As well as the building of locos etc. I'm also very interested in the theory side as well so the following are some notes and ideas on the design of locomotives in our scales. Please note that some of this is based on my interpretation of other peoples ideas so may not be strictly correct!

There appears to have been very little progress in the design of the small gauge locomotives (as opposed to full size) since the days of LBSC who could perhaps be suitably called the pioneer of the passenger hauling live steam 'model' (sorry Curly! 'miniature'.). Most of LBSC's advances were made through trial and error and his refusal to follow what was being preached at the times by the likes of Henry Greenly etc. It was thought that a small scale coal fired locomotive capable of continuous passenger hauling was a pipe dream but LBSC proved them all wrong, getting involved in some pretty furious arguments with his 'rivals' along the way. It is a great pity that the practical LBSC and the theoretical Greenly did not get on (understatement?) as I am sure they could have done great things working together.

I think it is fair to say that nearly all later locomotives designs have merely carried on from where LBSC left off. Martin Evans was a great fan of LBSC (unfortunately the reverse was not the case apparently) and he was happy to follow in his footsteps designing a great many locomotives using the principles laid down by LBSC.

During one of my many scourings of the internet for information I discovered the late Jim Ewins and his writings and theories about designing model locomotives. Jim had also searched out previous reasearch carried out over the years and found some, such as that by C M Keiller into boiler tubes, but there was very little else regarding increasing the efficiency of small locomotives.

He therefore sat down and came up with a few theories of his own based on analysis of various loco designs past and present and their performance, or apparent lack of. The following notes are based on his work and I'm designing various spreadsheets to carry out the calculations involved. I'm not going to repeat how the formulae have been devised as this can be read in *Jim's original writings* but will just give the formulae and basically what they mean. I am not saying that his theories and formulae are 100% correct but they do seem to fit the bill pretty well and in my opinion can help to design a locomotive that should perform well. I don't think anyone's come up with anything better anyway!

(* the web pages which had these seem to have disappeared unfortunately)

The basic reasoning behind the theory is that cylinders of a certain size require a certain amount of steam to be produced by the boiler continuously. If the boiler cannot supply enough steam to satisfy the demand the boiler pressure will keep dropping and this will require frequent stops for a 'blow up' to build up pressure again. Conversely, if the boiler produces too much steam the result will be constant blowing off of the safety valves and wastage of water and coal. This assumes, of course, that the draughting is correct as this will also affect the boiler's steaming ability.

The amount of steam used by the cylinders depends on the bore and stroke (swept volume) and the diameter of the driving wheels. The ability of the boiler to produce steam can be shown to be dependent on the area of the grate which affects the amount of coal that can be burnt and hence the heat produced. In the ideal loco there is a certain ratio between the steam used and the grate area and Jim calls this the Engine Factor (Ee). The formula for this is given as:

           Ee = Swept volume of the cylinders per revolution

                    Grate Area x Driving Wheel Diameter

Jim suggests that this figure should lie between 0.12 and 0.25. Analysis of loco designs which can be considered successful gives an average figure for Ee of 0.15

Moving on to the boiler we can analyse the components that affect it's ability to produce steam. The major component is the grate as seen before but the steaming is also affected by the tubes. The tubes must allow suficient gas flow from the firebox to the smokebox so that the draught produced by the exhaust can draw enough air through the grate and ensure that the coal burns hot enough. The ability of the tubes to pass the gasses without undue resistance is dependent on the cross sectional area of the tubes and also the length of the tubes. Long thin tubes have much more resistance to gas flow than short wide tubes. The length and area of the tubes also affect the amount of heat that can be extracted from the gasses before they enter the smokebox.

Thus there is a direct relationship between the grate area and the tubes and this Jim calls the Boiler Factor (Eb)

The formula for this is:

                                    Eb = Grate Area in square inches x Tube Length in inches

                                                     Number of tubes x (tube diameter in inches)²

The average figure for Ee obtained from the analysis of the successful locomotives is 80

In the above formula superheater tubes are classed as ordinary fire tubes as it is assumed that the area of the tube less that of the element will be the same as an ordinary fire tube. For example if a boiler has 18 firetubes and 4 superheater tubes, use the figure of 22 in the formula.

To complicate matters further there is a recommended relationship between the inside diameter of the tubes and their length for optimum heat transfer. This was investigated by C M Keiller back in the 1930's and he devised a figure known as the Tube Factor (Kt)

Kt   =      Length of tube in inches

                          (inside diameter of tube in inches)²

Keiller suggested that Kt should lie between 65 and 70 but analysis of the successful locos again suggests a figure of 80 as being nearer the mark.

Finally Jim devised a figure to show the overall 'efficiency' of the loco. This is obtained by multiplying the Engine Factor (Ee) by the Boiler Factor (Eb). This he calls the Overall Factor (Eo)

Eo = Ee x Eb

Using the 'ideal' figures for Ee of 0.15 and Eb of 80 gives a figure for Eo of 12 although Jim suggests that this can lie between 10 and 14 if the other criteria cannot be met exactly. For example it may not be possible to get sufficient grate area to fit the formula, especially if a 'scale' model is being designed.

So, from the above we now have a set of 'factors' which, hopefully, can allow us to design a successful loco or see how one we are building should perform. These factors are:

                                                                                  Ee = 0.15

                                                                            Eb = 80

                                                                                   Eo = 12

                                                                                    Kt = 80

I've written an Excel spreadsheet to automatically calculate the above factors from the data such as cylinder bore, stroke, grate size etc. Using this you can put the data in for you own loco and see how it compares to the suggested ideal.

If you enter the data for a published design you will probably find that one or maybe all of the factors calculated are nowhere near the optimum values. I've entered the data for quite a few locos and some, especially the 2½" gauge ones, do not 'fit' at all! What does this mean?

Looking at Eo:

High values for Eo indicate that the steam usage is greater than the capability of the boiler to produce it and such locos may tend to run out of steam.

Low figures for Eo indicate that the boiler may produce more steam than necessary leading to constant blowing off.

Looking at Ee:

High values of Ee indicate that the grate area is too small for the cylinders and the boiler will be have to run with a very hot fire to produce enough steam resulting in clinker formation and burning of the grate. Such locos may run well for a time but will eventually loose steam as the grate becomes clogged.

Low values of Ee indicate that the grate is too big for the cylinders and the loco will have to be worked really hard to get sufficient draught through the fire to keep it hot enough.

Looking at Eb:

High values of Eb indicate that the boiler may be a bad steamer, probably due to incorrect tube sizes and/or length.

Low values for Eb indicate that the boiler may be a good steamer but this may be the result of too free a gas flow leading to other problems such as clinkering and fire lifting.

It is interesting to note that a few of the LBSC's 2½" gauge designs I have looked at so far have very low values for Ee e.g. 0.05 which suggests that the grate areas are much too big for the size of the cylinders. One of the locos is 'Fayette' with Ee of 0.06. However, Eb and Kt are quite close to the ideal of 80. My only experience of a Fayette is of the one built and run by Peter de Salis Johnston and that seems to perform very well. The boiler does seem to produce steam very easily and is always blowing off. That would tie in with the low value for Ee.

Annie Boddie, another LBSC design, uses the same cylinder sizes as Fayette but has a much smaller grate and boiler. This gives a figure for Ee of 0.154 - virtually spot on - but the other figures are miles out. Eb is only 38 instead of 80 which suggests to me that the number and size of the tubes are incorrect i.e. the total cross sectional area of the tubes is much too great. The one Annie Boddie I have seen running was very difficult to keep in steam.

Jim Ewins did say though that his research was based on 3½" and 5" gauge locos and the factors for these may not suit other sizes. Possibly 2½" gauge may need a different set of factors?

My own Helen Longish actually fits the figures quite well (more by luck than judgement!) Ee is 0.162, Eb is 59.5 (a bit low), Eo is 9.6 (again a bit low), and Kt is 78.6. When I designed the boiler I squeezed in another tube which seems was a mistake as this has lowered Eb too much. If the number of tubes is decreased to 8 instead of the present 10, the figures match virtually perfectly. I could block 2 of the tubes up I suppose!

Return to ME home pageNext Page