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      |  Inconsistencies have not been corrected (hyphenated     |
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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

NUMBER 70

STEAM ENGINES




CONTENTS

  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.




CHAPTER I

ACTION OF STEAM ENGINES


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
Engine]

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.
          5

[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
follows:

  5 + 0
  ----- × 10 = 25 square feet,
    2

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.

TABLE I. CLEARANCE OF STEAM ENGINES

  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
practice.

_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
_E_.

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.




CHAPTER II

RATING AND GENERAL PROPORTIONS OF STEAM ENGINES


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
formula:

          _APLN_
  H. P. = ------
          33,000

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
written

          _PLAN_
  H. P. = ------,
          33,000

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.
                 33,000

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
non-condensing engines, and 3 pounds for condensing.

_Example 1_:--A non-condensing engine having 3 per cent clearance, cuts
off at 1/3 stroke; the initial pressure is 90 pounds gage. What is the
M. E. P.?

The absolute initial pressure is 90 + 15 = 105 pounds. The factor for 3
per cent clearance and 1/3 cut-off, from Table II, is 0.71. Applying the
rule we have: (105 × 0.71) - 17 = 57.5 pounds per square inch.

_Example 2_:--A condensing engine has a clearance of 5 per cent. It is
supplied with steam at 140 pounds gage pressure, and has a ratio of
expansion of 6. What is the M. E. P.?

The absolute initial pressure is 140 + 15 = 155. The factor for a ratio
of expansion of 6 (1/6 cut-off) and 5 per cent clearance is 0.5, which
gives (155 × 0.5) - 3 = 74.5 pounds per square inch.

The power of an engine computed by the method just explained is called
the indicated horsepower (I. H. P.), and gives the total power
developed, including that required to overcome the friction of the
engine itself. The delivered or brake horsepower (B. H. P.) is that
delivered by the engine after deducting from the indicated horsepower
the power required to operate the moving parts. The brake horsepower
commonly varies from 80 to 90 per cent of the indicated horsepower at
full load, depending upon the type and size of engine.

In proportioning an engine cylinder for any given horsepower, the
designer usually has the following data, either given or assumed, for
the special type of engine under consideration: Initial pressure, back
pressure, clearance, cut-off, and piston speed.

These quantities vary in different types of engines, but in the absence
of more specific data the values in Table III will be found useful. The
back pressure may be taken as 17 pounds per square inch, absolute, for
non-condensing engines, and as 3 pounds for condensing engines as
previously stated.

TABLE II. FACTORS FOR FINDING MEAN EFFECTIVE PRESSURE

  +--------------+-----------------------------------------+
  |              |            Point of Cut-off             |
  |  Percentage  +------+------+------+------+------+------+
  | of Clearance | 1/10 | 1/6  | 1/4  | 1/3  | 1/2  | 3/4  |
  +--------------+------+------+------+------+------+------+
  |     1.75     | 0.35 | 0.48 | 0.60 | 0.70 | 0.85 | 0.96 |
  |     3.00     | 0.37 | 0.49 | 0.61 | 0.71 | 0.85 | 0.96 |
  |     5.00     | 0.39 | 0.50 | 0.62 | 0.72 | 0.86 | 0.97 |
  |     7.00     | 0.41 | 0.52 | 0.63 | 0.73 | 0.86 | 0.97 |
  |     9.00     | 0.43 | 0.54 | 0.64 | 0.73 | 0.86 | 0.97 |
  +--------------+------+------+------+------+------+------+

The first step in proportioning the cylinder is to compute the
approximate mean effective pressure from the assumed initial pressure,
clearance, and cut-off, by the method already explained. Next assume the
piston speed for the type of engine to be designed, and determine the
piston area by the following formula:

           33,000 H. P.
  A = -----------------------.
      M. E. P. × piston speed

This formula usually gives the diameter of the piston in inches and
fractions of an inch, while it is desirable to make this dimension an
even number of inches. This may be done by taking as the diameter the
nearest whole number, and changing the piston speed to correspond. This
is done by the use of the following equation.

  First piston speed × first piston area
  -------------------------------------- = new piston speed.
              new piston area

In calculating the effective piston area, the area of the piston rod
upon one side must be allowed for. The effective or average piston area
will then be (2_A_ - _a_)/2, in which _A_ = area of piston, _a_ = area
of piston rod. This latter area must be assumed. After assuming a new
piston diameter of even inches, its effective or average area must be
used in determining the new piston speed. The length of stroke is
commonly proportioned to the diameter of cylinder, and the piston speed
divided by this will give the number of strokes per minute.

_Example_:--Find the diameter of cylinder, length of stroke, and
revolutions per minute for a simple high-speed non-condensing engine of
200 I. H. P., with the following assumptions: Initial pressure, 90
pounds gage; clearance, 7 per cent; cut-off, 1/4; piston speed, 700 feet
per minute; length of stroke, 1.5 times cylinder diameter.

TABLE III. PRESSURE, CLEARANCE, CUT-OFF AND PISTON SPEED OF STEAM
ENGINES

  +---------------------+------------+-----------+-------------+------------+
  |                     |  Initial   | Clearance,|   Cut-off,  |   Piston   |
  |   Type of Engine    | Pressure,  |  Per Cent |  Proportion | Speed, Feet|
  |                     |  (Gage)    |           |  of Stroke  | per Minute |
  +---------------------+------------+-----------+-------------+------------+
  |Simple high-speed    |  80 to  90 |4   to 10  | 1/4  to 1/3 | 600 to 800 |
  |Simple medium-speed  |  80 to  90 |3   to  8  | 1/4  to 1/3 | 500 to 700 |
  |Simple Corliss       |  80 to  90 |1.5 to  3.5| 1/4  to 1/3 | 400 to 600 |
  |Compound high-speed  | 130 to 140 |4   to 10  | 1/10 to 1/8 | 600 to 800 |
  |Compound medium-speed| 130 to 140 |3   to  8  | 1/10 to 1/8 | 500 to 700 |
  |Compound Corliss     | 130 to 140 |1.5 to  3.5| 1/10 to 1/8 | 400 to 600 |
  +---------------------+------------+-----------+-------------+------------+

By using the rules and formulas in the foregoing, we have:

  M. E. P. = (90 + 15) × 0.63 - 17 = 49 pounds.

        33,000 × 200
  _A_ = ------------ = 192.4 square inches.
          49 × 700

The nearest piston diameter of even inches is 16, which corresponds to
an area of 201 square inches. Assume a piston rod diameter of 2-1/2
inches, corresponding to an area of 4.9 square inches, from which the
average or effective piston area is found to be ((2 × 201) - 4.9)/2 =
198.5 square inches.

Determining now the new piston speed, we have:

  700 × 192.4
  ----------- = 678.5 feet per minute.
     198.5

Assuming the length of stroke to be 1.5 times the diameter of the
cylinder, it will be 24 inches, or 2 feet.

This will call for 678.5 ÷ 2 = 340 strokes per minute, approximately, or
340 ÷ 2 = 170 revolutions per minute.




CHAPTER III

STEAM ENGINE DETAILS


Some of the most important details of a steam engine are those of its
valve gear. The simplest form of valve is that known as the plain slide
valve, and as nearly all others are a modification of this, it is
essential that the designer should first familiarize himself with this
particular type of valve in all its details of operation. After this has
been done, a study of other forms of valves will be found a
comparatively easy matter. The so called Corliss valve differs radically
from the slide valve, but the results to be obtained and the terms used
in its design are practically the same. The valve gear of a steam engine
is made up of the valve or valves which admit steam to and exhaust it
from the cylinder, and of the mechanism which governs the valve
movements, the latter usually consisting of one or more eccentrics
attached to the main shaft.

[Illustration: Fig. 8. Longitudinal Section of Slide Valve with Ports]


The Slide Valve

Fig. 8 shows a longitudinal section of a slide valve with the ports,
bridges, etc. The valve is shown in mid-position in order that certain
points relating to it may be more easily understood. The valve, _V_,
consists of a hollow casting, with ends projecting beyond the ports as
shown; the lower face is smoothly finished and fitted to the valve seat
_AB_. In operation it slides back and forth, opening and closing the
ports which connect the steam chest with the cylinder. Steam is admitted
to the cylinder when either port _CD_ or _DC_ is opened, and is released
when the ports are brought into communication with the exhaust port
_MN_. This is accomplished by the movement of the valve, which brings
one of the cylinder ports and the exhaust port both under the hollow
arch _K_. The portions _DM_ and _ND_ of the valve seat are called the
bridges.

It will be seen by reference to Fig. 8 that the portions _OI_ and _IO_
are wider than the ports which they cover. This extra width is called
the _lap_, _OC_ being the outside lap and _DI_ the inside or exhaust
lap. The object of outside lap is that the steam may be shut off after
the piston has moved forward a certain distance, and be expanded during
the remainder of the stroke. If there were no outside lap, steam would
be admitted throughout the entire stroke and there would be no
expansion. If there were no inside lap, exhaust would take place
throughout the whole stroke, and the advantages of premature release and
compression would be lost. Hence, outside lap affects the cut-off, and
inside lap affects release and compression. A valve has _lead_ when it
begins to uncover the steam port before the end of the return stroke of
the piston. This is shown in Fig. 9, where the piston _P_ is just ready
to start on its forward stroke as indicated by the arrow. The valve has
already opened a distance equal to the lead, and the steam has had an
opportunity to enter and fill the clearance space before the beginning
of the stroke. The lead varies in different engines, being greater in
high-speed than in low-speed types.

[Illustration: Fig. 9. Illustration showing Lead of Slide Valve]

[Illustration: Fig. 10. Diagrammatical View of Eccentric]


The Eccentric

The slide valve is usually driven by an eccentric attached to the main
shaft. A diagram of an eccentric is shown in Fig. 10. An eccentric is,
in reality, a short crank with a crank-pin of such size that it
surrounds the shaft. The arm of a crank is the distance between the
center of the shaft, and the center of the crank-pin. The throw of an
eccentric corresponds to this, and is the distance between the center of
the shaft and the center of the eccentric disk, as shown at _a_ in Fig.
10. The disk is keyed to the shaft, and as the shaft revolves, the
center of the disk rotates about it as shown by the dotted line, and
gives a forward and backward movement to the valve rod equal to twice
the throw _a_.

[Illustration: Fig. 11. Relations of Crank and Eccentric]

In Fig. 11 let _A_ represent the center of the main shaft, _B_ the
crank-pin to which the connecting-rod is attached (see _H_, Fig. 1), and
the dotted circle through _B_ the path of the crank-pin around the
shaft. For simplicity, let the eccentric be represented in a similar
manner by the crank _Ab_, and its path by the dotted circle through _b_.
Fig. 12 shows a similar diagram with the piston _P_ and the valve in the
positions corresponding to the positions of the crank and eccentric in
Fig. 11, and in the diagram at the right in Fig. 12. The piston is at
the extreme left, ready to start on its forward stroke toward the right.
The crank-pin _B_ is at its extreme inner position. When the valve is at
its mid-position, as in Fig. 8, the eccentric arm _Ab_ will coincide
with the line _AC_, Fig. 11. If the eccentric is turned on the shaft
sufficiently to bring the left-hand edge _O_, Fig. 8, of the valve in
line with the edge _C_ of the port, the arm of the eccentric will have
moved from its vertical position to that shown by the line _Ab´_ in Fig.
11. The angle through which the eccentric has been turned from the
vertical to bring about this result is called the _angular advance_, and
is shown by angle _CAb´_ in Fig. 11. The angular advance evidently
depends upon the amount of lap.

If the valve is to be given a lead, as indicated in Fig. 12, the
eccentric must be turned still further on the shaft to open the valve
slightly before the piston starts on its forward movement. This brings
the eccentric to the position _Ab_ shown in Fig. 11. The angle through
which the eccentric is turned to give the necessary lead opening to the
valve is called the _angle of lead_, and is shown by angle _b´Ab_. By
reference to Fig. 11, it is seen that the total angle between the crank
and the eccentric is 90 degrees, plus the angular advance, plus the
angle of lead. This is the total angle of advance.

[Illustration: Fig. 12. Piston just beginning Forward Stroke]

The relative positions of the piston and valve at different periods of
the stroke are illustrated in Figs. 12 to 16. Fig. 12 shows the piston
just beginning the forward stroke, the valve having uncovered the
admission port an amount equal to the lead. The crank is in a horizontal
position, and the eccentric has moved from the vertical an amount
sufficient to move the valve toward the right a distance equal to the
outside lap plus the lead. The arrows show that steam is entering the
left-hand port and is being exhausted through the right-hand port.

[Illustration: Fig. 13. Steam Port fully Opened]

In Fig. 13 it is seen that the valve has traveled forward sufficiently
to open the steam port to its fullest extent, and the piston has moved
to the point indicated. The exhaust port is still wide open, and the
relative positions of the crank and eccentric are shown in the diagram
at the right. In Fig. 14 the eccentric has passed the horizontal
position and the valve has started on its backward stroke, while the
piston is still moving forward. The admission port is closed, cut-off
having taken place, and the steam is expanding. The exhaust port is
still partially open.

[Illustration: Fig. 14. Valve has started on Backward Stroke]

[Illustration: Fig. 15. Both Steam Ports Closed]

In Fig. 15 both ports are closed and compression is taking place in
front of the piston while expansion continues back of it. Release occurs
in Fig. 16 just before the piston reaches the end of its stroke. The
eccentric crank is now in a vertical position, pointing downward, and
exhaust is just beginning to take place through the left-hand port.
This completes the different stages of a single stroke, the same
features being repeated upon the return of the piston to its original
position. The conditions of lap, lead, angular advance, etc., pertain to
practically all valves, whatever their design.

[Illustration: Fig. 16. Exhaust Begins]


Different Types of Valves

In the following are shown some of the valves in common use, being, with
the exception of the Corliss, modifications of the plain slide valve,
and similar in their action.

[Illustration: Fig. 17. Engine with Piston Valve]

_Double-Ported Balanced Valve._--A valve of this type has already been
shown in Fig. 2. This valve is flat in form, with two finished
surfaces, and works between the valve-seat and a plate, the latter
being prevented from pressing against the valve by special bearing
surfaces which hold it about 0.002 inch away. The construction of the
valve is such that when open the steam reaches the port through two
openings as indicated by the arrows at the left. The object of this is
to reduce the motion of the valve and quicken its action in admitting
and cutting off steam.

[Illustration: Fig. 18. Section through Cylinder of Engine of the
Four-valve Type]

[Illustration: Fig. 19. Different Types of Corliss Valves]

_Piston Valve._--The piston valve shown in Fig. 17 is identical in its
action with the plain slide valve shown in Fig. 8, except that it is
circular in section instead of being flat or rectangular. The advantage
claimed for this type of valve is the greater ease in fitting
cylindrical surfaces as compared with flat ones. The valve slides in
special bushings which may be renewed when worn. Piston valves are also
made with double ports.

[Illustration: Fig. 20. Longitudinal Section through Corliss Engine]

[Illustration: Fig. 21. The Gridiron Valve]

_Four-Valve Type._--Fig. 18 shows a horizontal section through the
cylinder and valves of an engine of the four-valve type. The admission
valves are shown at the top of the illustration and the exhaust valves
at the bottom, although, in reality, they are at the sides of the
cylinder. The advantage of an arrangement of this kind is that the
valves may be set independently of each other and the work done by the
two ends of the cylinder equalized. The various events, such as
cut-off, compression, etc., may be adjusted without regard to each
other, and in such a manner as to give the best results, a condition
which is not possible with a single valve.

_Gridiron Valve._--One of the principal objects sought in the design of
a valve is quick action at the points of admission and cut-off. This
requires the uncovering of a large port opening with a comparatively
small travel of the valve. The gridiron valve shown in Fig. 21 is
constructed especially for this purpose. This valve is of the four-valve
type, one steam valve and one exhaust valve being shown in the section.
Both the valve and its seat contain a number of narrow openings or
ports, so that a short movement of the valve will open or close a
comparatively large opening. For example, the steam valve in the
illustration has 12 openings, so that if they are 1/4 inch in width
each, a movement of 1/4 inch of the valve will open a space 12 × 1/4 = 3
inches in length.

[Illustration: Fig. 22. The Monarch Engine with Corliss Valve Gear.--A,
Rod to Eccentric; B, Governor; C, Reach Rod; D, Radial Arm; E, Steam
Valve; F, Bell-crank; G, Wrist Plate; H, Exhaust Valve; K, Dash-pot]

_Corliss Valve._--A section through an engine cylinder equipped with
Corliss valves is shown in Fig. 20. There are four cylindrical valves in
this type of engine, two steam valves at the top and two exhaust valves
at the bottom. This arrangement is used to secure proper drainage. The
action of the admission and exhaust valves is indicated by the arrows,
the upper left-hand and the lower right-hand valve being open and the
other two closed.

Side and sectional views of different forms of this type of valve are
shown in Fig. 19. They are operated by means of short crank-arms which
are attached to a wrist-plate by means of radial arms or rods, as shown
in Fig. 22. The wrist-plate, in turn, is given a partial backward and
forward rotation by means of an eccentric attached to the main shaft and
connected to the upper part of the wrist-plate by a rod as indicated.
The exhaust valves are both opened and closed by the action of the
wrist-plate and connecting rods. The steam valves are opened in this
manner, but are closed by the suction of dash pots attached to the drop
levers on the valve stems by means of vertical rods, as shown.

[Illustration: Figs. 23 to 26. Action of Corliss Valve Gear]

The action of the steam or admission valves is best explained by
reference to Figs. 23 to 26. Referring to Fig. 23, _A_ is a bell-crank
which turns loosely upon the valve stem _V_. The lower left-hand
extension of _A_ carries the grab hook _H_, while the upper extension is
connected with the wrist-plate as indicated. Ordinarily the hook _H_ is
pressed inward by the spring _S_, so that the longer arm of the hook is
always pressed against the knock-off cam _C_. The cam _C_ also turns
upon the valve stem _V_ and is connected with the governor by means of a
reach rod as indicated in Fig. 23 and shown in Fig. 22. The drop lever
_B_ is keyed to the valve stem _V_, and is connected with the dash pot
by a rod as indicated by the dotted line. This is also shown in Fig. 22.
The end of the drop lever carries a steel block (shown shaded in Fig.
23), which engages with the grab hook _H_.

When in operation, the bell-crank is rotated in the direction of the
arrow by the action of the wrist-plate and connecting-rod. As the
bell-crank rotates, the grab hook engages the steel block at the end of
the drop lever _B_ and lifts it, thus causing the valve to open, and to
remain so until the bell-crank has advanced so far that the longer arm
of the grab hook _H_ is pressed outward by the projection on the
knock-off cam, as shown in Fig. 24. The drop lever now being released,
the valve is quickly closed by the suction of the dash pot, which pulls
the lever down to its original position by means of the rod previously
mentioned.

[Illustration: Fig. 27. Governor for Corliss Engine]

The governor operates by changing the point of cut-off through the
action of the cam _C_. With the cam in the position shown in Fig. 25,
cut-off occurs earlier than in Fig. 24. Should the cam be turned in the
opposite direction (clockwise), cut-off would take place later. A
detailed view of the complete valve mechanism described is shown
assembled in Fig. 26, with each part properly named. A detail of the
governor is shown in Fig. 27. An increase in speed causes the revolving
balls _BB_ to swing outward, thus raising the weight _W_ and the sleeve
_S_. This in turn operates the lever _L_ through rod _R_ and a
bell-crank attachment, as shown in the right-hand view. An upward and
downward movement of the balls, due to a change in speed of the engine,
swings the lever _L_ backward and forward as shown by the full and
dotted lines. The ends of this lever are attached by means of reach-rods
to the knock-off cams, this being shown more clearly in Fig. 22. The
connections between the lever _L_ and cam _C_ are such that a raising of
the balls, due to increased speed, will reduce the cut-off and thus slow
down the engine. On the other hand, a falling of the balls will lengthen
the cut-off through the same mechanism.

[Illustration: Fig. 28. Dash-pot for Corliss Engine]

[Illustration: Figs. 29 and 30. Plan and Longitudinal Section of
Adjustable Piston]

Mention has already been made of the dash pot which is used to close the
valve suddenly after being released from the grab hook. The dash-pot rod
is shown in Fig. 26, and indicated by dotted lines in Figs. 23 to 25. A
detailed view of one form of dash pot is shown in Fig. 28. When the
valve is opened, the rod attached to lever _B_, Figs. 23 and 24, raises
the piston _P_, Fig. 28, and a partial vacuum is formed beneath it which
draws the piston and connecting rod down by suction as soon as the lever
_B_ is released, and thus closes the valve suddenly and without shock.
The strength of the suction and the air cushion for this piston are
regulated by the inlet and outlet valves shown on the sides of the dash
pot.


Engine Details

Figs. 29 to 37 show various engine details, and illustrate in a simple
way some of the more important principles involved in steam engine
design.

[Illustration: Fig. 31. A Typical Cross-head]

[Illustration: Figs. 32 and 33. Methods Commonly Used for Taking Up Wear
in a Connecting-rod]

A partial cross-section of an adjustable piston is shown in Fig. 29, and
a longitudinal section of the same piston in Fig. 30. The principal
feature to be emphasized is the method of automatic expansion employed
to take up any wear and keep the piston tight. In setting up the piston
a hand adjustment is made of the outer sleeve or ring _R_ by means of
the set-screws _AA_. Ring _R_ is made in several sections, so that it
may be expanded in the form of a true circle. Further tightness is
secured without undue friction by means of the packing ring _P_ which
fits in a groove in _R_ and is forced lightly against the walls of the
cylinder by a number of coil springs, one of which is shown at _S_. As
the cylinder and piston become worn, screws _A_ are adjusted from time
to time, and the fine adjustment for tightness is cared for by the
packing ring _P_ and the coil springs _S_.

The points to be brought out in connection with the cross-head are the
methods of alignment and adjustment. A typical cross-head is shown in
cross and longitudinal sections in Fig. 31. Alignment in a straight
line, longitudinally, is secured by the cylindrical form of the bearing
surfaces or shoes, shown at _S_. These are sometimes made V-shaped in
order to secure the same result. The wear on a cross-head comes on the
surfaces _S_, and is taken up by the use of screw wedges _W_, shown in
the longitudinal section. As the sliding surfaces become worn, the
wedges are forced in slightly by screwing in the set-screws and clamping
them in place by means of the check-nuts.

[Illustration: Fig. 34. Outboard Bearing for Corliss Type Engine]

[Illustration: Fig. 35. Inner Bearing and Bed of Corliss Engine]

The method commonly employed in taking up the wear in a connecting-rod
is shown in Figs. 32 and 33. The wear at the wrist-pin is taken by the
so called brasses, shown at _B_ in the illustrations. The inner brass,
in both cases, fits in a suitable groove, and is held stationary when
once in place. The outer brass is adjustable, being forced toward the
wrist-pin by a sliding wedge which is operated by one or more
set-screws. In Fig. 32 the wedge is held in a vertical position, and is
adjusted by two screws as shown. The arrangement made use of in Fig. 33
has the wedge passing through the rod in a horizontal position, and
adjusted by means of a single screw, as shown in the lower view. With
the arrangements shown, tightening up the brasses shortens the length of
the rod. In practice the wedges at each end of the rod are so placed
that tightening one shortens the rod, and tightening the other lengthens
it, the total effect being to keep the connecting-rod at its original
length.

A common form of outboard bearing for an engine of the slow-speed or
Corliss type is illustrated in Fig. 34. The various adjustments for
alignment and for taking up wear are the important points considered in
this case. The plate _B_ is fastened to the stone foundation by anchor
bolts not shown. Sidewise movement is secured by loosening the bolts
_C_, which pass through slots in the bearing, and adjusting by means of
the screws _S_. Vertical adjustment is obtained by use of the wedge _W_,
which is forced in by the screw _A_, as required. The inner bearing and
bed piece of a heavy duty Corliss engine is shown in Fig. 35. The
bearing in this case is made up of four sections, so arranged that
either horizontal or vertical adjustment may be secured by the use of
adjusting screws and check-nuts.

Engines of the slide-valve type are usually provided either with a
fly-ball throttling governor, or a shaft governor. A common form of
throttling governor is shown in Fig. 36. As the speed increases the
balls _W_ are thrown outward by the action of the centrifugal force, and
being attached to arms hinged above them, any outward movement causes
them to rise. This operates the spindle _S_, which, in turn, partially
closes the balanced valve in body _B_, thus cutting down the steam
supply delivered to the engine. The action of a throttling governor upon
the work diagram of an engine is shown in Fig. 38. Let the full line
represent the form of the diagram with the engine working at full load.
Now, if a part of the load be thrown off, the engine will speed up
slightly, causing the governor to act as described, thus bringing the
admission and expansion lines into the lower positions, as shown in
dotted lines.

[Illustration: Fig. 36. Common Form of Throttling Governor]

The shaft governor is used almost universally on high-speed engines, and
is shown in one form in Fig. 37. It consists, in this case, of two
weights _W_, hinged to the spokes of the wheel near the circumference
by means of suitable arms. Attached to the arms, as shown, are coil
springs _C_. The ends of the arms beyond the weights are connected by
means of levers _L_ to the eccentric disk. When the engine speeds up,
the weights tend to swing outward toward the rim of the wheel, the
amount of the movement being regulated by the tension of the springs
_C_. As the arms move outward, the levers at the ends turn the eccentric
disk on the shaft, the effect of which is to change the angle of advance
and shorten the cut-off. When the speed falls below the normal, the
weights move toward the center and the cut-off is lengthened. The effect
of this form of governor on the diagram is shown in Fig. 39. The full
line represents the diagram at full load, and the dotted line when the
engine is under-loaded.

[Illustration: Fig. 37. Shaft Governor for High-speed Engine]




CHAPTER IV

STEAM ENGINE ECONOMY


Under the general heading of steam engine economy, such items as
cylinder condensation, steam consumption, efficiency, ratio of
expansion, under- and over-loading, condensing, etc., are treated.

The principal waste of steam in the operation of an engine is due to
condensation during the first part of the stroke. This condensation is
due to the fact that during expansion and exhaust the cylinder walls
and head and the piston are in contact with comparatively cool steam,
and, therefore, give up a considerable amount of heat. When fresh steam
is admitted at a high temperature, it immediately gives up sufficient
heat to raise the cylinder walls to a temperature approximating that of
the entering steam. This results in the condensation of a certain amount
of steam, the quantity depending upon the time allowed for the transfer
of heat, the area of exposed surface, and the temperature of the
cylinder walls. During the period of expansion the temperature falls
rapidly, and the steam being wet, absorbs a large amount of heat. After
the exhaust valve opens, the drop in pressure allows the moisture that
has collected on the cylinder walls to evaporate into steam, so that
during the exhaust period but little heat is transferred. With the
admission of fresh steam at boiler pressure, a mist is condensed on the
cylinder walls, which greatly increases the rapidity with which heat is
absorbed.

The amount of heat lost through cylinder condensation is best shown by a
practical illustration. One horsepower is equal to 33,000 foot-pounds of
work per minute, or 33,000 × 60 = 1,980,000 foot-pounds per hour. This
is equivalent to 1,980,000 ÷ 778 = 2,550 heat units. The latent heat of
steam at 90 pounds gage pressure is 881 heat units. Hence, 2,250 ÷ 881 =
2.9 pounds of steam at 90 pounds pressure is required per horsepower,
provided there is no loss of steam, and all of the contained heat is
changed into useful work. As a matter of fact, from 30 to 35 pounds of
steam are required in the average simple non-condensing high-speed
engine.

There are three remedies which are used to reduce the amount of cylinder
condensation. The first to be used was called steam jacketing, and
consisted in surrounding the cylinder with a layer of high-pressure
steam, the idea being to keep the inner walls up to a temperature nearly
equal to that of the incoming steam. This arrangement is but little used
at the present time, owing both to the expense of operation and to its
ineffectiveness as compared with other methods.

The second remedy is the use of superheated steam. It has been stated
that the transfer of heat takes place much more rapidly when the
interior surfaces are covered with a coating of moisture or mist.
Superheated steam has a temperature considerably above the point of
saturation at the given pressure; hence, it is possible to cool it a
certain amount before condensation begins. This has the effect of
reducing the transfer of heat for a short period following admission,
and this is the time that condensation takes place most rapidly under
ordinary conditions with saturated steam. This, in fact, is the
principal advantage derived from the use of superheated steam, although
it is also lighter for a given volume, and therefore, a less weight of
steam is required, to fill the cylinder up to the point of cut-off. The
economical degree of superheating is considered to be that which will
prevent the condensation of any steam on the walls of the cylinder up to
the point of cut-off, thus keeping them at all times free from moisture.
The objections to superheated steam are its cutting effect in the
passages through which it flows, and the difficulty experienced in
lubricating the valves and cylinder at such a high temperature. The
third and most effective remedy for condensation losses is that known as
compounding, which will be treated under a separate heading in the
following.


Multiple Expansion Engines

It has been explained that cylinder condensation is due principally to
the change in temperature of the interior surfaces of the cylinder,
caused by the variation in temperature of the steam at initial and
exhaust pressures. Therefore, if the temperature range be divided
between two cylinders which are operated in series, the steam condensed
in the first or high pressure cylinder will be re-evaporated and passed
into the low-pressure cylinder as steam, where it will again be
condensed and re-evaporated as it passes into the exhaust pipe.
Theoretically, this should reduce the condensation loss by one-half, and
if three cylinders are used, the loss should be only one-third of that
in a simple engine. In actual practice the saving is not as great as
this, but with the proper relation between the cylinders, these results
are approximated.

Engines in which expansion takes place in two stages are called compound
engines. When three stages are employed, they are called triple
expansion engines. Compounding adds to the first cost of an engine, and
also to the friction, so that in determining the most economical number
of cylinders to employ, the actual relation between the condensation
loss and the increased cost of the engine and the friction loss, must be
considered. In the case of power plant work, it is now the practice to
use compound engines for the large sizes, while triple expansion engines
are more commonly employed in pumping stations. Many designs of multiple
expansion engines are provided with chambers between the cylinders,
called receivers. In engines of this type the exhaust is frequently
reheated in the receivers by means of brass coils containing live steam.
In the case of a cross-compound engine, a receiver is always used. In
the tandem design it is often omitted, the piping between the two
cylinders being made to answer the purpose.

The ratio of cylinder volumes in compound engines varies with different
makers. The usual practice is to make the volume of the low-pressure
cylinder from 2.5 to 3 times that of the high-pressure. The total ratio
of expansion in a multiple expansion engine is the product of the ratios
in each cylinder. For example, if the ratio of expansion is 4 in each
cylinder in a compound engine, the total ratio will be 4 × 4 = 16. The
effect of a triple-expansion engine is sometimes obtained in a measure
by making the volume of the low-pressure cylinder of a compound engine 6
or 7 times that of the high-pressure. This arrangement produces a
considerable drop in pressure at the end of the high-pressure stroke,
with the result of throwing a considerable increase of work on the
high-pressure cylinder without increasing its ratio of expansion, and at
the same time securing a large total ratio of expansion in the engine.

In the case of vertical engines, the low-pressure cylinder is sometimes
divided into two parts in order to reduce the size of cylinder and
piston. In this arrangement a receiver of larger size than usual is
employed, and the low-pressure cranks are often set at an angle with
each other.

Another advantage gained by compounding is the possibility to expand the
steam to a greater extent than can be done in a single cylinder engine,
thus utilizing, as useful work, a greater proportion of the heat
contained in the steam. This also makes it possible to employ higher
initial pressures, in which there is a still further saving, because of
the comparatively small amount of fuel required to raise the pressure
from that of the common practice of 80 or 90 pounds for simple engines,
to 120 to 140 pounds, which is entirely practical in the case of
compound engines. With triple expansion, initial pressures of 180 pounds
or more may be used to advantage. The gain from compounding may amount
to about 15 per cent over simple condensing engines, taking steam at the
same initial pressure. When compound condensing engines are compared
with simple non-condensing engines, the gain in economy may run from 30
to 40 per cent.

TABLE IV. STEAM CONSUMPTION OF ENGINES

  +-------------------------+--------------------------------+
  |                         | Pounds of Steam per Indicated  |
  |                         |      Horsepower per Hour       |
  |  Kind of Engine         +----------------+---------------+
  |                         | Non-condensing |  Condensing   |
  +-------------------------+----------------+---------------+
  |        { High-speed     |       32       |       24      |
  | Simple { Medium-speed   |       30       |       23      |
  |        { Corliss        |       28       |       22      |
  |                         |                |               |
  |          { High-speed   |       26       |       20      |
  | Compound { Medium-speed |       25       |       19      |
  |          { Corliss      |       24       |       18      |
  +-------------------------+----------------+---------------+


Steam Consumption and Ratio of Expansion

The steam consumption is commonly called the _water rate_, and is
expressed in pounds of dry steam required per indicated horsepower per
hour. This quantity varies widely in different types of engines, and
also in engines of the same kind working under different conditions. The
water rate depends upon the "cylinder losses," which are due principally
to condensation, although the effects of clearance, radiation from
cylinder and steam chest, and leakage around valves and piston, form a
part of the total loss. Table IV gives the average water rate of
different types of engines working at full load.

The most economical ratio of expansion depends largely upon the type of
the engine. In the case of simple engines, the ratio is limited to 4 or
5 on account of excessive cylinder condensation in case of larger
ratios. This limits the initial pressure to an average of about 90
pounds for engines of this type. In the case of compound engines, a
ratio of from 8 to 10 is commonly employed to advantage, while with
triple-expansion engines, ratios of 12 to 15 are found to give good
results.

[Illustration: Fig. 38. Action of Throttling Governor on Indicator
Diagram]

[Illustration: Fig. 39. Effect of Shaft Governor on Indicator Diagram]

[Illustration: Fig. 40. Increasing Power of Engine by Condensing]

[Illustration: Fig. 41. Decreasing Steam Consumption by Condensing]

The _thermal efficiency_ of an engine is the ratio of the heat
transformed into work to the total heat supplied to the engine. In order
to determine this, the _absolute_ temperature of the steam at admission
and exhaust pressures must be known. These pressures can be measured by
a gage, and the corresponding temperatures taken from a steam table, or
better, the temperatures can be measured direct by a thermometer. The
absolute temperature is obtained by adding 461 to the reading in degrees
Fahrenheit (F.). The formula for thermal efficiency is:

  _T__{1} - _T__{2}
  -----------------
      _T__{1}

in which

  _T__{1} = absolute temperature of steam at initial pressure.
  _T__{2} = absolute temperature of steam at exhaust pressure.

_Example_:--The temperature of the steam admitted to the cylinder of an
engine is 340 degrees F., and that of the exhaust steam 220 degrees F.
What is the thermal efficiency of the engine?

                       (340 + 461) - (220 + 461)
  Thermal efficiency = ------------------------- = 0.15
                               (340 + 461)

The _mechanical efficiency_ is the ratio of the delivered or brake
horsepower to the indicated horsepower, and is represented by the
equation:

                          B. H. P.
  Mechanical efficiency = --------
                          I. H. P.

  in which B. H. P. = brake horsepower,
           I. H. P. = indicated horsepower.

All engines are designed to give the best economy at a certain developed
indicated horsepower called full load. There must, of course, be more or
less fluctuation in the load under practical working conditions,
especially in certain cases, such as electric railway and rolling mill
work. The losses, however, within a certain range on either side of the
normal load, are not great in a well designed engine. The effect of
increasing the load is to raise the initial pressure or lengthen the
cut-off, depending upon the type of governor. This, in turn, raises the
terminal pressure at the end of expansion, and allows the exhaust to
escape at a higher temperature than before, thus lowering the thermal
efficiency.

The effect of reducing the load is to lower the mean effective pressure.
(See Figs. 38 and 39.) This, in throttling engines, is due to a
reduction of initial pressure, and in the automatic engine to a
shortening of the cut-off. The result in each case is an increase in
cylinder condensation, and as the load becomes lighter, the friction of
the engine itself becomes a more important part of the total indicated
horsepower; that is, as the load becomes lighter, the mechanical
efficiency is reduced.


Effect of Condensing

So far as the design of the engine itself it concerned, there is no
difference between a condensing and a non-condensing engine. The only
difference is that in the first case the exhaust pipe from the engine is
connected with a condenser instead of discharging into the atmosphere.

A condenser is a device for condensing the exhaust steam as fast as it
comes from the engine, thus forming a partial vacuum and reducing the
back pressure. The attaching of a condenser to an engine may be made to
produce two results, as shown by the work diagrams illustrated in Figs.
40 and 41. In the first case the full line represents the diagram of the
engine when running non-condensing, and the area of the diagram gives a
measure of the work done. The effect of adding a condenser is to reduce
the back pressure on an average of 10 to 12 pounds per square inch,
which is equivalent to adding the same amount to the mean effective
pressure. The effect of this on the diagram, when the cut-off remains
the same, is shown by the dotted line in Fig. 40. The power of the
engine per stroke is increased by an amount represented by the area
enclosed by the dotted line and the bottom of the original diagram.
Assuming the reduction in back pressure to be 10 pounds, which is often
exceeded in the best practice, the gain in power by running condensing
will be proportional to the increase in mean effective pressure under
these conditions. For example, if the mean effective pressure is 40
pounds when running non-condensing, it will be increased to 40 + 10 = 50
pounds when running condensing, that is, it is 50/40 = 1.25 times as
great as before. Therefore, if the engine develops 100 I. H. P. under
the first condition, its final power will be increased to 100 × 1.25 =
125 I. H. P. under the second condition.

Fig. 41 shows the effect of adding a condenser and shortening the
cut-off to keep the area of the diagram the same as before. The result
in this case is a reduction in the quantity of steam required to develop
the same indicated horsepower. The theoretical gain in economy under
these conditions will run from about 28 to 30 per cent for simple, and
from 20 to 22 per cent for compound engines. The actual gain will depend
upon the cost and operation of the condenser which varies greatly in
different localities.




CHAPTER V

TYPES OF STEAM ENGINES


There are various ways of classifying steam engines according to their
construction, the most common, perhaps, being according to speed. If
this classification is employed, they may be grouped under three general
headings: High-speed, from 300 to 400 revolutions per minute;
moderate-speed, from 100 to 200 revolutions; and slow-speed, from 60 to
90 revolutions; all depending, however, upon the length of stroke. This
classification is again sub-divided according to valve mechanism,
horizontal and vertical, simple and compound, etc. The different forms
of engines shown in the following illustrations show representative
types in common use for different purposes.

The Ball engine, as shown in Fig. 42, is a typical horizontal single
valve high-speed engine with a direct-connected dynamo. It is very rigid
in design and especially compact for the power developed. The valve is
of the double-ported type shown in Fig. 2, having a cover plate for
removing the steam pressure from the back of the valve. The piston is
hollow with internal ribs similar to that shown in Fig. 29, and is
provided with spring packing rings carefully fitted in place. The
governor is of the shaft type, having only one weight instead of two, as
shown in Fig. 37.

[Illustration: Fig. 42. The Ball Engine]

The Sturtevant engine shown in Fig. 43 is a vertical high-speed engine
of a form especially adapted to electrical work. Engines of this general
design are made in a variety of sizes, and are often used on account of
the small floor space required. In the matter of detail, such as valves,
governors, etc., they do not differ materially from the high-speed
horizontal engine.

Fig. 44 illustrates a moderate-speed engine of the four-valve type.
These engines are built either with flat valves, or with positively
driven rotary or Corliss valves, the latter being used in the engine
shown. It will be noticed that the drop-lever and dash-pot arrangement
is omitted, the valves being both opened and closed by means of the
wrist-plate and its connecting rods. This arrangement is used on account
of the higher speed at which the engine is run, the regular Corliss
valve gear being limited to comparatively low speeds. All engines of
this make are provided with an automatic system of lubrication. The oil
is pumped through a filter to a central reservoir, seen above the center
of the engine, and from here delivered to all bearings by gravity. The
pump is attached to the rocker arm, and therefore easily accessible for
repairs.

The standard Harris Corliss engine shown in Fig. 45, is typical of its
class. It is provided with the girder type of frame, and with an
outboard bearing mounted upon a stone foundation. The valve gear is of
the regular Corliss type, driven by a single eccentric and wrist-plate.
The dash pots are mounted on cast-iron plates set in the floor at the
side of the engine, where they may be easily inspected. The governor is
similar in construction to the one already described, and shown in Fig.
27. The four engines so far described are simple engines, the expansion
taking place in a single cylinder. Figs. 46 to 48 show three different
types of the compound engine.

[Illustration: Fig. 43. The Sturtevant Vertical Engine]

The engine shown in Fig. 46 is of a type known as the tandem compound.
In this design the cylinders are in line, the low-pressure cylinder in
front of the high-pressure, as shown. There is only one piston rod, the
high-pressure and low-pressure pistons being mounted on the same rod.
The general appearance of an engine of this design is the same as a
simple engine, except for the addition of the high-pressure cylinder.
The governor is of the shaft type and operates by changing the cut-off
in the high-pressure cylinder. The cut-off in the low pressure cylinder
is adjusted by hand to divide the load equally between the two
cylinders for the normal load which the engine is to carry.

[Illustration: Fig. 44. Moderate Speed Engine of the Four-valve Type]

The engine shown in Fig. 47 is known as a duplex compound. In this
design the high-pressure cylinder is placed directly below the
low-pressure cylinder, as indicated, and both piston rods are attached
to the same cross-head. The remainder of the engine is practically the
same as a simple engine of the same type.

[Illustration: Fig. 45. The Harris Corliss Engine]

Fig. 48 shows a cross-compound engine of heavy design, built especially
for rolling mill work. In this arrangement two complete engines are
used, except for the main shaft and flywheel, which are common to both.
The engine is so piped that the high-pressure cylinder exhausts into the
low-pressure, through a receiver, the connection being under the floor
and not shown in the illustration. One of the advantages of the
cross-compound engine over other forms is that the cranks may be set 90
degrees apart, so that when one is on a dead center the other is
approximately at its position of greatest effort.


Selection of an Engine

The selection of an engine depends upon a number of conditions which
vary to a considerable extent in different cases. Among these may be
mentioned first cost, size and character of plant, available space,
steam economy, and utilization of the exhaust steam. The question of
first cost is usually considered in connection with that of operation,
and items such as interest and depreciation are compared with the saving
made through the saving in steam with high priced engines.

[Illustration: Fig. 46. The Skinner Tandem Engine]

[Illustration: Fig. 47. American Ball Duplex Compound Engine]

The principal use of the stationary engine is confined to the driving of
electric generators and the furnishing of motive power in shops and
factories. For the first of these uses, in cases where floor space is
limited, as in office buildings, and where the power does not exceed
about 100 I. H. P., the simple non-condensing high-speed engine is
probably employed more than any other type. For larger installations, a
saving may usually be made by the substitution of the moderate-speed
four-valve engine. The question of simple and compound engines in this
class of work depends largely upon the use made of the exhaust steam. In
winter time the exhaust is nearly always utilized in the heating system,
hence steam economy is not of great importance, and the simple engine
answers all purposes at a smaller first cost. In localities where the
heating season is comparatively short and fuel high, there is a decided
advantage in using compound engines on account of their greater steam
economy when operated within their economical range as regards load.

[Illustration: Fig. 48. The Monarch Corliss Engine]

In large central plants where low cost of operation is always of first
importance, it is common practice to use the best class of compound
condensing engines of moderate or low speed. Those equipped with some
form of Corliss valve gear are frequently found in this class of work.
In the generation of power for shops and factories, where there is
plenty of floor space, low-speed engines of the Corliss type are most
commonly used. When space is limited, very satisfactory results may be
obtained by using the moderate-speed four-valve engine. In deciding upon
an engine for any particular case, the problem must be studied from all
sides, and one be chosen which best answers the greatest number of
requirements.




CHAPTER VI

STEAM ENGINE TESTING


The principal information sought in the usual test of a steam engine is:

1. The indicated horsepower developed under certain standard conditions.

2. The friction of the engine, from which is determined the mechanical
efficiency.

3. The steam consumption per indicated horsepower.

4. The general action of the valves.

5. The pressure conditions in the cylinder at different periods of the
stroke.

The ultimate object of an efficiency test is to determine the
foot-pounds of work delivered by the engine per pound of coal burned in
the boiler furnaces. The general method of finding the pounds of dry
steam evaporated per pound of coal has been treated in MACHINERY'S
Reference Series No. 67, "Boilers," under the head of "Boiler Testing."
In the present case it is, therefore, only necessary to carry the
process a step further and determine the foot-pounds of work developed
per pound of steam.

The apparatus used in engine testing, in addition to that used in boiler
testing, consists of a steam engine _indicator_ and reducing device for
taking diagrams, and a _planimeter_ for measuring them afterwards. If
the test is made independently of the boiler test, a calorimeter for
measuring the amount of moisture in the steam should be added to the
outfit.

It has already been shown how a diagram may be made to represent
graphically the work done in a steam engine cylinder during one stroke
of the piston. The diagrams shown thus far have been theoretical or
ideal cards constructed from assumed relations of the pressure acting
and the distance moved through by the piston. An indicator is a device
for making a diagram of what actually takes place in an engine cylinder
under working conditions. Such a diagram shows the points of admission,
cut-off, and release, and indicates accurately the pressures acting upon
both sides of the piston at all points of the stroke.

A common form of steam engine indicator is shown in Fig. 49. It consists
of a cylinder _C_ which is placed in communication at _E_ with one end
of the engine cylinder by a proper pipe connection, provided with a
quick opening and closing cock or valve. The cylinder _C_ contains a
piston, above which is placed a coil spring of such strength that a
given pressure per square inch acting upon the lower side of the piston
will compress the spring a definite and known amount. Extending through
the cap or head of cylinder _C_ is a stem attached to the piston below,
and connected by suitable levers with a pencil point _P_. The
arrangement of the levers is such that a certain rise of the piston
causes the point _P_ to move upward in a vertical line a proportional
amount.

The springs used above the piston vary in strength, and are designated
as 20-pound, 40-pound, 60-pound, etc. A 20-pound spring is of such
strength that a pressure of 20 pounds per square inch, acting beneath
the piston in cylinder _C_, will raise the pencil point 1 inch. With a
40-pound spring, a pressure of 40 pounds per square inch will be
required to raise the pencil 1 inch, and so on for the other strengths
of spring.

The hollow drum _D_ rotates back and forth upon a vertical stem at its
center, its motion being produced by the string _H_, which is attached
by means of a suitable reducing motion to the cross-head of the engine.
The return motion to the drum is obtained from a coil spring contained
within it and not shown. The paper upon which the diagram is to be drawn
is wound around the drum _D_, and held in place by the spring clip _F_.

In taking an indicator card, the length of stroke must be reduced to
come within the limits of the drum, that is, it must be somewhat less
than the circumference of drum _D_. In practice, the diagram is commonly
made from 3 to 4 inches in length. There are a number of devices in use
for reproducing the stroke of the engine on a smaller scale. The most
accurate consists of a series of pulleys over which the cord passes on
its way from the cross-head to the indicator drum.

The indicator is connected with the engine cylinder by means of special
openings tapped close to the heads and either plugged or closed by means
of stop-cocks when not in use. In some cases two indicators are used,
one being connected to each end of the cylinder, while in others a
single indicator is made to answer the purpose by being so piped that it
can be connected with either end by means of a three-way cock. After the
indicator is connected and the cord adjusted to give the proper motion
to the drum, a card is attached, after which the three-way cock is
opened and steam allowed to blow through the indicator to warm it up.
The cock is now closed and the pencil pressed against the drum to get
the so-called atmospheric line. The cock is again opened, and the pencil
pressed lightly against the drum during one complete revolution of the
engine. The cock is then thrown over to connect the indicator with the
other end of the cylinder and the operation is repeated.

[Illustration: Fig. 49. Steam Engine Indicator]

The indicator card obtained in this way is shown in Fig. 50. It is
sometimes preferred to take the diagrams of the two ends on separate
cards, but it is simpler to take them both on the same one, and also
easier to compare the working of the two ends of the cylinder.

The analysis of a card for practical purposes is shown in Fig. 51.
Suppose, for example, that the length of the diagram measures 3.6
inches; the distance to the point of cut-off is 1.2 inch; and the
distance to the point of release is 3.3 inches. Then, by dividing 1.2 by
3.6, the cut-off is found to occur at 1.2 ÷ 3.6 = 1/3 of the stroke.
Release occurs at 3.3 ÷ 3.6 = 0.92 of the stroke. Compression begins at
(3.6 - 0.5) ÷ 3.6 = 0.86 of the stroke. The diagrams shown in Figs. 50
and 51 are from non-condensing engines, and the back-pressure line is
therefore above the atmospheric line, as indicated.

The indicator diagram gives a means of determining the mean effective
pressure, from which the power of the engine can be found from the
previously given equation

             _APLN_
  I. H. P. = ------.
             33,000

The method of determining the mean effective pressure is as follows:
First measure the area of the card in square inches, by means of a
planimeter (an instrument described later), and divide this area by the
length in inches. This gives the mean ordinate; the mean ordinate, in
turn, multiplied by the strength of spring used, will give the mean
effective pressure in pounds per square inch. For example, suppose that
the card shown in Fig. 51 is taken with a 60-pound spring, and that the
area, as measured by a planimeter, is found to be 2.6 square inches.
Dividing the area by the length gives 2.6 ÷ 3.6 = 0.722 inch as the mean
ordinate, and this multiplied by the strength of spring gives a mean
effective pressure of 0.722 × 60 = 43.3 pounds per square inch.

[Illustration: Fig. 50. A Typical Indicator Diagram]

In practice, diagrams taken from the two ends of the cylinder usually
vary more or less, due to inequalities in the valve action. Again, the
effective area of the piston on the crank end is less than that on the
head end, by an amount equal to the area of the piston rod. For these
reasons it is customary to compute the mean effective pressure of all
the cards separately, and take, for use in the formula, the average of
the various computations. The corrected value of the piston area is, as
already stated, equal to (2_A_ - _a_)/2, in which _A_ is the area of the
piston, and _a_ the area of the piston rod. Substituting these values
for _A_ and _P_ in the formula, together with the length of stroke and
average number of revolutions per minute, the indicated horsepower is
easily computed.

In making an ordinary test, diagrams are taken from both ends of the
cylinder at 10-minute intervals for several hours, depending upon the
accuracy required. The revolutions of the engine are counted for two or
three-minute periods each time a pair of cards are taken, or still
better, an automatic counter is used for the run, from which the average
number of revolutions per minute may be determined.

[Illustration: Fig. 51. Diagram for Illustrating Method of Computation]

The friction of the engine is determined by taking a pair of cards while
"running light," that is, with the belt thrown off, or the engine
uncoupled, from the dynamo, if part of a direct-connected outfit. The
friction load is then computed in horsepower from the indicator cards,
and subtracted from the indicated horsepower when loaded. Thus we obtain
the delivered or brake horsepower. The delivered horsepower divided by
the indicated horsepower gives the mechanical efficiency. This may be
expressed in the form of an equation as follows:

  I. H. P. - friction loss
  ------------------------ = mechanical efficiency.
         I. H. P.


Planimeter

The planimeter is an instrument for measuring areas in general, and
especially for measuring the areas of indicator cards. Some forms give
the mean effective pressure directly, without computations, by changing
the scale to correspond with the spring used in the indicator. A
planimeter of this type is shown in Fig. 52. The method of manipulating
this instrument is as follows. Set the arm _BD_ equal to the length of
the card _EF_, by means of the thumb screw _S_, and set the wheel at
zero on the scale, which must correspond to the spring used in the
indicator. Next, place the point _D_ at about the middle of the area to
be measured, and set point _C_ so that the arm _CB_ shall be
approximately at right angles with _BD_. Then move _D_ to the upper
left-hand corner of the diagram, and with the left hand move _C_ either
to the right or left until the wheel comes back exactly to the zero
point on the scale; then press the point firmly into the paper. Now, go
around the outline of the diagram with point _D_ from left to right,
finishing exactly at the starting point. The mean effective pressure may
now be read from the scale opposite the edge of the wheel.

When very accurate results are required, the tracer point _D_ may be
passed over the diagram several times, and the reading divided by the
number of times it is thus passed around. With short cards, 3 inches and
under in length, it is best to make the arm _BD_ twice the length of the
card, and go around the diagram twice, taking the reading directly from
the scale as in the first case.


Determining Steam Consumption

When it is desired to determine accurately the water rate of an engine,
a boiler test should be carried on simultaneously with the test upon the
engine, from which the pounds of dry steam supplied may be determined as
described in MACHINERY'S Reference Series No. 67, "Boilers." Knowing the
average weight of steam supplied per hour for the run, and the average
indicated horsepower developed during the same period, the water rate of
the engine is easily computed. Sometimes the average cylinder
condensation for a given type and make is known for certain standard
conditions. In this case an approximation may be made from an indicator
diagram which represents the average operation of the engine during the
test.

[Illustration: Fig. 52. General Construction of Planimeter]

A diagram shows by direct measurement the pressure and volume at any
point of the stroke, and the weight of steam per cubic foot for any
given pressure may be taken directly from a steam table. The method,
then, of finding the weight of steam at any point in the stroke is to
find the volume in cubic feet, including the clearance and piston
displacement to the given point, which must be taken at cut-off or
later, and to multiply this by the weight per cubic foot corresponding
to the pressure at the given point measured on the diagram. As this
includes the steam used for compression, it must be corrected, as
follows, to obtain the actual weight used per stroke. Take some
convenient point on the compression curve, as _Q_, in Fig. 53; measure
its absolute pressure from the vacuum line _OX_ and compute the weight
of steam to this point. Subtract this weight from that computed above
for the given point on the expansion line, and the result will be the
weight of steam used per stroke. The best point on the expansion line to
use for this purpose is just before release, both because the maximum
amount of leakage has taken place, and also because of the
re-evaporation of a portion of the steam condensed during admission. The
actual computation of the steam consumption from an indicator diagram is
best shown by a practical illustration.

_Example_--Let Fig. 53 represent a diagram taken from the head end of a
16 × 30-inch non-condensing engine, running at a speed of 150
revolutions per minute; the card is taken with a 60-pound spring; the
clearance of the engine is 6 per cent; the average cylinder condensation
is 20 per cent of the total steam consumption; the diameter of the
piston rod is 3 inches.

[Illustration: Fig. 53. Diagram for Calculating Steam Consumption]

Measuring the card with a planimeter shows the mean effective pressure
to be 48.2 pounds. The area of the piston is 201 square inches; the area
of the piston rod is 7 square inches; hence, the average piston area =
((2 × 201) - 7)/2 = 198 square inches, approximately. Then

             198 × 48.2 × 2.5 × 300
  I. H. P. = ---------------------- = 217.
                     33,000

In Fig. 53, _GH_ is the atmospheric line; _OX_ is the line of vacuum or
zero pressure, drawn so that _GO_ = 14.7 pounds on the scale; and _OY_
is the clearance line, so drawn that _ON_ = 0.06 _NX_. The line _PQ_ is
drawn from _OX_ to some point on the compression line, as at _Q_. From
_C_, a point on the expansion line, just before release, the line _CF_
is drawn perpendicular to _OX_. The following dimensions are now
carefully measured from the actual diagram (not the one shown in the
illustration), with the results given:

  _OX_ = 3.71     _OP_ = 0.42
  _NX_ = 3.50     _CF_ = 0.81
  _OF_ = 3.20     _QP_ = 0.81

On the indicator diagram, being taken with a 60-pound spring, all
vertical distances represent pounds per square inch, in the ratio of 60
pounds per inch of height. The stroke of the engine is 30 inches or 2.5
feet. The length of the diagram _NX_ is 3.5 inches; hence, each inch in
length represents 2.5/3.5 = 0.71 feet. From the above it is evident that
vertical distances in Fig. 53 must be multiplied by 60 to reduce them to
pounds pressure per square inch, and that horizontal distances must be
multiplied by 0.71 to reduce them to feet. Making these reductions
gives:

  _OX_ = 2.63 feet.     _OP_ = 0.30 foot.
  _NX_ = 2.49 feet.     _CF_ = 48.6 pounds.
  _OF_ = 2.27 feet.     _QP_ = 48.6 pounds.

As a card from the head end of the cylinder is taken to avoid
corrections for the piston rod, the area is 201 square inches or 1.4
square foot. With the above data the volume and weight of the steam in
the cylinder can be computed at any point in the stroke. When the piston
is at _C_, the volume is 1.4 × 2.27 = 3.18 cubic feet. When the piston
is at _Q_, the volume is 1.4 × 0.30 = 0.42 cubic foot. From a steam
table the weight of a cubic foot of steam at 48.6 pounds absolute
pressure is found to be 0.116 pounds. Therefore, the weight of steam
present when the piston is at _C_ is 3.18 × 0.116 = 0.369 pounds. The
weight of steam present when the piston is at _Q_ is 0.42 × 0.116 =
0.049 pound. That is the weight of steam in the cylinder at release is
0.369 pound, and the weight kept at exhaust closure for compression is
0.049 pound.

The weight exhausted per stroke is therefore 0.369 - 0.049 = 0.32 pound.
The number of strokes per hour is 150 × 2 × 60 = 18,000, from which the
steam accounted for by the diagram is found to be 18,000 × 0.32 = 5760
pounds, or 5760 ÷ 217 = 26.5 pounds per indicated horsepower per hour.
If the cylinder condensation for this type of engine is 20 per cent of
the total steam consumption, the water rate will be 26.5 ÷ 0.8 = 33.1
pounds per indicated horsepower per hour.

In the present case it has been assumed, for simplicity, that the
head- and crank-end diagrams were exactly alike, except for the piston
rod. Ordinarily, the above process should be carried out for both head
and crank ends, and the results averaged.