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

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

Postby Will L » Fri Aug 26, 2016 5:31 pm

In another thread not all that far away, there has been a long discussion about gauge widening. I’m not going to suggest you go away and read it, precisely because it is very long. And it is very long because it has been conducted in the absence of full facts about how best to treat Gauge Widening in the context of P4 standards. The discussion has been driven by the truth that some of the figures given in the standards relating to gauge widening appear, at best arbitrary, and there is no obvious logic to the characteristics of the current standard three point gauge which we use to implement it. To put future thinking on a firmer footing, its high time we understood and quantified the actual mechanisms that require gauge widening.

To this end I have worked out how to calculate what gauge widening is required to get a vehicle with particular characteristics round curves with a range of radii. Not that I think anybody would want to do that calculation routinely, but because you can use it to illustrate what degree of gauge widening is required on a given curve to suit the vehicles likely to run round it. The result is a spread sheet.

Nobody understands better than I, that introducing a spread sheet into the explanation does not necessarily mean what your trying to explain becomes easier to understand. For a fair chunk of our readership exactly the reverse is likely to be true. So I will primarily use the spreadsheet to generate graphs to illustrate the points I am trying to make. I’m going to take this slowly, in bite sized chunks, but if anybody wants to pick me up on something as I go along, please do, because if anything I say is wrong, I’d rather find out before I make too big a fool of myself.

The next episode follows shortly

Before we get to the graphs we will first have to understand the basic concepts, and I’m sorry if we start out saying things which seem a mite obvious. We will get to some interesting stuff in due course I promise.

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Will L
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Gauge widening, the basics

Postby Will L » Fri Aug 26, 2016 6:00 pm

Gauge widening is required to get a railway chassis with more than two parallel axles round sharp corners, how much gauge widening is required for a given radius of curve is very dependent on circumstances. To reduce some of the obvious complexity I am only going to consider a classic three axle rigid chassis, this is, in any event, the primary problem the real railway faced. To start with we are only going to consider a prototypical chassis in which the axles are not only fixed parallel to each other but also had no ability to slide sideways.

6 wheel basic.jpg


The next thing we need to consider is the Clearance between the wheels and the rails visible in the above picture.

Clearance.jpg


This Clearance is what enables trains to run round large radius curves without gauge widening, but as the curvature increases the space between the rails available to the chassis is effectively reduced, until we arrive in the situation illustrated below. If the curve gets any sharper a prototype loco will start to destroy the track, fortunately in the same circumstance a model will just derail.

No GW limit.jpg


The answer, assuming the totally rigid chassis and that you can’t avoid having a curve that sharp, is to apply gauge widening, i.e. move the outside track a bit further away from the inside rail. To decide how much we first need to calculate the Versine.

versine.jpg


N.B. if you interested here is a link to the article on the CLAG website which deals with the Versine in the context of a different but related topic.

Where the Clearance is greater than the Versine there is no need for gauge widening, but where its isn’t the formula needed to calculate the minimum amount of gauge widening (GW) required to get the loco round the curve are :-

Clearance (CL) = Track Gauge - (max Back to Back + 2* max Effective Flange Width)
Versine (V) = (Wheelbase)squared/(8*Curve Radius)
Gauge Widening (GW) = V-CL


Edited to correct a nomenclature error in the Clearance diagram
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby grovenor-2685 » Fri Aug 26, 2016 7:26 pm

This was a very early topic for the MRSG and thier graphs etc can be found in that other long topic!
http://www.scalefour.org/forum/viewtopic.php?f=5&t=4732&p=47162#p47162
Now I'm back home I'll try and find the promised Model Railways article.
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Martin Wynne
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Martin Wynne » Sat Aug 27, 2016 5:38 am

For those not happy with spreadsheets and versine calculations, you can measure sideplay and gauge-widening requirements in Templot without needing any maths.

tools > spacing-ring • dummy vehicle menu item.

dv_clearance1.png

The dummy vehicle clearance mouse action can also be used to measure the centre axle sideplay needed on 6-wheel vehicles at different radii, and or the gauge-widening needed if sideplay is limited or absent.

Set the gauge to P4. Set the track to the required radius. Click the dimensions... button and set the body length to match the wheelbase. Set the body width to match the track gauge. The dashed clearance marker can then be adjusted by the dummy vehicle clearance mouse action to align with the outer rail. If there is significant gauge slop on the wheels (e.g. 00 gauge), the available slop can be subtracted from the indicated sideplay.

dv_clearance2.png

dv_clearance3.png

The results are shown in prototype inches. To convert to P4 mm, divide by 3.

i.e. 4.94 divided by 3 = 1.65mm total sideplay+gauge widening needed here (very sharp curve shown for clarity).

Templot is free from: http://templot.com/downloads/download.htm

regards,

Martin.
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Julian Roberts
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Re: Gauge widening, the basics

Postby Julian Roberts » Sat Aug 27, 2016 6:36 am

Will L wrote:Gauge widening is required to get a railway chassis with more than two parallel axles round sharp corners,


Hi Will

Glad to see your professional approach with posh diagrams.

But is this right? Isn't gauge widening needed for 4 wheel vehicles too?

My understanding about gauge widening came in the first place from reading Iain Rice's book on making finescale track. Very near the beginning he explains about the flanges of a 4 wheel vehicle taking up more room on curves because the wheels remain parallel to each other, and not to the rails.

2016-08-03 20.53.38.jpg
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John Bateson
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby John Bateson » Sat Aug 27, 2016 8:06 am

Possibly feeling a bit grumpy this morning - but can I suggest respectfully that it would have been nice if Will could have finished his exposition in toto before admixing it with comments which have been covered in another thread - these threads are still open.
That way, we could read the whole story without the interpolations, just the work of one member who is putting a lot of time and effort into what could in the end be a definitive paper.
John
Slaving away still on GCR stuff ...

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

Postby Noel » Sat Aug 27, 2016 10:43 am

I mostly agree, John, but would suggest that requests or suggestions for clarification are acceptable, as they may help Will with the writing of the definitive version, as they can highlight ambiguities, potential lack of clarity where knowledge on the part of the reader is not as good as assumed, and the occasional mistake. This is not intended as a comment on Will's writing; just that it is difficult to put down in writing exactly what you are trying to say when dealing with complex subjects.

Julian, yes, you are correct in theory, but six wheel rigid vehicles are a worse case. If you put a ruler on Iain's diagram and image a central wheelset, you will find, allowing for Iain's freehand drawing, that the inner wheel already has its flange on the railhead, and the outer wheel has consequently probably dropped inside the track. Some improvement can be made by allowing sideplay, but that will be limited unless a Cleminson system is used.
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Will L » Sat Aug 27, 2016 10:51 am

Noel wrote:I mostly agree, John, but would suggest that requests or suggestions for clarification are acceptable, as they may help Will with the writing of the definitive version, as they can highlight ambiguities, potential lack of clarity where knowledge on the part of the reader is not as good as assumed, and the occasional mistake. This is not intended as a comment on Will's writing; just that it is difficult to put down in writing exactly what you are trying to say when dealing with complex subjects..


That right and I deliberately left a gap with that in mind. I want the discussion to centre on the real implications, not on any mistakes I might make along the way.

I will come back to the "Rice" diagram later.

Edited for spelling
Last edited by Will L on Sat Aug 27, 2016 4:30 pm, edited 1 time in total.

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The Spread Sheet – Backgound Figures

Postby Will L » Sat Aug 27, 2016 11:19 am

Our simple gauge widening equation can now be built on and analysed across a range of possible track curve radii, most conveniently by using a spread sheet. The spread sheet correlates a variety of Gauge Widening related factors with a series radii. Being a P4 4mm scale modeller I chose to start at a 800mm curve and go upward is steps of 50mm to 3000mm. If anybody wants to go lower than that, you can ask. You will see there would be very little point in going any higher.

To give an idea what sort of track curve radii we are talking about, I also used the power of the spread sheet to indicate what my 50 millimetre steps represent in feet and inches, and what the full size equivalents are in meters and chains. I shan’t mention these again but in case you’d prefer to think in something other than millimetres here they all are.

Radii table.jpg


To get us started, and to avoid trying to understand too many lines on one graph at once, I have plotted out the basic static information we are interested in. That is the two versions of gauge widening applied on the prototype, and two variations of how we tend to do it on the model using a 3 point track gauge.

As many of you will know, because of the practicalities of track laying on the prototype, the real railway does gauge widening in distinct steps as the radius of a curve reduces, while the 3 point track gauges we use provide a graduated amount proportional to the radius of the curve.

The core of the discussion being held elsewhere was whether the standard P4 society 3 point gauge produces sufficient gauge widening or whether we should use something a bit bigger. The key dimension on the standard gauge is 29.5mm, while the suggested alternative is 47mm.

The historic prototype figures come from the P4 archive. The modern ones from figures provided by Martin Wynne recently
N.B. the Versine calculation is also good for working out the gauge widening produced for any given size of three point gauge, so that is how I did it.

graph 1.jpg


The horizontal axis is the curve radius and the vertical axis shows the amount of gauge widening we are talking about in 4mm scale, both in millimetres. The fact that the gauge widening figures are so small is the first thing that should give us pause for thought. How accurately can you build this stuff? For now please take that as rhetorical.

The grey and red lines show the prototype approach and while different, they clearly occupy much the same space. It is also clear to see that the Society 3 point gauge (orange line) does not provide as much gauge widening as is used on the prototype, while a gauge with an effective length of 47mm (blue lone) certainly gets a bit closer.

I won’t repeat the modern prototype GW figures on future graphs but I will use the other three as a background to judge what comes next.

Edited for spelling
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The Spread Sheet – Gauge Widening and the Clearance Figure

Postby Will L » Sat Aug 27, 2016 1:25 pm

What the graph in the previous post doesn’t illustrate is how much gauge widening is actually required in P4. It’s time to apply the GW=V-CL formula derived a couple of posts ago.

Clearly for a P4 modeller “getting everything right”, prototype practice should be our guide, but we should also be aware of one significant difference between P4 and real life. Our P4 Back to Back gauge is not a strait scale reproduction of the prototype, and this has a significant effect on the Clearance figure in our formula. I can best illustrate this by comparing the P4 Clearance figure with that for S4. S4, we remember, does not make the same BtoB compromise and so is a good scale representation of the prototype.

N.B. like all such standards there are minimum and maximum figures specified for both Back to Back (BB) and the Effective Flange width (EF). I must use the max figure, as any gauge widening must accommodate any wheelset whose measurements fit within these upper limits.

CL for P4 = TG(18.83) – (BB (17.75) + 2*EF(0.4)) = 0.28
CL for S4 = TG(18.83) – (BB (17.89) + 2*EF(0.4)) = 0.14

The fact that the P4 figure is twice that for S4 should be the second thing that gives us pause for thought. The next graph is intended to illustrate what this difference means. In this case I have used the CW=V-CL formula to plot the minimum gauge widening needed for a specific length of chassis. To run the calculations you must decide on the wheelbase you are considering and I chose 15ft or 60mm (The wheel base of (most) black 5s) to illustrate how this works out. As promised I’ve left in the historic gauge widening line and the two triangular gauge lines from the last graph for comparison purposes.

S4 v P4 graph.jpg


This shows a number of things.

The light blue "Gauge widening required for S4" line (prototype equivalent)


This is a good match for real prototype practice and verifies that the prototypical gauge widening is a good match with the need for a loco the size of a black 5. It shows S4 modellers should be very wary of 3 point track gauges because neither really provides enough gauge widening, and that gauge widening is likely to be required on most of the curves you are likely to need. It also shows that it is probably not a good idea to send a real black five down a curve any sharper than 4.4 chains (1150 on the graph)


The dark blue "Gauge widening required for P4" line


This shows how much the extra Clearance given in P4 changes the picture. For a loco with a fixed wheelbase of a Black Five No gauge widening is required on any curve with a radius greater than 1600 mm (5 ½ feet), the society gauge is Ok down to 1200mm (3’11”) and the larger gauge will work down to 1000mm (3’3”)

Remember we are talking here about locos with no lateral flexibility, i.e. no end float on the centre axle.

The next graph I want to show you was a comparison of the gauge widening needs of a series of P4 locos with different fixed wheelbases.

P4 loco comp graph.jpg


I find this one is worrying, what this says is that while prototype practice is appropriate so long as you don’t send a big engine down a tight curve, it has to be questionable whether our triangular gauges, of any size, are really up to the job. However the fact that layouts do get built than run main line size locos round model rail curves suggest that something else must be going on.
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Noel » Sat Aug 27, 2016 4:17 pm

Will, locos are not necessarily the most extreme case. I have a vehicle with a four wheel fixed wb of 94mm [23ft 6ins] - a LNER LLCK [classed by BR as a lwb CCT]
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Will L
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Will L » Sat Aug 27, 2016 4:28 pm

Noel wrote:Will, locos are not necessarily the most extreme case. I have a vehicle with a four wheel fixed wb of 94mm [23ft 6ins] - a LNER LLCK [classed by BR as a lwb CCT]


Long 4 wheeled vehicle are another issue but I will get there, just not just yet.

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

Postby grovenor-2685 » Sat Aug 27, 2016 7:04 pm

Now I'm back home I'll try and find the promised Model Railways article.

Actually I had forgotten that I had already posted these articles!
Particularly relevant to curving/guage widening are:
http://www.norgrove.me.uk/history_files/mrc3/part-3.htm
and http://www.norgrove.me.uk/history_files/Mar73/Mar-73.htm
Click on illustrations for larger versions.
The whole set can be found via http://www.norgrove.me.uk/P4-articles.html
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Will L
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The Final Factor

Postby Will L » Sat Aug 27, 2016 7:35 pm

The key difference between our models and the real thing is down to axles. Unlike the prototype our axles are a nice uniform diameter all the way along and can be allowed to slide side to side.

End Float.jpg


Assuming a reasonable quality of build, of the full range of this movement (Lateral Flexibility [LF] aka End Float), half (LF/2) will be available to ease the locos path when going round curves, and like the Clearance can be set against the Versine. So the key equation becomes:-

GW = V- (CL + LF/2)

When I build a chassis I usually try and allow a full 1mm of movement on the central axle. It was only when I started to think about this seriously that I realised how big the additional 0.5mm added to the equation was compared with the Clearance or for that matter the Versine. I was going to provide a graph showing the difference this amount of End Float made to the amount of Gauge Widening required. However there is a problem.

GW - EF.jpg


The line on the graph never leaves 0. That is with 1mm end float on its middle axle our Black 5 doesn’t require any gauge widening at all.

For the sake of illustration I have also plotted in the Versine for a 60mm chassis, and you can see the Versine only becomes greater than 0.5mm (LF/2) for curves below 950mm (3’1”). In practice, with the Clearance added in as well, our Black 5 is good to go down to about 580mm (just under 2’0”). So now you know how the toy trains do it.

I wondered what the result would be if I halved the end float (to 0.5mm) and applied it to the range of loco chassis sizes I used before. I got this.

P4 loco comp with EF..jpg


This is telling us that with 0.5mm end float on its middle axle our Black 5 is in only need of Gauge Widening on curves below 850mm (2’9”), and only if we are run monsters like a J19* should we to need to worry about gauge widening.

*A J19 is a GER 0-6-0 built to pull big coal trains down main lines not round corners, it has a whopping 17’9” fixed wheel base.

That end the calculations, some conclusions and ancillary points will follow.
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Julian Roberts » Sat Aug 27, 2016 8:47 pm

Will L wrote: but if anybody wants to pick me up on something as I go along, please do,.


Hi all

I do apologize for my hastily written and rather brusque sounding post this morning. I should have said "sorry to interrupt your flow Will, maybe you are coming to this soon enough and will answer in due course, but can I just ask you this rather basic (probably dumb) question"

Please don't think I want to score points!

Anyway I am sure Will is covering everything to everyone's full satisfaction including mine in due course; as he has already said, he will come back to the Rice diagram.

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

Postby Will L » Sat Aug 27, 2016 9:26 pm

Julian Roberts wrote:I do apologize for my hastily written and rather brusque sounding post this morning.


Not necessary Julian, I saw John's point but I was inviting comments so I can't complain if I get them can I.

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Conclusions and other Issues

Postby Will L » Sat Aug 27, 2016 11:40 pm

Gauge widening conclusions.

The first thing to consider is that all the Gauge Widening figures we have been playing with are small, and we must remember that achieving accuracy down to two decimal places of a millimetre is definitely an issue. While the figures given represent a good theoretical position, practical modelling will probably suggest we do leave a bit more leeway.

Even without the concept of end float, the additional Clearance available in P4 means that the society 3 point gauge produces sufficient gauge widening at the sort of radii we are inclined to use for P4. I don’t see anything to suggest that an excess amount of gauge widening will improve running. This goes along with the societies general experience that the proper use of the society gauge produces perfectly usable track work.

With sufficient End Float on the centre axle (0.5mm) gauge widening is only necessary in extreme conditions. This goes along with my experience that suggests that most of the problems people have getting locos round corners are much more to do with insufficient clearance between the wheels and the bodywork than any issue gauge widening. Having a test curve of your minimum radius on the work bench and building so that your locos go round it should see you home and clear.

Applicability to other vehicles.

To keep things simple I have not tried to cover loco chassis with more than 3 axles, or other rolling stock with three or more fixed axles. There are several schemes for getting n-8-n and n-10-n loco chassis round corners, which involve the use of end float. The prototype didn’t add extra gauge widening to suit them either. Now I have the spread sheet I will be using it to work out how much end float I need on the centre axle of my next lot of 6 wheel coaches. Anybody building some of those strange LNWR rigid 8 wheel coaches should remember that the LNWR also found out they weren’t that good an idea.

Angle of incidence

I have said nothing about the issues that occur when a sharp curve means that the leading wheel meets the rail at too great an angle of incidence. This is because I was considering gauge widening. The two things get conflated because they both apply to sharp curves but they are separate phenomena. Applying gauge widening has no effect on the angle at which the flange of the leading wheel meets the rail. This problem is mitigated on the prototype by the use of check rails, although why it is better to rub the back of the flange on the check rail, rather than the front against the running rail I am unsure. We seem to be able to manage without such check rails if need be, which may be something to do with the physics not scaling.

The Rice Diagram.


I don’t have access to Ian Rice’s work on track so I’m not quite sure what he said, but quoted in isolation like this, it is, at best, misleading. The Clearance between track and wheels we have discussed before is sufficient to ensure that there will always be space between wheel and rail, whatever angle they are to each other. This is why a 4 wheel vehicle never requires gauge widening.

The Spread Sheet.


I write spread sheets in such a way as to allow me to alter basic parameters easily, but I haven’t tided this one up fully or tried to comment it to make self-explanatory. However anybody who would like a play is more than welcome.

GW.xlsx


A further conclusion, relating to the use (or otherwise) of Gauge Widening through point work has been added below.

Edited to replace the version of the spread sheet I posted orginaly which had a small problem, sorry
Edited again to point to a further conclusion a few post further on (and hence on the next page)
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Jol Wilkinson » Sun Aug 28, 2016 8:26 am

Will,

those strange 8 wheel LNWR 42' carriages incorporated radial axles at the outer ends, so benefited from a small degree of "flexibility". They were also mainline stock, at a time when carriages for the lower classes daily travel were either six or four wheeled, so they were unlikely to encounter too many sharp curves. Some were later converted to bogie underframes.

The kits produced with radial underframes incorporated internal bearing bogies, to take care of the smaller radius curves so beloved of 4mm modellers.

Thanks for bringing some common sense to this subject (as discussed in depth elsewhere). I was starting to lose the will to do any model making.

Jol

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

Postby grovenor-2685 » Sun Aug 28, 2016 9:46 am

Applying gauge widening has no effect on the angle at which the flange of the leading wheel meets the rail. This problem is mitigated on the prototype by the use of check rails, although why it is better to rub the back of the flange on the check rail, rather than the front against the running rail I am unsure.

The check rail keeps the flanges from causing sidecutting on the railhead of the outer rail. Sidecutting creates a railhead profile matching the flangeprofile with no clearance and makes it relatively easy for the flange to climb up and over the outer rail. Even without much sidecutting climbing can occur if there are other defects such as a poor wheel turning job or lack of flange lubrication.
The DLR originally was not provided with check rails for curves, they were added after we had a couple of rather embarrassing derailments from just this cause.
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Will L » Sun Aug 28, 2016 12:16 pm

grovenor-2685 wrote:
Applying gauge widening has no effect on the angle at which the flange of the leading wheel meets the rail. This problem is mitigated on the prototype by the use of check rails, although why it is better to rub the back of the flange on the check rail, rather than the front against the running rail I am unsure.

The check rail keeps the flanges from causing sidecutting on the railhead of the outer rail. Sidecutting creates a railhead profile matching the flangeprofile with no clearance and makes it relatively easy for the flange to climb up and over the outer rail. Even without much sidecutting climbing can occur if there are other defects such as a poor wheel turning job or lack of flange lubrication.
The DLR originally was not provided with check rails for curves, they were added after we had a couple of rather embarrassing derailments from just this cause.



Ah enlightenment, thank you. As a mater of interest at below what radius does the DLR now apply check rails?

Given that climbing the outside rail is not unknown on the model, its interesting to note the importance of the interaction between rail and wheel profile. While you have to doubt we will ever reproduce the DLR rail wear paten on a model, getting the wheel and rail profiles right is clearly still important to good running.

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

Postby Will L » Sun Aug 28, 2016 12:42 pm

Will L wrote:
Noel wrote:Will, locos are not necessarily the most extreme case. I have a vehicle with a four wheel fixed wb of 94mm [23ft 6ins] - a LNER LLCK [classed by BR as a lwb CCT]


Long 4 wheeled vehicle are another issue but I will get there, just not just yet.


Ops sorry I didn't get there did I beyond saying gauge widening isn't necessary. Problems with long wheel base 4 wheel vehicle are most likely to be down to (lack of ) suspension issues. The longer the wheel base the more they are affected by changes in the track top level (cant), either accidental or deliberate, and it is this that gives such vehicle a nasty tendency to go straight on at corners. I was quite serious when, in another pace, I suggested we should have an agreed standard for the amount change in cant allowed on the track and which can be accommodated by our vehicles.

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

Postby Noel » Sun Aug 28, 2016 2:28 pm

Will L wrote:Problems with long wheel base 4 wheel vehicle are most likely to be down to (lack of ) suspension issues


I was playing devil's advocate a bit, Will. My LLCK is compensated and generally behaves itself. I'm not sure I would want to put it through an A5 point though. Even with the clearance inherent in P4 standards there must come a point where it won't go, but a shorter wheelbase vehicle will.
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby grovenor-2685 » Sun Aug 28, 2016 4:25 pm

I was playing devil's advocate a bit, Will. My LLCK is compensated and generally behaves itself. I'm not sure I would want to put it through an A5 point though. Even with the clearance inherent in P4 standards there must come a point where it won't go, but a shorter wheelbase vehicle will.

The radius versius wheel angle issue that governs 4 wheel vehicles is discussed in the Model Railways article I linked above. You do need to click on the graph to get a readable version.
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby grovenor-2685 » Sun Aug 28, 2016 5:00 pm

Ah enlightenment, thank you. As a mater of interest at below what radius does the DLR now apply check rails?

The current standard requires check rails to be applied to all curves equal to or less than 75m radius. In practice most curves between 75 and 100m radius are also fitted.
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Re: Track Gauge Widening, All You’ll Ever Need to Know

Postby Will L » Sun Aug 28, 2016 11:33 pm

My apologies but I have just noted that there was a small problem with the version of the spread sheet I put up on the posting above. I have corrected it and I apologise to anybody who has already downloaded it.


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