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| Minor typographical errors have been corrected. |
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Machinery's Reference Series

Each Number Is a Unit in a Series on Electrical and
Steam Engineering Drawing and Machine
Design and Shop Practice




Action of Steam Engines 3
Rating and General Proportions of Steam Engines 11
Steam Engine Details 15
Steam Engine Economy 30
Types of Steam Engines 36
Steam Engine Testing 41

Copyright, 1911, The Industrial Press, Publishers of MACHINERY,
49-55 Lafayette Street, New York City.



A steam engine is a device by means of which _heat_ is transformed into
_work_. Work may be defined as the result produced by a force acting
through space, and is commonly measured in foot-pounds; a foot-pound
represents the work done in raising 1 pound 1 foot in height. The rate
of doing work is called _power_. It has been found by experiment that
there is a definite relation between heat and work, in the ratio of 1
thermal unit to 778 foot-pounds of work. The number 778 is commonly
called the heat equivalent of work or the mechanical equivalent of heat.

Heat may be transformed into mechanical work through the medium of
steam, by confining a given amount in a closed chamber, and then
allowing it to expand by means of a movable wall (piston) fitted into
one side of the chamber. Heat is given up in the process of expansion,
as shown by the lowered pressure and temperature of the steam, and work
has been done in moving the wall (piston) of the closed chamber against
a resisting force or pressure. When the expansion of steam takes place
without the loss of heat by radiation or conduction, the relation
between the pressure and volume is practically constant; that is, if a
given quantity of steam expands to twice its volume in a closed chamber
of the kind above described, its final pressure will be one-half that of
the initial pressure before expansion took place. A pound of steam at an
absolute pressure of 20 pounds per square inch has a volume of
practically 20 cubic feet, and a temperature of 228 degrees. If now it
be expanded so that its volume is doubled (40 cubic feet), the pressure
will drop to approximately 10 pounds per square inch and the temperature
will be only about 190 degrees. The drop in temperature is due to the
loss of heat which has been transformed into work in the process of
expansion and in moving the wall (piston) of the chamber against a
resisting force, as already noted.

Principle of the Steam Engine

The steam engine makes use of a closed chamber with a movable wall in
transforming the heat of steam into mechanical work in the manner just
described. Fig. 1 shows a longitudinal section through an engine of
simple design, and illustrates the principal parts and their relation to
one another.

The cylinder _A_ is the closed chamber in which expansion takes place,
and the piston _B_, the movable wall. The cylinder is of cast iron,
accurately bored and finished to a circular cross-section. The piston is
carefully fitted to slide easily in the cylinder, being made practically
steam tight by means of packing rings. The work generated in moving the
piston is transferred to the crank-pin _H_ by means of the piston-rod
_C_, and the connecting-rod _F_. The piston-rod passes out of the
cylinder through a stuffing box, which prevents the leakage of steam
around it. The cross-head _D_ serves to guide the piston-rod in a
straight line, and also contains the wrist-pin _E_ which joins the
piston-rod and connecting-rod. The cross-head slides upon the
guide-plate _G_, which causes it to move in an accurate line, and at the
same time takes the downward thrust from the connecting-rod.

The crank-pin is connected with the main shaft _I_ by means of a crank
arm, which in this case is made in the form of a disk in order to give a
better balance. The balance wheel or flywheel _J_ carries the crank past
the dead centers at the ends of the stroke, and gives a uniform motion
to the shaft. The various parts of the engine are carried on a rigid bed
_K_, usually of cast iron, which in turn is bolted to a foundation of
brick or concrete. The power developed is taken off by means of a belted
pulley attached to the main shaft, or, in certain cases, in the form of
electrical energy from a direct-connected dynamo.

[Illustration: Fig. 1. Longitudinal Section through the Ames High-speed

When in action, a certain amount of steam (1/4 to 1/3 of the total
cylinder volume in simple engines) is admitted to one end of the
cylinder, while the other is open to the atmosphere. The steam forces
the piston forward a certain distance by its direct action at the boiler
pressure. After the supply is shut off, the forward movement of the
piston is continued to the end of the stroke by the expansion of the
steam. Steam is now admitted to the other end of the cylinder, and the
operation repeated on the backward or return stroke.

An enlarged section of the cylinder showing the action of the valve for
admitting and exhausting the steam is shown in Fig. 2. In this case the
piston is shown in its extreme backward position, ready for the forward
stroke. The steam chest _L_ is filled with steam at boiler pressure,
which is being admitted to the narrow space back of the piston through
the valve _N_, as indicated by the arrows. The exhaust port _M_ is in
communication with the other end of the cylinder and allows the piston
to move forward without resistance, except that due to the piston-rod,
which transfers the work done by the expanding steam to the crank-pin.
The valve _N_ is operated automatically by a crank or eccentric attached
to the main shaft, and opens and closes the supply and exhaust ports at
the proper time to secure the results described.

Work Diagram

Having discussed briefly the general principle upon which an engine
operates, the next step is to study more carefully the transformation of
heat into work within the cylinder, and to become familiar with the
graphical methods of representing it. Work has already been defined as
the result of force acting through space, and the unit of work as the
foot-pound, which is the work done in raising 1 pound 1 foot in height.
For example, it requires 1 × 1 = 1 foot-pound to raise 1 pound 1 foot,
or 1 × 10 = 10 foot-pounds to raise 1 pound 10 feet, or 10 × 1 = 10
foot-pounds to raise 10 pounds 1 foot, or 10 × 10 = 100 foot-pounds to
raise 10 pounds 10 feet, etc. That is, the product of weight or force
acting, times the distance moved through, represents work; and if the
force is taken in pounds and the distance in feet, the result will be in
foot-pounds. This result may be shown graphically by a figure called a
work diagram.

[Illustration: Fig. 2. Section of Cylinder, showing Slide Valve]

In Fig. 3, let distances on the line _OY_ represent the force acting,
and distances on _OX_ represent the space moved through. Suppose the
figure to be drawn to such a scale that _OY_ is 5 feet in height, and
_OX_ 10 feet long. Let each division on _OY_ represent 1 pound pressure,
and each division on _OX_ 1 foot of space moved through. If a pressure
of 5 pounds acts through a distance of 10 feet, then an amount of 5 × 10
= 50 foot-pounds of work has been done. Referring to Fig. 3, it is
evident that the height _OY_ (the pressure acting), multiplied by the
length _OX_ (the distance moved through), gives 5 × 10 = 50 square feet,
which is the area of the rectangle _YCXO_; that is, the area of a
rectangle may represent work done, if the height represents a force
acting, and the length the distance moved through. If the diagram were
drawn to a smaller scale so that the divisions were 1 inch in length
instead of 1 foot, the area _YCXO_ would still represent the work done,
except each square inch would equal 1 foot-pound instead of each square
foot, as in the present illustration.

[Illustration: Fig. 3. A Simple Work Diagram]

In Fig. 4 the diagram, instead of being rectangular in form, takes a
different shape on account of different forces acting at different
periods over the distance moved through. In the first case (Fig. 3), a
uniform force of 5 pounds acts through a distance of 10 feet, and
produces 5 × 10 = 50 foot-pounds of work. In the second case (Fig. 4),
forces of 5 pounds, 4 pounds, 3 pounds, 2 pounds, and 1 pound, act
through distances of 2 feet each, and produce (5 × 2) + (4 × 2) + (3 ×
2) + (2 × 2) + (1 × 2) = 30 foot-pounds. This is also the area, in
square feet, of the figure _Y54321XO_, which is made up of the areas of
the five small rectangles shown by the dotted lines. Another way of
finding the total area of the figure shown in Fig. 4, and determining
the work done, is to multiply the length by the average of the heights
of the small rectangles. The average height is found by adding the
several heights and dividing the sum by their number, as follows:

5 + 4 + 3 + 2 + 1
- - - - - - - - - = 3, and 3 × 10 = 30 square feet, as before.

[Illustration: Fig. 4. Another Form of Work Diagram]

This, then, means that the average force acting throughout the stroke is
3 pounds, and the total work done is 3 × 10 = 30 foot-pounds.

In Fig. 5 the pressure drops uniformly from 5 pounds at the beginning to
0 at the end of the stroke. In this case also the area and work done are
found by multiplying the length of the diagram by the average height, as

5 + 0
- - - × 10 = 25 square feet,

or 25 foot-pounds of work done.

[Illustration: Fig. 5. Work Diagram when Pressure drops Uniformly]

The object of Figs. 3, 4 and 5 is to show how foot-pounds of work may be
represented graphically by the areas of diagrams, and also to make it
clear that this remains true whatever the form of the diagram. It is
also evident that knowing the area, the average height or pressure may
be found by dividing by the length, and _vice versa_.

Fig. 6 shows the form of work diagram which would be produced by the
action of the steam in an engine cylinder, if no heat were lost by
conduction and radiation. Starting with the piston in the position shown
in Fig. 2, steam is admitted at a pressure represented by the height of
the line _OY_. As the piston moves forward, sufficient steam is admitted
to maintain the same pressure. At the point _B_ the valve closes and
steam is cut off. The work done up to this time is shown by the
rectangle _YBbO_. From the point _B_ to the end of the stroke _C_, the
piston is moved forward by the expansion of the steam, the pressure
falling in proportion to the distance moved through, until at the end of
the stroke it is represented by the vertical line _CX_. At the point _C_
the exhaust valve opens and the pressure drops to 0 (atmospheric
pressure in this case).

As it is always desirable to find the work done by a complete stroke of
the engine, it is necessary to find the average or mean pressure acting
throughout the stroke. This can only be done by determining the area of
the diagram and dividing by the length of the stroke. This gives what is
called the mean ordinate, which multiplied by the scale of the drawing,
will give the mean or average pressure. For example, if the area of the
diagram is found to be 6 square inches, and its length is 3 inches, the
mean ordinate will be 6 ÷ 3 = 2 inches. If the diagram is drawn to such
a scale that 1 inch on _OY_ represents 10 pounds, then the average or
mean pressure will be 2 × 10 = 20 pounds, and this multiplied by the
actual length of the piston stroke will give the work done in
foot-pounds. The practical application of the above, together with the
method of obtaining steam engine indicator diagrams and measuring the
areas of the same, will be taken up in detail under the heading of Steam
Engine Testing.

Definitions Relating to Engine Diagrams

Before taking up the construction of an actual engine diagram, it is
first necessary to become familiar with certain terms which are used in
connection with it.

[Illustration: Fig. 6. The Ideal Work Diagram of a Steam Engine]

_Cut-off._ - The cut-off is the point in the stroke at which the
admission valve closes and the expansion of steam begins.

_Ratio of Expansion._ - This is the reciprocal of the cut-off, that is,
if the cut-off is 1/4, the ratio of expansion is 4. In other words, it
is the ratio of the final volume of the steam at the end of the stroke
to its volume at the point of cut-off. For example, a cylinder takes
steam at boiler pressure until the piston has moved one-fourth the
length of its stroke; the valve now closes and expansion takes place
until the stroke is completed. The one-fourth cylinderful of steam has
become a cylinderful, that is, it has expanded to four times its
original volume, and the ratio of expansion is said to be 4.

_Point of Release._ - This is the point in the stroke at which the
exhaust valve opens and relieves the pressure acting on the piston. This
takes place just before the end of the stroke in order to reduce the
shock when the piston changes its direction of travel.

_Compression._ - This acts in connection with the premature release in
order to reduce the shock at the end of the stroke. During the forward
stroke of an engine the exhaust valve in front of the piston remains
open as shown in Fig. 2. Shortly before the end of the stroke this
closes, leaving a certain amount of steam in the cylinder. The
continuation of the stroke compresses this steam, and by raising its
pressure forms a cushion, which, in connection with the removal of the
pressure back of the piston by release, brings the piston to a stop and
causes it to reverse its direction without shock. High-speed engines
require a greater amount of compression than those running at low speed.

_Clearance_. - This is the space between the cylinder head and the piston
when the latter is at the end of its stroke; it also includes that
portion of the steam port between the valve and the cylinder. Clearance
is usually expressed as a percentage of the piston-displacement of the
cylinder, and varies in different types of engines. The following table
gives approximate values for engines of different design.


Type of Engine Per Cent Clearance

Corliss 1.5 to 3.5
Moderate-speed 3 to 8
High-speed 4 to 10

A large clearance is evidently objectionable because it represents a
space which must be filled with steam at boiler pressure at the
beginning of each stroke, and from which but a comparatively small
amount of work is obtained. As compression increases, the amount of
steam required to fill the clearance space diminishes, but on the other
hand, increasing the compression reduces the mean effective pressure.

_Initial Pressure._ - This is the pressure in the cylinder up to the
point of cut-off. It is usually slightly less than boiler pressure owing
to "wire-drawing" in the steam pipe and ports.

_Terminal Pressure._ - This is the pressure in the cylinder at the time
release occurs, and depends upon the initial pressure, the ratio of
expansion, and the amount of cylinder condensation.

_Back Pressure._ - This is the pressure in the cylinder when the exhaust
port is open, and is that against which the piston is forced during the
working stroke. For example, in Fig. 2 the small space at the left of
the piston is filled with steam at initial pressure, while the space at
the right of the piston is exposed to the back pressure. The working
pressure varies throughout the stroke, due to the expansion of the
steam, while the back pressure remains constant, except for the effect
of compression at the end of the stroke. The theoretical back pressure
in a non-condensing engine (one exhausting into the atmosphere) is that
of the atmosphere or 14.7 pounds per square inch above a vacuum, but in
actual practice it is about 2 pounds above atmospheric pressure, or 17
pounds absolute, due to the resistance of exhaust ports and connecting
pipes. In the case of a condensing engine (one exhausting into a
condenser) the back pressure depends upon the efficiency of the
condenser, averaging about 3 pounds absolute pressure in the best

_Effective Pressure._ - This is the difference between the pressure on
the steam side of the piston and that on the exhaust side, or in other
words, the difference between the working pressure and the back
pressure. This value varies throughout the stroke with the expansion of
the steam.

_Mean Effective Pressure._ - It has just been stated that the effective
pressure varies throughout the stroke. The mean effective pressure (M.
E. P.) is the average of all the effective pressures, and this average
multiplied by the length of stroke, gives the work done per stroke.

_Line of Absolute Vacuum._ - In the diagram shown in Fig. 6, the line
_OX_ is the line of absolute vacuum; that is, it is assumed that there
is no pressure on the exhaust side of the piston. In other words, the
engine is exhausting into a perfect vacuum.

[Illustration: Fig. 7. Constructing a Steam Engine Work Diagram]

_Atmospheric Line._ - This is a line drawn parallel to the line of
absolute vacuum at such a distance above it as to represent 14.7 pounds
pressure per square inch, according to the scale used.

Construction of Ideal Diagram

One of the first steps in the design of a steam engine is the
construction of an ideal diagram, and the engine is planned to produce
this as nearly as possible when in operation. First assume the initial
pressure, the ratio of expansion, and the percentage of clearance, for
the type of engine under consideration. Draw lines _OX_ and _OY_ at
right angles as in Fig. 7. Make _OR_ the same percentage of the stroke
that the clearance is of the piston displacement; make _RX_ equal to the
length of the stroke (on a reduced scale). Erect the perpendicular _RA_
of such a height that it shall represent, to scale, an absolute pressure
per square inch equal to 0.95 of the boiler pressure. Draw in the dotted
lines _AK_ and _KX_, and the atmospheric line _LH_ at a height above
_OX_ to represent 14.7 pounds per square inch. Locate the point of
cut-off, _B_, according to the assumed ratio of expansion. Points on the
expansion curve _BC_ are found as follows: Divide the distance _BK_ into
any number of equal spaces, as shown by _a_, _b_, _c_, _d_, etc., and
connect them with the point _O_. Through the points of intersection with
_BP_, as _a´_, _b´_, _c´_, _d´_, etc., draw horizontal lines, and
through _a_, _b_, _c_, _d_, etc., draw vertical lines. The intersection
of corresponding horizontal and vertical lines will be points on the
theoretical expansion line. If the engine is to be non-condensing, the
theoretical work, or indicator diagram, as it is called, will be bounded
by the lines _ABCHG_.

The actual diagram will vary somewhat from the theoretical, as shown by
the shaded lines. The admission line between _A_ and _B_ will slant
downward slightly, and the point of cut-off will be rounded, owing to
the slow closing of the valve. The first half of the expansion line
will fall below the theoretical, owing to a drop in pressure caused
by cylinder condensation, but the actual line will rise above
the theoretical in the latter part of the stroke on account of
re-evaporation, due to heat given out by the hot cylinder walls to the
low-pressure steam. Instead of the pressure dropping abruptly at _C_,
release takes place just before the end of the stroke, and the diagram
is rounded at _CF_ instead of having sharp corners. The back pressure
line _FD_ is drawn slightly above the atmospheric line, a distance to
represent about 2 pounds per square inch. At _D_ the exhaust valve
closes and compression begins, rounding the bottom of the diagram up to

The area of the actual diagram, as shown by the shaded lines in Fig. 7,
will be smaller than the theoretical, in about the following ratio:

Large medium-speed engines, 0.90 of theoretical area.
Small medium-speed engines, 0.85 of theoretical area.
High-speed engines, 0.75 of theoretical area.



The capacity or power of a steam engine is rated in horsepower, one
horsepower (H. P.) being the equivalent of 33,000 foot-pounds of work
done per minute. The horsepower of a given engine may be computed by the

H. P. = - - -

in which

_A_ = area of piston, in square inches,
_P_ = mean effective pressure per square inch,
_L_ = length of stroke, in feet,
_N_ = number of strokes per minute = number of revolutions × 2.

The derivation of the above formula is easily explained, as follows: The
area of the piston, in square inches, multiplied by the mean effective
pressure, in pounds per square inch, gives the total force acting on the
piston, in pounds. The length of stroke, in feet, times the number of
strokes per minute gives the distance the piston moves through, in feet
per minute. It has already been shown that the pressure in pounds
multiplied by the distance moved through in feet, gives the foot-pounds
of work done. Hence, _A_ × _P_ × _L_ × _N_ gives the foot-pounds of work
done per minute by a steam engine. If one horsepower is represented by
33,000 foot-pounds per minute, the power or rating of the engine will be
obtained by dividing the total foot-pounds of work done per minute by
33,000. For ease in remembering the formula given, it is commonly

H. P. = - - - ,

in which the symbols in the numerator of the second member spell the
word "Plan."

_Example_: - Find the horsepower of the following engine, working under
the conditions stated below:

Diameter of cylinder, 12 inches.
Length of stroke, 18 inches.
Revolutions per minute, 300.
Mean effective pressure (M. E. P.), 40 pounds.

In this problem, then, _A_ = 113 square inches; _P_ = 40 pounds; _L_ =
1.5 feet; and _N_ = 600 strokes.

Substituting in the formula,

40 × 1.5 × 113 × 600
H. P. = - - - - - - - - - - = 123.

The mean effective pressure may be found, approximately, for different
conditions by means of the factors in the following table of ratios,
covering ordinary practice. The rule used is as follows: Multiply the
absolute initial pressure by the factor corresponding to the clearance
and cut-off as found from Table II, and subtract the absolute back
pressure from the result, assuming this to be 17 pounds for

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