad

ius

[m]

V=200 km/h V=280 km/h V=350 km/h

ht = 180 mm

104





200 250 280 300 330 350

100 1574 2458 3084 3540 4283 4818

150 1349 2107 2643 3034 3671 4130

200 1180 1844 2313 2655 3213 3614

250 1049 1639 2056 2360 2856 3212

0

1000

2000

3000

4000

5000

6000

100 125 150 175 200 225 250 275 300


Ho

rizo

nta

lcu

rve

rad

ius

[m]

V=200 km/h V=280 km/h V=350 km/h

ht = 200 mm

105


Figure 8-5 Horizontal curve radius R as a function of speed V.The different curves show conceivable values of cant deficiency hd.Cant ht = 150 mm.


0

1000

2000

3000

4000

5000

6000

100 150 200 250 300 350Speed [km/h]

Ho

rizo

nta

lcu

rve

rad

ius

[m]

Cant deficiency, hd=100 Cant deficiency, hd=150


ht = 150 mm

0

1000

2000

3000

4000

5000

6000

100 150 200 250 300 350Speed [km/h]

Ho

rizo

nta

lcu

rve

rad

ius

[m]



ht = 160 mm

106




0

1000

2000

3000

4000

5000

6000

100 150 200 250 300 350

Speed [km/h]

Ho

rizo

nta

lcu

rve

rad

ius

[m]



ht = 180 mm

0

1000

2000

3000

4000

5000

6000

100 150 200 250 300 350

Speed [km/h]

Ho

rizo

nta

lcu

rve

rad

ius

[m]



ht = 200 mm

107


8.2 Vertical curve radius

Possible vertical curve radii with limiting values according to CEN provisional standard[7] are shown in Table 8-5. In Figure 8-9 the vertical curve radius as a function of speedis presented. The values have been rounded up to nearest 100 m. There are differentminimum values of vertical curve radius dependent of different requirements of limitingvalues on a crest or in a hallow. The limited vertical accelerations have been presented inSection 3.6.6.

Figure 8-9 Vertical curve radius as a function of speed.Curves are shown for four different limiting values. Source: CENprovisional standard [7].

Table 8-5 Limiting values on vertical curve radiusSource: CEN provisional standard [7].

Speed [km/h]Vertical curve radius [m]

200[km/h]

250[km/h]

280[km/h]

300[km/h]

330[km/h]

350[km/h]

Recommended value 14100 22000 27500 31600 38200 43000

Minimum valuewithout tolerance

7100 11000 13800 15800 19100 21500

Minimum value on a crest 6400 10000 12500 14400 17400 19600

Minimum value in a hallow 5400 8500 10600 12200 15000 16600

0

10000

20000

30000

40000

50000

60000

200 250 300 350

Speed [km/h]

Ver

tica

lcu

rve

rad

ius

[m]

Recommended minimum value according to CEN/TC

Minimum value without tolerance according to CEN/TC

Minimum value with tolerance (on a crest) according to CEN/TC

Minimum value with tolerance (in a hallow) according to CEN/TC

108


9 Conclusions and further research

9.1 Conclusions on the literature study

Track cant in the range of 160-200 mm are possible to achieve. The higher values (180-200 mm) can be allowed where only high-speed passenger trains are intended to operate.However, when mixed traffic with freight trains would come into question, the lowervalue must be considered. This is mainly due to the risk of loads “moving around” on thefloor of the wagon. Hence, higher values of cant than 160 mm should not normally bechosen in such cases.

The literature study also made a compilation over different worldwide projects and theirused values of track cant, cant deficiency, horizontal curve radius, gradients and verticalcurve radius.

The recommended value of cant deficiency according to TSI is 100 mm (forconventional trains up to 300 km/h) but higher values may be allowed for lines withtough topographical constrains. Also, as described in Section 3.6.2, interoperable high-speed trains equipped with tilt technology may be admitted to run with higher cantdeficiency values. To further investigate this issue is one of the main contributions of thisstudy.

Transition curves should be long if tilting trains are considered. The duration in thetransition curves should at least be around 4-5 sec (i.e. 390 - 485 m for 350 km/h).Kufver says [16]: “A higher limit for cant, a lower roll coefficient and a higher degree ofcompensation in the body tilt system favour longer clothoids”. This proposalcorresponds also to the rate of cant and the rate of cant deficiency recommendationsaccording to TSI.

9.2 Conclusions on dynamic analysis of simulated vehicle response

According to hunting stability the following conclusions have been drawn:

The hunting stability simulations have given an insight on the hunting stability problem.It can be established that it is likely possible to run a properly designed train at a speed of350 km/h with the stability criteria being considered. In other words, it could beconcluded that the vehicle configuration has the required properties that was foreseenbefore the simulations started. The simulated wheelset quidance is stiffer than on currentSwedish self-steering bogie designs, but is more flexible than traditional quite stiffdesign from continental Europe. These characteristics of the vehicles have been studiedbefore but not simulated for speeds in this range.

It is important, however, that wheels and rails have suitable shapes in the wheel-railinterface, in order to limit the equivalent conicity to appropriate levels (e.g. 0.2 - 0.25,which is anyhow more liberal than TSI requirements of maximum 0.15).

109

Conclusions and further research

Concerning track shift forces the following conclusions have been drawn:

With properly designed vehicles this study shows that it would be possible to maintainthe European lateral track shift criteria at 350 km/h and at a cant deficiency in the orderof 250 mm. However, it is likely impossible to get required performance withoutimproving the track quality compared to current Swedish standards for 200 km/h. Inorder to achieve a top-speed of 350 km/h and a cant deficiency of 250 mm it seemsnecessary to improve the track quality with at least 25%, i.e. track irregularities shouldbe at least 25% less in magnitude. This conclusion is, however, just an indication basedon simplified assumptions. It is outside the scope and possibilities of this study to make adetailed complete investigation on this issue.

Following conclusions on vehicle overturning have been drawn:

With a modern high-speed train having a state-of-the-art aerodynamic performance, anda roof height in the order of 3.6 m, it is technically possible to make a train design forappropriate safety at strong side-wind at a cant deficiency up to 250 mm. In addition tothe aerodynamic requirements, also the mass and mass distribution of the leading carhave to be considered. The simulated case with a leading car mass around 55 tonnes(empty), the mass centre somewhat displaced towards the leading end, seems to beappropriate. The height of the c.g. should preferably be low. For motor-coaches withtraction equipment in bogies and underneath the floor, these properties are most likelyrealistic.

9.3 Conclusions on horizontal and vertical curve radii

The horizontal curve radius is a function of allowed cant, cant deficiency and speed. Thecurve radius must be sufficiently large to cope with the desired speed for bothconventional and tilting trains respectively. For example, if conventional high-speedtrains are to be run at 280 km/h and and tilting trains at 350 km/h, the horizontal curveradius should be at least in the order of 3200 m. This requires a track cant of 200 mm anda cant deficiency of 100 mm for the conventional train and 250 mm for the tilting train.Such a geometry requires that no freight trains of category I or II are allowed.

To be more conservative, if the track cant is limited to 160 mm and the cant deficiencyfor tilting trains to 225 mm, a minimum curve radius of 3750 m is needed for tiltingtrains at 350 km/h. In this case it would be possible to accomodate also freight trainscategory II (lighter freight trains for containers, swap bodies etc.).

It should be kept in mind, however, that such speeds are not necessary or possible at allsections of the line. For example, in the vincinity of stations where most trains arestopping, the speed will be lower and the curve radius can be accordingly less.

The standards of Banverket concerning vertical curve radius are quite conventional inrelation to the proposals from TSI. These standards are, in turn, close to the standards ofDB and several other railways. The minimum curve radius is 0.175 times the square ofspeed (in km/h), with tolerances 0.16 times the square of speed on a crest and 0.135times the square of speed in a hallow. This requires a minimum vertical radius of 21500m at 350 km/h (19600 and 16500 m with tolerances on a crest and in a hallow,respectively).

110


9.4 Conclusions on freight train operations

It is anticipated that heavy freight trains should normally not be allowed on high-speedlines for speeds above 250 km/h.

If only high-speed freight trains (category III, for express goods or mail) without goodsand pallets loaded directly on the floor are operated, it may be possible to have a quitelarge track cant in the range of 180 - 200 mm. If freight trains category II with containersand swap bodies) are allowed, a maximum cant of 160 mm is recommended.

A maximum allowed cant excess of around 120 mm seems to be acceptable for acategory II freight trains (containers and swap bodies) running at a modest speed of 120km/h.

If only freight trains category III - high-speed for light express or mail - are allowed thegradients may be as high as 35 ‰ (this is in accordance with TSI).

If freight trains category II are allowed, gradients up to 20 á 30 ‰ seems to be realistic.For example, at a gradient of 25 ‰ a total wagon mass of 650 - 700 tonnes can be haluedby one four-axled locomotive.

9.5 Further research

This study primary deals with track geometry, having vehicle dynamics as a secondaryissue.

It is important to include passenger comfort in further studies.

Also hunting stability simulations have to be done under a more complete set ofconditions.

A full study on the effect of track irregularities for different operational cases, includingsets of different high-speed rail vehicle configurations in various conditions, is outsidethe scope and possibilities of this study. A simplified procedure has been applied, just togive an indication whether lateral track forces and track quality would be in the rightorder of magnitude. Future studies should penetrate this issue in more detail. In thisconnection, also the issue of track maintenance requirements should be penetratedcomprehensively.

It should be further investigated (in each individual case) whether the recommendedgradients are appropriate with respect to the train´s ability to accelerate quickly on a linewith dence traffic and limited capacity.

Finally, an optimisation of track geometry with respect to required train performance(travel time etc.) and the cost of removing different topographical or other obstaclesshould be done. Such optimisation studies must be done for each individual section ofproposed high-speed line.

111

Conclusions and further research

112


References

[1] Andersson E. and Berg M.: Järnvägssystem och spårfordon (Railway systemsand Rail vehicles), Kompendium, Del 1 - Järnvägssystem, KTH Järnvägsteknik,1999.

[2] Andersson E. and Berg M.: Järnvägssystem och spårfordon (Railway systemsand Rail vehicles), Kompendium, Del 2 - Spårfordon, KTH Järnvägsteknik,1999.

[3] Andersson E., Berg M. and Stichel S.: Spårfordons dynamik (Rail vehicledynamics), Kompendium, KTH Järnvägsteknik, 1999.

[4] Banverket: Spårgeometrihandboken (Track geometry handbook), BVH 586.40,Banverket, Borlänge, 1996.

[5] Banverket: Tillåten hastighet mht spårets geometriska form (Permissible speedwith respect to track geometry), BVF 586.41, Banverket, Borlänge, 1996.

[6] Banverket: Spårlägeskontroll och Kvalitetsnormer - Central mätvagn Strix(Control and quality standards of track geometried irregularities), BVF 587.02,Banverket, Borlänge, 1997.

[7] CEN: Railway application - Track alignment design parameters - Track gauges1435 and wider - Part 1: Plain line, prENV 13803-1:2001, CEN/TC256/WG15.

[8] CEN: Railway application - Testing for acceptance of the runningcharacteristics of railway vehicles - Part 1: Testing of running behaviour, CEN/TC 256 WG 10; Draft September 1999.

[9] Deutsche Bahn, DB: Netzinfrastruktur Technik entwerfen; Linienführung (NetInfrastructure Technical Draft; Alignment), 800.0110, DB, Germany, 1999.

[10] Deutsche Bahn, DB: Bahnanlagen entwerfen - allgemeine Entwurfsgrundlagen,Druckschrift DS 800.01.

[11] Esveld, C.: Modern railway track, NS Permanent Way Department, 1989.

[12] European Association for Railway Interoperability (AEIF): Trans-EuropeanHigh-Speed Rail system, Technical Specification for Interoperability (TSI),“Infrastructure” Subsystem, Version A, April 2000.

[13] European Association for Railway Interoperability (AEIF): Trans-EuropeanHigh-Speed Rail system, Technical Specification for Interoperability (TSI),“Rolling stock” Subsystem, Version A, Dec 5, 2000.

113

References

[14] Förstberg, J.: Ride comfort and motion sickness in tilting trains, Humanresponses to motion environments in train and simulator experiments, Doctoralthesis, TRITA-FKT Report 2000:28, KTH Railway Technology, 2000.

[15] Hecke A.: Effects of future mixed traffic on track deterioration, Master ofScience thesis, TRITA-FKT Report 1998:30, KTH Railway Technology, 1998.

[16] Kufver, B.: Optimisation of horizontal alignments for railways, Proceduresinvolving evaluation of dynamic vehicle response, Doctoral thesis, TRITA-FKTReport 2000:47, KTH Railway Technology, 2000.

[17] Rail International: Planning and building of the German Federal Railway´s newlines and their consequences. W. Blind and M. Wölbing. Article in RailInternational - May 1985.

[18] S.N.C.F: La voie Ferrée, Techniques de construction et D’entretien. Alias, J etal, Paris, 1984.

[19] Central Japan Railway Company: Data Book 2000.

[20] Hohnecker, E.: Zukunftssichere Trassierung von Eisenbahn-Hochgeschwindigkeit-strecken. Forschungsarbeiten desVerkehrswissenschaftlichen Instituts an der Universität Stuttgart, 1993.

[21] Lippert, S.: On side-wind stability of trains, Master of science thesis, TRITA-FKT Report 1999:38, KTH Railway Technology, 2000.

[22] Krieg R.: Extreme wind statistics for Säve and Arlanda. Reportet by order ofABB Traction AB, Sweden, April 1993.

[23] Lukascewicz, P.; Energy Consumption and Running Time for Trains - Modellingof running resistance and driver behaviour based on full-scale testing. TRITA-FKT 2001:25. Doctoral thesis, KTH Railway Technology, Stockholm 2001.

[24] UIC: Test and acceptance of railway vehicles from the points of view of dynamicbehaviour, safety, track fatigue and quality of ride, Code 518 OR, Draft, January1999.

[25] Andersson, E.: The influence on cant excess on track deterioration –Simulations and field measurements. TRITA FKT Report 2002:03.

[26] Tengstrand, H.: Personal communication with Mr. Henrik Tengstrand,Bombardier Transportation, chairman of the TSI technical committee on theside-wind issue.

[27] Sima, M.: Personal communication with Mr. Mikael Sima, one of theareodynamic experts at Bombardier Transportation, Västerås.

114


[28] Andersson, E. : Personal communication with prof. Evert Andersson, KTHRailway Technology, also Company Senior Specialist in Vehicle Engineering atBombardier Transportation, Västerås.

[29] DEsolver: GENSYS user´s manual. Release 0003, Östersund 2000.

115

References

116


Appendix A - Notations

A.1 Latin letters

ay track plane acceleration [m/s2]

ay,lim permissible track plane acceleration [m/s2]

ayc carbody plane acceleration [m/s2]

A clothoid parameter [m]bt distance between middle of track plane and origin of resulting force[m]b0 semi-span of wheelset-to-rail contact points [m]c curve cant [mm]CD aerodynamic drag coefficient [-]CL aerodynamic lift coefficient [-]CP aerodynamic pitch coefficient [-]CR aerodynamic roll coefficient [-]CS aerodynamic side coefficient [-]CY aerodynamic yaw coefficient [-]d distance between wind force origin and vehicle front [m]e exposition length of vehicle [m]f aerodynamic rolling coefficient factor [-]F force [N]

g acceleration of gravity [m/s2]G track gauge [m]h height [m]heq quilibrium cant [m]ht track cant [m, mm]hd cant deficiency [m, mm]hd,lim permissible cant deficiency [m]he cant excess [m]heq,mm quilibrium cant [mm]ht,mm track cant [mm]hd,mm cant deficiency [mm]he,mm cant excess [mm]Jxx mass moment of inertia with respect to its centre of gravity and around the

x-axis [kgm2]

Jyy mass moment of inertia with respect to its centre of gravity and around the

y-axis [kgm2]

Jzz mass moment of inertia with respect to its centre of gravity and around the

z-axis [kgm2]

117

Notations

k curvature [m-1]KL topographical factor [-]KN probability factor [-]KS surface roughness factor [-]KT time-averaging factor [-]KZ height factor [-]l length [m]L length of alignment element [m]Lt length of transition curve [m]m mass [kg]M moment [Nm]Eint intercept method overturning risk factor [-]P0 static axle load of stillstanding vehicle [N]q wheel unloading ratio [-]Q vertical wheel force [N]Q0 static vertical wheel force of stillstanding vehicle [N]R horizontal curve radius [m]Rrec,min recommended minimum value of horizontal curve radius [m]Rmin minimum value of horizontal curve radius [m]Rv vertical curve radius [m]Rv,rec,min recommended minimum value of vertical curve radius [m]Rv,min minimum value of vertical curve radius [m]Rf resulting force [N]S track shift force [N]ΣS2m track shift force (sum of guiding forces over 2 m track) [N]t time [s]td duration time of gale [s]tg gradient time of wind velocity [s]vres resulting wind velocity [m/s]v train speed [m/s]veq quilibrium train speed [m/s]V train speed [km/h]Vlim Operating speed limit [km/h]

Vdim dimensional train speed, design speed [km/h]vwind constant wind velocity [m/s]vgale gale wind velocity [m/s]vW side wind velocity [m/s]

average wind velocity mean-hourly value at height 10 m [m/s]

w width [m]x longitudinal coordinate [m]y lateral coordinate [m]

ÿ dynamic track plane acceleration [m/s2]

v10'

118


∆y lateral shift [m]Y lateral wheel force [N]ΣY track shift force [N]

Y/Q flange climbing ratio [-]z vertical coordinate [m]

A.2 Greek letters

µ friction coefficient [-]

ρ density of air [kg/m3]

Ψ yaw angle [rad]

ϕt cant angle, roll angle [rad]

Φ lateral force angle [rad]

A.3 Indices

b bogie

c contact

cg centre of gravity

C carbody

l left

max maximum

min minimum

r right

start start

w wind

ww windward

x longitudinal direction

y lateral direction

z vertical direction

119

Notations

120


Appendix B - Abbreviations

APT Advanced Passenger Train

BV (=Banverket) Swedish National Rail Administration

BVF Banverket regulation (standard)

BVH Banverket handbook

CEN Comité Européen de Normalisation (Committé for EuropeanStandardisation)

DB German National Railways

DS German Railways standard

EMU Electrical Multiple Unit

EN European Norm (Standards)

ESDU Engineering Science Data Unit

EU European Union

GENSYS Multibody dynamics program

ICE InterCityExpress, German high-speed train

ICT Tilting ICE

ORE Office for Research and Experiments of UIC, now ERRI

SJ Swedish State Railways

S1002 Standard wheel profile

SNCF French National Railways

TGV Train a Grande Vitesse, french high-speed train

TSI Technical Specification for Interoperability (of European high-speed trains)

UIC International Union of Railways

UIC 60 Standard rail profile

X 2000 Swedish high-speed train with tilting technology

121

Abbreviations

122


Appendix C - Further diagrams on track shift forces

Figure C-1 Track shift force S as a function of cant deficiency hd.Track 2. 2nd wheelset, 1st bogie.


30

35

40

45

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55

60

50 75 100 125 150 175 200 225 250 275 300 325 350


Sm

ax[k

N]


25

30

35

40

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Sm

ax[k

N]



123

Further diagrams on track shift forces



20

25

30

35

40

45

50

55

50 75 100 125 150 175 200 225 250 275 300 325 350Cant deficiency [mm]

Sm

ax[k

N]


20

25

30

35

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55

50 75 100 125 150 175 200 225 250 275 300 325 350


Sm

ax[k

N]


124




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Sm

ax[k

N]


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Sm

ax[k

N]


125




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ax[k

N]


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N]



126



15

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Sm

ax[k

N]



127


Figure C-10 Track shift force Smax/Slim (-) as a function of cant deficiency hd.Cant ht = 160 mm. Track 2 - Track 6. 2nd wheelset, 1st bogie.


0

0,5

1

1,5

50 75 100 125 150 175 200 225 250 275 300 325 350Cant deficiency [mm]

Sm

ax/S

lim[-

]

Track 2 Track 3Track 4 Track 5

ht=160 mm

0

0,5

1

1,5

50 75 100 125 150 175 200 225 250 275 300 325 350


Sm

ax/S

lim[-

]

Track 2 Track 3Track 4 Track 5Track 6 No irregularities

ht=180 mm

128




0

0,5

1

1,5

50 75 100 125 150 175 200 225 250 275 300 325 350


Sm

ax/S

lim[-

]

Track 2 Track 3Track 4 Track 5Track 6 No irregularities

ht=200 mm

0

0,5

1

1,5

50 75 100 125 150 175 200 225 250 275 300 325 350


Sm

ax/S

lim[-

]

Track 7 Track 8Track 9 Track 10No irregularities

ht=160 mm

129




0

0,5

1

1,5

50 75 100 125 150 175 200 225 250 275 300 325 350


Sm

ax/S

lim[-

]


ht=180 mm

0

0,5

1

1,5

50 75 100 125 150 175 200 225 250 275 300 325 350


Sm

ax/S

lim[-

]


ht=200 mm

130


Appendix D - Further diagrams on vehicle overturning

Figure D-1 Intercept method risk factor E as a function of wind velocity where cantdeficiency hd = 150 mm.Vehicle speed V = 350 km/h and cant ht = 180 mm.


Intercept method risk factor, R=4380 m, hd=150 mm

0.000.100.200.300.400.500.600.700.800.901.00

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Wind speed [m/s]

Ein

t[-]

Overturning


0.000.100.200.300.400.500.600.700.800.901.00

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Wind speed [m/s]

Ein

t[-]

Overturning

131

Further diagrams on vehicle overturning


Figure D-4 Intercept method risk factor E as a function of wind velocity where cantdeficiency hd is 275 mm.Vehicle speed V = 350 km/h and cant ht = 180 mm.


0.000.100.200.300.400.500.600.700.800.901.00

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Wind speed [m/s]

Ein

t[-]

Overturning


0.000.100.200.300.400.500.600.700.800.901.00

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30Wind speed [m/s]

Ein

t[-]

Overturning

132


Appendix E - Overturning due to side-wind

The aim of this Appendix is to describe the calculation of the wind-induced forces andmoments and provide the reader with a short introduction of how to determine theaerodynamic coefficients and a reference wind velocity.

As exact aerodynamic train data as possible and a good knowledge of the windconditions at the track side are the most important conditions to get accurate values forthe forces acting on the train. Up to today it is not easy to get this data - especially thewind data - with a satisfying accuracy. A problem when trying to define side-windstability is that these two parameters with the highest uncertainty are also the mostsensitive ones to the overturning probability.

E.1 Wind-induced forces and moments

Two different wind velocities are acting on a running vehicle. The first is the ambientwind that is blowing at the track side. The speed of this natural wind is in the followingnamed as wind velocity vW. Apart from the natural wind velocity, also the wind caused bythe speed of the train has to be considered. This wind velocity has got the same absolutevalue as the train speed and is in the following called train speed vT. The wind velocityand the train speed can be summarized to a resulting wind velocity vres. The anglebetween train speed and resulting wind velocity is called yaw angle Ψ.

The quantities are shown in Figure E-1.

Figure E-1 wind velocity vW and train speed vT, added to resulting wind velocityvres. Yaw angle Ψ between resulting wind velocity and train speed.

To calculate forces and moments on the train from the resulting wind velocity,aerodynamic coefficients are needed, which can be obtained experimentally ornumerically (see Section E.2). They are usually assumed to be independent of train speedand density of air, but depend on the flow around the train, i.e. the yaw angle.

vT

vresvW

vT

Ψ

133

Overturning due to side-wind

It has been shown that the greatest side-wind forces are induced with a wind velocityapproximately normal to the train speed. Now the absolute value of the resulting windvelocity and the yaw angle can be calculate with the Pythagorean formula (Figure E-2):

Figure E-2 Calculation of resulting wind velocity and yaw angle for the special caseof a wind velocity normal to the train speed.

The coefficients allow - depending on yaw angle and resulting wind velocity - tocalculate the forces acting on the train according to Equations (E-1) to (E-6). The densityof air ρ is set as constant.

Drag force [N] (E-1)

Side force [N] (E-2)

Lift force [N] (E-3)

Roll moment [N] (E-4)

Pitch moment [N] (E-5)

Yaw moment [N] (E-6)

CD: Drag coefficient [-]

CS: Side coefficient [-]

CL: Lift coefficient [-]

CR: Roll coefficient [-]

CP: Pitch coefficient [-]

CY: Yaw coefficient [-]

vT

vresvW

ΨvT vW

vres vW2

vT2

+=

ΨvW

vT

------atan=

Fx w,12--- C⋅=

DΨ( ) ρ hC wC vres

2⋅ ⋅ ⋅ ⋅

Fy w,12--- C⋅=

SΨ( ) ρ hC lC vres

2⋅ ⋅ ⋅ ⋅

Fz w,12--- C⋅=

LΨ( ) ρ wC lC vres

2⋅ ⋅ ⋅ ⋅

Mx w,12--- C⋅=

RΨ( ) ρ h2

C lC vres2⋅ ⋅ ⋅ ⋅

My w,12--- C⋅=

PΨ( ) ρ wC l2

C vres2⋅ ⋅ ⋅ ⋅

Mz w,12--- C⋅=

YΨ( ) ρ hC l2

C vres2⋅ ⋅ ⋅ ⋅

134


ρ: density of air [kg/m3]

hC: height of car body [m]

lC: length of car body [m]

wC: width of car body [m]

vres: resulting wind velocity [m/s]

Note that the coefficients in this study are related to the geometrical measures of the carbody. Coefficients related to other geometrical parameters, like length over buffers, totalheight, projected areas etc., can also be found in other studies. This has to be consideredwhen comparing the coefficients from different studies. Secondly, the location of thecoordinate system is important when defining the forces and moments. The coefficientsused in this study are determined for a coordinate system located in the middle of the twobogie pivots in height of the track plane. The coordinate system is shown in Figure E-3.

Figure E-3 Coordinate system with the three wind-induces forces and moments.

yFy,w

Fx,w

Fz,w

My,w

Mx,w

Mz,w

track plane (top of rail)

x

vT

g

135


E.2 Aerodynamic train data

Aerodynamic coefficients can mainly be determined by three different methods:

(i) Numerical simulation

(ii) Windtunnel test on scale models

(iii) Test with full scale models

Aerodynamic tests with full scale models are not very practicable. Wind tunnels of theneeded size to take full scale models do not exist, and outdoor tests fail – though givingreal data - because of the rareness of suitable and well-defined wind conditions.Deutsche Bahn tried within the Transaero project, a project of the European Communitydealing i.a. with side-winds, to make full scale tests with trains on real track with windshielding devices. One of the greatest problems has been that much time got lost bywaiting for strong wind conditions. When high wind velocities were reached it was oftena problem to arrive without delay at the track sections where the measurements were tobe carried out. This because preparing a test train with necessary instrumentation andstaff requires some time. The highest wind velocity measured in the tests was 14 m/s.However, the measurements are important to enable a comparison between similar datafrom wind tunnels and computations, thus to obtain basic data for verifying scaled testsand computer models.

Another disadvantage of full scale model tests on real trains is that the train must alreadyexist. Changes in the shape are no longer possible if the coefficients are not sufficient.

In the past, wind tunnel tests with scale models have been the best and most commonway to obtain accurate coefficients. A good copy not only of the train but also of groundeffects (e.g. ground roughness due to trees, houses, etc.), turbulent flow, track (viaducts,embankments), etc. is necessary for good results. For instance, relative velocity betweenvehicle and track/ground is very important. Scale effects and critical Reynold numbershave also to be considered.

With improved computer capacity and falling computer prices the determination of theaerodynamical coefficients by numerical simulation (CFD calculation) is becoming moreand more common. To calculate the coefficients, different mathematical models exist.One of the biggest disadvantages of the computer models are the simplifications thathave to be made in order to get suitable simulation times. Nevertheless, carefully madeCFD calculations are able to give results with a good agreement with wind tunnel tests.A comparison that has been made at Bombardier between wind tunnel and computedforces and moments showed a good agreement of the results. For yaw angles between Ψ= 10°…30° the computered , and values are lower than the wind tunnel data,the maximum error is 20%, so that the wind tunnel aerodynamic coefficients can beregarded as more conservative in this range of these angles. It is very important to pointout that only the relative error between wind tunnel and computed results has beendetermined. Nothing is said about the error relative to the real coefficients of the vehicle.As a conclusion from this report, the computed values are regarded as good as the windtunnel results.

CS CL CR

136


It can be assumed that with further increased computer performance the results becomemore and more accurate.

A problem for all the three methods is the tilting of the train. The tilting angle of the trainis not constant when running on a track. On the one hand the train will be tilted to theleeward side by the wind loads and to the outer side when running in a curve with cantdeficiency. On the other hand, tilting to the inner side must be considered due to trackcant and a possible tilt system of the train when passing a curve. It is difficult to decidefor which tilting angle the coefficients should be determined. A comparison that has beenmade at Bombardier for the Norwegian airport shuttle between Oslo - Gardermoenshowed a difference between tilting 3,5° outwards and 6,5° inwards of andvalues of about 20% at 20° yaw angle [27]. A solution would be to combine themultibody simulation program with a CFD program to determine the aerodynamiccoefficients at every time step. However, this would cause unacceptable high computingtimes. Thus, there is a risk that the overturning wind forces are somewhat underestimatedon tilting trains. On the other hand, on a train with active tilt and a self-centering ability(like X 2000) the centre of gravity will move somewhat inwards to the curve centre. Thiseffect will reduce the risk of overturning. According to Prof. E. Andersson experience[28] the two effects of tilting with respect to overturning (one negative and one positive)will to a great extent compensate each other. When determining the coefficients that havebeen used in this study, track cant has been considered and the tilt has been neglected.

To examine an exact way of determining the moments and forces acting on a train wouldgo wide beyond the scope of this work. The aim of this section is to provide the readerwith the certainty that there are many things that have to be considered whendetermining aerodynamic coefficients. The used aerodynamic data in this study isassumed to be appropriate in the range of today’s determination possibilities. Furtherwork on the problem of determining aerodynamic coefficients is an important issue toget even more precise results than today.

E.3 Aerodynamic coefficients for the simulated vehicle

In the following, the aerodynamic coefficients for the simulated vehicle model in thisstudy are listed. The wind is blowing from the right side of the vehicle i.e. the inside ofthe curve. Notice that the coefficients are related to the geometrical measures of the car

body. These measures are listed in Table E-1. The used density of air is ρ = 1.205 kg/m3.

In Table E-1, the aerodynamic coefficients for the vehicle used in the present study areshown. They have been calculated by Bombardier Transportation by CFD [27]. They canbe seen as typical for state-of-the-art for well designed vehicles (2001).

CL CR

137


Table E-1 Aerodynamic coefficients for simulated vehicle model at different yawangles [27].

Ψ[degree]

CD

[-]CS

[-]CL

[-]CR

[-]CP

[-]CY

[-]

10 0 -0.1278 -0.0534 -0.05921 -0.01598 -0.0343

20 0 -0.3029 -0.211 -0.1446 -0.01196 -0.0592

30 0 -0.5190 -0.416 -0.2534 0.00368 -0.07655

40 0 -0.7251 -0.6042 -0.3598 0.03542 -0.09022

138


Appendix F - Train mass versus gradient

The locomotive of the freight train must be able to produce sufficient tractive force inorder to bring the train into motion and to maintain a certain speed or acceleration. Thetractive force has firstly to balance the total running resistance, including gradientresistance, secondly to accelerate the train. The basic requirement is to overcome theresistance at the starting moment and thus bring the train into motion.

F.1 Running resistance

F.1.1 General

The total running resistance FRT of a train can generally be expressed by [2], [23]:

(F-1)

where

FMA = Mechanical resistance on straight track, due to wheel rail friction, bearingfriction etc., independent of speed.

FM(v) = Mechanical resistance, linearly dependent of speed.

FD(v) = Air drag, linearly dependent of speed.

FD(v2) = Air drag, dependent on speed squared.

FC = Additional curving resistance

FG = Gradient resistance.

v = Speed (m/s).

In the following sections general formulas and experimental results from the abovementioned references are used.

FRT FMA FM v( ) FD v( ) FD v2( ) FC FG+ + + + +=

139

Train mass versus gradient

F.1.2 Mechanical resistance

For modern locomotives with three-phase induction motors as traction motors(combination of [2], [23]):

[N] (F-2)

where

Ks = 2 at the starting moment;

Ks = 1 otherwise.

aQl = aQw = (assumed that wheelset guidance has about the sameflexibility and alignment as ordinary European freightwagons)

g = gravitational acceleration = 9.81 m/s2.

ml = mass of locomotive

mw = total mass of all freight wagons

naxl = number of locomotive axles

naxw = number of freight wagon axles.

Thus, the mechanical resistance is higher at the starting moment than if the train is inmotion, i.e. Ks is 2 instead of 1. If the tractive force of the locomotive is maintained afterthe starting moment there will be a certain excess in tractive force and therefore an extrapush in train acceleration.

F.1.3 Resistance linearly dependent of speed

In this section mechanical resistance and air drag, linearly dependent of speed isconsidered, i.e. FM(v) + FD(v).

In [23] linearly speed dependent mechanical and air resistance is given for ordinarycovered freight wagons (type Hbis or similar). This is assumed to be approximatelyequivalent to container trains or trains transporting swap bodies. This assumption may beconservative, as future high-speed freight trains (140 - 180 km/h) will likely have betteraerodynamics than ordinary freight trains of today. However, in relation to other parts ofrunning resistance, these terms are quite small, which reduces the sensitivity forsomewhat conservative assumptions. Therefore, experimental results for coveredwagons from [23] can be expressed:

[N] (F-3)

where LT = total train length, including locomotive (m).

FMA Ks 30 naxl aQl ml g⋅ 65 naxw aQw+ mw g⋅ ⋅ ⋅+⋅+⋅( )=

0 6, 103–⋅

FM v( ) FD v( ) 22– 0.6 LT 0.6 LT⋅≈⋅+≈+

140


F.1.4 Air drag (air resistance)

Air resistance of container trains and trains with swap bodies are assumed to be approxi-mately equivalent to conventional European freight trains with covered wagons (typeHbis or similar). Air drag of the latter trains is given in [23]. As mentioned in theprevious section, these assumptions may be conservative, as future high-speed freighttrains (140 - 180 km/h) will likely have better aerodynamics than ordinary freight trainsof today. On the other hand, it is assumed that not more than one container location outof eight is empty, i.e. is run as an open wagon, in fully loaded trains. This assumptionmay be non-conservative or optimistic. Therefore, conservative and non-conservativeassumptions are believed to balance each other, which reduces the uncertainties andpossible resulting errors.

Thus from [23], assuming that the possible influence of ambient wind is negligible:

[N] (F-4)

where LT = total train length, including locomotive (m).

F.1.5 Curving resistance

Additional curving resistance FC mainly corresponds to the increased energy dissipationthat occurs in the wheel-rail interface, due to sliding motions (creep) and frictionphenomena, at curve negotiation. It is dependent on wheel-rail friction and the stiffnessand character of the wheelset guidance (radial self-steering or forced radial steeringproduce lower curving resistance than stiff wheelset guidance). In this context it isassumed that the wheelset guidance of future high-speed freight trains has almost aboutthe same flexibility and alignment as ordinary European freight wagons. This may be anoptimistic assumption; however as seen from the example following Equation (F-5), thecurving resistance will be low anyhow in great curve radii on high-speed lines.

Curving resistance is determined from a corrected formula of Röckl [2], [23]:

[N] (F-5)

where

g = gravitational acceleration = 9.81 m/s2

KC = correction factor (for European freight trains)

ml = mass of locomotive

mw = total mass of all freight wagons

R = curve radius (formula valid for R ≥ 350 m).

FD v2( ) 5.4 5.2 10

2–LT⋅ ⋅+( ) v

2⋅=

FC

KC ml mw+( ) g 0.65⋅ ⋅ ⋅R 55–( )

-----------------------------------------------------------=

0.7≈

141


Example: R = 400 m produces an additional curving resistance, according to Equation(5), of approx. 1.3 ‰ of the train load, which is in many cases not negligible(typically some 10 % of total running resistance for a freight train in a 10-‰gradient) R ≤ 2000 m produces an additional curving resistance of ≤ 0.2 %,which in most cases may be considered as negligible. Even if the realresistance for high-speed freight trains is as much as 30 - 50 % higher, due toa possibly stiffer wheelset guidance, curving resistance is still almost withoutsignificance in these large curve radii.

F.1.6 Gradient resistance

Gradient resistance FG is the composant of the train load against the direction of travel. Itis positive for uphill gradients and negative for downhill gradients (i.e. pushes the trainforward). Thus the gradient resistance is determined by:

[N] (F-6)

where

G = gradient along the track (‰)

g, ml and mw as in Section F.1.3.

This part of the running resistance is mostly dominating for freight trains in gradients(10 - 25 ‰). This is also the main issue in this special investigation.

F.2 Tractive force of the locomotive

F.2.1 Necessary tractive force

The locomotive(s) must be able to produce a tractive force which can balance therunning resistance and also give the train the desired acceleration. For ordinary freighttrains just a low acceleration is required; the basic requirement is to overcome thestarting resistance and the gradient resistance. Thus the total tractive force F from thelocomotive(s) must at least satisfy the following condition:

(F-7)

where the extra starting resistance is included in FRT.

After the train has been brought into motion (v ≥ 0, a = 1), the train forward accelerationax is determined by:

FC

ml mw+( ) g G⋅ ⋅1000

----------------------------------------=

F FRT≥

142


(F-8)

where me is the equivalent mass of the train, including the effect on inertia of rotatingmasses (me is sometimes called "dynamic mass" and is usually in the order of 2 - 5%higher than the train mass for a freight train).

If the train is subject to a deceleration.

F.2.2 Tractive forces and adhesion

The tractive force F of the locomotive (or the multiple-unit train) is determined andlimited either by the traction equipment on board the locomotive - i.e. by the tractiveeffort - or by the available wheel-rail adhesion α, whatever the lowest. Modern loco-motives are in most cases able to produce more tractive force than the lowest value ofavailable adhesion; this is also the case for locomotives geared for 140 - 180 km/h. Thusthe limiting factor is very often the available adhesion.

If adhesion is limiting and determining the tractive force:

(F-9)

In Equation (F-9) it is assumed that all axles of the locomotive are tractive, i.e. theadhesive load of the locomotive is equal to the total locomotive load on the track.

For modern locomotives with sophisticated slip control (for optimum use of availableadhesion) and sanding (for improving very low adhesion), an adhesion level α of at least0.25 can be almost guaranteed under most conditions (excluding leaves on the trackduring the autumn).

ax

F FRT–

me

-------------------=

F FRT<

F α ml g⋅ ⋅=

143


144


Appendix G - General Description of the GENSYS SoftwarePackage

The GENSYS software package consists of 51 programs for the analysis of railwayvehicle dynamic behavior. Some of these programs can be used for all kinds ofmultibody dynamics simulation. The following sections give a brief overview of thepackage. For more information, see [29].

Other comparable packages are for instance ADAMS, MEDYNA, SIMPACK andVAMPIRE.

G.1 Modelling phase

G.1.1 Local coordinate system

In GENSYS, two types of local Euler coordinate systems can be defined. They can beeither fixed systems relative to a fixed global coordinate system or can be guided by thethree parameters: design track curvature, design cant and design level of track centre.Another possibility are linear local coordinate systems which have to be related to anEuler coordinate system.

G.1.2 Track geometry

The design track can be assembled with tangent track parts, circular curves and differentkinds of transition curves. Transition curves and circular curves are defined by the threetrack design parameters: curvature, cant and vertical level of the track centre.

Track irregularities can be taken over either from library files or be created by functions.

It is possible to express the track irregularities in different forms. They can be expressedin cartesian coordinates, Mauzin diagrams, Plasser diagrams, Fourier series and powerspectral densities.

Routines included in the package interpolate the track irregularity arrays.

G.1.3 Mases and coupling elements

In GENSYS, different types of masses can be created. Possibilities are masses withoutany degree of freedom or with 6 degrees of freedom.

To create a coupling between two masses (bodies), the coupling coordinates andproperties have to be defined. Possible options are linear and non-linear properties.

Fourteen different types of couplings are available. The three basic elements are a linearspring, a linear viscous damper and a friction damper.

145

General Description of the GENSYS Software Package

G.1.4 Wheel-rail contact

The GENSYS package includes more than 20 modules to create a wheel-rail contactmodel, in order to simplify the model generation. The one used in the present simulationsinterpolates the creep forces in a 4-dimensional matrix. The calculation of the matrixelements is performed according to the simplified theory of J.J. Kalker.

G.2 Analysis phase

G.2.1 Quasi static analysis

This analysis is non-linear in every phase of the analyzing process. Element forcesbalance load and inertial forces. The basic output are quasi-static vehicle displacements.They can be used in a modal analysis or a frequency response analysis. In a timeintegration analysis they can be used as initial values for the simulations.

G.2.2 Modal analysis

The modal analysis is started with a linearisation of the model. The calculatedeigenmodes are, due to normally large damping, complex. The resultingeigenfrequencies are given both as complex roots expressed in [rad/s] and as dampedeigenfrequencies expressed in [Hz] and damping as a fraction of critical damping.

G.2.3 Frequency response analysis

As in modal analysis, first a linearisation of the model is started, in order to make a linearanalysis possible. The linearization amplitude and the type of spectra can be chosen.

Various transfer functions can be calculated in this analysis.

G.2.4 Time integration analysis

This analysis is in general non-linear. Several numerical integration methods areavailable. Possible are for instance Euler’s method, Heun’s method or the classicalmethod of Runge-Kutta.

146


G.3 Output phase

G.3.1 Output quantities

The most important railway-specific output quantities from GENSYS are:

- body acceleration and jerks

- wheel-rail contact forces

- track shift forces

- derailment ratios

- wheel unload ratios

- different wheel-rail wear indices

G.3.2 Filtering, statistics, etc.

Resulting time histories can be processed in several ways, for instance:

- different orders of low / high pass filtering

- Fourier analysis

- ride comfort determination (based on accelerations etc.)

- statistical analysis of the time histories

G.3.3 Plotting and animation

Time histories, spectra, eigenmodes etc. can be plotted. Vehicle motions can also beanimated.

147

General Description of the GENSYS Software Package

148

track geometry for high-speed railways

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