The orphan rule of cant design over a reverse transition

Motto: Tolle lege.

Most of the railway track design standards around the world are presenting the particular issue of the reverse transition.

All these standards are insisting on keeping a constant rate of change of curvature – a constant A. By doing this in fact the design will include a single continuous transition between the two opposite circular arcs. I’m sure you remember, dear reader, the two reverse infinite loops of the clothoid presented previously here.

10-reverse-transition-clothoid-pway-track-road-curvature-constant

The curvature diagram of this alignment will be something like this:

11-curvature-diagram-reverse-transition-equivalent-radius

Nothing spectacular till now. This is common sense alignment design engineering. That is why most of these standards, when presenting the reverse transition, don’t insist too much on this curvature rule but on something else, of similar importance but more subtle … an “orphan” rule of cant design.

What’s that?

Let’s see some snapshots from a few standards, perhaps you will notice too this orphan cant (superelevation) design rule:

1. Railway Track Design Standards, Norms and Design Handbooks

01-NR-L3-TRK-2049-mod02-Mathematics-Track-Design-Handbook-Reverse-Transitions-lift-reverse-constant-change-in-curvature-high-rail-low-pway-permanent-way

United Kingdom: NR/L3/TRK/2049/mod02 (2016). Track Design Handbook. Issue 13. Module 2 – Mathematics. Network Rail.

Hmm!
“Reverse transition should have a constant rate of change of curvature … Levels should be set out as shown in the diagram …”

reverse-curve-lift-TRK-2049-track-design-handbook-Network-Rail-guidance-cant-scissors-rule
Wait!
Lift?!
What lift?!
… let’s see some other standards first …

02-RIL-800.0110-Netzinfrastruktur-Technik-entwerfen-Linienfuhrung-gegenbogen-mit-ubergangsbogen-ohne-zwischengerade-gerade-uberhohungsrampe-gleisschere

Germany: RIL 800.0110 (1999 / 2008) Richtlinie – Netzinfrastruktur Technik entwerfen – Linienführun., Deutsche Bahn. (Directive – Infrastructure Network Technical design – Lines. German track alignment design standard)

Linke schiene – left rail
rechte schiene – right rail
Uberhohungsrampe – cant ramp (transition)

03-B50-OBB-Austrian-Track-design-standard-oberbau-gleisschere-gerade-rampe-uberhohunge

Austria: B50 (2004) Oberbau – Technische Grundsatze Linienfuhrung von Gleisen, OBB (Technical principles. Track alignment. Austrian track national standard)

04-BG-instruction-for-construction-of-railway-track-technical-norm-bulgaria-reverse-curve-orphan-rule-lift-reverse-point

Bulgaria: НКЖИ (2010). Инструкция за устройство и поддържане на горното строене на железния път и железопътните стрелки. Sofia, Bulgaria (Instruction for track construction and maintenance of track superstructure, plain line and switches and crossings. –Bulgarian national track standard).

05-RO-Instructia-314-norme-si-tolerante-constructia-si-intretinerea-caii-ferate-curbe-de-sens-contrar-suprainaltare-cant-orphan-rule-lift-of-the-reverse-point-vertical-alignment

Romania: Instructia 314 (1985). Instructia de norme si tolerante pentru constructia si intretinerea caii. Linie cu ecartament normal. INCERTANS. Romania. (Instruction of norms and tolerances for track construction and maintenance. Normal gauge lines – Romanian national track standard).

Indian Railways Permanent Way Manual (2004)

Indian Railways Permanent Way Manual (2004)

2. Light rail and tramway track design standards

06-TCRP-Report-155-Track-Design-Handbook-for-Light-Rail-Transit-superelevation-transitions-for-reverse-curves

United States: TCRP Report 155 (2012). Track Design Handbook for Light Rail Transit. Transportation Research Board. Washington

07-TPG-Ch-Switzerland-Directives-techniques-pour-TRAM-Clothoide-de-raccordement-geometrie-en-plan

Switzerland: Directives techniques pour TRAM. TPG. Geneva.(Tramway design standard)

Have you noticed the mystical triangle and the lift of the reverse point shown in all these standards?

3. Technical books

14-British-Railway-Track-vol-1-Design-part 2-S&C-Switches-and-Crossings-John-C-Morgan-Permanent-Way-Institution-PWI-Reverse-curve

Morgan, J.C. (2009). British Railway Track. Volume 1. Track Design. Part 2 Switches and Crossings. Permanent Way Institution.

13-Esveld-Modern-Railway-Track-MRT-reverse-curves-lift-cant-curvature-continuous-variation-scissors-station-orphan-rule-design

Esveld, C. (2001). Modern Railway Track. MRT Productions.

And this is not all. Lifting the reverse point of the transition is not only a railway (or tram) track design rule. You will find the same principle also in the road design standards.

4. Road design standards

When a reverse curve is used on a road project, and the radii are requiring superelevation, the runoff of the superelevation is designed to lift the reverse point:

32-WSDOT-Design-Manual-Road-Reverse-Curves-M-22-01.12-superelevation-runoff-continuous-transition-normal-crown

United States: M 22-01.12 (2015). Design Manual. Washington State Deportment of Transportation (WSDOT).

31-SANRAL-South-African-National-Roads-Agency-Limited-geometric-design-guide

South Africa: Geometric Design Guidelines. South African National Roads Agency Limited (SANRAL)

It is written in the books and standards … but can any of the design software we use do this?

5. Design software documentation.

Both Bentley Track alignment design software, Railtrack and MX, are able to automatically design the cant over the reverse in the way prescribed in the standards:

11-Bentley-RailTrack-PowerRail-OpenRail-OpenRoad-help-add-cant-at-Spiral-to-Spiral-reverse-adjust-over-both-Transitions-lift-reverse-point-clothoid-track-pway-design-scrissors-station

Bentley Railtrack Help (2015). Civil Help SELECT Series 4. Help file for Bentley Railtrack V08.11.09.84x Maintenance Release.

12-MX-Rail-help-cant-over-S-curves-reverse-adjust-over-both-Transitions-lift-reverse-point-clothoid-track-pway-design-scissors-station

Bentley MXRoad Suite Help (2012). MXROAD Suite Online Documentation. Help file for Bentley MXRAIL 08.09.04.XX Release.

But not only them. I’ve seen a demo on it using Ferrovia and designed so many such alignments with ProVI – a very good railway track design software, by the way.

Why?

Installing the cant in this way is keeping the track centerline on an almost constant level throughout the reverse transition in opposition with what is seen as the normal way of applying the cant – as two separate transitions, without the lift.

The difference between the two ways of applying the cant over the reverse transition can be seen in the animation below:

reverse_curve_transition_lift_railway_track_alignment_cant_superelevation_high_speed_HS2_pwemanent_way_dynamic_model_stanard_deviation_SD_TQI_track_quality_index

The axle movement over a reverse cant transition. Blue – lifted reverse point (continuous transition) . Red – separate cant transition.

Which one seems better for you?
Why did I called this “the orphan rule”?
You tell me, dear reader … why?
How significant is this?

The exact significance will be explored in a future post here and in more detail, probably, in a future article published in the Journal of the Permanent Way Institution.

References

Here is just a short list of the standards and books presenting this orphan rule:

 

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