How banked are railway curves?

[Bayum]

I was watching the following video, attempting to see if I could find the new paint scheme 322481 has had.

Throughout the video, I realised I hadn't noticed how far the train's sides came from the roof to the bogies and bottom of the train, as with the class 313.

However as the video ended, I saw the train was traversing a corner which exemplified any idea that the train carriage was a cuboid.

This leads to my above question - how banked are railway curves?

http://www.youtube.com/watch?v=69wFqLST9iY
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Oh. Wikipedia tells me that it's also known as 'camber', 'cant' or 'superelevation'.

 

[DownSouth]

Up to 150mm of superelevation (difference in height from inside rail to outside rail) on the network for which I have curve data - the entire Australian interstate network.

That's up to 10.5% as a gradient, or about 6° as a banking angle.

 

[asylumxl]

Up to 150mm of superelevation (difference in height from inside rail to outside rail) on the network for which I have curve data - the entire Australian interstate network.

That's up to 10.5% as a gradient, or about 6° as a banking angle.

I believe in the UK there is a maximum of 160mm plus the cant deficiency. But I may well be totally wrong.

 

[Joseph_Locke]

In the UK on Network Rail lines the Normal and Maximum cant is 150mm, over 1505mm rail centres (110mm in platforms and lower again for curves tighter than 290m radius) so about 1 in 10.

The exceptional limit is 180mm of cant, but this is not normally allowed for new work.

 

[miikey]

110mm through platforms, 90mm on jointed track and 150mm everywhere else.

 

[Welshman]

What is the cant on the down main line leaving Grantham station towards Newark?

When passing through at line speed you are unaware of it, so it works well. But after boarding at Grantham and walking through to find your seat, it is alarmingly noticeable as the train slowly accelerates.

 

[edwin_m]

Oh. Wikipedia tells me that it's also known as 'camber', 'cant' or 'superelevation'.

"Cant" is probably the favoured term for UK rail engineers, but "superelevation" is more likely to be understood internationally. I don't think "camber" is correct even for a highway - just googled it and it actually seems to be the slope down from the centre to the sides of a road which is needed for drainage.

 

[Trog]

There are one or two places with 200mm of cant, it was installed thus to avoid having short speed restrictions around curves in what would otherwise have been a long run at a higher speed.

 

[DownSouth]

"Cant" is probably the favoured term for UK rail engineers, but "superelevation" is more likely to be understood internationally.

My understanding is they are interchangeable, but for the sake of clear communication superelevation is the preferred technical term these days over the more traditional cant.

I agree that it would be very rare to hear a railway's curves being talked about as having camber. If anything, I would expect this to be used only when referring to the profile of the railhead.

I don't think "camber" is correct even for a highway - just googled it and it actually seems to be the slope down from the centre to the sides of a road which is needed for drainage.

These days in Australia, this has been separated into two different terms - crown for the convex surface of a straight road, and camber for the gentle banking in a curve which performs the dual functions of assisting handling and draining water to the inside of the curve.

A curve is said to be off camber where it is dead flat, crowned like a straight road or even set up with a reverse camber sloping down to the outside - something you'd only see in an old road running along a valley or in a case where the formation has subsided. A curve is said to be banked where it has camber in excess of the amount normal for neutral handling.

As a cyclist, I find off camber curves scary because you need to wipe off so much speed to get the bike to turn in, but banked curves are fun - there's one on a downhill road near me with a 25 km/h advisory sign that I can throw my carbon fibre Scott Foil into at 55 km/h! As a driver I don't mind off camber curves because the body leans on the outside wheels and they bite, but the same banked curves I love on my bike cause the front-right tyre on my car to lift off the surface if I go even a bit too fast.

 

[Taunton]

On UK railways the pioneers of actually getting into this properly and mathematically were the LNER when they introduced the A4-hauled "Silver Jubilee", for until that time speeds had not ben high enough to matter, and although there was some superelevation had previously been done on a hunch. Gresley was a member of the Institute of Civil Engineers, as well as a Mechanical, and the LNER did not have a Chief Civil Engineer, only regional ones, so much of the theoretical background was done by Gresley personally and his inner team. The early Jubilee runs had some notable shocks on curves, felt in the train.

There is a calculation of this which I would have to look up now, there's a cube root in it somewhere, which was developed at this time.

Because the track obviously does not change instantly from rails level to the degree of superelevated desired, there is a transition, and this is in conjunction with the same for the horizontal alignment, for transition curves, with a gradual change from straight to the required curve to give the required g forces. All this has to be calculated and then worked into instructions to be followed by the platelayers at the site to reballast and realign. The key issue, as discussed above, is that while the result may suit an express running at line speed, it has a negative effect on a very slow train, starting from rest, where the opposite force is felt, and leads to increased friction against the lower rail, and the need for more power to overcome this. There are a range of other issues as well, such as clearances from lineside structures and handling of points etc in the superelevated section. An extension of the technique allows for high speed points to actually introduce a degree of superelevation for the diverging track.

 

[snowball]

On a transition curve the sideways displacement of the track from the straight route is proportional to the 3/2 power of distance. That may be what you're thinking of when you refer to a cube root.

The basic formula for superelevation is very simple to derive. If a vehicle of mass m is going at speed v round a circular curve of horizontal radius r canted at an angle a, then its acceleration is v^2/r horizontally inward.

The forces on it are its weight mg vertically downward, and the reaction of the track, which we can regard as the sum of two components, R perpendicular to the track (i.e. an angle a off vertical), and S sideways to the track (i.e. an angle a off horizontal).

The total force sideways to the track is thus

m g sin(a) - S

while the component of mass acceleration sideways to the track is

m v^2 cos(a)/r

These two must be equal, so

S/m = g sin(a) - v^2 cos(a)/r

If all trains on the curve always travelled at the same speed, with no danger of being checked, the purpose of superelevation would be to make S=0, so

tan(a) = v^2/gr.

 

[Emyr]

Are you describing clothoid curves, or are they only used for horizontal deviations?

 

[snowball]

Are you describing clothoid curves, or are they only used for horizontal deviations?

Is that question for me?

The first paragraph of my post is about clothoid transition curves and is about the horizontal aspect only. Strictly speaking it's only an approximation, but might be good enough to use in railway applications.

The rest of my post is derived for circular curves, but could be applied to transition curves too, using r to mean the local radius of horizontal curvature.

On a superelevated transition curve, the curvature (1/r, reciprocal of the radius of curvature) is proportional to distance along the curve, so the cant, being proportional to 1/r, should also be proportional to the distance, measured from the straight end.

 

[Taunton]

On a superelevated transition curve, the curvature (1/r, reciprocal of the radius of curvature) is proportional to distance along the curve, so the cant, being proportional to 1/r, should also be proportional to the distance, measured from the straight end.

Wasn't this somewhat straightforward algorithm where the Advanced Passenger Train went wrong (particularly on reverse curves) and caused travel sickness, and where the Pendolino developed a more sophisticated approach and got it right?

 

[Ships]

Wasn't this somewhat straightforward algorithm where the Advanced Passenger Train went wrong (particularly on reverse curves) and caused travel sickness, and where the Pendolino developed a more sophisticated approach and got it right?

Actually the apt was too good at achieving equilibrium, which confuses the brain when it sees you're going round a curve and causes the travel sickness. The pendolinos tilt is I believe more crude and is preset into the TASS Belize which speak to the train telling it to tilt.

 

[Railsigns]

TASS Belize which speak to the train telling it to tilt.

TASS balise. Belize is a country in Central America.

 

[Ships]

TASS balise. Belize is a country in Central America.

Appologies, auto correct dropping a clanger.

 

[Railsigns]

Appologies, auto correct dropping a clanger.

Fair enough. I see you've turned it off now, anyway.

 

[LesF]

I think the difference between APT and Pendo is that APT was designed to eliminate all of the sideways force which, as Taunton says, confuses the passenger's brain and makes him queasy, and Pendo was designed to eliminate only 75% of the sideways force so the passenger feels what his eyes tell him to expect. But then I still sometimes feel ill at ease cornering in a Pendo. Maybe they're speeding.

 

[edwin_m]

I think the difference between APT and Pendo is that APT was designed to eliminate all of the sideways force which, as Taunton says, confuses the passenger's brain and makes him queasy, and Pendo was designed to eliminate only 75% of the sideways force so the passenger feels what his eyes tell him to expect. But then I still sometimes feel ill at ease cornering in a Pendo. Maybe they're speeding.

Correct, though some of the reported queasiness may have been due to the alcoholic refreshments consumed by the reporters on the press run. It also means the Pendolino doesn't have to tilt as far as the APT (6 degrees versus 9 I think) so the body cross section can be larger without going out of gauge. However in my view the small windows and poor interior design of the Pendolino negates this advantage and they feel far more claustrophobic than the APT ever did.

 

[LesF]

We're straying from the thread here. I view Pendos as fast, smooth and quiet, but cramped, claustrophobic and smelly. I read that the Pendo cabin is more cramped than necessary because they designed for every eventuality even though they will never all happen at the same time. I've suggested waisted carriages, i.e. narrower at the mid-length and wider at the bogies. I believe the idea is being incorporated into new designs. I often want to take a can opener to the windows to open them up. Virgin insisted they'd cure the toilet smells then said they'll have another try at it. If you have extract fans in the cabin that are stronger than the extract in the toilet, you are bound to draw smells out of the toilet. So fresh air should be supplied into the cabin and extracted from the toilets. My experience of ventilation engineers is that they will insist that it'll work while it's obvious that it won't.

 

[PaxVobiscum]

My experience of ventilation engineers is that they will insist that it'll work while it's obvious that it won't.

I too find they tend to talk hot air much of the time.

 

[edwin_m]

I too find they tend to talk hot air much of the time.

However, ventilation engineers do have their fans.

 

[Joseph_Locke]

Veering wildly back to the subject, like a galvo needle on a windy day; tilt has nothing to do with cant; it's train-generated cant deficiency mitigation ...