Cosining the Track

[43106]

OK chaps, this is a beauty - in technical terms.
In the early 1980's, my late father was in charge of the railway network within the Sellafield Nuclear Complex. This also used to include an array of sidings outside the BNFL (British Nuclear Fuels Ltd) site that was (technically) accessible by the Great British Public. When my Dad was there, these sidings were replaced by a 'bypass' which, in essence, was nothing more than a very tight curve. The trucks carrying the atomic stuff (called, ironically, 'coffins'!) were double bogie wagons, where each bogie had 3 axles. Because of the short radius of curvature of the bend, the bogies frequently jumped the tracks. My dad didn't have a clue what the problem was, so he called British Rail (as it was called then) for advice. Apparently, a BR bloke came down from Carlisle, looked at the problem and said "OK, no problem, we'll cosine the track."
Does anyone have any idea what he was talking about?

I've just had a look at Sellafield using the 'satellite' option of Google Maps, and the curve is still there, but the sidings have been put back.

 

[thelem]

Just guessing here, but bearing in mind its a curve was he referring to the sine / cosine wave? (http://en.wikipedia.org/wiki/Image:Waveforms.svg ). My not very good understanding after a quick search suggests he was maybe talking about making the curve and tension in the rails as even as possible, which would seem to be a solution to the problem.

 

[43106]

Just guessing here, but bearing in mind its a curve was he referring to the sine / cosine wave?

No, not entirely. Sine waves & Cosine waves do exist (they are identical in shape to each other, but in terms of phase, they are 1/4 of a cycle apart), but Sine & Cosine also exist as trigonometrical (probably spellt rong) terms that describe aspects of, say, a triangle. I'm 99% certain that 'Cosining the Track' refers to the latter.

43106 - an Ivatt 4MT that pulled my school train from Seascale to Egremont in 1965 & 1966 and went past the Sellafield complex.

 

[Dennis]

this might be a load of tosh but...

The equation of a circle is given as;

x = r cosθ
and
y = r sinθ

where the centre of the circle is at 0,0, r is the radius and θ is angle in radians around the curve from the x axis.

By using this geometric relationship, the coordinates of a smooth curve of constant radius may be calculated.

If the curve radius was uneven, any exceptionally tight (small radius) parts of the curve could have caused problems with trucks where a relatively long distance exists between non-articulated wheels. The minimum curve radius which may be traversed is often marked on wagons where problems may arise.

Buffer size may also be a consideration - smaller radius curves will result in a greater buffing width (for any given wagon length).

 

[DaveNewcastle]

Yeah, Denis has just about got it. Let me try explaining.
If you put a 3 axle bogie on a curve and imagine that the front and rear wheels are sitting nicely on the rail head with their flanges just inside the head, then the middle two wheels are going to be half way between the front and back one, and that means that the flange of the middle wheel on the INSIDE of the curve is going to be closer to the railhead ('cos the wheels are in a straight line and the track is curved).
The tighter the curve, the closer the flange gets to the rail until, on a very tight bend, the middle flange is scraping the inside rail and pushing the flanges on the opposite side (the front and back wheels on the outside of the curve) hard againt the outer rail - until something has to give!

The solution - make the track wider on tight curves.
How much wider? By the cosine of the bogie length and the angle thru which the track curves in that bogie-length.
And a cosine of an angle is (da, da!):-
the distance the curve has bent (to left or right) within the length of the bogie, divided by, the length of the bogie.

Some triple wheel sets leave out the flange on the middle wheel to avoid this. Their middle wheel can slide across the rail on bends - there were lots of steam and diesel traction with triple axle bogies.

 

[TheSlash]

The solution - make the track wider on tight curves.
How much wider?

We normally just guess

 

[43106]

Yeah, Denis has just about got it. Let me try explaining.
If you put a 3 axle bogie on a curve and imagine that the front and rear wheels are sitting nicely on the rail head with their flanges just inside the head, then the middle two wheels are going to be half way between the front and back one, and that means that the flange of the middle wheel on the INSIDE of the curve is going to be closer to the railhead ('cos the wheels are in a straight line and the track is curved).

I wasn't aware of this. I've always been under the impression that 3-axle bogies were designed/built so that the middle axle could slide laterally when the bogie was on ANY sort of curve. Clearly, I was wrong.

The tighter the curve, the closer the flange gets to the rail until, on a very tight bend, the middle flange is scraping the inside rail and pushing the flanges on the opposite side (the front and back wheels on the outside of the curve) hard againt the outer rail - until something has to give!

The solution - make the track wider on tight curves.
How much wider? By the cosine of the bogie length and the angle thru which the track curves in that bogie-length.
And a cosine of an angle is (da, da!):-
the distance the curve has bent (to left or right) within the length of the bogie, divided by, the length of the bogie.

Some triple wheel sets leave out the flange on the middle wheel to avoid this. Their middle wheel can slide across the rail on bends - there were lots of steam and diesel traction with triple axle bogies.

Thanks very much for that, Dave - your explanation makes sense. However, when the track has been cosined, does this ban ordinary TWIN-AXLED trucks/bogies from using the track? I'm thinking of the Class 24s & 25s that used to shunt the 'coffins' into and out of the Sellafield site.

43106

 

[TheSlash]

As long as the gauge doesn't exceed 1465mm any rail vehicle can use the track. Once the gauge exceeds 1465mm, the line is blocked to traffic

 

[DaveNewcastle]

Ah, well, its actually more complex!
"I've always been under the impression that 3-axle bogies were designed/built so that the middle axle could slide laterally when the bogie was on ANY sort of curve. "
Sorry to mislead you 43106. I meant to use that illustration of the flanges to help explain the need for widening the gauge, I did actually add: Some triple wheel sets leave out the flange on the middle wheel to avoid this. Their middle wheel can slide across the rail on bends.

But even with twin axle bogies or simply twin axled vehicles (such as Pacers) then tight curves can introduce high forces on the insides of the railhead as the bogie vehicle "tries" to go in a straight line. As The Slash notes, the increased track spacing should not be large enough to prevent any other vehicles from using the track (but see below), its only going to be 10 or 15 millimetres (I think).

But its actually a more complex matter - you'll recall that heavy-rail doesn't rely on the flanges to centre each vehicle on the track but on the chamfer of each tyre - each wheel having a bigger diameter at its inside than its outside, and the weight of the vehicle being enough to keep the vehicle centred. So if the middle wheelset slides across the track laterally, it will rise up at the curve's inside, taking more of the vehicle's weight and reducing traction from the wheels in front and behind it, and with the opposite effect on the outside of the curve (the middle wheel will have less pressure on the rail). Now this effect is going to be very slight, but remembering that the main reason for a triple wheeled bogies in traction is to INCREASE the tractive contact between wheel and rail, then although there might not be much vertical movement on a curve, there can be an adverse effect on traction. Widening the track spacing isn't going to fix this but it does help to keep most of the wheel rims in some sort of contact! Each axle's suspension will absorb the vertical differences between them.

Slightly different issue at nuclear plants:
Not often seen is the amazingly tight curves INSIDE nuclear reactor buildings. The track runs into the building and has to curve under each of the 2 reactor vessels. (Power stations are usually built with 2 reactors in each plant.) These very tight curves also have points on the curves to allow access to either reactor, which makes the design even trickier. There's very little space between the central concrete support for the reactor and the compact diameter of the vessel which the vehicle has to move beneath. From memory, they turn through 90 degrees in something under 10 meters - using very short wheelbase vehicles - and so clearly only very short vehicles can travel on these curves, the shunters and their short carriers. Sadly I don't know the gauge (and I don't have access there anymore). But there are similar special tracks in other industrial environments - so perhaps someone else has knowledge of the variations on track spacing on these exceptionally tight curves?