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Designing Model Boilers (Thermal Design)

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Martin Johnson 130/05/2018 09:03:59
129 forum posts
1 photos

I have a series of articles starting in ME 4584 that describe computer techniques I have developed over the last couple of years. The aim is to improve the THERMAL DESIGN of small steam boilers. The calculation is not concerned with strength considerations, which are well covered elsewhere.

The program is in .xls format and it can be found at the following link:


along with a detailed report on how the calculations are undertaken.

I would also be pleased to receive comments on the techniques. The program as presently constructed is completely free to use and if you want to develop it further, nobody will be more pleased than me.

Many thanks to Neil Wyatt who has uploaded the files onto this site.


Edited By Martin Johnson 1 on 30/05/2018 09:07:24

Brian H30/05/2018 10:22:57
1395 forum posts
100 photos

Many thanks for sharing this Martin.


Paul Horth24/07/2018 10:20:35
52 forum posts
15 photos


I have been reading your articles in the M.E and have just got around to looking on this forum. I really appreciate having access to your spreadsheet calculations and notes. I have spent much of my professional career doing calulations in heat transfer and fluid flow, and I admire a well-made spreadsheet as much as a well-made model.

I have a 2 inch scale traction engine, and I will enjoy using your spreadsheet to estimate the boiler performance, and comparing the results to my measurements of coal consumption, power, and efficiency. I will send the results back to you for your review and comments. I'll just make a couple of comments here first.

I think that the grate loading that a model boiler can be run at, depends on the draught. The draught in a traction engine is less effective than a loco, because the blast nozzle is right up in the chimney, well downstream of the tubes, and there is no petticoat pipe or choke to gather the flue gases. So in my engine, which is a similar size to Speedy, the grate loading is much lower than 40 lb/h ft2, it's typically 13 to 15 lb/h ft2. I have deliberately eased the draught with a larger blast nozzle, so that I can go for a drive without lifting the relief valves all the time. I also find no evidence for the large quantity of unburnt coal which you assume, the smokebox has a few spoonfuls of cinders in it after a long session. Probably due to the lower draught.

I will use your spreadsheet to see what difference these parameters make to the simulated performance.

Thanks again,

Paul Horth

J Hancock24/07/2018 10:48:39
337 forum posts

You might consider providing the losses incurred/ sq cm from the boiler surface with no lagging too.

richardandtracy24/07/2018 11:23:35
938 forum posts
10 photos

That is a remarkably comprehensive piece of work and the backup notes require considerable study. Thanks for sharing. There is a heck of a lot of work that has gone into it.

What is driving the limitation statement that it's applicable to 5" gauge only (Spreadsheet 'Summary of Results:D30' ) ? By the look of it, the statement is contradicted in the notes, section 2, 4th para. I suspect it's due to caution rather than lack of evidence or inapplicability.



william Powell24/07/2018 17:37:02
12 forum posts
2 photos

HI Martin

Thank you for posting this work. I build and run in the smaller gauges of 2 1/2" and 3 1/2" and am looking at way to improve the locos i run. I have been concentrating most of my efforts of late in to the exhaust set up, although i have been tinkering around the fire box end, with stainless arch and rosebud grate.



Martin Johnson 124/07/2018 20:55:35
129 forum posts
1 photos

Thank you all for your feedback. Dealing with the responses in turn:


I would be pleased to see any test results that you can obtain - tests are like gold dust!

I agree that coal consumption is basically a function of air flow. I wondered whether to discuss that in the article, but decided against it. However, I am convinced that rather than consider grate loading, we should probably be looking at air flow per unit grate area and this then dictates a combustion rate PROVIDED CONDITIONS ARE STEADY STATE - that is that the fire thickness is adjusted until it is not changing at a steady air flow.

I also agree that model traction engines tend to run at a lower grate loading than rail locos - generally, there is simply not the load on them (I have a 4" scale Burrell, which I rally). Having said that, the loading on 2" scale engines on a wet rally field can be massive. My friend's 2" Fowler can be "roaring away", while my 4" machine is having a leisurely time of it.

I am not convinced that all the difference between road and rail grate loadings is down to draughting. I agree that the base of a TE chimney is not great for free gas passages. However, the tall gently tapering chimney is a massive improvement in draughting over most rail locos (except tall chimney narrow gauge outline machines). I have been doing some work on draughting and have more planned, but the height and gentle expansion of the chimney is an important factor in effective draughting.

With regard to un-burnt fuel, you may not see evidence. From full size practice, about 4% of it will end up in the ashpan with the ash. Of the remainder most is ejected as fine (ish) particles which is the dirt that adorns most steam engines. Another "work in progress" is playing with the Navier Stokes equation to see if I can predict fuel loss on the basis that particles below a certain size will be blown through the fire by the draught. If you are working at relatively low grate loadings, then un-burnt fuel loss will be significantly lower anyway.

I have also been looking at full size practice and they generally recognise two limits to grate loading:

1) Grate limit - the point at which the curve of evaporation rate against grate loading has zero gradient - i.e. putting more coal on does not make any more steam. It should be possible to predict this with my program.

2) Front end limit - the point at which flow in the blast nozzle achieves sonic velocity. Thereafter, attempts to increase throughput result in rapidly increasing back pressure on the cylinders. It will be almost impossible to reach in a scale model where velocities are all scaled, but the working fluid sonic velocity remains constant.

Paul has also drawn my attention to an error in my calculation of heat loss from the boiler casing, which will be somewhat high in the calculation. Fortunately, it is a small part of the whole picture, so is not a major blow. Nevertheless, something to be corrected in the next issue - yes I am working on an upgrade.

J. Hancock

Yes, part of correcting the current lagging loss calculation will allow me to include that.


The calculation of "Available steam volume for power" depends on a curve fit of Bill Hall's test results of condensation loss on a 5" gauge cylinder (Speedy, actually). When you consider the effect of scale, the surface available for condensation changes as the square of scale, but the total volume of steam obviously varies as the cube. Hence, the condensation losses must be heavily dependent on scale. Hence my warning.

I have noodled around a bit to try and calculate a scale effect from first principles. Not happy with it yet, but that bit of work is "resting" - not dead.

In between all this, I am trying to build a model.

Thank you all for your interest.


duncan webster25/07/2018 19:21:30
2345 forum posts
38 photos

I'm not sure Martin's definition of front end limit is correct. I think it is where the putting more steam up the chimney doesn't produce enough extra draft to burn the coal to produce the extra steam. It can be well below the steam rate required to produce sonic velocity, and the evidence of locos like Red Devil which had convergent divergent blast nozzles suggests that they worked at supersonic steam velocity. I think it is accepted that UK locos were designed with lower front end limits thatn USA and others. Designing a setup which coped with the very rapidly varying steam flow as exhaust port first opened, then widened and closed again must have been a bit of a job, but all the literature I've read suggests you can just design for the mean flow.

julian atkins25/07/2018 21:56:37
1224 forum posts
353 photos

Hi Martin,

I have read your paper with much interest, and having had a sort of preview by our mutual 'Speedy' builder friend of your correspondence with him (not Bill Hall who is no longer with us).

3 superheater elements can be fed into and silver soldered direct to a plain wet header considerably simplifying the pipework in the smokebox. With 3 x 1/4" dia return bend type superheaters in 3 x1" dia OD superheater flues I have found this more than adequate in a medium sized 5"g loco. The whole superheater assembly and wet header can easily be removed via the smokebox door opening if ever this were required.

I have also used 2 x 1/4" dia superheater elements of both LBSC type and radiant stainless type in 2 x 3/4" OD superheater flues and 2 x 3/4" OD superheater flues on smaller boilers, with again the wet header pipework being very simple and easy to remove if required.

A double flanged throatplate of traditional type is a must IMHO as this aids water circulation, with a generous flange to to the throatplate where it abuts the rear of the barrel, and the barrel lower half can be belted to suit and relieved locally after silver soldering.

One of my earliest experiences was with LBSC's Maisee design. There is the combustion chamber boiler in the construction book with 4 superheater flues, and the much simpler 2 superheater flue design of 1936 with no combustion chamber. I can state quite categorically that the original 1936 simpler boiler was as good if not better in steam production when compared to the later construction book complicated design with combustion chamber.

In the above examples, both had LBSC type superheater elements.

The 1936 design with just 2 superheater flues made of radiant type out of stainless would be something else yet again!

I have always taken a keen interest in smokebox draughting. In my first loco I departed from the drawings quite considerably for the smokebox innards. I have never been a slave to drawings.

It takes a lot of skill in miniature to fire a sloping narrow grate. And a lot of clubs have coal nothing like the quality I remember of in the 1980s and what was carefully acquired or stocked up from the late 1980s in certain clubs. I have Welsh steam coal in my coal shed that dates back 30 years and some huge lumps from Rhymney depot that date back to pre 1964.



Paul Horth25/07/2018 22:09:54
52 forum posts
15 photos


Thanks for your comments. As well as being a great design aid, your spreadsheet provides a rational basis for setting the capacity of safety valves. Sizing the valve for the chosen capacity is another story, I published a method in the M.E some years ago, but I've since had my doubts about its accuracy.

If a Speedy boiler can be fired to produce 28 lb/h of steam, as your spreadsheet estimates, I wonder if the LBSC-style safety valves can pass that flow. On my engine, if I had the draught to get the grate loading, 28 lb/h would be well in excess of the feed pump capacity, and just about within the capacity of the two safety valves (estimated with uncertainty).

When I run the spreadsheet for my boiler with a reduced grate loading of 15 lb/hft2, it predicts a steam rate of about 13 lb/h, which matches what I actually see on tests. So your heat transfer calculations are pretty good. More details to come.

I agree with your comment on ash - there are always some still-burning cinders when I rake out the ashpan during a rally session, maybe not as much as 4% of the 3kg or so of coal that I use in a 5 hour rally. They do add some heat to the air intake.


Martin Johnson 126/07/2018 10:34:35
129 forum posts
1 photos

Thanks again for your interesting comments. As before, they demand a reasoned response:

Duncan - Hello again!

You are right and I was trying to be economical with words and probably over-simplified matters. Try this for a slightly better explanation:

"Over a good range of operation, the work done by the blast pipe / chimney combination roughly matches the resistance through the tube bank, fire and grate. As steaming rate is further increased, the flow in the blast pipe will become sonic. (This is not a well defined change as flow round bends etc. will start to gradually choke well before the whole passage chokes). Exhaust steam flow can be further increased but at the expense of rapidly increasing exhaust back pressure. As a consequence the pumping work done by the blast pipe / chimney no longer increases in proportion to the resistance through the tube bank, fire and grate. Hence, further increases in steaming rate are not possible."


My work has only looked at how many superheaters might be needed to achieve a certain superheat. You are right that some arrangements would need some "very innovative plumbing", and 3 (maybe 4) elements go into a typical loco very well. However, I took the view that if a thermodynamic need could be demonstrated, then maybe it would be worth inventing something - but design is always a balance of the desirable against the practical.

I have not looked at water circulation, but accept that restricted circulation is not going to be good. I know both Jim Ewins (thick tube plate unflanged) and Pete Rich (flanged, but well chamfered off) have tried some different approaches in this regard.

The use of combustion chambers in models is IMHO a very bad idea, so your comments are very interesting. They are a swine to build and maintain, and it seems to me that a slavish adherence to Keiller is one of the chief reasons for their use. The difference in firebox radiation between model and full size, that I describe is another reason why combustion chambers might work in full size, but not in models.

The observations you make on the relative performance of combustion chamber and non-combustion chamber designs illustrates what fascinates me about this whole boiler design problem. As part of the work I have done, I have compared the full size King boilers with different superheat layouts. I concluded that the changes they made would not have made much difference, the higher superheat being neatly offset by a reduction in steam quantity. It seems operational experience proved just that!

I hope you find the next instalment in ME interesting, as it makes a few observation about matching superheaters and flues!


I also have some concerns that taking a bland "40 lbs/sq. ft/hour" firing rate is not always appropriate. As you say, it can give a rather high steam output - and yet the analysis of IMLEC results is fairly conclusive although the spread in data is quite large. Another approach would be to work out steam demand from cylinder dimensions, cutoff, speed, and a Bill Hall condensation loss correction, then by trial and error work back to the firing rate required to achieve that - sadly a rather laborious process! In any case, keeping a standard firing rate for calculations will at least rank designs in the correct order - which is what I was trying to achieve at the outset - that and to find just how hard can a model boiler be fired.

I am very glad that the calculations match your observations at a reduced (probably more realistic) firing rate.

Anyway, I am off to fine tune some calculations on Sentinel type boilers which I intend to write up soon. I shall post something ASAP.


duncan webster26/07/2018 13:14:21
2345 forum posts
38 photos

Googling around I find there are 2 limits applicable to the smokebox arrangement, the front end limit and the discharge limit. I think Martin is conflating the two, see


It is also apparent that some locos were desiged for supersonic exhaust steam, with converging/diverging nozzles. How well they coped at low steaming rates when it wouldn't be supersonic is interesting

As regards water circulation, I can't see it makes a lot of difference to steam production, the problem is getting the heat from the combustion gasses to the tubes/firebox walls, not from the metalwork to the water. If there is a pocket at the throatplate where circulation is not good and heat transfer from the fire is high then the water in that area will boil faster, the bubbles will rise and more water will flow in. This might well give rise to localised temperature gradients in the firebox, which I do not suggest are a good thing, but in a small copper boiler where heat can flow in the metal very quickly, and distances are small I doubt it matters very much. There is plenty of evidence of Winson Britannias running with exposed firebox crowns with no ill effect, due to the bottom gauge glass fitting being too low. Again not something I'd recommend

I've never seen a report of a boiler with a simple WELL MADE butt joint between throatplate and shell failing on test or in service.

John Alexander Stewart26/07/2018 18:20:37
758 forum posts
51 photos
Posted by duncan webster on 26/07/2018 13:14:21:

As regards water circulation, I can't see it makes a lot of difference to steam production, the problem is getting the heat from the combustion gasses to the tubes/firebox walls, not from the metalwork to the water. If there is a pocket at the throatplate where circulation is not good and heat transfer from the fire is high then the water in that area will boil faster, the bubbles will rise and more water will flow in. This might well give rise to localised temperature gradients in the firebox, which I do not suggest are a good thing, but in a small copper boiler where heat can flow in the metal very quickly, and distances are small I doubt it matters very much. There is plenty of evidence of Winson Britannias running with exposed firebox crowns with no ill effect, due to the bottom gauge glass fitting being too low. Again not something I'd recommend

Duncan (and Martin, of course); my expertise is certainly not in mech. engineering, but I do find it an interesting topic.

With the thermal conductivity of copper being that about 10x that of steel and something like 1,000x that of water, I do tend to agree with your observation of exposed crown sheets and copper boilers not being as much of an issue as we might think.

An interesting calculation would be to see what temperature an exposed crownsheet would get to in a small copper boiler, with girder stays or with round stays. Any takers? There are lots of thermal conductivity paths on our small boilers (stays and mud-ring and tubes and firehole, and...) so I do wonder what the limits might be.

I do think we are very cautious with silver soldered copper boilers - true, low water and a good fire will heat'em up, but when the water finally goes, so will the fire, as the blower will stop. Yes, it's better to err on the side of safety, of course.

As an aside, my (again, novice) observations and calculations are that a butt joint will be fine on a copper boiler, given proper silver solder penetration. One prolific club member does build copper boilers without flanged plates, and these are very successful.

Very interesting - thanks all. John.

Martin Johnson 127/07/2018 09:08:08
129 forum posts
1 photos

Thanks for making me think carefully, Duncan.

I was attempting to explain what Ell called the "front end discharge limit" or the discharge limit in the link given to the 5AT website.

Now I am going to be a bit radical and say I don't really accept that there is a "Front End Limit" as described there. My analysis of air flow, both full size and model given in Fig. 7 of my article in ME, suggests there is a "fixed" relation between air flow and coal burned. I also think the independent variable here should be air flow - we set an air flow and then put in enough coal to keep up with it - NOT VICE VERSA. Now, as air flow increases, the fire burns hotter and faster and the air ratio tends toward the stochiometric value. At very high air flows, the fire will be so hot and the reaction so fast, that the oxygen cannot latch on to carbon to achieve complete combustion, at which point CO values will start to rise quite quickly. However, in Ell's tests on a King, he was up at grate loadings around 150 lbs/sqft/hr and still had 30% excess oxygen and "un-measurable CO values" - so that COMBUSTION limit is very high.

It seems to me that keeping at least 20% excess air is probably necessary to keep CO levels down, but the front end has very little to do with it. I would expect grate design, ashpan design, coal type, firebox gas mixing, brick arch.............. to have quite a big influence. But..........they are at the back end.

I would also concede that it is quite possible that the front end cannot pump enough gas through to achieve the required fire output and hence boiler output. However, in my view that is simply a blast pipe / chimney and grate / tube bundle combination that is poorly designed from the start. Exactly analagous to the pump curve and system curve not intersecting at the intended point on any pumping system - a phenomenon I have made a career from.

John Alexander Stewart

I completely agree with your order of magnitude numbers on thermal conductivity of copper, steel and water - and the conductivity of the gas film is even worse. Which is why I have tended to ignore water side design problems. That is not to say they don't exist, but dealing with the big stuff first is usually the way to do things.

You ask if there are any takers for a calculation of "dry" crown sheet temperatures. No, is my answer to that!

Thanks to all contributors,


SillyOldDuffer27/07/2018 09:46:27
5138 forum posts
1074 photos

Posted by Martin Johnson 1 on 26/07/2018 10:34:35: find just how hard can a model boiler be fired.


Julian mentioned the variable quality of fuel earlier. Struck me the difficulty of controlling the heat source in a single engine must be bad enough, but how safe is it to compare different boilers when the fire depends on the fuel and the skill of the fireman. (I don't think the variability invalidates Martin's work, just makes it harder to understand what's going on in the boiler!)

But my main point is a suggestion. For test purposes only how about replacing unreliable coal in a firebox with an electric element and an adjustable air blower. The arrangement would allow input power to be measured & controlled accurately, and - the exciting bit - allow more heat to be put into the boiler than a firebox full of coal would allow. Be fun designing and building an element capable of dissipating several kW inside a model firebox.

Model boilers are extremely interesting, many thanks to Martin for writing the article and casting light into my darkness!


duncan webster27/07/2018 11:18:58
2345 forum posts
38 photos


a typical 5"g loco might have 25 sq in of grate. At 40 lb/sqft/hr of coal that is 27 kW. My domestic supply is 60 A, 15 kW, and can you really make an electric heater that small dissipate 27kW and still allow air through?

Better would be gas fire, but I think size defeats us again, 27kW is a respectable size for a domestic central heating boiler which is a lot bigger

SillyOldDuffer27/07/2018 12:45:47
5138 forum posts
1074 photos
Posted by duncan webster on 27/07/2018 11:18:58:


a typical 5"g loco might have 25 sq in of grate. At 40 lb/sqft/hr of coal that is 27 kW. My domestic supply is 60 A, 15 kW, and can you really make an electric heater that small dissipate 27kW and still allow air through?

Better would be gas fire, but I think size defeats us again, 27kW is a respectable size for a domestic central heating boiler which is a lot bigger

Duncan, trouble with you engineers is you always let mere details get in the way! Surely your objection is the tail wagging the dog? Anyway, as a politician I'm only concerned with policy - never our fault when mere mortals fail to deliver. No way does my genius ever turn out to have been insanity all along.

On second thoughts, I think it would be possible to get 30kW into a square inch with an arc, but the temperature would be far too high. The notion has got to be a runner in the year's most dangerous idea competition: perhaps someone will suggest a suitable consolation prize?

Another of my brilliant ideas bites the dust. Ho hum...





Edited By SillyOldDuffer on 27/07/2018 12:46:32

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