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Prospect said:
GWR, I have searched the internet and my own book collection which is huge and I can't find any definite info on grate to flue area on model vertical boilers. On full scale boilers it appears to be about 5 to1. Just looking at the model drawing 5 to 1 appears to be excessive due to the short flue length, so I am going to go with 10 to 1 until I find other info.
I almost certainly I would have gotten (and hopefully accurately remembered) this ratio from one of three sources, either KN Harris, Martin Evans, or Jim Ewins, all of who wrote in Model Engineer. I am also certain this would have been in the context of horizontal locomotive type boilers in the cases of Evans an Ewins, but could have been either horiz or vert with Harris. How's THAT for authoritative and conclusive evidence!
I checked both Martin Evans book Model Locomotive Boilers and the boiler book by K.N. Harris and I did not find anything about the ratio of grate to tube area for a vertical boiler in writing.

The formula given by Martin Evans for length to area of tubes is based on best practice for full size locomotive type boilers so using it on vertical boilers will not have any basis to proven designs for either full size practice or model work in my opinion.

N.K. Harris does give us a vertical design to reverse engineer. If we look at design #5 and work out the ratio of the grate area to the tube area I got 4.87: 1. We could also try the length to area on the tubes but they need to be as long as possible so why should we really bother with that math?

I checked the 6" vertical boiler I mentioned in this thread for grate to tube area. It has a single flue tube that is larger for a superheater element which I assumed to have the same cross section as the other tubes with the superheater installed. The ratio I worked out is 4.3:1. This boiler has a 5" OD 13 SWG firebox and 52 3/8" OD 22 SWG tubes 7-11/16" long. It has a single flue tube with superheater element 1" OD 16 SWG. I did the calculations with 53 of the 3/8" tubes for simplicity.

It seams to me that a ratio of 5:1 is a much better design goal than the 10:1 ratio given by GWR from memory.

If you are working the heating surface calculations using Harris as a guide please give the bore and stroke of the engine and design RPM in this thread. I have done more than a few of these calculations over the years but as to this point I have never built a model boiler.

Prospect said:
In the short term could someone let me know if the mudring enters into the heating surface calculations or if it is considered a none heating surface. It would appear to me that the mudring would actually draw heat away from the water heating surface but is it included in the heating surface calcs.

Any surface that has water on one side and combustion gas on the other side can be considered heating surface. So no the mud ring does not count. If you are going with the submerged tube design the whole upper head and chamber below the the design water line does count. I did a few calculations on a small one of the submerged tube designs and there is very little if any loss of heating surface from a normal design with 2/3 of the tube submerged.

The #5 in Harris has the water line at 2/3 of the tube length and 60 sqin of heating surface. This is was my reference point.

The reason I know about submerged tube boilers is because they were used with early Shay locomotives.

None of the Shay vertical boilers survived and the drawings are not known to exist. We do have some engineering knowledge of them because the main dimensions were listed in early catalogs.

They came in 2 sizes. The 7 ton Shay with 2-7"x7" cylinders had a vertical boiler with a 44" OD shell 78" tall. The 125 tubes were 2" OD and 30" long. I made two assumptions a 3" mud ring making the firebox 38" ID and simply use the OD for the tubes. This gave me a 2.9:1 ratio for the firebox to tube area.

The 9 ton Shay had 2-8"x8" cylinders and had a boiler shell 48" OD and 90" tall. The 155 tubes were 2" OD and 34" long. Making the same two assumptions the firebox is 42" ID and use 2" for the tubes. I got 2.8:1 for the firebox to tube area ratio.

Now it is clear to me at least that the tubes are really short on a submerged tube design and most likely a standard design would use the very same tube OD as 2" is a very common boiler tube size. So that throws any rule of thumb relating the tube length to diameter ratios out the window. We could make a rule for normal vertical boilers and one for submerged tubes if we had a bunch of data points but I do not think a single simple rule of thumb will cover both types of vertical boilers.

Dan Rowe said:
I saw on the other thread you are working the problem with 120 rpm. Well I will say it has been a number of years since I have seen steam winches in regular service but that seams a bit high and as you say that is not continuous running.

With logging the cable is only under load while lifting just like the old ship rigging I saw as a cadet. The duty cycle has to be less than 50%.

Did you work the calculations for the original design for heating surface? If you worked that backwards you might get close to the model design RPM for your heating surface check.


Dan, 120 was the engine crankshaft rpm. The winch drum speed would be 30rpm. Playing with my toy this afternoon I think 250 crankshaft rpm would be a more realistic speed for the engine.

After reading your posts, I checked the heating surface of the W. M. Harris model I scaled up from, and the heating surface is about 322 sq. in. with an engine set adjusted piston area of 3.08 sq. in. and total displacement of 3.08 C.I. My donkey engine was scaled up by 2 and thus the engine piston area and displacement are over 4 times the origional model. This seems to make the heating surface of my boiler design small in comparison. 615 sq. in. vs 322 sq. in.

I'm going to have to think on this a bit. John
The point I was trying to make is you can reverse engineer the original design. As this is a simple boiler the safe assumption is that it will evaporate 1 cu in of water for every 100 sq in of heating surface. This is Chapter 1 of N.K. Harris. Now with the boiler design pressure you can figure out how much steam the original boiler design can produce. This figure can be used to get a ball park figure for the RPM of the original design.

You can change the RPM but that might require a larger boiler. At any rate the same assumption of 1 cu in of water evaporated for every 100 sq in of heating surface apples to the larger model. You need determine the heating surface required for your chosen engine RPM.

I knew you were talking about the crank speed with 120 RPM and I still think that is fast but it is your model so you are the one to pick the design RPM and match the boiler heating surface to the steam requirement of the engine.

My copy of Model Boilers & Boiler Making is somewhat dog eared form too many trips to in my sea bag when I was a Marine Engineer.

Edit: the evaporation rate of 1 cu in water per 100 sq in of H.S. is per minute.
GWR, I quite sure I've seen the 10 to 1 ratio somewhere too. I dug out my very crisp (literally) Little Engines drawings for their Pacific Loco. and checked the total flue ( area and the grate area (144 This gives a ratio of about 21 to 1. My Pacific loco. boiler was built by a licenced company as I wanted a stamped code boiler and when I measured it today the ratio is 15 to 1. While my loco has never run on a track, it has spent many hours running on its roller stand and its boiler works well. As Dan has suggested I checked the no.5 boiler in the Harris book and it is about 5 to 1. Lots and lots of tubes. Doesn't look like it would be fun to build or maintain. All this does confuse things a bit. I know 2 gentlemen both retired now who have built 1/3 scale traction engines. One has his first class steam ticket and the other a third class. After Christmas I'll try and get there opinions on the subject. Thanks again to all for your help. John
Prospect said:
One has his first class steam ticket and the other a third class.

I am also retired but for what is worth my ticket said Chief Engineer unlimited horse power.

Perhaps compiling an average of flue area ratios of a number known (and successful) vertical model boilers would give us a reasonable number to use, lacking any more definitive value. My recollection could certainly not be considered definitive, I wouldn't. A friend of mine produces vertical steel boilers commercially (installed in his 7.5"ga locomotives) of maybe 12" diam and it would be interesting to know the flue area ratio of those boilers. They are known as free-steamers, but then he uses a large number of small flues over a strong propane burner. I also have the drawings for the old "Dianna" (model) steam launch boiler. There have been many of those built, but I've never read a 1st-hand report (or any report) of their steaming attributes. I'll try to pull out those drawings and pull a ratio on that boiler. One thing these two boilers share in common, aside from a large number of small flues, is they are short and squat, larger in diameter than they are tall, so the flues need to be smaller in diameter.
Prospect said:
I checked the no.5 boiler in the Harris book and it is about 5 to 1. Lots and lots of tubes. Doesn't look like it would be fun to build or maintain.

Yes it is a lot of tubes in a small space. If we check the length of the tube to the internal diameter squared I got the length is about 65 times the diameter squared. This is what Martin Evans recommends for a locomotive boiler. He states that the best practice for full size locomotive boilers is 50 to 70 times the inner diameter of the tube squared and uses a figure in the middle of that range.

Now maybe you can see my point of the dangers of using design rules for locomotive boilers for vertical boilers.

The only bit I could find by Jim Ewins on the web is this link. He gives 80 for Kt which is the same ratio of tube length divided by the tube diameter squared. Again this is for a locomotive boiler not a vertical boiler.

I did find a table of vertical boiler dimensions in Boilers Types and Design ICS 1907.
The table lists 14 boilers ranging from 20" to 48" OD. I calculated the ratios of the grate area to the tube areas given and the values ranged from 3.4 to 5 to one. The average of the 14 boilers listed worked out to exactly 4:1 for the grate area to the tube area.

The grate sizes for the 48" boiler is 42.5" OD and the grate diameter for the 44" boiler is 38" OD in the table so my assumptions for the Shay submerged tube boilers was a good estimate.

I can work out the L/d2 ratios for the table for vertical boilers given in the table to get a ball park figure for vertical boilers as it is a good historical source of information, and that is what was done by other model engineers for locomotive type boilers.

Now why do you not want to simply double the size of the boiler like you did the engine? That seams like the simple approach to me. And speaking of successful vertical boilers it seams to me that the original W. Harris donkey boiler or the steam roller boiler have to fall into that category as I am sure many examples have been made to those plans.


I consider this type of discussion a learning exercise and a refresher course for more experienced boiler makers.

As most of the readers of this section of the forum have a copy of K.N. Harris handy and most likely have worked a few boiler calculations could you PLEASE give us the bore and stroke of the engine in question so we can use Chapter 1 of the book to follow along.

Dan, The twin engine bore is 2" and the stroke is 2". The pston rod is 3/8" in diameter. I know there is controversy about it, but I used a Viton o-ring for a piston rings. I've always had good luck with o-rings. The cylinder blocks are cast iron and the slide valves are bronze. John
I don't know why this should raise a controversy? A couple of things come to mind . . . .
1. Many model steam cylinders now operate perfectly happily with O-rings, as long as the ring material and cylinder wall finish is appropriate for the application and the grooves are properly proportioned. Yes 2"OD is a bit out of the ordinary as most O-ringed model cylinders are smaller, but most ain't All.
2. In the end do whatever you want to do. If you like and have time, report your experiences. It's the way model engineering works, . . . or used to.
GWR, The main reason I use o-rings is that i use them frequently on the farm and are readily available. In three steam engines the previous 2 being smaller bores, they,ve worked well. it's very true that the initial cylinder wall finish is important and one has to remember that 0-rings swell a touch in fluids and that has to be taken into consideration. On this engine I bored the cylinders, lightly removed the bit of fur with a brake hone and then lapped or polished the bores using an extended aluminum piston with 3 quadrings so that I could run one ring completely through. I used some Bon Ami and oil for abrasive. It was fast and the finish was very nice. John
The best answer to this is found in K.N Harris Chapter 8 about tubes and spacing.

K.N. Harris gives the proper credit to the formula found in both Martin Evens books and Model Engineers Handbook by Tubal Cain. The formula L/D2=60 to 80 where L is the tube length and D is the tube external diameter was produced by the investigations of C.M. Keiller.

I have read this several times over the years and missed the differences. The formula given by Martin Evans is very similar but slightly different. Slightly transposed the formula is L/d2=65. In this formula given by Martin Evans d is the internal diameter. Tubal Cain gives the same formula from Martin Evans book and it is the same with source credit given.

Martin Evans says that the length of the tubes divided by the square of the inner diameter is 50-70 for the most successful FULL size locomotives.

Tubal Cain says The most economical length to diameter for both models and full size boilers with induced draft is 70-90. Then he mentioned that that tests on FULL sized locomotives proved that the last 25% of the tubes only evaporated 10% of the total output.

The tests at Altoona PA on of course full size locomotives indicated that no advantage was gained by having a tube longer than 100-120 times the length of the inner diameter. This is from Steam Locomotive Design: Data and Formulae E.A. Phillipson 1936.

Tubal Cain then says that Martin Evans formula leads to ratios of 25-30 for loco boilers. This is the L/d ratio not the L/d2 ratio.

L is defined as tube length and d is defined as tube internal diameter.

Tubal Cain then talks about vertical boilers with natural or slight forced draft, and states that the L/d rations are as small as 15 due to mechanical issues with very small tubes.

To answer the grate to flue area question we turn back to K.N. Harris Chapter 8. The type of draft is an important consideration in selection a grate to flue area ratio. The numbers given by K.N. Harris for a locomotive boiler doing locomotive work or with induced draft is the tube area should be 1/7 the grate area and can be made as high as 1/6. The ratio for natural draft is given as 1/4 as a good all round figure. This is the same figure I got with the ICS vertical boiler data.


I don't see any reason why Orings should be controversial. I use solid teflon piston rings on my launch engine and have run 3 seasons now at 165 psi. with cast iron cylinders...with no worries or issues..

Orings should work a treat!

Here is the ICS vertical boiler data. The Stuart Swan is a 2.25"x2" twin cylinder vertical engine that can produce 3 HP @ 800 RPM and 100 Psi. I have a Cygnet which is the single cylinder version.

You should be able to produce 1.5-2 HP with that engine depending on what RPM and boiler pressure you choose.

Proportions of Vertical Boilers ICS 1907

HP Shell Height Tube Tube L Tubes H.S. Grate Grate Total Tube
OD OD # OD Area Area
In Ft In In Ft In SqFt In SqFt SqFt

34 48 10 8 2.5 7 8 91 340 42.5 9.722 2.584
28 44 11 4.5 2.5 8 5.25 64 282 38 8.08 1.8176
24 42 9 4.5 2 6 7.375 96 247 36 7.068 1.6992
23 40 9 8.5 2 6 11.25 85 233 34.25 6.398 1.5045
20 38 8 9.25 2 6 1 85 201 32.5 5.76 1.5045
17 36 8 8.5 2 6 1.25 73 177 30.5 5.073 1.2921
15 34 8 7.25 2 6 1.5 61 152 28.25 4.352 1.0797
12 32 7 6.25 2 5 1 61 124 26.5 3.83 1.0797
11 30 7 6.75 2 5 2.25 55 117 24.5 3.343 0.9735
10 28 7 8.5 2 5 5 42 100 232 2.885 0.7434
8 26 7 4.25 2 5 2 37 81 31 2.335 0.6549
6.8 24 7 10.75 2 5 9.5 26 68 19 1.967 0.4602
5 22 7 4.25 2 5 4 22 53 17 1.527 0.3894
4 20 8 3.5 2 6 4.5 14 42 15 1.227 0.2478

When I bought the plans and the castings for the Saturated Steam vertical boiler I asked about the steam capacity of the boiler. They contacted the designer and he did not know no one had ever asked that question. I still do not know but I see a large heavy package under the tree that I think is the 6" and 5" copper tube I need to build the boiler so I will have to build it to find the answer.

Hey guys I would appreciate some feed back here so I know if I am cutting the wrong side of the tree branch that I am standing on again.

Now that I know that the bore and stroke of the original W.M. Harris engine is a 1”x1” twin and your calculated boiler H.S. of 322 in2 the data can be used to approximate the RPM of the original design.

This calculation is nearly the same as the example problem in K.N. Harris Chapter 1. The area of the piston is .785 in2. That times the stroke of 1” gives us .785 in3 per stroke. There is no need with this type of rough calculation to consider the diameter of the piston rod which is how K.N. Harris made the calculations.

The cylinder is double acting and there are two cylinders so 4 times .785 in3 gives us 3.14 in3 per engine revolution.

The H.S. of the boiler is 322 in2 so using the figure given for a pot boiler as a conservative figure we can evaporate 1 in3 of water for every 100 in2 of H.S. per minute. That gives us an evaporation rate of 3.22 in3 of water per minute.

Turning to Table 1 we find from the steam tables provided that @ 100 Psi 1 in3 of water converts to 237 in3 of steam. That times the evaporation rate gives us 763.14 in3 of steam per minute @ 100 Psi.

Now we can calculate the revolutions per minute by dividing the boiler steam output by the volume of the engine per revolution and the answer is 243 RPM.

Well it looks like 250 RPM is a good design number for the engine. The scaled up calculations go just like the example in the book with a 2”x 2” twin cylinder engine.

I did get copper for the Saturated Steam boiler so I will be doing the calculations for that boiler again.


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