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.


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


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


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

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

What lift?!
… let’s see some other standards first …


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)


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


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).


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


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


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.


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:


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


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:


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


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.


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:


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.


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


5 thoughts on “The orphan rule of cant design over a reverse transition

  1. Potentially and theoretically yes. In one old book I read that some countries (France for example) used to have such smoothening of the cant diagram. Not sure if they are still using this today. At the point of change to higher constant cant the train will, over time, compact the ballast to achieve this. But that’s not the case at the points of change to low constant cant – where additional material is required to soften the transition.
    But I don’t really know how much this will influence the riding. For flat cant gradients I would expect the influence not to be that significant. Then this becomes more an theoretical exercise.


  2. Thanks for the very helpful page and site. I wondered if there are no requirements that the cant rate change smoothly? There are discontinuities in the cant rate at the point joining the circular sections and transition sections. Would smoothing this be of benefit ? Thanks


  3. Very good explanation. I like to see further in detail, can you please provide more details on where I can get this? Thanks.


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