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Ultra-pressure engine efficiency

Posted by Tim Nye 
Ultra-pressure engine efficiency
January 21, 2015 09:23PM
I've been pencilling some numbers and getting a surprising answer for estimated efficiency for a hypothetical engine running at near supercritical pressure. Maybe other eyes might find if I'm doing something wrong.

The example engine is a uniflow of 2" bore and 2" stroke. A spreadsheet is attached with calculations if anyone wants to play with it. It has the X-Steam IFS97 steam table functions added in as math functions.

The other inputs are:
Clearamce 3.0%
Cutoff 5.0%
Release 82.0%

Admission Pressure 3200 psia
Admission Temp 1200 deg F
Exhaust Pressure 20 psia
(saturated exhaust)
Expansion coeff 1.2
Compression coeff 1.3

(Some of you probably see where this example comes from.)

So, the calculation approach is calculating the corner points on an ideal indicator diagram. The summary results are:

(1) At Cutoff
Volume 0.5027 in^3
Steam mass 0.000978135 lb
Spec. Enthalpy, h 1598.7 BTU/lb
Enthalpy H 1.567 BTU

(2) At Release
Volume 5.3407 in^3
Pressure 187.7 psia
Spec. Enthalpy, h 1300.1 BTU/lb
Enthalpy H 1.274 BTU
Temperature 555 deg F

(3) At Exhaust Close
Pressure 20 psia
Mass 0.000151587 lb
Spec. Enthalpy, h 1155.9 BTU/lb
Enthalpy H 0.176 BTU
Temperature 227 deg F

(4) At End of Compression
Pressure 1545.3 psia
Mass 0.000151587 lb
Spec. Enthalpy, h 1737.3 BTU/lb
Enthalpy H 0.264 BTU
Temperature 1420 deg F

(5) Steam Mass Entering at Admission
Admitted mass 0.000826548 lb
Spec. Enthalpy, h 1573.2 BTU/lb
Enthalpy H 1.303 BTU

The last bit, admitted mass, comes from a circular calculation that mixes the compressed steam mass and enthalpy with the admitted steam mass and enthalpy and iterates to get the mixture proportion to fill the cutoff volume at the admission pressure. (The mixed steam at cutoff is a little hotter, as can be seen from the specific enthalpies.)

The pressures I got seem very close to those estimated by George Nutz.

The suspense is just about over. Here's the efficiency estimate:

Expansion work 1.567 - 1.274 = 0.293 BTU
Compression work 0.264 - 0.176 = 0.088 BTU

Net work 0.293 - 0.088 = 0.204 BTU

Admitted steam energy 1.303 BTU

Thermal efficiency = 15.68%

For comparison, I'm looking at the results of an analysis by Jerry Peoples also based on constructing an ideal indicator diagram. His example was a high-compression uniflow engine operating on steam of 1000 psi and 1000F. His result was 22.8% thermal efficiency, after subtracting engine friction, pump and blower work.

I've got to think about this some more, but it looks like the practical problem with getting efficiency out of ultra high pressures is to be able to make the cutoff short enough. Even at 5%, this engine exhausts at 188 psia and 555F, which is wasting a lot of energy.

5% cutoff is about 18 degrees of crankshaft rotation. At 3600 rpm, that's 0.84 milliseconds to open and close the admission valve. A gas engine with a 280 degree duration cam profile would have to turn 27,700 rpm to operate valves that fast. It's not physically likely a valvetrain could be made that could give less cutoff.

So, it looks to me like such pressures are just not practical for reciprocating engines. Is ultra pressure operation a dead end, or am I missing something here?

Let the flames begin!

open | download - Ultra pressure engine efficiency calcs.xlsm (223.4 KB)
Re: Ultra-pressure engine efficiency
January 21, 2015 11:54PM
Hey Tim,

Uhhh. . . a few things. . .

Firstly, the purely theoretical exponent of expansion is determined, generally speaking, by dividing the specific isobaric heat capacity by the specific isochoric heat capacity. Which for 3,200 psia and 1,200 F is 1.404.

Secondly, to get anywhere near the reality of the exponent in a real engine one needs to add at least a .1 if not a .2 to the exponent, depending on cylinder size, temperature differential and what not.

Thirdly, the exponent isn't figured until AFTER the steam is cut off. Until then it isn't a factor, for a purely theoretical diagram completely discluding valve flow losses and other factors.

Fourthly, the "work" performed by the cylinder isn't computed by the drop in the energy held in the steam, instead it is by the mean effective pressure during the stroke, which your spreadsheet doesn't apply.

Thusly, your spreadsheet is showing an INCREASE in efficiency with an INCREASE in the exponent of expansion, which is the opposite of what it should be showing.

Fifthly, take a look at the pressure left at the end of the power stroke in IC engines sometime, people make WAY too big of a deal about underexpansion around here. There once was an automobile with an internal combustion engine that ran compound! It was three cylinders, the outside two running with the four stroke Otto cycle and the middle one, larger then the outside ones running "two stroke" . It failed to get superior road economy as compared to the other cars.

Sixthly, the most efficient(legitimate and independently tested) dyno results I have seen for steam powered reciprocating piston engines were from pressures WELL under 1,000 psi, most all of them under 500 psi, exhausting to a hard vacuum. . . and of large cylinder size. They were superior to what. . . people. . . have been claiming to have achieved.

Seventhly, nothing under 1/8 cutoff has ever been proven to exhibit superior economy to 1/8 cutoff in a single cylinder, single expansion engine in an automobile size.

"So, it looks to me like such pressures are just not practical for reciprocating engines. Is ultra pressure operation a dead end, or am I missing something here?"

My own opinion is that using ultra pressure operation in hopes of superior economy is less of a dead end and more of a lively jaunt down suicide alley.

Caleb Ramsby
Re: Ultra-pressure engine efficiency
January 22, 2015 12:25AM

A word of advice.

Keep George Nutz's calculations out of this. The work he put into making them has nothing to do with how they are being perverted and abused.

Note that he made them back in 2005.

I reverse engineered Nutz's diagram by measuring the mep from the card he drew and the displacement and found roughly 5.88 lbs per hp hr from the pure ideal no losses standpoint. There is nothing wrong with his math. It being portrayed to portend to things that it does not by various other people is a BIG deal and only scum would do such things.

I am not referring to you Tim, but to others and they know exactly who and what they are. Take careful notice that there is another name at the top of the billing on that diagram.

Caleb Ramsby
Re: Ultra-pressure engine efficiency
January 22, 2015 12:41AM
I've been thinking about this, and I also read up on some experimental high pressure locomotives, and it seems to me that eficiency is related to the temperature of the steam. Higher pressure just makes your expander smaller

Re: Ultra-pressure engine efficiency
January 22, 2015 03:12PM
Well, first things first. Assuming moderately high rpm and an engine of any decent size, the acceleration a 5% cutoff imposes on the valve train is unsupportable in an engine expected to exhibit durability comparable to IC competitors. Figure 450 gees for pushrod engines and 700 for overhead cam---if you are interested in a product and not a racing engine.

Using my own eccentric means of calculation I come up with a polynomial coefficient of expansion that is 1.284 and a coefficient of compression that is 1.294; both of these values assuming isentropic expansion and compression.

At release I calculate a pressure of 132 PSI and temperature 348 F and a compression pressure is 2519 PSI. My overall MEP is 445.5 PSI and at 3000 rpm I make the output to be 21.2 HP. Assuming feed water at 20 PSI and 150F the theoretical thermal efficiency of the engine comes out to 22.9%. After taking into account indicator rounding & engine mechanical efficiency (let's call it 80%), boiler efficiency (85%) and auxiliary loads (10%) my rough estimate is about 13 to 15% overall efficiency.

Obviously, the high release pressure accounts a lot of potential lost work although perhaps some of that can be recovered through regeneration.

I hope the above descriptions made it clear that I am not a thermodynamicist and possibly the methodology may be a bit off the beaten track.

None of this gives me any hope that a supercritical engine will be challenging the Otto cycle engine any time soon, let alone the Diesel. But I'm wrong an awful lot.

Re: Ultra-pressure engine efficiency
January 22, 2015 03:51PM
Hey Ken,

Using a straight and consistent coefficient of expansion or compression is prone to error. Such as is shown in the indicator diagrams taken for the article in this bulletin:


They found that for compression the initial coefficient was 1.65 when the steam was cooler then the cylinder wall, then as the steam got hotter then the wall it dropped to 1.07. They didn't go into the same analysis of the expansion, but looking at the logarithmic chart they made of the card, even with the long cutoff, there are two distinct and different exponents of expansion. A larger one initially when the steam is hotter then the walls and a smaller one when the opposite is true during the latter part of expansion.

This effect is more pronounced with smaller cylinders/strokes and shorter cutoffs.

Quantifying steam thermaldynamics from an ideal standpoint to that of an actual engine is an "Enter at your own risk" deal.

As far as efficiency goes, the peak efficiency of Otto, Diesel or steam engines on the road is much less relevant, from my analysis, then the full "cycle" of cold starting, low speed low load, idling at stop lights and signs, accelerating and high speed cruising. Roughly, the peak efficiency of IC engines is found at 80% of max load at the rpm which gives the peak of the torque curve, exactly how often is that encountered on the road?

Although I don't think that equaling peak IC efficiency is something that the light steam engine is likely to do in a road vehicle, I believe that one which is properly designed and proportioned will be capable of equaling the "full cycle" MPG of IC vehicles.

Efficiency isn't everything though. If it were then every car in America would be running with a diesel under the hood. . . what percent of Chevy cars use the diesel?

Caleb Ramsby
Re: Ultra-pressure engine efficiency
January 22, 2015 04:18PM
Ken, a suggestion for calculations is to adjust the figurin' so that for the expansion that big number is used until the calculated steam temp goes bellow the average cylinder temp, the little engine in the article I linked to was around 500 F, then bellow that temp the exponent would be the small number. Then do the opposite with the compression cycle and use the big number until the steam temp rose above the cylinder temp and switch to the small number after that.

If nothing else, it would at least pump out data that is different then normally seen from ideal or hypothetical analysis.

Caleb Ramsby
Re: Ultra-pressure engine efficiency
January 22, 2015 04:59PM
Hi Caleb,

My process is to assume we know the steam density and entropy at cutoff. Entropy should be basically constant throughout the stroke (until release) if the process is basically isentropic; calculating density at any point is a simple algebraic solution knowing the change in volume and initial density. This gives me two variables. Then I employ a function in those steam tables you posted that finds density based on pressure and entropy. Ok, I really want to know the pressure since I already know the density, so I have Excel use the Goal Seek function to find the pressure that produces a density equal to that known to exist due to expansion in a sealed container. I do this for about 100 points of expansion and compression throughout the stroke. Actually, I am far too lazy to punch all those keys so I did it once and recorded it as a macro, then I went into visual basic and copied the line and placed it in an Excel sheet. Using a concatenation I can produce the macro for 100 iterations of the operation. This should give a nice curve describing an isentropic expansion.

I can get polynomial coefficients by using Goal Seek again. I have one cell into which the coefficient is entered and this is used to calculate a pressure in a cell adjacent to every pressure derived from the entropy and density. A cell adjacent to the polynomial coefficient contains the sum of least squares for the differences between the 100 Goal Seek and polynomial derived pressures. Goal Seek is then instructed to find the polynomial coefficient that produces a sum of least squares between the two data sets that equals zero.

Actually, I don't really need the polynomial coefficient but it provides a check on the other calculations. Despite all the brute force number crunching the process delivers polynomials that closely agree with other sources.

Re: Ultra-pressure engine efficiency
January 22, 2015 05:30PM
Hey Ken,

"Entropy should be basically constant throughout the stroke (until release) if the process is basically isentropic;"

It isn't, there is significant heat transfer and variably so, as I referenced in my post. Thusly the requirement for a variable polytropic exponent of expansion and compression. Averaging the variable polytropic exponent isn't effective either since the effects of each stage are not equal and opposite.

I remember your simulation, sounds like you have improved it a bit, it does what it does how it does it rather well. However, using a set entropy to dictate the polytropic exponent is prone to error since it is not an isentropic process.

The way your program is laid out it sounds like you could have the entropy adjusted in relation to the steam temp and cylinder temp, it lowering during initial expansion and then rising during later expansion, then rising during initial compression and lowering during later compression.

Have it graph out the variance in the polytropic exponent that it calculates then adjust the hand input "step of entropy change per step of calculation" until the polytropic exponents give the 1.65 and 1.07 for the compression side, less aggressive numbers for long cutoff expansion side, probably similar for high expansion rates.

Have fun!

Caleb Ramsby
Re: Ultra-pressure engine efficiency
January 22, 2015 07:24PM

Yeah, superheat has a massive influence on efficiency. It is all about balance though.

As has been shown by Ted Pritchard's work using superheat temps bellow 650 - 700 F results in a significant drop in efficiency. As has been shown by the SES research, which I have linked to about a thousand times on this forum, going much above 800 F or so doesn't result in much improvement.

The above has also been reported by numerous Stanley owners.

The exact temp F is less important then the degrees of superheat above saturation temperature.

With the higher temperature superheat the heat transfer rate from the steam to the cylinder is greater because of the greater temperature differentials involved. With the small engines one simply can't get the heads really hot without TONS of heat transferring down the walls towards the cold end. So the extra btu put into the steam at the boiler are countered by extra btus being transferred to the cylinder. Which results in minimal if any efficiency improvements over the "moderate" superheat temperatures.

The same is true for short cutoffs. With a cutoff shorter then 1/8 or 1/6 stroke around there, the portion of the cylinder that is being exposed to "live" full temp steam is reduces. This reduces the overall cylinder temp and increases the transfer to the cold end. The effect is a greater polytropic exponent of expansion for the earlier cutoffs and a delayed crossover point to the lower polytropic of expansion. The aggregate effect is to have a pressure drop in the cylinder during expansion that is so great that it kills the capacity for efficiency.

This is one of the main arguments for compound expansion, one uses a later cutoff in the cylinders so one can achieve larger expansion ratios with "less" heat loss. The "less" is in quotes because during a cold start the mass of metal that must be heated up to operating temperature by the live steam is much greater and there are other operational issues with a road vehicle.

There is one way to avoid all of the above issues and that is to invent a video game where the steam engine can drive a car using only ideal and loss less principles, otherwise avoiding or ignoring the above mentioned issues will just delay disappointment and failure.

Caleb Ramsby
Re: Ultra-pressure engine efficiency
January 22, 2015 09:12PM
Hi guys,

Lots of good discussion here.

OK, for the polytropic exponents, I've got my suspicions about the results shown in that old Steam Automobile article. The reason I say that is because the original report that discussed this method of finding the exponent from indicator diagrams, "A new analysis of the cylinder performance of reciprocating engines" at [www.ideals.illinois.edu] has many log-log indicator diagrams worked out, and the only ones that show a slope break in the expansion and compression lines are where significant leakage occurs.

The engines in those tests had quite a lot of "missing quantity", so a lot of condensing and evaporating was going on in them during the cycles, but the slopes were quite constant.

On superheated steam their tests showed an expansion exponent of 0.90 to 1.23.

Out of curiousity I worked out the specific entropy vs piston stroke during expansion for different values of the polytropic exponent. Hopefully, here's the plot:

If n = 1.4, entropy decreases, which means considerable heat would be leaving the steam.

At n = 1.3, entropy is about constant, so isentropic expansion.

For n = 1.1 and 1.2, entropy increases, which could be interpreted to represent some of the losses in the expansion.

In any event, it looks like there's a research opportunity to develop a method of predicting what the exponent will be for a given engine under given operating conditions.

Here are the pressures plotted:

The work per cycle calculated 3 ways gives:
1) from MEP, piston area and stroke: 3440 in-lb
2) from integrating the area on the graph: 3424 in-lb
3) using the polytropic work function (p2V2 - p1V1)/(1-n): 3420 in-lb

And, using the differences in enthalpies (my post yesterday), 1907 in-lb. From an energy balance, enthalpy loss is supposed to equal the work output, but I haven't found the mistake in my calculation yet.
Re: Ultra-pressure engine efficiency
January 22, 2015 10:36PM
Hey Tim,

As regards to the loco indicators you referenced, they are using relatively long cutoff, low temp steam and have a big volume as compared to surface area, all of those aspects, as I mentioned above, tend to blend the "hitch" in the exponent line. As does valve/piston leakage.

The test engine in the SACA article was very small and the number I quoted were from the uniflow compression which could be looked at in reverse as a short cutoff, since the same would happen, but in reverse. Plus it being a test engine, they are almost always tight, which would tend to exaggerate the "hitch" .

This further points out the vast chasm between small and large engines, long and short cutoffs and high and low superheat temps.

The mistake wasn't in your "calculation" or equation, it was in the principle or theory. As I pointed out last night, thermal heat loss does not equal mechanical energy transmitted. Look at it this way, an initial steam condition that "thermally" dictates a larger polytropic exponent means that the pressure will be dropping faster then one with initial steam conditions that have a smaller exponent, this means that the MEP to initial pressure ratio for higher exponents will be lower and the MEP to initial pressure of lower exponents will be higher.

With the program as it was last night, it figuring the mechanical work via the thermal loss, a greater thermal loss was giving a greater mechanical work output.

The easiest way of doing it is to calculate the mechanical work done by the MEP and divide that by the energy in the steam at cutoff, that will give the work per heat energy.

Caleb Ramsby
Re: Ultra-pressure engine efficiency
January 22, 2015 11:21PM
Hi Caleb,

I don't really buy those indicator diagrams either. For one thing, I'm not seeing steam temperatures displayed in the article, which is a HUGE red flag to me. Thermal conductivity is low when your steam is highly superheated and it declines slowly until you hit the condensation line, at which point it goes up as the steam quality drops. If you start out with steam that is highly enough superheated to avoid the condensation line altogether, the heat transfer with the cylinder wall is far less.

Another issue that isn't being described is the thermal conductivity of the cylinder head, walls and piston crown. If the head and walls are well lagged, the amount of escaping heat is minimal and the material tends to approximate the steam temperature more closely, especially in a high compression uniflow. Likewise, if lubricant plays against the bottom of the piston or other mechanisms promote heat loss through the piston crown, we are going to see vastly different results.

Since we know nothing about the condensation line on the engine in the article nor about its propensity to retain or shed heat, I can't see how we can extend the specific observations into a general rule.


Re: Ultra-pressure engine efficiency
January 23, 2015 02:38AM
Hey Ken,

As I stated the numbers I quoted from the article are for compression, where there is no superheat.

As I also stated expansion will be different, although I didn't emphasize that as much as I should have.

You need to look a bit closer, that is part two of a three part article. In the first part they show the heavily lagged cylinders. In part three they show the temperatures of the different parts of the engine, with the inlet temp shown to be 611 F.

The pressure used for the log analysis was 200 psia steam chest, using 600 F that is roughly 220 F of superheat, rather far removed from saturation temps. Look carefully at the indicator diagram and the temp chart in the third part of the article, effectively, there is no part of the cylinder that is bellow the saturation temperature of steam at 200 psia!

I wonder how the indicator cards from that article compare to the indicator cards taken from live steam and metal ones made by Williams and Cyclone? cough, cough

One thing I should point out, since people don't seem to be noticing things, is that the engine is running to a vacuum, seeing 5 psia or so at the exhaust ports. This would of course lower the compression pressure and temperature.

I must admit though, it is one of the least organized and poorly laid out articles I have seen in relation to the potential value of the data.

I can't help but laugh a little, you guys are making it out like this is the only engine tested in history that is showing results unique to the specificity of its design, bashing it for not being the same as the big locos or what one thinks high re-compression uniflows should look like is just too much, take it for what it is, because that's what it is.

What I found interesting, about 6 years ago or, probably longer then that, was comparing the data from this article to that of the MIT test on the Stanley, the one "regarding superheat" , the two engines are both small and were run at roughly the same temperature and superheat.

Whatever the case, I will always defer to steam and metal results, regardless of how "weird" they may seem to me or how difficult they are to quantify because of uncommon inlet conditions etc. , they were what that engine got under those conditions and there isn't any changing that, always defer to them over what theory "dictates" and especially over what some companies have claimed to gotten on their "steam and metal" dyno until I see the actual full results. Always modify the theory to fit the result instead of vica-versa. That is exactly what the late Professor Hall did with his engine simulation, he compared its output to known data from tests, then conducted his own dyno tests and always modified his simulations theory to replicate the known real world results.

These intricate aspects of engines are exactly why the old school was to apply a given card factor for a given type of engine with given steam conditions under given operating conditions. The big issue here is that industrial standards of that day were not to use extremely high pressures and temperatures with reciprocating engines, that was what turbines were for, so there are no proven card factors to go off of for the extreme steam conditions that so many people are adamant about. Especially none for engine the size we are dealing with, nor the extreme compression pressures you are talking about. I like card factors when they are used for the conditions they were made for, that is, well that's what they were made for.

In totality, if I could go back and not have posted my first reply to Tim's original reply and just left it alone, that is exactly what I would do. This is absolutely pointless.

Caleb Ramsby

Edited 1 time(s). Last edit at 01/23/2015 02:39AM by Caleb Ramsby.
Re: Ultra-pressure engine efficiency
January 23, 2015 09:34AM
At what pressure does an engine design become unpractical? I suspect a 3200 psi engine cannot be of the crank-conrod-piston variety. You need a really small piston to keep torque sane, but big conrods and crank. Seems mutually exclusive
Re: Ultra-pressure engine efficiency
January 23, 2015 12:31PM

In my simulations, I have found that as pressure and temperature increases , mpg increases at a decreasing rate. By the time you get to a level superior to ICE, those pressures and temperatures are too high to be feasible. Jerry
Re: Ultra-pressure engine efficiency
January 23, 2015 01:07PM
congratulations on your analysis and chosing coefficients of expansion and compression close to what I consider realistic.
You have left out the work of constant pressure admission, and much like a hydraulic cylinder much work is done by constant pressure
admission. My short formulae is p x v x 7.3 x10 to the minus 5th power wich for your pressure and specific volume is .1174
horsepower per pound per hour. or another 298 BTU/#/hr of work done . Add this to your net work and you might find the thermal efficiency approaching 30 theoretical %. I believe in your fractional method this would add ..2468 BTU or a theoretical(no losses) efficiency of 34%.
. Also in considering coefficients for "k" take a small increment of expansion for 1 pound of steam and compare its enthalpy drop to the small increment of PdV on the theoretical indicator diagram--the work done by each should be very close. This should be done with coefficients that do not give a reducing entropy, the entropy will always increase slightly as steam is an imperfect gas.
So many in the steam community are fascinated by achieving a very low steam rate per horsepower but more importantly it is the heat rate
that is most important. I believe Stumpfs engine had a heat rate of 144BTU/Min per HP-HR and that would be a dyno output efficiency of
29.4% using 461psi at 1018F with a steam rate of 5.67#/HP-Hr. Also consider that the brilliant Williams engine on the dyno using 1000F/1000psi steam had a dyno efficiency of about 30%.
I would agree that ultra high pressure does not necessarily lead a path, especially an easy path, to higher efficiency. You have correctly pointed out that going to higher temperatures involves exhausting steam at a higher temperature/enthalpy and we do in consideration of an automobile always have a condensing problem. It would be wonderful if someone
made an efficient variable pressure engine from 200-600psi on the road that could maintain a fairly consistent heat rate and not go to hell at lower pressures. As an example the Doble "F" engine had a steam rate of about11# at higher pressures but at below 400psi on the high pressure side ended up with a steam rate higher then the rare 2CYL DA Doble simple that had a steam rate of 14#/hp with 375psi pressure.
Excuse my old calculations as they are done by hand the old fashioned way and not with the mindless benefit of unknown computer programs written by whomever that at the press of a button do what takes me hours to compute. I do not trust unknown computer programs as I have fought with a few that proved to not include all the parameters that mattered.
Good luck to you younger and more modern guys.
Re: Ultra-pressure engine efficiency
January 23, 2015 03:13PM
Ted Pritchard experimented with the uniflow, poppet valved engine. Using steam temps of over 900 F.

His take on the exponent can be read here:


He states in it that the lowest exponent that will be close to what actually happens in these small engines is 1.3 and then says "The actual engine however is going to show lower efficiency figures"

Here is why this is pointless, back then, 1981, he got shit all over by people for using factors that were "too conservative" stating that "higher pressure, temperature and speed will show better results". He got shit all over because he was adjusting his theory and calculation to fit what he found by running actual automobile sized engines.

The big factor here in regards to the exponent is just how big of a balance is used on the card factor side, essentially using a lower exponent and a lower card factor will balance each other out and give similar btu efficiency results, so it is potentially a mute point. More so it is the difference between trying to get an accurate "actual" efficiency result from the calculations by adjusting the exponent of expansion or adjusting the card factor. The proven method being to use lower exponent numbers and heavy card factors.

As George so correctly pointed out, it isn't a lower lbs per hp hr rate in and of itself that makes for a more efficient engine, for some there is so much heat jammed into the steam that the heat balance isn't greatly improved, it is the % of energy extracted from the steam.

I would also like to point out in reference to the temperature of the cylinder from my earlier post, there is a well known and documented "skin" effect with steam engines where a very thin layer of metal on the inside of the cylinder is fluctuating rapidly with the steam temp. This is shown with graphs, etc. in Stumpfs book on uniflows.

Caleb Ramsby
Re: Ultra-pressure engine efficiency
January 23, 2015 03:55PM

Kent's Mechanical Engineers' Handbook, twelfth edition, circa 1950, Volume 2 "Power" states on page 5-02

"Isentropic change, no heat added or subtracted:

PVk = constant

k = specific heat at constant pressure / specific heat at constant volume"

Here is a graph I whipped up using that formula.

Steam however, as had been pointed out, is not a perfect gas.

Caleb Ramsby

Re: Ultra-pressure engine efficiency
January 23, 2015 04:43PM
George isn't the only one who distrusts unknown and mysterious computer programs, especially the ones trying to use bizarre words and math equations.
And as far as ultra high super critical pressure being the singular cure to getting a low water rate, he is right as hell again. There are far too many other places to conserve the heat losses and recover the otherwise wasted heat and return it back into the cycle to say that super steam conditions are the one and only dream du jour that goes into making a good steam car.
Consider the whoopee car buyer, do you think fuel mileage really matters? It s the pleasure and fun of driving such a car along with oneupmanship at the Club that matters.

What some people forget while getting their knickers all tied in knots, is just who actually ran any reciprocating steam engine at 3200 psi and some 1200-1400• F and at some very high rpm? Has anyone actually witnessed such a demonstration and has it been verified by reputable outside people? The answer is NO. What we have been told is wishful dreaming, ego and massive self delusion of non existaant expertise.
This fascination with ultra high pressure in itself does not produce a workable engine, especially some uniflow that would demand an insane short cutoff like 5% or less. The valve gear would self destruct, especially at the dubious high rpm claimed. The ring leakage at slow speeds would be horrible to even think about.
The same goes with this pixilation of over compression and exhausting below the actual condensation point. No reputable designer would be so dumb as to let this happen with some ridiculous expansion rate in just the one uniflow cylinder.

What's wrong with staying with what we all know can work, 1200-2000 psi and 900-1,000• F at the engine and concentrate on improving the rest of the system to minimize losses.
Some illusionary high fuel mileage is just not in the cards. The marvelous attributes steam brings to the automobile is certainly enough of a reward in itself.


Edited 2 time(s). Last edit at 01/23/2015 04:51PM by Jim Crank.
Re: Ultra-pressure engine efficiency
January 23, 2015 05:14PM
Chart for 1,200 psia with 900 F and 1,000 F.

Re: Ultra-pressure engine efficiency
January 23, 2015 05:29PM
If you are going to go to the trouble of building something that can handle supercritical water at 3200psi, wouldn't it make more sense to build a Malone Cycle machine (see attached PNAS-1981-Allen-31-5.pdf) that has no heat of evaporation loss? Just wondering.


Edited 1 time(s). Last edit at 01/23/2015 05:47PM by dullfig.
Re: Ultra-pressure engine efficiency
January 23, 2015 08:55PM
Boy, I figured I'd get a conversation going. There are a lot of great points being made, and just what I was hoping for. OK, I was probably a little provacative in the engine I used as an example... smileys with beer

Caleb, I see you've got a lot of passion for light steam power. That's a great thing. I'm here to learn, and I think we've got a great forum (or phorum) going.

A little further in that Ted Pritchard article he says:

"Unfortunately the lack of precision in predicting
steam engine efficiency, particularly with small engines,
has led to the downfall of a number of steam projects
since the Second World War. Several examples of such
projects follow this section, including one from the
Ricardo Company itself."

"There is little understanding of what goes on in the
steam cylinder and little published data on the subject."

I'd say this is pretty much still the case now. If Ted thought had thought n = 1.3 was the answer, he probably just would have said so. So, the question is, what do we do? My thinking is that the polytropic process is a pretty good place to start. What's going on with condensation and evaporation needs to be investigated and a better model incorporating these effects needs to be developed. But that's a longer term goal.

For particular exponent values, we need to understand where data is coming from. In the Kent's Handbook that says the exponent is the ratio of the specific heats, I'll bet a little earlier it says that's based on the ideal gas assumption. Steam (at least at our pressures and temperatures) isn't quite an ideal gas.

That engine test article from Steam Automobile gives a log-log indicator chart that shows two slopes on the compression line. Their data acquisition system didn't measure piston position. They used a "high speed rotary potentiometer" on the crankshaft. The oscilloscope image seems to show that the potentiometer gave a peak voltage at TDC and a minimum at BDC. It looks like the potentiometer would be two parallel linear resistor tracks powered at 0 degrees and grounded at 180 degrees, with the wiper picking up a linearly decreasing then increasing voltage with angle.

So, was the horizontal axis of their indicator diagram based on crank angle rather than piston position? Here's two log-log plots of the indicator graph I posted yesterday:

The one plotted on crank angle shows a definite decrease in slope of the compression line on the return stroke.

The article didn't say anything about converting indicator plots from crank angle to cylinder volume, and it would have been a tedious job with slide rules. They were also challenged by taking measurements off Polaroids of the oscilloscope screen. I suspect that if the potentiometer zero was off TDC a little, it would also distort the diagram, but I'll have to experiment with this later.

Most of the Clayton tests were run on a Corliss engine, not a locomotive. Tests were done up to 132 psig and 500F steam temperature, so like the little engine, they had plenty of superheat. Now for losses due to condensation and evaporation, would they be more likely in a small uniflow engine running at high speed, or a big counterflow engine running at low speed? I think that the counterflow engine would be more likely to show changes in the slope of the expansion curve, but that wasn't what they found.

Unfortunately we're not able to ask Ted Pritchard to clarify his remarks, but here's something that comes to mind. He said about n = 1.15:

"This may be excellent for the purpose of power and
stress estimates."

"However, estimates for efficiency of the theoretical
cycle based on this diagram will be ever-optimistic as
compared even to the theoretical cycle with adiabatic
expansion and compression of the steam."

I suspect the efficiency error is due to the "missing quantity", which probably all condenses during admission. The steam that's still vapor goes through a polytropic expansion, pushing on the piston and producing power according to the indicator diagram. The diagram, however, doesn't show the liquid water, which still costs boiler fuel that isn't represented in the diagram. His raising the exponent may have been an approximation to better estimate the efficiency.

Ultimately, though, we've got no limits to opportunity to play with steam engines!

Re: Ultra-pressure engine efficiency
January 23, 2015 09:44PM
Dear Jerry,

I may have to start by saying you're the one who got me thinking along these lines. I'd like to compliment you on some of the analyses you've done. Your development of models that show important insights into how various factors affect engine performance is an impressive achievement.

Off hand, it seems to me that a model that showed the efficiency trends with temperature and pressure also optimized the cutoff for each operating point. Am I remembering that correctly? Higher pressures lead to shorter optimal cutoffs?

I'll do a little numerical example here to illustrate a practical issue I came across. Ken with his engine model worked out an ideal 21 hp per cylinder at 3000 rpm. With six cylinders at 3600 rpm that would be about 150 hp, and applying an 80% card factor and subtracting 20 hp for parasitic losses brings that down to about 100 hp net. My model comes out with 120 hp net.

So let's say this engine is powering our sedan on the highway, and we only need 20 hp. (Or, in the case of Ken's car, a tightly wound rubber band.) If the steam generator is still operating at 3200 psi, we need to shorten the cutoff. But here's what I get:

Cutoff____MEP_____Net HP__Crank Angle__Time (ms)

With such high supply pressure, you simply can't get the MEP down. Here's what the 1% diagram looks like:

Of course this diagram could never come off a real engine, but bear with me.

The crank angle at cutoff assumes the connecting rod is four times the crank radius, and the time value is the number of milliseconds the admission valve is open for that cutoff value. As a comparison, an I/C engine running at 8,000 rpm with 280 degree duration cams takes 5.8 milliseconds to open and close a valve.

Now it's not the case that trying to operate valves 10 times faster needs 10 times the force. The inertial forces go up with the square of the speed, so 10 times as fast means 100 times the forces.

From a purely mechanical practicality point of view, this rules out using such high pressures. Either you'd have to make the admission valves hit-n-miss and only open them every several revolutions or cut out cylinders completely, or you'd have to throttle down the pressure.

It's looking like running supercritical pressure leads to a number of consequences that people haven't looked at yet.

George and Jim, I'm afraid I've got to go now, but I'll be back.

Re: Ultra-pressure engine efficiency
January 23, 2015 10:17PM
Hey Tim,

I have a lot of passion for a lot of things and it gets me into a lot of trouble. Steam ceased being "fun and play" for me many years ago.

"Now for losses due to condensation and evaporation, would they be more likely in a small uniflow engine running at high speed, or a big counterflow engine running at low speed?"

The Corliss engine from that paper is 12" bore by 24" stroke, that gives roughly 1,130.5 sq in cylinder+head surface area and 2,714.4 ci of steam, for a ratio of .416 sq in per ci of steam. The little 1.75" bore by 1.75" stroke engine has 14.43 sq in cylinder+head surface area and 4.2 ci of steam for a ratio of 3.435 sq in per ci. That is a difference of roughly 8.25 times between them.

So, looked at in another way for each btu of heat that goes from the steam to the cylinder in the small engine the effective drop in btus per lb of steam will be 8.25 times greater!

Two big factors in heat transfer equations are the gas mass flow and the turbulence. Both of which will effectively be greater in a smaller engine and cause a higher btu per sq ft per hr per deg F difference.

As for the Kent's equation, indeed that is why I mentioned steam being an imperfect gas. Page 4-06 of the same book flat out states, "The isentropic expansion of superheated steam follows closely the equation pv1.3 = constant." Which essentially suggests to use 1.3 for all superheated steam conditions, blanket rules disturb me.

Re-evaporation of steam during expansion is one thing that the "missing quantity" does and referring to the differences in volume between the two engines(big and small) it would act differently.

Caleb Ramsby
Re: Ultra-pressure engine efficiency
January 24, 2015 07:56AM

The University of Illinois, Engineering Experiment Station, published a Bulletin, No. 26, dated May 6, 1912: A new analysis of the cylinder performance of reciprocating engines. This Bulletin reports on an assessment of the polytropic exponent of expansion based on engine tests. it includes both saturated and superheated steam. It is worth the read.


My equation for cutoff that yields minimum steam rate is a pseudo equation that applies to both uniflow and counter flow. Never the less it gives a very good engineering answer to questions about optimum cutoff. It has four variables: clearance, pressure, frictional torque per cubic inch displacement and the polytropic exponent of expansion. My findings indicate that optimum cutoff is not a function of temperature. I have been using n = 1.3. By the way, Bulletin No. 26 gives the adiabatic value of n as being 1.3.


Do not underestimate the power of mathematics. Remember we flew to the moon hundreds of times with nothing but paper and mathematics before we made the rocket to get there.

Re: Ultra-pressure engine efficiency
January 25, 2015 12:39PM
Hey Jerry,

The guys at NASA had the incentive that if their calculations were incorrect then people would die, beyond that, specifically, their FRIENDS would be KILLED.

That is about as far removed as one can get from people that are attempting to figure out the efficiency of a reciprocating steam engine, where the only incentive is to have the prototype efficiency similar to that of the calculated efficiency.

Caleb Ramsby
Re: Ultra-pressure engine efficiency
January 25, 2015 01:19PM

Sorry for this late reply. I have just now had time to respond to your number crunching data of Jan. 23. First, let me confirm that the optimum cutoff will yield the maximum efficiency. However, I have found that mpg does not necessarily track efficiency very well.

Over the years, I have noticed a big variation in analyses data between we investigators. There are two fundamental reasons for this gap.

1. Some investigators base cutoff on engine displacement. I have always argued that a more plausible answers occur when events associated with crank angle are based on the absolute cylinder volume associated with the event. Also, as a conservative measure I disregard toe work. Cutoff is based on the absolute cylinder volume at release because blow down is not part of steam expansion that counts for what we are interested in. This approach causes the cutoff to be larger than otherwise based on piston displacement.

2. In order to get close to an actual answers, allowances must be made for engine friction, compression work, if any, pump and blower work. The bad news is that one correction "number" does not fit all combinations of pressure and displacement. And, it is technically improper to apply the PLAN equation to a paper engine. It requires an assumption for engine speed. Speed is pre determined by load. The PLAN equation is a definition of power and therefore cannot be used as a design tool.

In consideration of the above comments, I find that a mep of 548 psi is not consistent with 5% cutoff. The same applies to the others. This inconsistency spills over to the crank angle necessary to achieve the stated values of cutoff. Considering the above, a crank angle of 23.2 degrees at cutoff with a 3% clearance and a release of 140 degrees past TDC and a L/R ratio of 4 ,really yields a cutoff of 8.3 percent. Consideration for the absolute volume at cutoff (includes 3% clearance) and for expansions that end at release makes a big difference in what is really going on. My equation for what I call is too complex to give here. If you wish, I can get it and the deviation to you by other meas.

Re: Ultra-pressure engine efficiency
January 26, 2015 09:29AM

What is the genesis of the constant 7.3 x 10 minus 5th power?

Caleb Ramsby:

Why would any one excuse them selves from using the most up to date analytical tools available? Tools like Future Basic can be down loaded free. With this tool, you can do in a few minutes what other wise may take hours. And this tool is free of arithmetic mistake, unlike a human doing calculations for hours.

Re: Ultra-pressure engine efficiency
January 26, 2015 02:39PM
Jerry, just what in the hell are you talking about?

"The guys at NASA had the incentive that if their calculations were incorrect then people would die, beyond that, specifically, their FRIENDS would be KILLED.

That is about as far removed as one can get from people that are attempting to figure out the efficiency of a reciprocating steam engine, where the only incentive is to have the prototype efficiency similar to that of the calculated efficiency. "

Where in the above quoted statement do I mention abandoning mathematics or computers?

The point was attempting to make was that, well take SES for example, I point them out only because their data is to accessible to all reading this, they were continually stunned by the variance between their complex mathematical model and the results as seen on the road. If NASA had produced even a tiny fraction of the error found in the SES initial mathematical model and on road result, there would have been utter catastrophe and many astronauts would have been killed. The greatest repercussion at SES was some serious deflation of egos.

Take the group of guys working on the rocket nozzle, they could have changed their modeling to indicate that their "baby" was more efficient then it was and that more fuel would be converted to thrust. Doing so just out of ego would have resulted in the trajectory analysis being out of whack and people would be killed, plus there was a major timeline crunch, so not just quickness but dead on accuracy was required. From what I can tell your first technical article for the SACA was in 1970, I don't mean to pick on you, I just want to point out that to the best of my knowledge you have never had the opportunity to have your calculations verified by a powerplant being constructed and tested using the results of your data. So it is impossible to verify your results or those from anybody else for that matter, including mine, unless and until proven working powerplants have been made and tested.

I have nothing against mathematics nor computers doing the work for someone, I was doing calculus in the fourth grade and BASIC programming from about the same time, I know what math and computers can do. I also know how perverse of a result can be achieved by a fool applying ill conceived mathematical models, for I have been that fool more times that I care to admit.

Caleb Ramsby
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