In evaluating claims of steam locomotive thermal efficiency under different conditions and circumstances, I choose to consider the efficiency in which coal is converted into superheated steam by the boilers separately from the efficiency in converting steam into indicated horsepower or "power in the cylinders." I will get to power "at the wheel rim" and "at the drawbar" later on.
Alfred Bruce (1952) The Steam Locomotive in America, p 142 Chart 15 gives curves "of a 484 steam locomotive." He is being coy: a boiler capable of evaporating 110,000 lbs steam/hr to produce a peak of 6600 indicated horse power ("in the cylinders) is no garden-variety Northern -- it is probably Kieffer's Niagara built by Bruce's employer ALCo. This stated evaporation and horsepower is a steam rate of 16.7 lb/hp-hr -- under some unstated conditions of speed and cutoff.
Bruce goes on for some pages talking about "Cole ratios" (an ALCo employee preceding Bruce by some decades) and grate area and how it really isn't grate area that matters but firebox volume, with 7 cu ft of firebox volume typically provided for every square-foot of grate area leading to Chart 16 on p 176. Here, the evaporation in pounds of water/pounds of coal, my second efficiency factor, is charted to be about 7.5 at the low end of firing rate to 5 at the high end. The low end corresponds to about 50 lb coal fired/sq-ft of grate and the high end reaches 200 lb coal/sq-ft of grate.
Now 50 lb coal/sq-ft of grate is a rather low rate, but Tom Morrison (2018) The American Steam Locomotive in the 20th Century hints that towards the end of steam, some railroads were aiming to "derate" their steam locomotives to fire them at this low rate to get better efficiency. 200 lb coal/sq-ft, on the other hand, is what one would fire during test to have bragging rights as the the peak horsepower of a particular locomotive.
In Chart 16 on p 176 of Bruce, the efficiency of converting coal to superheated steam is about 70 percent at the low end whereas it dips to 45 percent at the high end, with nearly half coal being blown out the stack as partially combusted fines when "forcing" a boiler to high output. 70 percent boiler efficiency seems rather low, but remember that you don't want the flue gases condensing and ruining the tubes -- something that was tried to that unfortunate effect in the Franco-Crosti system of heat recovery for feed-water heating. So a boiler starts out with about 80% efficiency in recovering heat from the flue gases. From graphs in Wardale (2013), The Red Devil and Other Tales of the Age of Steam, the graphs of "combustion efficiency" seem to extrapolate to no better than 90% at zero rate of combustion. This suggests that fully 10% of the carbon in the coal is swept up and thrown out with the ashpan discharge, where Wardale hints at an "afterburning ashpan" as some attempt to not waste that fuel fraction.
Let's start with a "reference coal" that I assign 14,000 BTU/lb as its "low heating value."
Standard Grade Coal - Heat Value (engineeringtoolbox.com)
Since no one attempts to extract heat from coal until the water generated by burning its volatile component is condensed -- the sulfur in coal makes that water quite corrosive -- I am using the "lower heating value" where that water remains vapor as it exits the stack. There is also a much larger spread between the low and high heating value of natural gas with a much higher hydrogen fraction, and this is what a "high efficiency" gas furnace does with its "secondary heat exchanger", but we won't attempt that with coal.
Indulge me to use easier-to-remember rounded conversion factors of 3400 BTU/kWHr, .75 kHWr/hp-hr, a coal-rate of 3 lb/hp-hr works about to
(3 lb coal) (14000 BTU/lb) (1 kW Hr/3400 BTU)/ (.75 kWHr) = 16.47 BTU heat in/BTU work out or a thermal efficiency of 1/16.47 = 6.07 % thermal efficiency. I shall round this to 6% thermal efficiency for a locomotive burning three pounds of a high BTU coal per horsepower-hour of mechanical output.
These numbers should be easy to remember. Burning 3 lb/hp-hour is 6% thermal efficiency which is considered characteristic of "late-era" steam, about 2 lb/hp-hour (claimed as peak efficiency for some locomotives under some conditions) works out to 9% efficiency and so on.
OK, now let's break out these numbers into the two factors. Back to Chart 15 in Bruce -- if you are firing at a high rate, you are getting maybe 5.5 lb steam/lb coal from Chart 16, with 16.7 lb steam/hp-hr in the notes to chart 15, or about 3 lb coal/hp-hr and the 6% rule-of-thumb thermal efficiency of late-generation steam in American practice. 3 lb coal/hp-hr times 6600 Hp and you are at 19,800 lb coal/hr, 101 sq-ft of grate, this brings us to 196 lb coal/hr/sq-ft grate, where these numbers "tie up" with the low boiler efficiency under peak hp conditions.
Let me leave it for discussion right now as to where the 6% thermal efficiency for modern steam in US practice comes from and consider later on how the lbs steam/lbs coal ratio (coal ratio? Cole ratio?) along with the lbs steam/hp-hr can vary under different designs and operating conditions.
If GM "killed the electric car", what am I doing standing next to an EV-1, a half a block from the WSOR tracks?
Great post, Paul. I will leave it to you and others engineering pros to apply a derived formula to well-known locomotives in North America and Europe.
Keep in mind that all the factors you're considering are not necessarily scaled correctly for modern power, and that a number of trends in late big-steam practice were counterproductive in actual practice. In my opinion it's best to start with first principles to be sure you've modeled the subsystems reasonably 'accurately' (which is a big problem in Fry's detail formulae, which quietly rely on empirical constants from early-'20s practice not good for later designs).
I presume you have downloaded and read Fry's book now that it's been released as a PDF. It is one of the must-read references if you actually want to design locomotives.
I have lost the patent reference to Snyder's preheaters, but you should look them up (and, arguably, use them). These use relatively spent exhaust steam to preheat the primary air entering between the ashpan and the grate, with the option of further condensing or pumping the condensate into the tender to increase the effective water rate. Reportedly C&O on test got a better than 10% improvement (although I disremember exactly on what) -- the point being that all this improvement was substantially free as far as cost or flexibility of operation are concerned.
Likewise, DNB in the water legs, although a serious problem, cannot be directly observed or quantified, but it can be addressed with better 'waterwall' circulation. Best is probably still a Lamont firebox, which runs about 6x the steam demand per hour through waterwall passages and then uses a cyclone arrangement to do mechanical steam separation with the circulation velocity. But you can get a long way toward this by using the Cunningham arrangement, which is a jet pump fed from downcoming areas in the convection boiler that feeds nozzles strategically placed in the water legs with fan diffusers above them. Cunningham did not (to my knowledge) subsequently optimize where the enhanced leg circulation goes once it reaches to the crown (note that it has to get back through the convection section too, at some point) so there is still some opportunity to visit undiscovered country of great potential beauty.
At present it looks as if the 'late' Koopmans characterization of what multiple nozzle front ends do is the best 'working' principle, but there are still things that were done in front ends that I think make great common sense but may not 'work as anticipated'. One of these is precisely how the combustion gas becomes velocity-matched and then entrained in the 'jet' coming from the exhaust nozzles. At one point Wardale thought that putting a hollow flow-smoothed duct at the 'mouth' of the exhaust petticoat was the best way to induce the flow from 'all the tubes and flues' to converge cleanly around the base of the stack and then rotate direction through what may be a large number of degrees to line up with the steam exhaust. It is surprising how little attention this gets.
It is easy to forget that the whole of the fire, except for a few shocks in the gas flow, is subatmospheric, and that oxygen only represents about a fifth of the available air. This has implications for generating the kind of luminous flame that maximizes practical radiant uptake by the direct heating surfaces over a reliably wide range of 'turndown'. It also gives you another handle on why forcing the boiler to the grate limit can be a poor practice.
Somewhere in here we should take up Besler tubes as well, as once you have arranged not to throw random sticky soot in the tubes and flues, these make thermodynamic sense in the convection section. You have to understand what they actually do, though, and I was lucky to have come across a chemical-industry reference from the early '80s that actually covered this (in a different context).
As a fun exercise: see whether you can find parameters for the PRR Q2 boiler (as modified for the 8000hp mechanical turbine) and see if you can 'improve' it to provide the vaporware 9000hp that PRR advertised (circa 1948) it would be able to make 'in competition' with first-generation diesels.
The difficulties with long-path heat recovery in economizing sections a la Franco-Crosti have been long solved: the first order of business is to fire only with good washed 2" coal of the proper rank and ash characteristics -- as promoted in publications like Railway Age up to the end of the '40s -- and the second order of business is to avoid sulfur without co-firing with dolomite; in any case we now have better coatings and alloys to deal with corrosion below the dew point of sulfuric acid/sulfur trioxide, and again the most critical characteristic of a large modern locomotive -- water rate -- can be economized nicely even before we get into the joy of recovering the latent heat liberated by the condensation of the water in the fuel exhaust (which, for example, the multipass Donlee TurboFire XL could do within stack-train clearances...) and, at least theoretically, use some of that mass for water-rate reduction as well.
Proper use of the steam is a whole subject in itself, but definitely one that bears on locomotive performance when we eventually get around to it.
The place to start is with the coal fuel, and that right there opens a sort of can-of-worms controversy. There are some who advise designing the locomotive to burn 'run-of-mine' coal, to minimize cost -- perhaps the most glaring example of this was the ACE3000, which would have used sophisticated modular 'coal pods' designed to be taken off the tender and fueled remotely ... likely on swap-body truck chassis ... at mines offering the cheapest price. (Which I think would be suicide on a sophisticated heavy 4-8-4 with obligate condensing and at least the premise of semi-automated firing... but that's just an opinion.) The AAR and other industry sources recommended (through the late 1940s, after which it increasingly ceased to matter) the opposite approach: coal mix of good ranks and ashing characteristics, properly sized to about 2" and then handled to minimize fines, and kept well-washed. I would note that some clean-coal approaches recommend co-firing with dolomite (to flux the glassing components in the ash and knock down some of the sulfur if the coal contains it, as many do) and this can be applied as a slurry to the lump coal at a convenient time during the sizing and washing.)
Thermodynamics often fails to consider the effects of having to deal with the post-combustion ash. Porta did some studies (regrettably mostly still untranslated from his somewhat idiomatic Spanish) including Detroit-style 'ashaveyor' systems to move ash to modular storage for longer run time and better ecological 'optics' -- but there are issues to be dealt with. I believe Wardale's concern with unburned fuel falling through the grates and 'quenching' in the ash is interesting, but it may be much less difficult on a North American engine with proper FireBar-style rocking grates and good secondary-air arrangements -- the difficulty being that with proper 'fuel design' there is no more place for 'recycling' the remnants in the firebox than there was for all the crackpot schemes of recycling unburned 'sparks' from various places in the combustion-gas path that Angus Sinclair (and the locomotive in my avatar) so derided.
That the flame in as much of the radiant section be luminous is confirmed from other material (notably a somewhat sarcastic article about 'college boys ordering zero smoke' from around 1910 that discussed the empirical observation that sometimes visible smoke needfully accompanied best performance) and at least to me it has clear implications for practical North American firing if you're interested in chasing a practical method of GPCS. At some point you will hit the same quandary that Tom Burlingame did: the sophistication required to burn coal effectively rapidly hits the limits of what even a good human fireman can watch and respond to, and the required 'computer assistance', while practical in many stationary plants, rapidly goes out of cost and reliability bounds when implemented on a typical reciprocating locomotive (cf. Wardale's sarcastic invocation of Bulleid concerning 'computerized valve gear' saying 'well, it wouldn't be a steam locomotive then').
There are also implications for the draft, which tie fairly intimately with some characteristics of the steam circuit and of water-rate concerns. I recognized the need for fairly early prediction and anticipation of load changes as early as the 1970s; in a system of GIS-enabled GPS pervasiveness (as in Carnegie-Mellon's proposal to enhance autonomous-vehicle performance) this becomes almost trivial to incorporate in a firing-assistance system. But what is important is the ability to get sustainable but rapid steaming out of a boiler that is (1) not forced beyond its economical generation range, and (2) is not subjected to careful management of differential thermal expansion (something that seems to have repeatedly bit Porta's designs on the butt in practice).
Lima's late response (in keeping with the fascinating but regrettable story about why the Alleghenies were so grossly overweight and the fact then so carefully covered up) was to design the rear firebox to enhance radiant uptake... at the cost of enormous additional structure, sometimes in exotic alloys that didn't hold up well in practice, necessitating an additional carrying axle and other structure to support even on an eight-coupled design. One is tempted to note, as for Franklin type C valve gear, that the success of this approach aside from Alleghenies can almost be open-and-shut determined from how many of these dream locomotives Lima actually sold. Considerations have been noted that boiler design is different for 'long life' than it was at the height of cheapest-possible commodity locomotive use, where it was deemed feasible to design for an unrebuilt service life as short as two years before major maintenance. Armchair designers and crayonista thermodynamicist fiends tend to forget things like that...
There was an interesting tradeoff developing in the 1940s regarding the choice of pressure. As will be determined in later analysis in these posts, a reciprocating locomotive can run with reasonable thermodynamic efficiency on a fairly wide range of throttle pressure -- subject more to careful 'steam-drying' superheat management than actual use of nominal pressure in the engine itself -- with the Scylla being the mechanical problems with higher pressure and the Charybdis being effective water rate and its issues. One has to design the firing system to suit a boiler system that optimizes the tradeoff -- occasionally by taking elements of both depending on circumstance. Which is why I bring it up now.
There is no point, and never was any point, in having tubes much shorter, or much longer, than the 'magic ratio' that gives about 20' in practice. (The actual 'best ratio' was supposed to be right around 406 to 408-and-a-fraction, but this is a bit like calculating the events in British Caprotti to be accurate to 3% cutoff when in practice you'd never use anything less that about 15% unless actively drifting.) It would be nice to have confirmed results on optimal flue length with Besler tubes, but very little application of those to conventional firetube boilers was conducted (the Stanley boiler, which used a multiplicity of small tubes for structural strength, and use of tapered monotubes neatly bracketing the use in small vehicle boilers, and maintenance of flues containing them being onerous when crap fuel and to-a-price servicing are "economic" concerns) but I suspect that some approximation of hydraulic depth for flues containing Beslers can be easily confirmed even with CFD.
Where the low-hanging fruit is more easily plucked is in the Rankine cycle, particularly nonlinear places like Holcroft-Anderson recompression or long-gas-path 'steaming' economization not pressure-equalized with the convection section's nominal pressure. A reasonable guiding adage is 'a pound's worth of heat conserved is a pound that doesn't need to be burned' -- but that is subject to a number of economic considerations outside that of pure efficiency.
Paul Milenkovicwhere the 6% thermal efficiency for modern steam in US practice comes from
Overmod gives a synopsis of late-steam era efforts and technology to improve the notably poor thermal efficiency of the Stephensonian-pattern steam locomotive along with what may have worked and what may have not been worth the trouble.
As to why consider thermal efficiency at all, especially in a time and a place when coal was cheap and plentiful (although the post-WW-II labor actions to give miners their due changed the equation, hastening Dieselization it is said), Wardale explains that the sheer quantity of coal placed a capacity burden on the railroads consuming in. If you could use coal more efficiently, that would free up a lot of track capacity, a lesser-noted advantage to the thriftier diesels. Even today, the cost of transporting coal from mine to the power plants and other remaining users is said to exceed to the cost of digging it out of the ground, especially for the bulkier, low-BTU Powder River Basin coal that is extracted from open-pit mines with special-purpose jumbo-sized excavating equipment.
Apart from the discussed improvements to steam, I am posing the question as to what it even means if someone says "this locomotive is 8% thermally efficient" or "that locomotive required 3 lb coal/hp-hr."
Consider the efficiency of producing hp from superheated steam as claimed by annotations on cylinder indicator diagrams on pp 258-259 of Wardale's "Red Devil." This locomotive is claimed to have a particularly low flow resistance steam circuit although its boiler pressure is quite moderate by late-steam standards (1464 kPa translates to 212 psi in more conventional, human-centric units). At 42 MPH, 52% cutoff, it used 15.8 lb steam/hp-hr. This is data Wardale reduced from an electronic indicator diagram that he admits isn't an exact match to data from a mechanical indicator diagram no showing such rounded corners of the trace, but still, this is not that far off from the 16.7 lb/hp-hr for putatively a Niagara at peak power.
This speed and power is equivalent to 34,100 lb of tractive effort, before correcting for friction in the cylinders, rods and valve gear. I posted somewhat recently that John Knowles posting on mechanical efficiency vanished from the Web, Wardale appears to have only a weak grasp on that quantity, but Ralph Johnson's book quotes, "20 lb friction per ton of adhesive weight." In contrast with the much lower Davis formula rolling resistance, this puts the "effective" rolling resistance at 1 part in 100 for friction in the actual steam engine plus, say, 1 part in 500 from the Davis formula into the level of friction of a radial tire on a modern passenger car. Keep in mind that a diesel engine or your car engine has considerable internal mechanical friction. Knowles went into more detail, but I will assume the 1 part in 100 fraction is a constant addition to the locomotive rolling resistance and does not diminish with reduced power, differing from Wardale quoting a constant 90% as the steam engine "mechanical efficiency."
For the Red Devil engine number 3450 having 83 tons of adhesive weight, this puts the tractive effort "at the wheel rim" at 34100 - 83 times 20 or 32400 lbs.
Overmod or someone else can correct me on this, but when Wardale states "cylinder steam flow" of 27500 kg/hr (60500 lb/hr -- a rip-roaring steam flow for a 3.5-foot "Cape" gauge 4-8-4), he is talking about pounds of steam past the valves, and this does not account for any recovery of energy and water with a feedwater heater -- I shall include the benefits of a feedwater heater in improving efficiency and reducing the "water rate" into the lbs water (into the cylinders)/lbs coal half of the efficiency equation. This also applies to with the possible use of a combustion air preheater that Overmod talks about, Porta included in his future plans and Wardale hints at, which also improves efficiency and recovers some additonal water.
Wardale's published indicator diagrams are a "tease" of what is possible with his modified locomotive because they are few in number and they sample speed and cutoff in haphazard fashion. He also has indicator diagrams for an unmodified 25NC locomotive for comparison, but he doesn't give the steam rate. I offer the following table derived from Wardale's data:
15.8 lb/hp, 42 MPH, 52% cutoff, 3850 hp, 32400 lb, 19.5% adhesion
12.8 lb/hp, 43 MPH, 24% cutoff, 3000 hp, 24500 lb, 14.8% adhesion
12.1 lb/hp, 53 MPH, 28% cutoff, 3650 hp, 25800 lb, 15.6% adhesion
10.5 lb/hp, 53 MPH, 18% cutoff, 3136 hp, 16800 lh, 10.1% adhesion
I ranked these by steam consumption, and even the somewhat slower speed is showing somewhat higher steam consumption at a lower cutoff, suggesting that superheat has not fully vanquished the condensation problem.
The hp is indicated "in the cylinders" whereas the tractive effort at adhesion factors are "wheel rim" using the Ralph Johnson of Baldwin figure for mechanical friction in the actual steam "engine."
By the way, Wardale makes a big deal that the "proper" place to measure hp, tractive effort and efficiency is "at the drawbar", essentially the wheel rim values after the deduction for the Davis-formula rolling resistance and aero drag. The steam locomotive, especially for high-power, large-firebox, high boiler pressure modern steam carries a lot of its weight off the drivers, and then there is the tender to drag around because of its appetite for coal and water, but I still regard the "in the cylinders" value as a more reasonable base for comparison. Whereas I haven't accounted for the steam consumption of auxiliaries (air pump, turbogenerator, whistle, stoker engine, stoker steam jets) where auxiliaries are removed from the diesel ratings, diesels are commonly rated "at the input to the main generator" before losses in the electric drive come into play.
At the 27,500 kg/hr (60500 lb/hr) steam flow for the top entry in the table, Wardale Fig. 117 on p 299 gives 59% boiler efficiency or 6.3 lb water/lb reference coal (South African coal was of lower btu), giving 2.5 lb (reference, high-BTU) coal/hp-hr or 7.2% efficiency. This, of course, assumed that his gas-producer combustion system (GPCS) is working properly, which is not a sure thing as he writes about.
At the 15,000 kg/hr (33000 lb/hr) steam flow for the bottom entry in the table, Wardale's boiler efficiency gives 68% or 7.3 lb water/hp-hr, giving 1.44 lb coal/hp-hr or 12.5% efficiency, which is consistent with the chart in Fig. 82 on p 267.
Same locomotive, big range in efficiency numbers depending on how it is operated, as they say your gas mileage may vary (YMMV) from the EPA gas mileage sticker on the car you just purchased. Again, the 2018 Tom Morrison books suggests that the New York Central may not have operated its Niagara at its full 6600 (indicated) hp capability requiring an enormous 110,000 lb/hr evaporation rate, but rather at some lower power levels that save coal.
timz Paul Milenkovic where the 6% thermal efficiency for modern steam in US practice comes from If you mean how is the figure calculated -- no argument about that, is there? Convert the BTUs of the coal burned to foot-pounds, and compare to the foot-pounds in the cylinder, or at the drawbar.
Paul Milenkovic where the 6% thermal efficiency for modern steam in US practice comes from
If you mean how is the figure calculated -- no argument about that, is there? Convert the BTUs of the coal burned to foot-pounds, and compare to the foot-pounds in the cylinder, or at the drawbar.
Yes, what you say is well-known, but what I am asking, where does a figure of 3 lb coal/hp-hr come from? The case of Alfred Bruce's "mystery 4-8-4" (surprise, an ALCo product and the legendary Niagara), I speculate it could come from 16.7 lb steam/hp-hr, a figure I suggest comes from achieving peak hp by operating at high speed that lowers condensation loss but at a generous cutoff using a lot of steam, and from raising 5.5 lb steam/lb coal, which occurs at a high, inefficient firing rate. The coal consumption may have been considerably lower if the Niagara was not operated at peak horsepower, which author Tom Morrison hints may have been railroad practice.
I am just speculating here, but could we consider the Niagara to be operated at 7 lbs water/lb coal, 13 lbs water/hp-hr, 4000 hp, less than half peak evaporation at 52,000 lb water/hr, 7400 lb coal/hr.
This firing rate is 74 lb/sq ft, almost a third of the firing rate for max hp, consistent with the higher specific evaporation rate I assume above. By not "forcing" this locomotive, 4000 indicated HP is still quite a bit, and your coal rate is now 1.85 lb/hp-hr or 9.7%, putting in the range of figures quoted for the more efficient British steam locomotives?
This isn't from changing a thing about this excellent locomotive apart from how you choose to brag about its performance?
The Niagara has been observed to do even better than that.
Bill Tuplin ("The Steam Locomotive, Its Form and Function) was something of a low-pressure enthusiast, and seems to seldom have passed up an opportunity to note that increased maintenance of high-pressure boilers may have outweighed the thermodynamic advantages of higher throttle pressure (if adequate superheat is provided). It was therefore probably delightful to him to observe a Niagara, on what I recall being characterized as a way freight (probably break-in after service at Harmon) doing the job of a 2-8-0 on a 2-8-0's budget of fuel and water. The fireman was reportedly using sliding-pressure firing, probably to about 180psi, and of course there was lavish superheat available from shortly after opening the throttle. So things scaled still lower with that boiler.
There was a concern, though, with the steam separation in the 'domeless' boiler, particularly at the expected steam mass flow associated with higher firing rate. The Timken rods were extremely intolerant of priming carryover, and probably excessive peak compression, and one set of repairs of the resulting damage would pay for many, many tons of coal and pans worth of water.
NYC was also one of the roads to replace whistle use with 'pneuphonic' horns, recognizing the heat and mass loss involved (much greater than that expended in the air compressors for a horn blown on main-reservoir pressure). I'll grant you that the whistle had it all esthetically ... but particularly when aggressive water treatment has to be in use for alloy boilers, the mass loss and water-rate complication involved in even a little crossing-signal blowing adds up fairly dramatically.
There is, as far as I know, no good test result on use of the Hancock Turbo-Inspirator by extending its shaft to drive a dynamo, and then using that power to run some of the auxliiaries that did not 'scale' well to be driven directly by steam. Experiments on this are anticipated for 5550 when built out to the point the boiler can be steamed. While the Turbo-Inspirator was more designed to be light than particularly effective (the one fitted on C&O 614 was removed and its 'platform' actually used for a hose reel at one point!) I think it can be modified to do several jobs well if expanded to make use of a larger turbine running at more constant speed with adjustable load.
Paul Milenkoviccould we consider the Niagara to be operated at 7 lbs water/lb coal, 13 lbs water/hp-hr, 4000 hp, less than half peak evaporation at 52,000 lb water/hr, 7400 lb coal/hr.
You mean, could it do that? Sounds unlikely, of course. Are you considering something else?
Paul MilenkovicWhereas I haven't accounted for the steam consumption of auxiliaries (air pump, turbogenerator, whistle, stoker engine, stoker steam jets) where auxiliaries are removed from the diesel ratings, diesels are commonly rated "at the input to the main generator" before losses in the electric drive come into play.
Not quite. Diesels are rated at horspower into the main generator to be used for traction (at AAR standard conditions - 60 degree F air and fuel, 28.86" barometer). Power for auxiliaries is already taken out. (fans, aux gen, TM blower, etc.). Builders will usually provide RRs with info stating BHP, THP, and NTHP (BHP is Engine brake HP, THP is HP for traction into main generator, and NTHP is net HP out of main generator head to TMs).
-Don (Random stuff, mostly about trains - what else? http://blerfblog.blogspot.com/)
oltmannd Paul Milenkovic Whereas I haven't accounted for the steam consumption of auxiliaries (air pump, turbogenerator, whistle, stoker engine, stoker steam jets) where auxiliaries are removed from the diesel ratings, diesels are commonly rated "at the input to the main generator" before losses in the electric drive come into play. Not quite. Diesels are rated at horspower into the main generator to be used for traction (at AAR standard conditions - 60 degree F air and fuel, 28.86" barometer). Power for auxiliaries is already taken out. (fans, aux gen, TM blower, etc.). Builders will usually provide RRs with info stating BHP, THP, and NTHP (BHP is Engine brake HP, THP is HP for traction into main generator, and NTHP is net HP out of main generator head to TMs).
Paul Milenkovic Whereas I haven't accounted for the steam consumption of auxiliaries (air pump, turbogenerator, whistle, stoker engine, stoker steam jets) where auxiliaries are removed from the diesel ratings, diesels are commonly rated "at the input to the main generator" before losses in the electric drive come into play.
I think that is pretty much what I am saying. The 3000 HP rating of an SD40-2 is "before the traction generator" but "after the auxiliary loads."
I was contrasting this with my figures for a steam locomotive, also "before the mechanical rod transmission of power" but without taking deductions for auxiliary loads.
I suggest separating the auxiliary loads needed to 'run the boiler' or steam generator from those used to operate the engine -- with one special category (draft induction) kept separate from both. There is also a different set of 'auxiliaries' in play for starting (cylinder cocks open) and certain modes of drifting, when you get to operation.
I used the 'idling' consumption (in the absence of a Direct Steam type system, or electrical pressure maintaining as on rebuilt 8055) and this involves things like continuous blowdown that you might not know to account for (personally, I don't like current continuous blowdown as an option and plan to use different approaches that recover at least some proportion of the water mass and heat)
Problem is that many of the auxiliaries were designed to run efficiently at or near peak cylinder efficiency mass flow, or to suit the anticipated demand of a forced boiler, and are inefficient at idle. Therefore some of the heat-balance data are nonlinear and change nonproportionally.
timz Paul Milenkovic could we consider the Niagara to be operated at 7 lbs water/lb coal, 13 lbs water/hp-hr, 4000 hp, less than half peak evaporation at 52,000 lb water/hr, 7400 lb coal/hr. "Could we consider" a 4-8-4 producing 4000 hp on 7400 lb/hr of coal? You mean, could it do that? Sounds unlikely, of course. Are you considering something else?
Paul Milenkovic could we consider the Niagara to be operated at 7 lbs water/lb coal, 13 lbs water/hp-hr, 4000 hp, less than half peak evaporation at 52,000 lb water/hr, 7400 lb coal/hr.
"Could we consider" a 4-8-4 producing 4000 hp on 7400 lb/hr of coal?
Whereas I am offering speculation, I am indeed suggesting that a Niagara could be run that efficiently at part-power, and I am invoking Tom Morrison (2018) The American Steam Locomotive in the 20th Century as a source that this could have been a practice in the late steam era.
There is a narrative that especially the French and to some extent the Germans and the British were building much more efficient steam locomotives than the ham-fisted Americans. Perhaps some of the shade thrown on late-era US designs is in the way figures are quoted?
Paul MilenkovicThere is a narrative that especially the French and to some extent the Germans and the British were building much more efficient steam locomotives than the ham-fisted Americans.
There are equally clear explanations on the American side why cheap, robust construction and cheap maintenance concerns 'win the day' over expensive and often fragile or illusory thermodynamic improvements.
I will not make exhaustive (and ever more boring) lists or citations of the various issues. But one fairly dramatic one might serve. You may remember the 614T testing, 'supposedly' providing data for modern boiler design. Not only were some of those tests conducted with leaking staybolts, NONE of them was conducted with a working feedwater heater.
Paul MilenkovicI think that is pretty much what I am saying. The 3000 HP rating of an SD40-2 is "before the traction generator" but "after the auxiliary loads." I was contrasting this with my figures for a steam locomotive, also "before the mechanical rod transmission of power" but without taking deductions for auxiliary loads.
Oops. I misread it.... Sorry!
Another approximation useful for calculating locomotive efficiency is:
TE (lbf) X Speed (mph) X 1.99 = power in Watts ("2" is a good approximation for 1.99)
Kratville's book on the Big Boys had dynamometer data from eastbound runs from Ogden, recall coming up with a figure of 4 to 4.5% for efficiency converting energy in coal to DBHP.
Paul MilenkovicWhereas I am offering speculation, I am indeed suggesting that a Niagara could be run that efficiently at part-power
7400 lb/hr of 14000 BTU/lb coal = 103600000 BTUs per hour
= 80600800000 ft-lb per hour
= 40707 horsepower
So 4000 hp is 9.8% thermal efficiency. Offhand guess: no Niagara did better than 7% on any test. NY Central didn't care enough about efficiency to find out the 4-8-4 was actually that much better?
Other US engines could hope for 9% anyway? But tests never revealed their efficiency either?
timz Paul Milenkovic Whereas I am offering speculation, I am indeed suggesting that a Niagara could be run that efficiently at part-power The numbers again: 7400 lb/hr of 14000 BTU/lb coal = 103600000 BTUs per hour = 80600800000 ft-lb per hour = 40707 horsepower So 4000 hp is 9.8% thermal efficiency. Offhand guess: no Niagara did better than 7% on any test. NY Central didn't care enough about efficiency to find out the 4-8-4 was actually that much better? Other US engines could hope for 9% anyway? But tests never revealed their efficiency either?
Paul Milenkovic Whereas I am offering speculation, I am indeed suggesting that a Niagara could be run that efficiently at part-power
The numbers again:
William Withuhn (2019) American Steam Locomotives, p 253 gives the coal rate of the J3 Hudson as 2.03 lbs/indicated (cylinder) hp or 8.7 percent.
So performance under some operating condition of late-era American steam better than the well-quoted 3 lb/hp-hr or 6% thermal efficiency is not unheard of. The question is, under what operating condition are people talking about because boiler efficiency charts (lb water/lb coal) and Wardale's indicator diagrams (lb water/hp-hr) show that these supporting elements of efficiency can vary widely.
Again, efficiency percentages above 6% are widely quoted for French, German and British late-era steam, but did they have some "special sauce" that US designers ignored, or is it a question of how these locomotives were operated?
Paul Milenkovic Let me leave it for discussion right now as to where the 6% thermal efficiency for modern steam in US practice comes from and consider later on how the lbs steam/lbs coal ratio (coal ratio? Cole ratio?) along with the lbs steam/hp-hr can vary under different designs and operating conditions.
Paul,
I think you left a layer of mechanical conversion efficiency out of your calculation. I think the 6% rule of thumb applies to overall thermal efficiency of a typical late steam era locomotive, possibly operating under steady state conditions. There is a figure in Jeffries book, "Norfolk & Western: Giant of Steam" on page 62 that sheds some light on the assumptions of this 6% rule of thumb. Hopefully, you have this book and can reference, but it is a comparison of the operating cost between a diesel-electric locomotive and a steam locomotive on the basis of "work at the rail per dollar". It shows 400,000 BTU of work being done at the rail for 6,666,666 BTU/$1 of coal at the then-current cost of 13,666 BTU/lb coal. This works out to 6% thermal efficiency (400,000/6,666,666). I tried to post a scan of this figure, but apparently the Trains forum requires an image to exist somewhere on the internet to link. It is important to note that this is work at the rail (tractive force), and not work in the cylinders.
If we adjust your 6% number (derived from figures roughly applicable to the maximum indicated horsepower output levels of fthe NYC Niagara) for the rather jaw-dropping mechanical and resistance efficiency loss factor (4600 DBHP/6600 IHP @86mph)= 69.6%, we get an overall estimate of thermal efficiency of only about 4.2%. Of course, that would be at the very inefficient operating condition of maximum IHP and presumably very high (and inefficient) firing rate. And it should also be pointed out that we're being a little sloppy in mixing tractive force developed at the driver rim with drawbar pull (which is reduced by the rolling resistance of engine and tender and air resistance), but for discussion purposes requiring rough numbers, I think we can make some informed simplifications.
I was fortunate enough to be able to purchase a digital copy of the July 1948 NYC Niagara test report from the NYC Historical Society a few years ago, and it includes calculations of overall (drawbar) thermal efficiency for the road tests. Here are some of the comments from the report relevant to that testing:
"Full throttle operation with locomotives 5500 and 6023 throughout the entire working time was not practical with the train loadings used on account of their high power output and the speed limit of the division. Therefore, an arbitrary minimum cutoff for each locomotive had to be established on the basis of the riding qualities of the locomotive. Upon reaching this minimum cutoff, power output was controlled by throttle manipulation. Such operation naturally varied the average pressure at the steam chest. For the purpose of obtaining some information to establish a relationship between locomotive operation and economy, several tests were conducted with comparatively short average cutoffs with the necessary high average steam chest pressures. Operation of this type was not considered normal or practical."
"Locomotive 5500 (S2a equipped with poppet valves) had an economic advantage over locomotive 6024 (S1b equipped with Baker valve gear) as shown by the average curves for the thermal efficiency based on dynamometer horsepower (Figure 46). This amounts to from 0.60 to 0.80 percent thermal efficiency. The maximum thermal efficiency of locomotive 5500 was 5.86 percent obtained on test No. 141 and the minimum was 4.93 percent obtained on test No. 115. The maximum and minimum thermal efficiencies for locomotive 6023 were 4.94 and 4.22 percent obtained on test No. 111 and No. 137 respectively. For tests conducted with comparably short cutoffs the maximum thermal efficiencies were 6.57 and 5.58 percent for locomotives 5500 and 6023 respectively."
I suspect these tests involved stopping and starting the trains, rather than steady state operation (after all, these are passenger locomotives). The report makes the following comments that seem to relate to these operational effects on efficiency:
"During stationary testing (NYC 6000 had been tested for boiler capacity on the Selkirk test plant), the firing rates are consistent with evaporation, steam used, temperatures, and pressures. Coal rates in road operation, especially during periods of acceleration, usually are much heavier than the average temperatures, pressures, and steam requirements indicate. This is a result of the necessity to build up the fire or even force the fire in preparation for capacity operation. Evaporation and superheat temperatures naturally lag during these periods."
I would think well-designed superpower freight locomotives with large combustions spaces that are operated at efficient firing rates (<100 lb/sq ft/hr) with a minimum of stopping and starting could approach the 6% thermal efficiency.
A quick review of the PRR Altoona Test Plant report for T1 locomotive 6110 shows overall thermal efficiencies generally between 6 and 7%, with some as high as 7.5-8.0% (with cutoffs less than 25%). Of course, these are steady state tests under test plant conditions without losses due to standby periods, acceleration, or obviously rolling and air resistance.
Scott Griggs
Louisville, KY
On the topic of mechanical efficiency, the go-to reference I would offer as the John Knowles blog posting. I am told Mr. Knowles is still active on some railroad enthusiast sites but his lengthy blog posting is not longer available.
The next best source is the Ralph Johnson of Baldwin and his steam-locomotive book, offering a rule-of-thumb "20 lbs resistance for each ton of weight on drivers."
As I mention above, Withuhn claims a J3 Hudson achieved, under unspecified operating conditions, 2 lb coal/hp-hr putting it at 9% indicated (cylinder level) efficiency.
Do you a link or a reference to Altoona T1 data? I would think the test plant gives efficiency at the wheel rim (rollers) without deduction for the Davis formula terms for rolling resistance, especially of the "carrying" wheels and those on the tender. But what I am most interest is the breakdown into the indicator diagram-derived lbs steam/hp-hr and the test-plant pounds coal/pounds of steam.
The 2000 HP difference between indicated and drawbar values at 86 MPH is also found in Alfred Bruce's chart in his book.
By the HP = drag * mph/375 formula, the 2000 HP amounts to 8721 pounds of tractive effort to be supplied.
The Ralph Johnson formula for a constant mechanical friction as 1 part in 100 of the adhesive weight works out to 2750 lbs or about 631 hp at that speed. Interestingly enough, this is roughly 10% of the indicated HP giving the 10% "mechanical efficiency" that Wardale writes about, but from the John Knowles essay, it does not seem this loss decreases at a lower output of hp output?
This locomotive plus tender weigh in at 400 tons -- 800,000 lb, giving a rough Davis formula resistance of 1600 lb consuming 367 hp.
It is also interesting that the sum of 1600 lb from the Davis formula rolling resistance and 2570 for the mechanical resistance of pistons-to-wheels adds up to 4350 lbs, close to what I read at the low end of Bruce's chart for the difference between cylinder and drawbar tractive effort when air resistance vanishes.
This suggests that the aerodynamic drag was a full 4750 lbs consuming at least 1000 hp. The Niagara appeared to be quite unstreamlined, but this 1000 hp is pushing aside the air in which the train cars "draft", so I don't know if you could assign its full value as an inefficiency of the locomotive apart from arguing passenger locomotives need to have effective aerodynamic treatment.
A diesel also has a drive offering less than 100% efficiency, but its Davis rolling resistance is much less owing to many fewer axles -- let's say you are saving about 250 out of the 2000 hp.
This business of know-where-the-power-is-going ties into the Chapelon-Porta-Wardale-others claims of what could-have-been and what should-have-been.
Wardale talks about increasing the locomotive power-to-weight ratio. Even if you have a 4-8-4 wheel arrangement for guiding reasons, the Niagara and many late-era high-power locomotives have proportionately more weight on the carrying wheels as earlier designs -- Bruce's photo section gives stats on locomotives from the early 20th century to the end of steam. If you could Chapelon-ize or Porta-ize a locomotive to consume less coal and water, the smaller tender would also reduce the Davis rolling resistance cost, not to mention climbing even a modest grade, of a tender that a diesel doesn't need to drag around.
Of all the loss factors, I am most curious about the mechanical loss from cylinder to wheel rim and whether as Johson claims, this stays constant, even at reduced power output, if for any other reason than understanding those photos of the Timken Four Aces being towed by four women of slight build.
Paul Milenkovic On the topic of mechanical efficiency, the go-to reference I would offer as the John Knowles blog posting. I am told Mr. Knowles is still active on some railroad enthusiast sites but his lengthy blog posting is not longer available. The next best source is the Ralph Johnson of Baldwin and his steam-locomotive book, offering a rule-of-thumb "20 lbs resistance for each ton of weight on drivers." As I mention above, Withuhn claims a J3 Hudson achieved, under unspecified operating conditions, 2 lb coal/hp-hr putting it at 9% indicated (cylinder level) efficiency. Do you a link or a reference to Altoona T1 data? I would think the test plant gives efficiency at the wheel rim (rollers) without deduction for the Davis formula terms for rolling resistance, especially of the "carrying" wheels and those on the tender. But what I am most interest is the breakdown into the indicator diagram-derived lbs steam/hp-hr and the test-plant pounds coal/pounds of steam.
Hi Paul,
I figured out how to post the graphic from the N&W: Giant of Steam.
Note that N&W estimated its steam locomotives to have a thermodynamic efficiency of 6%, when measured at the rail (i.e. not based in Indicated HP).
Here is a summary page from the NYC Niagara test report. Note that the NYC determined thermodynamic efficiencies for this locomotive at 4000 IHP/2500 DBHP (not 6600 IHP/4500 DBHP). The Dry Coal/IHP is given with and without accounting for appliances and is 2.29 lb/IHP-hr with appliances and 2.10 lb/IHP-hr without appliances. Thermal efficiency based on 2500 DBHP was "only" 4.77% for the 6023 (baker valve gear S1b) and 5.51% for the 5500 (poppet valve S2a). As I said in the earlier post, the NYC test report suggests it was not possible to run the Niagara at low enough cutoffs to maximize thermal efficiency (riding qualities of the locomotive were unsatisfactory if operated with too-short a cutoff). Consequently, the locomotives were operated at a higher cutoff and at part throttle to avoid exceeding division speed limits.
The NYC was considering a duplex-drive 4-4-4-4 with poppet valves of its own (C-1 class, I think?). Maybe they were thinking having twice as many smaller cylinders with poppet valves would allow them to run at more efficient short cutoffs without the unacceptable riding qualities?
Do not be fooled by the broken-image picture. Click on it and the actual picture will likely open legibly; it did for me on a very ancient browser.
Watch what happens when you enter the correct modern factor costs of coal, water, and ash handling into the numbers for the steam locomotive.
Then add the cost for maintenance as practiced, say, by NYC to give the standby performance of 'contemporary' diesels ... hot suits, anyone? Bet that would cost more today if you could get permission to implement it as needed...
Meanwhile, in my opinion and observation, the machine resistance of a modern roller-bearing locomotive, particularly one with poppet valves, was much smaller than the numbers being bruited about here. This is particularly true of a locomotive like the T1 with Franklin wedges and roller-bearing boxes and rods. Do not conflate the machine resistance with the mass of the engine and tender being added to the Davis formula.
The added 'friction' of the carrying wheels was comparatively slight, and of course with the roller bearings the high starting resistance to establish the hydrodynamic film was much, much less -- as you can imagine from the girls being able to start those locomotives moving.
The real 'ringer' in those pictures is the effective friction between the piston rings and the bore; presumably these were designed to exert far less force without steam pressure 'behind' them and, in fact, I suspect a little promotional hanky-panky in adapting clearances in the glands and piston/valve rings to reduce friction which, had actual 265psi or whatever steam been present, would likely have allowed a veil of white and the sound of considerable blow...
The actual frontal resistance of a locomotive is important at the higher speed ranges, but it does not matter the way, say Cd of an automobile does. Very few locomotives appear to have been designed with quartering streamlining particularly in mind ... or with actual, functional drag reduction rather than its Art Moderne semantic representation being the design factor of importance. The cube-of-the-speed drag rising meets the functional cyclic steam circuit mass-flow and timing and compression issues falling at some speed, and if the valves in particular are not designed correctly, you're faced with the painful spectacle of, say, a C&NW E-4 or ATSF 3460 class, which probably gets up near 100mph reasonably well but by only a trivial additional number of mph more is clapped out -- the former couldn't even crack 100mph with the AAR test train; the latter probably couldn't get above 105mph unless it reached terminal velocity falling off a bridge. It would be interesting to see the effect of proper streamlining ... but other parts of the design have to be made right first.
Overmod Meanwhile, in my opinion and observation, the machine resistance of a modern roller-bearing locomotive, particularly one with poppet valves, was much smaller than the numbers being bruited about here. This is particularly true of a locomotive like the T1 with Franklin wedges and roller-bearing boxes and rods. Do not conflate the machine resistance with the mass of the engine and tender being added to the Davis formula.
Picking one test point from the PRR T1 test report (400 RPM/20% Cutoff), the locomotive produced 6442 IHP and 5829 HP at the drivers. So, 613 HP due to machine resistance alone at 95 mph. Johnson's MR estimate (20 lbs/ton of driver weight), would work out to 679 HP. So, a 10% savings in MR over Johnson's rule-of-thumb figure. I can't get my head around that much power being consumed in machine friction. Seems insanely high, as if some components would have to be glowing cherry red to dissipate that much power (457,300 watts!) continuously. I've always wondered if IHP figures were significantly overstated. Doesn't seem hard to believe when you look at how squirelly indicator diagrams look at high test speeds. Johnson himself speaks to indicated horsepower measurements having increasing excess error as speed increases. IHP was a sales tool, I think, so errors probably didn't really matter.
sgriggsI can't get my head around that much power being consumed in machine friction. Seems insanely high, as if some components would have to be glowing cherry red to dissipate that much power
I look forward to seeing how effectively reversible active compression control (following what Jay Carter did with steam automobiles) might relieve the practical effects of insanely high spot compression near FDC/BDC. To my knowledge there is no accounting for nucleate condensation (as opposed to wall condensation) in the ihp calculations, despite the fact that work extracted from cylinder contents has to result in cooling through the steam mass -- this is one of the important purposes of sufficient late superheat, but that promptly rises to bite your butt at exhaust release if you don't have really, really good exhaust arrangements...
Railway Age Gazette for 11 March 1910 p513 says a Mallet "will not drift down a 1 per cent grade." Then in the 15 Apr issue p997 it says GN towed some 2-6+6-2s with electrics and found the Mallet rolling resistance (speed unspecified) averaged 11885 lb. (Engine plus tender weighed 250 tons.)
Overmod sgriggs I can't get my head around that much power being consumed in machine friction. Seems insanely high, as if some components would have to be glowing cherry red to dissipate that much power Personally, I think some of it is in compression; at least one person thinks it is related to steam leakage at the poppet valves, perhaps partly related to uncontrolled valve bounce (I disagree in principle but can't prove it; it may take full-scale experience on 5550 to confirm or deny sufficiently). I look forward to seeing how effectively reversible active compression control (following what Jay Carter did with steam automobiles) might relieve the practical effects of insanely high spot compression near FDC/BDC. To my knowledge there is no accounting for nucleate condensation (as opposed to wall condensation) in the ihp calculations, despite the fact that work extracted from cylinder contents has to result in cooling through the steam mass -- this is one of the important purposes of sufficient late superheat, but that promptly rises to bite your butt at exhaust release if you don't have really, really good exhaust arrangements...
sgriggs I can't get my head around that much power being consumed in machine friction. Seems insanely high, as if some components would have to be glowing cherry red to dissipate that much power
Personally, I think some of it is in compression; at least one person thinks it is related to steam leakage at the poppet valves, perhaps partly related to uncontrolled valve bounce (I disagree in principle but can't prove it; it may take full-scale experience on 5550 to confirm or deny sufficiently).
The high apparent MR in the T1 example is not an anomaly specific to poppet valve locomotives. There is a large difference between IHP and DBHP on the NYC Niagara (6600 IHP - 4600 DBHP) at 85mph. Obviously, much of this can be attributed to air resistance and rolling resistance of the tender and locomotive non-drive wheels, but those can be estimated from Davis and accepted aero formulas and what's left over (Machine Resistance) still seems quite high (836 HP, by my calculation). The Johnson MR formula predicts 623 HP at 85mph for the Niagara.
The same can be said of the PRR Q2 duplex, which recorded 7987 IHP (highest ever measured, to my knowledge) and 6782 HP at the drivers on the Altoona plant. That is a whopping 1205 HP of just Machine Resistance at 57mph! Johnson's MR for this locomotive is 587 HP at 57mph. Maybe the drivers were slipping?
My conclusion has been that quoted IHP readings may not be accurate measures. R.P. Johnson discusses difficulties measuring IHP on page 353 of his book, and table XLVII shows that the excess of IHP could be as much as 14-17% at higher engine speeds (269 - 296 RPM). Such overstatement of IHP would appear as high machine friction when the difference between IHP and Drawbar or wheel rim HP is resolved into its components.
In all these cases, it obviously isn't "machine friction" of the usual kinds or, as you say, you'd be seeing it as heat.
Meanwhile, remember Chapelon noting that the only reason roller-bearing rods can possibly work is if they are laterally bending dramatically. (That is inherently in the "correct" alloy and fabrication procedure for modern lightweight rods, e.g. with cerium steel...)
It would be relatively very easy to assess most true 'machine friction' on something like the PRR test plant as improved, if you can motor the rollers and measure any slippage or 'jump' between wheeltread and roller (the contact patch being imho fairly dramatically smaller). I remember seeing estimates or figures for the T1 being somewhere in the 96 to 98% range, which implies that a very small amount of interference or 'stiction' or whatever would be producing higher overall machine resistance if it is coming from 'mechanism' somewhere. Which leaves steam-cycle issues as the place the 'cylinder horsepower' is going -- and when you look at compression alone, I think you're finding effects of sufficient magnitude to account for the 'missing power', with flow between port and exhaust tract after release being the 'next' source of lower actual expansion thrust.
I argued that proper calorimetry would reveal if the valves were actually bouncing or leaking to any significant degree; we now have test procedures using several different disciplines that could actually visualize the effects at high cyclic, as well as flow patterns at unshrouding, and in the non-flow-optimized tracts close to the ports, in the Franklin A and B-2 systems. But I'm not really expecting to find showstopping issues, either leakage or shock stall, at properly debounced valves, and there are methods (including those proposed to be tried in 1948) that should cure most of the issues for any high-speed cutoff that produces the necessary cylinder thrust for high speed. (I'm predicting that will be a duration corresponding to just over 40% but with timing and careful reversible-compression management for 5550)
There is another potential issue, related to high mass flow and excessive superheat at high cyclic. I would not be surprised to find that the actual mass flow of steam at very high demand but short cutoff induces substantial shocks in the starting-and-stopping flow, and these shocks might easily either throttle or wire-draw the actual steam getting into the cylinders under 'assumed steady-state' steam-supply conditions. This is one of the reasons I went to very large effective steam-chest 'reserve' volume combined with valves that rotated and reciprocated to increase the effect of long-lap long-travel fast port opening and closing -- but I have not modeled the result at all exhaustively.
IHP is not, and never will be, more than a theoretical estimate -- and not a particularly good one considering the non-ideal-gas nature of that female dog-goddess steam. The catch is to get rid of all the places you can where the steam gets to act out ... and then see where your losses are actually coming from, and which of them are cost-effectively addressable.
timz Railway Age Gazette for 11 March 1910 p513 says a Mallet "will not drift down a 1 per cent grade." Then in the 15 Apr issue p997 it says GN towed some 2-6+6-2s with electrics and found the Mallet rolling resistance (speed unspecified) averaged 11885 lb. (Engine plus tender weighed 250 tons.)
Drifting probably depends on reverser and throttle settings (Wardale has a favorite mode of drifting with neutral reversal and a little throttle of steam to keep from aspirating smokebox gases). This in turn may involve compression and other effects Overmod mentioned?
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