Idealized Indicator Diagram
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Now and again those interested in the restoration and operation of antique steam engines are confronted with the problem of rating a boiler in terms of boiler horsepower. Although this term has long been abandoned in the steam power field, it is nevertheless, one used often in historical journals. Over the years there have been articles written on the history of the unit of energy, horsepower, as applied to the reciprocating steam engines. One of the best of these was done by Carl Erwin and was in the July 1977 issue of The Iron-Men Album. However, this is not the same 'horsepower' as is used in the term 'boiler horsepower.'
The history of the development of the unit of boiler horsepower follows that of the early development of the steam engine. Once someone had built an engine he must supply it with steam, and a boiler serving an engine tested to have a certain horsepower rating must certainly have the same rating. Well, as we shall see, today this does not necessarily follow.
Steam power pressures have grown over the years from New-comen's atmospheric pressure level to the super-critical pressures of 3,500 pounds per square inch used in today's electric power generation plants. Early boilers were built of copper and were not greatly different from the pot stills used to distill grain mash in the service of Demon Rum. As metallurgy of steel developed and the art of building riveted boilers progressed we find a day in which 'modern' steam pressures were in the range of 60 to 70 pounds per square inch gauge (psig). It was at about that time that the unit known as the boiler horsepower originated. One boiler horsepower was said to be the equivalent of the evaporation of 30 pounds of 100 degree feed water into saturated steam at 70 psig in an hour.
Now, water at 100 degrees Fahrenheit (F) contains (100 - 32) = 68 Btu heat per pound (Btu/lb.). Saturated steam at 70 psig contains 1183.6 Btu/lb. So, if we take the difference between these two numbers and multiply by the 30 pounds we find that one boiler horsepower is equal to 33,468 Btu per hour of heat. It is simply that and no more. But, there is more to the story. Another definition says that one boiler horsepower is equal to the evaporation of 34.5 pounds per hour of water from and at 212 degrees F. And so now we have the 'from and at' term that is so often used. But here again, it is simply a rate for producing steam heat. Let us see how this one works.
Steam at 212 F can only exist at atmospheric pressure at sea level. It contains 1150.2 Btu/lb. Water, on the other hand, at 212 degrees contains 180 Btu/lb. In other words, it takes 970.2 Btu to convert one pound of hot water into steam-- 'from and at 212.' This 970.2 Btu times the 34.5 pounds per hour in the definition of one boiler horsepower equals 33,472 Btu per hour. Generally, it has been the practice to round out the figure to33,470 Btu/hr equals one boiler horsepower.
In practice a number of other factors have been related to boiler horsepower. In such boilers as the ones used on traction engines or in small plants where horizontal return tubular boilers are used it is often said that there needs to be 10 square
feet of heating surface per horsepower. Some other factors are 13 square inches of flue cross sectional area to minimize flue gas pressure drop. And similarly, it is said to be good practice to proportion the flue diameter to be about l/30th of its length. Also, with coal burning installations it is the practice to provide ? square foot of grate area per boiler horsepower.
But, so far we have not come up with a term that really relates directly to just how much steam a certain engine requires to run it at capacity. So now let us take a look at that part of the problem and see if one 'engine' horsepower equals one 'boiler' horsepower.
Without getting too deeply involved in mathematics, let us recall that once engine horsepower is equal to: 2PLAN 33,000
That is, horsepower in a double acting single cylinder steam engine is equal to the pressure in the cylinder (psig) times the length of stroke In Feet times the area of the piston In Square Inches times the RPM divided by 33,000. Everything about that formula is perfectly straightforward except for the pressure and that takes a bit of thinking.
A look at the Idealized Indicator Diagram will help to understand how the 'mean effective pressure' (m.e.p.) is determined. Here we have plotted a diagram which indicates what the pressure is in the cylinder at any part of the stroke. At point '1' the valve opens and steam pressure from the boiler is admitted and it pushes the piston along its stroke. Since steam can enter from the boiler the pressure remains constant until at, say 30% stroke, cut-off occurs and the steam is allowed to expand. This it does along line 2-3-4 and at point 4 the exhaust valve opens and the pressure drops to atmospheric in our case or point 5. At this point the piston begins its return travel and pushes the steam out the exhaust until the stroke reaches point 6 where the valve closes again and the energy stored in the flywheel starts to compress the remaining steam up to point 7 where the inlet opens and the pressure jumps up to point 1 and the cycle is complete. What we want to know is what is the average pressure represented by line 1-2-3-4-5.
We get that by determining the area under that curve and dividing by the length of the base or stroke. Some people have expensive plani meters for getting this area but let us just count squares. I got 16.3 but than there is the area under 6-7 which we must subtract. That left me with 15.6 squares each of which is 20 psig by 20%. So 15.6 times 20 times 20 and divided by the base (100) equals 62.5 psig m.e.p.
Let us take a practical case of an 8? x 10 double acting steam engine that runs at 200 rpm. That is really an 8? inch x 0.833 foot engine as far as our formula is concerned. When I put in all of those numbers and remembered that Pi is equal to 3.14161 got 35.8 horsepower (indicated). Now we can figure out how much steam this engine will require. But we must think of our 8?' x 10' engine as being an 0.708 foot x 0.833 foot engine so we can figure out the number of cubic feet the engine requires each revolution of the crankshaft. But don't forget that steam flows out of the boiler for only 30% of the stroke in our example. And, it will be useful to know that a pound of 100 psig steam takes up 3.878 cubic feet.
When all of these numbers went into my $12.95 assembled in Mexico Sears Roebuck calculator it came out as 610 pounds of steam per hour to run the engine of our example. Now it will be recalled that 100 psig steam contains 1192.4 Btu/lb. and that one boiler horsepower is 33,470 Btu/hour. Put all of these together and we find that we need 21.7 boiler horsepower to run 35.8 engine indicated horsepower.
What this all says is that there is only one unique set of figures for pressure and cut-off where the two horsepower numbers are the same. Boilers are best rated in their steam production capacity not in horsepower.
It has been a while since I have thought about the rating of boilers in horsepower and I had to do a bit of reviewing of some of my old books. These have gathered some dust over the years, but are still very much a part of my library. There is another term that is used and that is 'percent rating'. What that means is that if more than 33,470 Btu per hour per horsepower is being taken out of the boiler then it is running at more than 100% rating. How well I can remember a row of ten old sinuous header Babcock & Wilcox boilers with brick settings in Sungei Gerong on the Island of Sumatra. After the war these were being fired so hard that the brick work was melting. I figured that we were firing them at better than 250%! But they kept right on producing steam. A tribute to the boiler maker's art.
Then there is the matter of 'cutoff'. We have been talking about 30% cut-off. On a steam locomotive the cut-off is adjustable over a wide range of notches in the quadrant from neutral or zero to 100%. Every one of those notches is just another notch save for one. And that one is the 100% notch and that one is fondly known as 'the Wall Street notch'. When the tallow pot is firing the boiler to the point where the safeties are about to lift and the hogger has the throttle wide open and the Johnson bar in the 'Wall Street notch' the old girl is doing all that she can for the owners!
There is a great amount of nostalgia about old steam engines and those that can take the time and trouble and the expense to maintain them for posterity are to be complimented. But it is easy to see why they are of only historical value when one considers the efficiency of the overall system. Without going into detail, suffice it to say that the exhaust steam in our example still contains 1025.5 Btu/lb. That figures out to be 14% indicated efficiency. At best, the boiler efficiency of a traction engine is only 60%. Putting the two together we get an overall efficiency of about 8%. Compare that to a diesel tractor engine at better than 30% and the conclusion is obvious.
Why is this? Basically it is in what is called the 'latent heat of vaporization' for water. Remember in our 'from and at' steam we said that the conversion of water at 212 F to steam at 212 F took 970 Btu/lb. of water. Well that heat in the exhaust of an engine is lost. Efficiency is defined as being input minus output divided by input. Since we can not do anything about the properties of water all we can do is to increase the input figure and that is what modern power plants are doing. For example, the steam from a boiler operated at 2,400 psig will be at 1000 F and will contain 1486 Btu/lb. Now, if we could build an engine to withstand this pressure and temperature and then expanded the steam down to our 1025.5 Btu/lb. then the efficiency would be 31%. it has not been possible to do this with reciprocating engines but a steam turbine works very well under these steam conditions. Add a condenser so that our exhaust is into a partial vacuum and we get another improvement. But, how do we get around throwing away that 970 Btu/lb.?
It is accomplished by many stages of feed water heating. There may be as many as seven levels of feed heat in a modern power plant. Steam is extracted from various points along the path through the turbine beginning as high as 550 psig and it is fed to the heaters. The latent heat of vaporization is thus recycled, it does not go out the exhaust in that extracted steam. There is still more steam going out the exhaust to be condensed. But not as much. In fact, 80%, but the effect is so dramatic that power plants today operate in the 40% category of efficiency. And, there they will stay until one of two things happen. Either someone discovers a working fluid that is better than water with a lower latent heat of vaporization or until metallurgical developments bring out metals that will operate about 1100 F. It is as simple as that.
One day a little girl asked her father to tell her about that strange bird that she had seen at the zoo, the penguin. Being a perfectionist father, he took out a book from the library that discussed the penguin in quite some detail and he gave it to her to read. After she had struggled through the big book, he asked what she had learned. She replied, 'Father, I have learned more about penguins than I really wanted to know.' Perhaps my readers feel that way about boiler horsepower.