The speaker presented a comparison between the Track alignment design approach based on NR standards and the one based on the European Norms and the Technical Specifications for Interoperability (TSI), highlighting the main area where these approaches are different and touching the subject of the safety design factors embedded in the track alignment design procedures. The main topics: Cant parameters definition, the origin of the 11.82 cant constant. ways of applying cant. Track geometry recording. Quality Standard deviation. Inherent standard deviation. The advantage of using rolling SDs. Quality bands for low and high speed. Cant over a reverse transition - the orphan rule of lifting the reversing point to improve the quality of riding. Designing a sudden change in curvature. Virtual transition - TRK2049. The rules of the European Norm for track geometry EN 13803-1&2 The significance of transition shift.

1. Alternative Approach to Permanent
Way Alignment Design
Explained/Challenged
Constantin Ciobanu
Senior Pway Engineer
ATKINS
West of England Section
18/11/2015

2. About Constantin Ciobanu
Third generation railway professional
Graduated Technical University of Civil Engineering Bucharest
(TUCEB), Romania, in 1998
• Speciality: Railway, Road and Bridge Engineering
Lecturer / Assistant Lecturer – TUCEB, 1998 – 2011
• Track alignment design for plain line and S&C (including light rail and tramway)
• Realignment methods (Hallade and similar)
• Continuous welded rails (CWR) behaviour and CRT management
Joined Atkins in May 2013
• Main projects: Great Western Electrification Project +Great Western Route
Modernisation
• ATKINS - BRT Development Group under PhoD
Design Engineer – Romania, 2006 – 2013
• Railway, Light Rail, Tramway, Road designs
• Main project: Romanian sections - IVth Pan-European Railway Corridor (TEN-T)
Lead Track Design Engineer, CRE for two 100km sections

3. Lateral Acceleration. Cant. Cant Deficiency
• Circular movement - inertial centrifugal acceleration
𝑎 𝑐 =
𝑣2
𝑅
• The track is inclined towards the centre of the curve
with the cross-level angle α to compensate for a part
of the centrifugal acceleration
• The traditional way to measure this inclination is the
cant, E, defined as “the vertical difference in heights of
the two rails of a track, measured at centerline of the
rail heads (S)” (TRK2049 – 2010, B.1.1).

4. Lateral Acceleration. Cant. Cant Deficiency
The non-compensated lateral acceleration 𝑎 𝑞
𝑎 𝑞 = 𝑎 𝑐 𝑐𝑜𝑠 ∝ −𝑔 𝑠𝑖𝑛 ∝ = 𝑎 𝑐 − 𝑔
𝐸
𝑆
=
𝑣2
𝑅
− 𝑔
𝐸
𝑆
where:
• v is the speed of the vehicle
• R is the curve radius
• g is the gravitational acceleration
• E is the applied cant
• S is the cross-level standardised reference for rail heads
centerline distance (considered 1505mm in UK)
Cant Deficiency, D, is usually used instead of aq :
𝐷 =
𝑆
𝑔
𝑎 𝑞 =
𝑆
𝑔
𝑣2
𝑅
− 𝐸
𝑫 = 𝟏𝟏. 𝟖𝟐
𝑽 𝟐
𝑹
− 𝑬

5. Lateral Acceleration. Cant. Cant Deficiency
• The cant, E, defines the track inclination angle,
measured as level difference over rail centerline
distance (not over track gauge)
• The cant deficiency, D, defines the non-compensated
lateral acceleration
• Simplifications:
• Suspension behaviour
• Bogie attack angles
• Differences between the suspended and un-suspended
mass
• Dynamic behaviour – oscillations, damping effect
• Vehicle centre of mass – brought at track level
• etc
𝑫 = 𝟏𝟏. 𝟖𝟐
𝑽 𝟐
𝑹
− 𝑬 [𝒎𝒎]

6. Track Geometry Recording. Standard Deviation
• Periodic track measurement is required to
maintain an effective railway track system
– safe and with good vehicle ride
quality.
• Safety – well defined exception
(exceedance) levels
Intervention and Immediate remedial
actions
• Ride quality – track geometry Standard
Deviation (SD)
Quality Index defined based on speed and
various classes of lines

7. Track Geometry Recording. Standard Deviation

10. Signal Processing. Fourier Analysis. Standard Deviation
Fourier Analysis – signal simplification
Two (three) standard deviation wave length bands:
• 35m = 1m to 35m (H) and 0.5m to 35m (V)
(general track quality index)
• 70m = 1m to 70m (H) and 0.5m to 70m (V)
(comfort quality index for passenger trains at higher speed –
V≥80mph)
• 200m = 1m to 200m (H) and 0.5m to 200m (V)
(High Speed track quality index V>250km/h – EN13848)

11. Signal Processing. Fourier Analysis. Standard Deviation

12. Track Quality Standard Deviation
• Global track quality index
• Computed based on the inertial response of the measuring bogie
to the track irregularities
• Two (three) track quality standard deviation wave length bands:
• 35m = 1m to 35m (H) and 0.5m to 35m (V)
(general track quality index)
• 70m = 1m to 70m (H) and 0.5m to 70m (V)
(comfort quality index for passenger trains at higher speed – V≥80mph)
• 200m = 1m to 200m (H) and 0.5m to 200m (V)
(High Speed track quality index V>250km/h – EN13848)
• Two sets of SD values:
• AL – horizontal alignment
• TOP – top of rail - vertical alignment and cant
• WT35 – worst of the two tops (left rail and right rail).
• MT70 – mean top vertical variation (middle track vertical variation)

14. Any change in the vehicle lateral or vertical
acceleration due to the design, is a source
of oscillations:
- Horizontal transition (AL35 and AL70)
- Cant transition (WT35 and MT70)
- Gradient change (WT35 and MT70)
- Vertical curve (WT35 and MT70)
Inherent Track geometry
Standard Deviation
(SD present in the design
and not caused by installation)
Inherent Track Quality
Standard Deviation

15. Rolling design
(inherent) track quality
standard deviation
The normal approach
is hiding the maximum
SD and its cause.
A better way is to
consider in the design
the rolling SDs.
Gives the designer a
better understanding

16. Disclaimer
What will follow should not be considered (yet) a design guidance!
(Except the excerpt from TRK2049)

17. Applying cant
• The inside rail of the curved track stays at the
design level
• The outside rail is lifted with the full cant value
• The outer rail is the one that provides curve
guidance for the vehicle
• Vertical Profile for the high rail?
• Vertical curves for cant?

18. (Classic approach)
Cant applied by lifting
the outer rail
Cant applied by lowering
the inner rail
(Switzerland)
Cant applied symmetrically
-High speed track – Shinkansen
- tramway

19. Ways of applying cant
• For low speed the difference is not
significant (there are exceptions)
• As the speed increases and the track
tolerances are tighter the difference is
starting to be significant in the ride
quality and whole life behaviour of the
track
• Shinkansen (since 1968) V>160km/h
• Almost all slab track based HS lines
• Californian High Speed

21. Cant over a reverse curve
• Balancing the curvature variation – proportional
transition lengths
• Balancing the cant / rate of change of cant
• Balancing the cant gradient
• Balancing the deficiency / rate of change of cant
deficiency
• What else?

22. Cant over a reverse transition. “The orphan rule”
Romanian Railway track standard
Instructia 314 German Railway track standard
RIL 800.0110

23. Cant over a reverse transition. “The orphan rule”
Austrian Railway track standard
OBB – B 50 United Kingdom
Network Rail – Track Design Handbook – TRK 2049

24. Cant over a reverse curve. “The orphan rule”
All these standards are showing a mysterious triangle
All these standards recommend a lifting of the reverse point

25. Cant over a reverse curve. “The orphan rule”
All these standards are showing a mysterious triangle
All these standards recommend a lifting of the reverse point

26. Cant over a reverse curve. “The orphan rule”

27. Cant over a reverse curve. “The orphan rule”

28. Designing a sudden change in curvature
When is a transition curve not needed?
…when the cant is constant.

29. Designing a sudden change in curvature
When is a transition curve not needed?
• Horizontal alignment track quality standard
deviation - SD (mm) - Al35 Band for a straight
to a circular alignment with or without
transition curve
X 2.3
• In the case of the actual installation, the
sudden change in curvature is practically
impossible to be installed on track, as the rails
are not kept in place laterally by a perfectly
rigid system, especially for a ballasted track.
• An actual sudden change in curvature is in
fact impossible to install or maintain,
especially on ballasted track, because it will
always tend to become a short curvature
transition during installation respectively post-
installation, due to the modelling effect of the
passing trains.

30. Designing a sudden change in curvature
1. Limit the virtual rate of change of cant
deficiency, RcD (VT), calculated based on
the assumptions of the principle of Virtual
Transition.
This is the design approach used in the UK and defined
by the Track Design Handbook – NR/L2/TRK/2049
(2010) for Network Rail and by the track design standard
S1157 (2014) for London Underground.
2. Limit the sudden change in curvature by
limiting the instantaneous change in cant
deficiency (ΔD).
This design approach is the most common used in
continental Europe and around the world. It can be found
in the European Norm for track alignment design
parameters – BS EN 13803-2 (2006).

31. The Principle of Virtual Transition

32. TRK2049 - RcD
Normal
Design
Value
Maximum
Design
Value
Exceptional
Design
Value
35 mm/s 55 mm/s 70 mm/s
The limits of the Rate of Change of Cant Deficiency
(according to the Track Design Handbook TRK2049)
EN 13803-2 - ∆D
Speed
V [km/h]
V≤70 70<V≤170 170<V≤230
Recommended
∆Dlim [mm]
50 40 30
The limits of the Sudden Change in Cant Deficiency
(according to the European Norm EN 13803-2)

33. Comparison between the design restrictions for a sudden change in curvature
(∆D was computed from RcD for a virtual transition length LVT of 12.2m)
TRK2049
Normal
Design
Value
Maximum
Design
Value
Exceptional
Design
Value
35 mm/s 55 mm/s 70 mm/s
The limits of the Rate of Change of Cant Deficiency
(according to the Track Design Handbook TRK2049)
EN 13803-2
Speed
V [km/h]
V≤70 70<V≤170 170<V≤230
Recommended
∆Dlim [mm]
50 40 30
The limits of the Sudden Change in Cant Deficiency
(according to the European Norm EN 13803-2)

34. Comparison between the design restrictions for a sudden change in curvature
(the equivalent virtual RcD for EN13803 is computed for a virtual transition length LVT of 12.2m)
TRK2049
Normal
Design
Value
Maximum
Design
Value
Exceptional
Design
Value
35 mm/s 55 mm/s 70 mm/s
The limits of the Rate of Change of Cant Deficiency
(according to the Track Design Handbook TRK2049)
EN 13803-2
Speed
V [km/h]
V≤70 70<V≤170 170<V≤230
Recommended
∆Dlim [mm]
50 40 30
The limits of the Sudden Change in Cant Deficiency
(according to the European Norm EN 13803-2)

35. Speed
[mph]
RIL 800.0110 specifications
Sudden change of Cant
Deficiency
∆D
Equivalent virtual
Rate of change of
Cant Deficiency for
12.2m virtual
transition
RcD [mm/s]
Speed
[km/h]
Minimum radius not
requiring transition
curve [m]
Plain line S&C Plain line S&C Plain line S&C
25 40 220 180 86 105 79 96
32 50 340 280 87 106 100 121
38 60 490 400 87 107 119 147
44 70 670 545 87 107 139 171
50 80 875 710 87 107 159 195
56 90 1110 900 87 107 179 220
63 100 1370 1110 87 107 199 244
69 110 1735 1410 83 102 208 256
75 120 2170 1745 79 98 216 268
81 130 2680 2130 75 94 222 279
87 140 3275 2575 71 90 227 287
94 150 3990 3085 67 87 229 298
100 160 4825 3675 63 83 230 303
106 170 5810 4350 59 79 229 306
112 180 6975 5125 55 75 226 308
119 190 8365 6000 51 71 221 308
125 200 10000 7000 48 68 219 310
Cant deficiency parameters for the minimum radius not requiring transition to straight
according to the German track alignment design standard RIL 800.0110 (2008)
TRK2049
Normal
Design
Value
Maximum
Design
Value
Exceptional
Design
Value
35 mm/s 55 mm/s 70 mm/s
The limits of the Rate of Change of Cant Deficiency
(according to the Track Design Handbook TRK2049)
EN 13803-2
Speed
V [km/h]
V≤70 70<V≤170 170<V≤230
Recommended
∆Dlim [mm]
50 40 30
The limits of the Sudden Change in Cant Deficiency
(according to the European Norm EN 13803-2)

36. Comparison between the design restrictions for a sudden change in curvature
(the equivalent virtual RcD for EN13803 is computed for a virtual transition length LVT of 12.2m)
TRK2049
Normal
Design
Value
Maximum
Design
Value
Exceptional
Design
Value
35 mm/s 55 mm/s 70 mm/s
The limits of the Rate of Change of Cant Deficiency
(according to the Track Design Handbook TRK2049)
EN 13803-2
Speed
V [km/h]
V≤70 70<V≤170 170<V≤230
Recommended
∆Dlim [mm]
50 40 30
The limits of the Sudden Change in Cant Deficiency
(according to the European Norm EN 13803-2)

37. Transition curve shift
When a transition is to be installed
between two circular curves one of the
curves is shifted towards the centre
relative to the other.
This shift (theoretical slue), S, for a
clothoid transition, is dependent on the
curvature variation ∆K between the two
curves:
𝑆 =
𝐿2
24
∆𝐾 −
𝐿4
2668
∆𝐾3 + ⋯
where
∆𝐾 =
1
𝑅2
−
1
𝑅1
=
𝑅1 − 𝑅2
𝑅1 𝑅2
Best practice rule in some European countries :
If the required curve shift to install a transition is below 3mm, that transition should not be proposed in
the design as it is practically impossible to be installed on site, on ballasted track.

38. Transition curve shift

39. By inserting a 30m transition between R1 and R2,
the rate of change of cant deficiency changes as
follows:
• From 36mm/s to 15mm/s (21mm/s decrease)
• From 56mm/s to 23mm/s (33mm/s decrease)
• From 71mm/s to 29mm/s (42mm/s decrease).
…when the cant is constant.