CSBs a question of Gravity

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Will L
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CSBs a question of Gravity

Postby Will L » Sun Jul 24, 2011 10:21 pm

If you’ve been prepared to try reading postings on the Abstruse CSB Theory thread, you will have noted that I have established the validity of the usual criteria used for the design of CSB chassis. See this posting. That is, with the Loco Centre of Gravity (CofG) located centrally over the CSBed wheel base, proper placement of the fixed fulcrum point gives equal weight distribution across the wheels.

While it is nice to know that fixing the CofG centrally over the driving wheels will produce a good working chassis, what about those occasions when this is easier to say than to do. This covers loco’s with weight bearing carrying wheels, and 0-n-0 locos which, for what ever reason, don’t naturally lend themselves to a centrally placed CofG.

To try and keep the arguments simple, its better if we start by thinking about 0-n-0s chassis.

A question of balance and adhesion, the 0-n-0 chassis.

If a loco doesn’t naturally suit a CofG centrally over the driving wheels, wouldn’t it be better to design a CSB which allows for a more convenient balance point? Isn’t the fact that, to date, our method for setting out the fulcrum points doesn’t want to work that way a bit of a constraint?

Also, the implications of having a design location for your loco’s CofG is that, if the finished loco doesn’t conform to the design there have to be consequences. It is certainly true that a CSBed loco with the CofG out of place will not sit as level as it should, and, while this may not be all that visible there can be implications for its running. See the 04 story. So, isn’t having to be careful about the balance of the loco an extra complication implied by the use of CSB?

First of all I’m happy to say that we now have Alan Turners new fulcrum calculation tool which he has posted on the Abstruse CSB Theory thread. This does enable us to work with a chassis where the CofG isn’t central, and it also tells us how much weight is being placed on each axle.

But even given that we can now design a chassis with the CofG off centre, I’m not convinced there is any real value in doing it unless it is truly unavoidable.

This is all down to adhesion.

Beyond a certain, fairly light, weight, a well balanced CSBed loco should run OK. Additional weight is only required to enable you to pull a worthwhile train. We need to remember that, for a chassis with any pretensions to similar loads on each axle, adhesion is limited by the lightest loaded axle. This is why we want the axles to be as equally loaded as possible, and this is only possible with the CofG central on the chassis. Moving the CofG away from the chassis centre means that, while the axle at the end nearest the CofG will be more heavily loaded, weight must come off the axles the other side of the CofG. This implies that adding weight off centre may well mean you loco has less pulling power! Therefore it makes more sense to weight the loco less, and get the CofG central, than to just load it up as much as possible and living with an off centre CofG!

So yes, we do need to be careful in weighing and balancing our CSB loco, but before you call this a good reason for not considering a CSB chassis, just have a think about the alternatives. The adhesion limit being set by the most lightly loaded axle isn’t just a sprung chassis issue, it applies to any loco. The fact that you may not have considered how the weight distribution of your compensated loco affects is adhesion doesn’t mean it doesn't have an effect, and very few compensated chassis will allow the sort of even weight distribution we are designing for with a CSB. See digest sheet 41 The Principles of Model Locomotive Suspension, Worked Examples

So while CSB chassis design does mean you need to be aware of where you loco’s CofG is:-
    2. because we know just loading weight isn’t the answer, weighting to set the CofG by putting relatively small weight at the extreme ends of the loco is a lot easier than trying to get lots of weight in just anywhere.

The upshot is that the designing a CSB with the CofG central isn’t just a convenient design assumption, it actually is going to give you the best available performance from your chassis.

A question of balance and adhesion, CSB chassis with a load bearing bogie

So having got our head round the balance implications for a chassis which just has driving wheels all supported by the CSB, what about including carrying wheels, and in particular bogies, which don’t easily lend themselves to inclusion under a CSB.

To sort out this problem, firstly you need to realise that one key quality of a CSB chassis is that it sits level when the load it is carrying is applied at a given location, normally the centre the wheelbase. When considering the 0-n-0 chassis, this has been synonymous with the loco CofG, but when a loco has other load bearing wheels this is no longer true. None the less if the chassis is sitting level under load, then that load is still balanced over that design point, which in future I shall refer to the “Centre of Load” (CofL).

Next we need to remember a little school boy physics, and in particular, the Principle of Moments. While up to now it has been convenient to assume that all the loco’s weight is located at it’s CofG, the principle of moments tells us we can consider it as if it was divided into number of separate bits who's weights are distributed about the loco. Viewed this way, the weight times the distance from the CofG of all the pieces to one side of the CofG will exactly equal the weight times the distance from the CofG of all the bits on the other side. In particular we can divide the loco’s weight into two parts, one over the CSB CofL, and one over the bogie CofL.

For a loco putting some of its weight on a bogie, this tells us the actual CofG of the loco will be somewhere between the CSB CofL and the CofL of the bogie, which could well be a little CSB based chassis in its own right. We can chose how much weight is carried by the driving wheels , and how much is carried by the bogie, by deciding where the actual CofG is located.

Once you’ve got that, this diagram should summarise it all nicely..
CSB gravity 3.jpg
CSB gravity 3.jpg (139.05 KiB) Viewed 6242 times

From there on in all that is necessary is to decide how much of the loco weight you want to carry on the bogie, and arrange the CofG location accordingly. So,if you wanted, say, 10% of the loco weight on the bogie, the CofG will need to be 1/10th of the distance from the drivers CofL to the Bogie CofL, and you can see that the maths here isn't going to be to challenging. At this stage I’m not going to comment on what a reasonable weight distribution between drivers and bogie actually is. Mostly because I haven’t got any practical information on what works and what doesn’t. Perhaps others could lend there collected experience at this point.

As to getting the thing to sit level, your choices are as follows.
    1. Design the chassis to sit level for a given deflection of the CSBs (presumably 0.5mm) on both drivers and bogie. You still get the option to play with the CSB wire sizes to suit the actual finished loco weight, and even to adjust the level if it still isn’t quite right. I was planning to release a 4 wheel version of the old spread sheet so you could calculate the required wire size on the bogie for a given load and defection, though it is possible Alan might get there first. However until then, or because there are a number of variables in play here which may not stack up as expected, one might still want to consider one or other of the following as well. Or even in stead.
    2. Fitting an adjustable bogie rubbing plate so that you can adjust it up or down until the chassis sits level. Useful if your design proves imperfect and changing the wires will not produce a sufficient change in deflection to level up the chassis.
    3. Adjust the loco CofG position for or aft until the loco chassis sits level. This changes the balance of load between drivers an bogie and hence their relative deflections.

If you’ve read the CSBs and the Single Bogie thread, you will see that I have just generalised the argument I developed to deal with the C12 discussed there. It was option 3 I chose on that occasion.
Last edited by Will L on Mon Aug 01, 2011 10:14 pm, edited 1 time in total.

Alan Turner
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Re: CSBs a question of Gravity

Postby Alan Turner » Mon Jul 25, 2011 9:17 am

Whilst my new beta-test spreadsheet only has a six coupled chassis the real spreadsheet will have options for 4, 6, 8 and 10 coupled chassis.

The 4 coupled will enable you to design the bogie which can then be input back into the overall chassis design as set out by Will above.

If needed I can write a short explanation how that can be done.

regards

Alan

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Re: CSBs a question of Gravity

Postby grovenor-2685 » Mon Jul 25, 2011 11:34 am

We need to remember that adhesion is limited by the lightest loaded axle,

As a general statement this is just not true, it all depends!
Everyone is familiar with the 0-6-0 where the central axle does not carry any weight and hence by the above statement will not pull anything. However they do!
In the limiting case that axle just falls out of the calculation.
Each axle can contribute tractive effort up to the point where it slips, when an axle goes into slip its tractive effort does not go to zero but it falls from the limiting adhesion value to the slipping value. The tractive effort lost at that point has to be made up by the other axles, if they are close to slipping also then that may induce slip in them also. If the distribution is very uneven then the other axles will take the load and tractive effort can continue to increase until the next axle reaches the limiting value.
The overall limiting value is the sum of the heaviest axle limiting value plus the slipping tractive effort of all the other lighter loaded axles. This will be a bit less than the value achieved with the same total weight equally distributed but not by very much.
Keith

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Re: CSBs a question of Gravity

Postby Alan Turner » Mon Jul 25, 2011 11:46 am

Friction (static) = co-ef of friction x mass x gravity. Area of contact does not come into it.

Therfore a locomotive of a given weight will have the same friction available to it whether it has 2 axles, three axles, four axles or a hundred axles. The only difference axles make is to reduce axle loading.

I assume of course that all axles are driven. Obviouly undriven axles simply reduce the weight available for friction.

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Alan

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Will L
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Re: CSBs a question of Gravity

Postby Will L » Mon Jul 25, 2011 4:24 pm

grovenor-2685 wrote:
We need to remember that adhesion is limited by the lightest loaded axle,

As a general statement this is just not true, it all depends!


Yes sorry I did mean to have a few extra caveat-ty words in there, I also had pretty much the explanation you gave, but biased to the view that with relativity even loads, slipping of one was likely to lead to slipping on the next. However I was trying to keep the ideas as simple as possible and reduce the word count. I obviously went too far. Clearly not true if you assume a radically different weights per axle, but I was concerned with the unavoidable weight differences produced by moving the centre of gravity away from the centre point.

grovenor-2685 wrote:The overall limiting value is the sum of the heaviest axle limiting value plus the slipping tractive effort of all the other lighter loaded axles. This will be a bit less than the value achieved with the same total weight equally distributed but not by very much.


That depend on who much traction you do get from a slipping wheel, I always understood the answer to that was very little, but I don't have a specific value available to me. Are you saying you don't accept that argument that you get more benefit from a well balance chassis than just putting on the weigh and not worrying about the effects of uneven distribution?

Will

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grovenor-2685
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Re: CSBs a question of Gravity

Postby grovenor-2685 » Mon Jul 25, 2011 6:39 pm

Are you saying you don't accept that argument that you get more benefit from a well balance chassis than just putting on the weigh and not worrying about the effects of uneven distribution?
No, I was just trying to explain the light loaded axle a bit as I have seen the same statement made (by others) in other places and causing confusion. Part of the problem is that, with coupled wheels, its very difficult, if not impossible, to see when the first axle reaches its adhesion limit, you only see when the last axle loses it.
I certainly agree that it is best to get a balance as far as possible, and i would always try to have slightly less load on a centre axle to avoid any tendency to rock on it, which I have found leads to derailment.
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Will L
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Re: CSBs a question of Gravity

Postby Will L » Mon Aug 01, 2011 11:45 pm

In the first post of this thread I said
...We need to remember that adhesion is limited by the lightest loaded axle, which is why we want the axles to be as equally loaded as possible, and this is only possible with the CofG central on the chassis.


Keith rightly picked me up on this, because, when the loads on individual wheels are significantly different, it isn't true. The basic schoolboy physics, to which I am limited, certainly suggests that it is quite possible to build a chassis which proves it wrong. So a single driving axle will pull as much as a three axle chassis carrying the same weight evenly distributed, although for and aft stability might be an issue. This is good news for lovers of the Stirling Single or similar locos, but was not a solution available on the real thing due to a wish to avoid axle loads which would wreck the track.

However, my assertion is true on a chassis where axle loads are in the sort of proportions normally found on the prototype. When pulling hard, all the axles will be getting close to their adhesion limit. The load transfer that occurs when the first axle slips will be enough to take the rest of the axles with it. The adhesion limit for the chassis will therefore be the same as if the loco had all three axles carrying the same weight as the lightest loaded. So the reason this line gets repeated is that it is true in most practical circumstances. Indeed the likely result in our single axle example above, is that the single will pull more than the 3 axle version, unless the weight is accurately and evenly distributed.

It is also interesting to note that this cascading slipping effect becomes less of an issue as the number of axles increases.

Anyway I have changed the original posting to read
... We need to remember that, for a chassis with any pretensions to similar loads on each axle, adhesion is limited by the lightest loaded axle...


The key point was, and remains, that it is quite as important to worry about the distribution and balance of the chassis weight than its absolute magnitude.

Will

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jim s-w
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Re: CSBs a question of Gravity

Postby jim s-w » Thu Aug 04, 2011 9:42 pm

Hi Will

How, in a model does one axle slip when they are all mechanically linked together?

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Jim

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Re: CSBs a question of Gravity

Postby grovenor-2685 » Thu Aug 04, 2011 10:01 pm

Read my posts above.
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Keith

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jim s-w
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Re: CSBs a question of Gravity

Postby jim s-w » Thu Aug 04, 2011 10:18 pm

Hi Keith

I can see how a lightly loaded axle is not really contributing much to the effort of the loco but if you are reliant on the most grippy axle actually being the one that makes the loco stall does it actually matter what the others are doing in terms of traction? Yes good balance is better but is that just for roadholding purposes?


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Jim

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Russ Elliott
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Re: CSBs a question of Gravity

Postby Russ Elliott » Sat Sep 17, 2011 12:17 pm


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Will L
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Re: CSBs a question of Gravity

Postby Will L » Fri Mar 07, 2014 12:57 am

A measure of performance

The C12 4-4-2, the construction of whose CSB chassis was the subject of this thread, has been running quite happily on Knutsford since May 2011. One of the reasons for arguing the superiority of CSBs is that it should ensure that you make best use of the haulage capacity of the loco, but, for me at least this, has been a theory position as I hadn’t got the direct experience or evidence to prove it.

Now that Tony M has got his magnum opus running, see the Beyond Ambergate thread, I have had the opportunity to see just what the C12 is capable of doing. In fact I documented the occasion on Tony’s thread, and included a couple of photos of the C12 in action which I rather liked, so no apologies for repeating one of them here.

2013 October 4.jpg
2013 October 4.jpg (192.81 KiB) Viewed 3917 times

As I promised in that post, I’ve now had a chance to evaluate what this loco can actually do, and this is my opportunity to pass on the lessons learnt.

The C12 itself weighs in at 323 grams, of which 54 are carried by the bogie, that is 269 grams are available for adhesion (see note * below). The hardest job it’s asked to perform on Knutsford is to haul a heavy etched brass 5 coach rake up the 1 in a 100 grade which faces Chester bound services. The coaches weigh in at about 200 grams a piece giving a train weight of about 1Kg on 18 axles. For those worried by the maths of that I should point out there is an articulated twin set in the rake, so only 9 bogies. While not every loco in the stud has proved up to this, the C12 does it comfortably and will accelerate on demand up the hill.

On Ambergate, unconstrained by limited fiddle yards, you can run whatever length train amuses you. In the photo the C12 is happily pulling a 35 wagon rake through Ambergate station, and on this curvy and uphill stretch of the track this train is well within its grasp. However to complete the circuit there is a long strait 60:1 incline. Just at the apex of this hill is a curve of about 4 foot radius which will bring any loco which has been struggling up the hill to a final halt. This is a re-creation of the topography at Buxton, a prototype which went in for banking engines and train lengths limited to significantly less than 35 wagons, which, it turns out, is the maximum the C12 can pull up the hill and round the corner. The wagons, courtesy of John Sherratt, are all free running and weighted to a standard 25 grams per axle, giving a train weight of 1.75 kilos on 72 axles.

So what can we learn from this? The C12 is not alone in being able to pull that size of load. Tony has a 4F (0-6-0) which will pull a few more, and a Super D (0-8-0)which just isn’t in the same league. Neither of these are CSBd. Amusingly the O4, which is CSB fitted, and has 8 coupled wheels, hits the wall at a similar number of wagons as the C12. Given that this loco has an adhesive weight of about 285 grams and is pulling around a 113 grams of tender (i.e another 2 and a quarter wagons worth), it would seem that the O4 and C12 are roughly equal in their ability to convert loco weight into pulling power. In any case all but the super D are exceeding what the prototype would be expected to achieve.

Clearly adequate adhesive weight and its proper distribution are key factors, while the number of driving wheels apparently isn't. On the prototype, the weight to be carried by any single axle is kept within strict limits set by the permanent way people, and the proliferation of wheels under loco’s, as they got bigger, was more to do with spreading the weight than anything else. We have no such concerns, which leads to the view that in the model railway world prodigious feats of haulage by single drivers are possible.

There was one other significant learning point. From the picture you will notice the C12 is doing it’s stuff bunker first. What we discovered was that, when running chimney first up the gradient with the full weight of the train hanging on the draw gear, enough weight was being transferred off the bogie to make it prone to derailment. In digest 41.0 Russ Elliot has demonstrated that weight transfer of this sort is unavoidable. While this effect is not sufficient for the front of the C12 to lift visibly, it was sufficient to unload the bogie. When running bunker first, the effect is reversed and some weight is transferred onto the bogie but that makes no difference to its road holding. Should I want to solve the problem, I would be tempted to add weight to the bogie frames so that it is less dependent on transferred body weight to ensure it stays stuck to the track. It would then be interesting to see if the weight transfer to the driving wheels was sufficient to enable any more wagons to be lifted over the 60 to 1 when running chimney first.

It was also observed that the tender of the O4 showed an inclination for the occasional derailment when dragging such a heavy train up hill. The reasons for this were not established, but, as this problem doesn’t occur when pulling the trains normally allocated to it, there is little incentive to root out and correct the source of the problem.

Notes
* When I constructed the C12, and when writing this thread, I hadn’t sorted out how best to work out how much weight was being carried by the bogie. I weighted the loco so that it sat level and was satisfied with that. Since then I have sorted out a method for working it out, which is documented in the CSB a Question of Gravity thread.

In essence you need to know
1. The weight of the loco
2. The location of the centre of the CSB supported wheel base (a simplification of the general case but accurate in the case of a two axle chassis)
3. The distance of the loco’s CofG from 2
4. The distance of the bogie pivot point from 2

The distance from the CSB centre point to the location of the CofG (3 above) as a percentage of the total distance from the CSB center point to the bogie pivot (4 above) is the same as the percentage of the total loco weight that is carried by the bogie. All in accordance with the principle of moments as described by Russalso in digest 41.0.

Therefore, as the C12 weighs 323 grams and the CofG comes 9.5mm along the total CSB centre point to bogie pivot distance of 72mm(that’s 17%), 17% of the loco weight (54 grams) turns up on the bogie and 269 grams on the driving wheels. That is until you hang a heavy weight on the draw bar.

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Ian Everett
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Re: CSBs a question of Gravity

Postby Ian Everett » Fri Mar 07, 2014 8:35 am

In all sorts of regards Will's post above is very impressive. I wish I could achieve anything as good.

One thing still worries me and I remember it being debated on e4um many years ago. I just cannot see how it is that adhesion is limited by the lightest loaded axle. As Jim S-W suggests , the fact that the axles are coupled is surely significant. If one axle is relatively lightly loaded it might slip briefly but the other wheels will surely continue to pull and any slight slack in the system will be instantly taken up. (And now I'm wondering if I am answering my own question!) When one wheel set slips there will be an instantaneous increased loading on the other axles - is it this very brief increase in the load on the more heavily loaded wheels that then causes them to slip?

(Edit - I keep having second thoughts about this!

I realise I have talked about "loading" without distinguishing between adhesive weight loading and tractive loading in the comments above. I was referring to the latter but it will surely be the case that when one wheel set slips both tractive loading and adhesive loading will be transferred to the other wheel sets. Will one cancel out the other?)

(Still) confused of Askrigg.

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Re: CSBs a question of Gravity

Postby billbedford » Fri Mar 07, 2014 9:53 am

Will L wrote:The C12 itself weighs in at 323 grams, of which 54 are carried by the bogie, that is 269 grams are available for adhesion (see note * below). The hardest job it’s asked to perform on Knutsford is to haul a heavy etched brass 5 coach rake up the 1 in a 100 grade which faces Chester bound services. The coaches weigh in at about 200 grams a piece giving a train weight of about 1Kg on 18 axles. For those worried by the maths of that I should point out there is an articulated twin set in the rake, so only 9 bogies. While not every loco in the stud has proved up to this, the C12 does it comfortably and will accelerate on demand up the hill.


IIRC the load for a O4 over Woodhead was 50 loaded 10 ton mineral wagons, for a J11 it was 25 and for a J10 somewhat less, lets say 20. According RCTS Vol 1 the allowable load of a C12 was 8 minerals less than a J10. So for any sort of hilly route you can say that a C12 would be limited to 10 or 12 wagons, though this limit would have less to do with what they could haul and more to do with their braking capacity. Given these figures your C12 looks to be too heavy and your O4 too light, at least in the context of the Buxton layout. On the other hand if its principle duty is to handle 5 coaches on Knutsford, its weight is probably about right.

BTW what is the load on the C12's radial axle?
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Will L
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Re: CSBs a question of Gravity

Postby Will L » Fri Mar 07, 2014 11:03 am

billbedford wrote:IIRC the load for a O4 over Woodhead was 50 loaded 10 ton mineral wagons, for a J11 it was 25 and for a J10 somewhat less, lets say 20. According RCTS Vol 1 the allowable load of a C12 was 8 minerals less than a J10. So for any sort of hilly route you can say that a C12 would be limited to 10 or 12 wagons, though this limit would have less to do with what they could haul and more to do with their braking capacity. Given these figures your C12 looks to be too heavy and your O4 too light, at least in the context of the Buxton layout. On the other hand if its principle duty is to handle 5 coaches on Knutsford, its weight is probably about right.

BTW what is the load on the C12's radial axle?


Useful info Bill thanks, and I agree your conclusion. Neither loco was weighted to a particular value. The C12 was just heavy enough to keep its original craftsman OO chassis happy and there is plenty more room. The O4 was only weighted sufficiently to achieve balance, particularly after the heavy weight crew incident, there is again room for more over the CofG should it ever need to climb Woodhead in earnest, although I'll need to sort out the tender too. The C12's radial axle is carrying no loco weight, but does have a lump of lead of it own to keep it honest, which yes, I should have taken in to account as it isn't available for adhesion.

While I still have no real knowledge of what the rolling resistance of those 35 wagons is and hence no absolute knowledge of what sort of draw bar pull I'm getting, what I think I am demonstrating is a reasonably effective and consistent conversion of adhesive weight into draw bar pull and hence justification of the design claim for CSB chassis that such good performance is inherent in the designed.

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Will L
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Re: CSBs a question of Gravity

Postby Will L » Fri Mar 07, 2014 12:24 pm

Ian Everett wrote:In all sorts of regards Will's post above is very impressive. I wish I could achieve anything as good.

One thing still worries me and I remember it being debated on e4um many years ago. I just cannot see how it is that adhesion is limited by the lightest loaded axle. As Jim S-W suggests , the fact that the axles are coupled is surely significant. If one axle is relatively lightly loaded it might slip briefly but the other wheels will surely continue to pull and any slight slack in the system will be instantly taken up. (And now I'm wondering if I am answering my own question!) When one wheel set slips there will be an instantaneous increased loading on the other axles - is it this very brief increase in the load on the more heavily loaded wheels that then causes them to slip?

(Edit - I keep having second thoughts about this!

I realise I have talked about "loading" without distinguishing between adhesive weight loading and tractive loading in the comments above. I was referring to the latter but it will surely be the case that when one wheel set slips both tractive loading and adhesive loading will be transferred to the other wheel sets. Will one cancel out the other?)

(Still) confused of Askrigg.


Yes somebody would have to bring that up. I can explain but it will take time. Assume another posting to come.

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Will L
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Re: CSBs a question of Gravity

Postby Will L » Fri Mar 07, 2014 6:16 pm

Ok Ian it's like this...

Some may find this a bit like hard work. I have been deliberately vague about the units in play as the coefficient of friction is a unit less ratio and the same numbers work what ever unit's you chose. .

All this is bound up with the fact that there are two coefficients of friction between the wheel and rail that we need to consider. There is the static coefficient which applies when the wheel and rail are in contact but not moving one relative to each other, i.e. when the wheels are either standing still or rolling normally. Then there is the kinetic coefficient which applies when one is sliding over the other. The static coefficient is about 0.6 and the kinetic one is about 0.4 .
In either case multiplying the weight being carried by the coefficient gives you the maximum amount of force which can be transmitted through the wheel to rail contact point. You will notice that once a wheel starts to slip much less force can be transmitted.

It is easier to see what’s going on if we consider what happens if we try and push a loco along the track by applying a force to the coupling hook. Let’s say the loco has six wheels each carrying a weight of 50 and the wheels are locked solid by the motor and can’t turn. The applied force will be along the vehicle centre line and parallel to the track, so a moments thought about moments will tell you that, all else being equal, the force will be equally divided between the six contact points between wheel and track. The maximum force that can be resisted by each contact point before it begins to slide is given by multiplying the weight by the coefficient of static friction which gives 30 (50*0.06) per wheel or 180 for the whole loco. This is directly equivalent to the loco trying to pull a weight along and the 180 is the maximum force the loco can exert to pull a train before it will start to slip.

Going back to pushing the loco, once that 180 force has been exceeded and the chassis starts to slide the kinetic coefficient will apply. This is smaller than the static coefficient (0.4 as against 0.6) which means that less force is required to keep it sliding (thats 6*50*0.4 or 120) than it took to start it (180). This is the reason why it is harder to start something sliding than to keep it going when it is sliding and why, once all the wheels on a loco pulling a train starts to slip, it must reduce power significantly to stop slipping.

Ok now let’s assume that our loco has the same overall weight of 300, but it is now distributed unequally across the wheels. Let’s say 40 on two wheels and 55 on the other 4. When we try and push the loco, once the force per wheel exceeds he maximum force transmissible by the lightly loaded wheels, that's 24 per wheel (40*0.6) or 144 overall. Those two wheels will start to slip, and once that happens the kinetic coefficient applies and their contribution to resisting the force drops to 16 (40*0.4). The forces in excess of this will automatically and suddenly transfer themselves to the wheels that are not yet slipping. The shock of this may be enough to start all the wheels slipping, and if that happens it will keep on sliding until the pushing force drops below 120.

Even if the other 4 wheels do manage to hang on in there, the lightly loaded wheels can’t transmit their full share of the load and so will always be on the cusp of slipping. As a result they can’t reliably transmit any more than the 16 permitted by the kinetic coefficient. When the other 4 reach their limit at 33 (55*0.6) they will slip too giving a maximum force before slipping starts of 164 (that’s 4*33 plus 2*16). Net result this chassis may slip at a force of 144 or struggle on to reach 164. Compare that to the 180 when the wheels were equally loaded.

Again what applies to pushing the chassis with locked wheels apples equally to a the chassis under power pulling a train.
Ok this is all a bit of perfect world stuff but you see the way the wind is blowing. The fact that the wheels are coupled together doesn’t change things, particularly as they aren’t that rigidly couples and are capable of small amounts of movement relative to each other.

allanferguson
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Re: CSBs a question of Gravity

Postby allanferguson » Fri Mar 07, 2014 10:29 pm

I think Will is to be congratulated on the most understandable exposition I've seen of why some locos slip more than others. Thank you!

Allan F

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Paul Townsend
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Re: CSBs a question of Gravity

Postby Paul Townsend » Sun Mar 09, 2014 8:55 am

allanferguson wrote:I think Will is to be congratulated on the most understandable exposition I've seen of why some locos slip more than others. Thank you!

Allan F

Hear hear.
Some 30 plus years ago the late Derek Gunzel told us all the basic fact that unequally loaded axles will behave like this and many of us have striven to achieve equal axle loadings, with whatever form of suspension we prefer. He never explained it as clearly as Will.
I have become convinced that CSB is the easiest way to achieve this so am using CSBs wherever possible in new builds.

However there remains some difficulty with non-CSB locos in establishing just what the axle loading is in practice. This is relevant to older under-performing locos with probably beam compensation.

Derek led the way to measuring static axle loads so there is now no excuse for not testing and adjusting weight distributions towards the ideal. This is practicable as a retrofit to old locos by fiddling with bits of lead.
Highbridge has a pair of similar locos which underperform with premature slipping despite having adequate and equal driver loadings on the static test rig. It has been suggested that the dynamic loadings are different from those measured. I accept that as the likely explanation but have no idea how to measure dynamic axle loads!

Our current thinking is that this pair (Whitbourne beam-compensated chassis below Bachmann Manor bodies) will only become useful if re-chassised with CSBs. We have too many still skinned rice puddings hereabouts.


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