CASE STUDIES IN RAILWAY CONSTRUCTIONfischersz/Education/Case studies in... · for the track centre line and the longitudinal distance for the track centre line is defined in a ...

CASE STUDIES IN RAILWAY

CONSTRUCTION

MSC COURSE

2016/2017 AUTUMN SEMESTER

MODERN RAILWAY TRACK TRACING

(MSZ EN 13803-1, TRACK GAUGE IS 1435 MM)

SZÉCHENYI ISTVÁN UNIVERSITY Dr. Szabolcs FISCHER assistant professor

1. Introduction

Valid Hungarian regulation related to railway track alignment design:

Track alignment design regulation of national public railways (TADR) in Hungarian

(„Országos közforgalmú vasutak pályatervezési szabályzata”), KÖZDOK, Budapest, 1983

Decree of the minister of economy and transport (No. 103/2003), About the mutual

travarsability of the conventional railway systems (NRR) in Hungarian („103/2003. (XII. 27.)

GKM rendelet a hagyományos vasúti rendszerek kölcsönös átjárhatóságáról”), GKM,

Hungarian Gazette („Magyar Közlöny”), No. 2003/156, Budapest, 2003, pp. 12813−12894


Valid European railway track design standard:

MSZ EN 13803-1:2010 Railway applications - Track - Track alignment design parameters -

Track gauges 1435 mm and wider - Part 1: Plain line

MSZ EN 13803-2:2006+A1 Railway applications - Track - Track alignment design

parameters - Track gauges 1 435 mm and wider - Part 2: Switches and crossings and

comparable alignment design situations with abrupt changes of curvature

Valid European regulation related to railway infrastructure in the aspect of

interoperability:

COMMISSION REGULATION (EU) No 1299/2014 of 18 November 2014 on the technical

specifications for interoperability relating to the ‘infrastructure’ subsystem of the rail system

in the European Union (TSI)

TADR


NRR


EN 13803-1


EN 13803-2


Disadvantages of TADR and NRR:

The newest regulation is more than 10 years old.

NRR contains a lot of railway design parameters from TADR.

Railway design parameters are related only railway tracks with speed lower and equal than

160 km/h.

There is an other book for railway track alignment design:

Kerkápoly E., Megyeri J. Tables for railway track aligning (TRTA) (in Hungarian), Műszaki

Könyvkiadó, Budapest, 1980

TRTA contains design rules and parameters for railway tracks with speed lower and equal

than 250 km/h, but this book is not so called valid regulation.

These regulations permit using only clothoide and cosine transition curves in horizointal

geometry.

Advantages of EN 13803-1 standard:

Maximum permitted design speed is 300 km/h.

More types of transition curves can be used.

This European Standard also takes account of vehicles that have been approved for high

cant deficiencies.

Utilization of standard is not compulsory, but every member of EU should introduce all

harmonized standard into its national regulation system (MSZ EN 13803), and they can

determine special limit values for design parameters that suit EN standars values.


„Disadvantages” of EN 13803-1 standard:

Minimum design speed is 80 km/h, „however, the values and conditions stated for this speed

range can also be applied to lines where permissible speeds are less than 80 km/h, but in

this case, more or less restrictive values may need to be used and should be defined in the

contract”.

2. Terms and definition

alignment element: segment of the track with either vertical direction, horizontal direction

or cant obeying a unique mathematical description as function of longitudinal distance NOTE: Unless otherwise stated, the appertaining track alignment design parameters are defined

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

projection in a horizontal plane.

circular curve: alignment element of constant radius

transition curve: alignment element of variable radius NOTE 1: The clothoid (sometimes approximated as a 3rd degree polynomial, “cubic parabola”)

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

curvature is smoothed at the ends of the transition.

NOTE 2: It is possible to use other forms of transition curve, which show a non-linear variation of

curvature. Informative Annex A gives a detailed account of certain alternative types of transitions

that may be used in track alignment design.

NOTE 3: Normally, a transition curve is not used for the vertical alignment.

compound curve: sequence of curved alignment elements, including two or more circular

curves in the same direction NOTE: The compound curve may include transition curves between the circular curves and / or

the circular curves and the straight tracks

reverse curve: sequence of curved alignment elements, containing alignment elements

which curve in the opposite directions NOTE: A sequence of curved alignment elements, may be both a compound curve and a

reverse curve.

cant: amount by which one running rail is raised above the other running rail NOTE: Cant is positive when the outer rail on curved track is raised above the inner rail and is

negative when the inner rail on curved track is raised above the outer rail. Negative cant is

unavoidable at switches and crossings on a canted main line where the turnout is curving in the

opposite direction to the main line and, in certain cases, on the plain line immediately adjoining a

turnout (see EN 13803-2).


equilibrium cant: cant at a particular speed at which the vehicle will have a resultant force

perpendicular to the running plane

cant excess: difference between applied cant and a lower equilibrium cant NOTE 1: When there is cant excess, there will be an unbalanced lateral force in the running

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

NOTE 2: Cant on a straight track results in cant excess, generating a lateral force towards the

low rail.

cant deficiency: difference between applied cant and a higher equilibrium cant NOTE: When there is cant deficiency, there will be an unbalanced lateral force in the running

plane. The resultant force will move towards the outer rail of the curve.

cant transition: alignment element where cant changes with respect to longitudinal

distance NOTE 1: Normally, a cant transition should coincide with a transition curve.

NOTE 2: Cant transitions giving a linear variation of cant are usually used. In some cases, cant

is smoothed at the ends of the transition.

NOTE 3: It is possible to use other forms of cant transition, which show a non-linear variation of

cant. Informative Annex A gives a detailed account of certain alternative types of transitions that

may be used in track alignment design.

cant gradient: absolute value of the derivative (with respect to longitudinal distance) of cant

rate of change of cant: absolute value of the time derivative of cant

rate of change of cant deficiency: absolute value of the time derivative of cant deficiency

(and/or cant excess)

maximum permissible speed: maximum speed resulting from the application of track

alignment limits given in this standard


normal limit: limit not normally exceeded NOTE The actual design values for new lines should normally have a margin to the normal

limits. These values ensure maintenance costs of the track are kept at a reasonable level,

except where particular conditions of poor track stability may occur, without compromising

passenger comfort. To optimize the performance of existing lines it may be useful to go beyond

the normal limits.

exceptional limit: extreme limit not to be exceeded NOTE As exceptional limits are extreme, it is essential that their use is as infrequent as possible

and subject to further consideration. Informative Annex H describes the constraints and risks

associated with the use of exceptional limits.



Definition of track gauge

Definition of cant Source: LINDAHL: Track geometry for high speed railways


Definition of horizontal circular curve radius

Source: LINDAHL: Track geometry for high speed railways

3. Symbols and abbreviations



4. Requirements

4.1. Background

4.1.1. Track alignment design parameters

radius of horizontal curve R (m) (*S),

cant D (mm) (*S),

cant deficiency I (mm) (*S),

cant excess E (mm),

cant gradient dD/ds (mm/m) (*S),

rate of change of cant dD/dt (mm/s),

rate of change of cant deficiency (and/or cant excess) dI/dt (mm/s),

length of cant transitions LD (m) (*S),

length of transition curves in the horizontal plane LK (m),

length of alignment elements (circular curves and straights) between two transition curves Li (m),

radius of vertical curve Rv (m),

speed V (km/h) (*S).

Parameters followed by the (*S) note indicate safety-related parameters.


4.1.2. Parameter quantification

For most of the parameters, two different types of limits are specified:

a normal limit,

an exceptional limit which may have two different meanings:

a) For safety-related parameters, it shall be the absolute maximum limit of this

parameter; this maximum limit may depend upon the actual track mechanical and

geometrical state. NOTE 1: The exceptional limits are safety-related and may (for most parameters) induce a

reduced comfort level. These limits are extreme and should be used only under special

circumstances or after specific safety-case analysis.

NOTE 2: The limits are defined for normal service operations. If and when running trials are

conducted, for example to ascertain the vehicle dynamic behaviour (by continually monitoring of

the vehicle responses), exceeding the limits (particularly in terms of cant deficiency) should be

permitted and it is up to the infrastructure manager to decide any appropriate arrangement. In

this context, safety margins are generally reinforced by taking additional steps such as ballast

consolidation, monitoring of track geometric quality, etc.

b) For non-safety related parameters, the limits shall be considered as the limit above

which passenger comfort may be affected and the need for track maintenance

increased; however, to cope with special situations, values in excess of the limits may

be used, but they shall not exceed any safety limit.

The use of exceptional limits should be avoided, especially use of exceptional limits for several

parameters at the same location along the track.

For cant deficiency, not all vehicles are approved for the normal or exceptional limits. For such

vehicles, the operational limit shall be consistent with the approved maximum cant deficiency.


4.2. Normal limits and exceptional limits for track alignment design parameters

4.2.1. Radius of horizontal curve R

The largest curve radii and transition permitted by track design constraints should be used

where possible. Normal limit for radius is 190 m and exceptional limit is 150 m. Note that these

small radii will result in a permissible speed less than 80 km/h. Hence, normal and exceptional

limits for the radius shall also be derived from the requirements below.

The parameters that shall be considered in the determination of the minimum curve radius are:

the maximum and minimum speeds,

the applied cant,

the limits for cant deficiency and cant excess.

For every combination of maximum speed Vmax and maximum cant deficiency Ilim, the minimum

permissible curve radius shall be calculated using the following equation:

where C = 11,8 mm·m·h2/km2

Where D > Elim, the maximum permissible curve radius for the minimum speed Vmin shall be

calculated using the following equation:

where C = 11,8 mm·m·h2/km2, and D > Elim


NOTE 1: It is recommended that the radius of tracks alongside platforms should not be less

than 500 m. This is to restrict the gap between platform and vehicles to facilitate safe vehicle

access and egress by passengers.

NOTE 2: Small radius curves may require gauge widening in order to improve vehicle curving.

4.2.2. Cant D

Cant shall be determined in relation to the following considerations:

high cant on small-radius curves increases the risk of low-speed freight wagons derailing.

Under these conditions, vertical wheel loading applied to the outer rail is much reduced,

especially when track twist (defined in EN 13848-1) causes additional reductions,

cant exceeding 160 mm may cause freight load displacement and the deterioration of

passenger comfort when a train makes a stop or runs with low speed (high value of cant

excess). Works vehicles and special loads with a high centre of gravity may become

unstable,

high cant increases cant excess values on curves where there are large differences

between the speeds of fast trains and slow trains.

Normal limit for cant is 160 mm.

NOTE It is recommended that cant should be restricted to 110 mm for tracks adjacent to

passenger platforms. Some other track features, such as level crossings, bridges and tunnels

may also, in certain local circumstances, impose cant restrictions.

Exceptional limit for cant is 180 mm.


To avoid the risk of derailment of torsionally-stiff freight wagons on small radius curve

(R < 320 m), cant should be restricted to the following limit:

The application of this limit assumes a high maintenance standard of the track, especially

regarding twist. For further information, see informative Annex H.

4.2.3. Cant deficiency I

For given values of local radius R and cant D, the cant deficiency I shall determine the

maximum permissible speed through a full curve such that:


NOTE 1: Ilim can be replaced with the value (aq)lim:


Normal and exceptional limits for cant deficiency are given in Table 1. These limits apply to all

trains operating on a line. It is assumed that every vehicle has been tested and approved

according to the procedures in EN 14363, EN 15686 and/or EN 15687 in conditions covering its

own range of operating cant deficiency.


NOTE 1: The European signalling system ERTMS includes vehicle limits of cant deficiency Ilim

of 92 mm, 100 mm, 115 mm, 122 mm, 130 mm, 153 mm, 168 mm, 183 mm, 245 mm, 275 mm

and 306 mm. These values reflect the current practice of operating different train categories in

Europe.

NOTE 2: Freight vehicles are normally approved for a cant deficiency in the range 92 mm to

130 mm.

NOTE 3: Non-tilting passenger vehicles are normally approved for a cant deficiency of 130 mm

to 168 mm.

NOTE 4: Depending on the characteristics of certain special features in track, such as certain

switches and crossings in curves, bridges carrying direct-laid ballastless track, tracks with

jointed rails, certain sections of line exposed to very strong cross winds, etc., it may be

necessary to restrict the permissible cant deficiency. Rules in respect of these restrictions

cannot be formulated beforehand since they will be dictated by the design of the special

features; definition of such a frame of reference can only be left to the initiative of the

Infrastructure Manager.

NOTE 5: For further considerations of rolling stock required to operate at high cant deficiencies,

passenger comfort with respect to lateral acceleration may be analysed as written in

EN 13803-1.


4.2.4. Cant excess E

There is cant excess when the following has a positive value:


Normal limit for cant excess Elim is 110 mm.

The value of E affects inner-rail stresses induced by slow trains, since the quasi-static vertical

wheel/rail force of an inner wheel is increased.



Definition of track plane acceleration (ay) and lateral force angle (j)



The relationship between track plane acceleration, side force angle

and cant deficiency


4.2.5. Cant gradient dD/ds

The following limits apply everywhere along the track where cant is varying:


NOTE: For permissible speed lower than 80 km/h, a higher cant gradient may be used after a

safety-case analysis, see Annex H.

For cant transitions with constant cant gradient, can be calculated from the overall

cant variation DD and the length LD:

There are no further special limits for the tilting trains.

4.2.6. Rate of change of cant dD/dt

4.2.6.1. Rate of change of cant dD/dt for non-tilting trains

Cant transitions are normally found in transition curves. However, it may be necessary to

provide cant transitions in circular curves and straights.

For cant transitions with constant cant gradient, the following relationship with DD being the cant

variation shall apply:

where LD is the length of the cant transition in metres, V is vehicle speed in km/h and

qV = 3,6 km·s/(h·m)

Normal and exceptional limits for rate of change of cant are given in Table 2.



For cant transitions with variable cant gradient, the value of dD/dt is not constant.

NOTE 1: Due to limited experience with transitions with variable gradients, the limits for rate of

change of cant are indicative. They may be replaced by limits for second derivative of cant with

respect to time (d2D/dt2), see A.3.

NOTE 2: Informative Annex A gives further information on linear cant transitions and alternative

types of cant transitions.

4.2.6.1. Rate of change of cant dD/dt for tilting trains

Both active and the passive tilt systems need certain time to adapt the angle of tilt to the curve

radius and it is for this reason that curves shall include transition sections of sufficient length.

The transition curves should coincide with the cant transitions. If they do not, then special

running tests are recommended to determine to what extent the maximum cant deficiency may

need to be reduced.

The clothoid is normally used for transition curves, giving a linear variation of curvature. Where

using transition curves with non-constant gradients, the function of the tilt system shall be taken

into account for the analysis of the complex interaction between the vehicle and the track.


4.2.7. Rate of change of cant deficiency dI/dt

For track elements with a variation of curvature and/or a variation of cant the following

relationship has to be fulfilled.

NOTE 1: The variation of non-compensated lateral acceleration in the running plane may be

determined as

NOTE 2 The rate of change of the quasi-static lateral acceleration, at track level, but parallel to

the vehicle floor (dai/dt), which is a measure of the rate of change of acceleration felt by the

passenger inside the vehicle, is greater than the rate of change of non-compensated

acceleration in the track plane:

NOTE 3 The influence of rate of change of lateral acceleration on passenger comfort is

described in EN 12299. Normal and exceptional limits for rate of change of cant deficiency are

given in Table 3.



In case of using tilting trains on given alignment, the values of dI/dt are higher. The tilt control

system creates transient states at the entry to curves, which may give rise to even more

pronounced jerks. Both active and the passive tilt systems need certain time to adapt the angle

of tilt to the curve radius and it is for this reason that curves shall include transition sections of

sufficient length.

For transitions with constant gradients of curvature and cant with DI the overall cant deficiency

variation along the whole transition it follows:

where LK is the length of the transition in metres, V is vehicle speed in km/h and

qV = 3,6 km·s/(h·m)

NOTE 4: For transitions with constant gradients of curvature and cant with Daq the overall

variation of non-compensated lateral acceleration along the whole transition it follows:

The values of dI/dt and daq/dt are not constant for transitions with non-linear curvature variation

and non-linear cant application, see informative Annex A for further information.

4.2.8. Length of transition curves in the horizontal plane LK

For transition curves coinciding with cant transitions, LK = LD, with a constant gradient of

curvature and cant, the minimum length shall be determined using the parameters from 4.2.5

(cant gradient), 4.2.6 (rate of change of cant) and 4.2.7 (rate of change of cant deficiency) in the

following manner and a following formulae:


For transition curves coinciding with cant transitions, LK = LD, with a non-constant gradient of

curvature and cant, the minimum length shall be determined using the parameters from 4.2.5

(cant gradient), 4.2.6 (rate of change of cant) and 4.2.7 (rate of change of cant deficiency) in the

following manner :


For certain types of transitions with non-constant gradient of curvature and cant, the value of

the factor qN is defined in Table 4.

The length of transition curve shall comply with all three criteria. It has to be at least the largest

value derived from the above formulae for the selected values of


NOTE 5: Due to limited experience with transitions with variable cant gradients, this method

limiting the rate of change of cant is indicative. If it is replaced by limits for second derivative of

cant with respect to time (d2D/dt2), other formulas for the minimum transition lengths should be

applied, see A.3.

Where there is no transition curve or it is of insufficient length with respect to the dI/dt criterion,

the limits of the abrupt change of cant deficiency, defined in EN 13803-2, shall be complied

with.

4.2.9. Length of circular curves and straights between two transition curves Li

The normal limit for the length of a straight or a circular curve placed between two transition

curves is 20 m, Li ≥20 m.

NOTE: As an alternative to a short length of a straight or a circular curve, this alignment

element may be omitted and the two transition curves connected directly to each other.

For an alternative method to define the minimum lengths, see informative Annex B.

4.2.10. Vertical curves

Vertical curves should be at least 20 m long and may be designed without vertical transition

curves.

NOTE: Vertical curves are normally designed as parabolas (2nd degree polynomials) or as

circular curves.

A vertical curve shall be provided where the difference in slope between adjacent gradients is

more than:

2 mm/m for permissible speeds up to 230 km/h,

1 mm/m for permissible speeds over 230 km/h.

The limits for the vertical radii are defined in 4.2.11.



Definition of vertical curve between two adjacent

gradients


4.2.11. Radius of vertical curve Rv

The normal limit for radius of vertical curve is

Where qR,lim = 0,35 m·h2/km2 without going under 2000 m vertical radius.

NOTE 1: On lines where most of the passengers may be standing, it is recommended that qR

should be greater than 0,77 m·h2/km2.

The exceptional limit for radius of vertical curve is

where qR,lim = 0,13 m·h2/km2 for hollow, and qR,lim = 0,16 m·h2/km2 for crest.

For sections with switches and crossings laid in vertical curves, the limits defined in EN 13803-2

shall be complied with.


ANNEX A (informative): Supplementary information for track alignment

design related to shape and length of alignment elements

A.1. General

Among other features of track alignment design, all changes imposed in the lateral plane to

vehicle trajectory are important for providing good ride comfort. In such situations, the vehicle is

subjected to abrupt variations of cant and curvature gradients (second order derivatives). The

dynamic response to these types of excitations depends upon the suspension design. However,

a common feature is that this response lasts a few seconds before the effect is eliminated over

a following alignment element (circular curve or straight).

This annex provides detailed analysis methods with respect to design of transition curves and

track alignment elements.

Subclause A.2 includes a Table summarising the properties of the following transition curves,

compared with the conventional clothoid, sometimes approximated as a third degree polynomial

“cubic parabola”:

Bloss curve;

Cosine curve;

Helmert curve, also known as the Schramm curve;

Sine curve, also known as the Klein curve.

Subclause A.3 entitled “Further parameters that may be considered for transition curve design

and a progressive system of design rules” provides a more comprehensive analysis method of

the vehicle behaviour in complex curving situations with segments of varying curvature or / and

cant with respect to the roll movement and of the consequences in terms of track alignment

assessment.


A.2. Summary of the properties of different transition curves

Table summarising the properties of different transition curves shapes and the maximum values

of corresponding parameters for track with gauge 1435 mm:

K horizontal curvature (m),

v line speed (m/s),

1:n cant gradient,

rv vertical radius of smoothed outer rail at the beginning and the end of the uniform slope (m),

av vertical acceleration in the track centre line within the transition curve (mm/s2),

fL shift (m).

Table A.1 summarises the properties of different transition curves shapes compared with the

conventional clothoid, which is the bases of this European Standard and the maximum values of

corresponding parameters for track with gauge 1435 mm.



Transition curve geometries


O: CENTER POINT OF

CIRCULAR CURVE

R: RADIUS OF CIRCULAR

CURVE [M]

S: INTERSECTION POINT OF

TANGENTS

α: ANGLE BETWEEN

TANGENTS [°]

T: TANGENT LENGTH [M]

K: MID-POINT OF CURVE

ÁIE points=start of transition

curve

ÁIV points=end of transition

curve

Transition curve geometries


ÁIE=start of transition curve

ÁIV=end of transition curve

Curvature of railway track geometry

in case of accurate f(x) function is known:

in case of x=x(t), y=y(t) general parameters:

curvature radius:


]/1[

)(1

1)()(

2

32

2

2

m

dx

xdfdx

xfdx

]/1[)(

2

3m

yyxx

yxyxt

][1 m

Curvature of railway track geometry

straight element is a constant zero curvature geometry element, where:

circular curve is a constant curvature geometry element, where:

transition curve is not a constant curvature geometry element, where:


0

R

1

.const

Transition curves

in case (ℓ) function is known, the tangent angle function is:

tracing data are:


][0

radd

][cos1

][sin

][cos

][sin

][cos

][sin

][cos

2/

0

0

2/

0

0

0

0

0

0

mRYf

mdy

mdx

mdY

mdX

mdy

mdx

L

L

L

L

][

][sin

][

][arctan

][0

mtXt

mY

t

mtg

Yt

radX

Y

raddL

h

r

L

Transition curves

three types of transition curves that are demonstrated in the followings:

clothoide, use in case V≤120 km/h (Hungary),

cosine, use in case V≤160 km/h (Hungary),

Wiener Bogen, special Austrian transition curve (not used in Hungary).


Transition curves – CHLOTHOIDE

curvature function:

tangent angle function:

value of tangent angle function in x=L (in the end point of transition curve:

tracing data with using C=R×L parameter:


]/1[1

mLR

][22

11

0

22

radLRLR

dLR

d

][22

0

22

22

0

2

0

radR

L

LRLR

L

LRdL

LL

0

4

9

2

5

......345640

cosCC

dx

......422403366

sin5

11

3

73

0

CCCdy

Transition curves – CHLOTHOIDE

tracing data with using C=R×L parameter:


......345640

cos4

9

2

5

0

C

L

C

LLdX

L

......422403366

cos5

11

3

73

0

C

L

C

L

C

LdY

L

......1769472

12802......

3456

2

40

2

2cos

4

9

2

52/

0

4

9

2

5

0

C

L

C

LL

C

L

C

L

Ldx

L

..86507520

4300848......

42240

2

336

2

6

2sin

5

11

3

73

5

11

3

73

2/

0

0

C

L

C

L

C

L

C

L

C

L

C

L

dyL

Transition curves – COSINE (ATTENTION!!! It is COSINE used in Hungary! It is NOT the

same COSINE in EN 13803-1 standard!!!)

curvature function:

tangent angle function:



]/1[cos12

1m

LR

][sin2

1cos1

2

1

0 0

radL

L

Rd

LRd

][2

02

10sin0sin

2

1

sin2

1

00

radR

LL

R

LLL

R

L

L

RdL

LL



tracing data:


45

35

45

25

44

324

44

4

43

3

42

32

4

5

23

3

22

2

0

2

3

27648

cossin2

27648

cos32cos631504sin

384

cos32cos72

9216

cos48045

128

cos4sin

384

1cos4

1920

16

cos4sin

16

1cos4

24cos

R

LLL

R

LLLL

R

LLL

R

LL

R

LLL

R

LL

R

R

LLL

R

LL

Rdx



tracing data:


34

324

56

326

55

35

55

25

54

3224

54

24

53

33

52

42

5

6

56

546

33

3

32

22

3

4

2

22

0

576

cos4cos9cos609

8294400

cos160cos4725cos2277605400

55296

cossin18

55296

cos32cos631504sin

36864

cos32cos72

36864

cos48045

768

4cossin

3072

cos41

23040

8294400

cos432cos675

32

4cossin

64

cos41

1922

cos

4sin

R

LLLL

R

LLLL

R

LLL

R

LLLL

R

LLL

R

LL

R

LLL

R

LL

R

R

LLL

R

LLL

R

LL

RR

LL

Rdy



tracing data:


44

5

42

5

4

5

22

3

2

3

09216

485

128192016

3

24cos

R

L

R

L

R

L

R

L

R

LLdX

L

56

6

54

6

52

6

5

6

34

4

32

4

3

4

2

22

0

4050

223

36864

485

1024

230409

2

64

3

1924cos

R

L

R

L

R

L

R

L

R

L

R

L

R

L

R

L

R

LdY

L



tracing data:


45

5

44

5

43

5

42

5

4

5

23

3

22

3

2

32/

0

0

864

47

2048

5

128

3072614404321922cos

R

L

R

L

R

L

R

L

R

L

R

L

R

L

R

LLdx

L

56

6

55

6

54

6

53

6

52

6

5

6

34

4

33

4

32

4

3

4

2

222/

0

0

1036800

29219

3456

47

16384

5

1536491521474560

576

73

162563072216sin

R

L

R

L

R

L

R

L

R

L

R

L

R

L

R

L

R

L

R

L

R

L

R

Ldy

L

Transition curves – WIENER BOGEN (special transition curve geometry developed by

Austrian engineers: Gerard PRESLE, Herbert Leopold HASSLINGER)


Source: www.mp-video.at




Source: www.koocoo.at

Source: www.koocoo.at



curvature function:

curvature function in case of =arcsin(m/B)~m/B, B=1500 mm (m=cant in mm, B=distance

between rail vertical axes), hg=1,8 m (height of mass point of railway vehicle):


]/[2541420

207084351

322

2

324

mmLLLL

L

h

LLLLRL

g

]/[2541

504,020708435

1

32

2

2

324

mmLLL

LL

m

LLLLRL



tangent angle function (=ℓ/L):



L

m

L

m

L

m

L

m

R

L

R

L

R

L

R

LdL

345

65678

168,0504,0504,0

168,0714105,2

][2

1 radR

L



tracing data:


19

183

21

184

20

193

27

2445

25

243

22

194

24

233

26

2345

23

223

82

11

26

253

23

204

213

24

24

2144

18

173

18

1544

16

1534

164

21

162

172

142

17

163

19

284

33

17

163

194

24

182

192

102

13

272

163

234

28

222

232

224

27

8

9

214

26

282

292

204

25

273

30

132

16

262

272

92

12

21

203

264

31

10

11

254

30

263

29

244

29

183

21

11

102

243

27

9

10

12

112

12

13

9

82

232

242

25

2244

242

252

122

15

27

2634

112

14

13

14

20

1744

22

213

19

1644

252

262

17

1445

192

202

274

32

233

26

253

28

13

122

11

12

10

92

212

222

202

212

203

23

0

90520042879,0560014604226,0

1015083587,0106595712,190231483839,0

570016141513,040591673210,010524495583,9

107872128,0227272727,2020061325107,0

90013143803,090225,78108236928,7

40180367962,010460422656,110687936,3

76388889,450203378823,01838235294,05054736842,0

90493213383,0003803184,02604167,2828344648421,0

92307692,1202205,00208333,213730971304,4

6134259,3601306666667,0878205,453550015206896,0

7266668,42121875,05625,11473266667,0

6

491413006336,0216397848,6114909091,1

07986111,29565948276,181609197,92052,17

028224,036611111,20588,060192436363,0

6655384615,0010584,0270603,3103191424,3

65667824,1

3

17108784,925,1121,0

10664561694,9143829504,010563820799,4

59976,0108449792,22053528,28138020834,0

4175,43846875,6007056,0141,102352,0

051133818,594968,324930435,67cos

LR

m

L

m

LR

m

L

m

LR

m

L

m

LR

m

L

m

LR

m

LRLR

m

L

m

LR

m

L

m

LR

m

L

m

LR

m

LRLR

m

LRLR

m

LRLR

m

LRLR

m

LRLR

m

LRLR

m

LRLR

m

LRLR

m

LRLR

m

LRLR

m

LRLR

m

LRLR

m

LRLR

m

LRLR

m

L

m

LR

m

LR

m

L

m

LR

m

L

m

LR

m

L

m

LR

m

LRLR

m

LRLR

m

L

m

LR

m

L

m

LR

m

L

m

LR

m

LR

LR

m

LR

m

L

m

LR

m

L

m

LR

m

LR

m

LR

mdLx

14

132

172

182

28

2546

173

20

16

1346

14

15

28

2735

283

31

184

23

223

25

8

72

193

22

174

22

620010855384,019208,0

1032765696,13218,410553186462,2028,0

10317333333,730141129032,02463768,129

02068,68002016,006645455,4137878788,36

L

m

LR

m

L

m

LR

m

L

m

LR

m

LR

m

LR

m

LR

LR

m

L

m

LR

m

LR



tracing data:


345

40

29

2554

315

37

225

28

15

133

22

1856

193

23

6

6

19

173

173

21

28

2454

205

26

325

38

23

1955

7

7

4

4

27

2354

143

18

163

20

31

2755

203

24

5

5

20

1658

14

123

32

2855

30

2654

18

163

24

2055

13

1134

295

35

16

1433

21

1935

335

39

20

1834

133

17

183

22

213

25

26

2254

12

1035

4

6

285

34

305

36

17

153

25

2154

33

2956

275

33

7

9

355

41

153

19

215

27

123

16

255

31

34

3057

6

8

5

7

35

3158

0

4069010418,010232694157,209909911,998125,235

230051063729,0105055191,6336956522,7

084,0760016735171,0

3

16010990215388,2

386858973,560026042,2310670686791,2

024,0042,010120224752,372222222,51

75,7810638116559,5302083333,11008,0

10970199044,6002370816,010812251751,1

10288092782,1004148928,01061145735,7

10465861818,615625,73010112448,7

10159326316,4922943377,31095136,3

17647059,2047916667,241041666667,010537152451,2

1090272,7

6

7314951,13487256944,307

0066382848,01059478154,110037908407,4

122475,19542777777778,00198488313,0872807,78

87345678,51572916667,3221505,197010576159233,5

25,1210597522087,3sin

LRL

m

LRLR

L

m

L

m

LR

L

m

L

m

LRL

m

LRLRL

m

L

m

L

m

L

m

LR

LRL

m

LRL

m

L

m

L

m

L

m

L

m

L

m

L

m

L

m

LRL

m

L

m

LRL

m

LRLRLRL

m

L

m

LRLRLR

L

m

L

m

L

m

LRLRLRLR

LRLRLRL

m

LRLRL

mdLy

24

224

18

182

333

352

213

232

284

32

293

312

223

242

202

22

263

282

324

36

214

25

252

253

332

333

342

3433

302

303

312

313

303

322

35

3346

354

39

353

3724

352

3535

21

2123

242

243

262

263

272

273

203

222

32

304

33

3144

34

3245

202

2034

212

213

28

264

322

323

30

284

282

283

323

342

283

302

20

1845

314

35

343

362

19

192

243

262

25

234

152

17

273

292

20

202

132

15

292

293

304

34

16

162

344

38

14

142

192

21

22

204

29

274

13

132

244

28

334

37

313

332

212

23

31

294

222

223

172

19

245

30

235

29

265

32

21

1757

0109154524,0228144,015939,04209057391,0

3786719,32377386316,18261742,22625,0

775429,38141276042,739508,7138212956,1

60101178763,0102348,1473208288,0

181998367,09225325,810514501818,2

490070112179,0109932432432,910056,7

1068,16213348958,0583344147,1703332512,1

80366698181,0080015323374,010201366379,3

10148928,410680832,9011985792,0

40329016373,005149116,080124135925,0

428924672,185995,0608634,30102907776,1

3825,28018375,090828151578,050376492,17

0214142409,0684705882,998208855,3801764,0

9208,19348917762,025625,834851,0

13671875,0200592,0355,1680010621255,0

0229881344,050607901538,05055,243

251900338,1227184545,360228260869,0

930050880163,080694002501,0139157895,8

794444,13359691093,670343099,222310840281,9

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LRLRLRL

m

142

16

264

30

21

1944

12

122

254

29

15

152

253

272

294

33

204

24

274

31

23

214

233

252

232

233

162

18

224

26

26

244

122

14

234

27

182

20

17

172

27

254

62275,583975,467

10711978712,1008232,05491724,38638808,0

873928,292137879,1867002916667,06177258,439

560040880770,0548744,72492964563,0822,10

66142308,3660318858946,0294,02027037,113

12125,44063425882,030366931192,0

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m

LR

m



tracing data:


4

54

3

412

2

2926

2

3

4

3

371

0

311

10635,2103,110655,610174822,102167318,0

1014219,11077,710333,3cos

R

L

L

m

R

mL

L

m

R

L

R

mL

R

mL

RL

mLdLX

3

43

4

514

2

3102

3

5

65

2

310

2

411

4

47

2

251

0

3

22827

106547833,2108106,8138888889,0

102,1102,2103108182,210

10013604,11009,410001,1sin

R

L

L

m

L

m

R

L

mR

L

R

m

RL

m

R

mL

R

mL

R

mL

R

mdLY



tracing data:


4

58

3

413

2

210

27

2

345

3

395,0

0

311

0

10840566,21045485,210224645052,4

10874125893,510350924841,11060939323,1

10503049,510563221382,15,0cos

R

L

L

m

R

mL

L

m

R

L

R

mL

R

mL

RL

mLdLx

3

46

4

516

2

310

24

5

610

2

313

2

415

4

411

2

27

5,0

0

3

221228

0

10157504291,2101594,1102773808,4

50069444444,0106

1015946,310553364337,3

10633573462,91032184,710366078484,3

1003637,710925018,1sin

R

L

L

m

L

m

R

Lm

R

L

R

m

RL

m

R

mL

R

mL

R

mL

R

mdLy

Superelevation (cant) runoff (transition) geometries related to transition curves

three potential method for building cant:

elevate only the outer rail (Method No. 1),

lower only the inner rail (Method No. 2),

elevate the outer rail & lower the inner rail (special technique in subways, tubes)

(Method No. 3).

In Hungary Method No.1 is used by Railways.

Superelevation runoff functions related to clothoide, cosine and Wiener Bogen transition

curves:

linear runoff function for clothoide,

cosine runoff function for cosine,

Wiener Bogen runoff function for Wiener Bogen.

In the following formulae m=D [mm] (superelevation, cant) abbreviation is used.


Superelevation (cant) runoff (transition) geometries related to transition curves – LINEAR

mathematical function in coordinate system:

mathematical function in equation:

maximal gradient:


][mmL

mL

mm R

]/[1000tancot mmmm

Ln

Superelevation (cant) runoff (transition) geometries related to transition curves – COSINE

(Hungarian)



maximal gradient:


][cos12

mmL

mm

]/[619,6362000

tancot mmmm

L

m

Ln

Superelevation (cant) runoff (transition) geometries related to transition curves – WB



maximal gradient:


][20708435

324

mmLLLL

mm

]/[143,45735

16000tancot mmm

m

L

m

Ln

Superelevation (cant) runoff (transition) geometries related to transition curves – WB


Source: HASSLINGER

A.3. Further parameters that may be considered for track alignment curve design and a

progressive system of design rules

A.3.1. Symbols and abbreviations



A.3.2. Objectives

In conventional track alignment, design conditions for the circular curve are defined. For the

transition curve a more global approach is chosen with integral conditions for the whole transition.

To be more realistic local restrictions all along the track are used.

A.3.3. Progressive track alignment design

A.3.3.1. General

In a differential geometric approach, the alignment of track is described by the three co-ordinates

of a starting point and by the progress of two angles, the angle of direction j(s) in the horizontal

plane and the angle of inclination f(s) in the diagram of altitudes, all relative to the track centre

line in the plane of the top edges of the rails. Finally, the third angle, the angle of cant (s), is the

angle in which the horizontal axis perpendicular to the track centre line should be pivoted around

the latter to bring it into the plane of the track. The gauge is measured in accordance with this

pivoted axis perpendicular to the track centre line and they both define the track plane. These

three angles can be used in a matrix of a spatial rotation.

In this subclause, the cant angle is defined as the ratio of the length of the arc of this matching

circle of the third angle of rotation with its centre at the track centre line to the radius. The cant

d(s) itself is the length of the arc of the circle with radius equal to the distance between wheel

treads b of an axle. Applying cant gives different altitudes of the left and right rails. The cant can

be indicated and measured approximately in a vertical plane perpendicular to the horizontal

projection of the track centre line.

Along the track, all quantities vary with the curved abscissa s in the track centre line and,

according to their definitions, allocated signs and therefore absolute values have to be taken for

the comparison with limits.



Thus, the geometry can be described and static criteria formulated by the three angles and their

derivatives independently of and therefore valid for any gauge and also for systems without

defined gauge as monorails and magnetic levitated trains.

To obtain the accelerations and jerks induced by the alignment of the track at every point – also in

transition curves and other segments of varying curvature or / and cant – an exact physical model

for a cross section of a rigid vehicle is used and the kinematic variables are expressed. A

linearization gives the relation between track alignment geometry and accelerations and jerks

which should be limited. This linearization also leads to a difference between a sloping length at a

track gradient that can be approximated as the length projected in the horizontal plane.

In this subclause, also the effect on the non-compensated lateral acceleration and jerk due to the

roll movement is to take into account, see Figure A.1. This is an improvement on the previous

methods where a mass point travelling along the track centre line is taken as the basis. In reality,

the centre of gravity of the vehicle, the passengers and the freight are always situated at a certain

height above the track plane, which, for the purpose of this European Standard, is taken as mean

height h (track alignment for centre of gravity).

In circular curves, all the direct geometric limitations remain unchanged relative to the text this

European Standard and the two criteria containing the height convert for h = 0 to the conventional

rules.

Parameters that can be considered:

non-compensated lateral acceleration,

non-compensated lateral jerk,

angular acceleration about roll axis,

angular jerk about roll axis,

vertical acceleration,

vertical jerk.



A.3.3.2. Non-compensated lateral acceleration



A.3.3.3. Non-compensated lateral jerk


A.3.3.4. Angular acceleration about roll axis


A.3.3.5. Angular jerk about roll axis


A.3.3.6. Vertical acceleration


A.3.3.7. Vertical jerk

ANNEX B (informative): Length of alignment elements (circular curves and

straights) between two transition curves Li

In certain applications, the actual length of any alignment element (other than transition curves)

should be set equal to or above a limit given in Table B.1, taking into account the actual

alignment design parameters of the neighbouring alignment elements (cant, cant deficiency and

their variations); longer elements should be used for higher values of these parameters.

It is desirable where possible to join two reverse circular curves by a continuous transition curve

instead of placing a straight line element between the two transitions curves. Hence, in this

case, the length of straight line element is zero.

On high speed lines, a rapid succession of curves and straights may induce a reduction in

comfort, particularly when the length of individual alignment elements are such that the

passengers are subjected to changing accelerations at a rate which corresponds to the natural

frequencies of the vehicles.

There are no special limits for tilting trains.


5. Limits of railway geometry design parameters in other countries

5.1. Sweden

In Sweden does exist a regulation BVF 586.41 (BVF) and a handbook, BVH 586.40 (BVH)

concerning track geometry geometry parameters. The regulations is mandatory while the

handbook is informative.

5.1.1. 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.

5.1.2. Cant deficiency and cant excess

Cant deficiency

The non-compensated lateral acceleration, which is proportional to cant deficiency, shoul 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.



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 approval,

Category C: 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

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



5.1.3. Horizontal curve radius

The recommended horizontal curve radius in Banverket handbook BVH 586.40 is a value

calculated with cant D=150 mm and cant deficiency I=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 =1.3. This factor is used to get a margin with respect to ride

comfort and increased speed in the future.



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

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

assumption that trains of category A will be used.

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

Figure 3-1 below.





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 Botniabanan ((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).

5.1.4. 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. 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.



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.



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:

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:



Here Δht and Δhd 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.

5.1.5. 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.



5.1.6. Vertical curve radius

In Banverket regulation BVF 586.41 [5] the vertical curve radius shall be in accordance to

permissible speed as shown in the equation below:



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

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).



In Figure 3-2 shows the relations between recommended and minimum vertical curve radius

according to Banverket.





5.2. 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.



5.2.1. 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.



There is a recommended value of cant depending on the speed of the fastest trains and the

horizontal curve radius.

There is also a minimum value of cant which has to be arranged according to Equation below:

hd,lim: see in 5.2.2.



5.2.2. Cant deficiency

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



5.2.3. 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.

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

70 mm of cant deficiency.



The limit of horizontal curve radius (without permission) can be described of Equation below

and some examples are shown in Table 3-13.

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



A value of horizontal curve radius were permission is needed can be described by Equation

below according to DB.

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.

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.





5.2.4. Transition curve and superelevation ramp

Transition curvature shall coincide with superelevation ramps in both shape and position.

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 below.

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:



The minimum length of clothoid type of transition curves is according to DB [9]:

For tilting trains the following formula is valid for transition curves with linear change of

curvature and cant, respectively:

5.2.5. 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.



5.2.6. Vertical curve radius

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



Some examples are shown in the following table.



5.3. France

5.3.1. Cant, cant deficiency and cant excess

Recent information regarding France is scarce. The following was found in S.N.C.F: La voie

Ferrée, Techniques de construction et D’entretien. Alias, J et al., Paris, 1984. Experiment shows

that the non compensated lateral acceleration should not exceed 0.10…0.15×g (1.0 …1.5 m/s2)

according to comfort requirements. SNCF allows a cant deficiency of 150 mm (exceptional

value 160 mm) (The ‘Grande Vitesse Paris-Sud-Est’ line limited the value of cant deficiency to

100 mm) 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).



5.4. 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.



5.5. Technical Specification of Interoperability (1299/2014/EU)

5.5.1. Performance parameters of passenger traffic


Source: TSI, 1299/2014/EU



5.5.2. Performance parameters of freight traffic



5.5.3. Structure gauge



5.5.4. Distance between track centres



5.5.5. Maximum gradients



5.5.6. Minimum radius of horizontal curves



5.5.7. Minimum radius of vertical curves



5.5.8. Cant



5.5.9. Cant deficiency



5.5.10. Abrupt change of cant deficiency



CEN (2006). MSZ EN 13803-2:2006+A1 Railway applications - Track - Track alignment design

parameters - Track gauges 1 435 mm and wider - Part 2: Switches and crossings and

comparable alignment design situations with abrupt changes of curvature

CEN (2010). MSZ EN 13803-1:2010 Railway applications - Track - Track alignment design

parameters - Track gauges 1435 mm and wider - Part 1: Plain line

EC (2014). COMMISSION REGULATION (EU) No 1299/2014 of 18 November 2014 on the

technical specifications for interoperability relating to the ‘infrastructure’ subsystem of the rail

system in the European Union (TSI)

GKM (2003). Decree of the minister of economy and transport (No. 103/2003), About the mutual

travarsability of the conventional railway systems (NRR) in Hungarian („103/2003. (XII. 27.)

GKM rendelet a hagyományos vasúti rendszerek kölcsönös átjárhatóságáról”), GKM,

Hungarian Gazette („Magyar Közlöny”), No. 2003/156, Budapest, 2003, pp. 12813−12894

KÖZDOK (1983). Track alignment design regulation of national public railways (TADR) in

Hungarian („Országos közforgalmú vasutak pályatervezési szabályzata”), KÖZDOK, Budapest,

1983

LINDAHL (2001). Track geometry for high speed railways, Stockholm, ISSN 1103-470X,

http://www.europakorridoren.se/spargeometri.pdf

www.koocoo.at

www.mp-video.at

REFERENCES

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