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Jos Koopmans (PhD), a regular contributor to the steam_tech Yahoo group, has just had his first book published.  Jos spent the last few years earning his doctorate in engineering and his thesis was on steam locomotive exhaust systems.  His background work for earning his PhD provided the foundation for this excellent book.

The book is presently available from Camden Miniature Steam Services ( ) in the UK.  The book is softbound and 484 pages long, with numerous illustrations, tables, graphs, and formulae. 

The following three reviews were done at Jos' request and were originally posted the steam_tech group at Yahoo.  The first by Geoff Lambert, another by Michael Guy, and finally, one by me.

Review is by Geoff Lambert of Australia

Jos Koopmans has received word from a publisher that his recent successful Ph.D. thesis on locomotive front ends is to be published as a commercially-available book. Congratulations Dr Koopmans!

As you may know, Jos asked a few of us to assess the thesis for this purpose. I did so and, in addition, proof-read the manuscript and made some technical suggestions on graphics, etc. Jos has asked that my review be posted to steam-tech, so here it is.

The Fire Burns Much Better
Review of the Ph.D. thesis of Jos. Koopmans
December 2005

This paper is a critical review of the successful Ph.D. thesis of Jos. Koopmans, written at Jos.’ request for the purpose of assessing saleability of the thesis as a commercial publication. This has not been any easy task nor a short one, partly because of my own mental ossification- I must accept responsibility if I have misrepresented what Jos. has written.

The thesis deals with the “Front End” of steam locomotives and is fundamentally in three parts:
1.         A historical analysis of attempts to understand the front end (chapters 2-5, arranged by time period)
2.         Experiments with a real locomotive in the field (chapter 8)
3.         A proposed theoretical analytic method for designing front ends, with examples from recently modified and proposed locomotives (chapters 6 &7).

In addition there is an introduction (Chapter 1) and a summary and set of recommendations for loco. engineers (Chapter 9). The thesis, which is some 140 A4 pages in length, is accompanied by an extraordinarily comprehensive 34-chapter Appendix more than twice the length of the thesis itself which reviews in great detail the experiences of locomotive front end researchers over the last 200 years; the later chapters of the Appendix are linked to the theory chapters on the main thesis. The Appendix is more than this though: it contains much comment, many annotations, explanatory mathematics and other additional material that explain or expand what was written in the original publications of the last 150 years.

While reviewing this thesis on a recent long trans-Pacific flight, my seat companion (who turned out to be an academic who was on the governing board of a university which has a strong interest in historical aspects of engineering) leaned across and asked “Is such a thesis of any use to anybody in the real world these days?” I answered generally in the following terms: As I see it, the viability of such a book in the commercial publishing field will depend upon the attractiveness of part 3 to putative locomotive designers and operators in the heritage and
recreational railway sphere. There will be a small population of people (such as myself) who value it as much for its historical and mathematical analyses, especially in the Appendices. For us it is a wonderful eye-opener that codifies a confusing field and we value it more than any publication in the field for these reasons. To me, receiving the thesis was like
receiving a notification that I had won a lottery. But 90% of the potential market will come from those who would want to use it as a cookbook to build better locomotives. Chapter 7 of the thesis contains much cookbook material directed at exactly this market. This is most useful, although the recipes cover much more than the front-end.

The historical analyses and the corresponding Appendix chapters are an amazing tour de force in which Dr Koopmans has trawled the most obscure and difficult of references to assemble a superlative review of the evolving state of knowledge of the operation of the locomotive front end. As one who has spent much time in a similar, but often fruitless quest, I can express only the deepest admiration for what Jos. has achieved with this. To my mind, this is the greatest strength of the thesis and Jos. himself states in the Foreword that the thesis is primarily a literature review.

The laboratory experiment chapter is also a wonderful piece of work which shows what could have been done with such tests years ago if only modern technology and been available. It makes several advances on the preliminary work done along these lines by David Wardale and recounted in “The Red Devil.”

The theoretical chapters are a little more problematical though because it is not quite clear which of the many theories earlier described are “correct”. This arises I am sure, because the locomotive front end is one of the most complicated of all gas dynamic problems to face engineers and one which has led many engineers and theoreticians into fruitless dead-ends
because they did not fully understand the principles involved. These are still not understood- a recent text book on Fluid Mechanics [White] describes the “diffuser” (the tapered outlet portion of a loco chimney is one) as a combination of art, luck and a vast amount of empiricism. Whole fields of mathematics, especially dimensional analysis and the Buckingham
Pi Theorem were invented largely for making the analysis of fluid flow easier.

The Buckingham Pi theorem and Dimensional Analysis are, in the words of one fluids engineer “fun”- but the same engineer also cautions that they are deeper than they look and take some mastering. Fundamentally, the Pi theorem allows one to take an equation with N parameters and K dimensions and reduce it to a function containing N-K dimensionless numbers, by recasting all dimensionally identical parameters in terms of ratios of one to another. These ratios are known as Dimensionless Groups. The Reynolds Number is perhaps the most famous of them. The method does not allow one to determine the values of the unknown constants in any such sets of  equations, but it does enable one to reduce the number of expensive experiments needed to determine them empirically.

The Handbook of Chemistry and Physics lists 307 Dimensionless Groups, nearly all of them connected with engineering and most of those with heat transfer and fluid mechanics. This is a dismayingly large number. Why so many? Is it just because the science is intrinsically hard or are engineers taking the easy way out? In the thesis, Jos Koopmans comes to the
conclusion that the Euler number is a good criterion for front-end effectiveness because it may measure, in some way, the ability of a front end to create a vacuum. I am not so sure I agree with this- the Euler number is a Dimensionless Group which is primarily concerned with fluid friction in conduits (loco chimneys) and Jos himself has clearly demonstrated that the majority of entrainment does not occur in the chimney.

In the locomotive front end, one can perhaps discern the following parameters and properties- some vital, some optional

1. Steam properties
2. Nozzle geometry
3. Nozzle­chimney geometrical relationships
4. Chimney entry
5. Chimney length
6. Chimney diameter
7. Chimney choke
8. Chimney diffuser
9. Smoke properties
10.Smokebox partial vacuum
11. Steam flow rate
12. Gas flow rate

This is also a dismayingly large number. Some of these, particularly 3, are many properties masquerading under the one class- nozzle-choke diameters; nozzle-choke separation, expressed as ratios between one another in various ways. In the world of the locomotive front end, only the work of Wood comes close to producing a big enough data set for such analysis- and even he has left out some vital elements. Although Jos Koopmans does not rigorously develop the Pi theorem, he evokes its ideas and focuses upon those represented by the properties under 3 (above) and presents some intriguing data in completely new way in an attempt to draw out which of the geometric relationships are most important. Unfortunately, the locomotive world does not yet contain a big enough data set, nor a compatible one that allows such an analysis to reach any valid conclusions. A pity.

Even the text book writers become easily confused- a recent textbook on “Turbulent Jets” (important for understanding the entrainment of smoke-box gases by exhaust steam) makes an embarrassingly large number of typographical and conceptual faux pas. Entire web sites (<>http://www.informa\
) are devoted to the misinterpretation of fluid dynamics by professors of engineering. How are we to understand the difference between pressure and momentum if Professors of Engineering seemingly cannot?

It is altogether possible that, at this late stage, no resolution of the issues involved in the locomotive front end will ever be made they may not even be theoretically possible. Certainly one could say that analytical methods for complicated systems such as the Le Maitre, with its diffusers within diffusers within diffusers, represent a completely hopeless prospect. This is very dispiriting since (probably) the “best” front ends will encompass complicated features like this. Jos., for instance, is strongly of the view that multiple nozzles or chimneys offer a better
prospect that single ones. It was generally held that the efficiency of the front end was improved by increasing the area of the steam jet- often by “cookie cutters” or spreaders which had the contrary effect of needing more power to operate them. Some people (e.g. Kordina) even wanted to put a swirl on the jet. Analysing jets with complicated shapes and swirling
motions is demonstrably much more difficult than for circular steady jets. The research that has been done on them does not lead one to believe that they will soon provide definitive guidelines.

The title of Dr Koopman’s thesis The Fire Burns Much Better comes from a statement by Richard Trevithik in 1804 and describes the improvement in “steaming” of a locomotive resulting from the turning of the exhaust steam stream from the cylinders into the chimney of his locomotive (to silence it!) which had the effect of vastly increasing the air flow through the
fire (colloquially by “sucking” air through it) and hence led to much higher rates of steam raising. Without this effect locomotives would never have become practical. An amazingly serendipitous consequence of this finding was that the rate of burning achieved by it was very directly related to the amount of steam being used and passing through the exhaust.
Thus the locomotive front end became a prime example of a “self-regulating system”, where the demand directly controlled its own supply. The demand-supply relationship was so nearly linear over the range of operation of most locomotive front ends that a well designed front end would be well designed for nearly all rates of steaming. This attribute, through one of those accidents of history, came to be associated with the Stephensons and he whole relationship between steam use and supply became known as the Stephenson Cycle. But the process requires energy and this energy can only come from the same steam which is needed also to supply energy for moving the train. Thus the “problem” of the front end is to supply the right amount of air to the fire at all steam-use rates, with the minimal amount of energy drain from the steam production otherwise meant to propel the locomotive.

In the draft of my own unpublished book on locomotive thermodynamics, I have referred to the locomotive front end as a “citadel of mystery”, and it remains mysterious to us all even today. Many of the misconceptions about how it worked, such as the “plunger theory” whereby the puffs of steam pushed the smoke up the chimney, are with us still in the 21st century.
Most people settled for the idea that entrainment of smoke gases was by “friction”, “molecular collision” and closely related phenomena, but a person working outside the locomotive field might well assert that entrainment was due to vortices enfolding the surrounding fluid and they could produce pictures to prove it. Even someone noticing the entrainment
of air by a garden hose would be in a position to reject some of these old misconceptions.

It is fair to say that the principles involved in the front end have been extensively explored without definitive resolution. One of the reasons for this lack of resolution is that much of the exploration took place in isolation from other parallel fields of physics and engineering- fields in which many of the still unanswered questions about the locomotive were discovered in other contexts a century ago. Unfortunately the work outside the locomotive field was often on conditions and geometries vastly different from that found in the locomotive field. As fluid mechanics is not always scale invariant (some are), one could not necessarily extrapolate these numbers and perhaps not even the principles to the locomotive.

It is also true that much of the research done by researchers who focussed on the locomotive front end sank without trace, only to be redeveloped by others decades or even a century later. Much of what was done was also too often a repeat of the same ideas cloaked in different language or in different mathematical formulas whose underlying equivalence was not
obvious to those who created them. Many researchers also made outright mistakes in logic and physics which misled them and many who came after them. The steam locomotive field seems worse than most in these attributes. In its ten years of operation, the Yahoo Internet discussion group steam-tech (whose members hopelessly yearn for a world-wide return to the
use of railway steam locomotive traction) seems to have been unable to resolve a single technical issue on steam locomotive operation. Nor has it been able to acknowledge the truth of the statements made by the likes of Jos. Koopmans when they pointed out where their misconceptions lay.

The so-called “Lempor Theory” is a prime example of this- it is neither about the Lempor front end, nor is it correct. One of the reasons it is wrong is that the version used by everybody today was incorrectly transcribed by me from Porta’s own typescript in the 1990s- nobody has noticed the errors in the mathematical formulas which I introduced. Another reason Porta’s Lempor Theory is wrong is that it attempts to add vector quantities (momentum) arithmetically as though they were scalar quantities.  Nor are prophets appreciated at home- those who draw attention to these defects attract responses (even in steam-tech) characterised by “who cares?” or “so what?” and thus the defects are dismissed. This is a big worry. Jos. Koopmans has done the field a great service by pointing out the lack of communication and by demonstrating mathematically the errors and the duplications of much of the effort by locomotive engineers. Ideally, we should all in turn check Jos.’ mathematics, but it is impossible for the casual reader to do so without spending as much work on it as Jos. has done.

It is known that any measure of the performance of a front end depends upon a number of physical properties of the steam and gases and a number of the geometric attributes of the front end itself. One may express this performance measure as the left hand side of a generalized mathematical equation, the right hand side of which forms a multidimensional “field” or
“manifold”. In searching for a good front end, one searches the terrain of this field for extremal values of the performance measure, which represent “good” results. To my mind, defining this terrain is what front-end research should be about. However, it is probably true to say that there remain no unexplored magic nooks or crannies in this terrain which will yield vastly “improved” front ends (even if we could agree what “improvement” meant and even if we could agree which performance measure to use).

But that is not to say that such a search is entirely worthless. Really bad front ends were not uncommon and they arose because engineers failed to grasp the principles involved they were not familiar with the terrain. Good knowledge of front end theory would have avoided these catastrophes of the past and it can still lead to significant improvements in heritage
locomotives and it can lay down guidelines as to how to design a good front end from scratch for new locomotive projects. That advantage avoiding the errors of the past ­is something worth having and something Jos. Koopman’s thesis can provide.

Typical of the confusion in the front end research field is the general lack of acknowledgement of the role played by turbulent and compressible flow of the steam jet emerging from the nozzle. Jos. has been able to show again by going outside the locomotive research field that at least two-thirds of the action of a front end is totally independent of the geometry of the front end- i.e. that it is entrainment by the free steam jet that matters most. One can say that a locomotive without any chimney at all would still function tolerably well one really has to make a major mistake in other aspects of draughting to create a truly awful front end.

One of the early researchers, Zeuner in 1863, wavered between the ideas that the aim of the front end designer should be to produce the required entrainment of smoke gases or, alternatively that it should be to generate a desired vacuum in the smoke box and let the consequent “sucking” action deal with moving the air. It is arguable that the former would have been the better choice but eventually Zeuner chose the latter and all who followed him agreed. This lead to the situation where all of the luminaries of the front end world measured the “fitness” of the front end by plotting the smoke box vacuum against the exhaust steam flow rate or against the exhaust steam pressure. The steeper this line was the better the front end
supposedly was because the steepness supposedly measured both the “sucking” action of the front end, and the efficiency of it. This, however, is only a good measure when comparing different front ends of the same locomotive- it is useless as a means of comparing two different locomotives. A bigger vacuum is not always necessary, or even desirable. On the other hand a linear entrainment relationship will not be wanted at high rates of steaming either- one will want more than this because of the increasing proportion of unburned fuel.

Often front end theorists were forced to introduce arbitrary constants (Finagle Factors the cynics call them- Porta used several) to bring theory into line with observation. Then too, the mathematical formulas advanced by some to describe or predict the behaviour of a front end could not have conceivably been correct, because the two sides of their equations were
dimensionally incompatible. For a long time, front-end theory has made use of terms like “shock loss”­terms which seems exclusive to it and which are both unexplained and incompatible with modern fluid dynamics theories out in the wider world. People who work in the front-end field, and who were brought up on such terms, find it difficult to let go of them- Wardale cannot for instance. The field was full of misapprehensions and intransigence like this.

What one hopes of a good locomotive front end cookbook, I think, is a suite of recipes that allows the designer to tailor the geometry of the front end so as to produce that happy coincidence between steam demand and steam generation over the whole range of operation when given some information about the quantities and qualities of steam and fuel involved. One should be able to plug in the quantitative and qualitative information about the steam and get out at the other end a set of specification for how big the nozzle should be, how wide the chimney should be, how much taper the chimney should have, etc. One needs also, I think a fair assessment of the limitations of the recipes presented- e.g.  this recipe is no good if you intend to burn high ash coal or to push the locomotive past its grate limit.”

One might have thought that the 200 years of front-end research described by Jos. Koopmans was research directed towards exactly such a set of recipes. It wasn’t always­not least because the uncovering of the recipes proved so devilishly difficult. Many researchers were able to come up with a number of rules of thumb (such as (“diverging chimneys are better”) and some even felt that they could recommend some exact proportions (such as “the diameter of the chimney choke should be 2.9 times the diameter of the exhaust nozzle”). The trouble was that different people could often make different recommendations about the same thing, thus throwing into doubt both sets of recommendations. The prospective engineer was usually in no position to resolve such contradictions because resolution required greater mathematical aptitude than they thought it worth acquiring, and because the recipes might well be full of hidden assumptions or even outright mistakes anyway.

E.S.Cox, in one of his many books on steam locomotive design and operation bemoaned the fact that the recipes that emerged in the latter years of research (especially from British Railways) came too late to save the steam locomotive from its fate but that, even had they come earlier, would still not have saved it. This is the dilemma referred to by my seat companion on the plane- is any of this worth doing? Sadly, with the possible exception of heritage railways, the answer is “no”. Even in the heritage railway field, the potential is strictly limited because the desire of most heritage operators is to perpetuate the past in both appearance and reality, rather than to make improvements which have no historical precedent. Even David Wardale, a proponent of modern methods, was not interested in locomotives that didn’t “look like a duck, quack like a duck and behave like a duck”- i.e. that weren’t traditional Stephenson locomotives. In his dying days Porta made a number of suggestions about improvements that could have been made to the proposed A1 replica locomotive in Great Britain, but these were rejected outright by those who had the money to make them happen, because Porta’s ideas were seen as incompatible with the re-creationism.

I think the thesis should contain more­ and more detailed­recipes, perhaps explicitly favouring the best-developed theory. Jos. has in fact plumped for a particular theory to explain the operation of the front end. This is the so-called “Saunders Idealised Theory”, which unfortunately is based on “unpublished technical notes”.  Jos. uses this theory to demonstrate certain attributes of exhaust systems and certain “truths” about them- for instance, that a straight chimney is inferior to a flared (tapered) one. I have spent some weeks of time struggling with the concepts which crystallize in this, by far the most important chapter of the thesis. I have reluctantly come to the conclusion that my mathematical and conceptual skills are not up to the task of resolving whether the Saunders Theory or Jos.’ thesis has reached the ideal we all seek.

The bottom line is, therefore, will this thesis find a market and can it contribute to the way in which modern locomotive engineers should do their work? The answer to this is a definite “maybe”. Judged on the basis of its appeal to prospective designers, the book will be most useful if Chapters 6 and 7 are slightly altered to:-
l          explain in more detail the scope of the problem,
l          delineate and analyse the separate components of the exhaust system,
l          explain how to determine the optimal proportions for a design

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Review is by Michael guy of Toronto, Canada

In early December last year, Jos Koopmans was kind enough to send me a  copy of his thesis for review with a request for corrections and instructions to forward any comments to Steam-Tech. A few typo corrections were duly sent to Jos, I then forwarded a copy of the thesis to my partner in steam loco draughting matters, Richard Stuart of Perth, Australia. Our combined comments on Jos work follow.

Best regards,
Michael Guy
Michael's Locomotive Pages: updated November 23rd 2005


The steam locomotive emerged two centuries ago, when science was still in its infancy. The empirical engineers and artisans of the day developed it into a machine that powered the industrial revolution and changed the world. Nowadays, it is considered obsolete and relegated to museums and tourist railways. It is ironic, then, that this supposedly primitive device turns out to be one of the most analytically complex mechanisms developed by man. As Jos Koopmans’ unique work shows, even the formidable scientific knowledge and analytical tools of the 21st Century cannot yet resolve the complex and mutually interactive processes that power the steam locomotive.

Historical reviews of steam locomotive development are not new, but Dr Koopmans has been unusually meticulous in uncovering obscure references dating back to Victorian times. In a very readable style, he chronicles the historic, frequently flawed experimental work, its contradictory results and interpretations and shows how this influenced locomotive design of the day, for better or, sadly, sometimes for worse. This interesting, one could even say absorbing narrative is merged seamlessly into the mathematics of the subject such that one is barely aware of a transition from history to analytical theory.

The great contribution of Dr Koopmans is in breaking out of the "bubble" surrounding steam locomotive technology and applying the fundamental physical principles of fluid mechanics to the locomotive draughting system. Much of the research that Dr Koopmans cites was not available during the heyday of the steam locomotive, neither were the experimental and analytical techniques that are taken for granted today.

Where Dr Koopmans has succeeded is in "de-mystifying" the technology of steam locomotive draughting and treating it as a fluid mechanics device, subject to the basic laws of physics. This is a refreshing insight, which counters the folklore and old wives tales that have frequently masqueraded as steam locomotive design wisdom.

If there is a criticism, it is in his perceived dismissive approach towards the work of modern day practitioners of steam locomotive development such as the late L. D. Porta. Koopmans points, for example, to flaws in Porta's "Lempor" exhaust theory. The flaws may be real, but so also are the performance improvements achieved by users of the "Lempor" system, including David Wardale, engineer of the improved SAR 25NC class, "Red Devil". There are opportunities for Koopmans himself, or others, to bridge the gap between the practical experience of Porta and his "disciples" and the fundamental principles of fluid mechanics that he has highlighted.

One can ask the question "who cares about the technology of the steam locomotive?" Appropriate analogs would perhaps be horses and sailing craft. They are also obsolete methods of transport, yet millions of dollars are spent on them every year simply because people find them fundamentally worthwhile. It is true that for aeons academics have pursued their interests and specialities without regard for “practical” application of their researches and Dr. Koopmans need make no apology for a thesis tackling a subject left incomplete by others. Indeed, there may well be a future need for this technology and the globe is merely in a quiet period for steam traction. If so, "The Fire Burns Much Better" will be a timely addition to the technical literature.

In the present day there are a good many operators of steam traction engaged in experimenting with and having success with L.D. Porta’s Lempor exhaust theory. One could therefore, wish for an additional appendix to Dr. Koopmans’ thesis wherein he completes the loop between his Euler- number based theory and practical application of that theory. In suggesting this, we do so from the perspective of having ourselves attempted to make L. D. Porta’s Lempor theory accessible to the non-academic person with minimal mathematical skills and having first-hand knowledge of the difficulties involved in so doing. To compare Porta’s results with Koopmans theory by practical application of Dr. Koopmans own instructions would be to follow in the footprints and with the spirit, of scientific researchers proving or disproving theories by use of the scientific method. The history and the future of steam locomotive technology deserve no less.

Our congratulations go to Dr. Koopmans for a first class effort. "The Fire Burns Much Better" belongs on the bookshelf of every student of steam locomotive technology right alongside the works of Chapelon, Porta and Wardale.

Richard Stuart & Michael Guy
"The Lempor Calculator Team"
February 2006.

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Review by Hugh Odom, Summerville, SC, USA:

I was also given the pleasurable task of reviewing Jos Koopmans' (I should say Dr. Jos Koopmans') doctorial thesis, "The Fire Burns Much Better".  The amount of information in this work makes the composition of a concise review a daunting task, which should give you some idea of the scope of the thesis.

"The Fire" undoubtedly provides the most comprehensive account ever written of the history of steam locomotive front end design, from the earliest days to the present.  As with many significant inventions, there is some confusion about who exactly first came up with the idea of directing the steam exhaust from the cylinders up the chimney, contrary to what most steam history texts would lead us to believe. Jos thoroughly documents the many purely empirical experiments of the early days of steam development.  There are several cases that make you wonder "what were they thinking?", but eventually workable front ends were developed and installed in workable steam locomotives which made the successful steam locomotive designs of the next ~150 years possible.

Concurrent with the purely empirical efforts, Jos documents the attempts by designers to come up with a workable scientific theory to explain the performance of locomotive front ends and to allow their optimal design.  As might be imagined, there were many erroneous attempts to accomplish this, mainly because the complexity of the problem was beyond the engineering knowledge and/or calculation capabilities of the time.  Even later designers including Giesl and Porta included fundamental errors in their attempts to explain front
end operation.

Dr. Koopmans goes on to document the study of the action of jets (fundamental to the operation of steam locomotive exhausts) which occurred in other fields, chiefly in the area of jet aircraft and rocket design.  Unfortunately, the advances in the fields that could have lead to a true scientific understanding of front end performance were happening just as steam locomotive development was being terminated around the world.

Finally, Dr. Koopmans lays out his own theory of front end operation, beginning with the latest thinking on the action of jets and design of ejector devices.  The fundamentals of steam locomotive operation, including combustion, steam production, superheating, and steam expansion as they relate to the design of an optimal front-end are discussed.  This theory is checked against known locomotive exhaust performance data and shown to be accurate.  Additionally, theoretical designs are included for three steam locomotives.

One interesting point in Jos' historical analysis is that contrary to what would seem logical, the performance of locomotive exhausts did not show a constant, gradual improvement over time.  Some of this apparent lack of progress can be attributed to the ever-increasing size of steam locomotives, which unfortunately left less and less room for the exhaust systems, which compromised their design and performance. However, if a better understanding of exhaust system operation had been developed, it may have been possible to counteract
this influence.

"The Fire Burns Much Better" will be of great interest to those interested in the history of technology in general, the history of steam locomotive development, and hopefully those who are interested in future steam locomotive development.

Hugh Odom
The Ultimate Steam Page

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