What is Boiler Horsepower?

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.