Track Gauge Widening, All You’ll Ever Need to Know

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Russ Elliott
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Russ Elliott » Wed Sep 21, 2016 12:46 pm

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For wheelbase c on track radius r, the wheel to rail incidence angle a is given by sina = c/2r

If 'flange grinding' is considered to take place when a reaches or exceeds 3 degrees, then you should be ok if your c/r ratio is less than 0.1

Typically, P4 modellers tend to keep well on the safe side, with a maximum c/r ratio nearer the 0.05 area.

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Will L
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Will L » Thu Sep 22, 2016 10:47 pm

Julian Roberts wrote:...An LNER 2-8-2 "Cock o' the North" has 6' 2" drivers and coupled wheelbase of 19' 6" or 78mm. So looking at that graph and assuming the intermediate axles have necessary end float the minimum radius is around 2 foot 5 (if we can get the other wheels to take absurd angles.) But there's nothing about different sizes of wheels on this graph...I know I read somewhere that makes some difference.
How about a 9F? 22 foot coupled wheelbase with 5 foot wheels, if my info is correct. 2 foot 9 ins according to the graph assuming end float again. (According to Wikepedia the real thing with thinned 2nd and 4th flanges and no centre flanges managed a minimum curve of 400 ft. That's 5 foot 3 inches on our layouts, showing what very
unprototypical things we expect from our models that we make with such attention to get every detail exactly correct!)
So all this is possible without GW given sufficient end float...?


I think we can safely say you have got the hang of the graph. The wheel size thing is an issues but as far as I can make out the graph was created on the basis of a 6 foot wheel, and anything smaller should be more tolerant. What will actually work in a given situation is of course another things, as multiple factors go together to decide if a given vehicle will misbehave on a given curve or not. Of these GW is generally the least significant except when you go past the limit point, but will do no harm if it exist before then. But if you do get everything else right you should be able to get locos round remarkably silly corners GW free which is after all what the toy train manufactures have always been able to achieve. And yes they will look mildly ridiculous while they do it.

... I am not sure if you saw what I meant. What I was driving at in my question was, surely you have in setting out to show how the 31mm tool gives as much GW as we need, shown that we don't need to use it at all?

Yes I could argue that, but I can't see any point arguing for a change in our methods, honed and proved to work over time by numerous peoples, to remove small excess of GW than is not causing us any problems. On the other hand you seemed all for adjusting out standard track gauge to produce extra GW which, the evidence suggests, we already have in excess of requirement.

I would hope that this thread will enable people to know when GW becomes an issue that must be addressed, and when they can happily leave the standard 3 point gauge to do its thing.

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Will L
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Will L » Thu Sep 22, 2016 11:18 pm

Russ Elliott wrote:If 'flange grinding' is considered to take place when a reaches or exceeds 3 degrees, ....


The thing that worries me is that blanket 3 degree figure. I would have thought that, because the length of flange below the level of the rail head would be less on a small wheel than on a large one, the angles at which flange grinding would begin would less on a large wheel than on a small one. The question is how you verify/correct the 3 degree figure for different wheel sizes?. The wheel sized will certainly make a difference as to how large the angle of incidence can be before the clearance has been used up, the flanges are in contact with both rails and the need for Gauge Widening begin. Logically this can't occur before the angel at which flange grinding commences.

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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby grovenor-2685 » Fri Sep 23, 2016 8:28 am

Many years ago we took a video of all 4 wheelsets of a bogie on a run over the DLR, it was possible to see the shower of debris coming off the flange/rail interface on the corners. Unfortunately the video is no more.
The angle where grinding starts is critically dependent on the exact profile of wheel and rail as well as wheel diameter and as we don't know the first two to a requisite level of detail calculating the exact angle is pretty well impossible. Given a decent magnifying glass it should be possible to find it by experiment if anyone wants to play.
Regards

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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Will L » Fri Sep 23, 2016 8:40 am

grovenor-2685 wrote:Many years ago we took a video of all 4 wheelsets of a bogie on a run over the DLR, it was possible to see the shower of debris coming off the flange/rail interface on the corners. Unfortunately the video is no more.
The angle where grinding starts is critically dependent on the exact profile of wheel and rail as well as wheel diameter and as we don't know the first two to a requisite level of detail calculating the exact angle is pretty well impossible. Given a decent magnifying glass it should be possible to find it by experiment if anyone wants to play.
Regards


I rather though that might to true. Measuring angles of this size is going to be, um, tricky. How confident are we that the 3 degree assumption is a good one?

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Russ Elliott
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Russ Elliott » Fri Sep 23, 2016 9:56 am

Will L wrote:How confident are we that the 3 degree assumption is a good one?

I don't think we are confident - we are merely taking Malcolm Cross' historical assertion, but presumably he got it from somewhere, although I've yet to find any prototype analysis of the effect of incidence angle. (There's plenty of stuff on railhead and tyre wear.) The '3 degrees' is not an 'go, no-go' type of notion either. As the incidence angle increases, the contact area elongates asymmetrically, and I imagine the elongated parts of the contact area then begin to pass the railhead shoulder at increasingly different speeds, and that's when the friction and 'grinding' begins to build.

Looking at it from another way, if we take a P4 generally accepted wisdom that running an 80mm wheelbase (say) around a 3' curve (say) is not a very sensible idea, then that indicates a safer incidence angle is more in the region of 2 degrees, but I find that very slight difference doesn't really explain why our wheels still like to jump off the track so much more than the prototype does. It's almost counter-intuitive. Maybe it's because our model flange profiles aren't anywhere as conformant as they should be!

One thing that's always puzzled me is how flange depth (assuming a decent-ish flange angle in the region of say 70 degrees) affects the grinding situation on the front of the flange. Presumably flange depth only has an implication for the rear face, when squeezing through checks and wing gaps.

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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Martin Wynne » Fri Sep 23, 2016 10:51 am

Russ Elliott wrote:but I find that very slight difference doesn't really explain why our wheels still like to jump off the track so much more than the prototype does.

Loading. The presence of a few tons of load on a wheel is very effective at persuading it not to jump for joy. P4 trucks would hold the track just fine if stuffed full with lead, but then nothing locomotive-looking we could build would pull them along. Perhaps a motor on the axle of each one?

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Russ Elliott
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Russ Elliott » Fri Sep 23, 2016 11:09 am

Martin Wynne wrote:Loading. The presence of a few tons of load on a wheel is very effective at persuading it not to jump for joy.

I've struggled with some scaling sums on lateral forces trying to compare a vertical 10g on a model wagon wheel with a vertical 2.5t on a prototype wagon wheel, and I still can't satisfy myself why models seem to be more jumpy than the prototype. (In both cases, a reasonable starting assumption is that the interaction between flangeroot and rail shoulder is approx 45 degrees, and an interaction at the rear of the flange, where it might strike a knuckle or wing/check, of near-zero degrees.)

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Martin Wynne
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Martin Wynne » Fri Sep 23, 2016 11:21 am

Russ Elliott wrote:I've struggled with some scaling sums trying to compare 10g on a model wagon wheel with 2.5t

Forget scaling the load, it is the rolling pressure which needs to match the prototype (load per contact area). Prototype wheels and rails actually deform under load from being a point contact to create a finite contact area. Models do the same (if it was really a point contact of zero area, the pressure would be infinity), but the 1:76.2 ratio destroys any similarity in contact area or behaviour. (Area changes as the square of scale, load changes as the cube of scale.)

To get a model wheel to create a scale-size contact area, the wagon would need to be almost self-destructive in weight, certainly not made of plastic. Back to Hornby-Dublo 3-rail, anyone? That didn't jump off the track. Image

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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Russ Elliott » Fri Sep 23, 2016 11:44 am

Yes, Martin, but if one compares sideways impact forces (e.g. the front of a flange being shoved over abruptly* to a railhead shoulder, which is what will produce a vertical component of reaction force) between prototype and model, then, unless I've dropped an almighty clanger somewhere (always possible!), the sums seem to indicate our model wheels should be far more stable than the prototype. That's what I can't get my head around.

* by abruptly, I mean in a finite amount of time, which is necessary to calculate an impact force, taking vehicle speed into account as well of course

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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Martin Wynne » Fri Sep 23, 2016 11:56 am

How are you calculating the sideways force on the flange? And allowing for the forward momentum of the vehicle mass?

If I take a moving P4 wagon and blow hard at it I can derail it. Do you think 76 people could blow a full-size coal truck off the track?

Scaling the prototype exactly can make a model look like the prototype. But I never did believe it could make it behave like the prototype. CJF was not daft.

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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Russ Elliott » Fri Sep 23, 2016 11:58 am

Energy absorption. Hmmm. Does that scale to the fifth power of scale?

Martin Wynne wrote:How are you calculating the sideways force on the flange?

I'll dig out some sums later.

Martin Wynne wrote:If I take a moving P4 wagon and blow hard at it I can derail it. Do you think 76 people could blow a full-size coal truck off the track?

I think that would take 33 million people. (assuming fourth power scaling for force).

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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Julian Roberts » Fri Sep 23, 2016 10:03 pm

our wheels still like to jump off the track so much more than the prototype does.


Well it was such deviant behaviour of some of my 50g compensated short wheelbase wagons (which ran faultlessly at exhibitions) on my B8 points (which were not narrow to gauge) that prompted me to widen the gauge which solved the problem and caused me to start the discussion on the other thread in February!
Last edited by Julian Roberts on Sat Sep 24, 2016 8:38 am, edited 1 time in total.

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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby allanferguson » Sat Sep 24, 2016 12:35 am

This may be an inconsequential, irrelevant, thought, and I intervene with much trepidation in the presence of the several savants here. But in a number of real railway accidents mention has been made of flange climbing leading to derailments, and because of this attention has had to be paid to the condition of the railhead, particularly in relation to rail grinding activity; and also to flange lubrication. Weight on the wheel seems also to be a factor, with some incidents blamed on uneven weight distribution (due to suspension faults, leading to one wheel being unweighted). The thought occurred to me that compensated systems will always have the same weight distribution, whereas sprung systems will have a weight distribution which varies according to the bumps in the track.

Or am I havering? (Scots expression = talking nonsense)

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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby billbedford » Sat Sep 24, 2016 6:34 am

allanferguson wrote:The thought occurred to me that compensated systems will always have the same weight distribution, whereas sprung systems will have a weight distribution which varies according to the bumps in the track.


Compensation will always have the same unequal weight distribution.
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Will L » Sat Sep 24, 2016 8:01 am

allanferguson wrote:This may be an inconsequential, irrelevant, thought, and I intervene with much trepidation in the presence of the several savants here. But in a number of real railway accidents mention has been made of flange climbing leading to derailments.... (


Havering? No In the current snooze you will Find that Julian has pointed us at Derailment at Angerstein Junction in 2014 which is just such a one. It makes an interesting read. While the wagons we run may not share quite such a complex suspension system, generally the accidence report should sound very familiar to those who have spent time trying to workout why a single wheel on a particular wagon has suddenly chosen to go walkabouts, and provides a good checklist of reasons we could all do well to take note off.

billbedford wrote:
allanferguson wrote:The thought occurred to me that compensated systems will always have the same weight distribution, whereas sprung systems will have a weight distribution which varies according to the bumps in the track.


Compensation will always have the same unequal weight distribution.

Regrettably only too true.

Russ Elliott wrote:.... if we take a P4 generally accepted wisdom that running an 80mm wheelbase (say) around a 3' curve (say) is not a very sensible idea, then that indicates a safer incidence angle is more in the region of 2 degrees, but I find that very slight difference doesn't really explain why our wheels still like to jump off the track so much more than the prototype does. It's almost counter-intuitive. Maybe it's because our model flange profiles aren't anywhere as conformant as they should be!


I know it can feal like that some times but I'm not sure that its really true. A wagon waited to the normally recommendation isn't that inclined to leap off unexpectedly, if you can keep a fair share of it's weight on all 4 wheels. Which takes us back to the accident report.

Edited to get the link right and to add a rather important "not" in the final Partagraph
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Guy Rixon » Sat Sep 24, 2016 5:50 pm

Historically, there's a value called Nadal's limit that constraints the ratio, L/V, of lateral to vertical force on a wheel such that the chance of flange climbing is low. I think it was originally derived for French railways and later adopted by the UIC. The idea was to match speed limits to curvature such that Nadal's limit is never exceeded and everything is acceptably safe. The limit is probably a bit conservative.

V is clearly the weight bearing on the wheel. If a wheelset is self-steering properly, then L is the centripetal force exerted by the rail on the wheel, so it scales linearly with the mass supported by the wheel, as the square of the speed and inversely with the radius of the curve. So the fact that we tend to run our models faster than the prototype round sharp curves is raising L/V, maybe by factors of two or three. This may account for some flange-climbing derailments in models.

I've just watched, at Scaleforum, a number of centre wheelsets of 6-wheel coaches climbing off the rail. These were the only derailments I saw all day, so there seems to be a particular issue here. I suspect that these centre wheels get high lateral forces because of limited side-play, but carry almost no weight because the coaches have been set up a 4-wheelers with a floating extra axle. Hence, flange-climbing is to be expected. Note that this won't affect 6-wheel tenders so strongly as tenders have shorter wheelbases than coaches.

IIRC, the UIC value of Nadal's limit ignores details of wheel and track geometry (strictly, ignores the possibility of varying the geometry to improve track holding). Full-size LRT systems want sharper curves than main-line systems, and there is some research on how changing the shape of the flange can increase the L/V limit to allow sharper curves for a given speed. See http://www.railjournal.com/index.php/rolling-stock/flange-climb-derailments-causes-and-prevention.html.

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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Julian Roberts » Sat Sep 24, 2016 10:24 pm

Interesting quote from Guy's link here:
http://www.railjournal.com/index.php/ro ... ntion.html

Slightly widening the track gauge, which is a practice commonly applied in operation, can increase the rolling radius difference for tapered wheels on curves to assist wheelset steering,


This article is about flange climb on urban transit systems. It doesn't say, it doesn't need to, one can assume it, that the vehicles will be on 4 wheel bogies. Yet it mentions the practice of gauge
widening. I really wonder if it's right, the common assertion that 4 wheel vehicles don't need GW.

This quote along with Martin's earlier quote from BRT1 suggests to me we might at least re-visit the assumption that GW is (by implication SOLELY) for 6 (or more) wheel vehicles.

Or am I havering (living in Scotland though unaware of the expression before Allan F's post yesterday)?
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby ianpenberth » Sun Sep 25, 2016 6:26 pm

allanferguson wrote:sprung systems will have a weight distribution which varies according to the bumps in the track


Not true in every case. http://www.penbits.co.uk/Content/TechDesc.html#BogieS
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Russ Elliott » Mon Sep 26, 2016 4:58 pm

Martin Wynne wrote:How are you calculating the sideways force on the flange?

I promised earlier to dig out some sums, so here we go.

Imagine a typical prototype 3' wheel (weight 500kg, say) striking an 'immovable object' like a check or a wing knuckle at a sedate 15mph. If the the impact takes place over a duration of say 0.25s, the impact force is 26.8kN. That impact force will be transmitted laterally, because that is the shape of the interaction between the rear of the flange and the railhead, and the transmitted lateral will accelerate the wheelset toward the running rail, where the push will be resisted only when the wheeltread root collides, in a sort of dynamic glancing blow, with the running rail shoulder. For the sake of argument, let's take the common tangent of the flange root and rail shoulder at approximately 45 degrees (see diagram above), so the resulting force components will be 50% lateral and 50% vertical. Very simplistically, one can say the impact force will therefore result in a resultant vertical force on that wheel of 13.4kN, which will be transmitted to the body via the wheel spring. The ratio of that force to the weight the wheel is supporting, say one quarter of a 10t wagon, is a significant 54%.

For a model wheel (say 3g, which is too generous) of a 40g wagon at an equivalent scale speed (0.09m/s) but over the same impact duration, the resultant vertical impact force is 0.001N. The ratio of the vertical force to the weight being supported then becomes an insignificant 1%.

I accept the above impact analysis is crude, but it is the comparison of the prototype 50-plus% and model 1% ratios that is illuminating.

Guy Rixon wrote:So the fact that we tend to run our models faster than the prototype round sharp curves is raising L/V, maybe by factors of two or three. This may account for some flange-climbing derailments in models.

I don't think so.

Let's compare the same 10t prototype wagon travelling at 15mph around a 90m radius curve. The centripetal force is approximately 5kN. If this is apportioned equally between the front and the rear wheelsets of the wagon, a reasonable assumption I hope, each wheelset would be undergoing approximately 2.5kN sidethrust, which is approximately 10% of the 25kN vertical force on each wheel. In other words, for that speed and that flange angle (70 degrees is a reasonable value to take for our prototype and model profile), it is comfortably below the Nadal L/V limit, even in high friction situations. For an equivalent 40g model wagon traversing a 1.2m radius curve, the ratio of lateral to vertical force is, again, an insignificant 1%. (Even if the model speed is increased to 60smph, the model lateral to vertical force ratio becomes a very low 4%.)

In both the impact force analysis and via a Nadal analysis, the sums indicate our models should therefore be far more stable than the prototype. (For the model case, however, coupling forces will easily counter the opposing, but small, centripetals, and are likely to dominate the flange sidethrust situation.)

I'm still scratching my head a bit. Something doesn't add up.

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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Noel » Mon Sep 26, 2016 6:42 pm

Russ, is your 500 Kg the weight of one wheel or that of both wheels and the axle? It should be the latter at least, I think. Also, is no component of the weight of the remainder of the vehicle involved? Sorry if these are silly questions, but applied maths never was my strong point.
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Russ Elliott » Mon Sep 26, 2016 7:30 pm

Noel wrote:Russ, is your 500 Kg the weight of one wheel or that of both wheels and the axle? It should be the latter at least, I think. Also, is no component of the weight of the remainder of the vehicle involved?

Noel, I took 500kg as a guesstimated weight of a single 'solid' wheel (like a 3-hole disc), because I wanted the single wheel to be the cause of my chosen 'impact' scenario. It is true the resulting impact force will, in reality, accelerate the whole wheelset sideways (the wheelset as a whole probably being more in the order of 1200kg?), and an unknown proportion of the vehicle weight, the latter depending on sideways slop in the journals, but I thought for the sake of simplicity in my crude analysis that energy would be conserved to a large extent - which may or may not be a reasonable assumption! The wheelset will also have a forward (longitudinal) momentum (in the case I chose, in the region of 8000 kg m/s), but I thought this would also be largely conserved, and thus did not need to be considered in assessing the lateral actions and reactions.

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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby junctionmad » Mon Sep 26, 2016 10:24 pm

To try and deal with Russ's conundrum I think force analysis is rather less useful. I think it's clear that the various pressures on a model wheel from conventional prototypical horizontal and vertical forces are smaller in proportion

Hence we need to look elsewhere. Personally I think track irregularities play a far bigger part in model track them prototype track. Secondly coupling forces are far greater as a proportion then the prototype. Acceleration of model trains is also typically far greater then the prototype as well.

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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Guy Rixon » Tue Sep 27, 2016 7:57 am

Things likely to fall off, from observation:

    * Any vehicle moved fast through mis-aligned P&C work. Applies to any scale and standard, including full-size.
    * Models moved fast over very-irregular plain line. Seems to apply to all scales and standards, but especially to 00.
    * Stock hauled round tight curves at excessive speeds. Problem increases as the standards get closer to full-size practise, with tinplate models being almost immune. However, P4 stock seems to cope well enough at exhibitable speeds.
    * Six-wheeled coaches, on plain line. Happens each time anybody farts in the same postcode, on both P4 and EM. Not tested for coarse scale because
    there are so few 6-wheel coaches to that standard (but the N-gauge boys have a Stove R now, so I guess I should see how those manage).
    * Propelled stock. My impression is that rafts of, say, six wagons or so are more likely to go wrong than long trains or single vehicles, but this needs more observation.

The last two points look to me like the cases where the flanges climb because they are rammed against the rails by misalignment (so centripetal forces not very relevant), and the issue with the 6-wheel stock is where both Nadal's limit and gauge widening matter. So one could recast the gauge-widening recipe to "whatever is needed to get a D&S 6-wheel underframe round the curve at line speed".

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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby billbedford » Tue Sep 27, 2016 9:57 am

Guy Rixon wrote:I've just watched, at Scaleforum, a number of centre wheelsets of 6-wheel coaches climbing off the rail. These were the only derailments I saw all day, so there seems to be a particular issue here. I suspect that these centre wheels get high lateral forces because of limited side-play, but carry almost no weight because the coaches have been set up a 4-wheelers with a floating extra axle. Hence, flange-climbing is to be expected. Note that this won't affect 6-wheel tenders so strongly as tenders have shorter wheelbases than coaches.


It's likely that these coaches have some sort of lateral springing arrangement which would increase the tendency for flange climbing on tighter curves.
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