By re-arranging the formula given on the previous page it is possible to work 'backwards' and use them to 'design' a suitable boiler to work with a certain set of cylinders and wheel diameters. Note however that some of the results may not be practical and may have to be compromised. For instance, it may not be possible to make the grate area as large as calculated without making the firebox unduly long and sticking back into the cab too far. It may also not be possible to fit in as many tubes as calculated due to the tubeplates being too small to take them.

By re-arranging the formula for Ee it can be used to calculate the required grate area from the bore and stroke of the cylinders and the diameter of the driving wheels. The formula then becomes:

                                  Grate Area =     Swept volume of cylinders

                                                                      Diameter of driving wheels x Ee

We now need to calculate the number and diameter of tubes to go with the size of grate and this can be done using the formula for Eb re-arranged to give:

                                           Number of tubes =    Grate area x Tube length

                                                                                    Eb x Tube inside diameter²

We can alter this slightly to give:

                                          Number of tubes =   Grate area   x        Tube length

                                                                                            Eb             Tube inside diameter²

Now the second half of the formula is the formula for calculating Kt so our formula can be written as:

                                        Number of tubes =  Grate area  x  Kt

                                                                                          Eb

In the ideal boiler Kt and Eb are both 80 so they cancel out and the number of tubes simply equals the grate area rounded up or down to the nearest whole number. Obviously we can't have half or a quarter of a tube!

We now know how many tubes are required, whether we can fit them in is another matter!

We now need to know the length and internal diameter of the tubes and this is where it goes a bit pear shaped as so far as I can tell there is no way to calculate either of the two values individually using the formulae above.

If we know the length we can calculate the diameter using the formula for Kt, likewise if we know the diameter we can calculate the length.

                          Length of tube = Kt x Diameter of tube²

                          Diameter of tube = square root of     (length of tube)

                                                                                                                 Kt                                           

The only way out is to choose either the length of the tubes or their diameter and then calculate the other. The diameter may be limited by the number of tubes we need to fit in or the length may be fixed within a certain range by the length of the boiler barrel. It's really a case of trial and error until you get something that fits! Remember that the number of tubes includes the superheater flues which will be of bigger diameter than the fire tubes (more of this later hopefully)

I've devised another spreadsheet to work all this out for you.

The spreadsheet also calculates the total tube area as a percentage of the grate area and it would seem that a figure of 10 to 15% is about right here.

As an example let's look at the boiler for Helen Longish.

Putting a bore of 0.875", stroke of 1.125", number of cylinders 3, and a wheel diameter of 3.313" into the spreadsheet gives us a calculated grate area of 8.17 sq. ins. The maximum width for the grate is 1.188" as the firebox has to fit between the frames so this gives us a required length for the grate of 6.88"

We also have been given the number of tubes as 8. Putting in the length of the tubes as 8.125" (the maximum length that will fit into the barrel) gives us an inside diameter for the tubes of 0.319". This also gives us the tube area as 7.81% of the grate area which is a bit on the low side. Alternatively, we could have perhaps chosen tubes of 0.382" inside diameter (maybe had a load in stock!). Using this figure instead gives us a tube length of 11.67" which would have been too long for the barrel. However, this diameter tube gives us a tube area of 11.23% of the grate area which is more acceptable. We could have used that size tube and reduced it's length and accepted the effect on Eb and Kt.

How do the results compare to the real Helen Longish boiler? Well, the grate on the real boiler is 6.25" long which is slightly (1/2") short so the area is slightly less than it perhaps should be. The tubes are 0.319" internal diameter by 8.125" long but there are 10 instead of 8. The increased number of tubes has decreased Eb down to 60.47 but increased the tube area to 10.55% of the grate area so has improved that aspect. It would be interesting to block 2 of the tubes off and see if it made any significant difference to the steaming.

Let's have a look at another design - Don Young's Black Five in 5" gauge. Don was reputed to design pretty good boilers which steam well so let's see what the formulae give us.

Entering the data for the cylinders (1.625" bore and 2.5" stroke) and wheel diameter (6.375") gives us a grate area of 21.69 sq. inches. The grate is 2.625" wide so entering this gives us a grate length of 8.26".

The number of tubes comes out at 22 and using a length of 14.75" (the actual length used by Don) gives us an inside diameter for the tubes of 0.43". The tube area as a percentage of the grate area comes out at 14.69%.

So how do these calculated figures compare to Don's? Pretty close actually. Don's grate area is 22.3 sq. inches which is spot on. He specified 25 tubes of 0.375" i.d. which gives a total tube area of 12.4% of the grate area. The only fly in the ointment as I see it is that his tubes are too long for the diameter giving a value for Kt of 105.

Let's try another example, the very popular Simplex by Martin Evans.

Entering the cylinder data and wheel diameter gives us a grate area of 22.89 sq. ins and with a grate width of 2.813" gives us a grate length of 8.14". There is a major discrepency here straight away as the design for the boiler gives a grate length of only 5.625" giving an actual grate area considerably less than the formula calls for i.e. only 15.82 sq. ins.

The formulae also give us a value for the number of tubes of 23. Entering the length of the tubes - 11.188" - gives a diameter for the tubes of 0.374". There is no way we can fit in that many tubes of that diameter! Basically, in my opinion (and those of the formulae!) the boiler is much too small for the size of the cylinders.

Playing around with the figures would suggest that the grate area (and the rest of the boiler) is much better suited to a cylinder bore of only 1.25" which matches the actual grate area very well. The tube number now comes down to 16, which at a length of 11.188" gives an internal diameter of 0.374".

This doesn't mean that the Simplex design is a particularly bad one. It just means that the boiler may struggle to supply enough steam over long periods as it's going to have to be run flat out. As the grate area is small, the fire is going to have to be run very hot to get enough heat to produce the steam with it's attendant problems of clinkering and burning of the grate.

It's a strange coincidence but a question has just been posted on one of the ME forums as to which locos are best suited to passenger hauling on club tracks. One reply suggested NOT a Simplex as they are difficult to keep in steam for long periods! I wonder why!

I am just about to start work on my own Simplex but there doesn't seem an awful lot I can do to try and balance the figures a bit better. The cylinders have already been bored to size and I don't fancy fitting a sleeve to reduce the bore. In any case this would reduce the power output quite a bit. That leaves the boiler. The only way to enlarge the grate would be to extend the firebox into the cab which would probably look silly so I'm probably stuck! I could be worrying about nothing of course as there's plenty of Simplexes running around quite happily!

It's interesting to note that Super Simplex (the upgraded Simplex) fairs even worse as the cylinders are 1/16" bigger in the bore with virtually the same grate area! Where Super Simplex does score over Simplex is that the boiler barrel is bigger enabling more tubes to be fitted. This brings Eb down from 97 for Simplex to 79 for Super Simplex. On the whole the Super Simplex boiler is better balanced with regards tubes and grate area (still too small for the cylinders though!).

The big question after all this is can we rely on the Jim Ewins formulae to design a boiler?

I think we can because the formulae seem to tie in with a lot of existing loco designs. All the figures don't match exactly but most are within a limited range either side of the 'ideal'. The problem is that we can't always physically produce a boiler that matches all the criteria, especially if we are trying to build a loco that closely resembles an actual prototype. A lot of the time we are going to have to compromise on one or more things. It may be impossible to get the right grate area without making the firebox excessively long (as with Simplex). It may not be possible to get the calculated number of tubes of the calculated diameter inside the boiler so we are going to have to use less and/or smaller diameter tubes. Perhaps the most important thing about the tubes is that the total cross sectional area should be great enough to draw sufficient air through the fire by keeping the ratio of tube area to grate area between 10% and 15% as mentioned before.

As I said at the beginning of all this rambling, the above is only my personal interpretation of Jim Ewins' formulae and should not be taken as 'gospel'. I intend to look at as many loco designs as I can and calculate the 4 factors using the spreadsheets. I'll eventually print a chart with them all on and put it on the site.

The greatest discrepencies seem to be with the 2½" gauge locos which have wildly varying figures and these definitely need more study. I think part of the problem with these is the tendency to use 'standard' items such as cylinders for widely differing locos with different boiler sizes e.g. using the same sized cylinders for Fayette and Annie Boddie when Annie's boiler is only half the size of Fayette's!

To be continued!

28/10/2015

I've been meaning to update these pages for some time with my latest thoughts but other things get in the way.

I now think that the Keiller ratio for the tubes (Kt) is not particularly important. This of course then throws some of the other factors (Eb and Eo) into some doubt. Jim himself did some experiments on his 0-6-0 loco and measured the temperature of various parts of the boiler under varying conditions using thermocouples. The results of this experiment were published in the Model Engineer magazine for 18th March 1966.

Part of the experiment was to measure the temperature at different positions in the fire tubes. To cut a long story short, Jim concluded that only the first 1/3 of the firetubes actually contributed anything towards steam production under normal running conditions. The majority of the steam production came from the firebox. I think this idea is now generally accepted by most.

As the Keiller formula was devised to decide the best diameter for a tube compared to it's length, it's obvious that in practice it doesn't hold up if only the first third of the tube actually does anything. I believe the formula was based on full size loco designs where the conditions in the tubes are completely different to that in a model. Full size tubes are much larger in diameter and the gas flow through the tubes is turbulent which increases the heat transfer along the length of the tube. In small diameter tubes you don't get this turbulence and the gas flow is mainly laminar ie. in a straight line. This causes a stagnant layer of gas to adhere to the inside surface of the tube and this 'boundary layer' prevents heat transfer from the gas to the tube. You probably do get some turbulence in the first section of the tube as the gases pass over the sharp end of the tube but it soon settles down to a laminar flow.

In the USA many people fit 'turbulators' into the tubes of oil or gas fired locos which greatly increases the efficiency of the boiler. Turbulators are simply twisted strips of stainless steel inserted in the tubes. They reintroduce turbulence into the gas flow through the tubes and increase the heat transfer. I don't think they would be very practical in a coal fired loco as the tubes would probably get blocked with coal and ash fairly quickly but would be worth trying as an experiment.

So, my present thoughts on boiler design?

Make sure the grate area is large enough to produce the steam required by the cylinders (Ee) and try and fit enough tubes to match the grate area i.e. the free gas area through the tubes should be something like 12 to 15% of the grate area. The tube length is not really important within reason as in my opinion the Keiller ratio doesn't make much difference in models. Modern thinking is that only the first few inches of the tube contributes anything to steam production.

Getting enough tube area can be a big problem though. It can be done with a narrow firebox design boiler but it's very difficult with the wide firebox designs due to the huge grate area these produce. You may be lucky to get 10% of the grate area unless the barrel diameter is greatly increased (I've managed to get 11.4% for Red Devil). When Jim Ewins built the boiler for his Loadstar he made the front tubeplate of the firebox without flanges just so he could squeeze more tubes in.

For the wide firebox designs the low tube area is perhaps not such a problem. The grate area tends to be much higher than that actually needed and so the fire doesn't need to be worked hard to keep up steam production. In any case, you can adjust the draughting to increase the air flow through the fire if necessary but that will probably increase the back pressure in the cylinders as you will probably have to reduce the diameter of the blast nozzle.

Although not related to boiler design, make sure the valve gear works efficiently and allows the loco to be run at 50% cut off with good valve events. That will reduce the steam consumption and reduce the demand on the boiler. It's amazing how many drivers run their locos in full gear all the time wasting steam. It's perhaps not all their fault though as some valve gears are so badly designed that the locos will probably only run in full gear anyway!

< Previous Page