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White Witch, Concept Layout by PaxAeternum White Witch, Concept Layout by PaxAeternum
Doing an animation project with a locomotive in it.  Naturally the locomotive is taking up more time than the entire rest of the assignment because I decided to draft design her from the ground up.  This is three-cylinder simplex "White Witch", a 7 foot gauge 4-8-0 loosely inspired by the churchward shape and the Stanier simplex-three propulsion, but with basically no loading gauge.   This locomotive stands 18 feet tall at the top of her stack, has ten foot driving wheels and has a common cylinder bore of 42".  Valves are deismodromic poppet type driven by an oscillating cam setup, actuated by three seperate internal Bakers valvegear.
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:icondinodanthetrainman:
dinodanthetrainman Featured By Owner Mar 9, 2014  Hobbyist Digital Artist
"I decided to draft design her from the ground up" That is the only way to do it! :)
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:iconbartpaaddiator:
bartpaaddiator Featured By Owner Feb 20, 2014
I wonder what the project itself is and what is the role of this locomotive in it, if that info can be disclosed. I am happy that you are able to incorporate those things into assignments.

Now about that engine, I see most questions that could have been asked, had been asked, however I wonder about that short, open cab. It looks, maybe due to the large size of the rest of the engine, uncomfortably small. Is there going to be an Indian style half-cab on the tender or something of the sort?
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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 20, 2014  Professional General Artist
You shall see, sir.  


She will indeed have a half-cab, yes, but I always saw her as rather spartan.  Uncomfortable it may be, but exhilerating and invigorating there is no denying.   The cab is larger than you'd think, with the engine being 7 foot gauge.  
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:iconatticus-w:
Atticus-W Featured By Owner Feb 19, 2014
This reminds me of that conceptual Great Western 4-8-0, although, of course, with deranged dimensions. X3 She does have nice clean lines.

Definitely liking the French-esque cylinders and valve design.  That always struck me as a paradoxically elegant look, given all  of the complicated outside machinary that it entails.  (But then, French locomotive design comes across that way in general, doesn't it. XD)
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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 20, 2014  Professional General Artist
Yessssss that is SORT of what I was aiming for.  THe king and castles would have looked excellent as 4-8-0's.   I of course love deranged dimensions.  XD



You and I both know that french stuff is marvelous.
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:iconsteamrailwaycompany:
SteamRailwayCompany Featured By Owner Feb 19, 2014  Hobbyist Writer
With no loading game to challenge designers nor constrain designs, do steam locos have more potential ability necessarily? 
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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 19, 2014  Professional General Artist
THe answer to that question is undoubtedly yes.................... British locomotives suffered incredibly from their own loading gauges.  The fact that the largest cylinder bores in england permitted by these designs were about 22" bore is a testament to that.

The question is almost absurd, I don't understand it....
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:iconsteamrailwaycompany:
SteamRailwayCompany Featured By Owner Feb 19, 2014  Hobbyist Writer
Personally, I somewhat like the different loading gauges as they posed a challenge for designers to make the most of their locomotives, and made a diversity of sizes of locomotives even amongst identical track gauges. But a steam railway without a loading gauge altogether would be interesting to see. 

Well, excuse me. 
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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 19, 2014  Professional General Artist
Loading gauge, whereas in some cases it is positively required, is a telltale of backward thinking.   Whereas I am not usually a fan of American practices, there was one thing we did incredibly well in this country, and that was make things bigger when they needed to be.  Here, the loading gauges grew as the locomotives got bigger, whereas in Britain they stayed the same, and even got smaller.  

It is not to say however that the loading gauge did not result in creative thinking, hence why british locomotives tend to be more elegant than our monsters, however the laws of physics dictate that constrained to certain limits there are things one cannot do.  This is why things more powerful than a King class never happened in England.  Boiler diameter and hence firebox size, wheel diameter, and cylinder diameter were all constrained to almost nonsensically small dimensions.  


Even if no loading gauge were instituted, there would be a natural one that designers would not tend to exceed, when the locomotive began getting ungainly tall and wide in relation to the track gauge as to become topheavy and unstable.  However not even in America did we reach this point.
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:iconlocomaster:
locomaster Featured By Owner Feb 20, 2014  Hobbyist General Artist
What about The LMS Princesses? and the BR standard 9F's? Sure they don't compare with the Big Boys or Challengers but they were definitely more powerful than the Kings...
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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 20, 2014  Professional General Artist
This is true, and forgive me if I had forgotten the engines, it just seems to me that the Kings were far more elegantly built than the 9F's and such;  Beit especially that the kings were not compounds and functioned like two-cylinder simplex engines, but had four cylinders to multiply the cylinder area because the loading gauge could not permit the locomotive to be built with two massive cylinders and still incorporate structurally integral frames, etc.  Also the four cylinder 180-degree-per-side opposed crank idea counterbalanced the engine far better (even if the drive was shared between two axles.)

Honestly, nothing compares to a big boy or challenger, and I say this in the opposite way.  Almost any british, central european, African or Asian steam locomotive is far more elegant and built with far more thought than those inadequately designed, over-engineered corporate money-printing war-neccesetated monsters.   The reason the big boy spewed such clouds of black smoke was because, to withstand 300 PSI steam, the firebox sheets were so thick that they inhibited heat transfer and forced the fireman to over-fire.  If the firebox had been shaped, stayed and thermic-syphoned with a more educated mindset, as well as been made of copper, the black clouds of overfiring smoke so common in america would have vanished.   

I equate the Princess and 9F to fine clocks, compared to a big boy or challenger to which I see a bucket of bolts.
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:iconlocomaster:
locomaster Featured By Owner Feb 21, 2014  Hobbyist General Artist
There is a rugged beauty to them... But I, like you, have a different taste in locomotive designs ^_^
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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 21, 2014  Professional General Artist
To me, the locomotives we built without the drive for war had rugged beauty, such as our 1920's Baldwin locomotives, or the marvelously experimental things the ATSF built in the 30's.   The locomotives from UP, the biggest corporate mindset railroad in america, to sustain the war effort, to me are condemned by their very nature, if not their lacking design.


Yes, you and I seem to have a very specific yet broad taste in engines
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:iconlocomaster:
locomaster Featured By Owner Feb 19, 2014  Hobbyist General Artist
I see Great Western, Austrian/German and American influence...And it sounds classy when call rotary cam valve gear "Caprotti" valve gear :D
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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 19, 2014  Professional General Artist
Yes sir, mostly Churchward and Chapelon on this one.  I considered giving her a double kylchap exhaust.....

She does not have rotary cam valvegear so it could never be Capriotti.  This engine has oscillating cams driven by the usual reciprocating gear.
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:iconlocomaster:
locomaster Featured By Owner Feb 20, 2014  Hobbyist General Artist

I have display models of locomotive from both designers... but for me Gresleys designs seem the most elegant...but the Kings come in very close second and they were a slight evolution of Churchwards Star class


Ah another fopa on my part ^^;



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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 20, 2014  Professional General Artist
Gresley's engines looked good on paper but fared many problems, they were entirely too delicate.  The conjugated valvegear linkages were known to "whip" at speed.
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:iconlocomaster:
locomaster Featured By Owner Feb 20, 2014  Hobbyist General Artist
I said they looked good... I didn't say they were the most reliable or efficient ^_^ In my view the Walschaerts is the one of if not the most reliable and efficient valve gears... I could be wrong.
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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 20, 2014  Professional General Artist
To me that would be the Bakers valvegear, as unlike the walschaerts it contains no sliding parts.  It is the most elegant of them.

The most efficient valvegear award probably goes to the Franklin AB or D type oscilating poppetvalve gear however.  


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:iconlocomaster:
locomaster Featured By Owner Feb 20, 2014  Hobbyist General Artist

Haha... I was expecting that... the Baker was a slight modification of the Walschaerts and its an American innovation so I'd think you take some pride in that ^_^, Strictly speaking its not a valve gear but a variable expansion mechanism adapted to the Walschaerts layout ...


It too had its problems...

"the main criticism being the number of pin joints and possible lost motion. Western United States and British railroads tended to continue with the Walschaerts pattern. In Britain Baker gear was popular amongst model engineers but in full-size practice the length of the yoke and the width of the assembly may have been difficult to accommodate within the restricted loading gauge."


There must be a reason Walschaerts valve gear was used extensively on many gauges from 1910 onwards. it was simple to understand and build, easy to maintain and got the job done...


I'd have to take your word for it ^_^


Though wouldn't Reidinger Poppet valve gear or a refined Conjugated valve gear prove more efficient?


  



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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 20, 2014  Professional General Artist
I actually take no pride in it being an american invention, as I said I really do not see national boundaries.  

It does indeed require a bit more space, but I see no more possibility for lost motion in a bakers than with a worn walschaerts, where the die-block in the link has worn especially it will slam and lose quite a bit of motion, also in the inferior way of build when the radius rod lifting armature is on the vertical plane in front of the expansion link, the die block will be sliding in the link even as the gear is held in one position.  

To me the Walschaerts was used because it was simply the most widely understood gear.  The loading gauge comment you made also seems to make a lot of sense.


Poppetvalves have the distinct ability of independantly controlling inlet and exhaust steam, as the valves are not constrained to eachother like they are in a pistonvalve.   I know Reidinger gear as "Lentz", and the advantage with oscillating cams to me is they can be driven by the more commonly known types of valvegear, and can be cut off this way.  ROtary cams require scroll gears and tend to have segmented cutoff limitations rather than an infinitely variable range, unless it is that variant (that I forget the name of) where there are tappet assemblies with two rollers and a cam that varies position versus another cam along a coaxial scroll gear
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(1 Reply)
:iconlocomaster:
locomaster Featured By Owner Feb 20, 2014  Hobbyist General Artist
Interestingly, the troubles with the Franklin oscillating cam poppet valve gear did prompt the PRR to experiment with 2 other, more conventional valve gears namely Caprotti valve gear and Walschaerts
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:iconlocomaster:
locomaster Featured By Owner Feb 19, 2014  Hobbyist General Artist
Whoops just saw the description hehehe... Churchward designed many fine Great Western engines :D
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:iconccmarc:
CCMarc Featured By Owner Feb 19, 2014

I'm interested. The Bavarian smokebox door is a nice touch, as alwasys.

 

What would you say her top speed is?

 

Also, is she mechanically fired?

 

The firebox design is very clever in itself, as well. Manages to work well with what space it has.

 

Will she be painted white, as the name implies? I love your white engines.

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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 19, 2014  Professional General Artist
The smokebox door is not quite as canted a bavarian one, it is more French inspired.  The top speed is undoubtedly in the low 140's, due to size, size of the firebox and square feet of evaporation surfaces, the enormous superheater, pump economisers, driver diameter and cylinder size, this is probably one of the fatest engines I have created.   Because of the wheel arrangement, the engine has an unprecidented adhesion factor, too.  The best engines for adhesion besides the 0-X-0's are of course 2-X-0's and 4-X-0's, where the weight of the firebox (heaviest part of the boiler) is over powered wheels.  

Mechanically fired of course because of the firebox size however the crew prefers to hand-fire unless the demands on the engine reach a certain point.  This engine is a long range sprinter. 
''

Yes she is white
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:iconccmarc:
CCMarc Featured By Owner Feb 20, 2014

I should've known it wasn't conical enough! :)

This is really shaping up to be a mechanical marvel of an engine. I can't wait to see her finished, especially in white.

Will she feature stripes? If so, what color?

I recently saw a great documentary on the last days of the Big Boy engines, called "Last of the Steam Giants". I'm certain you've seen it before.

Anyway, it was the first time I'd seen footage of a stoker screw in motion. It was terrific fun to watch for myself how one worked.

Mechanical stokers are most important on broad gauge lines, unless you either have three firemen or a single blue-blooded giant who can throw coal at least three and a half meters ahead of their shovel's end!

You'd think they're always used on my "International Gauge" engines, which I may reduce from 102" to 92.5". This isn't the case. The very smallest of engines on this gauge, (think LBSCR Terriers and smaller) are often handfired.

The very largest of engines often utilize BOTH a screw and a supplementary man. This man, called a "tertiary fireman", throws coke into the corners the screw may not reach.

You may think tertiary firemen have it easy, but believe you me, they must be prepared in the event of a screw failure!

Mechanical stokers don't typically exist on any engine less than 5 foot in gauge, unless they climb mountains or any other particularly demanding line of course.

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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 20, 2014  Professional General Artist
Unfortunately you must understand that the manual limit for throwing the coal with the best energy content that two humans can sustain through two seperate firedoors in a boiler only equals an even power delivery from the coal of about 1500 horsepower, with sustained bursts of higher horsepower only possible for short distances.

As you may or may not know, in the year 1940, almost every locomotive in this country larger than a consolidation on standard gauge tracks had, and needed, an automatic stoker.
It is impossible to keep a Lima Berkshire adequately fired by hand even with two firemen, and this is on a medium weight excursion train with reduced speed and power demands, as the crew of 1225 found when their stoker stripped a gear.  

To keep one of your 102" gauge engines adquately fired without its stoker would be impossible simply for the fact that if eight fireman all occupied the space of the same firedoor or pair of them, they would end up smashing into eachother.  Furthermore, having the firedoors open for that long would shock and warp the boiler sheets with cold air.


Even the comparatively small 4-8-2's running on 3 foot 6 inch gauge in Africa needed automatic stokers.  To give you a practical idea on the capability of the best human fireman; hand-firing a 15E or 15F class 4-8-2 on the SAR was deemed the most effort any fireman could humanely exert without serious injury or without simply dropping the coal or failing to perform his task.  This is a narrow gauge locomotive.  


What would happen if the stoker failed on one of those immense engines would be, unless a siding could be found instantly, even with the dampers shut and the man stoking full on, the incredible firegrate area would simply burn off all its coal in its extremities, and while the fire where the fireman could stoke would keep going, the cold air rushing in where the fire had spent itself would quickly destroy the firebox.


Realistically, to fire a locomotive as large as 102" gauge, with an incredibly large firebox held up by say a 4-10-6 or 4-12-6 wheel arrangement as I am sure you dream of, you would need on the order of three seperate mechanical stokers of either the screw or the chain-bed type, each driven by a seperate engine and each having its own assembly of modulation jets, throwing arms and dispersion jets.   of course for fires that big you cannot do without GPCS firing and secondary overfire air and steam and combustion air preheating, or else you end up with the hideously inefficient smoke-spewing volatile-hucking fires that the UP's mallets had.  
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:iconccmarc:
CCMarc Featured By Owner Feb 20, 2014

That makes sense. Thank you.

I'm not sure what I want for the 102" gauge lines. I want them to have an Anglican taste to them, I know that.

I figure they would be categorized into separate periods, representing different design eras in our continuum. However, this is difficult to pinpoint perfectly. Different collectives (for lack of a better term) would use different technologies.

Good examples of conflicting technologies are the method of boiler cladding, draughtiness of cabs (!), wheel arrangements, and so on. A 'design era', therefore, is very loosely tied together.

For example, the First Era would represent engines built with 1830-40s experience. This is called the First Era because it is the first period of engines for 102" gauge.

The Second Era would represent engines built with 1840-60s mechanical knowledge.

And so on and so forth.

By the 1010s, the latest I plan to write, engines are being built as though reciprocating engines had continued to be built into the 1980s-90s.

An important note on the 1010s is that more modern techniques are appearing in experimental shunting engines. More and more engines are being built with water tube boilers, chain drive, and other Sentinellian features.

This doesn't matter much, because Inglica (England) has achieved it's designated 'edge of industrialization' by this point.

An 'edge of industrialization' isn't so much a plataeu, but how much a country is allowed to expand before a certain balance of nature vs. civilization is at risk.

As I've told you, this planet has a much larger land-to-ocean ratio than we. Therefore, there are more countries to create, and more importantly, PORTRAY.

I think it would be the 1030s before we see anything similar to Bulleid's "Leader" on the main line, albeit much more successful.

Bear in mind, 'conventional' engines with firetube boilers, direct drive, tenders and so on will never, EVER go away.

There's no obsoletion of technologies in my world, trust me.

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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 20, 2014  Professional General Artist
Keep in mind almost everything about Bulleid's "Leader" was an example of modernism creating flawed designs.


A dry-wall firebox is such an elementary mistake it is very mysterious how a company such as Bulleid would even make it.........At the best of times the only uses for a drywall firebox is in something such as a small launch boiler or that of a wood-burning non superheated locomotive, where the combustion will never be as vigorous or heat-producing as to bend or warp the sheets, and even then they will sustain burning.  Some locomotives and live steam models have Briggs boilers with this design.  


In short you would never be able to make anything even remotely resembling a "Leader", either mechanically or asthetically, without it being an almost dismal failure unless used for light work and demonstrations only.  These cab-forward semi or fully automated steam motors may look pretty and polished, but their performance quickly degrades to zero when they are subjected to the same conditions that traditionally layed out and worked reciprocating engines simply do not notice.   The same problems happened with the steam-electric turbine locomotive the C&O had, and would have been encountered with the mutant that was the ACE3000, if it had been built.  Steam does not lend itself to that way of engineering.



On the subject of land to ocean ratio, it is the oppsite in the islands.  The largest island is about half the size of Great Britain, and although there are hundreds of them, the smallest are no more than a mile wide.  The ocean to land ratio is far greater in favor of the oceans, about 90% of the world is water.


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:iconccmarc:
CCMarc Featured By Owner Feb 21, 2014

A dry wall firebox? What kind of educated CME thinks that'll work?!

New scenario.

Sentinellian shunters begin making an impact sometime in the 1010s. They seem to work well, though opinion is mixed amongst enginemen who may favor conventional engines.

A band of individuals of all ranks, 'modernists', are cruel men. They insist conventional engines be totally wiped out in every line of duty.

These men are obviously not popular with railwaymen or the public.

However, a particular foreman has a plan to make this 'revolutionary' nonsense stop.

He provides the modernists with a bet. They give him a road engine design, and he builds it. If the engine is successful, he'll build more.

The public is horrified. But, they don't know just how cunning this foreman is.

The engine is built, and on it's first high speed run, fails with multiple faults. Seized chain drive, melted firebars, blocked firetubes, the works.

This shuts the modernists up, and the engine becomes the first to be scrapped in hundreds of years.

Now, the engine would've failed on it's own well enough, but this foreman made sure poor metal was used in the construction, as well as slack coal burnt, to speed up the process. XD

Thankfully, the scenario was engineered so none of the enginemen were injured.

The modernists became changed men, it's safe to say.

They still have no idea of the foreman's plan. Nor do they know how hard they and their engine were laughed about in the local railwaymen's pub that night!!

Neat on the subject of the islands. Are there a lot of viaducts involved?

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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 21, 2014  Professional General Artist
Take note how the bad idea never works.  THe Leader did not come to late, it never appeared because of its horriffic design.  There was a reason you saw Bulleid's pacifics EVERYWHERE (even though they were comparatively very modern) and did not see even one leader in regular traffic.  


Your story sounds a bit naive and simplistic in the personality traits.

Furthermore I do not see all modernists as cruel, as cruelty and sadism seems to be a sporadic trait that exists in all humans regardless of their aims, goals and wants in life.   I regard modernists principally as restless and uneducated, and I feel rather sorry for them (even though I do not bend in my directive to stop them from performing their actions on the world at any cost.)  


Furthermore, the CME who purposefully sabotaged one of his own locomotives, beit of any design, stoops him to and below the level of those he is fighting........I would call a man who did that very small in character.  A true CME would build and run the engine to the best of his ability.  If such a thing did unfold, there would be firstly receipts pointing to where he got the bad coal as well as evidence of the pile being used, there would be scientific studies performed on the locomotive as to why it failed and these purposeful sabotages would be discovered almost instantly, and the CME would most likely be discredited.  
The far better option would be to let the properly built machine perform regular and very demanding work and watch it either fall apart, or suck down incredible maintenance time and resource costs as it is fiddled with at every station to ensure it will keep running........

Furthermore, believe me, the modernists would not change, as people never do change.  They would fall further into their delusions and only try harder.



The dry-wall firebox would at the very least be covered in waterwalls (water-jacketing made of water-tubes ganged up against eachother so there is no space for gas to pass through) if not fully stayed water jackets themselves.  







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(1 Reply)
:iconmensjedezeemeermin:
MensjeDeZeemeermin Featured By Owner Feb 18, 2014
Man, she looks like a mover.  Could she start a big train without spinning her drivers?
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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 19, 2014  Professional General Artist
This engine it should be evident to you that she would not be much of a slipper.  Large drivers do not inherently mean the engine is a slipper, rather it seems that way due to most locomotives with very large drivers were slippery wheel arrangements such as Atlantics, pacifics, 4-4-4's and hudsons.

For one thing, engines such as those, which have good boilers, often support their fireboxes with trailing trucks, which of course are non-powered axles.  The firebox is the heaviest part of the boiler and has much useful weight that could press the drivers to the track, but it does not.  Even 4-8-4's suffer from this problem, even though trailing trucks means that the firebox can be deeper and larger and hence make more steam.  THe 4-4-4 in Bavaria suffered from the same problem.  Usually fast passengers engines like this are meant to go at terriffic speeds but not pull very much, so their adhesion factors can be low.

The best pullers are Anything-Anything-0's, 0-10-0, 2-10-0, 4-8-0, 4-6-0, 4-10-0, etc.  This means of course that the drivers are located at least partially under the firebox, meaning that basically all of the locomoives larger weight is over powered axles and the power is pressed to the track.  Whereas most of these were shunting and freight engines, the anomalies happened mostly in britain, where the 4-6-0 wheel arrangement was a favorite for insanely fast and powerful passenger locomotives.  Churchward did the best of these on the GWR, with the King and Castle classes.  THese locomotives had staggering adhesion factor, tractive efforts ranging into the 40,000 LbF range and could clock sustained speeds of 112 MPH.  I essentially took the basic shape and layout of a Churchward 4-6-0 and enlarged it both in size and wheelbase, making it a 4-8-0, what I (and Chapelon!) apparently believed and still believe to be the best arrangement for a fast passenger locomotive if can purpose build to the one constraint which is a narrow-bottom bellpaire firebox.  
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:iconmensjedezeemeermin:
MensjeDeZeemeermin Featured By Owner Feb 20, 2014
I see. o_o  Ground to pieces as they were, I see from your definitive response that my concerns were not wildly unreasonable, just WRONG.

Have you ever had a chance to play with a big Marine triple-expansion engine?  I walked over the Jeremiah O'Brien's in San Francisco, and experienced awe.
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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 20, 2014  Professional General Artist
Fear not, I always enjoy clearing up discrepancies.    I would not say wrong, because if not looked at in a strictly pragmatic but a historical way, the locomotives with the larger drivers tend to slip (just not because of the large diameters, but the wheel configuration itself, such as the 4-2-2's and Atlantics and Pacifics in britain, etc)


I have had much experience with triples, the largest of which is this five-story high beauty here, larger than that of Titanic.  www.deviantart.com/art/Natural…

The engine is not for driving propellers or wheels, it instead pumps water to a city.  (Rather it used to.)  It is however nearly identical in configuration to a marine engine except for notable features better adapated to stationary non-reversibles, such as the governed rotary valve gear and the placement of wet air and condensate pumps, as well as the condenser itself.


They are by far works of art, the vertical triple of the largest size is probably the most efficient and elegant machine to ever exist in the field of the steam engine itself.  
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:iconzephyr303:
Zephyr303 Featured By Owner Feb 18, 2014  Hobbyist General Artist
Hmm...does she have a Belpaire firebox and combustion chamber?
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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 18, 2014  Professional General Artist
obviously, by the diagrams I illustrated.  Dark blue is boiler shell, light blue is firebox and thermic syphons.   For an engine with these rapid combustion properties, a combustion chamber is a must.   The firebox, syphons and chamber are of course copper.
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:iconzephyr303:
Zephyr303 Featured By Owner Feb 18, 2014  Hobbyist General Artist
Well, Belpaires do have more volume above the crown sheet than non-Belpaire fireboxes...
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:iconpaxaeternum:
PaxAeternum Featured By Owner Feb 19, 2014  Professional General Artist
That is not really the reason they are shaped that way.  Bellpaire fireboxes are square cornered to position sheets flat to eachother to be stayed more easily, and to point the tension stress on those stays in a uniform direction, thus increasing the available pressure stress on the boiler.  Notice how in Britain it is the Bellpaire fireboxes that first reached 225 and 250 PSI.  Now of course flat sheets and square corners by design are geometrically inferior to pressure compared to cylinders, but the staying effects yields a greater benefit.  (adequate metalwork can temper almost any shape of boiler to these pressures.)   Keep note that semiwides and other round topped boilers do not have a cylinder shape either, but a parabolic shape, and as such they need horizontal wrapper stays across their tops.  

The volume of a boiler's various spaces is comparatively negligible unless they are extraordinarily small.
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