Track geometry for high-speed railways

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




                 Track geometry for
                 high-speed railways
                      A literature survey
                              and
            simulation of dynamic vehicle responce

                                by

                        Martin Lindahl




Stockholm                 Railway Technology
 2001                 Department of Vehicle Engineering
                        Royal Institute of Technology
                                Track geometry for
                                high-speed railways
                               A literature survey
                                       and
                     simulation of dynamic vehicle responce


                                                   by

                                            Martin Lindahl




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

Postal Address                  Visiting address        Telephone         E-mail
Royal Institute of Technology   Teknikringen 8          +46 8 790 76 28   everta@fkt.kth.se
Railway Technology              Stockholm               Fax
S-100 44 Stockholm                                      +46 8 790 76 29
Abstract

The present work consists of two main parts. The first part (Chapter 2 and 3) deals with a
literature survey where a short introduction is given for track geometry and track/vehicle
interaction. After the introduction, a survey over the present standard in Europe and
Japan is made. In particular the recent proposals for a common European Standard
(CEN) and TSI (Technical Specification for Interoperability) are reviewed.
The second part (Chapter 4, 5 and 6) starts with an attempt to foresee the performance of
a train that would be available from the industry around 2010. Furthermore, the second
part deals with simulations. Firstly, hunting stability is simulated to establish a vehicle
configuration that could deal with higher speeds. Secondly, track shift forces are
simulated with Prud´hommes criteria as boundary condition. Thirdly, a risk factor for
vehicle overturning was calculated in the most adverse case where the train was running
on a curve and the wind was directed outwards. In the simulations, two sets of track
irregularities were used.
Some consequences of different kinds of freight train operations are discussed in Chapter
7.
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; in
    freight train operations some 20-50 mm lower.
- A cant deficiency of 225-250 mm could be allowed when using carbody tilt and
    suitable bogie technology. The tilt is a basic requirement when using such high values
    of cant deficiency.
- The transition curves should be long, i.e. the duration in the transition curve should be
    in the order of around 4-5 sec, if carbody tilt is anticipated.
- It could be concluded that hunting stability can be achieved.
- The track quality has too be improved relative to current standards for 200 km/h in
    order to meet requirements on lateral track shift forces. The degree of improvement
    should be further investigated.
- It is concluded that safety criteria for side-wind exposure can be met, if the trains have
    favourable, although, realistic, aerodynamic performance.
- The maximum gradient shall be chosen according to the type of freight traffic
    foreseen 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, track
shift force, vehicle overturning, track irregularity, freight trains



                                                       i
ii
Sammanfattning

I Sverige finns behov av spårgeometri för höghastighetsbanor. Bl.a. har frågan
aktualiserats i samband med studier av den s.k. Europakorridoren (Stockholm -
Jönköping - Köpenhamn/Göteborg). I dessa sammanhang har det framförts önskemål om
en hastighetsstandard för 350 km/h, vilket är den standard som åtminstone delvis
projekteras och byggs i Mellan- och Sydeuropa. För Sveriges del, som är ett land med
långa transportavstånd, finns det behov av korta restider på långa avstånd, vilket talar för
hög hastighet. Detta ställer krav på stora kurvradier. Samtidigt finns ett starkt behov av
att bygga banorna med relativt låga investeringskostnader samt små intrång i natur och
bebyggelse. Detta ställer krav på att inte göra kurvradierna större än absolut nödvändigt
och även att kunna tillåta relativt större lutningar i banan.
En litteraturgenomgång har utförts där förslagen till europastandard för spårgeometri
studerats (CEN och TSI). Dessa förslag till europastandard skapar flera möjligheter att
minimera både horisontella och vertikala kurvradier. Det föreslås även vara möjligt att
tillåta tåg med korglutning efter särskilt tillstånd av banhållaren. Lutningar i banan upp
emot 35 ‰ föreslås även vara tillåtet.
Rapporten tar även upp den framtida tågteknologin om vad som är tekniskt möjligt vilket
har diskuterats med tekniska experter inom industrin. Optimerad passiv hjulparsstyrning
är en del som diskuterats. I detta sammanhang har utvecklingen av aktiv
sekundärfjädring nämnts som ett alternativ men dock inte studerats ingående. Den
aerodynamiska utformningen har förfinats och senast känd teknologi har används.
Simuleringarna har utförts i tre olika steg. Först görs en gångstabilitetssimulering för att
fastställa att använd teknik klarar av hastigheterna som eftersträvas. Nästa steg var att
beräkna spårförskjutningskrafter med Prud´hommes kriterium som gränsvärde. I denna
del simulerades olika fall där spårläget varierades för att ge en uppfattning om vad som
krävdes för att klara gränsvärdet. Slutligen simulerades säkerheten mot vältning vid
kraftig 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 och
    lämpliga 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
iv
Preface and acknowledgements

This study has been carried out at the Division of Railway Technology, Department of
Vehicle Engineering, Royal Institute of Technology (KTH, Kungliga Tekniska
Högskolan), Stockholm, in close cooperation with the Swedish National Rail
Administration (Banverket), Europakorridoren AB, Helsingborg, Bombardier
Transportation, Västerås, and the Swedish National Road and Transport Research
Institute (VTI), Linköping. The bulk of this study constitutes my Master of Science
thesis.
The financial support from Banverket, Bombardier Transportation and Europakorridoren
for the present work is gratefully acknowledged. Thereby it was possible to give an
extra-ordinary support and supervision from KTH senior staff.
I would like to thank my supervisor Sebastian Stichel and my examiner Professor Evert
Andersson for their knowledge and support during the course of this work.
There have been four reference group meetings. This reference group consisted of
persons from Banverket, Europakorridoren, Bombardier Transportation, VTI and KTH. I
would like to state my kind regards to Bertil Eriksson and Per Hurtig from Banverket,
Mikael Stamming from Europakorridoren, Olle Ek and Jan Ågren from Bombardier
Transportation and Björn Kufver from VTI.
The vehicle model used in the simulations have been provided by courtesy of
Bombardier Transportation.
Thanks are also delivered to Ingemar Persson from DEsolver AB for his support and
help during the simulations.
Due to the great extent of this work, some contributions have been delivered from
Sebastian Stichel and Evert Andersson. Part of Chapter 4 has been written by Sebastian
Stichel 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 and
encouragement. I should not managed this without you.




Stockholm, December 2001




Martin Lindahl




                                          v
vi
Table of contents
Abstract .............................................................................................................................i
Sammanfattning ............................................................................................................ iii
Preface and acknowledgements......................................................................................v
1 Introduction.................................................................................................................1
     1.1 Background to the present study ....................................................................1
     1.2 Objective and approach of the present study..................................................1
     1.3 Thesis contribution .........................................................................................2
2 Track geometry and track/vehicle interaction .........................................................3
    2.1 Design track geometry....................................................................................3
       2.1.1 Track gauge................................................................................................3
       2.1.2 Track cant...................................................................................................3
       2.1.3 Horizontal curve.........................................................................................4
       2.1.4 Transition curve and superelevation ramp.................................................5
       2.1.5 Gradient......................................................................................................6
       2.1.6 Vertical curve.............................................................................................6
    2.2 Track/vehicle interaction ................................................................................8
       2.2.1 Track plane acceleration ............................................................................8
       2.2.2 Equilibrium cant and balanced speed ........................................................9
       2.2.3 Cant deficiency and cant excess ..............................................................10
       2.2.4 Permissible speed with respect to radius, cant and cant deficiency.........12
       2.2.5 Rate of cant and rate of cant deficiency...................................................13
3 Standards, practices and TSI...................................................................................15
     3.1 Track gauge ..................................................................................................15
     3.2 National standards in Sweden.......................................................................15
        3.2.1 Track cant and track distance...................................................................15
        3.2.2 Cant deficiency and cant excess ..............................................................15
        3.2.3 Horizontal curve radius............................................................................16
        3.2.4 Transition curve and superelevation ramp...............................................18
        3.2.5 Gradient....................................................................................................19
        3.2.6 Vertical curve radius ................................................................................20
     3.3 National standards in Germany ....................................................................22
        3.3.1 Track cant.................................................................................................23
        3.3.2 Cant deficiency ........................................................................................23
        3.3.3 Horizontal curve radius............................................................................24
        3.3.4 Transition curve and superelevation ramp...............................................26
        3.3.5 Gradient....................................................................................................26
        3.3.6 Vertical curve radius ................................................................................27
     3.4 Practices in France........................................................................................28
        3.4.1 Cant, cant deficiency and cant excess......................................................28
     3.5 Practices in Japan..........................................................................................29
     3.6 Technical Specifications of Interoperability and CEN proposal ..................30
        3.6.1 Track cant and track distance...................................................................30
        3.6.2 Cant deficiency and cant excess ..............................................................31



                                                                 vii
           3.6.3 Horizontal curve radius............................................................................34
           3.6.4 Transition curve and superelevation ramp...............................................35
           3.6.5 Gradient....................................................................................................37
           3.6.6 Vertical curve radius ................................................................................37
        3.7 Comparison between different projects and standards .................................39
           3.7.1 Horizontal curve radius............................................................................39
        3.8 Recent resarch on nominal track geometry ..................................................41
           3.8.1 Optimisation of horizontal alignments for railways ................................41
           3.8.2 Ride comfort and motion sickness in tilting trains ..................................41
        3.9 Summary and conclusions ............................................................................43
4 High-speed train technology year 2010...................................................................45
    4.1 Maximum train speed ...................................................................................45
    4.2 Train configuration .......................................................................................45
    4.3 Tilt technology..............................................................................................46
       4.3.1 General.....................................................................................................46
       4.3.2 Possible overspeed with tilt technology...................................................46
    4.4 Running gear design .....................................................................................47
    4.5 Aerodynamic shape ......................................................................................48
    4.6 Track irregularities .......................................................................................48
5 Track/vehicle dynamic simulations - models, conditions and criteria .................49
    5.1 Simulation strategy .......................................................................................49
    5.2 Simulation software......................................................................................49
    5.3 Test speed .....................................................................................................49
    5.4 Hunting stability ...........................................................................................50
    5.5 Track shift forces ..........................................................................................51
    5.6 Vehicle overturning at strongly side-wind ...................................................52
       5.6.1 General.....................................................................................................52
       5.6.2 Tolerable wind velocities.........................................................................52
       5.6.3 Intercept method risk factor .....................................................................53
       5.6.4 Disadvantages with intercept method ......................................................55
       5.6.5 Aerodynamic train design ........................................................................55
    5.7 Rails, wheels and equivalent conicity...........................................................56
    5.8 Track irregularities .......................................................................................57
       5.8.1 Classification of track irregularities.........................................................57
       5.8.2 Track irregularities for dynamics analysis...............................................58
       5.8.3 Peak values of track irregularities............................................................62
    5.9 Model of the EMU coach .............................................................................65
       5.9.1 Three different vehicle configurations.....................................................65
       5.9.2 Hold-off-device........................................................................................68
6 Dynamic analysis of simulated vehicle response....................................................69
    6.1 Hunting stability on tangent track and on curve...........................................69
       6.1.1 Conditions ................................................................................................69
       6.1.2 Track irregularities...................................................................................70
       6.1.3 Criteria for hunting stability.....................................................................70
       6.1.4 Hunting stability on tangent track............................................................70
       6.1.5 Hunting stability on large radius curves ..................................................72



                                                            viii
        6.2 Evaluation of track shift forces.....................................................................74
           6.2.1 Conditions ................................................................................................74
           6.2.2 Track irregularities...................................................................................75
           6.2.3 Track shift forces variation along the track .............................................76
           6.2.4 Track shift forces for different cant .........................................................76
           6.2.5 Comparisons between different track irregularities.................................78
           6.2.6 Improvements of track irregularities........................................................80
        6.3 Evaluation of vehicle overturning ................................................................84
           6.3.1 Conditions ................................................................................................84
           6.3.2 Track irregularities...................................................................................85
           6.3.3 Safety against vehicle overturning at different conditions ......................85
           6.3.4 Conclusions..............................................................................................88
7 Consequences of freight trains operations..............................................................89
    7.1 Different categories of freight trains ............................................................89
    7.2 Permissible axle load and track loadings......................................................91
    7.3 Track cant and cant excess ...........................................................................93
    7.4 Gradients versus train mass ..........................................................................96
       7.4.1 Freight trains category I - heavy freight trains.........................................97
       7.4.2 Freight trains category II - fast trains for unit-loads and heavy express..97
       7.4.3 Freight trains category III - high-speed for light express or mail ............99
8 Possible track geometry..........................................................................................101
    8.1 Horizontal curve radius ..............................................................................101
    8.2 Vertical curve radius...................................................................................108
9 Conclusions and further research .........................................................................109
    9.1 Conclusions on the literature study ............................................................109
    9.2 Conclusions on dynamic analysis of simulated vehicle response ..............109
    9.3 Conclusions on horizontal and vertical curve radii ....................................110
    9.4 Conclusions on freight train operations......................................................111
    9.5 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
x
                            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’, a
high-speed line intended to connect Stockholm with Gothenburg and Copenhagen. The
objective 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 curve
radii tend to be large (6000 m according to Banverket). In some cases it is also
recommended 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 ordinary
locomotives are to be used.
Altogether, this would cause a very rigid and non-flexible alignment, both horizontally
and vertically. There would be a substantial need for bridges, high embankments and
tunnels, depending on the topography of the landscape. The cost may increase so much
that the project would be unprofitable from the social-economics point of view. Due to
the rigid alignment the project would also run the risk to cause excessively large
infringements in nature and culture environments. The project could therefore be
politically questioned.
The present Swedish standards and recommendations are principally the same as for
lower speeds. A separate standard for high-speed railways in Sweden does not exist at
the moment. The standard for higher speeds have the same margin for future higher
speed as for the lower speeds, i.e. speeds less than or equal to 200 km/h. In some
feasibility studies there have been attempts to copy standards prepared for the first
generation German high-speed railways, which give very large curve radii and modest
gradients.



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 to
achieve high-speed performance. One important boundary condition is the use of latest
known 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 for
  high-speed railways in Japan and Europe including the TSI (Technical Specification
  for 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 10
  years? The problem should especially focus on tilting technology and modern running
  gear, track forces, aerodynamics, on side-wind stability etc. Among other things
  results from present research and experience at Bombardier Transportation, KTH and
  VTI will be used.
- Vehicle dynamic simulations will be performed to investigate possible limits within
  which 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 standard
concerning 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 taken
  different train categories into account.
- In particular, give examples of horizontal curve radius and cant deficiency that could
  be allowed for high-speed trains when safety related factors like hunting stability,
  track shift forces and vehicle overturning are taken into consideration.
- Foresee, and discuss the performance of a train that would be available from the
  industry around 2010.




                                             2
                            Track geometry for high-speed railways



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 an
introduction to the most common quantities of track geometry will be presented. These
quantities 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 called
superelevation) and is arranged to compensate part of the lateral acceleration, see Figure
2-2. A cant angle arise where a cant is arranged. The angle can be determined by
                                                 ht
                                    ϕ t = asin --------                              (2-1)
                                               2b o
where 2bo = 1.500 m on standard track gauge.




                                               3
                          Track geometry and track/vehicle interaction



The cant is maximized with respect to stationary conditions and slowly running trains. A
maximum value is set for cant because of the following problems which arise if a train is
forced 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 high
  lateral and low vertical load on the outer wheel at low speed;
- possible displacement of wagon loads;




Figure 2-2     Cant ht and cant angle ϕt.


2.1.3    Horizontal curve

The most distinguished parameter for a circular curve is the radius, R = constant, which
is inverse proportional to curvature, k = 1 ⁄ R . The radius is related to the centre of the
track. 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 a
number of undesirable effects”. These effects can be:
- possible passenger discomfort;
- possible displacement of wagon loads,
- risk of vehicle overturning in combination with strong side winds;
- risk of derailment caused by flange climbing of a wheel on the outer rail or by
  loosening of rail fastenings;
- high lateral forces on the track.




                                               4
                              Track geometry for high-speed railways




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. Transition
curves are used between tangent track and circular curves or between two adjacent
curves to allow a gradual change in curvature and lateral acceleration. The centre line of
a 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 the
value of the other [11].
Transition curves also introduce cant via superelevation ramps. A superelevation ramp is
a section of the track where the cant changes gradually.
The clothoid type of transition curve has a linear function of chainages, i.e. of the
longitudinal coordinate [16]
                                                       s-
                                     k ( s ) = k 0 + -----                            (2-2)
                                                         2
                                                     A
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 circle
with the radius R, we obtain the following relation:
                                          2
                                        A = Lt ⋅ R                                    (2-3)




                                                  5
                         Track geometry and track/vehicle interaction



2.1.5   Gradient

The topographical conditions usually require some kind of vertical-longitudinal
gradients, along the way. Building bridges and tunnels is a very expensive way to
manage the topography constraints. In particular heavy railway traffic has problems to
overcome large longitudinal gradients. Therefore restrictions for the amount of gradient
are needed. The following requirements need to be considered because they have an
affect 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 the
  gradient.
- Braking distances increase for high-speed and freight trains in an ascending gradient
Thus, large gradients result, principally, in heavier locomotives, increased locomotive
power, and/or less freight train weight, and/or reduced speed and line capacity, and/or
requirement 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 the
railway profile. In changes of gradients a suitable radius must be used. If the vertical
acceleration on a crest is too great, the loads on the vehicle wheels can cause the wheels
to climb the rail and thus cause a derailment. Furthermore, the resistance against vehicle
overturning at side-winds will be lower It is also important that passenger comfort is
being ensured. How two adjacent gradients are related to the vertical curve radius and the
profile elevation is shown in Figure 2-4.




                                              6
                           Track geometry for high-speed railways




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

With the simple parabola in Figure 2-4, using small-angle approximations, the vertical
offset at any given longitudinal coordinate x, is given by:
                                                                      2
                                     (a – b) 2              – Ax -
                         z ( x ) = – ---------------- x = --------------           (2-4)
                                      2000L               2000L
where A is the algebraic difference between two gradients with grades a and b (expressed
in ‰, positive uphill) and L is the length of the curve between the tangent points ta and
tb. (Note that negative z coordinates are measured downwards from the tangents for a
crest and positive z coordinates are measured upwards for a hallow). The maximum z for
x = L/2, is given by

                              L                        L-
                            z -- = e = – ( a – b ) -----------
                               -
                              ö æ                                                  (2-5)
                              2
                              ø è                  8000
Given values of a, b and Rv gives the following condition

                                         Rv ( a – b )
                                     L = ----------------------
                                                              -                    (2-6)
                                              1000
                                                                  2
                                 L           (a – b )
                               z -- = – Rv ⋅ ------------------
                                  -
                                 ö æ
                                                            6
                                                              -                    (2-7)
                                 2
                                 ø è
                                               8 ⋅ 10




                                                     7
                            Track geometry and track/vehicle interaction



2.2      Track/vehicle interaction

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


2.2.1    Track plane acceleration

In case of quasistatic curving (i.e. curving at constant speed, radius and cant on perfect
track geometry) the vehicle is exposed to two accelerations: horizontal centrifugal
acceleration and gravitational acceleration, see Figure 2-5(a). The resultant of the
acceleration vector can be split up into two composants; ay is parallel to the track plane
and a z 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 a y is called track plane acceleration or, simply, lateral acceleration.
The equations can be written as follows [1]:
                           2                              2                   ht
                        v-                             v-
                  a y = ---- ⋅ cos ϕ t – g ⋅ sin ϕ t = ---- ⋅ cos ϕ t – g ⋅ --------   (2-8)
                         R                              R                   2bo
                                        2
                                    v
                               az = ---- ⋅ sin ϕ t + g ⋅ cos ϕ t
                                       -                                               (2-9)
                                     R




                                                     8
                              Track geometry for high-speed railways



Assuming small angels (ϕt ≤ 0.15 rad) the equations can be approximated by:
                                 2                   2        ht
                        a y ≈ v - – g ⋅ sin ϕ t = v - – g ⋅ --------
                              ----                ----                                (2-10)
                               R                   R        2b o

                                               az ≈ g                                 (2-11)

The lateral force angle Φ in Figure 2-5 are related to the acceleration ay and az in
accordance to the following equation
                                                    ay
                                           Φ = atan ----
                                                       -                              (2-12)
                                                    az


2.2.2   Equilibrium cant and balanced speed

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

                                                 2b 0 v 2
                                          h eq ≈ -------- ⋅ ----
                                                               -                      (2-13)
                                                    g R
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)

                                         2b o, mm                             2
                                                                   V
                              h eq, mm ≈ ----------------- ⋅ ------------------
                                                                     2
                                                                                      (2-14)
                                                g            3.6 ⋅ R
The equation can be simplified further if the values 2bo for standard track gauge and the
gravitational acceleration g are used
                                                            2                     2
                                  1500                V -                  V-
                       h eq, mm ≈ ----------- ⋅ ----------------- ≈ 11.8 ⋅ -----
                                            -
                                                        2
                                                                                      (2-15)
                                   9.81 3.6 ⋅ R                             R
It is very common to write the formula in the way shown in Equation (2-15), but it is
important to be careful with the units.
The vehicle speed giving ay = 0 for a given radius and a given cant is called the
equilibrium speed or balanced speed, veq and is defined as

                                                      R ⋅ g ⋅ ht
                                      v eq =                            -
                                                      ------------------- .           (2-16)
                                                            2b o
Thus, at equilibrium speed the lateral acceleration in the track plane, ay, is zero. With
speed expressed in [km/h] and cant in [mm] this equation transforms to (for standard
gauge):




                                                           9
                          Track geometry and track/vehicle interaction



                                               R ⋅ h t, mm
                                 Veq =                            -
                                               --------------------                 (2-17)
                                                    11.8


2.2.3    Cant deficiency and cant excess

For several reasons, fully compensated track plane acceleration can not be achieved in all
cases according to [3]:
- It is a possibility that a train stops or runs slowly in a curve. Therefore, the maximum
  cant has to be limited. Other reasons to limit the cant have been discussed earlier in
  Section 2.1.2. It is then desirable to allow a cant deficiency, i.e. a certain amount of
  uncompensated lateral acceleration ay remains in the track plane.
- Not all trains have the same speed. Therefore, it would not be possible to achieve fully
  compensated lateral acceleration for all trains anyway.


Cant deficiency

When the cant is less than the equilibrium cant a so called cant deficiency arises. The
cant deficiency is the additional cant that is needed to achieve equilibrium cant. Cant
deficiency hd is the difference between equilibrium cant heq and actual cant ht and is thus
determined by the following equation:
                                     h d = h eq – h t                               (2-18)
With Equation (2-13) substituted into (2-18) we get in SI-units:

                                       2b 0 v 2
                                 h d = -------- ⋅ ---- – h t
                                                     -                              (2-19)
                                          g R
A common way to write the formula is shown in Equation (2-20). The speed V is
expressed in km/h and cant and cant deficiency is expressed in [mm].
                                                       2
                                              V-
                           h d, mm   = 11,8 ⋅ ----- – h t, mm                       (2-20)
                                               R
An additional way to express cant deficiency is to solve Equation (2-10) for v2/R and
substitute the expression into Equation (2-19) and relate cant deficiency to the track
plane acceleration which gives (in SI-units) [1]
                                           2b o
                                     h d = -------- ⋅ a y                           (2-21)
                                              g
where ay > 0




                                                   10
                                  Track geometry for high-speed railways



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

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

  Track plane acceleration              Lateral force angle                 Cant deficiency
         ay (m/s2)                             Φ (°)                            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



The cant deficiency allowed in real train operations is determined by the following
factors 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 track
components must be designed accordingly and there must be no risk of exceeding the
lateral track resistance immediately after tamping.




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




                                                     11
                            Track geometry and track/vehicle interaction



Cant excess

If the actual cant is higher than the equilibrium cant something called cant excess will be
introduced. Cant excess is the difference between actual cant and equilibrium cant and is
defined as:
                                            h e = h t – h eq                                             (2-22)
Cant excess is achieved when the vehicle is running at a lower speed than the design
speed of the track. Cant excess can be related to lateral acceleration in the same way as
cant deficiency shown in Equation (2-21)
                                                  2b o
                                          h e = – -------- ⋅ ay                                          (2-23)
                                                     g
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, or
permissible cant deficiency, hd,lim, an expression for permissible speed, vlim, can be
expressed in many different ways [1]:

                                             ht                        R⋅g
               v lim =     R ay, lim + g ⋅ -------- =
                             æ                             ö           ---------- ( hd, lim + h t )
                                                                                -                        (2-24)
                             è             2b o            ø            2b o
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.

                                                  12.96g             R ( h d, lim + h t )
                Vlim =     R ( h d, lim + h t ) ⋅ ---------------- ≈ ---------------------------------
                                                                 -                                       (2-25)
                                                      2b o                      11.8




                                                            12
                            Track geometry for high-speed railways



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]

                                 dh t      ∆h t ⋅ v max
                                 ------- = -----------------------                   (2-26)
                                  dt                Lt


Rate of cant deficiency as a function of time

Rate of cant deficiency describes the change of lateral acceleration (in the track plane) as
a 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 with
linear variation of cant, the following relationship is derived, where ∆hd is the cant
deficiency variation: [3], [7]
                                 dh d       ∆h d ⋅ v max
                                 -------- = ------------------------                 (2-27)
                                   dt                 Lt




                                                      13
Track geometry and track/vehicle interaction




                    14
                            Track geometry for high-speed railways



3        Standards, practices and TSI

In this Chapter standards and practices according to Sweden, Germany, France and Japan
are being presented. The proposal from the European Association for Railway
Interoperability (AEIF), Technical Specifications of Interoperability (TSI) [12] is also
demonstrated. TSI do often refer to the European (CEN) provisional standard [7]. This
report 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. All
content 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 handbook
is informative. In the following text the regulation is called BVF while the handbook is
called BVH.


3.2.1    Track cant and track distance

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


3.2.2    Cant deficiency and cant excess


Cant deficiency

The uncompensated lateral acceleration, which is proportional to cant deficiency, should
not be too large. Table 3-1 shows the permissible cant deficiency and its corresponding
lateral acceleration for three different categories of rolling stock according to Banverket.




                                             15
                                    Standards, practices and TSI




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

                                    Permissible cant                               Lateral acceleration, ay
        Train category
                                    deficiency (mm)                                         (m/s2)

              A                                100                                          0.65
              B                                150                                          0.98
              S                                245                                          1.60

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 with
radius larger than 1000 m. On tracks with radius less than 1000 m cant excess should not
exceed 70 mm.


3.2.3     Horizontal curve radius

The recommended horizontal curve radius in Banverket handbook BVH 586.40 is a
value calculated with cant ht = 150 mm and cant deficiency hd = 100 mm in the formula
for equilibrium cant, i.e. Category A trains. For new lines it is recommended that the
dimensional speed is multiplied with a speed factor γ = 1.3 This factor is used to get a
margin with respect to ride comfort and increased speed in the future.
                                                                         2
                                            ( 1.3 ⋅ Vdim ) ⋅ 11.8
                             R rec, min                                                 -
                                          = ---------------------------------------------                      (3-1)
                                                               250

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

                              200          250                  280                  300      330        350
                             km/h         km/h                 km/h                 km/h     km/h       km/h

    Recommended              3200          5000                 6300                 7200     8700      9800
      radius [m]




                                                          16
                                                 Track geometry for high-speed railways



Minimum value of the horizontal radius according to Banverket can be expressed as
                                                                             2
                                                                V dim ⋅ 11.8
                                                       Rmin                                -
                                                              = ----------------------------                           (3-2)
                                                                          250

Corresponding radii, as a function of target speed, are shown in Table 3-3. There is an
inherent assumption that trains of category A will be used.

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

                                                 200       250                 280               300    330    350
                                                km/h      km/h                km/h              km/h   km/h   km/h

 Minimum radius [m]                             1888      2950                3700              4248   5140   5782

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

                                  11000          Recommended radius according to BVH 586.40
                                  10000
                                                 Minimum radius according to BVF 586.41 and
                                   9000
    Horizontal curve radius [m]




                                                 BVH 586.40
                                   8000
                                   7000
                                   6000
                                   5000
                                   4000
                                   3000
                                   2000
                                   1000
                                      0
                                          100     150                200                       250      300      350
                                                                       Speed [km/h]


Figure 3-1                            Recommended and minimum horizontal curve radius as a function of
                                      speed. Source: Banverket [4].

In reality, however, it is often difficult to meet these recommendations. On several newly
built 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) and
the Mälar Line (Stockholm - Örebro), where no margin exists for future improvement in
speed 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 of
this line such a speed will only be achieved by using tilting trains (Category S).




                                                                         17
                                  Standards, practices and TSI



3.2.4    Transition curve and superelevation ramp

According to Banverket [4] transition curves should be arranged with linear curvature
changes (clothoids) and superelevation ramps should be arranged with linear changes of
cant. The transition curve shall coincide with the superelevation ramp in both shape and
position. Generally, the length of transition curves depends, among others, on the
permitted gradient of cant, which is an important safety aspects because of wheel
unloading and thus the risk of derailment. However, in long transition curves, which is
the case in high-speed operations, ride comfort aspects usually determine the minimum
length of transition curves.
The change of lateral acceleration with respect to time is called jerk. The jerk can also be
described 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. The
allowed rate of cant deficiency is a question of comfort. In Sweden used values for
maximum rate of cant and rate of cant deficiency is shown in Table 3-4.
Table 3-4       Maximum rate of cant and rate of cant deficiency
                Source: 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

In a superelevation ramp the cant changes linearly. The twist 1:n states the change of rate
of cant per unit length. n is called ramp number.
                                          ∆h t, mm
                                    1 = --------------------
                                     -
                                    --                     -                                 (3-3)
                                    n   1000 ⋅ L t
where
Lt            = 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 trains
category S that the curve radius allows. The recommended transition curve length
according to Banverket [4] is:

                                     Lt = 5 ⋅ R                                              (3-4)
for R ≤ Rrec and
                                                   3
                                            V dim
                                                     -
                                      L t = ----------                                       (3-5)
                                            9⋅R
for R > Rrec.




                                                  18
                           Track geometry for high-speed railways



There are other formulas used by Banverket that state the permitted speed in transition
curves. 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 following
statements:
                                   L t ≥ 0.4 ⋅ ∆h t, mm                            (3-6)
                                           L t ⋅ 1000
                                 Vdim ≤ -------------------------
                                                                -                  (3-7)
                                        q t ⋅ ∆ h t, mm
                                             Lt ⋅ 1000
                                 V dim ≤ ---------------------------
                                                                   -               (3-8)
                                         q d ⋅ ∆ h d, mm

Here ∆ht and ∆hd are the changes of cant and cant deficiency, respectively, over the
transition curve. The constants qt and qd can be found in Table 3-5 and are depending on
train category.

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


3.2.5   Gradient

Banverket prescribes in their handbook BVH 586.40 [4] a largest permissible gradient of
10 ‰ on track with heavy freight trains. 12.5 ‰ can be permitted if the mean value does
not exceed 10 ‰ over each kilometre. On tracks with only passenger trains and light
freight trains higher values may be allowed.




                                                    19
                                 Standards, practices and TSI



3.2.6   Vertical curve radius

In Banverket regulation BVF 586.41 [5] the vertical curve radius shall be in accordance
to permissible speed as shown in Equation (3-9):
                                         2
                                      V dim                2
                            Rv, min ≥ ---------- = 0.16 ⋅ Vdim
                                               -                                         (3-9)
                                      6.25

Equation (3-9) leads to vertical curve radii shown in Table 3-6.
Table 3-6      Minimum vertical curve radius.
               Source: Banverket [5].

                                     200       250           280      300     330     350
                                    km/h      km/h          km/h     km/h    km/h    km/h

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


Banverket prescribes in their handbook BVH 586.40 [4] a recommended vertical curve
radius:
                                                                 2
                         R v, rec, min ≥ 0.25 ⋅ ( 1.3 ⋅ Vdim )                          (3-10)

Some recommended vertical curve radii are shown in Table 3-7.
Table 3-7     Recommended vertical curve radius.
              Source: Banverket [4].

                                     200       250           280      300     330     350
                                    km/h      km/h          km/h     km/h    km/h    km/h

 Recommended vertical curve        16900      26500      33200       38100   46100   51800
       radius [m]


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).
                                                        2
                               R v, min ≥ 0.25 ⋅ Vdim                                   (3-11)




                                              20
                                                Track geometry for high-speed railways



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

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

                      Vertical curve radius              200      250       280       300      330    350
                                                        km/h     km/h      km/h      km/h     km/h   km/h

 Minimum vertical radius [m]                            10000    15625     16900     22500   27225   30625


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


                                60000          Minimum vertical radius according to BVF 586.41
                                               Minimum vertical radius according to BVH 586.40
    Vertical curve radius [m]




                                50000          Recommended vertical radius according to BVH 586.40

                                40000

                                30000

                                20000

                                10000

                                    0
                                        100       150           200            250           300       350
                                                                Speed [km/h]

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




                                                                 21
                                Standards, practices and TSI



3.3     National standards in Germany

In Germany different train categories are not used in the same manner as in Sweden. A
classification is used where values are prescribed with or without permission. Design
values for equilibrium cant according to German standards, 800.0110 [9], are shown in
Table 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 in
                                               Table 3-10 and Table 3-11)
                   Exception                   heq = ht + hd (values are shown in
                                               Table 3-10 and Table 3-11)




                                            22
                             Track geometry for high-speed railways



3.3.1     Track cant

Values for cant according to [9] are shown in Table 3-10. The recommended value for
cant is 100 mm and the maximum value with permission is 180 mm.
Table 3-10      Design values of cant.
                Source: Deutsche Bahn [9]

 Without permission
        Recommended               ht = 100 mm

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

 Permission necessary
        Permission                160 < h t ≤ 180 mm (Ballast track)
                                  170 < h t ≤ 180 mm (Ballastless track)

        Exception                 ht > 180 mm

There is a recommended value of cant depending on the speed of the fastest trains and
the horizontal curve radius.
                                                               2
                                               7.1 ⋅ Vdim
                                                                    -
                                    h t, rec = ----------------------             (3-12)
                                                         R


There is also a minimum value of cant which has to be arranged according to Equation
(3-13)
                                                         2
                                       11.8 ⋅ Vdim
                                                               -
                            h t, min = ------------------------- – h d, lim       (3-13)
                                                  R

hd,lim, See 3.3.2 “Cant deficiency”
Examples of horizontal curve radius according to German standard are shown in section
3.3.3.


3.3.2     Cant deficiency

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




                                                        23
                                      Standards, practices and TSI




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

               Without permission
                    Recommended                                  hd = 70 mm

                    Limit                                        hd = 130 mm

               Permission necessary
                    Permission                                   hd = 150 mm



3.3.3   Horizontal curve radius

The recommended horizontal curve radius according to DB is derived from the
following formula and some examples are shown in Table 3-12.
                                           2                               2
                               Vdim ⋅ 11.8                    Vdim ⋅ 11.8
                     R rec   = ---------------------------- = ----------------------------
                                                          -                              -                   (3-14)
                                          heq                           170
This recommendation is based on an equilibrium cant of 170 mm, i.e. 100 mm of cant
and 70 mm of cant deficiency.

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

                                           200              250               280             300    330    350
                                          km/h             km/h              km/h            km/h   km/h   km/h

 Recommended radius [m]                   2776             4338              5542            6247   7559   8503


The limit of horizontal curve radius (without permission) can be described of Equation
(3-15) and some examples are shown in Table 3-13.
                                                             2
                                          Vdim ⋅ 11.8
                                                                     -
                                   Rlim = ----------------------------                                       (3-15)
                                                    290
This limit value is based on an equilibrium cant of 290 mm.

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

                                           200              250               280             300    330    350
                                          km/h             km/h              km/h            km/h   km/h   km/h

 Limit radius [m]                         1628             2543              3190            3662   4431   4984



                                                           24
                                                     Track geometry for high-speed railways



A value of horizontal curve radius were permission is needed can be described by
Equation (3-16) according to DB.
                                                                                   2
                                                                      Vdim ⋅ 11.8
                                                     R permission                                -
                                                                    = ----------------------------                     (3-16)
                                                                                330
This permission value is based on an equilibrium cant of 330 mm with a cant of 180 mm
and a cant deficiency of 150 mm.
Some examples are shown in Table 3-14.

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

 Horizontal curve radius                                200          250                280           300      330    350
                                                       km/h         km/h               km/h          km/h     km/h   km/h

 Permission value [m]                                  1430         2234               2803          3218     3894   4380


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



                                  9000              Recommended minimum value according to DB
    Horizontal curve radius [m]




                                  8000              Limit value (without permission) according to DB
                                                    Permission value according to DB
                                  7000
                                  6000
                                  5000
                                  4000
                                  3000
                                  2000
                                  1000
                                     0
                                         100         150             200                       250          300      350
                                                                       Speed [km/h]


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




                                                                         25
                                   Standards, practices and TSI



3.3.4    Transition curve and superelevation ramp

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, are
the same as Equation (3-6) [10], [15]:
                                   L t ≥ 0.4 ⋅ ∆h t, mm                               (3-17)
The lower permissible limit of Lt according to this formula is applied on low speed track
only; for high-speed lines the transition length is determined by the rate of change in cant
deficiency according to Equation (3-20).
The permitted speed in transition curves with linear change of cant, however, is partly
different from Sweden. In Germany the maximum speed for non-tilting trains is
according to [10], [15]
                                           L t ⋅ 1000
                                 V dim ≤ ------------------------
                                                                -                     (3-18)
                                         8 ⋅ ∆ h t, mm

                                           L t ⋅ 1000
                                 V dim ≤ -------------------------
                                                                 -                    (3-19)
                                         4 ⋅ ∆ h d, mm
The minimum length of clothoid type of transition curves is according to DB [9] in
accordance with Equation (3-19) which after rewriting can be obtained as follows
                                          4 ⋅ V dim ⋅ ∆hd
                               L t, min ≥ -------------------------------
                                                                        -             (3-20)
                                                    1000
For tilting trains the following formula is valid for transition curves with linear change of
curvature and cant, respectively [10] [15]:
                                            L t ⋅ 1000
                                   Vdim ≤ ------------------------
                                                                 -                    (3-21)
                                          6 ⋅ ∆ h t, mm


3.3.5    Gradient

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




                                                       26
                           Track geometry for high-speed railways



3.3.6    Vertical curve radius

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

Table 3-15    Design value for vertical curve radius

               Without permission
                    Recommended                              2
                                              R v = 0.4 ⋅ V dim
                    minimum value
                    Limit value                              2
                                              Rv = 0.25 ⋅ Vdim

               Permission necessary
                    Permission                               2
                                                 Rv = 0.16 ⋅ Vdim on a crest
                                                               2
                                                 Rv = 0.13 ⋅ Vdim in a hallow
                                             Rv ≥ 2000m

                    Exception value          -

Some examples are shown in the following table.

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

 Vertical curve radius             200        250        280         300     330     350
                                  km/h       km/h       km/h        km/h    km/h    km/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




                                            27
                                      Standards, practices and TSI



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 cant
of 180 mm was utilized as limiting value at the high-speed line Paris-Sud Est. The cant is
given to respect the limiting values of cant deficiency (150 mm) and cant excess (100
mm).




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




                                                   28
                            Track geometry for high-speed railways



3.5      Practices in Japan

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

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

                                           Tokaido             Sanyo       Tohoku-Joetsu
                                          Shinkansen         Shinkansen     Shinkansen

 Start of operations                          1964               1972          1982
 Maximum operating speed [km/h]                270               300a          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
 a. Planned speed




                                             29
                                Standards, practices and TSI



3.6     Technical Specifications of Interoperability and CEN proposal

The purposes of the Technical Specifications of Interoperability (TSI) [12] are according
to 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 performances
  for 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 special
             features 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 by
  European specifications, including European standards which are needed to achieve
  interoperability within the trans-European high-speed rail system while meeting the
  essential requirements;
Furthermore, according to TSI, the performance levels of high-speed trains can also be
enhanced 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 be
limited to 180 mm to agree with the specifications set out by CEN/TC 256/WG15, Track
alignment design parameters, a provisional European norm, prENV 13803-1 [7]. Further
the 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 mm
maximum on tracks reserved for passenger traffic alone in accordance with the
specifications 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 to
the 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
                            Track geometry for high-speed railways



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

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

                                                  Mixed traffic lines
                                                    with passenger
                                                         train
                          Mixed traffic lines      V ≤ 230 (or 250      High-speed lines
                            designed for          on upgraded lines)     with dedicated
   Traffic categories      passenger train                              passenger traffic
                                                     with vehicles
                           200 < V ≤ 300            incorporating        250 ≤ V ≤ 300
                                                   special technical
                                                        design
                                                    characteristics

    Recommended                   160                     160                 160
 limiting value [mm]
      Maximum                     180                     180                 200
 limiting value [mm]


3.6.2   Cant deficiency and cant excess

Cant deficiency

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

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)

                  250 ≤ V ≤ 300                     100

                        V > 300                     80



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




                                             31
                                Standards, practices and TSI




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

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

                      V ≤ 160                     160

                   160 < V ≤ 200                  150

                   200 < V ≤ 230                  140

                   230 < V ≤ 250                  130

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


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

                                                        Cant deficiency range for
                          Maximum limiting            which the length of curves is
 Speed range (km/h)
                            value (mm)                 limited to 20% of the total
                                                           curve length (mm)

       V ≤ 160                     180                         160 < h d ≤ 180

   160 < V ≤ 230                   165                         150 < h d ≤ 165

   230 < V ≤ 250                   150                         130 < h d ≤ 150

   250 < V ≤ 300                   130                         100 < h d ≤ 130



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




                                            32
                             Track geometry for high-speed railways



According to the CEN provisional standard the values of cant deficiency and its
corresponding 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 CEN
provisional standard [7].

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

                                                 Recommended          Maximum limiting
                                              limiting value [mm]       value [mm]
             Traffic categories
                                              Freight     Passenger   Freight   Passenger

   Mixed traffic lines     200 < V ≤ 250        100          100       150        150
 designed for passenger
         trains                                    80         80       130        130
                           250 < V ≤ 300
     200 < V ≤ 300
  Mixed traffic lines                           110          160       160        180
                                  V ≤ 160
  with passenger train
         V ≤ 230                                   x         140        x         160
                           160 < V ≤ 200
     (or 250 km/ on
    upgraded lines)                                x         120        x         160
                           200 < V ≤ 230
 with vehicles incorpo-
 rating special techni-                            x         100        x         150
       cal design          230 < V ≤ 250
     characteristics
 High-speed lines with                             x         100        x         150
                              V = 250
  dedicated passenger
         traffic                                   x          80        x         130
                                  V > 250
    250 ≤ V ≤ 300


Cant excess

The TSI does not discuss cant excess. However, CEN provisional standard gives as
guidance, the following limiting values for cant excess:
- 110 mm as recommended limiting value;
- 130 mm is a maximum limiting value.




                                              33
                                      Standards, practices and TSI



3.6.3   Horizontal curve radius

The parameters that shall be considered in the determination of the minimum curve
radius 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 be
calculated using the following equation:
                                            11.8             2
                                     R = --------------- ⋅ V max
                                                       -                                             (3-22)
                                         ht + hd
The minimum allowable curve radius for the minimum operating speed shall be
calculated using the following equation:
                                          11.8             2
                                    R = -------------- ⋅ V min
                                                     -                                               (3-23)
                                        ht – he
The minimum curve radius should be optimised so that the values of cant, cant
deficiency and cant excess comply with the limits specified in [7] and satisfy the
following condition:
                                         2                                   2
                          11.8 ⋅ Vmin                     11.8 ⋅ Vmax
                          ------------------------- ≥ R ≥ --------------------------
                                                  -                                -                 (3-24)
                               ht – he                         ht + hd


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 trains
              without tilt) and slowly running freight trains. Values of cant deficiency
              and cant excess are recommended values according to TSI [12].

                 Vmax       Vmin                 hd                   he                 ht    R
                [km/h]     [km/h]               [mm]                 [mm]              [mm]   [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




                                                           34
                            Track geometry for high-speed railways



For lines specially built or upgraded for high-speed having special features a cant
deficiency of 130 mm can be applied for speed up to 300 km/h. Still no tilt system is in
use. Table 3-24 give some examples.
Table 3-24     Examples of horizontal curve radius with a cant deficiency of 130 mm
               for 250 km/h and 300 km/h with different values of cant.
               Conventional trains without tilt.

                  Vmax       hd                 ht                  R
                 [km/h]     [mm]              [mm]                 [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


3.6.4    Transition curve and superelevation ramp

Rate of cant

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

                           dh t      ∆h t ⋅ Vmax                dh t
                           ------- = ------------------------ ≤ -------
                                                               æ          ö                       (3-25)
                            dt           3.6 ⋅ L t             è dt       ø   lim

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

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].

                          Mixed traffic lines                Mixed traffic lines    High-speed lines
                             designed for                     with passenger         with dedicated
   Traffic categories      passenger trains                    train speeds         passenger traffic
                            200 < v ≤ 300                         v ≤ 230            250 < v ≤ 300

    Recommended                       50                                       50          50
    limiting values
        [mm/s]
  Maximum limiting                    60                                       60          60
   values [mm/s]




                                                       35
                                      Standards, practices and TSI



Limiting values of rate of cant as a function of length (dht/dx)lim shall apply to the
following values, although not critical at high-speed operations:
Recommended limiting value: 2.25 mm/m
Maximum limiting value:     2.5 mm/m

Rate of cant deficiency

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

                           dh d       ∆h d ⋅ V max                dhd
                           -------- = ------------------------- ≤ --------
                                                                    æ        ö                        (3-26)
                             dt           3.6 ⋅ L t                 dt
                                                                    è        ø    lim

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

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].

                          Mixed traffic lines                   Mixed traffic lines     High-speed lines
                             designed for                        with passenger          with dedicated
   Traffic categories      passenger trains                       train speeds          passenger traffic
                            200 < V ≤ 300                           V ≤ 230              250 < V ≤ 300

    Recommended                        50                                         50           50
    limiting values
        [mm/s]
  Maximum limiting                     75                                         90           75
   values [mm/s]


Length of transition curves in the horizontal plane

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

                                     V max              dhd                 –1
                                Lt ≥ ----------- ⋅ ∆h d --------
                                                            æ           ö                             (3-27)
                                       3.6                dtè           ø   lim

                                                 dh t               –1
                                     Lt ≥ ∆h t ⋅ -------
                                                       æ        ö                                     (3-28)
                                                  dx   è        ø   lim

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




                                                           36
                               Track geometry for high-speed railways



3.6.5    Gradient

According to TSI, gradients as steep as 35 ‰ shall be allowed for main tracks at the
design 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 lines
dedicated to passenger traffic. Exceptions are made for France, which already has
gradients up to 40 ‰ on one line (Paris-Sud-Est). Furthermore, the new line between
Cologne and Frankfurt is also using gradients as high as 40 ‰. Other restrictions are
valid for freight trains.


3.6.6    Vertical curve radius

The vertical curve radius shall be designed using the following formula
                                                2
                                            V max
                                 Rv = ---------------------- ≥ Rv, lim
                                                           -                                 (3-29)
                                      12.96 ⋅ a v

The vertical acceleration, av, used in Equation (3-29) shall be selected taking into
consideration ride comfort where there is a possibility of a non optimal track bed. In
addition, consideration shall be given to safety to guard against derailment due to wheel
unloading when running over humps (crests). However, this safety limit is not
considered unless the maximum limiting values for av are exceeded. The limit values of
vertical acceleration are shown in Table 3-27.

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

                          Mixed traffic lines           Mixed traffic lines   High-speed lines
                             designed for                with passenger        with dedicated
  Traffic categories       passenger trains                   train           passenger traffic
                            200 < V ≤ 300                   V ≤ 230           250 < V ≤ 300

   Recommended
   limiting values                 0.22                            0.22             0.22
       [m/s2]
 Maximum limiting                 0.44a                            0.31            0.44a
   values [m/s2]
 a. With a tolerance of +10% on a crest, +30% in a hallow




                                                     37
                                 Standards, practices and TSI



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

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

                        Mixed traffic lines    Mixed traffic lines   High-speed lines
                          designed for          with passenger        with dedicated
  Traffic categories     passenger train             train           passenger traffic
                         200 < V ≤ 300              V ≤ 230           250 < V ≤ 300

   Recommended                     2                        2                 2
                            0.35Vmax                0.35Vmax            0.35Vmax
 limiting values [m]
 Minimum limiting                  2                        2                     2
                           0.175Vmax                 0.25Vmax           0.175V max
    values [m]




                                              38
                            Track geometry for high-speed railways



3.7     Comparison between different projects and standards


3.7.1   Horizontal curve radius

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

              Line                Vlim     Rmin         ht,max       hd,max     ay
                                 [km/h]    [m]          [mm]         [mm]     [m/s2]

              DBa                 300      3200          200         130      0.85

              JRb                 350      4000          200         160      1.05

              SNCFa               350      4000          200         160      1.05
              a. Ballast track
              b. Ballastless track




                                             39
     Table 3-30       Comparison between different quantities on different railway companies throughout the world.
                      Exceptional values not considered.

                     Organisation                 TSI/CEN      JR           JR           JR          DB           DB         SNCF         SNCF            BV
                                                                                        Tokyo-
                                                             Tokaido       Sanyo                   Hannover-   Köln-Rhein/   TGV Paris-     TGV        Botniabanan
      Item                                                                              Joetsu
                                                            Shinkansen   Shinkansen                Würzburg      Mann         Sud Est     Atlantique     (partly)
                                                                                      Shinkansen

      Maximum design speed               [km/h]                                                      280          300          300          350           250
      Maximum service speed              [km/h]               270          300          275          250                       270          300         200a/
                                                                                                                                                        250b
      Cant                                [mm]      180       200          180          180          65           160          180          180           150




40
      Cant deficiency                     [mm]      100       100          100          100          80           150           85           60        100/220
      Cant excess                         [mm]      110                                              50                                                   100
                                                                                                                                                                     Standards, practices and TSI




      Minimum curve radius                 [m]               2500         4000         4000         7000         3350         4000         6250          3200
      Minimum radius of                    [m]                                                      5100         3425         4000         6020         2950/
      design speed                                                                                                                                      2000
      Track distance                       [m]      4.5       4.24          4.3          4.3                                   4.2          4.2           4.5
      Minimum vertical curve               [m]              10000        15000        15000        22000                     12000                      11000
      radius                                                                                                                 14000
      Maximum gradient                    [‰]       35         20           15           15         12.5          40            35           25           10
      a. Category A trains
      b. Category S trains (tilt technology)
                            Track geometry for high-speed railways



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 single
horizontal 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 of
horizontal 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, placed
between two tangent tracks. If a lengthening of the transition curves is wanted then it
will require a reduction of the radius in the circular part of the curve. This is valid for a
single curve between two fixed straight lines.
The present study does not bring up passenger comfort as an object function. According
to Kufver the PCT functions are the most reasonable overall comfort functions because
PCT includes the lateral acceleration, lateral jerk and roll velocity. These physical
quantities are the most basic ones when calculating alignment and cant.
Kufver came to the conclusion that S-shaped ramps and corresponding types of
transition curves have no substantial advantages compared to transition curves with
linear change of curvature (clothoids).
The optimal lenghts of the clothoids depend on the limit for cant, the roll coefficient of
the vehicle and the degree of compensation in the body tilt system. One of the most
important findings is that a tilt system with a large degree of compensation for lateral
acceleration favours long transition curves (clothoids). Thereby the roll velocities are
reduced. Within an alignment restricted by existing obstacles longer transition curves
will in many cases lead to less radius in the circular curve and thus a higher lateral
acceleration. However, the latter problem will to a large extent be compensated by means
of the carbody tilt, which reduces the lateral acceleration on passengers. However, the
curve radius must always be sufficiently large in order to cope with the desired speed for
conventional (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 motion
sickness. Firstly, in the tilting tests, the concept of symptoms of motion sickness
incidence (SMSI) was used. Those tests utilised different strategies for active tilt of the
carbody to reduce lateral acceleration during curving. For example, when using a lower
ratio of tilt compensation a reduction of reported symptoms of motion sickness was
found.




                                             41
                                Standards, practices and TSI



Secondly, when evaluating the simulator tests, the evaluation variable nausea rating
(NR) was used. Förstberg found that it was likely that lower compensation and limited
tilt velocity are favourable in a everyday population of passengers. The main conclusions
drawn by Förstberg are:
- Roll motions presented alone are not very nauseogenic and only small differences
  were found between gender.
- Lateral accelerations alone seem to be medium challenging.
- Combinations of high roll and high lateral accelerations seem to be highly
  provocative for motion sickness. However, it is necessarily not nauseogenic with high
  compensation ratios alone. For example, low roll velocity and low lateral acceleration
  with a compensation rate of 75%, show low nausea ratings.
- Both high lateral acceleration and high roll velocity have negative effects on the
  ability to work and/or read as well as the ride comfort.
One consequence of Förstberg’s research is that long transition curves would be
desirable from a motion point of view. This is essentially the same conclusions as made
by Kufver described in the previous Section.
For more detailed descriptions, see Förstberg [14].




                                            42
                            Track geometry for high-speed railways



3.9      Summary and conclusions

In Europe it is a clear trend to make specifications for high-speed track geometry less
strict, i.e. to allow tighter horizontal curves and steeper gradients for a given speed. The
most 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 a
gradient 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 ‰ for
operation at 300 km/h. The CEN provisional standard and the newly drafted TSI confirm
this trend. This is along the same line as part of the Japanese Shinkansen, where a
horizontal 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 for
high-speed passenger trains, not mixed traffic including heavy freight trains. Quite light
passenger trains with high traction forces and power (per tonne of train) are able to climb
much steeper grades than locomotive-hauled heavy freight trains. Also, for passenger
trains a higher track cant can be arranged, in some cases up to 200 mm, because there is
no risk of danger if a passenger train stops at a section with high cant - in an ordinary
freight train there is risk for load displacement in wagons. The higher cant on high-speed
lines allows somewhat reduced horizontal curve radius for the same cant deficiency and
speed.
However, this seems not to be the main reason for the smaller horizontal curve radius. In
the new practice and proposed European standards a quite high cant is allowed also on
lines with mixed traffic (normally 160 mm, exceptionally 180 mm). The earlier
requirements on (a low) cant excess for slowly running freight trains had typical limit
values of just 50 - 70 mm in, for example, Germany and Sweden. This, in turn, required
low cant to be arranged on high-speed lines with mixed traffic and slowly running freight
trains. In the final draft of the CEN proposal (prENV 13803-1) it is now recommended to
have a limit value of 110 mm (maximum 130 mm) for cant excess. The suitability of
such a change is also confirmed by recent Swedish research [25]. This produces much
better conditions for increasing the cant while reducing curve radius on high-speed lines.
Similar trends are obvious also for the maximum allowed cant deficiency (lateral
acceleration in the track plane). For conventional trains (without carbody tilt) on lines
specially built for high-speed a limit value of 100 mm is recommended (80 mm for
speeds above 300 km/h). However, in cases of very strict topological constraints a limit
value of 130 mm is allowed.
Another important feature of the drafted TSI is the allowance for rising speeds by using
tilt technology, or inversely, to reduce the necessary horizontal curve radius for a given
speed. 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 take
decisions on tilting trains running at a higher cant deficiency than conventional trains.
Regarding length of transition curves, recent Swedish research [16] allows optimisation
of transition lengths within a defined terrain corridor with a number of obstacles. The
optimisation has passenger comfort as an object function. According to this research the
optimum transitions lengths are depending on (among others) the position of obstacles
and also on whether carbody tilt is applied or not. There is a clear tendency that the



                                             43
                                 Standards, practices and TSI



introduction of carbody tilt favours longer transition curves in relation to cases where tilt
is not applied. This is mainly due to the additional roll velocity introduced on tilting
trains. Longer transition curves reduce the roll velocity, which is favourable from a
comfort point of view. In this context, recent Swedish research [14] also shows that
lower roll velocity is very favourable also with respect to the provocation of motion
sickness, which is shown to be a certain problem on tilting trains. All this is in
accordance with CEN proposed standard, which limit the rate of change in cant and cant
deficiency. It should be pointed out, however, that for tilting trains the optimum rate of
change 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 larger
than the minimum limiting radius. This is the case in most standards. The minimum
requirements are quite similar to each other, including Banverket standard. Normally, the
required vertical radius is somewhat larger on crests than in hallows. This is due to the
risk of wheel unloading on crests.
Some of the above mentioned design parameters are believed to have significant
influence in the average construction cost of newly built high-speed railways, namely
horizontal curve radius, vertical curve radius and gradient.
The technical feasibility of using tilting trains in very high-speed operations is
investigated in Chapter 4 - 6 in the present study. This would reduce the necessary
horizontal curve radius. In Chapter 7 a brief investigation is made on the permissible
gradient and cant for various types of freight trains.




                                             44
                            Track geometry for high-speed railways



4        High-speed train technology year 2010

To be able to make realistic suggestions regarding track lay-out for high-speed lines, it is
important to reflect upon the trains which are going to run on these lines. Possible
maximum train speed without hunting problems or possible cant deficiency in curves
without exceeding limits for track shift forces, are strongly depending on design and
performance of the running gear. The aerodynamic shape of the train plays an important
role 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 available
from industry around 2010, i.e. at the earliest time regular traffic on e.g. The European
Corridor (Europakorridoren) or other high-speed lines in Sweden is about to start. This is
important 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 are
made in close co-operation between the author and a number of experts from KTH and
industry (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 (KTH
Railway Technology, as well as Company Senior Specialist in Vehicle Technology,
Bombardier).
It is aimed that assumptions on possible future vehicle technology should not be too
optimistic, but rather be at the safe side. The assumed future technology should be
known today, although not always implemented in commercial high-speed trains of
today. 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 commercial
trains. It is mainly a question whether such trains will be demanded on the European
market.



4.1      Maximum train speed

To our opinion it is realistic to achieve maximum train speeds of 350 km/h within ten
years. 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) where
many axles in the train are driven. Advantages compared to loco-hauled trains are mainly
higher possible acceleration and lower maximum axle load. Therefore an EMU unit was
chosen 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 speeds
200 - 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 hypothesis
is that it may be possible to operate tilting trains also at speeds of 300-350 km/h in the
future. 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 deficiency
and hence at higher speeds in curves. The possible percentage of overspeed is, among
other things, limited by:
- Possible lateral accelerations and roll motions with respect to passenger comfort. This
  is 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, as
  well as suspension in the running gear. For vertical track forces also the unsprung
  mass, 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 the
following figure.




                                             46
                                                  Track geometry for high-speed railways




                                70%
      Permitted overspeed [%]   60%                                       Cant deficiency hd=150mm

                                50%                                       Cant deficiency hd=250 mm

                                40%
                                30%
                                20%
                                10%
                                0%
                                      0              50                 100                150        200
                                                                   Cant [mm]

Figure 4-1                            Permitted overspeed in a circular curve as a function of cant.
                                      The permitted overspeed in relation to conventional trains with an
                                      allowed cant deficiency of 100 mm (recommended value according to TSI
                                      for the speed range up to 300 km/h). Note: For a cant deficiency of 150
                                      mm 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 the
design of the running gear, especially the suspension. A train with a maximum speed of
350 km/h on tangent track and with up to 250 mm of cant deficiency in curves has to be
equipped with well designed running gear. Using the experience from the Swedish
running gear design, this study will test if this is possible or not.
In principle, an optimised combination of wheelset guidance and damping has to be
applied. A very flexible wheelset steering will likely lead to problems with the hunting
stability, 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 for
steering wheelsets. Therefore a decision was made not to take such possibilities into
consideration in the present study.
One of the developments which will likely be introduced on a larger scale during the
next 5-10 year is the so-called Hold-of-device (HOD). It is added in order to center the




                                                                   47
                            High-speed train technology year 2010



carbody in curves. This will make it possible to negotiate curves with high cant
deficiency without worsening passenger comfort by hitting the lateral bump stops in the
suspension, thus producing less dynamic forces on track and passengers. Also, if the
carbody 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 further
investigated and developed in this study.



4.5      Aerodynamic shape

The aerodynamic shape of a high-speed train is important for the running resistance and
energy consumption of the train. Furthermore, side-wind stability (i.e. the ability to be
safe against overturning in strong side winds) has become a more and more important
issue to study in combination with high-speed train operation. There are at least three
reasons for this: Speeds are getting higher, vehicles are getting lighter and high-speed
lines are often exposed to wind because of frequent use of high embankments and
bridges.
In this study an aerodynamic shape representative for the best trains existing today is
assumed. The aerodynamic coefficients for the used vehicle model are revealed in
Appendix E. In comparison, such a train would generate about 20% less overturning
moment 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 standard
regarding track irregularities. It should be possible on future built high-speed lines to
achieve and maintain a track quality better than current Swedish main lines standards,
without increasing maintenance costs to an unrealistic level. This assumption has been
confirmed by personal communications with specialists from Banverket. One of the aims
with 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
                            Track geometry for high-speed railways



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


5.1      Simulation strategy

The simulations have been carried out in three different parts. Firstly, simulations of
hunting stability is performed to appoint that used technology can be managed in such
high speed as 350 km/h. Secondly, the track shift forces will be calculated according to
Prud´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 the
oldest and largest packages currently in use. There are more than a few options regarding
the 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 scale
testings 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 must
be evaluated at a slightly higher speed then the intended permissible speed. CEN stated
that the test speed should be the lower of 110% of permissible speed and the speed which
corresponds to 110% of permissible cant deficiency.
Kufver [16] says that it would be relevant in certain studies to compare alignments with
different radii. Kufver suggested that it would be reasonable to use the same test speed in
all alternatives and hence a different cant deficiency.
In simulations concerning hunting stability a test speed of 385 km/h was chosen. This
speed corresponds to 110% of the intended permissible speed (350km/h).
When evaluating track shift forces a test speed of 360 km/h was regarded to
approximately fulfil the condition of 110% of permissible cant deficiency. The horizontal
curve radius at a cant of 180 mm, cant deficiency of 250 mm and speed of 350 km/h is
equal to the horizontal curve radius at a cant of 180 mm, cant deficiency of 275 mm and
speed of 360 km/h (R=3361m in both cases). 110% of 250 mm is equal to 275 mm. A
cant deficiency of 275 mm was chosen as boundary condition.
In the simulations concerning vehicle overturning it was judged to be adequate to choose
a 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 high
cant deficiency and strong side-winds - is still more unlikely to happen and should
therefore not be considered as a realistic case.



5.4      Hunting stability

Two types of instabilities will be studied in the present work. High frequency instability
occurs at high-speeds and high equivalent conicity. Low frequency instability tends to
occur if the wheelset hunting frequency and a natural frequency of the vehicle on its
suspension are rather similar. Thus, low frequency instability is more or less similar to a
resonance phenomenon. The matter of equivalent conicity is explained in detail in the
course 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 with
  the lateral bending mode of the carbody. Wheelset steering will be chosen to fulfill
  this requirement.
- The decay of the hunting amplitude must be at least 60% in two cycles after a sudden
  disturbance. 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 speed
according to Section 5.3. The equivalent conicity is varied according to Section 5.7.




                                                50
                             Track geometry for high-speed railways



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 are
               the lateral forces.
               The track shift force is represented by ΣY.

The safety-critical limit for track shifting according to Prud’homme criterion is
                                                        2Q 0
                       ΣYlim = S lim = k s ⋅ k 1 ⋅ 10 + --------- [kN]
                                                    æ         ö -                         (5-1)
                                                    è       3 ø

where ks = 0.85 in the simplified statistical analysis in this study. 2Q0 is the static vertical
axle load and k1 is a factor usually set to 1 for passenger vehicles, according to CEN and
UIC 518 [8], [24]. The value of ks = 0.85 was chosen because track shift forces usually
are 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 on
the conservative side”. Further, the track shift forces are filtered before evaluation. The
mean value over 2 metres is compared with Prud’hommes limit. The limit refers to 46
kg/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 ballasted
track gives also a certain safety margin, see further CEN [8].




                                               51
                Track/vehicle dynamic simulations - models, conditions and criteria



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 there
exists a risk for vehicle overturning around the outer rail. This is particularly true if they
are 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 of
overturning. A tight lateral bump stop, or a Hold-off-Device (HOD), both limiting the
lateral 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 without
any shielding trees, buildings, hills or similar. The strongest winds usually occur in
vicinity of the sea, especially at the West Coast. The wind velocity increases at higher
height 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, the
wind varies over time and occurs as “wind gales”. It is usually very difficult to
summarise these complex phenomena into a limited number of simple load cases for
each 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 decisive
for the aerodynamic forces acting on the train. In particular, the lateral force and the roll
moment are important aerodynamic characteristics with respect to overturning; for
example a higher roof height of the train will usually increase the risk. Also the height of
centre of gravity is important for the risk of overturning. See further Appendix E and
Lippert [21] for details.
Another factor increasing the risk of overturning is the lateral deflection of the centre of
gravity, i.e. how much the c.g. is moved outwards in the curve under influence of the
centrifugal forces and the side wind forces. Thus a large lateral spring travel due to
suspension flexibility is not desirable from this point of view (although improving the
ride 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 a
comprehensive effort was made in the 1980´s, related to the design of X 2000. Large
efforts have recently been made in Germany and France.




                                                52
                            Track geometry for high-speed railways



The European standard for evaluating safety against vehicle overturning at strong side
winds is under development within the framework of TSI [12] [13]. In this study the
preliminary 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 strong
side winds. Although the exact level of side wind velocity is yet not settled, a level
around 23 m/s of tolerable side wind from the most adverse direction is discussed. This
level is related to the “Vector intercept” criterion presented in the next Section 5.6.3. The
level 23 m/s is quite equivalent to the safety level set down for X 2000, although the
overturning risk criteria were formulated in another way [28].
Secondly, if there is an unacceptable risk that the wind velocity on specific locations will
be higher than the basic level mentioned above, the infrastructure manager is responsible
for taking adequate measures to maintain the level of traffic safety [12]. This can be
made by temporary speed restrictions at strong side winds (which requires an
appropriate wind reporting system and traffic management). The infrastructure manager
may also install protective equipment such as wind barriers.
In this study the strategy is to investigate whether the high-speed train meets the
appropriate overturning criteria (see Section 5.6.3), with a constant side wind velocity of
23 m/s applied to the train from the most adverse direction, when the train is running at
its 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 is
the intercept method, which is based on the vertical track forces of the vehicle. The
intercept method calculates a resulting force as a result of all wheel forces. Figure 5-2
and Table 5-1 show the definition of quantities for calculation of the risk of vehicle
overturn with the intercept method.




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



                                             53
                Track/vehicle dynamic simulations - models, conditions and criteria



bt is a measure for the risk of the vehicle turn-over and describes the distance between
the centre of the track plane and the point where the resultant force is acting. bt can be
calculated by replacing the wheel forces with a resultant force under the restriction that
the resultant force causes the same forces and moments as the wheel forces.
Table 5-1      Quantities for the calculation of the overturning risk according to the
               intercept 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 of                [m]
                    left and right wheel

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

                                         Σ Ql – Σ Qr
                                  b t = -------------------------------- ⋅ b o
                                                                       -                      (5-2)
                                          Σ Ql + Σ Qr
The absolute value in the nominator is needed to consider overturning to both the left and
right side. When the wheels on one side are totally unloaded, bt has got the value bo and
stays constant. The permissible value for bt can be defined as

                                    b t = b t, lim = E ⋅ b o                                  (5-3)
Put Equation (5-3) into Equation (5-2) and solve E in the new equation. We get a ratio of
bt and bo that defines a risk factor according to Equation (5-4):

                              Σ Ql – Σ Qr
                             -------------------------------- ⋅ b o
                                                            -
                       bt                                               Σ Ql – Σ Qr
                               Σ Ql + Σ Qr - = --------------------------------
                         -
                  E = ---- = ------------------------------------------            -          (5-4)
                      bo                        bo                      Σ Ql + Σ Qr
Typical values for E are between 0.8-1. In the present study a limit value of 0.9 has been
used.
With the intercept method risk factor, E can be calculated for one wheelset, one bogie or
the whole vehicle. In this study, E is calculated for the whole vehicle, considering the
forces of all wheels.




                                                          54
                            Track geometry for high-speed railways



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


5.6.4    Disadvantages with intercept method

According to Lippert [21] the intercept method has two disadvantages. Firstly, the vector
intercept is calculated by using the wheel forces which are - due to fast dynamic
variations - a conservative criterion to show side-wind stability, especially when real
track with track irregularities is simulated. As commented above, the signals must be
low-pass filtered to be appropriate to a quite slow process like overturning. Secondly, bt
of the intercept method can not become larger than bo. This means that as soon as all
wheels on one side loose contact, bt stays constant, independent from changes in the
force acting on the train. Although losing contact with all wheels at the same time is a
critical situation, it must not necessarily immediately overturn the vehicle due to the
vehicle’s inertia.
A low-pass filtering of 1.5 Hz is considered as slightly conservative. It has been used for
overturning investigations of the Swedish X 2000 train and has been used in the
preliminary 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 vehicle
overturning.


5.6.5    Aerodynamic train design

A good aerodynamic shape, according to Section 4.5 is assumed. In combination with a
roof 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
                Track/vehicle dynamic simulations - models, conditions and criteria



5.7      Rails, wheels and equivalent conicity

Equivalent conicity is a geometrical property between wheels and rails, describing the
magnitude of rolling radius difference (between right and left wheel) when the wheelset
is displaced laterally relative to a tangent track (where the wheelset is nominally at its
centre 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 rail
head) as well as on the rail inclination in the track and on the track gauge. It is also
dependent on built-in geometrical tolerances and on the actual wear shapes of both
wheels and rails.
In the TSI and CEN specifications the maximum equivalent conicity shall apply for
different maximum speeds V (km/h) corresponding to Table 5-2:
Table 5-2      Maximum equivalent conicity at different maximum speed.
               All according to CEN and TSI.

                                            Design value             In service, taking into
                   Speed (km/h)
                                            (maximum)             account wheel and rail wear

                  230 < V ≤ 250                  0.25                           0.30
                  250 < V ≤ 280                  0.20                           0.25
                          V > 280                0.10                           0.15

Thus, on tracks and vehicles for these speeds the rails and wheels shall be obtained and
maintained that the above shown equivalent conicity can be achieved. As one of several
measures to meet these conicity requirements, the track gauge must be in the range of
1434 - 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 in
order 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 certain
limits.
Two kinds of rail profiles have been used in the present study; UIC 60 rail profile and a
BV 50 rail profile, both with the Swedish rail inclination of 1:30. The UIC 60 rail profile
is standardised by the UIC and is used on many lines and new-built lines in Europe. This
rail profile has been used in the simulations of track forces and vehicle overturn. A worn
BV 50 rail has been used for stability simulations on tangent track thus leading to a
higher value of equivalent conicity than new nominal rail head shapes. For stability
simulations on curves the UIC 60 rail profile is used.
The above-mentioned rail profiles are combined with wheel profiles type UIC/ORE
S1002, see Section 5.9. In this procedure the equivalent conicity can be varied up to a
value of at least 0.40, which can be used in the stability simulations.




                                                56
                            Track geometry for high-speed railways



5.8      Track irregularities


5.8.1    Classification of track irregularities

Most railway companies classify their tracks with regard to the level of permissible track
irregularities. On main lines, in particular on high-speed lines, less irregularities are
permitted than on lines for lower speeds. This section refers to the classification in the
CEN/TC 256 WG 10 [8] as well as Banverket BVF 587.02 [6]. Three classes of track
qualities are defined with regard to the necessity of maintenance and to the applicability
for 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 or
  taking 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 excluded
  from the analysis because the track quality encountered is not representative of usual
  quality standards.
Banverket uses the following levels:
- A. New-built or recently adjusted track.
- B. Lower quality limit. States target value of maintenance actions. The track
  irregularities should normally be adjusted before this level attains. This limit is often
  related to comfort aspects.
- C. This limit should not be exceeded. The track irregularity must be corrected as soon
  as possible. Reduced speed limits should be taken into consideration until the
  irregularities have been corrected.
Each level refer to a certain quality class, K0 - K5, depending on the permitted speed on
that particular track [6].




                                             57
                    Track/vehicle dynamic simulations - models, conditions and criteria



5.8.2      Track irregularities for dynamics analysis

As input data for analysis of vehicle dynamics the absolute irregularities as function of
distance have to be known or assumed. Track irregularities can be represented by the
following 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 characteristics
were 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 of
irregularities can be permitted, without exceeding the safety-critical limit of track shift
forces at 275 mm cant deficiency (i.e. 110% of the cant deficiency 250 mm. The
amplitude of the described track irregularities are varied by multiplication with different
factors. 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 train
   X 2000.




                                                      58
                            Track geometry for high-speed railways



To make a quality control of the track irregularities a methodology was set out in this
study. 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 limits
of Banverket’s standard classification. A Q-value of 80 means the standard deviations
are 0.7 times the limit. A Q-value of 100 means that the standard deviations are 0.5 times
the limit value of the current quality class. Thus, the aim of this part of the study was to
find 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 be
achieved. 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 class
defined for speeds in the range of 200 km/h (above 145 km/h for conventional trains and
above 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.

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

                    Q-value      Lateral    Vertical    Gauge         Cant    Multiplication
     Track
                   (class K0)    factor      factor     factor       factor      factor

 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 and
               Nyköping (tangent track).

                    Q-value      Lateral    Vertical    Gauge         Cant    Multiplication
     Track
                   (class K0)    factor      factor     factor       factor      factor

 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

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




                                             59
                                   Track/vehicle dynamic simulations - models, conditions and criteria




                       15
      Vertical [mm]    10
                        5
                         0
                        -5
                       -10
                       -15
                             600             700              800             900             1000          1100
                                                                                                     Distance [m]

                        15
                        10
        Lateral [mm]




                         5
                         0
                        -5
                       -10
                       -15
                             600              700             800             900             1000          1100
                                                                                                     Distance [m]

                       15
                       10
        Cant [mm]




                         5
                         0
                        -5
                       -10
                       -15
                             600              700             800             900             1000       1100
                                                                                                  Distance [m]

                 1445
   Gauge [mm]




                 1440

                 1435

                 1430

                 1425
                             600              700             800             900             1000        1100
                                                                                                  Distance [m]

Figure 5-4                         Track irregularity characteristics of Track 5.




                                                                    60
                                       Track geometry for high-speed railways




                    15
   Vertical [mm]    10
                     5
                     0
                    -5
                   -10
                   -15
                         600           800             1000             1200    1400
                                                                                Distance [m]

                    15
                    10
   Lateral [mm]




                     5
                     0
                     -5
                    -10
                    -15
                          600           800            1000             1200    1400
                                                                                Distance [m]

                    15
                     10
   Cant [mm]




                      5
                      0
                     -5
                    -10
                    -15
                          600           800            1000             1200    1400
                                                                                Distance [m]

                   1445

                   1440
   Gauge [mm]




                   1435

                   1430

                   1425
                          600           800            1000             1200    1400
                                                                                Distance [m]

Figure 5-5                 Track irregularity characteristics of Track 10.




                                                        61
                 Track/vehicle dynamic simulations - models, conditions and criteria



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 track
recording coach called STRIX [6] and are shown in Table 5-5.

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

                                                       Deviation from base value [mm]

                                                       Longitudinal level              Cant
                     Speed limit      Speed limit
                                                                            Long
    Quality         conventional      high-speed       Short wave
                                                                            wave           Deviation
     Class              train            train         fault 1-25 m
                                                                            fault
                       (km/h)           (km/h)
                                                       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]

                                                Alignment                     Gauge

               Speed limit     Speed limit      Short wave
                                                                    Long
 Quality      conventional     high-speed       fault
                                                                    wave            Deviation
  class           train           train         wavelength
                                                                    fault
                 (km/h)          (km/h)         1-25 m

                                                A     B     C       A   B      A       B          C

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



The track quality values according to CEN/TC 256 WG 10 [8] have been obtained from
measurements 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 system
may 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 5-5
and Table 5-6, as the measuring system has different transfer functions from real to
recorded irregularities.




                                                 62
                                                             Track geometry for high-speed railways




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

                                                             Alignment                                                      Longitudinal level
  Permissible
 local speed in                                                    Values of quality level in mm
     km/h
                                                       QN1              QN2                                                 QN1               QN2

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

 200 < v ≤ 300                                           4                6                                                  4                 8

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


                                       5                                                                                5
                                                                                   vertical irregularity, right rail,
   vertical irregularity, left rail,




                                                                                         peak value [mm]
         peak value [mm]




                                       0                                                                                0




                                       -5                                                                               -5
                                         600    700   800    900 1000 1100                                                600     700   800    900 1000 1100
                                                                distance [m]                                                                      distance [m]

                                       5
   lateral irregularity, left rail,
        peak value [mm]




                                       0




                                   -5
                                     600        700   800    900 1000 1100
                                                                 distance [m]


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




                                                                              63
                                                 Track/vehicle dynamic simulations - models, conditions and criteria



In Figure 5-7 the STRIX values of Track 10 are shown. The maximum peak values of
vertical 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 the
curve) rail is 2.25 mm.


                                        5                                                                                    5




                                                                                        vertical irregularity, right rail,
    vertical irregularity, left rail,
          peak value [mm]




                                                                                              peak value [mm]
                                        0                                                                                    0




                                        -5                                                                                   -5
                                          600     800     1000     1200 1400                                                   600   800   1000   1200 1400
                                                                   distance [m]                                                                   distance [m]

                                        5
    lateral irregularity, left rail,
         peak value [mm]




                                        0




                                        -5
                                          600     800     1000     1200    1400
                                                                    distance [m]


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

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




                                                                                   64
                            Track geometry for high-speed railways



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 in
a train will interact. However, the results will most likely be on the conservative and safe
side, because the interaction between coaches rather improves the running behaviour
than worsens it. Especially, this is true with respect to low-frequency dynamics (0.5-2
Hz) due to long-waved track irregularities, low frequency instability and vehicle
overturning.
As mentioned in Section 5.7, in the stability simulations a worn UIC/ORE S1002 wheel
profile 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 a
theoretical 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 the
following 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
                  Track/vehicle dynamic simulations - models, conditions and criteria




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

                                                                            Height of mass centre
                      Mass              Mass moments of inertia
                                                                             above track plane

                        M             Jxx          Jyy            Jzz
                                                                                        (m)
                       (kg)        (kgm2)        (kgm2)        (kgm2)

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

 Bogie framea         6 000         1 590        5 300          8 500                   0.70

 Wheelsetb            1 600          960           300           960                    0.42

 a. Including frame-mounted traction motors.
 b. Including traction gear and bearings.

The static axle loads are 126 kN for all wheelsets, which is a very low axle load for a
motored coach of full length. The vehicle data used for the simulations are not taken
from 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 of
gravity (c.g.). The first simulations on side-wind stability showed that vehicle
configuration 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 leading
bogie centre and 0.4 m above the track plane. This was judged to be a realistic approach
to 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 configuration
A. Mass distribution data for vehicle configuration B are shown in Table 5-10.
Table 5-10       Rigid bodies in the model of the EMU, vehicle configuration B

                                                                            Height of mass centre
                      Mass              Mass moments of inertia
                                                                             above track plane

                        M             Jxx          Jyy            Jzz
                                                                                        (m)
                       (kg)        (kgm2)        (kgm2)        (kgm2)

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

 Bogie framea         6 000         1 590        5 300          8 500                   0.70

 Wheelsetb            1 600          960           300           960                    0.42

 a. Including frame mounted traction motors.
 b. Including traction gear and bearings.




                                                  66
                                 Track geometry for high-speed railways



The static axle loads for vehicle configuration B (in empty condition) are 142.4 kN for
the wheelsets in the leading bogie and 129.3 kN for the trailing bogie. The higher axle
loads (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 strong
side-winds a third vehicle configuration C was defined. This vehicle has the carbody
centre of gravity located 0.10 m above that of configuration B. Otherwise, configuration
C is identical to configuration B. See Table 5-11.

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

                                                                          Height of mass centre
                      Mass              Mass moments of inertia
                                                                           above track plane

                        M             Jxx           Jyy           Jzz
                                                                                  (m)
                       (kg)        (kgm2)        (kgm2)        (kgm2)

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

 Bogie framea         6 000         1 590         5 300         8 500             0.70

 Wheelsetb            1 600          960           300           960              0.42
 a. Including frame mounted traction motors.
 b. Including traction gear and bearings.


Vehicle configurations B and C are considered as being realistic for future high-speed
EMUs. It should be pointed out that the “extra mass” located behind the leading bogie in
reality may be part of ordinary vehicle equipment, such as heavy electrical transformers
or similar. It may not be necessary to put in additional “ballast mass”, but rather to
consider the desired mass and mass distribution when the ordinary equipment is located
in future vehicles. The resulting total mass and axle loads of configurations B and C are
quite normal according to recent vehicle technology; compare for example with the
German ICE 3 and the Swedish Öresund Train.
As said above, configurations B and C have been used only for side-wind stability
evaluations, although they are considered as the most realistic for future high-speed
trains. Only configuration A has been used in the hunting stability and track shift
analysis. The reason is that the investigations started with hunting stability and track shift
forces, 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 the
new configurations B and C. The carbody mass and centre of gravity normally have no
significant influence on hunting stability or the risk of exceeding the track shift force
limit, all this according to Prof. Andersson´s experience.




                                                  67
                Track/vehicle dynamic simulations - models, conditions and criteria



5.9.2   Hold-off-device

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




                                                68
                            Track geometry for high-speed railways



6         Dynamic analysis of simulated vehicle response

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



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, in
the latter cant deficiency was varied in order to use the same test speed. A test speed of
385 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 tangent
track and in different curve combinations this condition satisfies the intention. This also
corresponds to the other condition stated of CEN and UIC. This condition says that the
test speed must be evaluated at 110% of permissible cant deficiency. For example: Speed
V = 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 cant
deficiency hd = 340 mm. This results in 136% of permissible cant deficiency. This is
more 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            Cant             Cant deficiency        Horizontal curve radius
        [km/h]               [mm]                  [mm]                       [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




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

    Train speed              Cant              Cant deficiency        Horizontal curve radius
      [km/h]                 [mm]                   [mm]                       [m]

        385                   200                      50                      6995
        385                   200                     100                      5829
        385                   200                     150                      4997
        385                   200                     200                      4372
        385                   200                     250                      3886
        385                   200                     300                      3498


6.1.2    Track irregularities

In the hunting stability simulations the track is without irregularities except a single
lateral disturbance (i.e about the same amplitude as the lateral wheel/rail clearance) have
been used in the stability simulations. The irregularity used will excite a lateral motion of
the wheelsets and bogies. The wheel flanges will hit the rails. Thus also high wheel/rail
contact angles are taken into account, not limiting the hunting investigations to small
motions around the centre position. The wavelength and the amplitude of the single
lateral 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 accelerations
in the carbody shall have a decay of at least 60% in the first two cycles from the highest
peak. I addition, no sustained vibration shall be visible after 200 – 400 m. Finally, the
frequency of vibration should not be higher than 10 Hz, in order to limit the risk of
exciting 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 up
to about 0.3 has been investigated. This is very much above the required conicity
according 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 (between
wheelsets and bogie frame) and yaw damping (between bogie frame and carbody). It was
found that an intermediate stiffness in the wheelset guidance was near optimum with



                                              70
                                   Track geometry for high-speed railways



respect to hunting stability. This intermediate stiffness is something in between the quite
flexible guidance stiffness on X 2000 (for 200 - 210 km/h) and the traditional stiff
guidance normally used in Continental Europe. It is believed (although not proved in this
study) 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 385
km/h - can be achieved at an equivalent conicity of 0.20 – 0.25, according to the
simulations. This is above the required value of 0.15, but it should be noted that stability
should 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 at
three different locations in the simulations. The three locations on the floor was above
each bogie and in the middle of the carbody. In Figure 6-1 to 6-3 an example of the
lateral accelerations is shown for these three locations. In this case the vehicle is fully
stable without any hunting motion, according to the criteria defined in Section 6.1.3. A
lot of other cases, with different equivalent conicity, have been simulated, but are not
shown in detail.

                                  Lateral acceleration in the carbody above 1st bogie


                    2,00
      ayc [m/s ]
     2




                    1,00
                    0,00
                   -1,00
                   -2,00
                           500      600            700           800            900     1000
                                                    Distance [m]


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


                                  Lateral acceleration in the middle of the carbody


                    2,00
      ayc [m/s ]
     2




                    1,00
                    0,00
                   -1,00
                   -2,00
                           500      600            700           800            900     1000
                                                     Distance [m]


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




                                                    71
                                     Dynamic analysis of simulated vehicle response




                                       Lateral acceleration in the carbody above 2nd bogie


         ayc [m/s ]     2,00
        2

                        1,00
                        0,00
                       -1,00
                       -2,00
                               500        600           700            800            900    1000
                                                          Distance [m]


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 the
dynamic behaviour but also a quasi-static contribution which occurs when a vehicle runs
with constant speed on ideal track with a constant curve radius, cant and wheel-rail
friction. 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 the
carbody is not tilted. The lateral accelerations in the carbody for a case where the radius
is 4067, cant is 180 mm and cant deficiency is 250 mm are presented in Figure 6-4 to 6-6

                                       Lateral acceleration in the carbody above 1st bogie

                  5.00
                  4.00
    ayc [m/s ]
    2




                  3.00
                  2.00
                  1.00
                  0.00
                 -1.00
                          500          600             700            800             900    1000
                                                         distance [m]

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 mm
                           and cant deficiency is 250 mm. Speed V = 385 km/h.




                                                          72
                                      Track geometry for high-speed railways




                                     Lateral acceleration in the middle of the carbody
                  5.00
    ayc [m/s ]    4.00
   2

                  3.00
                  2.00
                  1.00
                  0.00
                 -1.00
                         500         600            700            800            900      1000
                                                       distance [m]

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 mm
                          and cant deficiency is 250 mm. Speed V = 385 km/h.


                                     Lateral acceleration in the carbody above 2nd bogie
                  5.00
                  4.00
    ayc [m/s ]
   2




                  3.00
                  2.00
                  1.00
                  0.00
                 -1.00
                         500         600            700            800            900      1000
                                                      distance [m]

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 mm
                          and 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 the
case 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 large
horizontal curves with a high cant deficiency. The hunting frequency is much lower than
the stated condition of 10 Hz.




                                                       73
                         Dynamic analysis of simulated vehicle response



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, as
a final consequence, lead to a derailment of the following vehicle. The limit value
according to CEN/TC 256 WG 10 depends on axle load and is calculated using the
Prud’homme formula (see Section 5.5). The limit value for the used vehicle
configuration A in the present study is 44.2 kN which allows an extra margin of 15% for
statistical scatter.
According to CEN TC 256 WG 10 and UIC 518, track shift forces must be evaluated at a
slightly higher speed then the intended permissible speed. CEN stated that the vehicle
must be evaluated at 110% of permissible cant deficiency in curves. Kufver [16] came to
the conclusion that it may be reasonable to modify this condition slightly when
alignment alternatives with different radii are being evaluated, in order to use the same
test 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 these
cant deficiencies correspond to 110% of admissible cant deficiency, as earlier discussed
in Section 5.3. These relations are shown in shown in Table 6-3. The corresponding test
speed is 360 km/h in these investigations.

Table 6-3      Used values of cant deficiency and admissible cant deficiency according
               to 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 to 6-6 show simulation conditions for the evaluation of track shift forces.

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

      Train speed             Cant             Cant deficiency        Horizontal curve radius
        [km/h]               [mm]                   [mm]                       [m]

         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
                           Track geometry for high-speed railways




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

    Train speed              Cant            Cant deficiency        Horizontal curve radius
      [km/h]                [mm]                  [mm]                       [m]

        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              Cant            Cant deficiency        Horizontal curve radius
      [km/h]                [mm]                  [mm]                       [m]

        360                  200                    100                      5098
        360                  200                    150                      4369
        360                  200                    200                      3823
        360                  200                    250                      3398
        360                  200                    275                      3220
        360                  200                    300                      3059


6.2.2   Track irregularities

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




                                            75
                                Dynamic analysis of simulated vehicle response



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 dynamic
contribution of track irregularities which starts at 600 metres. Figure 6-7 shows the
whole simulated track including the transition curve. Note that these simulations are
made under the conditions of a lateral bumpstop between carbody and bogie. With a
smother suspension, i.e. a Hold-off-Device (HOD) or a tilting bogie bolster below the
secondary suspension, the dynamic peaks of the track shift forces would have been
reduced. The peak values of the track shift forces would have been much less with a
Hold-off-device in operation.



                              Track shift force 1st bogie, 2nd wheelset

                50000
                              Start of the horizontal
                40000         curve radius (360 m )

                30000
        S [N]




                20000

                10000

                      0
                          0      200        400         600   800      1000      1200   1400
                                                                                  Distance [m]


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 mm
                     and cant deficiency is 275 mm. Speed V = 360 km/h.
                     The slight disturbance from the transition curve is almost damped out
                     when 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 is
varied from 160 mm to 200 mm at a vehicle speed of 360 km/h, are shown in Figure 6-8
to Figure 6-9. The simulation results for other tracks are shown in Appendix C. No
significant differences between different cant values can be observed. The limit value is
reached 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.




                                                        76
                                     Track geometry for high-speed railways




                                   S2m (ht=160mm)                        S2m (ht=180mm)
                                   S2m (ht=200mm)                        S2m,lim
                   55
                   50
                   45
    S max [kN]




                   40
                   35
                   30
                   25
                   20
                        50   75 100 125 150 175 200 225 250 275 300 325 350
                                              Cant deficiency [mm]


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.



                                  S2m (ht=160mm)                        S2m (ht=180mm)
                                  S2m (ht=200mm)                        S2m,lim
                   50
                   45
                   40
      S max [kN]




                   35
                   30
                   25
                   20
                   15
                        50   75 100 125 150 175 200 225 250 275 300 325 350

                                             Cant deficiency [mm]

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.




                                                      77
                                       Dynamic analysis of simulated vehicle response



6.2.5                 Comparisons between different track irregularities

In this section comparisons between different track irregularities are presented. In Figure
6-10 and Figure 6-11 the track shift forces in relation to limit value (Smax/Slim) are
shown for cant ht = 180 mm. A comparison with a simulation without irregularities
shows the dynamic contribution.
It can be observed in Figure 6-11 that the maximum peak forces Smax in relation to the
limit Slim are not always increasing monotonously with increasing cant deficiency or
increasing magnitude of track irregularities. This is mainly due to non-linearity in the
wheel-rail contact or in the lateral bump-stop suspension. It is quite typical for cases
where just an occasional peak is registered and evaluated for each simulated case, which
leads to results with a limited statistical significance. Within the scope of this study it has
not been judged as possible to perform a full set of simulation on different tracks to gain
a full statistical significance. Instead, we have chosen the approximate approach to have
a margin of 15% in the limit value of track-shift forces, to allow for typical statistical
scatter; c.f. Section 5.5.



                                  Track 2                 Track 3                       Track 4
                                  Track 5                 Track 6                       No irregularities
                       1,5
        S max /Slim




                         1


                       0,5

                                                                                        ht=180 mm
                         0
                             50    75 100 125 150 175 200 225 250 275 300 325 350

                                                   Cant deficiency [mm]

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




                                                            78
                                        Track geometry for high-speed railways




                              Track 7                   Track 8                  Track 9
                              Track 10                  No irregularities
                   1,5


                    1
      Smax /Slim




                   0,5
                                                                                 ht=180 mm
                    0
                         50   75 100 125 150 175 200 225 250 275 300 325 350
                                                  Cant deficiency [mm]


Figure 6-11 Track shift force S (in relation to limit) as a function of cant deficiency
            hd 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 sources
of track irregularities, produce approximately the same results if the Q-values are the
same. 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.




                                                         79
                        Dynamic analysis of simulated vehicle response



6.2.6    Improvements of track irregularities

As mentioned earlier, a full study on the effect of track irregularities for different
operational cases, including sets of different high-speed rail vehicle configurations in
various conditions, is outside the scope and possibilities of this study. Therefore a
simplified procedure has been applied, just to give an indication whether lateral track
forces 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 cant
irregularities into account. There is no statistical analysis on different types and
amplitudes 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 this
study would produce somewhat optimistic results.
Also from the vehicle point of view there are simplifications, mainly due to the
assumption of a lateral bump stop in the suspension between bogie and carbody, instead
of 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 a
better ride and likely somewhat reduced peak lateral track forces. From this point of view
this study would produce somewhat conservative results.
With the above mentioned in mind some preliminary results and indications will be
shown and discussed below.




                                             80
                                                   Track geometry for high-speed railways



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



                                      150
     Track irregularity relative K0




                                      125
                                                                                      ht = 180 mm
                                      100

                                       75
                 [%]




                                       50

                                       25

                                        0
                                            100 125 150 175 200 225 250 275 300 325 350
                                                               Cant deficiency [mm]

Figure 6-12 Necessary improvements of track irregularities as a function of cant
            deficiency. Track 2 - 6.
            The results are presented relative quality class K0 according to Banverket
            based on the track irregularities measured on a curve between
            Simonstorp and Katrineholm.




                                                                    81
                                                Dynamic analysis of simulated vehicle response



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



                                100
    Track irregularity relative K0




                                                                                      ht = 180 mm
                                     75


                                     50
                [%]




                                     25


                                      0
                                          200    225          250         275          300       325   350
                                                              Cant deficiency [mm]

Figure 6-13 Necessary improvements of track irregularities as a function of cant
            deficiency. Track 7 - 10.
            The results are presented relative quality class K0 according to Banverket
            based on the track irregularities measured on tangent track between Åby
            and Nyköping.




                                                                     82
                                             Track geometry for high-speed railways



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



                                            Cant = 180 mm, 1st bogie, 2nd wheelset
                            60
                            55                                                              S2m,till
   Track shift force [kN]




                            50
                            45
                            40                                                              Track 3
                            35                                                              (K0)
                            30
                            25                                                              Track 5
                            20
                            15
                            10                                                              No track
                             5                                                              irregularities
                             0
                                 50   100    150      200       250       300         350
                                            Cant deficiency [mm]


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




                                                              83
                         Dynamic analysis of simulated vehicle response



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 vector
intercept of all wheel forces. The distance of the intercept vector from the middle of the
track plane can be determined by only knowing the vertical wheel forces. This distance
in relation to half the distance between contact points (bo) will lead to the intercept risk
factor E. The vehicle will run safe for E < 1 and begin to turn over for the value of 1. It
will become 1, when all windward wheels are unloaded. The value of E can not exceed
the value 1. In this study the intercept method risk factor E is calculated for the whole
vehicle, i.e all vertical forces for one side of the vehicle are summarized. Before
evaluation, 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 radii
were varied in accordance. After a few preliminary simulations where both a cant of 180
mm and 200 mm were used, a difference between these two values of cant were hard to
discern when evaluating the risk of vehicle overturning. As a result, only simulations
with 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 shall
not reach more than 0.9 x 0.75 m from the track centre towards the outer rail. In this
criterion there is a margin before the train really turns over. According to simulations this
margin is typically 3 – 5 m/s of wind velocity above the stated wind velocity of 23 m/s.




                                              84
                            Track geometry for high-speed railways



According to the above mentioned requirements the simulated speed is 350 km/h, i.e. the
tested 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 of
180 mm is chosen. The horizontal curve radius is chosen to suit speed and cant
deficiency, according to Table 6-7 below.
Table 6-7      Simulation conditions for vehicle overturning.
               Speed V = 350 km/h and cant ht = 180 mm

    Train speed              Cant             Cant deficiency        Horizontal curve radius
      [km/h]                 [mm]                  [mm]                       [m]

        350                  180                     150                      4380
        350                  180                     200                      3804
        350                  180                     250                      3362
        350                  180                     275                      3177


6.3.2    Track irregularities

The track irregularities that were used in the present study for simulations of vehicle
overturning are Track 5 and Track 10. The reason for not using other tracks in the
simulations were that it is important to have a suitable and adapted track standard when
evaluating vehicle overturning. If several very unlikely events are combined the resulting
worst 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 a
function of wind velocity for vehicle configuration B. Vehicle speed V = 350 km/h and
cant ht = 180 mm. The results are shown at four different values of cant deficiencies and
their corresponding radius.




                                             85
                                Dynamic analysis of simulated vehicle response




                  Intercept method risk factor,                        Intercept method risk factor,
                     R=4380 m, hd=150 mm                                  R=3804 m, hd=200 mm
               1,00                                                 1,00

               0,90                                                 0,90

               0,80                                                 0,80
    Eint [-]




                                                          Eint[-]
               0,70                                                 0,70

               0,60                                                 0,60

               0,50                                                 0,50
                      20 22 24 26 28 30                                    20    22 24 26 28 30
                        Wind velocity [m/s]                                     Wind velocity [m/s]

                  Intercept method risk factor,                        Intercept method risk factor,
                     R=3362 m, hd=250 mm                                  R=3177 m, hd=275 mm
               1,00                                                 1,00

               0,90                                                 0,90

               0,80                                                 0,80
    Eint [-]




                                                        Eint[-]




               0,70                                                 0,70

               0,60                                                 0,60

               0,50                                                 0,50
                      20    22 24 26 28 30                                 20    22 24 26 28 30
                           Wind velocity [m/s]                                  Wind velocity [m/s]

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

Permissible wind velocity from the most unfavourable direction for three different train
configurations are presented in Figure 6-16. Train configuration B has 4000 kg more
weight in the carbody behind the leading bogie. This condition must be taken into
consideration when evaluating safety against vehicle overturning.
The permissible wind velocity according to the intercept method risk factor for vehicle
configuration B at a cant deficiency of 250 mm is 23.4 m/s. In vehicle configuration C
the permissible wind velocity is calculated to 22.5 m/s. The difference between
configuration B and C is the height of c.g. for the carbody, c.f. Section 5.9.1. These




                                                     86
                                                      Track geometry for high-speed railways



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


                                           Permissible wind speed according to intercept method risk factor
                                28
                                27                                                             Train configuration A
   Wind velocity, vwind [m/s]



                                26                                                             Train configuration B
                                25                                                             Train configuration C
                                24
                                23
                                22
                                21
                                            ht = 180 mm
                                20
                                19
                                18
                                     125        150        175      200      225     250                 275       300
                                                                 Cant deficiency [mm]

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




                                                                       87
                                                   Dynamic analysis of simulated vehicle response



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


                                              Intercept method risk factor                     Vehicle overturning
                               30
  Wind velocity, vwind [m/s]




                                                                                                    ht = 180 mm
                               28

                               26

                               24

                               22

                               20
                                    125      150         175       200       225     250                 275         300
                                                                Cant deficiency [mm]

Figure 6-17 Allowed wind velocity as a function of cant deficiency.
            According to intercept method risk factor at simulated vehicle
            overturning. 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 about
350 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 the
time of this study. Therefore, there is some incertainty on this matter.




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                              Track geometry for high-speed railways



7         Consequences of freight trains operations

This chapter will discuss some consequences of different kinds of freight train operations
from a track geometry point of view. In order to do this, it is initially necessary to
identify the different categories of future freight trains that are likely to occur, with
speeds, total train mass, axle loads and other characteristics.
The main issue is how steep gradients that can be allowed with respect to possible train
mass hauled by different sizes of locomotives. Also other aspects will be discussed, such
as the influence of gradients with respect to braking performance, as well as possible
track cant and cant excess. Very briefly also the issue of permissible axle load will be
discussed.



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 flat
      wagons, also containing a various amount of road vehicle semitrailers are included
      in this category. The unit-loads are loaded and unloaded at large-scale terminals on
      non-electrified track, with cranes or heavy mobile lifts. Sometimes the wagons of
      such trains have long-stroke end buffers to limit the impact on sensible goods at
      wagon shunting operations. It is quite common that wagons for heavy mass goods
      are 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 an
      axle load of up to 22.5 tonnes and a maximum speed of 90 - 100 km/h, in some
      special cases up to 120 km/h. Freight wagons have a traditional design with
      standardised 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 25
      tonnes, in some cases likely up to 28 - 30 tons. In some cases they will have a wider
      and higher loading gauge (height 4.8 m), at least in Swedish domestic traffic, than
      today's internationally exchangeable wagons (maximum height 4.3 - 4.6 m). Train
      length is believed to stay within the internationally standardised 750 m, although
      longer trains may be considered in special cases. Train mass may in most cases stay
      within about 2000 - 2500 tonnes, which is 30 - 50% higher than today's ordinary
      trains. If high-strength automatic couplers are introduced in the future, train mass
      may be further increased on certain trains.
      Speeds will be maintained in the present range: around 90 - 120 km/h, possibly with
      an increased amount of traffic in the higher range. However, the use of tarpaulin
      covers on many loads, semi-trailers and swap bodies may prevent higher speeds than
      about 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 to
    category 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 in
    the 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. In
    the future, transport of containers and swap bodies (with stiff covers) may be
    transferred 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, on
      suitable 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 or
      automatic load transfer equipment.
    - Goods and pallets are in many cases loaded directly on the floor, thus goods is in
      many cases not secured from sliding on the floor or ‘moving around’ to some
      extent 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 may
      be self-propelled multiple-unit freight trains, with traction equipment in the
      wagons.
    - Locomotives and loaded wagons have a total centre of gravity lower than 2 m
      above 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 proper
      electronic wheel skid protection.
    - Trains have a limited mass and length, for quick acceleration, short stops and
      suitability for fast loading/unloading at small-scale terminals.
    - Due to the high average speed and short stops this type of trains will be able to
      follow - or almost follow - the speed pattern of fast regional and inter-regional
      passenger trains. This will increase the capacity on lines with a great share of fast
      passenger traffic. It will also enhance the productivity of such trains, making it
      possible to run 1000 - 1500 km per day, also under day-time, with an average
      annual performance of at least 200 - 300 kkm.




                                              90
                              Track geometry for high-speed railways



III. Freight trains for light express goods or mail, with high punctuality and service
     level.
      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 as
      such trains. The French TGV trains for ordinary mail are of this category. It has been
      discussed also to introduce similar fast mail trains in Sweden, but limited line
      capacity in mixed heavy freight operation makes it inconvenient. The possible
      introduction of future dedicated high-speed lines would make such trains more
      convenient.
      The characteristics of category III trains are:
      - Maximum speed 200 - 300 km/h, average speed in the range 160 - 250 km/h, on
        suitable track. Due to a good traction performance these trains will also be able to
        climb the same gradients as high-speed trains.
      - Trains just make very short underway stops for fast loading and unloading (3 - 10
        min), on electrified track sidings with loading platforms.
      - Goods are loaded in small containers or ‘baskets’ on board the train, thus
        preventing 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 to
        follow approximately the same speed pattern as high-speed passenger trains.
        They will be able to run at night- or daytime, likely without special restrictions
        due to limited capacity. They will have a high productivity, in most cases in the
        order 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-speed
passenger (or mail) trains only. As far as known there are two exceptions: (1) the first
generation of the German high-speed lines (Neubaustrecken) and (2) the North East
Corridor (New York - Washington DC) in the USA, in both cases with heavy freight
mixed with high-speed passenger operations. It is reported that some extra wear and
track maintenance has occurred. In Germany, axle loads up to 22.5 tonnes are allowed; in
the 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 freight
trains 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 the
      line capacity, although these problems can be reduced with proper infrastructure
      facilities (possibilities of quick overtaking) and a high time precision.
2.    Dynamic track loadings and track maintenance. Freight trains with heavy axle loads
      and simple suspensions may likely cause high dynamic track loadings and a quite
      high rate of track deterioration. A poor track standard with significant geometrical




                                               91
                            Consequences of freight trains operations



    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 normally
not allow heavy freight trains, i.e. trains of category I. In most cases other parallel lines
are available, otherwise it is anticipated either that speed is kept at 250 km/h as a
maximum, or that special measures are taken to maintain the track properly. As a third
alternative it would be possible to improve the rail vehicles in order to reduce their
sensitivity to track irregularities (active suspensions etc.).
For trains of category II a maximum axle load in the range of 20 - 22.5 tonnes is
foreseen. This is the range which is used for passenger trains on modern track in some
countries. In Germany, France and USA such passenger trains are run with ordinary
modern locomotives at axle loads between 20 and 23 tonnes. In the latter case - 23
tonnes in the USA, with a maximum speed of 200 km/h - the track is built up by 68 kg/m
rails. In Germany and France axle loads of locomotives in passenger trains are 20 - 21
tonnes 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 18
tonnes is used on locomotives in speeds around 200 km/h. In Sweden this track loading
was 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 elastic
rubber pads laid on concrete sleepers (type S3) with a spacing of 0.6 - 0.65 m. The elastic
rubber 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 and
is still used on several railways. To further increase the resistance against track
deterioration concrete sleepers with a larger support area may be considered in the
future [25] [27].
All the three major European rail vehicle suppliers - Alstom, Bombardier (former
Adtranz) and Siemens - offer passenger locomotives for around 200 km/h with an axle
load of 20 - 21 tonnes. They typically have a maximum tractive power of 6000 - 6500
kW (at the wheel periphery) and would be suitable for category II freight operations.
It is assumed that the Swedish authorities (mainly Banverket) will put relevant
requirements on freight wagons for speeds in the range of 160 - 180 km/h, i.e. not only
accepting the poor dynamic performance of ordinary freight wagons at these speeds. It
would 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 applicable
to the locomotives.
For freight trains of category III, i.e. high-speed trains, axle loads are assumed to be
within the range as defined in TSI; i.e. generally a maximum of 167 kN, although driven
axles are allowed to have static axle loads up to 177 kN at speeds not exceding 250 km/h.




                                               92
                             Track geometry for high-speed railways



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 kN
       160 km/h < Vlim ≤ 200 km/h           Qmax,lim ≤ 190 kN
       200 km/h < Vlim ≤ 250 km/h           Qmax,lim ≤ 180 kN
       250 km/h < Vlim ≤ 300 km/h           Qmax,lim ≤ 170 kN
       300 km/h and above                   Qmax,lim ≤ 160 kN
Note that it would be possible - also in this case - to give incentives for a good dynamic
performance 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 a
normal cant on lines with ordinary freight traffic. Similar cant is used in many other
countries, although up to 160 mm is applied in a few cases. There are at least two reasons
for 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 and
      pallets may be loaded directly on the floor and is secured from moving around just
      by friction, it seems important not to have too large track cant if the trains are
      stopped or is moving slowly on a canted curve. Because of the generally good track
      standard on high-speed tracks, with small anticipated dynamic lateral accelerations
      at low speeds, it would be possible to increase the track cant without infringing the
      safety against ‘moving around’. From this point of view it would likely be possible
      to increase the maximum cant to 160 or 170 mm. This is also the limit values of cant
      in the newly proposed CEN provisional standard on track for mixed freight and
      passenger traffic [7].
2. Cant excess should not be too high for slow trains. On high cant, the low wheels and
   rails would be highly loaded, possibly causing track deterioration. In the popular
   railway engineering traditions it is also said that high cant excess leads to excessive
   wear and damage on the low rail, due to the higher vertical force. According to
   investigations made by KTH in co-operation with Banverket [25] the latter problem
   is 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 wheels
   and rail are very small. Also from the track deterioration point of view it is very
   likely that a cant excess of 110 - 130 mm is acceptable occasionally, at least for
   vehicles with an axle load limited to 22 tonnes and a centre of gravity at maximum 2
   m above rail level (1.8 m for locomotives); i.e. freight trains category II. At a cant
   excess 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 force
   according to UIC 518.




                                              93
                                Consequences of freight trains operations



These principles and conclusions are also reflected in the newly proposed CEN
provisional 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, for
example mail trains, it may be possible to have a larger track cant, i.e 180 - 200 mm. This
is 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 and
a track cant of 160 mm. The cant excess at this speed is 112 mm. At 140 km/h the cant
excess is 94 mm.
More examples: Let us consider a case were heavy freight train (category I) is allowed to
run at 90 km/h. This is combined with conventional high-speed trains where the
permissible cant deficiency is maximised to 80 mm according to TSI for speeds over 300
km/h. At a top speed of 350 km/h for the high-speed train the corresponding cant is 123
mm and the smallest possible horizontal curve radius is 7120 m. This pertains to a cant
excess 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 according
to the preliminary conclusions of this study. Thus, the permissible cant is 135 mm and
the horizontal curve radius is 3755 m. Even this would be valid with a cant excess of
110 mm. This reduces the horizontal curve radius with 47%. The results are presented in
Table 7-1.

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

                                                              Conventional   Train with tilt
                                                                 train        technology

 Speed of high-speed trains                        km/h            350            350
 Speed of heavy freight trains                     km/h             90             90

 Cant deficiencya                                  mm              80b            250

 Cant excess                                       mm              110b           110b
 Cant (optimised)                                  mm              123            135
 Horizontal curve radius (optimised)                 m             7121          3755
 a. Valid for high-speed passenger train
 b. Recommended value according to CEN and TSI

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




                                                   94
                                Track geometry for high-speed railways



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

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

                                                            Conventional   Train with tilt
                                                               train        technology

 Speed of high-speed trains                      km/h             350           350
 Speed of freight train of category II           km/h             120           120

 Cant deficiencya                                 mm              80b           250

 Cant excess                                      mm             110b          110b
 Cant (optimised)                                 mm              135           158
 Horizontal curve radius (optimised)               m             6723          3543
 a. Valid for high-speed passenger train
 b. Recommended value according to CEN and TSI




                                                 95
                                 Consequences of freight trains operations



If the permissible speed for freight trains of category II increases to 160 km/h the
conditions become more favourable concerning maximised cant and optimised
horizontal curve radius. According to TSI a cant of 160 mm is allowed for mixed traffic
lines. For a conventional high-speed train the permissible cant deficiency is 80 mm at
speeds 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 the
tilting train a calculation gives a horizontal curve radius of 3526 m. The cant excess is
for this case only 74 mm, which is significantly lower than the permissible value. The
results are shown in Figure 7-3.
Table 7-3       Optimised horizontal curve radius for high-speed lines with fast freight
                trains of category II.
                Vmin = 160 km/h.

                                                               Conventional   Train with tilting
                                                                  train         technologya
 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
      Horizontal curve radius (optimised)             m             6023            3526
 a. High-speed passenger train
 b. Recommended value according to CEN and TSI




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 uphill
gradient, if the train has been stopped.
Secondly the train must be able to accelerate after it has been brought into motion. The
desired amount of acceleration, however, is dependent on the performance requirements
of the trains and on the desired capacity of the line - a slow acceleration of a freight train
will 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 on
downhill gradients. This is a question of braking capacity of the trains and also of
signalling distances.
We will briefly investigate these issues for the three train categories defined in 7.1.




                                                    96
                             Track geometry for high-speed railways



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 be
built 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 for
high-speed passenger trains.
With the current four-axled locomotives, class Rc (mass 78 tonnes), a maximum
trainload of 1400 tonnes can be hauled in gradients of 10 ‰. With this train load the
locomotive is able to bring the train in motion, with an available adhesion α = 0.25 and
running 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, be
very slow. In cases where the adhesion is just 0.25 all the time, it will not be able to reach
the normal maximum speed of the train (usually 90 - 100 km/h) in that gradient. In short
gradients, however, this limitation may not be severe, because the train will accelerate as
soon as the train has left the steep gradient.
The required signalling distance is dependent on the gradient: a long downhill gradient
will usually increase the required signalling distance in order to stop the train with
normal 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 normally
not be allowed on high-speed lines with a maximum speed of more than 250 km/h. It is
also believed that many lines for the speed range 200 - 250 km/h will not either be
designed for heavy freight trains, if gradients are considered. In many cases there are
parallel lines for heavy freight traffic. A limited number of lighter category I freight
trains 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 lines
for speeds above 250 km/h. Some of these technical conditions have been briefly
discussed in Section 7.2 (axle load) and 7.3 (cant and cant excess). In this section, the
gradients will be discussed.
The first requirement is that the gradient is limited in order to assure that the train can be
brought in motion with the available tractive force of the locomotive and the available
wheel-rail adhesion. Or inversely: the train mass must be limited depending on the
gradient.
As for trains in category I the tractive force with an available adhesion of 0.25 must
balance 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 of
3000 - 5000 m instead of down to 300 á 400 m. Therefore, in this case the curve radius is
assumed to be 3000 m. This will reduce the running resistance at starting, thus allowing
some more train mass in the same gradient.




                                              97
                            Consequences of freight trains operations



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

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

                 Gradient     Number           Train mass          Wagon mass
                   (‰)        of locos          (tonnes)            (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

The trains are assumed to contain 50 axles in the case of one locomotive and 100 axles in
the case of two locomotives. This is simple stepwise assumptions. However, a sensitivity
analysis has been made, showing that variation of the number of axles with 40% in the
case of one locomotive, changes the permissible train mass by just approx. 6 tonnes in a
25 ‰ gradient, which is not considered as significant. Thus, the number of axles in the
train 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 to
bring 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 remains
in the gradient. This may not be acceptable in long gradients, if high train performance
and/or capacity of the line are required. As a rough limit of what is considered as a long
gradient, 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 what
is indicated in Table 7-4. This is particularly important if the uphill gradient is located
immediately after a station or a signal, where freight trains stop frequently. These issues
have not been investigated in detail in this study. However, it is recommended to make
proper investigations in each real case of a high-speed line, provided that category II
freight trains are planned to be run on the actual line. Traffic simulations must be done
with a proper simulation model.
It should be noted that the braking performance of category II freight trains must be
higher 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



                                               98
                                                          Track geometry for high-speed railways



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



                                      2500                                                 Wagon mass, one loco
                                                                                           Wagon mass, two locos
                                                                                           Train mass, one loco
        Possible train mass [tonne]




                                                                                           Train mass, two locos
                                      2000

                                                       2 locos á 84 ton
                                      1500

                                                  1 loco á 84 ton
                                      1000


                                        500


                                          0
                                              0             10            20              30        40         50
                                                                           Gradient [‰ ]


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




                                                                           99
Consequences of freight trains operations




                  100
                            Track geometry for high-speed railways



8        Possible track geometry

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



8.1      Horizontal curve radius

Examples of possible horizontal curve radius are given in the following tables and
figures. Tables 8-1 to 8-4 show examples of horizontal curve radius at different values of
cant deficiencies. The applied cant will be varied from 150 mm to 200 mm at different
speeds 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 independent
variables and parameters.
Note that the cant, and consequently also the curve radius, may be limited if freight trains
of category I or II are to be run on the high-speed track. This issue has been dealt with in
Section 7.3.




                                            101
                                                             Possible track geometry




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

          Speed [km/h]
                                                      200         250         280        300          330     350
 Cant deficiency [mm]

                                   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




                                                  V=200 km/h                V=280 km/h                V=350 km/h
                                  6000
    Horizontal curve radius [m]




                                  5000
                                                                                             ht = 150 mm
                                  4000

                                  3000

                                  2000

                                  1000

                                    0
                                         100    125     150       175       200        225      250     275   300
                                                                Cant deficiency [mm]


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.




                                                                      102
                                                     Track geometry for high-speed railways




Table 8-2                                Examples of horizontal curve radius at four different values of cant
                                         deficiencies.
                                         Speeds varied from 200 km/h to 350 km/h. Cant ht = 160 mm.

          Speed [km/h]
                                                      200         250         280         300         330     350
 Cant deficiency [mm]

                                   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




                                                 V=200 km/h              V=280 km/h                  V=350 km/h
                                 6000
   Horizontal curve radius [m]




                                 5000
                                                                                              ht = 160 mm
                                 4000

                                 3000

                                 2000

                                 1000

                                    0
                                        100    125     150     175     200    225              250     275    300
                                                              Cant deficiency [mm]

Figure 8-2                               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 = 160 mm.




                                                                     103
                                                            Possible track geometry




Table 8-3                                Examples of horizontal curve radius at four different values of cant
                                         deficiencies.
                                         Speeds varied from 200 km/h to 350 km/h. Cant ht = 180 mm.

          Speed [km/h]
                                                      200        250         280            300          330     350
 Cant deficiency [mm]

                                   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




                                                 V=200 km/h                V=280 km/h                   V=350 km/h
   Horizontal curve radius [m]




                                 6000

                                 5000
                                                                                             ht = 180 mm
                                 4000

                                 3000

                                 2000

                                 1000

                                    0
                                        100    125      150     175        200        225         250     275   300
                                                              Cant deficiency [mm]


Figure 8-3                               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 = 180 mm.




                                                                     104
                                                     Track geometry for high-speed railways




Table 8-4                               Examples of horizontal curve radius at four different values of cant
                                        deficiencies.
                                        Speeds varied from 200 km/h to 350 km/h. Cant ht = 200 mm.

          Speed [km/h]
                                                      200         250         280          300          330     350
 Cant deficiency [mm]

                                  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




                                                 V=200 km/h                V=280 km/h                  V=350 km/h
   Horizontal curve radius [m]




                                 6000

                                 5000                                                         ht = 200 mm
                                 4000

                                 3000

                                 2000
                                 1000

                                    0
                                        100    125      150      175       200       225         250     275   300
                                                               Cant deficiency [mm]


Figure 8-4                              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 = 200 mm.




                                                                     105
                                                            Possible track geometry




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

   Horizontal curve radius [m]                     Cant deficiency, hd=200            Cant deficiency, hd=250
                                 6000

                                 5000

                                 4000

                                 3000

                                 2000
                                                                                            ht = 150 mm
                                 1000

                                   0
                                        100         150            200       250              300               350
                                                                    Speed [km/h]

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.



                                                   Cant deficiency, hd=100            Cant deficiency, hd=150
                                                   Cant deficiency, hd=200            Cant deficiency, hd=250
   Horizontal curve radius [m]




                                 6000

                                 5000

                                 4000

                                 3000

                                 2000
                                                                                            ht = 160 mm
                                 1000

                                   0
                                        100         150            200       250              300               350
                                                                    Speed [km/h]

Figure 8-6                               Horizontal curve radius R as a function of speed V.
                                         The different curves show conceivable values of cant deficiency hd.
                                         Cant ht = 160 mm.




                                                                     106
                                                                 Track geometry for high-speed railways




                                                              Cant deficiency, hd=100                Cant deficiency, hd=150
                                                              Cant deficiency, hd=200                Cant deficiency, hd=250
                   Horizontal curve radius [m]   6000
                                                 5000
                                                 4000
                                                 3000
                                                 2000
                                                 1000                                                       h t = 180 mm

                                                    0
                                                        100      150            200            250            300              350
                                                                                 Speed [km/h]


Figure 8-7                                          Horizontal curve radius R as a function of speed V.
                                                    The different curves show conceivable values of cant deficiency hd.
                                                    Cant ht = 180 mm.



                                                              Cant deficiency, hd=100              Cant deficiency, hd=150
                                                              Cant deficiency, hd=200              Cant deficiency, hd=250
   Horizontal curve radius [m]




                                       6000
                                       5000
                                       4000
                                       3000
                                       2000
                                       1000                                                                ht = 200 mm

                                                  0
                                                   100         150             200            250             300              350
                                                                                Speed [km/h]

Figure 8-8                                          Horizontal curve radius R as a function of speed V.
                                                    The different curves show conceivable values of cant deficiency hd.
                                                    Cant ht = 200 mm.




                                                                                 107
                                                         Possible track geometry



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 speed
is presented. The values have been rounded up to nearest 100 m. There are different
minimum values of vertical curve radius dependent of different requirements of limiting
values on a crest or in a hallow. The limited vertical accelerations have been presented in
Section 3.6.6.

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

                 Speed [km/h]                            200         250      280       300       330       350
 Vertical curve radius [m]                             [km/h]      [km/h]   [km/h]    [km/h]    [km/h]    [km/h]

 Recommended value                                     14100       22000     27500    31600     38200      43000
 Minimum value                                          7100       11000     13800    15800     19100      21500
 without tolerance
 Minimum value on a crest                               6400       10000     12500    14400     17400      19600
 Minimum value in a hallow                              5400       8500      10600    12200     15000      16600



                                                 Recommended minimum value according to CEN/TC
                                  60000          Minimum value without tolerance according to CEN/TC
      Vertical curve radius [m]




                                                 Minimum value with tolerance (on a crest) according to CEN/TC
                                  50000          Minimum value with tolerance (in a hallow) according to CEN/TC

                                  40000

                                  30000

                                  20000

                                  10000

                                      0
                                          200                250                     300                    350
                                                                   Speed [km/h]


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




                                                                   108
                             Track geometry for high-speed railways



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 lower
value must be considered. This is mainly due to the risk of loads “moving around” on the
floor of the wagon. Hence, higher values of cant than 160 mm should not normally be
chosen in such cases.
The literature study also made a compilation over different worldwide projects and their
used values of track cant, cant deficiency, horizontal curve radius, gradients and vertical
curve radius.
The recommended value of cant deficiency according to TSI is 100 mm (for
conventional trains up to 300 km/h) but higher values may be allowed for lines with
tough 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 cant
deficiency values. To further investigate this issue is one of the main contributions of this
study.
Transition curves should be long if tilting trains are considered. The duration in the
transition 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 of
compensation in the body tilt system favour longer clothoids”. This proposal
corresponds also to the rate of cant and the rate of cant deficiency recommendations
according 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 of
350 km/h with the stability criteria being considered. In other words, it could be
concluded that the vehicle configuration has the required properties that was foreseen
before the simulations started. The simulated wheelset quidance is stiffer than on current
Swedish self-steering bogie designs, but is more flexible than traditional quite stiff
design from continental Europe. These characteristics of the vehicles have been studied
before but not simulated for speeds in this range.
It is important, however, that wheels and rails have suitable shapes in the wheel-rail
interface, 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 maintain
the European lateral track shift criteria at 350 km/h and at a cant deficiency in the order
of 250 mm. However, it is likely impossible to get required performance without
improving the track quality compared to current Swedish standards for 200 km/h. In
order to achieve a top-speed of 350 km/h and a cant deficiency of 250 mm it seems
necessary to improve the track quality with at least 25%, i.e. track irregularities should
be at least 25% less in magnitude. This conclusion is, however, just an indication based
on simplified assumptions. It is outside the scope and possibilities of this study to make a
detailed 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, and
a roof height in the order of 3.6 m, it is technically possible to make a train design for
appropriate safety at strong side-wind at a cant deficiency up to 250 mm. In addition to
the aerodynamic requirements, also the mass and mass distribution of the leading car
have 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 be
appropriate. The height of the c.g. should preferably be low. For motor-coaches with
traction equipment in bogies and underneath the floor, these properties are most likely
realistic.


9.3      Conclusions on horizontal and vertical curve radii

The horizontal curve radius is a function of allowed cant, cant deficiency and speed. The
curve radius must be sufficiently large to cope with the desired speed for both
conventional and tilting trains respectively. For example, if conventional high-speed
trains are to be run at 280 km/h and and tilting trains at 350 km/h, the horizontal curve
radius should be at least in the order of 3200 m. This requires a track cant of 200 mm and
a 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 deficiency
for tilting trains to 225 mm, a minimum curve radius of 3750 m is needed for tilting
trains at 350 km/h. In this case it would be possible to accomodate also freight trains
category 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 all
sections of the line. For example, in the vincinity of stations where most trains are
stopping, the speed will be lower and the curve radius can be accordingly less.
The standards of Banverket concerning vertical curve radius are quite conventional in
relation to the proposals from TSI. These standards are, in turn, close to the standards of
DB and several other railways. The minimum curve radius is 0.175 times the square of
speed (in km/h), with tolerances 0.16 times the square of speed on a crest and 0.135
times the square of speed in a hallow. This requires a minimum vertical radius of 21500
m at 350 km/h (19600 and 16500 m with tolerances on a crest and in a hallow,
respectively).



                                            110
                            Track geometry for high-speed railways



9.4      Conclusions on freight train operations

It is anticipated that heavy freight trains should normally not be allowed on high-speed
lines for speeds above 250 km/h.
If only high-speed freight trains (category III, for express goods or mail) without goods
and pallets loaded directly on the floor are operated, it may be possible to have a quite
large track cant in the range of 180 - 200 mm. If freight trains category II with containers
and 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 a
category II freight trains (containers and swap bodies) running at a modest speed of 120
km/h.
If only freight trains category III - high-speed for light express or mail - are allowed the
gradients 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 halued
by one four-axled locomotive.



9.5      Further research

This study primary deals with track geometry, having vehicle dynamics as a secondary
issue.
It is important to include passenger comfort in further studies.
Also hunting stability simulations have to be done under a more complete set of
conditions.
A full study on the effect of track irregularities for different operational cases, including
sets of different high-speed rail vehicle configurations in various conditions, is outside
the scope and possibilities of this study. A simplified procedure has been applied, just to
give an indication whether lateral track forces and track quality would be in the right
order of magnitude. Future studies should penetrate this issue in more detail. In this
connection, also the issue of track maintenance requirements should be penetrated
comprehensively.
It should be further investigated (in each individual case) whether the recommended
gradients are appropriate with respect to the train´s ability to accelerate quickly on a line
with 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 obstacles
should be done. Such optimisation studies must be done for each individual section of
proposed high-speed line.




                                            111
Conclusions and further research




             112
                         Track geometry for high-speed railways



References
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       and Rail vehicles), Kompendium, Del 1 - Järnvägssystem, KTH Järnvägsteknik,
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[2]    Andersson E. and Berg M.: Järnvägssystem och spårfordon (Railway systems
       and Rail vehicles), Kompendium, Del 2 - Spårfordon, KTH Järnvägsteknik,
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[3]    Andersson E., Berg M. and Stichel S.: Spårfordons dynamik (Rail vehicle
       dynamics), Kompendium, KTH Järnvägsteknik, 1999.

[4]    Banverket: Spårgeometrihandboken (Track geometry handbook), BVH 586.40,
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[5]    Banverket: Tillåten hastighet mht spårets geometriska form (Permissible speed
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[6]    Banverket: Spårlägeskontroll och Kvalitetsnormer - Central mätvagn Strix
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[7]    CEN: Railway application - Track alignment design parameters - Track gauges
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[8]    CEN: Railway application - Testing for acceptance of the running
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[9]    Deutsche Bahn, DB: Netzinfrastruktur Technik entwerfen; Linienführung (Net
       Infrastructure Technical Draft; Alignment), 800.0110, DB, Germany, 1999.

[10]   Deutsche Bahn, DB: Bahnanlagen entwerfen - allgemeine Entwurfsgrundlagen,
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[11]   Esveld, C.: Modern railway track, NS Permanent Way Department, 1989.

[12]   European Association for Railway Interoperability (AEIF): Trans-European
       High-Speed Rail system, Technical Specification for Interoperability (TSI),
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[13]   European Association for Railway Interoperability (AEIF): Trans-European
       High-Speed Rail system, Technical Specification for Interoperability (TSI),
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                                         113
                                      References




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[15]   Hecke A.: Effects of future mixed traffic on track deterioration, Master of
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[16]   Kufver, B.: Optimisation of horizontal alignments for railways, Procedures
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[17]   Rail International: Planning and building of the German Federal Railway´s new
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[18]   S.N.C.F: La voie Ferrée, Techniques de construction et D’entretien. Alias, J et
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[19]   Central Japan Railway Company: Data Book 2000.

[20]   Hohnecker, E.: Zukunftssichere Trassierung von Eisenbahn-
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[21]   Lippert, S.: On side-wind stability of trains, Master of science thesis, TRITA-
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[22]   Krieg R.: Extreme wind statistics for Säve and Arlanda. Reportet by order of
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[23]   Lukascewicz, P.; Energy Consumption and Running Time for Trains - Modelling
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[24]   UIC: Test and acceptance of railway vehicles from the points of view of dynamic
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                                         114
                         Track geometry for high-speed railways



[28]   Andersson, E. : Personal communication with prof. Evert Andersson, KTH
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                                         115
References




  116
                          Track geometry for high-speed railways



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]
v 10'        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]




                                           118
                              Track geometry for high-speed railways



∆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
                      Track geometry for high-speed railways



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 European
                  Standardisation)
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
                                   Track geometry for high-speed railways



Appendix C - Further diagrams on track shift forces


                                  S2m (ht=160mm)                       S2m (ht=180mm)
                                  S2m (ht=200mm)                       S2m,lim
                 60

                 55

                 50
    S max [kN]




                 45

                 40

                 35

                 30
                      50   75 100 125 150 175 200 225 250 275 300 325 350
                                             Cant deficiency [mm]

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



                                  S2m (ht=160mm)                        S2m (ht=180mm)
                                  S2m (ht=200mm)                        S2m,lim
                 55

                 50

                 45
    S max [kN]




                 40

                 35

                 30

                 25
                      50   75 100 125 150 175 200 225 250 275 300 325 350
                                             Cant deficiency [mm]

Figure C-2             Track shift force S as a function of cant deficiency hd.
                       Track 3. 2nd wheelset, 1st bogie.



                                                   123
                                   Further diagrams on track shift forces




                                 S2m (ht=160mm)                             S2m (ht=180mm)
                                 S2m (ht=200mm)                             S2m,lim
                55
                50
                45
    Smax [kN]




                40
                35
                30
                25
                20
                     50   75 100 125 150 175 200 225 250 275 300 325 350
                                     Cant deficiency [mm]

Figure C-3            Track shift force S as a function of cant deficiency hd.
                      Track 4. 2nd wheelset, 1st bogie.



                                 S2m (ht=160mm)                             S2m (ht=180mm)
                                 S2m (ht=200mm)                             S2m,lim
                55
                50
                45
    Smax [kN]




                40
                35
                30
                25
                20
                     50   75 100 125 150 175 200 225 250 275 300 325 350
                                            Cant deficiency [mm]

Figure C-4            Track shift force S as a function of cant deficiency hd.
                      Track 5. 2nd wheelset, 1st bogie.




                                                   124
                                   Track geometry for high-speed railways




                                  S2m (ht=160mm)                        S2m (ht=180mm)
                                  S2m (ht=200mm)                        S2m,lim
                 50

                 45

                 40
    Smax [kN]




                 35

                 30

                 25

                 20
                      50   75 100 125 150 175 200 225 250 275 300 325 350
                                             Cant deficiency [mm]

Figure C-5             Track shift force S as a function of cant deficiency hd.
                       Track 6. 2nd wheelset, 1st bogie.



                                  S2m (ht=160mm)                        S2m (ht=180mm)
                                  S2m (ht=200mm)                        S2m,lim
                 55
                 50
                 45
    S max [kN]




                 40
                 35
                 30
                 25
                 20
                      50   75 100 125 150 175 200 225 250 275 300 325 350
                                             Cant deficiency [mm]

Figure C-6             Track shift force S as a function of cant deficiency hd.
                       Track 7. 2nd wheelset, 1st bogie.




                                                   125
                                    Further diagrams on track shift forces




                                  S2m (ht=160mm)                             S2m (ht=180mm)
                                  S2m (ht=200mm)                             S2m,lim
                 50

                 45

                 40
    S max [kN]




                 35

                 30

                 25

                 20
                      50   75 100 125 150 175 200 225 250 275 300 325 350
                                             Cant deficiency [mm]

Figure C-7             Track shift force S as a function of cant deficiency hd.
                       Track 8. 2nd wheelset, 1st bogie.



                                  S2m (ht=160mm)                             S2m (ht=180mm)
                                  S2m (ht=200mm)                             S2m,lim
                 50
                 45
                 40
    S max [kN]




                 35
                 30
                 25
                 20
                 15
                      50   75 100 125 150 175 200 225 250 275 300 325 350
                                             Cant deficiency [mm]

Figure C-8             Track shift force S as a function of cant deficiency hd.
                       Track 9. 2nd wheelset, 1st bogie.




                                                    126
                                  Track geometry for high-speed railways




                                 S2m (ht=160mm)                        S2m (ht=180mm)
                                 S2m (ht=200mm)                        S2m,lim
                 50
                 45
                 40
    S max [kN]




                 35
                 30
                 25
                 20
                 15
                      50   75 100 125 150 175 200 225 250 275 300 325 350
                                         Cant deficiency [mm]

Figure C-9            Track shift force S as a function of cant deficiency hd.
                      Track 10. 2nd wheelset, 1st bogie.




                                                  127
                                       Further diagrams on track shift forces




                                     Track 2                                    Track 3
                                     Track 4                                    Track 5
                      1,5
    S max /Slim [-]



                       1


                      0,5

                                                                                     ht=160 mm
                       0
                            50   75 100 125 150 175 200 225 250 275 300 325 350
                                            Cant deficiency [mm]

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.



                                     Track 2                                    Track 3
                                     Track 4                                    Track 5
                                     Track 6                                    No irregularities
                      1,5
    Smax /Slim [-]




                       1


                      0,5

                                                                                     ht=180 mm
                       0
                            50   75 100 125 150 175 200 225 250 275 300 325 350
                                               Cant deficiency [mm]

Figure C-11 Track shift force Smax/Slim (-) as a function of cant deficiency hd.
            Cant ht = 180 mm. Track 2 - Track 6. 2nd wheelset, 1st bogie.




                                                       128
                                      Track geometry for high-speed railways




                                    Track 2                                Track 3
                                    Track 4                                Track 5
                                    Track 6                                No irregularities
                     1,5
    Smax /Slim [-]



                      1


                     0,5

                                                                               ht=200 mm
                      0
                           50   75 100 125 150 175 200 225 250 275 300 325 350
                                           Cant deficiency [mm]

Figure C-12 Track shift force Smax/Slim (-) as a function of cant deficiency hd.
            Cant ht = 200 mm. Track 2 - Track 6. 2nd wheelset, 1st bogie.



                                    Track 7                                Track 8
                                    Track 9                                Track 10
                                    No irregularities
                     1,5
    Smax /Slim [-]




                      1


                     0,5
                                                                                ht=160 mm
                      0
                           50   75 100 125 150 175 200 225 250 275 300 325 350
                                               Cant deficiency [mm]

Figure C-13 Track shift force Smax/Slim (-) as a function of cant deficiency hd.
            Cant ht = 160 mm. Track 7 - Track 10. 2nd wheelset, 1st bogie.




                                                      129
                                       Further diagrams on track shift forces




                                     Track 7                                    Track 8
                                     Track 9                                    Track 10
                                     No irregularities
                      1,5
    S max /Slim [-]



                       1


                      0,5
                                                                                    ht=180 mm

                       0
                            50   75 100 125 150 175 200 225 250 275 300 325 350
                                                Cant deficiency [mm]

Figure C-14 Track shift force Smax/Slim (-) as a function of cant deficiency hd.
            Cant ht = 180 mm. Track 7 - Track 10. 2nd wheelset, 1st bogie.



                                     Track 7                                    Track 8
                                     Track 9                                    Track 10
                                     No irregularities
                      1,5
     Smax /Slim [-]




                        1


                      0,5
                                                                                     ht=200 mm

                        0
                            50   75 100 125 150 175 200 225 250 275 300 325 350
                                                Cant deficiency [mm]

Figure C-15 Track shift force Smax/Slim (-) as a function of cant deficiency hd.
            Cant ht = 200 mm. Track 7 - Track 10. 2nd wheelset, 1st bogie.




                                                       130
                                   Track geometry for high-speed railways



Appendix D - Further diagrams on vehicle overturning


                            Intercept method risk factor, R=4380 m, hd=150 mm
               1.00
               0.90
               0.80
               0.70
               0.60
   E int [-]




               0.50
               0.40
               0.30                                                           Overturning
               0.20
               0.10
               0.00
                      15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
                                        Wind speed [m/s]

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




                            Intercept method risk factor, R=3804 m, hd=200 mm
               1.00
               0.90
               0.80
               0.70
               0.60
   Eint [-]




               0.50
               0.40
               0.30                                                         Overturning
               0.20
               0.10
               0.00
                      15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
                                       Wind speed [m/s]

Figure D-2             Intercept method risk factor E as a function of wind velocity where cant
                       deficiency hd = 200 mm.
                       Vehicle speed V = 350 km/h and cant ht = 180 mm.



                                                   131
                                 Further diagrams on vehicle overturning




                          Intercept method risk factor, R=3362 m, hd=250 mm
              1.00
              0.90
              0.80
              0.70
              0.60
   Eint [-]




              0.50
              0.40
                                                                           Overturning
              0.30
              0.20
              0.10
              0.00
                     15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
                                      Wind speed [m/s]

Figure D-3           Intercept method risk factor E as a function of wind velocity where cant
                     deficiency hd = 250 mm.
                     Vehicle speed V = 350 km/h and cant ht = 180 mm.




                          Intercept method risk factor, R=3177 m, hd=275 mm
              1.00
              0.90
              0.80
              0.70
              0.60
   Eint [-]




              0.50
              0.40
                                                                      Overturning
              0.30
              0.20
              0.10
              0.00
                     15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
                                      Wind speed [m/s]

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




                                                  132
                            Track geometry for high-speed railways



Appendix E - Overturning due to side-wind

The aim of this Appendix is to describe the calculation of the wind-induced forces and
moments and provide the reader with a short introduction of how to determine the
aerodynamic coefficients and a reference wind velocity.
As exact aerodynamic train data as possible and a good knowledge of the wind
conditions at the track side are the most important conditions to get accurate values for
the forces acting on the train. Up to today it is not easy to get this data - especially the
wind data - with a satisfying accuracy. A problem when trying to define side-wind
stability is that these two parameters with the highest uncertainty are also the most
sensitive 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 ambient
wind that is blowing at the track side. The speed of this natural wind is in the following
named as wind velocity vW. Apart from the natural wind velocity, also the wind caused by
the speed of the train has to be considered. This wind velocity has got the same absolute
value as the train speed and is in the following called train speed vT. The wind velocity
and the train speed can be summarized to a resulting wind velocity vres. The angle
between train speed and resulting wind velocity is called yaw angle Ψ.
The quantities are shown in Figure E-1.




                      vT                                             vT
                                                                      Ψ

                                                                          vres
                                                              vW



Figure E-1     wind velocity vW and train speed vT, added to resulting wind velocity
               vres. 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 or
numerically (see Section E.2). They are usually assumed to be independent of train speed
and density of air, but depend on the flow around the train, i.e. the yaw angle.




                                            133
                                        Overturning due to side-wind




It has been shown that the greatest side-wind forces are induced with a wind velocity
approximately normal to the train speed. Now the absolute value of the resulting wind
velocity and the yaw angle can be calculate with the Pythagorean formula (Figure E-2):
                                                                               2   2
                          vT                                 v res =    vW + v T
                     Ψ
                                             vT    vW
   vW                    vres                                         vW
                                                             Ψ = atan -----
                                                                          -
                                                                       vT

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

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

                                        1
        Drag force              Fx, w = -- ⋅ C ( Ψ ) ⋅ ρ ⋅ h C ⋅ w C ⋅ v res
                                         -                               2             [N]         (E-1)
                                        2 D

                                        1
        Side force              Fy, w = -- ⋅ C ( Ψ ) ⋅ ρ ⋅ h C ⋅ l C ⋅ v res
                                         -                               2             [N]         (E-2)
                                        2 S

                                        1
        Lift force              Fz, w = -- ⋅ C ( Ψ ) ⋅ ρ ⋅ w C ⋅ lC ⋅ v res
                                         -                              2              [N]         (E-3)
                                        2 L

                                        1
        Roll moment             Mx, w = -- ⋅ C ( Ψ ) ⋅ ρ ⋅ h 2 C ⋅ lC ⋅ v res
                                         -                                2            [N]         (E-4)
                                        2 R

                                         1
        Pitch moment            M y, w = -- ⋅ C ( Ψ ) ⋅ ρ ⋅ w C ⋅ l 2C ⋅ v res
                                          -                                2           [N]         (E-5)
                                         2 P

                                        1
        Yaw moment              Mz, w = -- ⋅ C ( Ψ ) ⋅ ρ ⋅ h C ⋅ l 2C ⋅ v res
                                         -                                2            [N]         (E-6)
                                        2 Y

CD:           Drag coefficient                                                               [-]
CS:           Side coefficient                                                               [-]
CL:           Lift coefficient                                                               [-]
CR:           Roll coefficient                                                               [-]
CP:           Pitch coefficient                                                              [-]
CY:           Yaw coefficient                                                                [-]




                                                     134
                             Track geometry for high-speed railways



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 car
body. Coefficients related to other geometrical parameters, like length over buffers, total
height, projected areas etc., can also be found in other studies. This has to be considered
when comparing the coefficients from different studies. Secondly, the location of the
coordinate system is important when defining the forces and moments. The coefficients
used in this study are determined for a coordinate system located in the middle of the two
bogie pivots in height of the track plane. The coordinate system is shown in Figure E-3.




                        g
                                                                                     vT

                                                                          x




                                                      Fx,w

                                             Mx,w
                                                         Fy,w
                                                                                     y
                                                      My,w
                                                  Mz,w
                                           Fz,w
                                                         track plane (top of rail)




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




                                             135
                                 Overturning due to side-wind




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 the
needed size to take full scale models do not exist, and outdoor tests fail – though giving
real data - because of the rareness of suitable and well-defined wind conditions.
Deutsche Bahn tried within the Transaero project, a project of the European Community
dealing i.a. with side-winds, to make full scale tests with trains on real track with wind
shielding devices. One of the greatest problems has been that much time got lost by
waiting for strong wind conditions. When high wind velocities were reached it was often
a problem to arrive without delay at the track sections where the measurements were to
be carried out. This because preparing a test train with necessary instrumentation and
staff 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 data
from wind tunnels and computations, thus to obtain basic data for verifying scaled tests
and computer models.
Another disadvantage of full scale model tests on real trains is that the train must already
exist. 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 common
way to obtain accurate coefficients. A good copy not only of the train but also of ground
effects (e.g. ground roughness due to trees, houses, etc.), turbulent flow, track (viaducts,
embankments), etc. is necessary for good results. For instance, relative velocity between
vehicle and track/ground is very important. Scale effects and critical Reynold numbers
have also to be considered.
With improved computer capacity and falling computer prices the determination of the
aerodynamical coefficients by numerical simulation (CFD calculation) is becoming more
and more common. To calculate the coefficients, different mathematical models exist.
One of the biggest disadvantages of the computer models are the simplifications that
have to be made in order to get suitable simulation times. Nevertheless, carefully made
CFD 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 computed
forces and moments showed a good agreement of the results. For yaw angles between Ψ
= 10°…30° the computered C S , C L and C R values are lower than the wind tunnel data,
the maximum error is 20%, so that the wind tunnel aerodynamic coefficients can be
regarded as more conservative in this range of these angles. It is very important to point
out that only the relative error between wind tunnel and computed results has been
determined. 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 wind
tunnel results.




                                            136
                             Track geometry for high-speed railways



It can be assumed that with further increased computer performance the results become
more and more accurate.
A problem for all the three methods is the tilting of the train. The tilting angle of the train
is not constant when running on a track. On the one hand the train will be tilted to the
leeward side by the wind loads and to the outer side when running in a curve with cant
deficiency. On the other hand, tilting to the inner side must be considered due to track
cant and a possible tilt system of the train when passing a curve. It is difficult to decide
for which tilting angle the coefficients should be determined. A comparison that has been
made at Bombardier for the Norwegian airport shuttle between Oslo - Gardermoen
showed a difference between tilting 3,5° outwards and 6,5° inwards of C L and C R
values of about 20% at 20° yaw angle [27]. A solution would be to combine the
multibody simulation program with a CFD program to determine the aerodynamic
coefficients at every time step. However, this would cause unacceptable high computing
times. Thus, there is a risk that the overturning wind forces are somewhat underestimated
on 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. This
effect 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 have
been 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 would
go wide beyond the scope of this work. The aim of this section is to provide the reader
with the certainty that there are many things that have to be considered when
determining aerodynamic coefficients. The used aerodynamic data in this study is
assumed to be appropriate in the range of today’s determination possibilities. Further
work on the problem of determining aerodynamic coefficients is an important issue to
get 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 this
study are listed. The wind is blowing from the right side of the vehicle i.e. the inside of
the 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 are
shown. They have been calculated by Bombardier Transportation by CFD [27]. They can
be seen as typical for state-of-the-art for well designed vehicles (2001).




                                             137
                            Overturning due to side-wind




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

    Ψ         CD           CS           CL             CR       CP         CY
 [degree]     [-]          [-]          [-]            [-]      [-]        [-]

    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
                              Track geometry for high-speed railways



Appendix F - Train mass versus gradient

The locomotive of the freight train must be able to produce sufficient tractive force in
order to bring the train into motion and to maintain a certain speed or acceleration. The
tractive force has firstly to balance the total running resistance, including gradient
resistance, secondly to accelerate the train. The basic requirement is to overcome the
resistance 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]:

                                                            2
                 FRT = F MA + F M ( v ) + F D ( v ) + FD ( v ) + F C + FG              (F-1)

where
   FMA       = Mechanical resistance on straight track, due to wheel rail friction, bearing
               friction 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 above
mentioned references are used.




                                              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]):

          FMA = K s ( 30 ⋅ n axl + a Ql ⋅ m l ⋅ g + 65 ⋅ n axw + a Qw ⋅ m w ⋅ g ) [N]   (F-2)

where
   Ks        = 2 at the starting moment;
   Ks        = 1 otherwise.
                           –3
   aQl = aQw = 0, 6 ⋅ 10         (assumed that wheelset guidance has about the same
                                 flexibility and alignment as ordinary European freight
                                 wagons)
   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 in
motion, i.e. Ks is 2 instead of 1. If the tractive force of the locomotive is maintained after
the starting moment there will be a certain excess in tractive force and therefore an extra
push in train acceleration.


F.1.3     Resistance linearly dependent of speed

In this section mechanical resistance and air drag, linearly dependent of speed is
considered, i.e. FM(v) + FD(v).
In [23] linearly speed dependent mechanical and air resistance is given for ordinary
covered freight wagons (type Hbis or similar). This is assumed to be approximately
equivalent to container trains or trains transporting swap bodies. This assumption may be
conservative, as future high-speed freight trains (140 - 180 km/h) will likely have better
aerodynamics than ordinary freight trains of today. However, in relation to other parts of
running resistance, these terms are quite small, which reduces the sensitivity for
somewhat conservative assumptions. Therefore, experimental results for covered
wagons from [23] can be expressed:

                    FM ( v ) + F D ( v ) ≈ – 22 + 0.6 ⋅ L T ≈ 0.6 ⋅ L T [N]             (F-3)

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




                                                140
                                Track geometry for high-speed railways



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 (type
Hbis or similar). Air drag of the latter trains is given in [23]. As mentioned in the
previous section, these assumptions may be conservative, as future high-speed freight
trains (140 - 180 km/h) will likely have better aerodynamics than ordinary freight trains
of today. On the other hand, it is assumed that not more than one container location out
of eight is empty, i.e. is run as an open wagon, in fully loaded trains. This assumption
may be non-conservative or optimistic. Therefore, conservative and non-conservative
assumptions are believed to balance each other, which reduces the uncertainties and
possible resulting errors.
Thus from [23], assuming that the possible influence of ambient wind is negligible:

                            2                                      –2                  2
                     F D ( v ) = ( 5.4 + 5.2 ⋅ 10                       ⋅ L T ) ⋅ v [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 dissipation
that occurs in the wheel-rail interface, due to sliding motions (creep) and friction
phenomena, at curve negotiation. It is dependent on wheel-rail friction and the stiffness
and character of the wheelset guidance (radial self-steering or forced radial steering
produce lower curving resistance than stiff wheelset guidance). In this context it is
assumed that the wheelset guidance of future high-speed freight trains has almost about
the same flexibility and alignment as ordinary European freight wagons. This may be an
optimistic assumption; however as seen from the example following Equation (F-5), the
curving 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]:

                              K C ⋅ ( m l + m w ) ⋅ g ⋅ 0.65
                                                                                       -
                        F C = ---------------------------------------------------------- [N]   (F-5)
                                                 ( R – 55 )

where

  g        = gravitational acceleration = 9.81 m/s2
  KC       = correction factor ≈ 0.7 (for European freight trains)
  ml       = mass of locomotive
  mw       = total mass of all freight wagons
  R        = curve radius (formula valid for R ≥ 350 m).




                                                           141
                                     Train mass versus gradient




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 real
         resistance for high-speed freight trains is as much as 30 - 50 % higher, due to
         a possibly stiffer wheelset guidance, curving resistance is still almost without
         significance 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. It
is positive for uphill gradients and negative for downhill gradients (i.e. pushes the train
forward). Thus the gradient resistance is determined by:

                                  ( ml + mw ) ⋅ g ⋅ G
                            F C = ---------------------------------------- [N]         (F-6)
                                                1000

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 the
running resistance and also give the train the desired acceleration. For ordinary freight
trains just a low acceleration is required; the basic requirement is to overcome the
starting resistance and the gradient resistance. Thus the total tractive force F from the
locomotive(s) must at least satisfy the following condition:

                                             F ≥ FRT                                   (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 acceleration
ax is determined by:




                                                      142
                            Track geometry for high-speed railways



                                          F – F RT
                                    a x = ------------------
                                                           -                       (F-8)
                                                me

where me is the equivalent mass of the train, including the effect on inertia of rotating
masses (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 F < FRT 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 and
limited either by the traction equipment on board the locomotive - i.e. by the tractive
effort - 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 of
available adhesion; this is also the case for locomotives geared for 140 - 180 km/h. Thus
the limiting factor is very often the available adhesion.
If adhesion is limiting and determining the tractive force:

                                    F = α ⋅ ml ⋅ g                                 (F-9)

In Equation (F-9) it is assumed that all axles of the locomotive are tractive, i.e. the
adhesive 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 available
adhesion) and sanding (for improving very low adhesion), an adhesion level α of at least
0.25 can be almost guaranteed under most conditions (excluding leaves on the track
during the autumn).




                                                 143
Train mass versus gradient




          144
                            Track geometry for high-speed railways



Appendix G - General Description of the GENSYS Software
Package

The GENSYS software package consists of 51 programs for the analysis of railway
vehicle dynamic behavior. Some of these programs can be used for all kinds of
multibody dynamics simulation. The following sections give a brief overview of the
package. For more information, see [29].
Other comparable packages are for instance ADAMS, MEDYNA, SIMPACK and
VAMPIRE.



G.1      Modelling phase


G.1.1    Local coordinate system

In GENSYS, two types of local Euler coordinate systems can be defined. They can be
either fixed systems relative to a fixed global coordinate system or can be guided by the
three 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 an
Euler coordinate system.


G.1.2    Track geometry

The design track can be assembled with tangent track parts, circular curves and different
kinds of transition curves. Transition curves and circular curves are defined by the three
track 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 expressed
in cartesian coordinates, Mauzin diagrams, Plasser diagrams, Fourier series and power
spectral 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 without
any degree of freedom or with 6 degrees of freedom.
To create a coupling between two masses (bodies), the coupling coordinates and
properties 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 linear
spring, 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 contact
model, in order to simplify the model generation. The one used in the present simulations
interpolates the creep forces in a 4-dimensional matrix. The calculation of the matrix
elements 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 forces
balance 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 time
integration 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 calculated
eigenmodes are, due to normally large damping, complex. The resulting
eigenfrequencies are given both as complex roots expressed in [rad/s] and as damped
eigenfrequencies 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 linear
analysis 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 are
available. Possible are for instance Euler’s method, Heun’s method or the classical
method of Runge-Kutta.




                                             146
                               Track geometry for high-speed railways



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 be
animated.




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General Description of the GENSYS Software Package




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