# How is the cant measured?

##### The good old times

Since the early beginnings of the railway, the track engineers were aware of the centrifugal forces influence to the train riding when passing through a curved section of track. To compensate this influence, the track was inclined laterally by creating a positive level difference between the outer and inner rails of a curved track. This inclination is called cant or superelevation.

Since then, the cant is measured as the level difference between the rail heads. In the picture below is shown an old measuring device device, showing a 5 inch cant. The level difference was reported to a horizontal reference defined by a spirit level. This principle of measurement, refined and modernised, is still in use today in almost all the guided systems of transport.

Railroad track spirit level in place indicating 5″ of superelevation between the inside and outside rail of a curve along the Keystone Corridor near Narberth, PA. (Source of the image – Wikipedia)

Here is a picture of another old cant measuring device using spirit level and a 20mm stepped cut wood plank:

Old cant measuring device

##### The theory

The permanent way engineering theory behind the definition of cant was explained briefly here, in an older post: Cant and Cant Deficiency. Where is the 11.82 coming from?

The the cross-level angle, α , and the cant reference definition.

The main thing to consider, from the point of view of understanding how the cant is measured, is that all the cant parameters (cant, deficiency, rates of change of cant and cant deficiency, cant excess, non-compensated lateral acceleration etc) are defined based on the track cross-level angle, α . If this angle is kept constant, all the cant parameters do not vary. They will stay the same, no matter how the track cross level elements and dimensions vary, as long as the cross-level angle does not change.

For a few guided transport systems (e.g. maglev, monorail) this inclination angle, α, is used directly to express the cross-inclination of the infrastructure support system. For railway and tramway track the angle is converted to a length dimension – the cant, E, expressed in mm.

The cant value, E, is directly related to the reference base S, used to define the cant constant:

Around the world, there are a few versions of the nominal value for normal gauge: 1435mm (what we generally call “normal track gauge”) ,1432mm, 1433mm, 1438mm.  There are also different  types of rails – with different rail head profiles and head width. The rails are placed on track with different inclinations: vertical (for switches and crossings), 40:1 (in Germany) or 20:1 (the most common rail inclination). For tramways, some of the rails are installed vertical and the inclination is embedded in the grooved rail head profile.

Due to all these factors there are a wide range of track layouts that can provide the same track cross-level angle, α. But, as we saw above, the same angle should always mean the same cant.  Hence, it was required to define a constant cant reference base, S, one that is independent of the different factors mentioned above and provide for the same track inclination the same cant value. This constant cant reference base, S, can also provide a coherent and unified calibration method for the cant measurement devices. All these devices are measuring the track inclination angle, α, reported to a horizontal plane. This horizontal plane is defined by spirit level (for almost all the hand held measuring devices), balancing weights (for old track maintenance machines) or gyroscopes (used by modern measuring and maintenance machines).

Taking into consideration the factors mentioned above, UIC (International  Union of Railways) has conventionally established for normal track gauge the cant reference base S to be 1500mm. This was initially based on the the wheel/rail theoretical contact points distance for the most used rail at the time – S49 (the one called now CEN49E1). But, as we can understand from all the things mentioned here, this is just a convention and is independent of rail type, rail inclination, gauge variance etc.

##### The Standard defining the cant measurement

The way to measure the cant is currently standardised in the European Norm (BS) EN 13848-1: Railway applications — Track — Track geometry quality — Part 1: Characterisation of track geometry:

Cross level definition in EN 13848-1 (Figure 5)

4.4 Cross level
4.4.1 Definition
The difference in height of the adjacent running tables computed from the angle between the running surface and a horizontal reference plane. It is expressed as the height of the vertical leg of the right-angled triangle having a hypotenuse that relates to the nominal track gauge plus the width of the rail head rounded to the nearest 10 mm (refer to Figure 5).
NOTE:
For nominal gauge of 1435 mm the hypotenuse is 1500 mm in length.
For nominal gauge of 1524 mm the hypotenuse is 1600 mm in length.
For nominal gauge of 1668 mm the hypotenuse is 1740 mm in length.

##### measuring CANT

The most used cant measuring device is the track gauge.

To measure the gauge the tool requires its measuring pads to be in contact with the rail running edges, at 14mm below plane of rail:

Track gauge device – gauge measurement

To measure the cant it is sufficient to place the two pads on the rail heads, allowing the device to have the plane of rail defined (see the image below). Although the sliding pad used to measure the gauge is usually in contact with the running edge of the rail, this is not a mandatory condition to provide a correct measurement of the cant.

The modern cant measuring devices, as well as the old ones, are not considering the gauge, as nominal value nor its variance, when measuring cant.

Track gauge – measuring cant

##### Can we check this?

This can be checked easily:

Place the track gauge device on two canted rails or on an inclined surface and measure the cant for this specific inclination.

Keeping the same inclination angle, α , vary the “track gauge” by moving the mobile sliding pad used to measure gauge (see the figure above).

If the device is correctly calibrated the cant will be shown the same as the initial one, not being influenced in any way  by any kind of gauge variance, as long as the inclination angle is kept constant.

No matter if the gauge is 1432mm, 1435mm, 1438mm, or any other such value, no matter the rail type or rail inclination, for the same track inclination angle α, the cant shown by any officially approved and well calibrated measuring device will the same, always reported to a 1500mm base reference (the hypotenuse mentioned in the European Norm).

###### References
• BS EN 13848-1: Railway applications — Track — Track geometry quality — Part 1: Characterisation of track geometry. BSI Group, London 2003
• Volker Matthews: Bahnbau. 4. Aufl. B.G. Teubner Stuttgart / Leipzig 1998

## 10 thoughts on “How is the cant measured?”

1. “What is non-compensating Lateral Acceleration (m/s *s)? How is this worked out? “

Check this post:
https://pwayblog.com/2015/10/29/11-82_cant-deficiency-un-compensated-acceleration-pway/
The formulas there contain the non-compensated lateral acceleration (aq) and explain what this is.
The non-compensated lateral acceleration is what we actually measure by cant deficiency but we use the later because it is expressed in the same units as the cant (mm) and it is easy to compute cant adjustments that can compensate to a certain level this lateral acceleration.

“For example 64kph (40mph) speed, Radius (1544.957), cant 75mm and Cant deficiency 43mm. The Lateral acceleration is 0.281m/s but how has this been worked out?”

Careful, for the data you gave the cant deficiency is -43 mm (cant excess).
The non-compensated lateral acceleration can be calculated directly from D – aq = D*g/S = D * 9.81 /1500

I hope the image of the calculation is visible below:

“How does the linear interpolation work for Cant Transition? If you have 25m transition and one side is 45mm cant and its continuing through a straight with cant 0?”
You are joking?
cant = 45 mm/ 25m * length where length is the position inside the transition for which you want to calculate the cant.

https://en.wikipedia.org/wiki/Linear_interpolation

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2. Shoaib Mahmood says:

Thanks Constantin for your feedback much appreciated. I would like to ask another two questions please and if you have the answer. Please provide examples.

What is non-compensating Lateral Acceleration (m/s *s)? How is this worked out? For example 64kph (40mph) speed, Radius (1544.957), cant 75mm and Cant deficiency 43mm. The Lateral acceleration is 0.281m/s but how has this been worked out?
How does the linear interpolation work for Cant Transition? If you have 25m transition and one side is 45mm cant and its continuing through a straight with cant 0?

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3. “what is Cant Deficiency in detail? What its purpose is? How does it work in real life scenario on the railway?”

Cant deficiency is in fact the remaining lateral acceleration, not compensated by the installation of cant.
Purpose? – to push the vehicle out of the track. That’s why we need to keep it under control and below well defined limits.
How does it work? – as any centrifugal acceleration (and inertial force); it tends to keep the vehicle on its straight path, pushing outwards when the vehicle moves on a curve.

“What is Cant transition? How do we work out cant change through a transition i.e. from straight, Transition and connected to a radius.”

Cant transition – the design variation of cant over defined length.
How do we work out? – linear interpolation relative to the constant values at start and end of the transition.

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4. Hello. Could someone explain me what is Cant Deficiency in detail? What its purpose is? How does it work in real life scenario on the railway? What is Cant transition? How do we work out cant change through a transition i.e. from straight, Transition and connected to a radius. I appreciate for the response which shall help me.

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5. Hi Kev. First of all there a conventional way of annotating cant in relation with curvature – a normal cant for right hand curve (outer/left rail raised) is considered positive and a normal cant for left hand curve (outer/right rail raised) is considered negative. See my article on the curvature convention : https://pwayblog.com/2016/01/21/why-a-right-hand-curve-is-positive/

For conventional railways, the cant is applied by lifting the outer rail of the curve relative to the inner rail. For the networks where this rule is in place “negative” or “adverse” cant is when the inner rail is lifted compared to the outer rail. I will prepare an article about this …

I don’t understand your second question.

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6. Kev says:

Hello Constantin,How can you tell if a cant is positive or negetive, is it a matter of left and right? Secondly how can you tell if a curve in a single tunnel is inside or outside curve. Thanks

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7. Hi Nii. Thank you for your comment and, please, excuse my late reply.
A cant transition should be kept as far as possible from an S&C layout. The switch and the crossing are inherent irregularities of the track, inducing oscillations at vehicle level. The cant transition has a gradual change in the elevation of one rail relative to the other – that can increase the vehicle response, increasing the dynamic forces transmitted from the vehicle to the track.
Nevertheless, some railway network allow cant transitions to be installed on S&C – especially when there is a difference between the cant of the main/through line and the one of the siding/turnout line. That is imposing a two-levelling design of the cant and the vertical alignment through the S&C. The case is even more complex for tramway designs, where not only the tracks are to be considered but also the road/street layout.

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8. Nii says:

Hello Constatin, thanks for this post. How do cant transition work on S&C layout

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9. cosci says:

For normal gauge tram-track the cant measurement is similar and, in fact, the same devices as the ones used for railways can be used to measure the cant on normal gauge tramway track.
If the gauge is different – narrow gauge tram-track for example – then, of course, the cant constant and the measurement parameters are different. But the principle described here should be applied, is not the gauge value to be considered but the reference base S.

Thank you for your comment, Victor!

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10. Victor Duicu says:

Hello, thank you for this article. Long time I searched for a formula to be applied for tramway and have real results..

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