Track Curvature Methodology

[Legolash2o]

Is there any good sources on how NR calculate curves of tracks, methodology and any diagrams/books that highlight the curves as well please?

My hope is to add the ability on my routing tool to show all the curvatures/bends along the entire route.

A possible alternative, which could work, would be to split the journey into 50m segments and calculate the radius of each segment?

Thanks in advance.

 

[hexagon789]

Is there any good sources on how NR calculate curves of tracks, methodology and any diagrams/books that highlight the curves as well please?

My hope is to add the ability on my routing tool to show all the curvatures/bends along the entire route.

A possible alternative, which could work, would be to split the journey into 50m segments and calculate the radius of each segment?

Thanks in advance.

It used to be done with engineer's chains (hence the name for the measurement) but I suspect NR are a bit more scientific with it now.

 

[Legolash2o]

Cool fact! Learning something new everyday on this forum.

 

[zwk500]

If you're talking about Radius, then some of the 5 miles will show it. Somebody somewhere presumably has a master set (possibly broken down by areas) but I tried to dig it out before I left and nobody had heard of it.

 

[Legolash2o]

I have all the 5 mile diagrams but it doesn't give much hints on how it was calculated unfortunately.

 

[zwk500]

Are you asking how the nominal value is calculated, or how the engineers check that that the rails are curved to the intended amount?

 

[Legolash2o]

I'm asking how they are calculated. From my initial investigation, I believe transition curves are used.

 

[John Webb]

"Transition Curves" take trains from the straighter sections of track and sort of 'ease them in' to the sharper curves.

I read some years back a description of how curves were laid out 'on the ground' and the term 'Offsets' is at the back of my mind. Obviously on a model railway one can literally use a length of string and the centre of the required circle and mark out on the baseboard the required curve to which one lays the track. At full scale you set up a series of straight survey lines running through marked fixed points and then by geometry calculate by how much the track needs to be 'offset' by at points along each of the straight lines to get the required radius curve.
I assume one can 'reverse engineer' this and if you drew a chord across a curve and measured the track offset at the centre of the chord, then you should be able to calculate the curve's radius.

 

[zwk500]

I'm asking how they are calculated. From my initial investigation, I believe transition curves are used.

Yes, transition curves (which are a Euler spiral, IIRC) are at either end. They do not form part of the actual quoted radius though. Quoted curvature values (i.e. the design baseline) will have been calculated by a variety of methods over time. I also suspect there are multiple methods used today depending on the type of survey and what the data will be used for. These will vary from Laser measurements and surveyor's instruments to GPS traces, to a length of rope and a ruler.

What I do not know is how much of the baseline data is actually that calculated by Locke, Stephenson and Bruenl et al., or if it has been remeasured. And how the baseline data that gives 1 radius for a multi-track route reaches that number, especially when there are things like Island platforms or diverging alignments that vary the curvature.

 

[furnessvale]

There is a book called "British Railway Track" published by the Permanent Way Institution. My copy is so old it doesn't even have an ISBN number I can quote but it was the bible when I was a junior perway engineer.

No doubt all is computerised these days!.

 

[DelW]

Transition curves may be of various geometries, but they are always straight at one end and a circular curve at the other. Spirals and clothoids have been used for road alignments.

In my time setting out roads and motorways in the 1970s, we used deflection angles, equal (in minutes of arc) to 1718.9 × C ÷ R, where C = chord length and R = radius. The procedure for pegs at (say) 20m intervals was to set up a theodolite over a point on the curve and align it with the tangent at that point. Then turn through one deflection angle and put a peg on that line at 20m (measured by steel tape), turn through another deflection angle and put the next peg on that line at 20m further on, then turn another deflection angle and put another peg on that line at another 20m, etc. For approximate setting out, e.g. for fences, earthworks and drainage, the pegs alone were accurate enough, but for paving, white lines etc. we used a nail in the top of each peg.

I've no idea whether the original railway engineers used the same methods, but they might well have done, they're not particularly high tech.

 

[zwk500]

I've no idea whether the original railway engineers used the same methods, but they might well have done, they're not particularly high tech.

I don't think it's what the OP was after, but this video:

shows the peg, nail and string method being used by the LMS.

 

[Railsigns]

Transition curves may be of various geometries, but they are always straight at one end and a circular curve at the other.

A transition curve can also appear between two circular curves with different radii.

 

[DelW]

A transition curve can also appear between two circular curves with different radii.

Oops, good point, of course it can

 

[Ploughman]

A 2 week course at Derby will give you some answers.
Including the 6 hour open book exam on the final day.
They also suppled the answers to the questions, but what they wanted was the method of working it out.

Hallade surveys are still in use on the ground for curve realignments, although for totally new works then GPS and Total stations linked with landscape profiling giving earth moving machine control can be used.

 

[Legolash2o]

A transition curve can also appear between two circular curves with different radii.

The most complex one that may be similar is just outside Hull where the track curves to the right and then to the left.

Thanks for the answers so far everyone, appreciated!

 

[Taunton]

Too long ago I did the calcs for this, I seem to recall that logarithms came into it. I am aware that tarmac laying machines on new roads (and presumably thus track laying machines on rail) now incorporate this in their telemetry settings.

If you think how you steer a car round a bend, you don't approach steering straight, then suddenly snap the steering wheel to the required circumference, then snap it back straight; you progressively increase then decrease the turn radius, effectively making your own transition curve. If the bend has been laid out by the engineer to suit this, that's what one is trying to do. Small scale drawings normally do not do this, but larger ones can usefully do so.

What has not been mentioned above in a 2-dimension discussion is superelevation (or cant; call it what you want) as well, which is an associated calculation. Even on a flat road your car will achieve this itself, automatically to a limited extent, by the forces acting on the suspension on different sides.

I believe one of the first applications of proper mathematically-calculated transitions on the railway was on the LNER in the 1930s, when the Silver Jubilee high speed service was introduced. This initially had some notable and reported shocks entering and leaving curves, whereupon Gresley and the civils worked together to understand what needed to be done, and there were various minor track realignments. I think Gresley spoke about this in an Institution paper somewhere, bringing Sir Isaac Newton's laws of dynamics into it, so maybe that's something to follow up.

 

[Boodiggy]

A 2 week course at Derby will give you some answers.
Including the 6 hour open book exam on the final day.
They also suppled the answers to the questions, but what they wanted was the method of working it out.

Hallade surveys are still in use on the ground for curve realignments, although for totally new works then GPS and Total stations linked with landscape profiling giving earth moving machine control can be used.

Exactly this. Hallade is taught on the basic track surveying course and all good track techs should understand it, but it isn’t as often it is done on site with a string line as there are better are probably more accurate ways to do it now, that can be done with less people and the data manipulated in excel. Understanding the Hallade method will give a good base knowledge but once you move on to more advanced things like vertical curves and managing geometry there is so much to learn. I was a tech 22 years before moving on and thoroughly enjoyed it

 

[edwin_m]

What has not been mentioned above in a 2-dimension discussion is superelevation (or cant; call it what you want) as well, which is an associated calculation. Even on a flat road your car will achieve this itself, automatically to a limited extent, by the forces acting on the suspension on different sides.

A car will actually lean outwards on a curve unless it has some clever suspension to correct this. The force pushing it inwards acts at road level, below the centre of mass, resulting in an outward rotating couple which is counteracted as the outer springs compress and the inner ones stretch. A motorcycle or bicycle will lean inwards but that's because if it didn't it would overturn.

An early and primitive form of tilt, used by some Talgo trains, effectively hung the coach body from high level pivots on frames attached to the bogies. With the centre of mass being below the pivot, it would swing outwards on curves without the need for powered actuators as used by later tilting trains.

 

[Taunton]

An early and primitive form of tilt, used by some Talgo trains, effectively hung the coach body from high level pivots on frames attached to the bogies. With the centre of mass being below the pivot, it would swing outwards on curves without the need for powered actuators as used by later tilting trains.

Indeed. Some fairground rides are specifically constructed to do this, to excess!

 

[Annetts key]

The procedure for pegs at (say) 20m intervals was to set up a theodolite over a point on the curve and align it with the tangent at that point. Then turn through one deflection angle and put a peg on that line at 20m (measured by steel tape), turn through another deflection angle and put the next peg on that line at 20m further on, then turn another deflection angle and put another peg on that line at another 20m, etc. For approximate setting out, e.g. for fences, earthworks and drainage, the pegs alone were accurate enough, but for paving, white lines etc. we used a nail in the top of each peg.

I've no idea whether the original railway engineers used the same methods, but they might well have done, they're not particularly high tech.

In the past when they have done some track realignment, wooden pegs with nails appeared in the cess. Darned annoying as if you don’t see one, they are a tripping hazard…

Now you are more likely to see targets used by surveying equipment. They glue them on to rails, pegs, any any other equipment. Although often this is more about monitoring track formation movement rather than intended track alignment changes.

 

[furnessvale]

I may have missed it, but I have seen no mention of virtual transitions in this thread.

Any vehicle, two axled or bogie, will make its own transition even if leaving straight track directly onto a circular curve with no built in transition in the track itself. The first axle starts around the curve and until the second axle meets the curve the vehicle is forming its own transition.

Of course, such transitions are far too short for any sort of speedy running, but are relevant in sidings etc.

 

[edwin_m]

I may have missed it, but I have seen no mention of virtual transitions in this thread.

Any vehicle, two axled or bogie, will make its own transition even if leaving straight track directly onto a circular curve with no built in transition in the track itself. The first axle starts around the curve and until the second axle meets the curve the vehicle is forming its own transition.

Of course, such transitions are far too short for any sort of speedy running, but are relevant in sidings etc.

For a bogie vehicle the virtual transition is approximately equal to the bogie centres.

Reminds me of when I had a tram tour of Amsterdam with a conference group on one of the then-new Combinos. I was sitting at the very rear, where the other cab would be on a double-ended version, in the overhang of a longish module with two axles rigidly attached further forward. The driver, less aware of conditions at the back and possibly enjoying the novelty of driving non-stop round the city, accelerated out of every corner so the rear was going quite fast on leaving the curve. As the axles took up the straight orientation this would whip the rear end around noticeably.

 

[furnessvale]

For a bogie vehicle the virtual transition is approximately equal to the bogie centres.

Yes indeed. I suppose the maths could get quite complicated. The two axles on the first bogie are making their own little virtual transition, but before they can complete it, the bogies centres come into play. At the other end, before the bogie centres can complete their virtual transition, the two axles on the rear bogie start their own!

I am glad to say maths is not my strong point. No doubt others will be along shortly quoting the formulae which are probably in British Railway Track, if I could reach the top shelf of my bookcase!

 

[Legolash2o]

Thankfully virtual transitions is not something I plan to worry about at the minute!

 

[zwk500]

Thankfully virtual transitions is not something I plan to worry about at the minute!

Are you intending to replicate your other railmaps with Gradient, Speed etc, and have colour-coded map with the nominal stated curvature marked on it?

If so, I fear the dataset simply doesn't exist in one piece. I have no doubt the track maintenance teams know the information you're seeking, but where it is kept and in which format I dread to think. If you do find a dataset, please DM me, I have a few former colleagues who'd be very interested to know!

 

[Legolash2o]

I'm thinking of adding it to add it to my RailMaps but the hope is to be able to automatically calculate using the geospatial data, the lat/longs for each point along a track.

I can already calculate angles and bearings in x metre segments and degrees i.e. this 10m segment goes 4 degrees left, then next 6 degrees, etc. It's currently used to prevent the routing algorithms from making sharp turns. It's just whether that would be good enough for the industry to do research but nothing safety critical.