# Calculating the Horsepower of a Steam Engine

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#### GreenTwin

##### Well-Known Member
HMEM Supporting Member
Here is a continued discussion of how to calculate steam engine horsepower.

.

Someone with a screen name of Gary K posted this online.
It seems to make sense.

Steam Engine Horsepower

Example: An engine with a 9” bore, a 10” stroke, a speed of 250 rpm, and 150 lbs. boiler pressure – The size of a 50 H.P. CASE steam engine.
P = 50% of 150 = 75 lbs.
L = 10 / 12 or .833 feet.
A = 9 x 9 x .7854 = 63.617 square inches.
N = 250 x 2 = 500 power strokes per minute. (This is for a double-acting engine, for a single-acting engine, power strokes are the same as the revolutions.)

75 x .833 x 63.617 x 500
----------------------------- = 60.2 indicated horsepower
33,000

Since this is the power developed by the steam in the cylinder, it represents the indicated horsepower, which is greater than the brake horsepower by about 10%. Subtracting 10% we have: .10 x 60.2 = 6.02 ( 60.2 – 6.02 = 54.18 or rounded off to 54 B.H.P.)

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I found my PLAN spreadsheet, and it is as follows:

P = mean effective pressure (psi)
L = length of stroke
A = area of piston
N = revolutions per minute (rpm)

When I punch in the numbers for the 10hp 7" bore engine from the previous chart, I have to crank down the mean effective pressure to 40 psi to get to 10 hp (indicated).

The equation in my spreadsheet is:

(2*P*L*A*N) / 33,000

Where P is in psi, L is in feet, A is in sq.in., N is rpm.

I assume the 2 is because there are two power strokes per revolution for a double-acting steam engine.

The 33,000 is a constant number, I think determined by Watt.

So cranking down a 2.25" bore engine with a 2" stroke, to P=40, I get about 0.5 hp at 300 rpm.

I think the mean effective pressure can be determined from the "card", which is the printout made by a steam engine indicator.

An indicator was a mechanical machine that graphed the cylinder pressure vs piston stroke.
A card was taken on one end of the cylinder, and then another taken on the opposite end of the cylinder.

The efficiency of a steam engine can be determined from the data on the cards, but I forget exactly how that is determined.

Charles Porter (the father of the high speed steam engine) describes some exhibitors at the mid-1800's steam exposition where he introduced the first "high speed" steam engine running at 150 rpm, who refused to allow an indicator to be attached to their engines, since it would show how poor the efficiency was.

Charles Porter revolutionized the entire steam engine industry overnight, and obsoleted every steam engine that had ever been made up to that point.

Porter was a lawyer by trade, but an extremely observant and intuitive individual.
Porter definitely had an engineer's mind, or actually better than the renowned steam engineer's of the time mindset.
His engine supposedly rivaled a Corliss in efficiency, which I think few other engines (if any) at the time could do.

Porter's engine designs could produce the same power as a Corliss at approximately 1/3 the size.

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There is a story in Charles Porter's book about how he delivered one of his steam engines to a steel mill, and it was about 1/3 the engine it was replacing.

The manager saw the engine when it was delivered, and ordered that it be sent back to Porter, saying something like "That tiny engine will be of no use to us".

Porter contacted the steel mill owner and assured him that the engine had sufficient horsepower for anything the mill wanted to do.

The Owner instructed the manager to install the engine, and the plant operators tried to stall the engine by loading it with everything they possibly could .
They could not stall Porter's engine no matter what they threw at it.
The steel mill output I think doubled overnight.

Charles Porter, the lawyer with no engineering training radically changed the world of steam engine design for many years.

Most folks have heard of Tesla; few have heard of Charles Porter.
I consider Porter the "Tesla" of steam engine engineering.
Like Tesla with his 3-phase power distribution system (which completely obsoleted the Edison DC systems overnight), the Porter steam engine obsoleted all stationary steam engines before it.
Ushering in the era of modern high speed steam engines was a huge development in technology with worldwide impact.

Stuff of legends.

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Porter, Charles T January 18, 1826 – August 28, 1910

Porter-Allen Engine 1888

Ah, here is MY mistake: the 2/12 for lenght of stroke is in FEETS! So the division by 12 converts the length to feets. The problem with this I thimpfks is that if the L is done in feets, so the area (A) should be converted to square feets. mixing measurment types is a bad thing to do. Undoubtedly, the formula is correct but not "right", as in right in the head!. It seems to me that NASA made that mistake on some of the early moon shots--they made calculations in Imperial measures (stone, inch feets pounds, etc), converted them to metric and viola! the male and female parts were off by micro inches or mili milimeters. They had to be reworkt to fit.

Mixing these measurment types are sure to cause mistakes, and I made one because of that. (It's the machines fault, not MINE.)

I seem to recall that the first docking stations in space where precision machined and polished surfaces, and when they docked, they stuck together like superglue.

I think that is when they started coating the mating surfaces with teflon.

I will have to look this up, but I am sure it is true.

I had a similar story when I made the green twin engine.
I had a LOT of bronze boat shaft, and so I thought "This is perfect for bearings", never having made an engine before.

The boat shaft machined like a dream, and the bearings came out great..........but when I assembled the engine, it would not rotate.
I loosened the bearings a bit, added lots of oil, and still, very poor rotation.

Removed the bearings, reamed them oversize, and still, it was like I was using glue instead of oil.
I discovered the property that some metals have called "stiction", and I discovered that while boat shaft bronze is awesome stuff, it is not bearing bronze by any means.

The second set of bearings I made using certified bearing bronze.

Who would have known ?

.

I seem to recall that the first docking stations in space where precision machined and polished surfaces, and when they docked, they stuck together like superglue.

I think that is when they started coating the mating surfaces with teflon.

I will have to look this up, but I am sure it is true.

I had a similar story when I made the green twin engine.
I had a LOT of bronze boat shaft, and so I thought "This is perfect for bearings", never having made an engine before.

The boat shaft machined like a dream, and the bearings came out great..........but when I assembled the engine, it would not rotate.
I loosened the bearings a bit, added lots of oil, and still, very poor rotation.

Removed the bearings, reamed them oversize, and still, it was like I was using glue instead of oil.
I discovered the property that some metals have called "stiction", and I discovered that while boat shaft bronze is awesome stuff, it is not bearing bronze by any means.

The second set of bearings I made using certified bearing bronze.

Who would have known ?

.
LOL, that's a good one. Still, you were able to use the first piece for something? I thimpfks NASA's little problem occurred before the space station stuff. it wasd when the Apollo projects were active (me thimpfks.)

After their error, they started doing it all in metric from the start. I had a friend, who, after college went to work for Boeing in the Seattle area. He was surprized and horrified that they used stone, ft-lbs, feets, inches and so so. In college all we used was metric.

This PLAN formula can be used to calculate indicated power for any engine, external or internal combustion.
Its sometime written as Pm L A N. Pm is Mean effective pressure which is defined as a hypothetical pressure, which is thought to be acting on the piston throughout the power stroke.
This is indicative power only and actual shaft power will depend on losses suffered by engine.

Regards
Nikhil

The mean effective pressure is the area enclosed by the indicator diagram divided by the stroke. Here is an example
Indicator diagram
While the pressure at the start of the stroke might be near to line pressure, as the expansion proceeds pressure drops away quite quickly. You also have fluid friction in ports and passages which tends to round off the corners of the indicator diagram. Then on top of that you have exhaust back pressure which is pushing the piston the "other way". So the MEP is always a lot less than inlet pressure.
All the friction losses increase rapidly with rpm (everything goes faster so friction losses get bigger) then MEP drops away even more. It can all be calculated to a reasonable degree of accuracy, but needs a time step spreadsheet that calculates everything by the fraction of a degree. There is a good paper by Prof Bill Hall on how to calculate it from zip here:
Prof Bill Hall paper
Martin

There is a technical issue in determining the efficiency of an engine and calculating a horsepower. Horsepower is a defined number. Its a defined by the time rate of doing work. You can have a measured high horsepower and a very lousy efficiency. One horsepower is defined as doing 33,000 ft-lb force/min. So if you know the torgue and the rpm you can calculate the horsepower. This is usually done by measuring the torgue at the shaft and multiplying it times the rpm.

If you want the efficiency start with the carnot cycle which gives the rules for any heat engine and this is maximum efficiency. You can convert horsepower to btus or calories or units of your choice to get an efficiency number. Simply devide the horsepower in btus by the input btus. 1 hp-hr=2545 btus.

If you want to predict steam consumption then rpm and volume displacement gives you those numbers. But without doing any measurements its just a guess.

I know the concept of Carnot efficiency, but have never seen it as really useful in the context of a steam engine, where you have combustion losses, exhaust heat losses, fluid friction losses, exhaust losses, back pressure, mechanical friction, internal leakage, condensation losses etc.
Certainly back in the day, "build one and test it" was the method used to derive output and efficiency or steam consumption for a given power. I was only suggesting that in this day and age it is possible to calculate things from scratch, but if you look at the maths in Bill Hall's paper most folk will probably not want to. For those with a curious mind, Bill Hall sets out the various factors involved very well.
Martin

I know the concept of Carnot efficiency, but have never seen it as really useful in the context of a steam engine, where you have combustion losses, exhaust heat losses, fluid friction losses, exhaust losses, back pressure, mechanical friction, internal leakage, condensation losses etc.
Certainly back in the day, "build one and test it" was the method used to derive output and efficiency or steam consumption for a given power. I was only suggesting that in this day and age it is possible to calculate things from scratch, but if you look at the maths in Bill Hall's paper most folk will probably not want to. For those with a curious mind, Bill Hall sets out the various factors involved very well.
Martin
One of the reasons I start with the carnot cycle its the best you can ever do for efficiency. And all the other factors can be ignored if you know the heat energy going in and the work coming out of the cycle. That is not to say knowing the other factors has no value because you can work to improve those numbers if you know what they are. I have several older papers on calculating the efficiency of GE steam turbines and the paper is filled with equations. So in some cases more detail is good. I will go back give Hall's paper a read.

The mean effective pressure is the area enclosed by the indicator diagram divided by the stroke. Here is an example
Indicator diagram
While the pressure at the start of the stroke might be near to line pressure, as the expansion proceeds pressure drops away quite quickly. You also have fluid friction in ports and passages which tends to round off the corners of the indicator diagram. Then on top of that you have exhaust back pressure which is pushing the piston the "other way". So the MEP is always a lot less than inlet pressure.
All the friction losses increase rapidly with rpm (everything goes faster so friction losses get bigger) then MEP drops away even more. It can all be calculated to a reasonable degree of accuracy, but needs a time step spreadsheet that calculates everything by the fraction of a degree. There is a good paper by Prof Bill Hall on how to calculate it from zip here:
Prof Bill Hall paper
Martin

Bill Hall created some awesome steam engine white papers.
I have some of those.

.

I know the concept of Carnot efficiency, but have never seen it as really useful in the context of a steam engine, where you have combustion losses, exhaust heat losses, fluid friction losses, exhaust losses, back pressure, mechanical friction, internal leakage, condensation losses etc.
Certainly back in the day, "build one and test it" was the method used to derive output and efficiency or steam consumption for a given power. I was only suggesting that in this day and age it is possible to calculate things from scratch, but if you look at the maths in Bill Hall's paper most folk will probably not want to. For those with a curious mind, Bill Hall sets out the various factors involved very well.
Martin
I read professor Halls paper and found it interesting. He mentioned in the first paragraph the actual fired btu to the drawbar power which is actually a heat rate for power stations. He also quietly mentioned the efficiency was way below the maximum but did not emphasize that. So he obviously looked at analysis from a carnot cycle but I was not able to determine what the high and low temperature was used. But thats not what he was doing. Apparently he also left out more complex details to make the paper easier to read based on his comments.

He has built a computer model probably using C to do the calculations of mass steam flow within the cylinder system including velocity of steam through the system. He was looking for instances of sonic flow or choke flow which is flow limiting throughout the cycle. You pretty much need a computer to calculate that many points in the cycle. However you could reproduce the results by making an electronic indicator and data logging the valve position with pressure. The method he used was Numerical Analysis which is a powerful tool for variables. Not sure when the paper was written but he was using a relatively modern technique using older indicators. If you new where to get the source code you could reproduce it. At that time all you had to do was contact him. The fact he was looking for such things as limiting conditions on steam flow is impressive.

Today computational fluid dynamics would probably be used but it has its own steep learning curve. He would be an interesting person to talk to. Thanks for posting the paper I enjoyed reading it. Be good project for a grad student to modernize if for small steam engines. HMEL

If you actually have an engine, a simple Prony brake with a scale will work fine. If heat disipation is an issue, spray water on it.

Lohring Miller

https://en.wikipedia.org/wiki/Prony_brake
I agree a simple solution is always a good answer. And probably just as accurate given accounting for errors which can occur in gages and instruments.

The mean effective pressure is the area enclosed by the indicator diagram divided by the stroke. Here is an example
Indicator diagram
While the pressure at the start of the stroke might be near to line pressure, as the expansion proceeds pressure drops away quite quickly. You also have fluid friction in ports and passages which tends to round off the corners of the indicator diagram. Then on top of that you have exhaust back pressure which is pushing the piston the "other way". So the MEP is always a lot less than inlet pressure.
All the friction losses increase rapidly with rpm (everything goes faster so friction losses get bigger) then MEP drops away even more. It can all be calculated to a reasonable degree of accuracy, but needs a time step spreadsheet that calculates everything by the fraction of a degree. There is a good paper by Prof Bill Hall on how to calculate it from zip here:
Prof Bill Hall paper
Martin
Thank you ever so much - - - - now to reading and digesting and hopefully understanding!!!

A small prony brake build would be interesting to see!

I seem to recall that the first docking stations in space where precision machined and polished surfaces, and when they docked, they stuck together like superglue.

I think that is when they started coating the mating surfaces with teflon.
I've welded brand new AN aircraft fittings together just by spinning them on by hand while chatting. It wasn't like galling and torque was mostly from the inertial spinning. The threads had welded together at atom level and removal left two cylinders. From then on I learned having an interface as simple as natural oil from handling was enough to keep it from happening.

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