Alternative Approach to Permanent way Alignment Design

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

8. 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)

9. Signal Processing. Fourier Analysis. Standard Deviation

10. 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)

11. 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

12. 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

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

14. 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?

15. (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

16. 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

17. 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?

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

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

20. 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

21. 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

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

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

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

25. 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.

26. 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).

27. The Principle of Virtual Transition

28. 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)

29. 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)

30. 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)

31. 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)

32. 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)

33. 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.

34. Transition curve shift

35. 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.