equal to the length of stroke multiplied by twice the number of
revolutions. Then in the formula for horse-power, _ -^- 7r ,
N = the number of strokes
L X N ==. the piston speed.
In case the stroke is stated in inches, the piston speed in feet
In determining the allowable piston speed, local conveniences,
durability and the character of the work to be done should be
considered. Other things being equal, the piston speed increases
slightly with an increase in the length of stroke.
The piston speeds in common practice are as follows :
Direct acting pumping engines 100 to 150 feet per minute
Small stationary engines 300 to 500 feet per minute
Large stationary engines 500 to 900 feet per minute
Corliss engines 400 to 800 feet per minute
Locomotives 700 to 1,200 feet per minute
Marine engines 750 to 1,000 feet per minute
THE STEAM ENGINE.
RATIO OF EXPANSION.
The ratio of expansion as usually understood is the piston
displacement divided by the volume of the cylinder to the point
of cut-off. Thus if the piston is 10 inches in diameter and the
stroke is 12 inches, the piston displacement is 10 2 X .7854 X 12
= 942.48 cubic inches. If cut-off occurs at J the stroke, or when
the piston has moved 4 inches, the volume to cut-off is 10 2 X
.7854 X 4 = 314.16 cubic inches, and the ratio of expansion is
q \cy i o
= 3. This may be stated thus:
area of_cyllnder_X length of stroke = ratio Qf nri(m>
area of cylinder X distance to cut-ore
Since the area of the cylinder appears in both numerator and
denominator, we may cancel and write :
Ratio of expansion = length of stroke $
distance to cut-off
If clearance is taken into account, the true ratio of expansion
is different from the apparent ratio as found above. The steam
which expands in the cylinder is not merely the volume equal to
the piston displacement, but is this volume plus the volume of the
With a late cut-off and small clearance the true ratio of ex-
pansion differs but little from the apparent. But when the cut-off
is early and the clearance is large there is considerable difference,
as shown in Fig. 11.
In this diagram D E represents the stroke, and is 2|- inches
long. D' D represents the clearance volume, which is equal to
the piston displacement, and is therefore .31 inch long. Let cut-
off occur at i of the stroke ; than the apparent ratio of expansion
is equal to ___ = _^!_ = 8. If we consider the clearance, the
diagram is changed, as shown by the dotted lines, and the true
ratio of expansion is
D' E 2.80
A77J " .62- =: 4>5<
Thus we see that the vatic of expansion is not 8 but 4.6.
THE STEAM ENGINE.
WORK DONE IN THE CYLINDER.
The amount of work done per stroke in the engine cylinder
is usually found by means of an indicator. It is often desirable,
especially in designing engines, to know the work that may be
expected under given conditions before the engine is built. The
work done in the cylinder is proportional to the mean effective
pressure, so that if we are to determine the probable power of our
engine we must in some way ascertain the probable mean effective
pressure. If the initial pressure, the back pressure and the ratio
of expansion are known, we can find the probable M. E. P. by
means of a formula. This formula does not provide for the losses
due to compression, clearance, condensation and leakage, so that
the value thus obtained must be multiplied by a factor depending
upon the type of engine.
Let P = absolute initial pressure
R = ratio of expansion
p =. back pressure (absolute)
Then neglecting all losses, the theoretical M. E. P. will be ex-
pressed by the formula,
M. E. P. = P G + hyp, log. R)
In order to allow for the losses due to compression, clearance
118 THE STEAM ENGINE.
condensation, wire-drawing, etc., it is customary to multiply this
value by factors given in. the following table :
Engines with special valve gear and
independent cut-off valves, about .90
Plain slide-valve engines .75 to .90
Compound engines .65 to .80
Triple expansion engines .50 to .70
These factors are for unjacketed engines ; with jackets the
factor might be .05 more in each case. On account of wire-draw-
ing and large compression, high-speed engines would have the
smaller value in its respective class. Only the best-designed
engines with good valve gears and under favorable conditions will
warrant the use of the larger factor in their respective classes.
Large engines will of course have larger factors than small engines.
Example. What is the probable M. E. P. when the initial
pressure is 95.3 pounds (gage), the back pressure 3 pounds
(absolute) and the ratio of expansion 4 ? The engine is large,
of the plain slide-valve type with steam jackets.
P = 95.3 -f 14.7 = 110 pounds
p = 3 pounds
R = 4
From the following table, hyp. log. R = 1.3863
MBP _ 110(1 + 1.8863) _ a
For a large plain slide-valve engine, unjacketed, we might
expect a factor of .85 to .90, depending upon the conditions. Sup-
pose we call the factor .87, then adding. 05 for the effect of the
steam jacket we get .92.
62.02 X .92 = 57.6 pounds as the probable M. E. P.
A rough approximation to the power to be expected of a
compound, or triple expansion, engine, may be found in a similar
manner by assuming that all the expansion takes place in the low-
pressure cylinder, neglecting losses as before.
Example. Find the probable I. H. P. for a triple expansion
engine with the following dimensions and data :
Steam Cylinder 58 x 108 x 60 inches. Air Cylinders 108 inches diameter
Total Weight of Engine 1,270,000 Pounds.
William Tod Company.
THE STEAM ENGINE.
Total ratio of expansion,
115 per minute
140.3 pounds (gage)
2 pounds (absolute)
Diameter of low-pressure cylinder, 60 inches
Stroke, 30 inches
M. E. P. = P (1 + hyp- log- R) _
In practice only about .65 of this is actually obtained, so the
probable M. E. P. is .05 X 43.01 27.95 pounds.
P I A N
The I. H. P. is now found from the expression ../..-. as
I H P = 21M X ^ X 2 ' 827 - 4 X 2 X 115 = l
TABLE OF HYPERBOLIC OR NAPIERIAN LOQARITHHS.
In the steam engine the steam exerts a pressure on the crank
pin through the piston rod and connecting rod. When the crank
is at the dead center, the entire pressure is on the bearing of the
crank shaft ; there is no tendency to turn the crank. In any other
position the steam pressure tends to turn the crank pin. As the
crank pin moves from dead center, the tendency increases until it
THE STEAM ENGINE.
reaches a maximum and then decreases until, at the other dead
center, it is zero again. If the connecting rod were of infinite
length, and steam were admitted throughout the whole stroke, the
maximum teriden.fr , or the maximum turning moment as it is
called, would occur with the crank at right angles to the line
connecting the dead points.
In the actual engine the thrust along the rod is constantly
varying even though the pressure on the piston remains the same.
This is due to the angularity of the connecting rod. The turning
moment is always equal to the thrust along the connecting rod
multiplied by the perpendicular distance from the connecting
rod to the center of the shaft. If the steam pressure on the
piston remains constant, the maximum turning moment occurs
when the connecting rod is at right angles to the crank, for in
this position the perpendicular distance from rod to center of
shaft is a maximum equal to the length of the crank, and as the
rod makes its greatest angle with the line connecting the dead
center at this point the thrust along it will also be a maximum.
If the cut-off is very early, -| stroke for instance, the maximum
thrust along the rod will occur earlier than at the point previously
mentioned, but the leverage of the force will be less, so that really
there will be little change in the point of maximum turning
moment no matter where the cut-off may occur.
To represent this turning moment, diagrams of crank effort
are drawn. These diagrams may be drawn with rectangular co-
ordinates having the crank angles represented as abscissae and
THE STEAM ENGINE. 121
the turning moments corresponding to these angles as ordinates.
Besides the thrust of the connecting rod we must take into
account friction and the inertia of the reciprocating parts. At
rirst this may be thought of small consequence, but with a fairly
heavy piston and connecting rod we can easily see that at high
speed the momentum would be great. On a vertical engine, on
the up stroke the steam has to lift this heavy mass and impart a
very considerable velocity to it, while on the down stroke the
acceleration of the mass is added to the steam pressure. This
makes the effective force on the up stroke less than that due to
the actual steam pressure, and greater on the down stroke. The
crank effort diagram represented in Fig. 12 is from a horizontal
engine of practical proportions. The initial steam pressure is 50
pounds per square inch. Cut-off at * stroke. The engine makes
240 revolutions per minute. The dotted lines represent the
crank effort, without considering friction. The full line is the
diagram when weight of moving parts and inertia are considered.
In drawing a crank effort diagram, friction is often neglected,
but the effect of inertia of the moving parts is of great importance,
especially in the case of high speed.
It has been mentioned in connection with compounding that
if there are two or more cranks on the shaft the turning moment
is more nearly constant. We can now see that this is so. In
Fig. 13, A D B represents the curve of turning moments on one
crank, and A'D'B'the curve of turning moments on the other
crank, which is at right angles to the first. To find the total
turning moment on the shaft the dotted line curve is drawn.
THE STEAM ENGINE.
The points are obtained by adding the ordinates. Thus, to find
the point d add ac to ab. Then ad = ac -f- ab. It is easily seen
that the dotted line curve is more nearly a straight line than the
curve A D B.
ECONOnY OF THE STEAM ENGINE.
The effects of various devices and methods employed to in-
crease the economy of the steam engine cannot be studied from
the theoretical side alone if we wish to obtain satisfactory results
So complicated and important is the action of the cylinder walls,
that if we would learn the conditions favorable to economy we
must study the actual tests of engines in service conditions.
Effect of Raising Steam Pressure. In general there is a
gain in thermal efficiency by increasing the steam pressure and
the total number of expansions, provided proper means are taken
to lessen the undesirable effects due to increased condensation and
re-evaporation caused by the increased expansion. The initial con-
densation, of course, places a pretty strict limit upon the number of
expansions profitably used in a simple expansion engine.
If we raise the steam pressure and keep the same cut-off, the
conditions will be slightly different. The losses from external
radiation increase with the rise of steam pressure, but the horse-
power increases more rapidly, hence there is a net gain, and since
the changes of temperature are greater, the higher the pressure, it
is reasonable to suppose that the loss, from condensation and re-
evaporation will increase. It is not difficult to imagine a point
where these losses may offset the gain, and where, indeed, if the
pressure is raised too far there will be a net thermal loss. This
has actually happened in some cases. At first the gain from rais-
ing the steam pressure is rapid. As the pressure rises, the gain
increases more slowly, and finally it is not worth the expense, if,
indeed, there is not actual loss.
If we bear in mind that there is little gain in economy to be
obtained by increasing the steam pressure beyond a certain mod-
erate limit, unless the ratio of expansion is also increased, and that
the losses from condensation, re-evaporation and exhaust waste
limit the number of expansions profitably used in a simple expansion
engine, we shall at once see that we must look to other devices
THE STEAM ENGINE. 123
for decided gains in economy. The most important of these have
already been briefly considered.
Superheated Steam. Tests show a very decided gain in
'economy from using superheated steam, yet practically no perma-
nent results have been obtained, on account of the difficulty of
maintaining the superheating apparatus. To superheat to the
best advantage we must have a coil of pipe in the flue and thus
make use of the otherwise wasted heat. But the intense heat
soon burns out the metal and together with the great pressure it
is rapidly wasted away. Gains of from 15 per cent to 20 per
cent from using superheated steam have actually been observed
on simple engines. There has also been some gain noted by the
use of superheated steam in triple expansion engines, but the gain
is less than in the simple type, because naturally there is less con-
densation in the triple than in the simple engine.
Steam Jackets supply a small amount of heat to the cylinder
during expansion which can be converted into work, but the chief
advantage of a jacket is that it keeps the inner walls of the cylin-
der warmer at admission and thus reduces initial condensation and
saves much loss of re-evaporation at exhaust. It will be evident
that a large part of the heat of the steam jacket flows to the cylin-
der during exhaust and is thus entirely lost in the simple engine.
In the triple engine this heat passes into the intermediate and low-
pressure cylinders ; consequently we might expect a greater gain
from using a jacket on a triple than on a large simple engine.
The main advantage of the jacket has been previously pointed
out, and it may be stated that in all cases the gain from the jacket
is small and there is to be found a considerable diversity of opinion
as to its real advantages. On some engines there is undoubtedly
little if any gain. The largest gain is in the smaller engines of
say under 200 H. P. ; on very small engines the gain is quite
large, having been as much as 30 per cent on a 5" X 10" engine
when developing only 11 H. P. under light load. On a 10 H. P.
engine the gain might be as much as 25 per cent. On engines of
about 200 H. P. the gain would probably be 5 per cent to 10 per
pent for simple condensing and compound condensing, and from
10 per cent to 15 per cent for triple expansion. The saving on
large engines, of say 1,000 H. P., is very small, the reason being
1iM THE STEAM ENGINE.
that large engines offer less cylinder surface per unit of volume
than small ones, and hence we find proportionately less cylinder
condensation in large engines than in small ones. The very small
engines, in which the gain would be greatest, are seldom jacketed,
because they are built for inexpensive machines and the first cost
is of more consequence than the later economy.
Compounding is the most effective method of increasing the
number of expansions and at the same time avoiding excessive
cylinder condensation. We know that increase in boiler pressure
and increase in expansion in simple engines are economical only
to a certain limit. We shall now discuss the gain due to com-
pounding and the conditions under which it is advantageous.
A direct comparison between tests of different engines is
impossible because of the different steam pressures, etc., but a
careful study seems to show that for simple condensing engines
there is no advantage in raising the steam pressure above 80
pounds. In compounding, the pressure can be advantageously
raised to 135 pounds. The gain due to the higher pressure,
greater number of expansions and compounding maybe 20 per
cent to 30 per cent. For triple-expansion engines the most
economical steam pressure .is of course higher than for compound
and may be used to advantage up to 180 pounds or more. The
gain from using a triple over a compound may be about 5 to 10
per cent or more. These figures are good only for engines under
full load and proper point of cut-off. A compound will usually
suffer more loss of economy under light load than a simple, and
the triple will suffer more than a compound.
Cut-off and Expansion. The best point for cut-off for a
simple engine, whether jacketed or not, is about ^ stroke if the
engine is noncondensing and about i stroke if condensing. The
total expansions of a triple engine or a compound is commonly
ratio of low pressure to high pressure
fractional part of stroke at cut-off in high *
For instance, if the cylinders are as 1:3:8, and cut-off is |
stroke in high, then the total expansions as conventionally used is
- = 20. For the best service of triple engines on land 20
THE STEAM ENGINE. 125
expansions are used. The conditions of service make it impos-
sible to use as many expansions in marine work, hence the rela-
tively poor economy of marine engines. For compound engines 15
expansions seems to be the best in general. Of course it must be
understood that the type of engine and conditions of service may
necessitate different arrangements, but when such is the case a
less economy of steam consumption usually results.
Variation of Load. An engine should be designed to give a
fair economy over a reasonable variation of load. Ordinarily if it
gives its best economy at normal load there will be a sufficient
range. Usually, it happens that the best mechanical efficiency
is obtained with a little longer cut-off than that which shows the
most economical steam consumption per indicated horse-power.
This is because, as the cut-off lengthens, the power increases faster
than the frictional losses. It will be evident from this that in-
creasing the cut-off slightly reduces the thermal efficiency, but the
gain in mechanical efficiency may offset the thermal loss. Short-
ening the cut-off causes loss of both thermal and mechanical effi-
ciency. It would then seem that if the engine were given a little
longer cut-off than that which would produce the best thermal
efficiency at normal load, the power could be reduced with less
actual loss. For a slight reduction we should lose mechanical
efficiency and gain thermal, and for a slight increase we should
gain mechanical and lose thermal. Thus there would be a wider
range with good results. There is always more loss by decreasing
cut-off below the point of maximum efficiency than by lengthening
it. That is, the engine works at a greater disadvantage when
running under a light load than when running under a heavy one.
The allowable range of load for a simple engine is greater than
for a compound or triple. If the power of a compound is reduced
by shortening the cut-off of the high-pressure cylinder without
shortening the low proportionally, there is likely to be an uneven
distribution of work and, consequently, a wide fluctuation of tern-
perature, which will cause so much condensation as to offset the
advantages of compounding. Moreover, the large expansion in
the high-pressure cylinder may reduce the admission pressure to
the low cylinder so much that the expansion in the low may be
carried below the atmosphere in a noncondensing engine and thus
THE STEAM EXG1NK.
cause a loop at the end of the card, as we have learned in " Steam
Engine Indicators." This loop means a loss of power, and tint
the high-pressure piston is dragging the low and the engine is
using up power on itself as it were. A triple engine is even more
troublesome than a compound, and besides giving the trouble
already mentioned, the dragging of the low-pressure piston may
injure the cylinder and loosen the guides. There is little difficulty
in increasing the power of a compound or triple. A simple engine
may easily be run at reduced power, either by shortening the cut-
off or reducing the steam pressure or both.
Effect of Speed. The transfer of heat between the steam and
walls of the cylinder, although very rapid, is not instantaneous.
The longer the steam can remain in contact with the cylinder
Widls, the more heat will be lost. Hence it is reasonable to sup-
pose that an increase of speed will reduce condensation. This has
been found by tests actually to bo the case. Other things being
equal, a reasonable increase of speed results in better economy,
but as we can seldom get as good a valve motion at high speed, we
may lose almost as much in this way as we gain by decreasing our
condensation. The most efficient valve gears are to be found on
slow-speed engines, and hence we usu illy find that the most *con-
omical engines are slo\v speed. Nevertheless, with a given A live
gear, an increase of speed gives better economy up to the limit of
good valve motion. High-speed engines also require more clear-
ance, which means another loss. These two factors, valve motion
and clearance, limit our increase of speed beyond a certain point, just
as condensation will limit our indefinite increase of boiler pressure.
Feed Water Heaters. The use of f jed water heaters has been
discussed in the instruction papers on boilers, but it may be well
to observe here that in many places where water is expensive
condensing engines cannot be run ; nevertheless, a very consider-
able saving can be effected by allowing the exhaust steam to con-
dense in a feed water heater, and thus save the heat th<.t would
otherwise be wasted, or the exhaust steam may be used for heating
purposes. Of course in such cases the steam consumption of the
engine is high, but if proper allowance is made for the heat used
.for other purposes, the actual fuel consumption rightfully charged
to the engine is not excessive. If the feed water is heated by
THE STEAM ENGINE.
waste gases, then the gain belongs to the boiler and not to the
The following represents the average steam consumption in
pounds per I. II. P. per hour for various types of engine:
Triple expansion stationary 11 to 14 pounds
Triple expansion marine 13 to 16 pounds
Compound stationary 12 to 15 pounds
Compound marine 18 to 21 pounds
Simple condensing 17 to 20 with jacket
Simple condensing 18'a to 22 without jacket
Simple noncondensing 24 to 33 or more
All these figures have been taken from the results of careful
tests of engines in actual service, and represent good engines of
their respective types.
Direct-acting steam pumps, although very important engines,
are extravagant in their consumption of steam. The absence of a
fly wheel makes it almost impossible to use steam expansively, and
hence the pump takes steam full stroke.
The steam consumption for a simple direct-acting steam pump
may be anywhere from 60 to 200 pounds p<jr horse-power per
hour, depending upon the size and conditions of service.
The economy of an engine is usually stated in terms of steam
per horse-power per hour, or of B. T. U. per horse-power per min-
ute. The latter is more useful for purposes of comparison with
other engine tests, but the real criterion of economy is the actual
cost of power in terms of fuel consumption, for this can at onco
be reduced to dollars and cents, and the manufacturer or the
builder of the engine can determine the effect of devices for econ-
omy in terms of money, which to him is worth more than B. T. II.
It may often happen that some expensive device, while effecting a
saving of heat consumption, may not save fuel enough to pay for