(A commented extract from BSEN 13803-1 (2010) Railway Applications – Track – Track alignment parameters – Track gauges 1435 and wider – Part 1: Plain Line)
The track alignment design PARAMETERS (BSEN 13803-1 – 5.1.2)
In the design process the values of the track alignment parameters are chosen to ensure a safe riding with at least a minimum comfort level. A good compromise has to be found between train dynamic performance, maintenance of the vehicle and track, and construction costs.
The European Norm for track alignment geometry BSEN 13803-1 (2010), names the following track alignment design parameters:
- speed (km/h);
- radius of horizontal curve (m);
- cant (mm);
- cant deficiency (mm);
- cant excess (mm);
- cant gradient (mm/m);
- length of cant transitions (m);
- rate of change of cant (mm/s);
- rate of change of cant deficiency (and/or cant excess) (mm/s);
- length of transition curves in the horizontal plane (m);
- length of alignment elements (circular curves and straights) between two transition curves (m);
- radius of vertical curve (m).
The parameters in bold are safety-related. If these parameters are well chosen, the others will provide an increased comfort and are considered comfort-related.
For most of the parameters, two different types of limits are specified:
- a normal limit;
- an exceptional limit (or a maximum/minimum limit in the British Track Standards NR/L2/TRK/2049 and NR/L2/TRK/2102).
The exceptional limit may have two different meanings:
- For safety-related parameters, it shall be the absolute maximum limit of this parameter; this maximum limit may depend upon the actual track mechanical and geometrical state.
The exceptional limits in this case are safety-related and may (for most parameters) induce a reduced comfort level. These limits are extreme and should be used only under special circumstances or after specific safety-case analysis.
The limits are defined for normal service operations. If and when running trials are conducted, for example to ascertain the vehicle dynamic behaviour (by continually monitoring of the vehicle responses), exceeding the limits (particularly in terms of cant deficiency) should be permitted and it is up to the infrastructure manager to decide any appropriate arrangement. In this context, safety margins are generally reinforced by taking additional steps such as ballast consolidation, monitoring of track geometric quality, etc.
- For non-safety related parameters, the limits shall be considered as the limit above which passenger comfort may be affected and the need for track maintenance increased; however, to cope with special situations, values in excess of the limits may be used, but they shall not exceed any safety limit.
The use of exceptional limits should be avoided, especially use of exceptional limits for several parameters at the same location along the track.
For cant deficiency, not all vehicles are approved for the normal or exceptional limits. For such vehicles, the operational limit shall be consistent with the approved maximum cant deficiency.
Unnecessary use of the exceptional limits should be avoided. A substantial margin to them should be provided, either by complying with the normal limits or by applying a margin with respect to permissible speed.
Exceptional Design Values shall only be used after an assessment of the additional risks involved has been undertaken and consideration given to the amelioration of those risks. Such assessment shall accompany the design for approval.
New lines should, whenever possible, make use of Normal Design Values. Values up to the Maximum (or Minimum) Design Values may be used when necessary for new construction and realignments.
Constraints and risks associated with the use of exceptional limits (BSEN 13803-1 Annex G)
The use of exceptional limits results in a reduced level of comfort for the passengers and may lead to higher track maintenance costs, particularly if associated with undesirable track geometry and equipment quality.
Therefore, the designer should avoid unnecessary use of the exceptional limits for the permissible speed, either by complying with the normal limits specified in this standard or by using a margin with respect to design speed.
It is permissible to use the exceptional limits specified in this standard if use of the normal limits incurs unacceptable costs in achieving the maximum desired speed. However, every effort shall be made to design the alignment with substantial margin to the limits.
The above policy is equally valid for the upgrading of existing lines for higher speeds, when observance of normal limits would lead to unacceptable costs being incurred.
The exceptional limits are only acceptable for certain designs of passenger vehicles and even then, it will lead to lower comfort levels for the passengers and almost certainly higher maintenance costs.
The use of exceptional limits has to be agreed by the appropriate body that shall ensure that the vehicle stability and lateral track force criteria are met.
Where exceptional limits are used, maintenance should be kept within the accepted limits and additional inspection of the track may be required.
In comparison with the normal limits, the values used by the designer within a specific project should in normal cases be as low (high) as reasonably possible.
Note
NR/L2/TRK/2049 defines at B.2.4 Curving Design Values – Guidance on Circular Curves, the normal and exceptional values of the cant deficiency/applied cant ratio. This parameter is mainly maintenance related and the above statements about the exceptional limit shouldn’t be considered for it, if both cant and cant deficiency are under the normal limits.
It should become a good practice to ignore this parameter in the design, if the cant and the cant deficiency are acceptable and significantly below their normal limits, as it introduces artificial constraints in the cant design process with no gain both for safety and comfortable riding (See the PWI Journal article: Designing curves for speed. The basic principles resuscitated).
References
- BSEN 13803-1 (2010) Railway Applications – Track – Track alignment parameters – Track gauges 1435 and wider – Part 1: Plain Line, British Standards Institution
- NR/L2/TRK/2049 (2010) Track Design Handbook, Network Rail.
- *** (2014) Designing curves for speed. The basic principles resuscitated, The Journal, April 2014/Volume 132 – Part 2, Permanent Way Institution.
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I’m not familiar with the studies done for EN 12299.
UIC has done some tests in the 2000’s – summarized here: https://vti.diva-portal.org/smash/get/diva2:670177/FULLTEXT01.pdf Probably these were the basis and start for EN12299.
But I think the track design limits were established well before.
There are some papers presenting tests done in the 50’s – for example BR did some between 1949 and 1951, briefly presented here:
https://www.icevirtuallibrary.com/doi/10.1680/ipeds.1952.11271
The limits for the rate of change of cant have not changed much since then.
Not sure about the rate of change of cant, but I have a constant feeling that for the rate of change of cant deficiency, the limits we are working with are over-conservative for the world we live in today.
i think the misalignment between the cant transition and geometrical transition you are alluding to is also a good idea, forgotten or left unexplored. There is probably the issue of how much benefit will that bring to compensate for the complication of designing, installing and maintaining it.
The limits are older than us, established for vehicles that were 80 years behind the ones we travel with today. Obeying to these limits today arguably brings some additional comfort.
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Oh, and I’m properly logged in this time. Username fbfree.
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Hi Constantin,
I basically have a question and a point.
The question is, how is the 55 mm/s cant limit determined? Is it the actual change in cant or an associated acceleration induced in the studies that causes discomfort? If it’s the acceleration, then it should be possible to smoothly exceed a 55 mm/s cant transition. It would be useful to know exactly which studies the EN 12299 bases its limits on in order to check this.
The point is, where you measure the cant and acceleration makes a difference to passenger comfort. Track geometry standards measure these parameters at the top of the rail while the passenger comfort standards measure this from floor height (there may be some that use seat height). The actual cant deficiency at floor height, lets call it D’, is
D’ = D + h / S * (d²C/dt²) * (S/g)
where h is the floor height, S is the rail cross-level, and (S/g) is the conversion from horizontal acceleration to cant deficiency. The two factors of S cancel, giving
D’ = D + h / g * (d²C/dt²)
Thus, the change of change of cant has a direct relation with cant deficiency as defined for passenger comfort.
The actual effect of this term will depend on the response of the rail vehicle’s suspension to roll. Assuming the suspension has a 1 Hz cutoff frequency in roll, f_c , the additional cant deficiency from an extreme step change in change of cant gives
h/g*d²C/dt² = h/g (dC_2/dt – dC_1/dt) * 2 pi f_c = (915 mm) / (9810 mm/s²) (55 mm/s – (-55 mm/s)) * 2 pi (1 Hz) = 64.4 mm
That’s quite the additional cant deficiency, even if only applied for under a second.
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Hi @luminous5532d6d9d3 . Interesting point of view. Tell me more!
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There’s one parameter that’s missing that trouble’s me: the rate of the rate of change of cant.
The issue here for passenger comfort is that any axis used to measure cant is below the floor of the vehicle, whereas passenger comfort standards for lateral acceleration and rotational velocity (i.e. EN 12299) base the axis of rotation on the floor of the vehicle. The lever between the two heights causes a small, but not insignificant, lateral acceleration and jerk, especially on taller rolling stock.
The standards try to mitigate this effect a little with non-linear curve transitions, but it would seem more appropriate to calculate the combined effect of both changes of cant and cant excess when designing for passenger comfort. Some consequences on design would be to, for instance, begin the cant transition around 0.3 seconds before the start of the curve; to tighten the curve at the end of the cant transition, where the end of the cant transition gives an effective reduction in lateral acceleration; or to avoid starting the cant and the curve at the same location.
I’m also a little doubtful as to the reason why cant and cant deficiency are limited to 55 mm/s. This value translates pretty much directly from the limits on roll velocity expressed in EN 12299, which I imagine comes from studies similar to this NASA study examining passenger comfort in aviation. https://ntrs.nasa.gov/api/citations/19800011520/downloads/19800011520.pdf
However, this study, and I imagine most laboratory studies that don’t run down a track or in the air, combine the effects of rotational velocity and rotational acceleration, while only parameterizing rotational velocity. This doesn’t capture the situation of running through a significant reversal in curve, where it might still be comfortable to have a larger peak change in cant as long as the rotational acceleration and lateral acceleration at floor/seat level are kept within limits.
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Hi, have you come across a curve with its circular length as zero. It does not make much sense to me. I am said it is allowed in LRT. why would someone choose this over a simple curve (if there is space constraints)
wont there be additional jerk due to sudden change in direction at the junction of two transitions?
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