UNIVERSITY OF CALIFORNIA.
Class
THE STEAM ENGINE INDICATOR
Published by the
McGrawrHill Book. Company
^
Successors to theBookDepartments of tKe
McGraw Publishing Company Hill Publishing" Company
Publishers of E>ooks for
Electrical World TKe Engineering and Mining Journal
TKe Engineering Record Power and TKe Engineer
Electric Railway Journal American Machinist
THE
STEAM ENGINE INDICATOE
BY
F. R. LOW
Editor of POWER and THE ENGINEER
THIRD EDITION, REVISED AND ENLARGED
McGRAW-HILL BOOK COMPANY
239 WEST 39TH STREET, NEW YORK
6 BOUVERIE STREET, LONDON, E.G.
1910
Copyright, 1910
BY THE
McGRAW-HILL BOOK COMPANY
PREFACE
THE steam-engine indicator has become at once the tool of a trade
and the instrument of a science. The operating engineer employs it
to perfect the adjustment of valves and to measure power, the physicist
to investigate thermodynamic transfers and to trace the cycle of the heat
engine. It is to steam engineering at once the commercial scale and the
chemical balance.
The following contributions to the literature of the instrument and
its diagrams have been prepared from time to time by the writer for the
columns of Power, and are addressed to the practical man who desires
to apply the indicator as an instrument of ordinary precision to the prob-
lems of steam-engine design and operation.
F. R. LOW.
211748
CONTENTS
CHAPTER I
SELECTION AND CARE OF THE INSTRUMENT
Degree of accuracy required Lightness Freedom from friction Paral-
lelism Lost motion Proportional movement The spring Size of drum
Vacuum springs Scales Duplicate parts Leads Lubrication Paper.
CHAPTER II
REDUCING MOTION 11
The pendulum lever Directions for proportioning and for leading off the
cord Defects of pendulum motions Lever of fixed length Lever of variable
length Connection to cross-head Distortion from improper connection The
pantograph Adjusting the length of diagram Setting the pantograph Locat-
ing the pantograph Reducing wheels Testing the accuracy of the motion.
CHAPTER III
APPLICATION 27
Location of instrument Tapping the cylinder Cock connections Side
pipes and three-way cocks Objectionable connections Attaching the instru-
ment The cord Management of the cord Centering the diagram Drum
tension Preparing and fixing the lead Selection of springs Lubrication
Testing in position Putting on the card Care of instrument after use.
CHAPTER IV
THE DIAGRAM 40
Graphic representation applied to the action of steam in the cylinder The
ideal diagram Departures therefrom in the actual Definition of the various
lines.
viii CONTENTS
CHAPTER V
PAGE
THE ADMISSION LINE 44
Typical admission lines The proper form Effect of late admission Of
tardy exhaust closure Loops due to lateness Loops due to excessive com-
pression Points at top of admission line Effect of excessive lead.
CHAPTER VI
THE STEAM LINE 47
The loss from boiler pressure The desirable form Effect of wire-drawing
Steam-chest diagrams Locating cause of loss of pressure Proportioning
steam mains arid ports Initial humps in steam lines Effects of increased pis-
ton speed Throttle-governed engines Diagrams without any steam line-
Modified by the admission.
CHAPTER VII
THE EXPANSION LINE 53
Relation of volume and pressure in a perfect fluid Rule for finding the pres-
sure at any point in the stroke Plotting the expansion curve by several meth-
ods Determining the point of cut-off Locating the clearance line What
the theoretical expansion line shows Departures from it in practice
Transparent chart of theoretical expansion lines and its use.
CHAPTER VIII
THE POINT OF RELEASE 64
The desirable form The form to be avoided A frequently necessary com-
promise Value of early release with condenser Effect of terminal pressure
Loop from excessive expansion.
CHAPTER IX
THE COUNTER-PRESSURE LINE 67
The unbalanced or effective pressure Effect of pipe and port friction Pro-
portioning exhaust pipes and ports Back pressure inappreciable with good
design Uniform back pressure Effect of tardy release and compression
Humps in compression line Effect of excessive compression.
CHAPTER X
THE COMPRESSION LINE 70
The inverse of expansion Same curve applicable to the ideal case Locat-
ing clearance line from compression curve Compression in a condensing engine
Effect of counter pressure on compression Use of compression in taking
CONTEXTS ix
PAGE
up the momentum of the moving parts Effect of compression on clearance
l oss Amount of compression advisable Typical compression lines Loop
from excessive compression Falling off from the ideal curve Effects of con-
densation and leakage.
CHAPTER XI
MEASUREMENT OF THE DIAGRAM FOR MEAN EFFECTIVE PRESSURE 77
The "mean effective pressure " explained The ordinate method Spacing
the ordinates Measuring the ordinates. Use of parallel rules and engineer's
scales Measuring negative loops.
CHAPTER XII
THE PLANIMETER 83
The mean height of the diagram is proportional to the mean effective pres-
sure Reducing the diagram to its mean height from its known area Use of
planimeter for determining area Description of instrument Reading the ver-
nier Best position for use Tracing the diagram Treatment of loops Check-
ing the readings Measuring the length of the diagram Rule to find the mean
effective pressure Planimeters with adjustable tracing arms Reading
directly in horse-power Directions for making and using the hatchet planim-
eter The Coffin averaging instrument.
CHAPTER XIII
COMPUTING THE HORSE-POWER : 96
Force Work The foot pound^-The horse-power Simple formula for
horse-power Rules and examples The horse-power constant Rule for find-
ing same Table of horse-power constants Use of table Allowing for the
piston rod The power of the individual strokes Balancing the effort.
CHAPTER XIV
MEAN EFFECTIVE PRESSURE AND POINT OF CUT-OFF BY COMPUTATION 113
Relation of hyperbola to containing rectangle Directions for finding the
mean pressure represented by an ideal diagram of a given pressure and ratio
of expansion Allowing for departures from the ideal Table for computing
mean and initial pressures, points of cut-off, ratios of expansion and clearance
Examples The effect of clearance The real and apparent ratios of expan-
sion.
CHAPTER XV
STEAM CONSUMPTION FROM THE DIAGRAM 119
Volume generated per hour per horse-power Value of ihat volume in
pounds of steam Correction of volume for clearance Rule to find steam con-
CONTENTS
13750
sumption from diagram Example Table of values of Volume of new
JVl.xLi.-r.
steam indicated by distance between expansion and compression lines Rule
for determining consumption by this line Computing steam consumption
from compound engine diagrams.
CHAPTER XVI
DIAGRAMS FROM COMPOUND ENGINES, CLEARANCE NEGLECTED 134
Use of different scales for the different cylinders Reducing diagrams to the
same scale Comparison of diagrams in this condition Reduction of diagram
to same scales of volumes The combined diagrams Comparison of the com-
bined diagram with the ideal.
CHAPTER XVII
DIAGRAMS FROM COMPOUND ENGINES, CLEARANCE CONSIDERED 139
Locations of the diagrams with reference to the line of zero volume Rela-
tion of the steam line of the low-pressure diagram to the counter-pressure line
of the high Effect of receiver capacity Effect of change of load Effect of
varying cut-off in low-pressure cylinder.
CHAPTER XVIII
ERRORS IN THE DIAGRAM 145
Error from the use of the pendulum motion Error with lever of fixed length
vibrating 90 Error with same lever vibrating 35 to 40 Amount of error
allowable Error from lack of parallelism between cord and guides Error due
to indirect connection of indicator.
CHAPTER XIX
MEASURING THE CLEARANCE 155
Direction for measuring by equal volumes of water Correction for riser pipe
By calculated volume of water By weight of water By time required to
fill Professor Sweet's method of equal weights Diagram to determine
without calculation the proportion of clearance to displacement.
THE STEAM ENGINE INDICATOR
CHAPTER I
SELECTION AND CARE OF THE INSTRUMENT
THERE are at this writing nine or ten different steam engine indicators
upon the market. As a guide to its readers in determining which of
these is best suited to their purpose, it shall be the province of this work
only to specify the requirements of a perfect instrument, point out
the possible sources of error in the instrument as made, detail the
methods of testing foi such faults, and leave the reader to purchase
the degree of accuracy necessary for his purpose at the lowest available
price.
For certain classes of work, such as the ordinary setting of valves,
the measurement of horse-power for purposes of daily record in factory
work, etc., extreme accuracy is not essential. A man does not buy
a chemist's balance to weigh sugar, nor an expensive chronometer for
a kitchen clock. An instrument which is ordinarily correct will answer
many purposes to which an indicator may be advantageously applied,
and its inherent errors will probably be less than those of manipula-
tion and observation.
For other classes of work, however, the utmost attainable precision
must be insisted upon, and the very best instruments made are not
good enough. In a 72-inch low-pressure cylinder there will be developed
over 100 horse-power per pound of mean effective pressure. The varia-
tion of one one-hundredth of an inch in the mean height of a diagram
from one end of this cylinder would mean, with a 10-pound spring, a
difference of over five horse-power in the result. If this engine were in a
vessel, built as others have been with a bonus or forfeit of one hundred
dollars per horse-power above or below that called for in the contract, the
omney involved in its exact determination would warrant the extreme
of expense and pains in securing the utmost attainable precision in the
measuring instruments.
THE STEAM ENGINE INDICATOR
In a perfect indicator the pencil should, by its vertical position on
the diagram, represent exactly the pressure beneath the indicator pis-
ton at any instant; and by its horizontal position, the point which the
piston has reached in its stroke at the same instant. This simple con-
dition is impossible of attainment in practice, from the fact that the
materials of which indicators are made have mass. As soon as they
are put into motion we have momentum to carry both the pencil and
the drum away from the point to which they would have been carried
by the pressure and reducing -motion alone, and their inertia to prevent
their instantaneous response to a change in conditions.
Lightness. It may, therefore, be concluded that, other things being
equal, that instrument will give the best results in which the least weight
is moved through the least distance for the production of diagrams of
equal size, assuming always that enough material is used to give the
necessary strength and rigidity.
Freedom from Friction is a quality that an indicator should possess
in the greatest possible degree. Detach the piston and see that the pencil
levers will drop freely and with-
out any suspicion of a catch from
any position within the working-
range of the instrument. With
the piston attached, but without any
spring, raise the piston by taking
hold of the pencil delicately, and
work the pencil lever up and
down through the full limit of its
motion, feeling carefully for any
interruption to its movement.
Then raising the pencil nearly to
the top of the paper-drum, cover
the hole through which steam is
admitted to the indicator with the
thumb, as in Fig. 1. The pencil
FIG. 1. should sink slowly through the
whole range of its motion, but
should drop instantly from any point upon the removal of the
thumb.
Do not get the piston too tight through fear of its leaking. It
has a whole boilerful of steam behind it part of the time, and a
large volume always, and no noticeable difference in pressure will
result from any leakage which can take place unless the leakage is so
excessive as to increase the pressure on top of the piston. On condens-
ing engines the vacuum, as indicated by the indicator, may be materially
SELECTION AND CARE OF THE INSTRUMENT 3
reduced if the piston is too loose, and it is unpleasant and uncleanly to
have too much steam and . water leaking and spattering about the
instrument. The piston which will sustain the test shown in Fig. 1
will be found tight enough without excessive friction.
Parallelism. The line in which the point of the pencil moves should
be parallel with the axis of the paper-drum, in order both that the pencil
may bear upon the paper equally in all portions of its stroke, and that
its vertical movement may be at right angles with the horizontal move-
ment of the paper. With the piston attached but with no spring, adjust
the stop so that you can just see daylight between the point of the pencil
and the paper on the drum. Then raise the pencil slowly
through its full range by pushing the piston, and notice if the
pencil point keeps the same distance from the paper. If it does
not, either the spindle of the barrel is out of line with the
indicator cylinder, or the pencil motion is out of line. Still
sighting between the pencil and the paper, rotate the barrel by
drawing out the cord. If the paper touches the pencil,
or moves away from it, the drum is out of shape or
improperly centered. Now, allowing the pencil to
touch the paper, push the piston upward, drawing a
fine vertical line upon the card; then, with the spring
attached, rotate the barrel, and
draw a fine horizontal line. These
lines should be perfectly straight
throughout their lengths, and at
right angles with each other, a
condition which may be tested
with the triangles after the card
is removed from the paper-drum as
FIG. 2. shown in Fig. 2.
If the lines do not comply with
these conditions, the natural inference will be that the pencil movement
is incorrect, although the horizontal line may be thrown out by any
vertical movement of the cylinder upon its spindle.
Lost Motion is usually a matter more of adjustment than of manu-
facture. Put a stiff spring into the indicator, and carefully feel at the
end of the pencil lever for any unrestrained movement. Should such be
found, its cause should be searched for in the connection of the piston
rod to the piston and pencil motion, through all the joints of the parallel
motion, in the fit of the collar which carries the mechanism, and if it can-
not be corrected by adjustment without making the instrument too stiff
to comply with the friction test above described, the instrument should
be rejected.
4 THE STEAM ENGINE INDICATOR
Proportional Movement. The movement of the pencil should be
proportional to that of the piston. This is an important requirement,
but more difficult of test. A screw of perfectly uniform pitch should be
arranged to communicate its movement to the indicator piston. With
a little ingenuity a micrometer caliper can be adapted to this purpose.
Turn the screw up until it has a firm bearing against the piston, then
apply the pencil of the indicator to the paper and make a line by moving
the drum. Then turn the screw through a number of equal distances,
repeating the marking process each time. The piston having been
moved through an equal space after each marking, the spaces between
the lines upon the paper should be equal. Care must be taken in arrang-
FIG. 3.
FIG. 4.
ing and manipulating this test. The pencil movement is from four to
six times that of the piston, and any failure to move the piston through
equal spaces will introduce apparent errors which will be magnified
upon the card.
Count the spaces between the lines which you have drawn, then
count off the same number of spaces upon an equally divided scale of
such magnitude that the aggregate length of the given number of spaces
on the scale will not be less than the distance between the outside lines
upon the paper. Then lay the scale across the pencil lines, as shown by
Fig. 3, in such a way that the number of spaces laid oft 7 on the scale will
SELECTION AND CARP: OF THE INSTRUMENT 5
just reach from the top to the bottom line on the diagram. For example,
in the diagram shown in Fig. 3 there are 25 spaces. A "ten to the inch"
scale is laid diagonally across with its zero and 25 lines upon the out-
side lines of the diagram. If the lines of the diagram are equally spaced
they will coincide with the divisions of the scale, as in Fig. 3. If the
multiplying motion of the indicator is incorrect the spaces of the diagram
will be unequal, and their inequality will be apparent by their failure
to meet the divisions of the scale, as in Fig. 4.
The Spring is the actual measuring factor of the indicator, and
the apparatus required for its testing is too complicated and expensive
to be at the command of the average purchaser. The test ought to be
made under as nearly as possible the conditions of use, i.e., under steam
pressure, so that all the factors of temperature, etc., will be present.
Most of the manufacturers will make such tests of springs for purchasers,
and the diagrams of the test may be kept as a record of the degree of
accuracy of the instrument at that time. It is well also to have such
tests made occasionally after the instrument has been in use, and espe-
cially just before and after applying it to work of particular importance.
The test consists of applying steam to the indicator piston at pressures
increasing by equal amounts, say, for ordinary springs, five pounds.
As each five pounds is reached a line is drawn upon the card, a standard
gage or, better, a mercury column, being used to indicate the pressures.
The pressure is then allowed to fall, and marks are again made as the gage
passes the points which were noted in the upward series. If the spring
and all the transmitting and recording mechanism were perfect, and the
indicator without friction, the spaces for equal changes in pressure
would be of equal width, and the lines indicating the same pressures
would be coincident, whether drawn when the piston was going up or
coming down. This degree of perfection is rarely if ever reached, for
even if the spring compresses equal distances for equal increments of
pressure throughout its entire range, and its movement is transmitted
correctly to the pencil, the friction of the piston, of the pencil movement,
and of the pencil on the paper all combine in opposing the motion of the
piston in both directions, so that the lines of the upward series are too
low and those of the downward series too high by an amount .equivalent
to the frictional resistance upon the scale of the spring.
A very small amount of pressure at the piston would, however, take
care of all this, so that the wide discrepancy often shown between the
upward and downward diagrams is more liable to be due to the failure
of the operator to catch the pencil at the same point than to the inordinate
amount of friction which they indicate.
The above qualities are necessary to an indicator for accuracy. Other
points, more in the nature of conveniences than essentials, but which
6 THE STEAM ENGINE INDICATOR
may be well considered in selecting an instrument, are the comparative
simplicity of changing springs, adjustment for height of- atmospheric
line, changing from right to left hand and vice versa, adjusting the drum-
spring and leading pulley, attaching the indicator to the cock, etc.
Pencil Holder. For holding the lead, the end of the pencil lever in
some indicators is formed into a light steel quill of a size which will hold
the lead firmly when forced through it. In other makes the end of the
pencil lever is reinforced and threaded internally, the lead being screwed
through it. The preference of the writer is decidedly for the first method.
The quill being split lengthwise adapts itself by its elasticity 'to varying
sizes of lead, and may be closed with a pair of pincers if it fails to close
upon a lead of small diameter after being used with a larger size. As
the point is shortened by resharpening, the lead can be pushed forward,
and if it breaks off short it is easily pushed out of the holder with a match
or toothpick. The threaded end is adapted to only one size of lead,
which, with the short bearing afforded, is apt to get loose and wabble.
If it breaks off short, it must be dug out of the threaded portion; and if
the threaded method offers any compensating advantages the author
has yet to learn of them.
Selection of Springs. If the use of the instrument is to be confined
to one's own plant it is easy to select a spring or set of springs adapted
to the pressures and speeds to be encountered. If the instrument is
to be used promiscuously, the more springs the operator can own the
better will he be equipped to meet the conditions of practice. In select-
ing a spring, aim to get as large a diagram as possible without undue
distortion. If a diagram be taken with a 20 spring an error of measure-
ment of one one-hundredth of an inch would influence the results only
one-fifth of a pound. With a 50 spring the same error in measurement
would represent a departure of one-half pound. Or since the average
useful pressure upon which the power indicated by the diagram depends
is proportional to the area of the diagram, consider a diagram taken
with a 20 spring having an average height of 2 inches and a length of
4 inches as compared with one taken from the same cylinder with a 40
spring and a length of 2 inches. The area of the first diagram would
be 8 inches, of the second 2 inches, and the average useful or "mean
effective pressure " of course 40 in both cases.
area scale area scale
8 X 4 2 =40. 2 X 2 4 =40.
length length
In the large diagram 40 pounds of pressure are represented by 8 inches
of area, or 5 pounds to an inch, and an error in measurement of the area
SELECTION AND CARE OF THE INSTRUMENT 7
of one one-hundredth of a square inch would involve an error of but
five one-hundredths of a pound in the indicated pressure. In the case
of the smaller diagram 40 pounds pressure is represented by 2 square
inches of area, 20 pounds to the inch, and a deviation of one one-hun-
dredth of a square inch from the truth in measuring this area will involve
an error of two-tenths of a pound.
It is therefore advisable to have the area as large as possible and
have it right.
On the other hand, the allowable movement of both the pencil and
the drum is limited by the effects of momentum. At high speeds a
light spring and long movement of the drum would result in a diagram
so distorted by the effects of momentum and inertia as to introduce
errors much more serious than those which are likely to occur from
inaccurate measurement of a smaller and more perfect diagram. The
speed as well as the pressure will therefore have a bearing upon the
spring selected, and w r ill also influence the selection as between the
standard size of paper-drum which is used for moderate speeds, and
the smaller drums which some of the makers supply for high-speed work.
Some manufacturers furnish two sizes of drums, which may be used inter-
changeably upon the same instrument, adapting it to higher and lower
speeds.
In some instruments the position of the atmospheric line is fixed,
in others it is adjustable, so that in indicating a non-condensing engine
the base line may be lowered and the whole of the allowable movement
of the pencil utilized for the height of the diagram. The springs made
by American manufacturers are usually scaled decimally, that is, 10,
20, 30, 40, etc., pounds to the inch.
Vacuum Springs. It is frequently desirable in condensing engines to
obtain the lower or condensing portion of the diagram upon a larger
scale than that of the spring available with the initial pressure used.
With an initial pressure which demands a 60 spring, a realized vacuum
of 12 pounds would be represented by a line only one-fifth of an inch
below the atmospheric line, Fig. 5, giving a very small area to th3
condenser portion of the diagram. In order to obtain this area upon
a larger scale, giving increased accuracy of measurement, showing more
clearly the points of release and compression, etc., springs of low tension
are sometimes fitted with bosses or studs, which prevent their closing
beyond a certain point, while they are free to extend to any amount.
In Figs. '5 and 6 are shown two diagrams, the first drawn to a 60
scale; and in Fig. 6 the shaded portion of the first diagram is shown
expanded to a 10 scale. Notice how much more prominently the points
of release and compression are shown, on account of the more rapid
vertical movement with the same horizontal movement; and how much
8
THE STEAM ENGINE INDICATOR
less an error of a few hundredths of a square inch in measuring the area
of the condensing portion of the card would affect the result. A spring
made especially for this purpose by the American Steam Gauge Co.
is shown in Fig. 7. It is wound so closely that the coils close upon
themselves before the pencil movement can attain a dangerous amount
of motion. The large number of coils lying in so nearly a horizontal
Atmospheric Line
FIG. 6.
direction admits of sufficient elasticity with a good-sized wire, while
there is a uniformity of movement throughout the desired range. These
springs are scaled for extension only.
SELECTION AND CARE OF THE INSTRUMENT 9
Scales. For a measuring scale, the author uses a 6-inch engineer's
rule, triangular in cross-section, as shown in Fig. 8, and graduated upon
its six edges to 20ths, 30ths, 40ths, 50ths, GOths, and SOths of an inch.
This rule not only furnishes the six scales mentioned in one rule, but
by estimating half spaces a 50 scale can be used for 100 and the 60 for
120, etc. With the lower scales, where the distances are greater, half
pounds can be measured accurately by using the 60 scale for a 30 spring
or the 40 for a 20, the 20 for a 10, etc. The 50 scale is also useful for
measuring the length of the diagram, each division representing 0.02
of an inch, and the length of 6 inches being more than sufficient for
any diagram.
Duplicate Parts. Much annoyance and loss of time may be saved
by carrying in the indicator box duplicates of those parts liable to loss
40
FIG. 7. FIG. 8.
or derangement. An additional drum-spring, and two or three of the
smaller screws which have to be frequently removed in changing springs,
etc., and which are liable to disappear down a crack or somewhere else
when most wanted, will allow a test to proceed smoothly, when its
interruption would be particularly annoying from the insignificance of
its cause.
Leads. Select a hard lead of good smooth quality and of small
diameter, and use but a small piece at a time. At the end of the pencil
lever, where the motion is greatest, the weight should be reduced to
the smallest possible value. If pointed with a fine file, and rubbed down
with an emery stick, such as is used for sharpening draftsmen's pencils,
or a fine stone, it will wear longer and be smoother and more satisfac-
tory than if whittled into shape. A little metallic case of such leads
already pointed is a^very convenient portion of an outfit.
10 THE STEAM ENGINE INDICATOR
Lubrication. For lubricating the bearings of the instrument a light
machinery oil, one which will not gum or corrode, should be used. A
small vial of such oil usually accompanies the instrument, some makers
furnishing porpoise oil, such as is used for clocks and watches. The
piston, however, is better lubricated with cylinder oil, and the small
flat cans which are furnished for bicyclists' use, and which fit readily
into the tray of the indicator box, furnish a convenient means of carry-
ing a filtered supply in a form readily available for cleanly use. The
manufacturer's filtering should not be accepted. Filter the oil carefully
yourself, and see that the can is perfectly clean. A small particle of
grit upon the piston of an indicator will not only throw the diagram
into the most unaccountable contortions, but may scratch and injure
both cylinder and piston to a serious degree.
Paper. Use hard, tough, smoothly calendered paper of a width
sufficient to include the highest allowable pencil travel and about an
inch longer than the circumference of the barrel. Such paper can be
procured cut to the desired size, of almost any printer. If a blank
form is printed upon the back for the recording of data and observations,
do not allow the printer to use so much impression as to spoil the
smoothness and uniformity of the surface upon which the pencil works.
I have seen cards so roughened up by leading points sticking through
that it would be a wonder if a diagram could be drawn without the
pencil point hitting some of them.
Metallic paper is made by treating ordinary paper with sulphate of
zinc. A metallic point will then trace a line upon it and such a hard,
sharp point may be used instead of the ordinary lead.
It would seem as though a tubular or trough pen might be made
light and fine enough to replace the pencil point. The liquid contact
once established, scarcely any pressure w r ould be required to make a
record, and the diagram would be clean cut and legible. With the fine
point and light pressure necessary with a pencil the diagram is often
hard to see, and is quickly obliterated by handling. If inked in by
hand there is always a question of the accuracy of the work and a diagram
originally drawn with ink would present so many advantages that it is
surprising that none of the various makers has applied to the indicator
this device, which is used so universally upon other recording apparatus.
CHAPTER II
REDUCING MOTION
IN order to use the indicator, a means must be provided for mov-
ing the paper-drum in time with the engine piston. This movement
is usually derived from the cross-head, and the appliance used to reduce
the movement to that adapted to the paper-barrel is spoken of as the
"reducing motion."
The Pendulum Lever. The most primitive expedient for this pur-
pose is a lever suspended from the ceiling or other suitable support, and
connected at its lower end with the cross-head in such a way that it
will be swung back and forth as the engine makes its revolutions, as
in Fig. 9. The motion of the lever increases from nothing at the point
of suspension to approximately the full stroke of the engine at the cross-
11
12 THE STEAM ENGINE INDICATOR
head end, the amount of motion being directly proportional to the dis-
tance from the point of suspension. A point midway of the lever would
have a motion equal to one-half the stroke; one-quarter of the way
from the point of suspension, one-quarter stroke, etc. Letting
/ = distance between pivot and cord pin,
L= length of lever,
s= desired length of diagram,
S = stroke of engine,
then the diagram will be yths of the stroke, and the cord must be
attached at a point -^ths of the total length of the lever from the point
o
of suspension. For
that is, as the distance between the pivot and the point to which the
cord is attached is to the total length of the lever, so is the motion at
that point and the length of the diagram to be derived from that motion,
to the stroke of the engine.
Is Ls IS
-j =-~ and l=-^r and S= T~-
To Find the Point of Attachment, or the distance from the point
of suspension at which the cord should be attached to produce a
given length of diagram:
RULE. Multiply the total length of the lever by the desired length of
diagram, and divide by the stroke of the engine, all in inches.
EXAMPLE. With a lever 60 inches in length on an engine of 24-inch
stroke, how far would you attach the cord from the point of suspension
to produce a diagram 4 inches in length?
60X4
Operation : = 10 inches.
To Find the Length of Diagram produced by a cord at a given
point of attachment:
RULE. Multiply the distance from the pivot to the point of attachment
by the stroke of the engine, and divide by the total length of the lever, all in
inches.
EXAMPLE. What length of diagram would be produced by attach-
ing the cord 4^ inches from the pivot on a lever 20 inches in length at-
tached to a cross-head having a stroke of 12 inches?
4.5X12
Operation: " =2.7 inches.
REDUCING MOTION
13
The total length of the lever is measured from the point of suspension
to the point of attachment to the cross-head, and is variable in some
of the arrangements to be shown. As the variation bears a small pro-
FIG. 10.
FIG. 11.
portion to the total length, and the length of diagram is usually figured
only to keep within the limits of the paper-drum, especial refinement
in this particular is unnecessary. In order to get the full motion of
FIG. 12.
the pin, the cord must be led off in the direction of the pin's greatest
movement, i.e., at right angles to the lever when the lever is itself at
right angles to the guides. It will be readily seen that if the cord were
14
THE STEAM ENGINE INDICATOR
led off parallel to the lever it would receive very little motion. It is
desirable to avoid the use of leading pulleys as in Fig. 9; and Figs. 10
and 11 show two methods of accomplishing this, the latter by putting
on a segment of a circle, called a brumbo pulley, having a radius equal
to the distance / from the pivot to the point of attachment of the cord,
and so placed that the cord may be led straight to the indicator without
running on to the corners of the segment at the extremes of the stroke.
In Fig. 10 a supplementary lever is added in such a position that when
FIG. 13.
the main lever CC is at right angles to the guides the line AD will be at
right angles to the cord when the latter is led in the desired direction.
In all motions of this kind there is a radical defect due to the fact
that while the cross-head moves in a straight line any point on the lever
swings through the arc of a circle. In Fig. 12 let the line ox represent
the stroke of an engine. A lever attached to the cross-head and suitably
suspended at the other end would take, as the stroke progressed, the
positions 1 1', 2 2', 3 3', etc., and a pin attached to the lever at 1' would
move through the arc shown. Divide the stroke into eight equal parts,
as indicated by the numbered divisions, and as the cross-head completes
each division of the stroke the position of the pin will be indicated by
REDUCING MOTION
15
the corresponding number upon the arc. The length of the diagram
will be the horizontal distance, between I' and 9', but the distribution
of motion between these points will not be equal for equal movements
of the cross-head. When the cross-head moves from 1 to 2, one-eighth
of the stroke, the pin will move from 1' to 2,' and the cord will be moved
only through a distance A a instead of through A A' one-eighth of its
own length; and for each division of the stroke the proper division of
the diagram is indicated by the full lines, and the division that would
be derived from the motion of the pin by the dotted lines. Supposing
the cut-off to take place at a quarter of the stroke, this point should
be at B, but would appear at 6, and the dotted and incorrect instead
of the full-line correct diagram would be drawn. The points coincide
in the middle of the diagram, and become as much too late at the end
as they were too early at the beginning, the points which should be at
c, d, and e being at c', d', and e f respectively. The distortion shown
here is exaggerated on account of the shortness of the lever. It decreases
as the length of the lever in proportion to the stroke is increased, and
for this reason it is advisable never to use a lever less than one and a
half times the length of the stroke. The point of suspension of the lever
should be directly over its point of attachment to the cross-head when
thd latter is in the center of its stroke.
16 THE STEAM ENGINE INDICATOR
The amount of distortion varies also with the manner of attachment
to the cross-head. Fig. 13 represents a slotted lever working over a pin
in the cross-head. As each eighth of the stroke is completed the lever
will occupy the positions shown by the lines passing from the point of
suspension through the corresponding divisions, and the straight motion,
as AB, to be derived from any point upon the lever will be unequally
divided, as shown by the intersections of the dotted lines. Fig. 14
represents a lever fitted with a pin, which is carried by a slot in the
cross-head. As the cross-head and the slot move through successive
eighths of the stroke, the pin is carried also through equal divisions,
and motion in a line CD, at right angles to the lever in its central position
would be equally distributed, as shown by the -intersections of the dotted
lines referring the positions of the pin for the eight equal divisions of
the stroke to the line of motion CD. If it were not for the angular move-
ment of the cord with which this motion is taken off, and which pro-
duces an inequality in the transmitted motion, just as a connecting rod
does in the travel of the piston for equal movements of the crank, this
arrangement would be perfectly accurate. The cord is usually so long,
however, that its angular motion is immaterial. This feature cannot
be eliminated by using the arc or brumbo pulley, for while the latter
disposes of the angular movement of the string, it gives a movement
proportional to the angular motion of the lever, which is not equally
divided, i.e., the lever does not move through equal arcs of a circle for
equal movements of the cross-head. The use of the brumbo in this
case would therefore introduce rather than eliminate an error. While
this arrangement produces upon paper an almost perfectly proportional
reduction of the motion, its effects in practice are not so precise. The
long lever is cumbersome, the slotted guide an awkward thing to make
and attach to the cross-head, and unless the pin is accurately fitted,
the distortion and annoyance due to lost motion will
be greater than the inherent error of simpler construc-
tion.
Instead of the slot upon the cross-head a short con-
nection rod may be used, as in Fig. 15. In this case the
end of the main lever, instead of working up and down
j in a vertical slot, is swung in the arc of a circle of the
radius of the short connecting rod. The departure from
__--' the vertical line will be least if the levers are so at-
rj~" tached that the vibrating end of the small lever will
FIG. 15. be as much ^elow the path of the cross-head end when
the main lever is in its central position as it is above
it when in the extreme positions. This will be understood by referring
to Fig. 16, in which the levers are represented by the lines A B and BC,
REDUCING MOTION
17
the cross-head traveling on the line numbered to 8. When the cross-
head is in the middle of its stroke at 4, the ends B of the levers are
as much below the line in which the cross-head travels as they are
above it in the extreme position shown at B' and 6. When the cross-
FIG. 16
\
<C
/
/
/
i
\
/'*
\
*^
**s
^"\ o'
::: ^ 5; ^3J_.__B
_41_ Zg^S^ZSL-
rtr
Co] i
f* 31 4
5
i i
j i
FIG. 17.
head in its movement arrived at the points 1, 2, 3, etc., representing
equal subdivisions of its travel, the ends of the levers would be respect-
ively at the figures 1', 2', 3', etc., crossing the line of motion of the
cross-head twice during the stroke. Referring these points to the straight
line, OX by the dotted lines, it will be seen that the subdivisions very
18
THE STEAM ENGINE INDICATOR
nearly reproduce the equal subdivisions of the movement of the cross-
head from they are derived.
If the levers had been arranged at a right angle when in the center
of the stroke, as in Fig. 17, the entire vibration of the levers would
take place above the plane in which the cross-head moves.. The greater
distance to which the end of the small lever is carried from that plane
FIG. 18.
would increase the angle between them and introduce a greater dis-
tortion, as will be seen from Fig. 17, in which the same process has
been carried out as in Fig. 16, the movement derived from any point in
the main lever being represented by the subdivisions into which the
dotted lines divide, the line OX, which as will be seen, are far more
irregular than in Fig. 16.
The Pantograph. Engravers and draftsmen have an instrument
called- the " pantograph ^ for reproducing drawings upon a different
scale. One of the cheaper forms of the
A instrument is shown in Fig. 18. A
/'I drawing followed with the tracing point
' is reproduced upon a smaller scale by
/ the pencil point, as shown. If the
/ tracing point draws a circle the pencil
/ draws a smaller circle; if the tracing
/ point draws a straight line the pencil
/ point draws a shorter straight line, and
the movement of the pencil point and
tracing point are proportional through-
/"* out. When the tracing point has drawn
one-tenth of its line the pencil has drawn
one-tenth of its line and so on to com-
FIG. 19. pletion. It "will readily be seen that if
the tracing point of the pantograph be
attached to an engine cross-head the pencil will accurately reproduce the
stroke upon a reduced scale, and substituting a cord pin for the pencil we
REDUCING MOTION
19
have a perfect reproduction of the motion of the cross-head for trans-
mission to the paper-barrel. The two forms in which the pantograph is
used for indicator purposes are shown in Figs. 19 and 20. Of both forms
it is true that the cord pin C must be directly in line with the stationary
point A and the point of attachment to the cross-head B, as indicated
by the dotted lines; also that the distance from the point of suspension
A to the cord pin C is to the distance between A and B as the length
of the diagram is to the stroke of the engine, so that the rules given for
the lever will apply equally well to the pantograph. The distance AC
may be varied by moving the strip C to one or another of the holes 1,
2, 3, etc., and then moving the cord pin into that hole in the strip which
is in the center line of the instrument. The author has pasted into the
cover of his indicator box the following table, correat for the pantograph
which he uses, which is like Fig. 20.
PANTOGRAPH TABLE
Hole.
No.
Proportion Card
to Stroke.
Decimal Fraction
of Stroke.
Divided
by
Longest
Stroke.
1
1:16
.0625
16
72'
2
1:12
.0833
12
54'
3
5:48
.1042
9.6
42'
4
1: 8
.1250
8
36'
5
7:48
.1458
6.9
31'
6
1: 6
.1667
6
27'
7
3:16
.1875
5.3
24'
8
5:24
.2083
4.8
22'
9
11:48
.2292
4.4
20'
10
1: 4
.2500
4
18"
11
13:48
.2836
3.7
16"
This shows that when the pin is in the first hole (No. 1) the diagram
will be one-sixteenth or 0.0625 of the length of the stroke; in the fifth
hole seven forty-eighths, or 0.1458, etc. To find the movement of the
cord pin at any hole with an engine of given stroke, multiply the stroke
in inches by the decimal fraction opposite the number of hole given;
or divide the stroke in inches by the number in the column headed
"divided by" opposite the number of the hole given.
To find the proper hole to use with an engine of given stroke to pro-
duce a diagram of a required length: Divide the length of the stroke
in inches by the desired length of diagram in inches. The number nearest
to the quotient in the column headed " divided by" will be opposite
the number of the hole which will nearest produce that length. The
ratio of the diagram to the stroke may coincide with one of those given
in the table. Thus, if it was desired to produce a four-inch diagram
20
THE STEAM ENGINE INDICATOR
from a thirty-two-inch stroke, the ratio would be 4:32=1:8, and it is
apparent from the columns of proportions given that the pin in the
fourth hole will have the required movement. The same result may
be arrived at by dividing the length of the diagram in inches by the
stroke in inches and selecting the pinhole which is opposite the nearest
decimal fraction to that obtained. The last column of the table gives
the longest strokes allowable for the various positions of the pin to pro-
duce diagrams not exceeding four and a half inches in length, which
is about the capacity of the ordinary drum. Additional columns for
FIG. 20.
other lengths may be made out if desired by multiplying the figures in
the column headed " divided by" by the length of diagram desired.
Such a column, for instance, might be added for the maximum length
of diagram allowable with the smaller drum, although the smaller in-
struments are usually used upon engines of high rotative speeds, where
the pantograph is not adapted as a reducing motion.
In the other form of pantograph, Fig. 19, holes are provided for dif-
ferent positions of the strip C, and other holes in C for bringing the cord
pin in line with A and B. Other holes are sometimes provided for chang-
ing the point of attachment to the cross-head, in which case the cord
pin must always be in line with the stationary point A and the hole
which is used for the cross-head attachment, and the length of the diagram
will be to the length of the stroke as AC is to A B.
REDUCING MOTION
21
In view of this latter fact, if the pantograph is opened until AB
equals the stroke of the engine, then AC will be the length of the diagram
at once, and with the shorter strokes this fact may be used to advantage
in setting the pantograph. Suppose the stroke to be 24 inches. Open
the pantograph until a two-foot rule w r ill just extend from center to
center of pins A and B, as in Fig. 21, then the distance C to A will be
the length of diagram to be expected, and the pin may be so adjusted
as to make this distance equal to the length of diagram desired. For
greater lengths of stroke this principle may still be used by halving.
Take a 72-inch stroke, for instance. One-half of this is three feet. Qpen
the pantograph to three feet, then the distance AC will equal one-half
the length of the diagram.
There is no patent upon the pantograph in either of these forms,
and anybody who has tools and know^s how to use them can make for one
FIG. 21.
FIG. 22.
himself. The members are usually made of strips of hard wood one and
one-eighth by five-sixteenths of an inch, and sixteen inches between
the pivoted points. These strips are put together in the manner indi-
cated in the illustration, the single strips running between the double
making it stiff and substantial. The levers must work easily, and all
lost motion be avoided. The joints must be well made and the pivot
holes should be bushed. A good form of joint, designed by Mr. E. K.
Conover, is shown in Fig. 22. It allows for taking up lost motion by
filing off the bush, and permits the bearing to be taken apart and oiled
occasionally. The holes which are used for the different positions of
the strip and of the cord pin are usually tapped directly into the wood,
but the tops are apt to be forced out or the threads crossed and cut, and
a better arrangement would be to insert strips of brass at these places,
and drill and tap the holes into them.
So far as the correctness of the reduction goes it makes no difference
where the stationary end of the pantograph is placed. We have seen
engineers measure with a great deal of care to locate this point accurately
in the center of the stroke, knowing probably that this had to be done
22
THE STEAM ENGINE INDICATOR
for the lever and assuming that the pantograph required similar arrange-
ment. The cord, of course, should be led off in the line of rnotion of the
pin, i.e., parallel to the guides, and, since it is desirable to dispense
with the use of leading pulleys, when the pantograph is used horizon-
tally, as in Fig. 23, the post should be placed at such a distance from the
guides and at such a height as will bring the cord pin directly in line
with the indicators, so that the cord can be led direct as shown in the
plan. The point to be looked out for is that the corners A and B of the
pantograph do not come in contact with the guides at the extremes of
the itroke. We have seen several good pantographs spoiled in that way,
and plead guilty to one wreck ourselves from that cause. Now we try
it by having the engine turned over, if this can be done easily, while
holding the stationary end of the pantograph, moving it, if it hits, into
a position in which it will clear; or if the engine is a large one, by locating
the extreme points of the pantograph's travel by measurement, and carry-
ing the cross-head end through the range so determined in as nearly
as possible the line that it will travel, observing that it clears through-
out the stroke. When the pantograph is all attached and running,
place your eye at C and sight the cord pin. It should move in a straight
line to and from your eye. If it has any side wise motion something is
wrong; probably the pin is not in the center line of the instrument. The
stationary post will come about in the middle of the guide, with this
arrangement, as if moved much to either end it will bring the corner at
that end in contact.
Remembering that it makes no difference how the pantograph is
set, horizontally, perpendicularly, or obliquely, so long as it will clear,
it may be placed in any position to favor leading the cord to the indicators.
Fig. 24 shows how it may be used on an engine whose stroke does not
exceed the length to which the pantograph may be easily opened. The
other form of pantograph may be attached to the floor, as in Fig. 25,
in which case a leading pulley is required, but where the stroke of the
engine will allow it had better be attached as in Figs. 26 and 27.
Fig. 28, from the catalogue of the Buckeye Engine Co., shows an
adaptation of the pantograph for that engine. The cord is attached
REDUCING MOTION
23
to the end of a short bar which slides freely in a bearing in the carrying
post. This bar is connected to the lever CD by means of a short link
AB. The lever is connected to a stud attached to the cross-head at E
by the bar DE. The proportions of the parts are such that the points
FIG. 24.
FIG. 25.
CBE are in a straight line at all times, and this being the case the
distortions of the movement of the lever due to the vibration of the
link DE will be corrected by the equal vibration of the short link. This
makes a good rig for a permanent fixture, but must be proportioned
FIG. 26.
FIG. 27.
for the engine upon which it is used, as it cannot, except within very
narrow limits, be adjusted for engines of different sizes. The cord must,
of course, be led off in the line of motion of the short bar.
24
THE STEAM ENGINE INDICATOR
Fig. 29 shows a very good motion for short strokes. The amount
of motion given to the bell crank may be varied by changing the inclina-
tion of the plane which is attached to the cross-head, and the vertical
arm may be of such length as to bring the cord in line with the indicator.
FIG. 28.
The catch C holds the foot up off the plane and stops the instrument
without unhooking the cord or leaving it flapping as with a detent on the
indicator drum.
Fig. 30 shows a method of reducing the motion by means of wheels
or sheaves of different diameters.
FIG. 29.
A standard upon the cross-head is clamped at c to a cord which passes
around the pulleys W and w, the hub H, from which motion is taken
to the indicator, bearing the same proportion to the wheel W that the
length of diagram is to bear to the stroke. This arrangement has the
OF THE
UNIVERSITY
OF
jdUFOR!
REDUCING MOTION
25
advantage that the wheel W is kept in time with the piston by being
held from overturning through momentum by the cord. Another
cord can be led from H to the indicator upon the back end of the cylinder.
The trouble with those reducing wheels which are pulled out by the cord
and returned by means of a spring has been that having considerable
mass they acquired a momentum which carried them after the cross-
head had stopped pulling, and distorted the stroke, like a heavy paper-
barrel with a weak drum spring on an indicator at high speed. Several
w ft-
S
FIG. 30.
forms of reducing wheels are now upon the market, however, in which
lightness of material and construction have combined to form a device
which is not only handy in application to different sizes and kinds of
engines, but reasonably accurate at considerable speeds. Finally, what-
ever form of motion is used, there are two tests which should be tried.
The first of these is shown in Fig. 31, where the stroke of the cross-head
is divided into eight equal parts. With the reducing motion attached to
the indicator, put the engine on the center, the corner A of the cross-
head being at zero. In this position make a vertical mark upon the
indicator card by raising the pencil lever. Then move the cross-head
26
THE STEAM ENGINE INDICATOR
successively to 1, 2, 3, etc., at each point making a mark upon the card.
If the diagram is found to be equally spaced your motion is correct so
far as the reduction is concerned. Now give the engine steam, and while
it is turning over slowly apply the pencil, and hold it on during a complete
revolution, making an " atmospheric " line. Raise the pencil about
FIG. 31,
a sixteenth of an inch, let the engine get up to speed, and draw another
line in the same way. If there is a considerable difference in the length
the diagram will be distorted by the momentum of the reducing motion,
or of the paper-drum of the indicator itself, or by the stretching of the
cord. The most that you can do is to take up all lost motion, use short
cord or wire, and adjust the drum spring to get the least possible dis-
crepancy.
CHAPTER III
APPLICATION
HAVING selected an instrument and laid out an appropriate reduc-
ing motion, we are prepared to consider the attachment of the indicator
to the cylinder and the method of its manipulation.
Most engines of recent build are sent out of the shop with the cylinder
drilled and tapped for the application of the indicator, and plugged holes
for this purpose will be found in the side or top of the cylinder by remov-
ing the lagging. When a cylinder is not tapped, the two points to be
considered in locating the point for drilling are, first, to so place the hole
that throughout the stroke there shall be a constant uninterrupted
communication between the cylinders of the indicator and the engine;
and secondly, to so locate the instrument as to lead off from it most
conveniently to the reducing motion.
The first object is most readily attained by tapping directly into
the heads, and as this is rather a more simple process for the machinist
than tapping into the counter-bore, especially when room is limited,
it is frequently done. Except in a few instances, however, as in working
from the crank end of an upright cylinder, it brings the instrument out
of easy reach of the line from the reducing motion, and this line should
be kept as short and direct as possible. The most advantageous method
of connection will usually be found to be by tapping through the
cylinder wall into the counter-bore, as at A, Fig. 32. Whether this will
be at the side as in Fig. 34, or top as in Fig. 33, of the cylinder will
depend upon the location of the steam chest and the direction of the
cord. Usually in the larger engines with vertical cross-head the indicators
are most conveniently located at the side, while in the small self-con-
tained engines, with horizontal cross-head, the indicator is most accessible
on top of the cylinder.
Having determined where the indicator is to be located, drill and
tap the cylinder for a half-inch pipe thread, being careful to see that the
hole is not covered by the piston, but that it is in free communication
with the cylinder at all points of the stroke. When the counter-bore
is too close and the clearance small, access may be had by chipping a
channel from the tapped hole out into the clearance. Of course every
27
28
THE STEAM ENGINE INDICATOR
attention should be paid to cleaning out chips and borings so that the
cylinder may not be cut nor the indicator injured.
Into the hole so prepared, screw the indicator cock direct whenever
possible. When the cylinder is tapped upon the side, this will bring
the instrument horizontal, as in Fig. 34, but the author much prefers
this arrangement to the more common one shown in Fig. 35, where a
nipple and elbow are used to bring the indicator into a vertical position.
The shorter . and more direct the connection between the cylinder of
the indicator and the engine, the more accurate will be the results, and
it must be remembered that all the pipes and connections to be rilled
FIG. 32.
with steam represent so much added clearance to the engine, which
on a small machine might amount to a considerable percentage.
In all cases where accuracy is important, a pair of instruments should
be used, one on each end of the cylinder, and diagrams taken simul-
taneously. Where only one indicator is available it is more convenient
to attach it to a three-way cock connected with both ends of the cylinder,
so that it may be thrown into communication, first with one end and
then the other, as at Fig. 36. This method cannot be depended upon
for accuracy, however, and no important changes or deductions which
could be affected by the intermediate connections should be made from
the indications of an instrument attached in that way. Its convenience,
however, will lead to its continued use in cases where a single instru-
ment is in frequent use upon the same engine; and if proper allowance
APPLICATION
29
is made for the distortions produced by wire drawing and clearance, no
harm will result.
A proper precaution is to take a diagram with the indicator attached
directly to the cylinder, and then take another through the three-way
cock, under as nearly as possible the same conditions, upon the same
paper. This will enable you to make an intelligent estimate of the
difference due to the different methods of connection. We have seen
diagrams taken with the three-way cock which could scarcely be dis-
tinguished from those taken with the direct connection, while others
have shown distortions which utterly unfitted them as indications of
FIG. 33.
the action of steam in the cylinder.* The side pipes, when used, should
be ample in size to convey the steam to the indicator without wire-
drawing, but not any larger than necessary, on account of the increase
in clearance.
The method of connection shown in Fig. 37 is especially to be
avoided. Here angle valves are attached to the ends of the cylinder
and connected with a side pipe, in the center of which is a T for the
insertion of the indicator cock. To connect the indicator with either
end of the cylinder, the angle valve at that end is opened, the valve
at the other end being closed. It is evident that in order to get any
* See Chapter on Errors in the diagram.
30
THE STEAM ENGINE INDICATOR
pressure to the indicator the entire length of the side pipe must first
be filled with steam at each stroke; and for every reason that the
ordinary side pipe is bad, this is twice as bad. There is also no know-
FIG. 34.
ing whether the valve which is supposed to be shut is tight, or whether
it is entirely closed every time. Should it remain slightly open, as
is frequently the case even when a valve feels- tight, some unaccountable
FIG. 35.
effects may appear in the lines of the diagram taken supposedly from
the other end alone.
In putting up piping or connections for use with the indicator, use
no red lead or other mixture, as it will be carried by the steam to the
APPLICATION
31
indicator cylinder and produce trouble by sticking the piston up. A
few drops of oil on the thread is usually all that is required, but should
a joint persist in leaking, a string of waste wound in the thread will
make it tight.
Particular pains should be taken to remove from all pipes and
fittings all dirt, scale, and burr which can become detached and work
into the cylinder. A little piece of grit upon the indicator piston can
cut some funny freaks upon the paper-barrel, as well as leave its mark
upon the walls of the indicator cylinder. When the connections are all
up, allow the steam to blow through them freely some time before attach-
ing the instrument, rapping the pipe sharply in the meantime, to remove
any scale or dirt which is liable to become detached.
FIG. 36.
The cylinder having been tapped and the reducing motion arranged,
we are now ready to apply the indicator to the cylinder; and here is
where we begin to appreciate the fallacy of making indicators in pairs
right and left, for if one is right for the side of the engine you are upon,
the other is certainly wrong. You are bound to want either two right-
hand indicators or two left-hand indicators at the same time, and when
the makers recognize this and make their instruments so they can be
changed from right to left, there will be fewer burnt knuckles and less
profanity connected with the use of the indicator. The owner can
adapt his instrument to the change by simply filing a slot in the bottom
of the barrel opposite the present slot, so that the clips and pencil bar
may be brought to that side of the instrument which is away from the
cylinder when in use.
32
THE STEAM ENGINE INDICATOR
Do not undertake to turn the instrument backwards to bring the
clips on the outside, but in putting the instrument upon the cock, let
the arm which holds the barrel point in the direction which the string
is to lead. It is better to take off the working parts of the instrument
and leave them in the box while doing this, avoiding the risk of bending
the levers and connections in handling, or catching them on the cord
while rigging up. Put a little waste in the cylinder meanwhile.
A good idea for one who used his indicators a good deal and in dif-
ferent places would be to have duplicate cylinder caps without holes.
The regular cap with the attached pencil motion and piston could then
be replaced by the solid cap while rigging up, saving the delicate parts
of the instrument from possible harm and keeping the cylinder, upon
FIG. 37.
the perfection of the inside surface of which so much depends, shut up
tightly.
The connection between the paper-barrel and the reducing motion
may be made with a 'flexible cord, as the drum is rotated in one direc-
tion by a spring. It has already been explained that in order to secure
a distribution of the pressure on the diagram corresponding to the dis-
tribution in the cylinder, it is essential that the paper-drum shall correspond
in its movement with the movement of the piston. To secure this, even
with a correct reducing motion, it is essential that there shall be no
stretch in the cord which forms the connection, through the reducing
motion and cross-head, with the piston.
If the engine piston has to move an inch before the stretch is taken
out of the cord sufficiently to enable it to start the drum, it is evident
that the admission end of the diagram produced will not present correctly
APPLICATION 33
the action of the steam with reference to the beginning of the stroke.
The distortions produced will be explained in a chapter devoted to the
errors to which the diagram is liable* It is enough now to appreciate
that no stretch is allowable if accurate work is to be done.
A closely braided cord, prepared especially for indicating purposes,
is supplied by dealers in the instruments. It is well to hang a weight
upon this cord, and allow it to remain suspended some time before using,
to take out any tendency to stretch which may remain in it.
Where the distance from the indicator is considerable, as in the case
of a Corliss engine, with the pantograph in the middle of the guides,
the author uses, instead of a cord, annealed iron wire of about 22 gage.
This wire is subject to occasional breakage, but does not stretch, and a
dime will buy enough of it to serve for many applications. It should
be straightened and all the kinks taken out by being made fast at one
end and wrapped about a round piece of wood, such as a screw-driver
handle or hammer handle, as shown in Fig. 38, which is drawn along
FIG. 38.
for the length desired. Braided picture cord wire of small size is also
recommended for this purpose.
Whatever is used to lead to the reducing motion, the closely braided
cord referred to will be used to run over pulleys and around the paper-
drum. Such a piece, terminating with a small wire hook, will be found
attached to the instrument when purchased, the hook being intended
to engage in a loop at the end of the cord leading to the reducing motion.
If such hook is used, it should be kept as close to the instrument as prac-
ticable, as if it is some distance out it is liable to cause the line to vibrate
disagreeably, especially when the speed is high. When the distance
from the indicator to the reducing motion is short enough to make the
use of cord advisable, the author prefers to dispense with the hook alto-
gether, using a cord on the instrument long enough to loop over the pin
in the reducing motion, and hooking on and unhooking at that point.
This gives a smooth, continuous line, free from loops, knots, and other
encumbrances, which will not look only better but run smoother, "stay
34
THE STEAM ENGINE INDICATOR
put" better (for knots and loops are always giving and stretching more
or less), and give more satisfactory results.
There are a number of other advantages which point to the reducing
motion as the place for hitching and unhitching, rather than having a
hook at the indicator. It is usually easier to attach the cord at this
point. When the indicators are unhooked there is no attached cord
being whipped about by the motion, and where a pair of instruments
are used, the throwing on or off of one loop is made to start or stop the
pair. There are circumstances, however, where this is impracticable,
and the hook near the indicator must be used. To keep the moving
cord out of mischief when not attached to the indicator, it may carry
the hook, the loop being made in the indicator cord, and be hooked
FIG. 39.
into an elastic band attached to or near the indicator when not working
the paper-drum. Another method is to attach one end of the cord to
the indicator, as in Fig. 39, leaving it long enough not to pull tight with
the extreme motion, and looping it near the indicator for hooking on.
In any event, the end of the cord or wire which goes over the reduc-
ing-motion pin should be looped, to permit the pin to turn easily within
it, and not tied down closely upon the pin as by a slip-knot.
The next step is to adjust the length of the cord so that the diagram
may come in the center of the card. With the indicator in position and
the engine in motion, loop the cord between your fingers and put it
over the pin or hook, drawing it up enough to set the paper-barrel in
motion and clear the stop. Now draw the cord carefully up until the
barrel touches the stop on the outward stroke, then let it slip back through
your fingers until it touches very lightly on the backward stroke.
Midway between these two positions is where the point of the loop
ought to be. Take back nearly half as much cord as you have let slip
APPLICATION 35
past, tie the loop, and the length should be pretty nearly right. Do
not throw the tied loop over the pin, however, nor hook it on, until
you have first held it against the pin or hook while the motion is running
and made sure it is long enough. If it is hitched on too short, some-
thing is bound to give way. If, when you get to taking diagrams, it
is found to be desirable to move them a little toward one end or the
other of the card, this may be done by knocking the indicator around
in the cock enough to take up or let out the required amount of cord.
This is better than tying knots in the cord to take it up, as is frequently
done.
A device which may be used for adjusting the length of the loop if
desired on slow speeds is shown in Fig. 40. It may be made of a small
piece of sheet brass, of sufficient thickness to be stiff, in which are
drilled four holes about a quarter of an inch apart. Pass the end of
the cord up through the first hole, down through the second, up through
the fourth, down through the third, and out over the side and under
FIG. 40.
\
the loop, as shown. This link ma}' be slid along upon the cord, lengthen-
ing or shortening the loop, but under the strain of the paper-drum spring
it will remain where placed.
Be very sure that the passage to the cylinder is free and that the
piston does not even partially obstruct it at the end of the stroke. The
beginning of the stroke is when the indicator makes its quickest move-
ment, and a choking of the passage will produce apparently unaccount-
able results. By throwing a ray of light into the hole tapped for the
indicator you can satisfy yourself as to the directness of the passage
and perhaps get a point as to evening up your clearances besides.
The tension of the drum or barrel spring should now be seen to.
When the engine is making its outward stroke this drum is put into
motion, and, having mass, acquires momentum, so that when the piston
arrives at the end of its stroke and the string stops pulling, the drum
continues to move by reason of its momentum until its stored energy
is absorbed by the spring. If a high-speed engine be run at a very
moderate speed and an atmospheric line be drawn, then with the engine
running at governor speed if another line be drawn just above it, there
will be found to be a difference in the length of the lines. This produces
36 THE STEAM ENGINE INDICATOR
a distortion in the diagram, of course, and can be reduced by tighten-
ing the barrel spring. For high-speed engines this spring will have to
be kept under considerable tension, but on slower moving machines
it may be let down, and should in all cases be run only tight enough
to keep the barrel well under the control of the cord.
The working parts are now to be arranged and the instrument put
together. The pencil lever must be fitted with a lead. Do not use
any more lead than is necessary to hold firmly in the quill or stub.
Any extra weight is especially to be avoided at this point, where it has
so much motion, and if allowed to stick out on the barrel side of the
arm it furnishes a lever to work itself loose in the holder or to twist
the pencil arm sideways in its bearings. Bring the lead to a fine round
point, not sharp enough to catch in and scratch the paper. Then let
it stick through as little as possible, leaving a little stock for filing up
the point as it wears on the side toward the paper, and break it off
short at the other side.
In selecting a spring, be sure to get one stiff enough. If the maximum
pressures allowable with the different springs, as given by their several
makers, are not exceeded, no harm will result to the springs or to the
instrument, but it may be found desirable to use stiff er springs to secure
freedom from excessive vibration at high speeds. Attach the spring
selected in its position, being careful to screw everything up to its place,
put a drop or two of cylinder oil on the piston, open the cock on the
indicator and let the steam blow once or twice through the cylinder,
then put in the piston and screw the instrument together. If you get
the cylinder oil from the can used about the engine room, look at the
piston after the oil has spread around on it, and pick off any specks of
dust or grit, which will show plainly against the bright brass. If it is
a condensing engine, do not open the cock when that end is exhausting,
or you may make more work for the air-pump than it can conveniently
handle.
When the instrument is together, take hold of the pencil lightly
and try the lever for lost motion. If it can be moved without pulling
at once on the spring, take the instrument apart and take up the con-
nections. This point should be borne in mind and looked after from
time to time as the taking of cards progresses, for the connections are
liable to get loose, and introduce some very curious features in the
diagrams. The cards should also be watched, to see that the cord
connections do not stretch so as to let the pencil bring up against the
clips at the end of the diagram.
When the instrument has been put together properly, open the cock
and let steam into it, setting the piston and levers in motion, and press
your finger lightly on the top of the piston rod, to see if everything is
APPLICATION
37
working smoothly. If the least indication of gritty, scratchy action is
felt, shut off the steam at once, take the instrument apart, and find
the cause. If it runs smoothly, you are ready to take a diagram.
The paper used with the indicator should be a rather heavy, well-
calendered, smooth, tough stock, something that will stand being handled,
and over which the pencil will pass without too much friction. It should
be cut of such width as to reach nearly to the top of the barrel, and of
a length about an inch longer than the circumference of the barrel on
which it is to be used. The beginner will consider it necessary to provide
himself with printed blanks, containing spaces for all sorts of observa-
tions of the engine, boiler, weather, etc.; but inasmuch as few of these
FIG. 41. ,
observations have to be recorded on each card, and many of them,
such as the dimensions of the engine, but once in a test, he will as he
progresses get to using slips of plain paper, marking upon the back of
each card such particulars as are needed for the purpose for which it
is to be used.
The paper is put upon the barrel by placing the lower right-hand
corner under the longest clip, bending it around, and allowing the ends
to stick out between the clips at the top; then by taking the lower
corners as they protrude between the clips between the thumb and
forefinger, as shown in Fig. 41 and at the left in 42, the paper may be
drawn down over the barrel as smoothly as a glove. An additional
38
THE STEAM ENGINE INDICATOR
pinch near the top, and a squaring of corners if they need it, will render
the operation complete.
Another method is to put the paper under both clips, as at the right
in Fig. 42. This prevents the ends from sticking out, and keeps the
FIG. 42.
paper smooth. It is sometimes drawn through one clip only, as is
shown in Fig. 43.
Now turn on the steam and warm up the instrument. On non-
condensing engines it is well to turn the cock so that the steam will blow
out into the atmosphere until it shows blue and dry. When the water
FIG. 43.
has disappeared and the pencil is vibrating smoothly, the paper-drum
being in motion, hold the pencil lightly against the paper and allow
it to trace the diagram. For ordinary purposes of exhibition, showing
the valve action, distribution, etc., one revolution is sufficient to hold
the pencil on. To show the governor action, variation of load, etc., the
APPLICATION 39
pencil will have to be held on for a number of revolutions; and when
measuring power, the pencil should be allowed to pass from ten to
twenty times over, and the/average diagram measured. Turn the cock
off and bring the pencil again to the paper, tracing the atmospheric
line. It is not good practice to trace the atmospheric line first, as the
indicator and spring are not then heated and under the same conditions
as when the diagram is taken.
When through indicating, remove the spring, piston, etc., from the
indicator, and allow the steam to blow through the cylinder once or twice,
t'nscrew the spring from the piston and cap, dry it thoroughly, and
wipe it clean with a greasy cloth. The springs are the vital part of the
instrument. Upon their integrity and accuracy the value of all your
work depends. Too much pains cannot be taken to have them per-
fectly accurate when bought, to keep them from deteriorating by rust
or otherwise, and to ascertain their condition from time to time. Wipe
up and clean the levers, oiling the joints, and you will find the instru-
ment all ready for application next time. When the lighter parts have
been attended to, the main body of the indicator will be found to be
quite dry, from having had the steam blown through it, and may be cleaned
like the rest and put together.
CHAPTER IV
THE DIAGRAM
WE have learned how to correctly set up a motion, apply the in-
dicator, and obtain a diagram. It now remains to consider what this
diagram is, and what can be determined from it.
When the mathematician or statistician desires to record the results
of a series of observations or experiments in such a manner that they
may be at once apparent and easily comprehended, he has recourse
to what is known as the graphic method. Suppose, for instance, it
I 86
\
180
1 75
Time 10 .16 .30 .45
A.M.
11 .15 .30 .45 12 .16 .30 .45
M.
FIG. 44.
1 .16 30 .45
RJL
was desired to represent in this way the result of a series of observa-
tions of the temperature of feed-water during a test. Taking a piece
of paper ruled in squares, as represented in Fig. 44, and which is known
as ordinate paper, set off the time upon one of the horizontal lines, as
shown at the bottom of the figure, allowing two spaces for each fifteen
minutes. Allow each of the vertical divisions to represent one degree
of temperature, making the lines so figured correspond to 175, 180, and
185. At 10 o'clock the observation showed 176, so upon the line
representing that time, and at a height representing 176, make a dot.
Fifteen minutes later the temperature had gone up to 178, and upon
the line representing 10.15 and at a height representing 178 another dot
is made. Continuing in this way to represent the results of each
40
THE DIAGRAM
41
observation, and connecting the dots by lines, we obtain a diagram
showing at a glance how nearly regular the pressure was maintained
through the test, to what extent it varied, and at what time variations
occurred.
Let us apply this method to the variations of pressure in the cylinder
of a steam engine. Suppose we have an engine with a stroke of 32 inches,
working with steam of 60 pounds gage pressure and a vacuum of 12
pounds, cutting off at 8 inches, with the exhaust valve opening for re-
lease when the piston is 2 inches from the end of the stroke and closing
for compression when the return stroke is within 5 inches of completion.
I !
60-Lbs
Foil.
of Cut oft
Steam Lint-
46-Lbs
Sea e h
30-Lbs
15-Lbs
^il t-r
c Line
1-Ali
FIG. 45.
Upon a sheet of paper ruled as in Fig. 45 draw the line OX, 32 spaces
long, which will represent the 32 inches of the stroke, so that we can
represent the successive positions of the piston or volumes by propor-
tional distances from upon this line. We will also consider each of
the spaces in a vertical direction to represent 3 pounds pressure, and
starting with OX as the zero line can lay off to this scale the pressures
corresponding to the different positions of the pistons, the point being
the zero point of both volumes and pressures.
In the first place since the pressure of the atmosphere is 15 pounds,
approximately, above the absolute zero of pressure; we will lay off
42 THE STEAM ENGINE INDICATOR
the line A A, five spaces above the zero line, to represent that pres-
sure; and as gage pressures are reckoned from the pressure of the atmos-
phere as zero, we will lay off above the atmospheric line 20 spaces to
indicate the 60 pounds of steam with which the engine is supplied; and
as steam is allowed to enter freely for one-quarter of the stroke, we will
draw the " steam line" at this height and 8 of the horizontal spaces
in length. At this point the supply is cut off, and the volume of steam
inclosed allowed to expand, the pressure decreasing practically in an
inverse ratio to the volume; so that when the piston has arrived at -the
vertical line 16, and the volume has been doubled, the pressure will
be halved; at the line 24, where the volume is 3 times that at the point
of cut-off, the pressure will be one-third, etc., and we can calculate the
pressure for each ordinate, as the vertical lines are called, and lay out
the curved expansion line, as will be more fully explained when we
come to consider that line particularly. At a point in this line two
inches from the end of the stroke the exhaust valve opens, locating the
point of release, and the pressure falls away to that of the condenser,
12 pounds below the atmospheric pressure, and 3 pounds above the
zero line. Five spaces from the end. of the return stroke we locate
the point of compression, where the exhaust valve closes, and the steam
remaining in the cylinder is compressed, as shown by the compression
line, until steam is again admitted and another stroke commenced.
From the diagram thus laid out the actual action of the steam in
the cylinder will vary from many causes; and an actual diagram taken
from the cylinder with a steam engine indicator in which the vertical
distances are determined by the pressure of the steam against a spring
of known tension and the horizontal distances by a movement derived
from and proportional to that of the piston itself, will enable us, if
correctly taken, to determine the actual pressure in the cylinder at
each point of the stroke, and to compare these pressures, and the lines
which they generate in connection with the changing volumes, with
the theoretical diagram constructed as above. We are thus enabled
to see how much of the available pressure is realized in the cylinder,
With what degree of promptness it is admitted, and how well the pressure
is maintained behind the moving piston; to observe how the valve
performs its functions, how much of the vacuum is realized in the
cylinder, or with what facility the spent steam is gotten rid of. We
have also the data for calculating the average unbalanced pressure
against the piston, and thus of determining the work performed. In fact,
a properly taken diagram, with all data concerning it, is full of interest
and instruction, and its study can be profitably carried to great refine-
ment. In succeeding chapters we shall consider the separate lines of
the diagram successively, show the correct form and common depart-
THE DIAGRAM 43
ures tnerefrom, with their causes, and lead up to calculations from the
diagram, of the power developed, steam consumption, etc.
RECAPITULATION MOVEMENT OF THE PISTON AND THE ACTION OF
STEAM IN THE CYLINDER.
We give below a tabulated summary of the entire diagram showing
the formation of the various lines composing it. " Reference will be had
to Fig. 45.
Admission Line. During the formation of this line, steam is admitted
into the clearance space, raising the pressure from that of compression
to the steam chest pressure.
Steam Line. The piston is moving ahead and steam is being admitted
behind it.
Expansion Line. At the point of cut-off, the steam port closes and
the steam behind the piston expands into a gradually increasing volume
and with a gradually falling pressure.
Release Line. At the point of release the exhaust port opens,
releasing the pressure. The steam rushes into the exhaust chamber,
the pressure falling rapidly meanwhile.
Exhaust Line. By the time the piston has started on its return
stroke, the pressure has reached its minimum and the piston makes its
return stroke, pushing out before it through the exhaust port the steam
which has just been used in propelling it through its forward stroke
from to 32.
Compression Line. At the point of compression the exhaust port
closes, confining in the cylinder a small quantity of steam at a low
pressure. This steam fills the clearance space and the end of the
cylinder up to the face of the piston. As the piston completes its
return stroke, this confined steam is compressed into a continually
decreasing space, its pressure rising meanwhile, until at the lower end
of the admission line of the steam port again opens, admitting live steam
which runs the pressure up to that of the steam line.
CHAPTER V
THE ADMISSION LINE
THE admission line shows the manner in which steam is admitted
to the cylinder. Under normal conditions admission takes place
suddenly while the piston is practically standing still at the end of
the stroke, resulting in a straight line perpendicular to the atmospheric
line, into which the compression line merges, as shown at A, Fig. 46.
In order that the admission line may be thus erect, it is necessary
that the steam valve shall be open so as to admit the full pressure before
the piston commences to move away; and this involves the question of
lead, or the amount of opening which the valve has when the engine
is on the center, and which, for many reasons, it is desirable to keep
as small as possible and yet allow the admission line to be perpendicular.
As the steam valve is allowed to become late in opening, and the piston
gets into motion before the steam is admitted, the admission line com-
mences to curve inward, as at B and (7, the leaning tendency increasing
as the line progresses and the motion of the piston becomes faster. At
D is shown a peculiar admission line on a diagram taken by the author
from a slide-valve engine, the eccentric of which had slipped so as to
make the whole valve motion late. The exhaust closure being late as
well as the steam opening, the compression was entirely cut out, and the
back-pressure line b continued straight up the end of the stroke. When
the piston commenced its return stroke the steam valve had not opened.
The exhaust-valve had by that time closed, the space between the
cylinder head and the retreating piston was entirely shut in, and as the
piston moved away a vacuum was created, running the pressure down
toward a, as is shown by the arrow. At a the steam was admitted and
the admission line ran up, leaving the loop on the heel of the diagram,
as shown.
The admission line may lean in, however, from another cause than
that of the steam-valves being late, as the author found in procuring
the diagram whose admission line is reproduced at E. The natural
inference from the appearance of the diagram would be that the engine
was late all around, but the fact is that the steam-valve has plenty of
lead and opens before the return stroke is completed; but the exhaust-
valve is so late that it not only does not close for compression, but does
44
THE ADMISSION LINE
45
not close until the piston has got well started on the forward stroke,
so that the steam is blowing right through into the exhaust and cannot
keep the pressure up. As the exhaust closes, however, the pressure is
increased, but the piston is moving away so rapidly that the line never
becomes-erect.
The amount of compression has a great deal to do with the appear-
ance of the admission line. The effect shown at F is a very common
one, produced by the pressure running up by compression to the point
ir
FIG. 46.
and falling away on account of late admission as the piston starts back
before the steam-valve opens, forming the loop. A more aggravated
case of the same action is shown at G, which represents the condition in
which an old-fashioned, upright Corliss engine ran for a number of
years. This loop assumes all sorts ef forms, according to the relations
of the compression and admission, and the proportions of the openings
and the piston speed; and may even be formed when the steam-valve
opens promptly, by excessive compression, as frequently seen on diagrams
from the ordinary type of single valve, high-speed engines with shaft
governors, where the compression is increased as the load diminishes,
resulting in admission lines like those shown at H and L In the first
46 THE STEAM ENGINE INDICATOR
of these the pressure is so low that the compression line extends above
it, and when the steam-valve opens, there is an escape of steam from
the cylinder and the pressure is lowered to that at which the steam will
flow from the chest. The appearance at / is produced when the engine
is lightly loaded, so that the compression is very considerable.
A sharp point at the top of the admission line is usually an indica-
tion of too much lead, and it will be found to result in smoother running
if the corner is just given an indication of rounding, as at A. The pro-
jection is due to the fling of the moving parts carrying the pencil above
the point due to the pressure.
Just as a tardy action of the steam-valve results in producing an in-
ward leaning of the admission line, so a too early opening of that valve
will result in the production of a line which leans outward, as shown
at K. This is to be avoided, as it puts an injurious strain on all the work-
ing parts of the engine, pushing with all the force of the steam pressure
per square inch multiplied by the piston area upon the crank as it is com-
ing up over the center, and crowding the shaft hard into the main bear-
ing to no purpose. It simply sets the steam pressure to work against
the desired movement of the engine, and robs the diagram of the effective
area between the admission line and the perpendicular dotted line K,
which indicates the position the admission line should really occupy.
Any engine which is in line and properly adjusted in the connections
should run at the speed for which it is designed better with enough lead
to bring the admission line upright, than it does with more, and if the
upright is to be departed from at all, it had better be in the direction
of making the valve late than in that of giving the engine steam before
it is ready for it.
CHAPTER VI
THE STEAM LINE
FROM the steam line of the indicator diagram may be determined
what percentage of the boiler pressure is realized in the cylinder and
how well this pressure is maintained up to the point of cut-off. Steam
or any other fluid will not flow without a difference of pressure between
the vessel from which it flows and that into which it is delivered, and
this difference in pressure must be sufficient to overcome the frictional
resistance of the connecting pipes and passages. It is absolutely im-
possible, therefore, to maintain in the cylinder the same pressure that
is carried in the boiler, although with short connections, ample passages,
and low piston speeds a very large percentage can be realized.
In a really good diagram the steam line will appear about as at A, Fig.
47, approaching, in its height above the atmospheric line, the distance
indicated by the boiler pressure laid off to the same scale as that of the
spring with which the diagram is taken, as shown by the dotted line,
and remaining horizontal, or very nearly so, up to the point of cut-off.
When the connecting pipe and passages are small for the piston speed
and diameter, the linear velocity of the flow becomes so great that a
greater difference in pressure is necessary to overcome the increased
resistance, and the steam line falls away, as at B, sufficiently to keep
up the difference necessary for such a rate of flow, as at a and b, the
difference at a being sufficient to maintain the lesser velocity at the begin-
ning of the stroke, while the greater difference in pressure at 6 is necessary
when the piston has gained the greater speed due to that position in the
stroke.
Such a falling away may be due either to faulty design or setting
of the ports and valve of the engine itself, in which case the loss of
pressure will occur chiefly between the steam chest and the cylinder;
or to a long, tortuous, or insufficient connection between the engine
and boiler, in which case the loss of pressure would occur between the
boiler and the steam chest.* To which of these causes the loss is mainly
due, and how much of it is due to each, may be determined by applying
the indicator to the steam chest, taking the motion from the cross-head
just the same as when the indicator is upon the cylinder. Such a diagram
* See Chapter XIII on Errors of the Diagram.
47
48
THE STEAM ENGINE INDICATOR
should be taken by transferring the indicator from the cylinder to the
steam chest without disturbing the paper on which the cylinder diagram
has been taken, and maintaining the boiler pressure, load and speed
constant, in order to best show the relations of the diagrams. A still
better way, when plenty of indicators are available, is to have an instru-
ment on both the chest and cylinder, take simultaneous diagrams, to
the same scale, and transfer them to one card, by making the atmos-
\
V
FIG. 47.
pheric lines identical. This may be handily done by cutting the card
from the cylinder close to the steam line at the top, and reducing its
length so as only to include the diagram. Then extend the atmospheric
line to the ends of the card, extend the atmospheric line on the steam
chest card, and place the two cards so that the atmospheric lines will
coincide as i'n Fig. 48, one diagram being directly beneath the other.
Being made from the same reducing motion, their lengths should be
the same.
The diagram shown above the ordinary cylinder diagram in Fig.
48 is a conventional steam chest diagram. At a the valve opens to let
steam into the cylinder, and the outrush of steam reduces the steam
THE STEAM LINE
49
pressure in the chest until there is the difference between the boiler
pressure and the pressure in the chest indicated by the space be, between
the line of boiler pressure (which should be drawn in on the diagram at
a height measured from the atmospheric line by the same scale with
which the diagrams were taken) and the lower line of the chest diagram.
Understand, the vertical distance between the line of boiler pressure
and the lower line of the chest diagram represents the loss of pressure
between the boiler and the steam chest at that point. The space between
the lower line of the steam chest diagram and the steam line of the cylinder
diagram at any point in the stroke is a measure of the loss of pressure
between the steam chest and the cylinder. The greater the distance from
the boiler, the smaller the pipe, and the greater the number of turns,
the greater the loss of pressure between the steam chest and the boiler,
Boiler Pressure
FIG. 48.
and the greater the area of the steam chest diagram. The smaller,
longer, and more crooked the ports, the greater the reduction between
the steam chest and cylinder and the greater the lost area between the
diagrams. Following out the outline of the steam chest diagram, the
pressure continues to fall along the line acd as the piston moves faster
and faster until the cut-off valve closes and the draft of steam from the
chest ceases, when the pressure in the chest commences to recover and
runs well or quite up to boiler pressure as the flow of steam is stopped.
It may even run above the boiler pressure on account of the momentum
of the moving column of steam in the connecting pipes. A similar
action upon the other end completes the diagram. It will be seen
that in this way the cause of any excessive loss of pressure can be
located exactly and the relative importance of changes in the engine
or piping determined.
50 THE STEAM ENGINE INDICATOR
The" fall of pressure in the steam chest, and thus the shape of the
steam line, may be considerably affected by the amount of compres-
sion used. Suppose an engine to cut off at quarter stroke and to have
5 per cent clearance. The total displacement up to cut-off is 25 + 5=30
per cent of the whole displacement. This is the volume which must
be filled from the boiler, and the clearance is ^ or ^ of it. But even
a good engine uses 20 per cent more steam than would be accounted
for by filling this volume the given number of times an hour. This
steam is condensed upon the containing surfaces which have just been
exposed to the exhaust pressure and refrigerated by the evaporation
from them of the water which, in a vacuum, evaporates at very low
temperatures and even in a non-condensing engine at a temperature
below that of the metal. Suppose that another sixth is thus disposed
of and you have one-third of the total steam which the engine requires
to be furnished from the steam chest before the piston moves off from
the center. If the clearance is empty when the admission valve opens,
this draft will make a serious reduction in the steam chest pressure
and will reduce the height of the steam line. If the clearance
has been largely filled by compression the draft will be correspond-
ingly less and the steam line will be higher, especially at its com-
mencement. This is the reason why compression often makes a steam
line fall away, not by lowering its final but by raising its initial
- pressure.
In order to prevent an undue fall of pressure, and wire drawing of
the steam, the passages leading to the cylinder should be so propor-
tioned that at no point the linear velocity of flow shall exceed 6000 feet
per minute. This can be done by making the passages bear the same
proportion to the cross-sectional area of the cylinder that the piston
speed does to 6000; i.e., take for the smallest cross-sectional area of
the steam pipe or passages such as fraction of the cross-sectional area
of the cylinder as is indicated by writing the piston speed in feet per
minute as a numerator over 6000 as a denominator.
For a piston speed of 600 feet per minute, for instance, the smallest
cross-section of the pipe or port should not have an area less than - vt
or one-tenth of the cross-sectional area of the cylinder.
On engines with large steam chest capacity the appearance at C,
Fig. 47, is often met, the large volume of steam already at hand sufficing
to keep the pressure up at the commencement of the stroke, but when
the piston movement becomes more rapid and the draft from the boiler
begins in earnest, a greater difference in pressure is required to maintain
the flow, and the line drops away, as shown.
If there is any tendency to fall away on the part of the steam line,
it will, under equal conditions, manifest itself most decidedly on the
THE STEAM LINE
51
head end of the cylinder, as the piston movement is faster on that end,
owing to the angularity of the. connecting-rod.
The downward tendency of the steam line increases with its length,
for, as the stroke progresses, the velocity of the piston movement becomes
greater up to midstroke and the rate of flow accelerated. It is there-
fore very rarely that we find a long steam line on a cut-off engine, which
FIG. 49.
does not commence to fall away seriously from the initial pressure, al-
though it may hold up nicely during the earlier portion of the stroke.
A decided example of this action is seen in diagrams from cut-off
engines when cut-off does not take place. Such a diagram is shown
at E, Fig. 47, and it will be seen that although the steam line is well
maintained at the commencement of the stroke, the steam follows the
FIG. 50.
piston with more difficulty during the rapid movement in the middle
of the cylinder and the pressure falls away, recovering somewhat as the
movement grows slower on approaching the other end. The same effect
is observable at times upon diagrams from throttle-governed engines;
but as the steam lines of such diagrams depend upon the vagaries of a
governor situated between the cylinder and the source of steam supply,
little interest attaches to their study as denoting the action of the steam.
In throttle-governed engines the area of the diagram, which is the
measure of the amount of work performed, is varied in accordance with
52 THE STEAM ENGINE INDICATOR
the demands of the load by increasing the vertical distance between the
steam line and the line of counter pressure, as from a to b (Fig. 49) for
a light load and form a to c for a heavy load, while in the automatic
cut-off engine the same object is effected by varying the length of the
steam line by cutting off the steam earlier or later in the stroke, as
from a to b (Fig. 50) for a light load and from a to c for a heavy load.
Diagrams are sometimes met with which have no steam line, the
load being so light that the expansion of the steam in the clearance is
sufficient to keep the engine in motion. In this case the expansion
line meets the admission line at a point, as at D, Fig. 47.
The shape of the steam line is often modified by the admission, and
it will be realized from the remarks about the admission line in the last
chapter that it is difficult to say when the one leaves off and the other
begins, under frequently occurring conditions.
CHAPTER VII
THE EXPANSION LINE
IN all engines in which any pretension ig made to economy, steam
is used expansively, the supply being cut off at some point in the stroke,
determined either automatically by the governor or positively by the
valve. By this means the piston is urged not only while there is a direct
draft of steam from the boiler, but by the expansive force of the steam
in the cylinder after this draft has ceased.
Referring to Fig. 51, let OX represent the stroke of an engine, and
OA the pressure of steam in the cylinder at the commencement of the
stroke; then, since the energy is
^ A r> n
the pressure multiplied by the
space through which it is exerted,
we should have for the energy
developed in a cylinder in which
the initial pressure is continued
to the end of the stroke a value
proportional to the area of the
rectangle ABXO, and the cylin-
der would require to be com- 6"
pletely filled with steam from the
boiler at each stroke. If instead
of allowing the steam to follow full stroke the supply is cut off at mid-
stroke, as indicated at C, there would be behind the piston at this point a
half-cylinderful of steam at the initial pressure, which, as the piston moves
onward, will be expanded, allowing its pressure to fall along the curved
line CD. The energy generated will now be proportional to the area
ACDXO, less by the area BCD than it was before; but the amount of
steam called for from the boiler has been only one-half as much as when
the engine followed full stroke, and the energy represented by the shaded
area CDXE has been gained at no expense for extra steam.
Steam in expanding in an engine cylinder under the conditions of
ordinary practice varies in pressure so nearly in an inverse ratio to its
volume that we can use this law in laying out the approximate path
that the curve CD, Fig. 51, will take.
Supposing an engine with a 48-inch stroke to cut off at 8 inches or
53
E
FIG. 51.
54
THE STEAM ENGINE INDICATOR
one-sixth of the stroke, with steam of an absolute pressure of 90 pounds
B (about 75 pounds by the gage). Representing the
stroke of this engine by the base line of the diagram
Fig. 52, we should have, when the piston had com-
pleted the eighth inch of its stroke, one-sixth of
the cylinder full of steam at 90 pounds pressure,
represented by the area OARS. The supply
is now cut off, and when the piston has arrived
at the 16-inch point the steam will have ex-
panded to double its volume at cut-off, and
its pressure will be reduced to one-half or 45
pounds, represented by the height of the
point C. When the piston had pro-
ceeded another 8 inches, or to the
24-inch mark, its volume would
have been trebled and the initial
pressure divided by three, giving
16
24
FIG. 52.
48
a pressure at this point of 30 pounds, represented by the length of the
line 24Z), which is one-third of the line 8J5, representing the pressure of
the initial volume.
In the same way we would find one-fourth the pressure when the
steam had been expanded to four times the initial volume at E, one-
fifth the pressure when the volume had attained five times the original
at F, and one-sixth the pressure at G, where the volume is six times
what it was at the point of cut-off. In this way the pressures at various
points in the stroke may be calculated and set off upon ordinates
representing by their position upon the horizontal line the corresponding
point in the stroke, and a curve drawn through these points will be the
theoretical expansion curve.
As a simple rule for finding the pressure at any point in the stroke :
Multiply the absolute pressure at the point of cut-off by the fraction made
by writing the number of inches of the stroke completed at cut-off as a numerator
over the number of inches completed at the given point as a denominator.
THE EXPANSION LINE 55
For example, to determine the pressures at C, D, E, F, G in the
above described diagram we have:
At C the pressure = 1^X90 =45 pounds
" D
" E "
" F
11 G "
Notice also that the product of the volume and pressure is constant.
At B we have one volume and 90 pounds and
Volume. Pressure.
Product.
At B
1
X
90
= 90
" C
2
X
45
= 90
" D
3
X
30
= 90
" E
4
X
22.5
= 90
it p
5
X
18
= 90
" G
6
X
15
= 90
The pressure for any volume may be found therefore by dividing the
initial pressure by the given volume in terms of the first volume.
This is a case of inverted proportion and may be readily solved by
the slide rule by inverting the slide and setting the index to the initial
pressure. In Fig. 53 the index of the inverted slide is set at 120 on
the lower scale. Under the 2 of what is now the top of the slide read
60 on the bottom scale for two volumes under the 3, 40 for three volumes,
etc. There is a special rule called the Duplex made with an inverted
scale, shown in Fig. 54, so that the two scales in use are contiguous and
the number right side up.
In applying this curve to an indicator diagram, the fact must be
taken into account that besides the volume of steam represented by
the piston displacement up to the point of cut-off there is the steam
in the clearance spaces, which will share in the expansion, and the initial
volume must be made to include this steam. We will apply the curve
to the diagram in Fig. 55 by one of the simplest methods. This diagram
is 4 inches in length, and we will assume a clearance of 2^ per cent.
Two and a half per cent of 4 inches is one-tenth of an inch, by the
addition of which we will increase the length of the diagram at the
admission end by drawing in the clearance line AO one-tenth of an
inch from the extreme end of the diagram. Draw the line of absolute
pressure 14.7 pounds below the atmospheric line. With ordinarily high
scales 15 pounds is sufficiently accurate. Now at the point of cut-off
C there will be in the cylinder a volume of steam proportional to the
area AC 10 of a pressure proportional to the line 1C. At right angles
to the line of absolute zero, OX, erect perpendiculars at points where
it is desired to locate the curve. As the curve changes more rapidly
*
I
CO
__E|J5CT
eico -
THE KXPAN<ln\ LINE
57
just after cut-off, it is advisable to put in these perpendiculars more
closely in the earlier portion of the stroke, as shown, and this is especially
true of diagrams with large ratios of expansion, i.e., early points of
cut-off. Xow take in the dividers the width of the space representing
the initial volume, i.e., the length of the line AC or 01, and from the
base of the first ordinate a measure off an equal distance aa' =AC,
upon the zero line. A line connecting the point of' cut-off C with a'
will cross the vertical ordinate a at the point through which the curve
must pass. From the base of the second ordinate 6 set off the same
distance W =A C, and a line joining the point of cut-off and b' will cut
the ordinate 6 at the point through which the curve should pass at that
point of the stroke. Proceeding in this manner with c and c', d and d',
and as many other ordinates as are essential, the
points through which the curve will pass may be
located and the curve traced in as indicated by
the dotted line. In practice it is not necessary
to draw the lines from the point of cut-off,
but simply to mark the point at which the
straight edge crosses the ordinate, as
shown upon the ordinate d. By spac-
ing the ordinates abc, etc., the same
distance from each other that
the point of cut-off is from
the clearance line, i.e., mak-
ing the distance between the ordinates equal to AC or 01, the base of
one line may be used as the point from which to rule to the point of
cut-off to locate the curve on the preceding ordinate, but this method
does not, with ordinary diagrams, give a sufficient number of ordinates
to locate the curve accurately in the earlier portion of the stroke.
Another method frequently used for laying out the theoretical curve
is shown in Fig. 56. Allow OX, as in the previous examples, to represent
the line of absolute zero, the line AC, by its distance from the zero line,
the initial pressure, and by its length the volume of steam up to the
58
THE STEAM ENGINE INDICATOR
point of cut-off, including that in the clearance, determined as pre-
viously shown. Erect any number of perpendicular ordinates, as 1,
2, 3, 4, 5, 6, 7, 8, at points where it is desired to locate the position of
the curve. Continue the line AC for the full length of the diagram AD.
The point through which the cruve would pass on any ordinate, as 6,
for example, is found by connecting its top E, as determined by the line
AD, with the point 0. The line EO will cross the line 1C at the point e,
which indicates the height at which the curve would pass on the line 6E 1 ,
and may be transferred to that line by drawing the horizontal ee' '. In
the same way the point /' is located upon the ordinate 5F, and at as
many other positions as are necessary to determine the course of the
curve with the necessary accuracy.
1234
6
FIG. 56.
The curve which we have been describing, and which corresponds
with a constant product for pressures and volumes, is a rectangular
hyperbola; rectangular because the asymptotes, as the lines OA and
OX are called, are at right angles. Let the rectangle OABl, Fig. 57,
represent by its height the pressure and by its width the volume of an
amount of steam. The area of a rectangle representing this amount
of steam at any other volume (the pressure changing accordingly) will
be the same as the area of OABl, for the area is the product of height
and width, which represent respectively the pressure and volume, and
with hyperbolic expansion the product of the pressure and volume is
THE EXPANSION LINE
59
constant, as shown on page 55. With the volume doubled, therefore,
the rectangle representing the new condition would be OCD2, one-half
the height and twice the width, and at 4 volumes the rectangle becomes
a square, the lines representing the pressure and volume being of equal
length. After this point the lines representing volumes become longer
than those representing pressure, but we shall have simply a repetition
of the rectangles for the earlier volumes with their length horizontal
instead of vertical. The rectangle OGH8, representing
24o~~| B 8 volumes and 2 units of pressure, is the same as the rect-
angle OCD2, representing 2 volumes and 8 units of pressure.
Thus it will be seen that the curve is the same on both sides
of the diagonal OF, which is called the axis, and that the
portion of the curve which lies between F and J is precisely
similar to that which lies between B and F.
It is a property of this curve that a line drawn across so as
to intersect it in two places, as KL, mN, WP, will cut the
\ | \ curve at equal distances from the asymptotes at both ends.
It is easily seen that the point D on the curve is the
same distance from K that H is from L. As the top
of the line is carried downward from D as to W, the
distance is decreased as to WD, but the curvature
is such as to make the distance QP upon the
other end precisely equal. So also the in-
creased length in the position mD is met
by a similar increase in the distance
RN at the other end of the line.
. This is true whatever point is
chosen upon
whatever
the curve
inclination
or
is
given to the line, so
long as it cuts the curve in two places and both asymptotes. For instance,
on the line ST placed at random, the distances SV and Tu are equal.
This property is made use of in several constructions used upon
indicator diagrams, one of which is laying out the curve as shown in Fig.
58. Through any point upon the expansion line, as C, draw straight
lines to the line bounding the clearance in one direction and to the line
60
THE STEAM ENGINE INDICATOR
of absolute vacuum in the other. Upon the line 1 1' set off a distance
from 1', equal to 1C. Upon the line 2 2', set off a distance from 2'
equal to 2C, and continue the process upon the other lines as shown.
The theoretical curve passes through the points just found. In prac-
tice it is unnecessary to draw lines, distances being laid off by means
of the dividers against the edge of the ruler. This principle is also used
to determine at what point cut-off should occur, assuming initial pres-
sure to be uniformly maintained, in order that the expansion line
may pass through point A. Drop a perpendicular line from A,
Fig. 59, to the line of zero pressure, and connect the point
B of its intersection with the point P upon the line of zero
volumes, indicating by its height the given pressure. A
line pb, parallel to PB and passing through the given
point A, will cut the line PC at the required point at
which expansion should commence in order that the
curve may pass through A. For under these, con-
ditions the triangle PpC is the same as the triangle
A Bb, and upon the line bp the points A and C are
equidistant from the asymptotes. The point of
cut-off for any other initial pressure may be
determined in the same way by varying
the position of the point P, as indi-
cated by the dotted lines.
Another construction some-
times used upon the ex-
pansion line of an indi-
cator diagram is
FIG. 58.
shown in Fig. 60. This is for the purpose of finding the position
of the line OA, bounding the clearance space. From any two points,
as BC, upon the established portion of the curve draw lines as
BD and CE, parallel to the atmospheric line, also the perpendicu-
lar lines BE and CD, forming a rectangle. At a distance below
the atmospheric line corresponding to 14.7 pounds on the scale of
the diagram draw the line of absolute zero of pressure OX. The
diagonal DE of the rectangle BDCE will, if continued, cut the line of
THE EXPANSION LINE
61
zero pressure at the point of zero volume, from which point the per-
pendicular line OA , the position of which we are seeking, may be erected.
FIG. 59.
The theoretical curve is of value in showing what, under given condi-
tions of pressure and expansion, a diagram may be expected to be,
and serving as a basis of comparison for the
actual diagram. It is not precise, however,
and too much stress should not be placed
upon itS indications unless very marked.
The law that the product of the vol-
ume and pressure remains contant
is true only of a perfect gas, and
of this only when its tempera-
ture remains constant. The
temperature of steam falls
as it is expanded and
/O
FIG. 60.
62
THE STEAM ENGINE INDICATOR
the volume would be expected to contract by such cooling so as
to bring the expansion curve below that drawn upon the pv= constant
assumption. And it would so fall if a constant quantity of steam were
being dealt with. But steam is being generated in the cylinder through-
out the expansion. As explained above considerable of the steam
FIG. 61.
admitted to the cylinder is condensed and is present as hot water. When
the pressure has fallen by expansion so that the water is above the boiling-
point at the new pressure the water commences to pass into steam, taking
from the cylinder surfaces and the other water the latent heat needed
for its evaporation, and the additional steam thus made is, with ordinary
FIG. 62.
un jacketed engines and steam which is not superheated, just about enough
to keep the expansion line up to that laid out according to this law.
Any serious departure from the curve thus laid out indicates something
which should be looked after. The line drawn by the indicator is likely
to run below the plotted curve at the commencement and above it at
THE EXPANSION LINE 63
the end, as re-evaporation becomes more vigorous. The curve and law
are also of use in designing, and in computing probable mean effective
pressures, as will be shown later. If the actual curve runs much
above the theoretical, it is an indication that steam is leaking into the
cylinder during expansion. If it runs much below, a leaky exhaust
valve is probable, but the indication should be regarded only as an
intimation and be followed out by an investigation of the engine itself.
The actual line may follow the plotted curve better with a leaky than
with a tight engine. As an instance of this may be shown two dia-
grams taken by F. Ruel Baldwin, from an engine the exhaust valves
of which leaked very badly. The first of these, Fig. 61, was taken while
the valves were in their leaky condition, but the expansion curve fits
the line of the diagram very nicely. Fig. 62 was taken after the valve
had been made tight, but there is a considerable difference between
the theoretical and the actual lines.
The accompanying transparent chart will be- found convenient in
comparing the expansion lines of actual diagrams with the theoretical
curve. Draw upon the diagram the line of absolute zero 14.7 pounds
(or whatever the barometric pressure may have been at the time it was
taken) below the atmospheric line, and the clearance line locating its
position by calculation, as in Fig. 55, if the percentage of clearance is
known, or by construction, as in Fig. 60. Place the diagram beneath
the transparent chart with the zero line under OX and the clearance
line under OA and the theoretical curve may be studied directly or
transferred to the diagram by pricking through the chart.
CHAPTER VIII
THE POINT OF RELEASE
WHEN it is possible of attainment we like to see the release end of
a diagram given the appearance shown at A in Fig. 63, the release
occurring early enough to allow the pressure to fall nearly or quite to
the line of counter pressure by the time the end of the stroke is reached.
If the release is delayed until the end of the stroke the appearance
will be more like that indicated at B. If the pressure could be carried
to the end of the stroke and immediately reduced to the line of counter
pressure, as indicated by the outside edge of the black space, it would
be advisable to retain the full area; but since some area must be lost
here in expelling the exhaust, it is better that it should be above the
diagram, as at A than below as at B. When the piston is approaching
the end of its stroke, it has come to be a question of stopping it and
sending it in the other direction. To do this smoothly compression
is applied on the other side of the piston, and obviously there is no
object in keeping up the forward pressure, as at B, unless- we can add
to the effective area of the diagram (which represents the useful work
done by the steam) by doing so. It is therefore better to let the
pressure fall off, as at A, assisting, instead of opposing, the compression
in bringing the moving parts quietly to rest, and by this early release
removing the back pressure represented by the black portion at B, so.
that the piston encounters less resistance in starting upon its back-
ward stroke when it is an object to get it into motion. In this way
nothing is sacrificed in the area of the diagram, and a better distribution
of the pressures with reference to the practical work of the engine is
obtained. The difficulty of attaining the result on most engines is that
where the lap is removed from a valve to cause it to open early and
give an early release, this very lack of lap retards the closure and does
not give sufficient compression. On the Corliss valve this may be
corrected .by setting the eccentric ahead, making both release and com-
pression earlier, but disadvantages attend upon too great an angular
advance of the eccentric, in the way of shortening the range of cut-off,
and the advantages of the valve motion in quick movement at admission,
so that it is often necessary to divide the difference and compromise upon
64
THE POINT OF RELEASE
65
a point like that shown at C. The benefit of an early release is very
apparent when a condenser is used, for with an early release and a
prompt realization of the vacuum, as at D, the largest possible per-
centage cf the load is thrown upon the condenser; while a tardy release
and a dragging action of the steam in leaving the cylinder results in
the loss of a large area in the vacuum portion of the diagram as shown,
by the shaded portion of E, calling for a later cut-off and more steam.
The shape of this end of the diagram depends largely upon the
amount of expansion and consequent terminal pressure. If the steam
D
FIG. 63
is expanded to the line of counter pressure the diagram will terminate
in a sharp point as at F, and at the end of the stroke the cylinder will
be full of steam of the same pressure as that existing in the exhaust
pipe. When the exhaust valves are opened there is, therefore, no flow,
either out of or into the cylinder, except such as is caused by the move-
ment of the piston. When the cut-off is late more steam is admitted,
and has to be expelled, and we get an appearance more like G\ and
between this and the point shown at F there may be any variety of
shapes, according to the terminal pressure and setting of the valves.
66 THE STEAM ENGINE INDICATOR
When the steam is cut off so early that the expansion extends below
atmospheric pressure, or the pressure against which the engine is exhaust-
ing, we get an appearance like that shown at ft. Here at the moment
of release the pressure in the exhaust pipe is greater than that in the
cylinder, and when the valve is opened at a there is an inrush of the
previously exhausted steam, raising the pressure to the counter-pressure
line. This condition is apt to cause a disagreeable slamming of the
exhaust valve, which is lifted from its seat when the pressure in the
cylinder becomes less than that beneath the valve, and is slammed closed
again when steam is admitted. It may be stopped by throttling the
initial pressure so that the lessened expansion does not cause a loop.
During the formation of this loop the pressure urging the piston
forward has been less than that against which the piston moves, the
forward motion continuing only by reason of the momentum of the
fly-wheel and moving parts, so that the area of the loop represents just
so much work exerted against the piston, and must be subtracted from
the other area of the diagram to get at the effective work. This point
will be considered in detail when we come to working up the diagram
for power.
CHAPTER IX
THE COUNTER-PRESSURE LINE
THE tendency of a piston to move depends upon the difference in
pressure upon its two sides. If there were 30 pounds pressure in both
ends of the cylinder at once the piston would not move any more than
though there were no pressure at all. If there were 30 pounds pressure
on one side and 15 pounds on the other, the force with which the piston
would tend to move would be the same as though there were 15 pounds
on one side and nothing on the other. In other words, the "effective"
pressure is the unbalanced pressure, or the difference in pressure between
the two sides.
The pressure upon the piston during the forward stroke is repre-
sented by the steam and expansion lines, the pressure in the same end
of the cylinder during the backward stroke is represented by the exhaust-,
counter-pressure, or back-pressure line, as it is variously called. Obviously
an engine will be doing the greatest amount of work when the pressure
urging the piston forward is greatest and the retarding effect of the back
pressure is least. Steam will not flow, however, from one place to another
without a sufficient difference in pressure to overcome the resistance to
movement through the connecting pipes and passages. If at the end
of the stroke the steam has been expanded to atmospheric pressure in a
non-condensing engine, there will be no immediate outrush of steam
from the cylinder when the exhaust valve opens, because there is no
greater pressure in the cylinder than that of the atmosphere into which
the steam must flow. The steam must therefore be pushed out by
the piston, and the resistance to its movement will depend upon the
velocity with which it flows and the length and directness of the exhaust
pipe. The size of the exhaust pipe and passages is involved in the
velocity of flow. If the exhaust pipe were as large as the cylinder and
directly open to it the rate of flow in linear feet per minute would be
the same as the piston speed. If the area of the pipe or the passage
leading thereto were one-half the cross-sectional area of the cylinder
the rate of flow would be twice the piston speed, because to get through
a passage of one-half the area in the same time the steam must travel
twice as fast. As the resistance to flow increases with the velocity, it
67
68
THE STEAM ENGINE INDICATOR
is found desirable to limit the rate of flow in the exhaust passages to
6000 linear feet per minute, which, for a piston speed of 600 feet per
minute, requires for the exhaust passages a cross-sectional area of one-
tenth that of the cylinder. For other piston speeds the proper area
of the exhaust passages may be found by multiplying the cross-sec-
tional area of the cylinder by the piston speed in feet per minute and
dividing by 6000.
The compression of the steam by the piston pushing it out of the
cylinder against the resistance to flow through the pipes and passages,
will show on the indicator diagram in raising the line of counter-pres-
sure above the atmospheric line in a non-condensing engine. In a well-
FIG. 64.
proportioned engine at moderate piston speeds and exhausting through
a short and ample exhaust pipe this moving pressure will not be notice-
able with an ordinary spring, and the line of counter-pressure will merge
into the atmospheric line, as at A, Fig. 64. Under less advantageous
circumstances, however, the back-pressure line will be elevated above
the atmospheric line, as at B, and the distance between them will be
a measure of the force required to overcome the resistance to the out-
flow of the exhaust.
The beginning of the back-pressure line depends, as may be seen
from the last chapter, very much upon the point of release and the ter-
minal pressure. When at the end of the stroke the cylinder is full
of steam of a high pressure, we have a rapid outflow of steam as soon
THE COUNTER-PRESSURE LINE 69
as the valve is opened for release, but even with the greater impelling
pressure a sufficient velocity is not generated to discharge this greater
volume of steam (which expands when the pressure is reduced) before
the piston gets some distance on its way back, making the beginning
of the back-pressure line like C; and sometimes the back pressure does
not reach its lowest point until the backward stroke is practically com-
pleted, as at D.
Sometimes we find a diagram where the back-pressure line starts
in well enough, but makes a gradual rise toward the center of the dia-
gram, falling again as the stroke is completed, as at E. This may be caused
by too great velocity in the middle of the stroke, either from contracted
ports or too much inside lap on a slide valve narrowing up the exhaust
passage as the center of the stroke is reached, and where the piston,
and consequently the steam, has the greatest velocity. The same
effect may be produced upon a Corliss engine. It is also found where
a pair of cylinders working on cranks set at 90 degrees exhaust into the
same pipe, the release of one cylinder occurring practically in the middle
of the stroke of the other and the efflux of steam into the pipe causing
a rise of pressure.
The end of the back-pressure line depends for its shape upon the
amount of compression. At c in diagram B, Fig. 64, for instance, the
exhaust -valve closes and the steam remaining in the cylinder is compressed,
the pressure rising upon the curve shown. With no compression the
back-pressure line- would continue straight to the end of the diagram,
and with a prompt admission we should have a square corner at the
end. When the compression commences earlier in the stroke the com-
pression curve runs proportionally higher, as is well shown at F, taken
from an engine where the compression varies with the load, and showing
the effect upon the counter-pressure line of closing the exhaust valve
at different points in the stroke. It is even possible to carry the pres-
sure, by compression above that in the steam chest, so that when the
valve opens for the admission of steam, the pressure in the cylinder
being greater than that in the steam chest, there is a drop instead of a
rise to the line of realized pressure, as shown at Q.
CHAPTER X
THE COMPRESSION LINE
COMPRESSION is the inverse or opposite of expansion. In making
the expansion line the volume of steam admitted up to the point of
cut-off is increased in volume, the pressure falling in an inverse ratio,
and we remember that the product of the volume and pressure was
constant. In compression the volume of steam inclosed when the ex-
haust-valve closes is diminished in volume with a consequent increase
in pressure, and in this case too the product of the volume and pres-
sure is constant. If we compress the steam into half the space which
it occupies when the exhaust-valve closes we shall double its absolute
pressure; into one-third the space, treble its pressure, etc. The clearance
space, being in most cases a large proportion of the volume inclosed,
becomes of increased importance.
In Fig. 65 suppose the exhaust-valve to close at and the clearance
to be bounded by the line OA. There is then shut into the cylinder
when the exhaust closes a volume of steam proportional to the line 08
and of an absolute pressure equal to 8C. When the piston has ad-
vanced to 4 this volume will be one-half of 08 and the pressure will
be twice 8C: so at 6 the volume will be f of that at C and the pressure
I; at 1 the volume will be J- and the pressure 8 times that at C. The
pressure at the various points can be calculated and measured upon
the ordinates by scale, or the line can be laid out graphically for the
compression line by any of the methods shown for the expansion line
by using C in the same manner that the point of cut-off was used in lay-
ing out the expansion line, and spacing off vertically upon the line
OA, or on an extension of 8(7 instead of upon 08, as for the expansion
line. In Fig. 65 the curve is laid out by the method described in Fig.
55, page 57. It is rarely that it is of service to apply the curve to the
compression of an actual diagram unless it is from a single-valve auto-
matic engine, where under light loads the compression line becomes nearly
as large and important as the expansion. It will be remembered that
in Fig. 60, page 61, it was shown that if a rectangle was constructed upon
the expansion line, with sides parallel and perpendicular to the atmos-
pheric line, its diagonal prolonged would cut the zero line OX at the
70
THE COMPRESSION LINE
71
intersection of the line OA bounding the clearance. This is equally
true of the compression line, and it will be seen in Fig. 65 that the diagonal
OD of the rectangle abed cuts 08 at the intersection of the clearance
line OA. In Fig. 65 the admission valve commences to open at about
e, and as the piston comes to a standstill merges the compression into
the admission line. The dotted line shows where the pressure would
go if the piston advanced further into the clearance.
It is difficult for some engineers to understand how there can be
compression in a condensing engine. There is, they reason, a vacuum
in the cylinder when the exhaust valve closes, and nothing to com-
press. This would be true if the vacuum were complete, but the " vacuum "
of practice is simply an absolute pressure less than that of the atmosphere.
The less the absolute pressure the more complete the vacuum. The
pressure of the atmosphere is equal to about 15 pounds or 30 inches of
mercury. When we have a vacuum of 26 inches we have still in the
condenser an absolute pressure of 30 26=4 inches of mercury, or two
pounds available for compression.
The amount of pressure or the effective compression obtained by
closing the exhaust-valve does depend, however, upon the tension or
72
THE STEAM ENGINE INDICATOR
pressure of the vapor inclosed in the cylinder when the exhaust-valve
closes. Referring to Fig. 66, suppose we have an engine where the
clearance space OA is one-quarter of the total volume, 0(7 between the
piston, cylinder head, and valves after the exhaust-valve closes. If
the counter-pressure line of the diagram was only 3 pounds above the
line of absolute zero, corresponding to a vacuum of 24 inches, there
would be three pounds less than the atmospheric pressure at the end
of the stroke, as shown at a. If there were only 12 inches of vacuum
or 9 pounds absolute to start the compression with we should get up
to 21 pounds, as at 6. With a non-condensing engine and no back
pressure (above the atmosphere) we should get 45 pounds by com-
pression, as at c, while with 6 gage pounds back pressure we should
6 Gauge Pounds = 21 Pounds Absolute Back Pressure
12~Inches Vacuum or 9 Pounds Absolute Back Pressure
24 Inches Vacuum or 3 Pounds Absolute Back Pressure
O A
Absolute Zero of Pressure
FIG. 66.
get up to 69 pounds above the atmosphere with the same valve setting
and point of exhaust closure that gave 3 pounds less than atmospheric
pressure with the low counter-pressure line.
The smaller the clearance, too, the greater the pressure realized by
compression, with the same point of exhaust closure, on account of
the small final volume possible. In Fig. 65, with the clearance AB,
a pressure equal to e was realized. If we had half the clearance, i.e.,
if the piston could have advanced to F, we should have realized a pressure
equal to /. In engines with a variable compression it is necessary to
have a considerable proportion of clearance or the pressure would be
excessive with the early exhaust closure usual with light loads. As it
THE COMPRESSION LINE
73
is, the pressure generated by compression frequently exceeds the initial
pressure (see diagram G, Fig. 64, page 68).
The object of compression is initially to furnish a cushion or gradually
increasing resistance, to bring the moving parts to rest and change the
direction of the push upon them without t-he shock which would follow
upon the sudden opening of the steam-valve. In Fig. 67 the piston
is moving to the right, or toward the shaft, and the engine is about in
the position shown in the small sketch between the diagrams. Every
joint between the piston and the main crank pin is in compression, and
the main shaft is pushed hard against the outer face of the bearing.
When the crank reaches the center, and the pressure acts on the other
side of the piston, the connecting rod will pull instead of push, every
joint will be extended, and the main shaft pulled against the back of
the bearing. If this change in pressure is effected suddenly every par-
ticle of lost motion in every joint and bearing will be taken up with a
thump, and it is only by changing, the pressure gradually from one side
to the other that we can make it run smoothly. When the piston is
at the point in the stroke indicated at al, there is behind it the pressure
/c, and no pressure but that of the atmosphere in front of it. As it
moves along, the pressure behind it decreases while at d the pressure
in front .of ,it begins to increase, and at e the pressures on both sides
are equal. After this the pressure in front exceeds that behind the
piston, but the change is gradual, the direction of thrust is changed
under a slight difference of pressure, and when the steam is admitted
the bearings and journals are already firmly pressed against the surfaces
upon which they are to bear. In addition to the steam pressure moving
the piston forward there is the momentum of the moving parts to be
reckoned with.
Aside from its cushioning effect compression has another advantage
in reducing the loss from clearance. Take an exaggerated instance.
Suppose an engine with a clearance equal to 100 per cent, i.e., that the
74
THE STEAM ENGINE INDICATOR
volume of steam required to fill the space behind the piston, including
ports, etc., when the engine is on the center, is equal to the volume
generated by the piston's movement, i.e., the piston area multiplied
by the length of the stroke. It is understood that the indicated power
is in proportion to the inclosed area of the diagram. Before the piston
can move, the clearance must be filled with steam, and supposing the
engine to work without expansion, it would take two cylinderfuls of
steam to do the work of one stroke, one to fill the clearance, and one
to supply the space behind the moving piston. In Fig. 68, then, there
would be required a volume of steam proportional to the rectangle
A BCD to do an amount of work proportional to the rectangle EFCD.
Now suppose the exhaust-valve to close at c so as to fill the clearance
by compression with steam at the initial pressure, the area of the
diagram has been reduced by the amount below the dotted line, but
CLEARANCE
FIG. 68.
we have still considerably more than half of it left, and as the clearance
is already full, have used only half the volume of steam.
Where there is no expansion the steam required to fill the clearance
space is a dead waste. With a cut-off engine it gets a chance to expand
with the other steam and does some good, but still there is, theoretically,
at least, a saving by compression and for the abstract case unmodified
by such practical consideration as cylinder condensation, etc., the greatest
area of diagram will be produced by a given volume of steam when the
ratio of compression equals the ratio of expansion, i.e., when the clear-
ance bears the same relation to the volume at the commencement of
compression that the volume at cut-off does to the volume at the end
of the stroke.*
It remains only to consider some of the forms obtained in practice.
When the engine is of a type in which the compression is constant, the
best results will generally be attained under normal loads by having
the compression round up nicely into the admission line, as at a, Fig. 69,
meeting the perpendicular line at about one-third of its height. This
* See Compression as a Factor in Steam Engine Economy, Proc. A.S.M.E
XIV, 189.
Vol.
THE COMPRESSION LINK
75
will require a different setting of the exhaust-valve for different heights
of the counter-pressure line, as explained on page 72, and can be deter-
mined only by the indicator. If no indicator is used, put on only enough
compression to make the engine run smoothly. At 6 is shown excessive
compression, the pressure running up above that in the steam chest,
so that when the valve opens for admission, steam flows from the cylinder
to the chest and the pressure falls. A form of compression line often
met which is shown at c, where the pressure instead of continuing upward
along the dotted curve falls away as shown. When this occurs the cause
for the reduction of pressure will usually be found in a leak. As the
piston approaches the end of its stroke its movement becomes very slow,
the volume of steam involved is small and growing smaller, and if there
FIG. 69.
is even a slight leak in the exhaust-valve, drip- valve, or piston there will
come a time when the volume of steam discharged through the leak
will equal the volume generated by the movement of the piston in the
same time. To state it more simply, at all times the pressure will be
lower than if there were no leakage, and there will come a time
when the escape through the leak with the increasing pressure will pull
the pressure down as fast as the movement of the piston increases it,
and the line will become horizontal as at d, or it may even fall away
as at e. As soon as the pressure, from compression, behind the piston
becomes greater than that in front of it a leak in the piston becomes
effective to reduce the compression pressure. Such a diagram as Fig. 70,
which was sent to the author for explanation as to the formation at A,
might be caused by a badly leaky piston. It will be seen that the com-
pression rises after the valve closes much more abruptly than it should
76
THE STEAM ENGINE INDICATOR
have done at that distance from the end of the stroke. This would be
accounted for by leakage from the other side, where the pressure is still
high, into the confined space in front of the piston. As the pressure
behind the piston decreases, this action falls off, allowing the line to lean,
and after the release occurs on the other end the leak is reversed, from
the compression space into the other end, now opening to the exhaust,
allowing the pressure to fall off as shown. It is probable, as the exhaust
closure is early and the release late on this diagram, that a diagram
from the other end of the cylinder would show opposite conditions,
early release and little compression, which would locate the turn in the
curve about where it occurs in the diagram. As a general rule, when
; FIG. 70.
you see a compression line falling off badly, look out for leaks. Jt is
a better indication than a failure of the expansion line to follow the
theoretical.
It is a matter for consideration, however, if condensation does not
play an important part in the formation of such departures from the regular
curve. The surfaces of the cylinder head, piston, and ports have just
been exposed to the temperature of the exhaust, and as the piston iiears
the end of its stroke they bear a large proportion to the small volume
of steam inclosed. Enough steam must be condensed upon those sur-
faces to bring them up to the temperature corresponding to the pres-
sure before the steam can remain as steam in contact with them, and this
condensation might account for the falling off in pressure necessary to
produce these deviations from the true curve.
CHAPTER XI
MEASUREMENT OF THE DIAGRAM FOR MEAN EFFECTIVE
PRESSURE
ONE of the principal" uses of the indicator diagram is to determine
the horse-power which the engine is developing. One of the important
factors in this problem is the pressure urging the piston forward, and this
can be found with any accuracy only from the indicator diagram. The
Diameter 24 inches
Stroke 48 inches
Revolutions 70.
Scale 40.
FIG. 71.
-.
pressure varies through the stroke, and is opposed by a varying amount
of back pressure, so that the average unbalanced, or, as it is commonly
called, the "mean effective pressure," must be determined. The most
elementary way of doing this is by measuring the pressure upon the
diagram at a number of equidistant points and taking the average.
To do this, divide the diagram into a number of equal parts lengthwise,
(ten for ordinary work) as shown in Fig. 71 by the dotted lines and,
with a scale corresponding to the spring with which the diagram was
taken, measure the pressure in the center of each of these divisions;
that is, upon the full lines or ordinates. Notice that this pressure must
be measured between the lines of the diagram, as from a to 6, whether
77
78
THE STEAM ENGINE INDICATOR
the engine is condensing or non-condensing, and not from the atmos-
pheric or any other line.
Performing this operation on the diagram shown in Fig. 71 we find,
with a 40-pound scale, 87 pounds on the line or "ordinate" 1; 89.5
pounds on 2; 65.5 on 3; 47 on 4; 37 on 5; 29.5 on 6; 23.5 on 7; 18.5
on 8; 15 on 9; and 12 on 10. Adding these values we have 424.5 for
the sum, and dividing by 10, the number of measurements, find the
average or mean effective pressure to be 42.45 pounds.
Several expedients may be resorted to for shortening the labor of
dividing the diagram and locating the ordinates. The simplest of these
is to have a rule, a little longer than the ordinary length of your diagrams,
divided as shown in Fig. 73 just as you want your diagram to be divided,
FIG. 73.
with nine spaces of equal length in the middle, the two end spaces,
to 1 and 10 to 0, being one-half the width of the others. Four inches
between the zero marks is a good length for diagrams from 3| to 4 inches
in length, and one each of 3^ and 4^ inches, with a short one for the
diagrams from small cylinders, will cover all ordinary cases.
Draw the lines OA and XB at the extreme ends of the diagram
and perpendicular to the atmospheric line. Place the rule between them,
MEASURE OF THE DIAGRAM FOR MEAN EFFECTIVE PRESSURE 79
as shown in Fig. 73, at such an inclination that both zeros come upon
the perpendiculars. Then with a needlepoint prick the card opposite
each division of the rule, and draw the ordinates perpendicular to the
FIG. 74.
atmospheric line and through these points. An engineer's scale, such
as that referred to on page 9 and shown in Figs. 8 and 72, may be used
to advantage in this work. If the diagram is just 4 inches long
FIG. 75.
the 20-pound divisions of the 50 scale will just divide it into ten equal
parts. If it is less than four inches incline the scale as in Fig. 74, so
that the zero is upon one line and the 20 on the other. The figured
divisions will divide the space into ten equal parts. In order to get a
80
THE STEAM ENGINE INDICATOR
half space on each end (that is, to locate the ordinates in the center of
the equal tenths), slide the scale to the position shown in Fig. 75 so that
the 1 mark is on one line and the 21 mark on the other. Make a needle
hole or pencil mark at the edge of the scale against each numbered division
and erect the ordinates square with the atmospheric line and passing
through the points indicated. The 50 scale works very well down to
diagrams 3J inches in length, which are exactly divided into tenths
by the numbered divisions of the 60 scale; and for this length and below,
the 60 scale will preferably be used, as the inclination of the 40 scale
becomes too great. For diagrams between 4 and 5 inches the 40 scale
is used in the same way. No calculation is required. If the diagram
is, on trial, too long for the 50 scale, use the 40; if you have to use the
FIG. 76.
50 scale at too much of an angle, use the 60. A little use will make
the process perfectly natural.
The principal advantage of such a scale, however, especially the
12- or 14-inch scale, is in measuring the length cf the ordinates. Usually
the pressure on each ordinate is measured with the minute divisions
of the common scale, the ten observations added, and the sum divided
by ten to get the average. Now we can divide by ten to start with
by dividing the value of the scale and at the same time get the advantage
of the coarser reading. With a 40 spring, instead cf calling 1 inch 40
pounds, suppose we call it 4 pounds. Then we can measure the ordinate,
add the results, and have the mean effective pressure at once. The
pound, instead of being ^ of an inch will be J. The finest divisions
of the scale will represent tenths of pounds instead of full pounds, so
MEASURE OF THE DIAGRAM FOR MEAN EFFECTIVE PRESSURE 81
that they can be read much more accurately, and the numbers on the
scale will correspond with the pound marks. Thus in Fig. 76 we have
on the ordinate to which the scale is applied, 10.5 pounds pressure. This
FIG. 77.
is, of course, only one-tenth of the pressure which that particular ordinate
represents, but we shall give the pressure ten records, so that the aggregate
will be the same as though we measured each on the given scale and then
divided the aggregate by ten. v
FIG. 78.
There are also procurable from the instrument makers parallel rules,
as shown in Figs. 77 and 78, whose method of application is too obvious
to require description.
82
THE STEAM ENGINE INDICATOR
Instead of measuring each ordinate with the scale corresponding to
the spring with which the diagram was taken, some engineers prefer
to lay off the lengths of the ordinates continuously on the edge of a
strip of paper, then to either measure the whole length with a long scale
of the proper unit, or with a scale of common inches, and multiply the
length by the scale of the spring.
In the measuring of the mean effective pressure by ordinates there
remains to be explained the treatment of diagrams having negative
or back-pressure areas. For example, in Fig. 79, after the point a is
FIG. 79.
passed, the forward pressure in the cylinder is less than the back pressure
during the return stroke. The piston is actually hanging back upon
the engine, and the loop not only represents no addition to the useful
mean effective pressure, but a force acting against the motion of the
engine equivalent to so much back pressure. The average pressure of
the loop portion of the diagram must therefore be subtracted from that
of the other portion. Erecting the ordinates as before directed, and
measuring with a 40 scale, we have 98+93+40+20+5=256 as the
sum of the measurements in the main portion of the diagram, and
3+8 + 13 + 15 + 11=50 as the sum of the measurements in the loop.
Taking the difference and dividing by 10 to get the average, we have
256-50
10
'20.6 Ibs. M.E.P.
CHAPTER XII
THE PLANIMETER
THE area of a rectangle, as A, B, C, D, Fig. 80, is found by multi-
plying its height by its length. If the figure shown were 2 inches high
and 4 inches long it would obviously contain 2X4=8 square inches
of area. If on the other hand it were known that its area was 8 square
inches and its length 4 we could easily tell that it was 8 -=-4 =2 inches
high. If we wanted to know how high it would be if it were any other
length to contain the same area, we would simply divide the area by
the new length. If the rectangle in Fig. 80 were lengthened to 8 inches
4 inches
Area 8 sq. in.
C
FIG. 80. FIG. 81.
it could, to contain the same area, be only 8-^-8 = 1 inch high, or if
lengthened to 6 inches 8 -T-6=1J- inches.
Suppose now we have a figure like Fig. 81, and wish to know its
average height. We could divide it into a number of rectangles, as
shown by the dotted lines, and find the height which each rectangle
would be if extended to the full length, of the diagram. Supposing the
diagram to be 4 inches long, the area A would be one-half an inch high
and an inch long, containing therefore one-half a square inch of area.
If this were extended to 4 inches its height would be reduced to J-j-4=J
of an inch. The area B is 2XJ = 1 square inch, and would be l-*-4=J
of an inch high if 4 inches long. Similarly C, containing 1^ square
inches, would be lj-f-4=| of an inch high, and D, already 4 inches long,
is one-half an inch high. So for the total average height we should
have J+J+J+i = l} inches, bringing the average height at the line xy.
That this is right is evident at a glance, for the area A will just fill the
space a, and that part of B which is above the line xy will just fill the
83
84
THE STEAM ENGINE INDICATOR
space b below it. But if we know in the first place the area of the
whole figure we can get at the average height at once by dividing that
area by the length, for obviously the whole is equal to the sum of all
its parts, and we shall get the same result by dividing the whole area
by 4 as by dividing each of its parts by 4 and adding the quotients.
Thus the whole area of Fig. 81 is ^ + 1+1^+2=5 square inches, and
5^-4 = 1^, the same as the sum of the several divisions.
In an indicator diagram the height is proportional to the pressure,
and to find the average pressure we must find the average height. We
have an irregular figure which we wish to reduce to a rectangle of the
same area and to know the height of the rectangle. Imagine the diagram
stepped off into the boundaries of rectangles, as in Fig. 82, and it will
FIG. 83.
be clear, in view of what has been said about Fig. 81, that dividing its
area by its length will give its. average height; and inasmuch as this
is true however fine the divisions or steps, we may imagine them to be
so fine as to be included in the width of the line which bounds the
diagram, and arrive at the fact that the area of an indicator diagram,
or any other plane figure for that matter, divided by its length equals
its average height.
Fortunately a means is at hand for easily and accurately measuring
the area of such diagrams. The planimeter, the instrument used for
this purpose, is made in a variety of forms, and is cold at prices ranging
from five to thirty-five dollars. The Amsler was the first upon the
market, and as a typical example is shown in Fig. 83. It consists of
two arms pivoted at the top, upon one of which is carried a roller free
THE PLANIMETER
85
to revolve upon an axis parallel to the arm itself. The roller is divided
circumferentially into ten equal parts, each of which represents a square
inch of area, and each of these parts is further divided into equal parts
representing each one-tenth of a square inch, as shown in Fig. 84. Close
to the edge of the roller is a stationary plate having the same curvature-
and containing a vernier made by dividing a space nine-tenths as long
as one of the large divisions of the roller into ten equal parts.
In Fig. 85 let the space between A and B represent one of the larger
divisions of the wheel, and the space between C and D the vernier.
In reading the instrument take the number on the wheel which has
passed the zero mark of the vernier when the wheel is turning to the left
as indicated by the arrow, as the number of whole square inches, in
this case 6. The tenths of a square inch are indicated by the number
of spaces, such as a, which have passed the zero mark, in this case 1;
so that the reading of the scale as laid down in Fig. 85 is 6.1 square inches.
10
1234 67
f I I 1
8 9
bed
FIG. 84.
FIG. 85.
Since the vernier CD is nine-tenths as long as AB each division of the
vernier must be nine-tenths of each division of the scale. From to
1 on the vernier is nine-tenths of the space beneath it on the wheel, then
the space between the line b on the wheel and the line 1 on the vernier
is just one-tenth of one of the spaces such as a upon the roller, the space
between the lines 2 and c is just two-tenths, between 3 and d three-
tenths, etc. If, then, the wheel rolls in the direction of the arrow
one-tenth of one of the spaces o, corresponding to an area of one one-
hundredth of a square inch, the lines 1 and b will coincide, for two one-
hundredths 2 and c would coincide, so that we get the hundredths of a
square inch by writing that number on the vernier which is opposite
any line on the wheel. For instance, in reading the instrument as it
stands in Fig. 84 write, first, the number on the wheel to the left of the
zero mark, in this case 4; then the number of whole spaces between
that number and the zero mark, in this case 7; and last the number
on the vernier which is in line with a mark on the wheel, in this case 3.
86
THE STEAM ENGINE INDICATOR
The whole reading therefore is 4.73 square inches, the decimal point
being placed after the 4, the 7 and 3 being tenths and hundredths as
before explained. It will be noticed that only the zero, 5, and 10, are
FIG. 86.
numbered on the vernier in Fig. 84, and this is, the case in the actual
instrument, the intermediate marks being easily known by their
position.
FIG. 87.
The eye soon becomes accustomed to quickly determining the mark
upon the vernier which coincides with one upon the wheel, the marks
at either side of it being just within the marks upon the wheel, giving
the arrangement shown at A in Fig. 84.
THE PLANIMETER
87
The plammeter should be used upon a smooth but not slippery sur-
face, such as that of heavy drawing paper or Bristol board. Place a sheet
of this large enough to include the planimeter and the diagram upon
the drawing board, and fasten it with thumb tacks. Set the stationary
point of the pianimeter into the paper in such a position that the tracing
point can be carried around the outline of the diagram without bringing
the wheel into contact with the edge of the paper. The instrument
can be worked to the best advantage when it is neither allowed to close
up too closely, as in Fig. 86, nor to extend too widely, as in Fig. 87. A
better position for the stationary point than either of these is shown
in Fig. 88, the motion of the roller being easiest when the arms are
near a right -angular position. When the areas to be measured are large,
or when there is considerable space between the top of the diagram
and the top edge of the card, contact of the roller with the edge of the
FIG. 88.
card may be avoided by inverting the diagram, as indicated by the
dotted diagram in Fig. 88, using the planimeter always in the same
direction, that in which the hands of a watch run; for obviously the
area of the diagram remains the same in whatever position the card is
placed.
Place the tracing point on any convenient point in the line of the
diagram and, by pressing upon it, make an incision, to mark the point
of starting. Take the reading of the instrument as it stands, then with
the tracing point follow the line of the diagram in the direction in which
the hands of a watch move, as indicated by the arrows in Figs. 89 and
90. Follow the line as made by the pencil, not necessarily in direction
(for on a right-handed diagram, as in Fig. 89, you will have to trace
in the opposite direction from that of the pencil which made it, in order
to carry the tracing point in the direction of the hands of a watch) , but
88
THE STEAM ENGINE INDICATOR
in course. For instance, in Fig. 79, do not leave the expansion line at
a and run out on the back-pressure line, but follow the diagram naturally
all the way around, as the arrows indicate, and as it was drawn by the
pencil; and in Figs. 89 and 90 do the same, although in tnis case you
will trace the diagram backward from the direction in which the pen-
cil went over it. If the pointer traces in the opposite direction to the
hands of a watch the wheel will take out the area instead of adding it.
In Fig. 79 we saw that the area of the loop was negative, and that it
needed to be subtracted from the other apart of the diagram to get the
mean effective pressure. It will be seen that by following the lines of
the diagram as directed the tracing point of the planimeter will pass
around the negative portions of the diagram in a direction contrary
to the hands of a watch, and that therefore these areas will be automat-
ically subtracted. In this connection, be careful when starting to trace
a diagram with loops, to move the tracing point in a direction that will
FIG. 89.
FIG. 90.
carry it with the hands of a watch over the main portion of the diagram,
If Fig. 90, for instance, were started at the point a or anywhere within
one of the loops the first movement of the tracing point would have tc
be in the opposite direction from that of the hands of a watch.
Having traced around the diagram and brought the pointer around
and into the hole from which it started, take the reading in the ne\v
position, subtract from the reading in the starting position, and the
difference will be the area of the figure traced. If the roller were
placed at zero to start with, the reading would give the area at once
but it is easier to take the instrument as it stands and subtract the
initial reading. Suppose we start with the wheel at 1.42, and aftei
tracing the diagram find the reading to be 4.69, then the area will be
4.691.42=3.27 square inches. Now to prove the work, trace the
diagram again, write the result above the former reading, again take
THE PLANIMETER
89
the difference, and if the work has been accurate the last reading
should be 7.96. If we run around still again the reading would be 1.23.
This value would really be 11. 23, as we started from 7.96 and added
3.27 inches, but as the capacity of the wheel is limited to 10 inches, we
have to understand the addition in the tens column and simply borrow
one when we subtract the 7.96. The readings are as follows:
11.23
7.96=3.27
4.69=3.27
1.42=3.27
The three readings agreeing, we may feel certain that our work has
been correctly done and that the area of the diagram is 3.27 square inches.
By dividing this area by the extreme length the average height is found.
To measure the length of the diagram, draw lines as ab } cd, Fig. 91,
perpendicular to the atmospheric line and touching the extreme end
of the diagram. No matter what the shape of the diagram may be,
no portion of its line must extend outside of these perpendiculars, which
FIG. 91
must, however, touch the diagram at both ends. When two diagrams
are taken on one card, however, remember that you want the length
of each diagram, not the extreme length between both, as shown in Fig.
91. Now measure the horizontal distance between these vertical lines.
This is very handily done with the 50 scale of the 6-inch triangular
scale, each 50th being equivalent to 0.02, so that the length may be ex-
pressed directly in decimals.
Divide the area as found by the planimeter by the length, and multiply
the quotient by the scale of the spring ivith which the diagram was taken.
The product will be the mean effective pressure.
In a planimeter the length of the tracing arm multiplied by the
movement of the wheel equals the area traced. If in Fig. 92 the length
of the tracing arm (the distance between the tracing point and the hinge)
90
THE STEAM ENGINE INDICATOR
is 4 inches, the circumference of the roller must be 2.5 inches in order
that one revolution may equal 10 square inches. Inversely the wheel
movement equals the area divided by the length of the tracing arm.
If with the wheel having a circumference of 2.5 inches we used a tracing
arm 5 inches long instead of 4 inches, in tracing an area of 10 square
inches the wheel would not turn a full revolution. Its circumferential
movement would have to be only 2 inches in order that that movement
multiplied by the length of the arm might still be equal to the area, 10.
The movement of the wheel, and thus the reading, is inversely propor-
tional to the length of the arm. If the length of the arm is doubled the
reading will be halved. If the arm is one-third as long the reading will
be three times as large, etc. It has been explained that to get the mean
effective pressure the area must be
divided by the length of the dia-
gram. If the diagram were twice
as long, with a given area the mean
effective pressure would be half as
much. In other words the mean
effective pressure varies inversely
as the length of the diagram. Since
the reading varies inversely as the
length of the arm, and the mean
effective pressure varies inversely
FIG. 92.
as the length of the diagram, we can, by making the length of the arm
equal to the length of the diagram, make the reading proportional to
the mean effective pressure. Suppose an instrument with an arm of
4 inches and a wheel having a circumference of 2.5 inches. One revo-
lution of the wheel will mean 10 square inches. Suppose it is applied
to a diagram 3 inches long and registers 3.75 square inches area. If the
diagram was taken with a 40 spring the mean effective pressure would be
Area X scale 3.75X40
Length
3
50lbs.
THE PLANIMETER
91
Suppose now we adjust the length of the arm so that it equals the
length of the diagram, 3 inches, the reading will then be J of what
4X3 75
it was before or - =5.00 and by shifting the decimal point we have
o
at once 50 pounds. Changing the length of the arm performed me-
FIG. 93.
chanically the division before required. For a 40 scale, therefore, this
instrument will give us at once on the wheel the mean effective pressure
and for other scales the pressure can be taken proportionally; one-half
for a 20 scale, three-fourths for a 30, five-fourths for a 50, etc. An Ams-
FIG. 94.
ler planimeter with an adjustable tracing arm is shown in Fig. 92. The
length of the diagram is taken between the two points M and N, which
are always the same distance apart as the tracing point A and the joint
C upon which it hinges.
In another type of planimeter the reading is indicated by the
sidewise movement of the wheel read against a contiguous scale as in
92 THE STEAM ENGINE INDICATOR
Fig. 93, or upon the shaft upon which it slides as in Fig. 94. As these
scales are changeable and the arms adjustable, the mean effective pres-
sure can be read direct for any scale or length of diagram. The
instrument shown in Fig. 92 can be set to read directly in horse-power
by making the length of the arm equal to
Length of diagram X 40 X 33000
Scale X revs, per min. X area X stroke'
in whfch the stroke should be taken in feet. Instruments like those
shown in Figs. 93 and 94, in which a scale corresponding to that of the
diagram can be used to measure the wheel movement, can be set to read
directly in horse-po'wer by making the length of the tracing arm equal to
Length of diagram X 33000
Revs, per min. X area X stroke*
If this gives an impracticable length of arm the required length can be
multiplied or divided by a number which, will make it practicable and
FIG. 95.
the reading multiplied or divided by the same number. If, for instance,
the formula called for an arm of 1.5 inches it would be better to have the
arm 3 inches and multiply the reading by 2.
A home-made planimeter with which it is possible to do quite accurate
work may be made by bending a piece of wire as in Fig. 95, flattening
and sharpening into a knife edge the end at B and pointing the end
at A. The distance AB should be 10 inches.
Locate roughly, by judgment, the geometrical center of the figure,
its center of gravity, so to speak; the point upon which it would balance
if cut out of cardboard as in Fig. 96. In -the indicator diagram, Fig.
97, this point would be at about A. Draw the line AB } connecting the
center with any point upon the circumference, set the planiraeter arm
roughly at right angles with A B, and press the knife edge lightly into
the paper to mark the point of starting as at X. Carry the tracing
point out over AB and around the diagram in the direction that a clock
runs as indicated by the solid arrows and back over A B, making another
depression as at Z to mark the position of the knife edge when the trac-
ing point is again at the center A. Then being careful to move neither
UNIVERSITY
OF
THE PLANIMETER
93
the tracing point nor the knife edge, revolve the diagram 180, using
the tracing point as a center, bringing it into the dotted position of Fig.
97. Having secured the diagram in this position trace it again in the
opposite direction from that followed by the hands of a watch as shown
by the dotted arrows, and make still another depression to mark the
position of the knife edge when the tracing point returns to the center.
This will probably be somewhere near .Y, as at F. We have now three
marks: X, that at which the knife edge started; Z, that to which it de-
parted; and F, that to which it returned when the diagram was retraced.
FIG. 96.
For plainness I have reproduced them at the left. Make a mark as
" ab" half way between XY, then the distance between this mark and
Z, i.e., the length of the dotted line, multiplied by the length of the
planimeter arm AB, Fig. 95, will be the area in square inches approxi-
mately, and the approximation will be very close when the arm is of
considerable length compared with the area to be measured. By making
the planimeter arm 10 inches in length the multiplication may be done
by shifting the decimal point, or as each inch of length will indicate 10
square inches the area may be measured directly by taking the distance
ZX with a scale of 10 to the inch, each tenth representing 10 square
94
THE STEAM ENGINE INDICATOR
inches, or a scale of 100 to the inch, each unit of which would repre-
sent one-tenth of a square inch.
The function of the other arm of the planimeter, one end of which
is stationary, is simply to guide the hinged end in a definite path. This
end, otherwise hinged, may be guided by a straight groove as in Fig. 99.
In Fig. 98, start with the tracing point at A and the wheel at zero
and trace the rectangle A BCD. The wheel motion gained in moving
from A to B is neutralized by the movement from C to D. The line
BC is in the neutral axis, so the wheel gets no movement while the tracer
passes over it. When the point arrives at D, therefore, the wheel will
have returned to zero, and the full area of the rectangle will be recorded
while the tracing point passes down the line DA. For a rectangle, there-
FIG. 1)8.
FIG. 99.
fore, with its left-hand edge in the neutral line of the instrument, all
that is necessary to find the area is to start at the upper right-hand
corner with the wheel at zero and carry the tracing point down the right-
hand edge, as DA in Fig. 98. Conversely, if we have a given area re-
corded on the wheel, we can find the height of a rectangle of equal area
for a given length by running the tracing point up the line marking
its right-hand edge (the left being in the neutral line), until the wheel
returns to zero. Suppose, for instance, we start at A, Fig. 98, with
the planimeter wheel at zero and trace the outline of the indicator diagram.
When the tracing point gets around to A again the area of the diagram
will be recorded on the wheel. Now, suppose we run the tracing point
up the line AD until the wheel comes back to zero, the line AD will be
the average height of the indicator diagram, that is the height of a rectangle
THE PLANIMETER 95
of equal area, and by measuring the length of AD with the scale correspond-
ing to the spring with which the diagram was taken, we find the mean
effective pressure of the diagram at once without calculation.
This principle is made use of in the Coffin averaging instrument,
a form of planimeter especially adapted to measuring the mean effective
pressure represented by indicator diagrams and shown in Fig. 99. The
indicator card is placed under the clips A and C, with the atmospheric
line parallel with the horizontal leg of the stationary clip C, and the
left-hand edge of the diagram against the inside vertical edge of that
clip. The inside edge of the movable clip A is then placed against the
right-hand extremity of the diagram, so that the length of the diagram
is just included between the two clips. The tracing point of the plan-
imeter is then placed upon any portion of the diagram which is against
the right-hand clip, the wheel set to zero and the point gently pressed
into the paper to mark the starting point. The tracing point is then
carried around the diagram in the direction of the hands of a watch,
and when it returns to the point from which it started the area of the
diagram will be recorded upon the wheel. No attention need be paid
to this reading. Simply carry the point upward against the edge of the
clip A until the wheel returns to zero, at which point press the tracer
again into the paper. The distance between the starting point and the
point thus made will be the average height of the diagram and measured
with the scale of the spring with which the diagram was taken will give
at once the mean effective pressure. It is not necessary even to set the
wheel at zero in starting. You can record the reading, whatever it may
be, after the tracer has been set at the starting point, trace the diagram
and then run the tracing point upward beside the clip until the wheel
returns to the reading with which you started. The whole apparatus
is mounted on a rosewood board with an inset tablet of suitable surface
for the planimeter wheel to run upon. A weight Q is placed upon the end
opposite the tracing point to hold it in the guiding groove.
CHAPTER XIII
COMPUTING THE HORSE POWER
FORCE is that which tends to produce motion or change of motion
in matter. The pressure of steam or of water under a head, the pull
of a weight, the pull or push of a muscle, are all familiar examples of
force.
When force is exerted through space, Work is done. The full steam
pressure may stand upon the engine piston for hours, but no work will
be done unless the piston moves. A suspended weight does no work
except while it is being lowered, and it is only in its ability to be lowered,
i.e., in its elevated position, that its capacity for doing work exists.
The Foot-Pound is the unit of work or energy. It is the equivalent
of 1 pound of force exerted through 1 foot of space. To lift 100
pounds 1 foot would require 100 foot-pounds of energy, as it would
also to lift 1 pound 100 feet. If a horse has to pull 50 pounds to draw
a wagon, and draws it 100 feet, he will develop 5000 foot-pounds.
Notice that this has no reference to the Weight of the wagon, simply to
the force required to drag it.
A Horse-Power is the unit of the rate of development, or of consump-
tion of energy or of work. It is 550 foot-pounds per second, 33,000 foot-
pounds per minute, or 1,980,000 foot-pounds per hour.
The indicator gives us a means of determining the average force
pushing the piston (the mean effective pressure per square inch multi-
plied by the number of square inches in the piston), and this multiplied
by the number of feet through which the piston moves in a minute and
divided by 33,000 will give the horse-power which the engine is developing.
The simplest formula for horse-power is, therefore,
_ Area XM.E.P.X piston speed
33000
The area of the piston is found by multiplying the square of the
diameter of the cylinder by 0.7854. Table I at the end of the volume
renders this calculation unnecessary.
The mean effective pressure (M.E.P.) is found by measurement
from the diagram, as explained in the previous chapter.
96
COMPUTING THE HORSE-POWER 97
PISTON SPEED
The piston speed in this sense is the number of feet through which
the pressure acts upon the piston per minute. In a double-acting
engine, (that is, an engine which takes steam at each stroke, or twice
a revolution) this is the revolutions per minute X 2 X the length of the
stroke in feet. If the engine is single-acting, but takes steam every revolu-
tion, the piston speed is the product of the revolutions per minute and
the stroke in feet. Gas engines of the 4-cycle type make a working
stroke once in two revolutions, and their piston speed when this is done
is the stroke in feet times one-half the revolutions per minute; but
when the governing is accomplished by the hit and miss method, their
piston speed can be determined only by counting the explosions, the
piston speed being the stroke in feet multiplied by the number of explo-
sions per minute.
Notice that "piston speed" as used in this formula is not the actual
speed of the piston, which is continually changing from nothing at the
centers to the maximum near the middle of the stroke, nor the number
of feet passed through by the piston per minute, but the number of
feet through which the pressure acts per minute. Notice too that it is
per minute. If it were per second the divisor would have to be 550
instead of 33,000; and if per hour the divisor would be 1,980,000.
The double-acting cylinder being the usual case, and the data
usually given being the stroke in inches and the revolutions per minute,
Table II, has been prepared for these conditions. In a single-acting
steam engine, taking steam only once per revolution, or at every second
stroke, the "piston speed" of the formula on page 96 would be the prod-
uct of the stroke in inches and the revolutions per minute divided by
12, or one-half the value given by the table for a double-acting engine.
For a gas engine this "piston speed" would be the stroke in inches mul-
tiplied by the number of explosions per minute and divided by 12.
USE OF THE TABLE
When the given number of revolutions can be found at the head
of the column the piston speed will be found in the column under it
opposite the stroke in inches.
EXAMPLE. What is the piston speed of an engine having a stroke
of 38 inches when running at 70 revolutions per minute?
Follow the horizontal line opposite 38 to the column under 70 and
find 443.33 feet per minute, the value sought.
If the number of revolutions is even hundreds instead of tens, as
given in the table, the values of the table should be multiplied by 10,
98 THE STEAM ENGINE INDICATOR
which may be done by adding a cipher when the tabular value is a whole
number, or by moving the decimal point one point to the right, if it
contains a fraction.
EXAMPLE. What is the piston speed of an engine having a stroke
of 8 inches when running at 300 revolutions per minute?
Opposite 8 and under 30 find 40, to which add a cipher, giving 400
feet per minute.
Or take the same engine running 400 revolutions. Opposite 8 under
40 find 53.33, which multiplied by 10 by moving the decimal point one
place to the right, gives 533.3, the value sought.
If the number of revolutions given is a unit the tabular value must
be divided by 10 by cutting off a cipher or pointing off one space if it
is a whole number, or by moving the decimal point one place to the left
if there is a fraction. Thus the piston speed of an engine with a stroke
of 138 inches would be, when running at 9 revolutions, 207 feet, found
by dropping the final cipher from the value given for 90 feet. The
piston speed of an engine with a stroke of 136 inches at 8 revolutions
would be 181.333 feet, found by moving the decimal one point to the
left in the tabular value for 80 feet.
When the given number of revolutions contains more than one figure
the values for the units, tens, hundreds, etc., must be found separately
and added together.
EXAMPLE. What is the piston speed of an engine having a stroke
of 72 inches when running at 46 revolutions per minute?
First look up the value for 40, then the value for 6 as directed above.
Their sum will be the value for 46 ; thus :
Value for 40=480
" 6= 72
46=552
EXAMPLE. What is the piston speed of an engine having a stroke
of 68 inches running at 54 revolutions per minute?
Value for 50 =566.667
4= 45.333
612.000 ft. per min.
The only two fractions occurring in the table are J and =33333 +
and 66666 + . They can be carried out to any degree of accuracy desired
by adding additional 3's and 6's, making the last 6 a 7. This was done
in the above value for 50.
COMPUTING THE HORSE-POWER 99
EXAMPLE. What is the piston speed of an engine having a stroke
of 62 inches when running at 126 revolutions per minute?
Value for 100-1033.33
20= 206.67
" 6= 62.00
126 = 1302.00 ft. per min.
If the number of revolutions has a fraction, simply reduce it to a
decimal and continue as above, shifting the decimal point in the tabular
value one point to the left for each place the decimal figure is to the right.
EXAMPLE. What is the piston speed of an engine having a stroke
of 72 inches at 63^ revolutions per minute?
63J =63.25.
Value for 60. =720.
3. = 36.
" 2 = 2.4
.05= 0.6
63.25 =759.0 ft. per min.
A simple and easily remembered formula for horse-power is :
PANS
H.P.
33000 '
Where P=mean effective pressure,
A =area of piston in square inches,
N= number of working strokes per minute,
S= length of stroke in feet.
RULE. Multiply together the mean effective pressure, the area of the
piston in square inches, the number of working strokes per minute, and the
length of the stroke in feet and divide by 33,000. The quotient will be the
horse-power.
EXAMPLE. What is the horse-power developed by a 24X48 inch
engine running at 70 revolutions per minute with 42 pounds M.E.P.?
The pressure P= 42 Ibs. given
" area A =452.39 sq.in. 24 2 X.7854
' ' number N = 140 stroke per min. 70 X 2
-"stroke S=4 feet 48 ins. -i- 12
PANS 42X452.39X140X4
33000 ' 33000
100 THE STEAM ENGINE INDICATOR
THE HORSE-POWER CONSTANT
In figuring a number of diagrams from one engine running at a con-
stant speed it is most convenient to compute first the horse-power developed
per pound of mean effective pressure, and multiply this " horse-power
constant" by the mean effective pressure of each diagram to find the
horse-power represented by that diagram. This can be done by con-
sidering the M.E.P. in formula 1 as unity, in which case, as it is a multi-
plier, it may be left out, and we get
Area X piston speed ANS ^ i r TVT -n r>
33QOO r 33ooo=H.P. per pound of M.E.P.,
and this H.P. constant multiplied by M.E.P. =H.P.
To FIND THE HORSE-POWER CONSTANT OR HORSE-POWER PER POUND
OF MEAN EFFECTIVE PRESSURE,
RULE. Multiply the piston area in square inches by the piston speed
in feet per minute and divide by 33,000, or
Multiply together the piston area in square inches, the number of work-
ing strokes per minute, and the stroke in feet, and divide the product by
33,000.
EXAMPLE. What is the horse-power constant of the above engine?
ANS 452.39X140X4
= 7.o7by.
33000 33000
This multiplied by the mean effective pressure will give the horse-
power thus
7.6769X42=322.4298
as before.
Table III gives these constants, i.e., the horse-power per pound of
mean effective pressure, directly when the piston-speed is in even hun-
dreds of a single figure. The values for thousands, tens, units, or frac-
tional quantities can be found by changing the decimal point as explained
in connection with the previous table.
EXAMPLE. What horse-power is being developed by a 4JX 8-inch
engine running at 300 revolutions per minute with 40 pounds mean
effect ve pressure?
From Table II we see that the piston speed is 400 feet per minute.
From Table III we see that an engine 4 J inches in diameter will develop
0.2149 horse-power per pound of mean effective pressure at this piston-
speed. Then,
H.P. =40X0.2149 -8.596.
COMPUTING THE HORSE-POWER
TABLE II
PISTON SPEED IN FEET PER MINUTE
(2 X stroke X revolutions) -T- 12 = (stroke X revolutions) -7-6.
101
Stroke in
Inches
REVOLUTIONS PER MINUTE.
10
20
30
40
50
60
70
80
90
1
1.67
3.33
5
6.67
8.33
10
11.67
13.33
15
2
3.33
6.67
10
13.33
16.67
20
23.33
26.67
30
3
5
10
15
20
25
30
35
40
45
4
6.67
13.33
20
26.67
33.33
40
46.67
53.33
60
5
8.33
16.67
25
33.33
41.67
50
58.33
66.67
75
6
10
20.00
30
40
50
60
70
80
90
7
11.67
23.33
35
46.67
58.33
70
81.67
93.33
105
8
13.33
26.67
40
53.33
66.67
80
93.33
106.67
120
9
15
30
45
60
75
90
105
120
135
10
16.67
33.33
50 .
66.67
83.33
100
116.67
133.33
150
11
18.33
36.67
55
73.33
91.67
110
128.33
146.67
165
12
20
40
60
80
100
120
140
160
180
13
21.67
43.33
65
86.67
108.33
130
151.67
173.33
195
14
23.33
46.67
70
93.33
116.67
140
163.33
186.67
210
15
25
50
75
100
125
150
175
200
225
16
26.67
53.33
80
106.67
133.33
160
186.67
213.33
240
17
28.33
56.67
85
113.33
141.67
170
198.33
226.67
255
18
30
60
90
120
150
180
210
240
270
19
31.67
63.33
95
126.67
158.33
190
221.67
253.33
285
20
33.33
66.67
100
133.33
166.67
200
233.33
266.67
300
22
36.67
73.33
110
146.67
183.33
220
256.67
293.33
330
24
40
80
120
160
200
240
280
320
360
26
43.33
86.67
130
173.33
216.67
260
303.33
346.67
390
28
46.67
93.33
140
186.67
233.33
280
326.67
373.33
420
30
50
100
150
200
250
300
350
400
450
32
53.33
106.67
160
213.33
266.67
320
373.33
426.67
480
34
56.67
113.33
170
226.67
283.33
340
396.67
453.33
510
36
60
120
180
240
300
360
420
480
540
38
63.33
126.67
190
253.33
316.67
380
443.33
506.67
570
40
66.67
133.33
200
266.67
333.33
400
466.67
533.33
600
42
70
140
210
280
350
420
490
560
630
44
73.33
146.67
220
293.33
366.67
440
513.33
586.67
660
46
76.67
153.33
230
306.67
383.33
460
536.67
613.33
690
48
80
160
240
320
400
480
560
640
720
50
83.33
166.67
250
333.33
416.67
500
583.33
666.67
750
52
86.67
173.33
260
346.67
433.33
520
606.67
693.33
780
54
90
180
276
360
450
540
630
720
810
56
93.33
186.67
280
373.33
466.67
560
653.33
746.67
840
58
96.67
193.33
290
386.67
483.33
580
676.67
773.33
870
60
100
200
300
400
500
600
700
800.00
900
102 THE STEAM ENGINE INDICATOR
TABLE II Continued
PISTON SPEED IN FEET PER MINUTE
(2 X stroke X revolutions) -f- 12 = (stroke X revolutions) -f- 6.
REVOLUTIONS PEK MINUTE.
Stroke in
Inches.
10
20
|
30
40
50
^
60
\
70
I
80
90
62
103.33
206.67
310
413.33
516.67
620
723.33
826.67
930
64
106.67
213.33
320
426.67
533.33
640
746.67
853.33
960
66
110
220
330
440
550
660
770
880
990
68 113.33
226.67 |
310
453.33
566.67
680
793.33
906.67
1020
70 116.67
233.33
350
466.67
583.37
700
816.67
933.33
1050
72
120
240
360
480
600
720
840
960
1080
74
123.33
246.67
370
493.33
616.67
740
863.33
986.67
1110
76
126.67
253.33
380
506.67
633.33
760
886.67
1013.33
1140
78
130
260
390
520
650
780
910
1040
1170
80
133.33
266.67
400
533.33
666.67
800
933.33
1066.67
1200
82
136.67
273.33
410
546.67
683.33
820
956.67
1093.33
1230
84
140
280
420
560
700
840
980
1120
1260
86
143.33
286.67
430
573.33
716.67
860
1003.33
1146.67
1290
88
146.67
293.33
440
586.67
733.33
880
1026.67
1173.33
1320
90
150
300
450
600
750
900
1050
1200
1350
92
153.33
306.67
460
613.33
766.67
920
1073.33
1226.67
1380
94
156.67
313.33
470
626.67
783.33
940
1096.67
1253.33
1410
96
160
320
480
640
800
960
1120
1280
1440
98
163.33
326.67
490
653.33
816.67
980
1143.33
1306.67
1470
100
166.67
333.33
500
666.67
833.33
1000
1166.67
1333.33
1500
102
170
340
510
680
850
1020
1190
1360
1530
104
173.33
346.67
520
693.33
866.67
1040
1213.33
1386.67
1560
106
176.67
353.33
530
706.67
883.33
1060
1236.67
1413.33
1590
108
180
360
540
720
900
1080
1260
1440
1620
110
183.33
366.67
550
733.33
916.67
1100
1283.33
1466.67
1650
112
186.67
373.33
560
746.67
933.33
1120
1306.67
1493.33
1680
114
190
380
570
760
950
1140
1330
1520
1710
116
193.33
386.67
580
773.33
966.67
1160
1353.33
1546.67
1740
118
196.67
393.33
590
786.67
983.33
1180
1376.67
1573.33
1770
120
200
400
600
800
1000
1200
1400
1600
1800
122
203.33
406.67
610
813.33
1016.67
1220
1423.33
1626.67
1830
124
206.67
413.33
620
826.67
1033.33
1240
1446.67
1653.33
1860
126
210
420
630
840
1050
1260
1470
1680
1890
128
213.33
426.67
640
853.33
1066.67
12SO
1493.33
1706.67
1920
130
216.67
433.33
650
866.67
1083.33
1300
1516.67
1733.33
1950
132
220
440
660
880
1100
1320
1540
1760
1980
134
233.33
446.67
670
893.33
1116.67
1340
1563.33
1786.67
2010
136
226.67
453.33
680
906.67
1133.33
1360
1586.67
1813.33
2040
138
230
460
690
920
1150
1380
1610
1840
2070
140
233.33
466.67
700
933.33
1166.67
1400
1633.33
1866.67
2100
COMPUTING THE HORSE-POWER 103
What horse-power would be developed by an engine 24 inches in
diameter running at 523 feet of piston-speed per minute at 34 pounds
M.E.P.?
Use Table III for the tens and units, just as before. In the line
opposite 24 find the
value of 500=6.8544
20=0.27417
3=0.041126
" 523=7.169696
horse-power per pound of mean effective pressure. Then
H.P. =7.1697X34 =243.77.
When the piston-speed contains a fraction, its value can be found
by shifting the decimal point, as in the previous table, to the left.
EXAMPLE. What horse-power would be devolped by a 30-inch
engine running at 617.23 feet of piston-speed with a mean effective pres-
sure of 47.5 pounds?
Opposite 30 find the
value of 600 =12.852
" of 10 .2142
"of 7 .14994
"of 2 - .004284
" of .03= .0006426
617.23 = 13.2210666
horse-power per pound of mean effective pressure. Then
H.P. =47.5 = X 13.22 =627.95.
In the above examples the mean effective pressure given is assumed
to be the average of both ends, and the horse-power as calculated is
that of the whole engine. If it is desired to know the horse-power of
each end, they must be calculated separately, each with its own mean
effective pressure, and the constant taken at one-half the piston speed,
or with the constant taken at the full piston-speed and one-half the mean
effective pressure.
EXAMPLE. An engine 48X84 inches, running at 36.5 revolutions
per minute, has a mean effective pressure in the head end of 42.7 pounds,
and in the crank end of 41.3 pounds, what is the horse-pow r er of each
end, and of the whole engine?
104 THE STEAM ENGINE INDICATOR
The "horse-power constant/' or the horse-power per pound of mean
effective pressure for each end, will be one-half that given by the table
for both ends, or that given by the table for an engine of the given diam-
eter at one-half the piston-speed. From the piston-speed table we
find that the piston-speed at 36.5 revolutions of the double-acting engine
is 511 feet per minute. The piston speed of each would be one-half
of this, or
511-^2=255.5 ft. per min.
From the Table III we find that the horse-power per pound of mean
effective pressure for a 48-inch engine at this speed is
value for 200 -10.9673
50 = 2.74182
5 .274182
0.5- .0274182
255.5 = 14.0107202
H.P. Head end =14.01X42.7-598.227
H.P. Crank end -14.01 X41.3 -578.613
H.P. Both ends- 1176.84
ALLOWING FOR THE ROD
When a portion of the area of the piston is cut off by a rod, as is usually
the case in the crank end, and as occurs in the head end of a cylinder
tandem to one behind it, or with a tail rod, it is essential to accuracy
that an allowance be made for such loss of area. In the usual case', that
of a cylinder having a rod only in the crank end, the allowance may
be made by subtracting from the horse-power computed as in the first
example, the horse-power which would be developed by a single-acting
engine having a diameter equal to that of the piston rod, and with the
mean effective pressure acting in the crank end.
EXAMPLE. What horse-power would be developed by a 24-inch
engine with a 4J piston-rod running at 620 feet piston speed with 46.5
pounds mean effective pressure in the head end and 47.2 in the crank
end?
From the table the constant for this engine would be
value for 600=8.2253
20= .27417
' ' 620 = 8.49947 horse-power
per pound of average mean effective pressure.
COMPUTING THE HORSE-POWER 105
The average mean effective pressure would be
46.54-47.2
=46.85 pounds.
The horse-power uncorrected for the rod would therefore be
8.49947X46.85=398.2001695 H.P.
The horse-power lost by the presence of the rod is that which would
be developed by an engine 4f inches diameter at 310 feet of piston speed
and at 47.2 pounds mean effective pressure.
From the table we find the constant for such an engine to be
for 300 feet 0.1367
"10 " 0.00456
" 310 " 0.14126
horse-power per pound of mean effective pressure.
The mean effective pressure which would have acted upon this area
is 47.2 pounds.
The horse-power to be deducted, therefore, is
0.14126X47.2=6.667472 H.P.
Deducting this from the uncorrected horse-power we have
398.2001695
6.667472
391.5326975
as the horse-power corrected for the rod.
A more convenient way when a large number of diagrams are to be
figured up from the same engine, as in making out daily reports or com-
puting the results of a long test, is to correct the constant for the engine
by subtracting from it the constant of the rod at half the piston speed
and multiplying this corrected constant by the average mean effective
pressure. Performing the above example in this way,
constant for cylinder 8.49947
"rod .14126
corrected constant 8.35821
106 THE STEAM ENGINE INDICATOR
which multiplied by the average M.E.P. gives
835821X46.85=391.5821385 H.P.
by other method 391.5326975 H.P.
difference .049441
If the mean effective pressure were the same in both ends this method
would be perfectly accurate. The inaccuracy which it involves, and
which is the cause of the above difference, is due to multiplying the rod
constant by the average M.E.P., instead of that in the crank end.
M.E.P. in crank end 47.2
average M.E.P. 46.85
difference 0.35
0.14125X0.35=0.049441
The error thus is seen to be the product of the rod constant and the
difference between the average and the actual M.E.P. in the crank end
neither of which factors are large enough in the ordinary case to make
the error of any considerable magnitude.
THROUGH RODS AND TAIL RODS
When the rod is in both ends of the cylinder, as in the cylinder nearesl
the guides in a tandem compound, or in a cylinder with a tail rod, anc
the rod is the same diameter in both ends, it is necessary only to sub-
tract the constant for an engine of a diameter equal to that of the rod
at the full piston speed from the constant for the diameter of the cylinder
and multiply by the average mean effective pressure.
When there is a rod in each end, but of different size, each rod should
be allowed for separately by multiplying its constant at half piston speed
by the mean effective pressure acting in its own end of the cylinder,
and subtracting the products successively from the horse-power found by
multiplying the cylinder constant at full speed by the average mean
effective pressure.
In strictness, in order to find the power which is being developed
by one end of the cylinder, a diagram made of the line showing the for-
ward pressure in the end which is being computed, and the back pres-
sure- or counter-pressure line of the diagram from the other end should
be used. The counter-pressure line diagram from the head end does
not show the back pressure against the piston when the head end was
doing work, but while the piston is being forced backward by the steam
COMPUTING THE HORSE-POWER
107
TABLE III
HORSE-POWER PER POUND OF MEAN EFFECTIVE PRESSURE
(Area X piston speed) -f- 33 . 000.
Diameter
of
Cylinder
or Rod.
Inches.
PISTON SPEED IN FEET PER MINUTE.
100
200
300
400
500 600
700
800
900
2
.00134
.0027
.0043
.0054
.0067 ! .0030
.0094
.0107
.0120
H
.00157 .0031
.0047
.0063
.0079 i .0091
.0110
.0126
.0141
i
.00182 .0036
.0055
.0073
.0091 .0109
.0128
.0146
.0164
.00209' .0042
.0063
.0084
.0105
.0126
.0146
.0167
.0188
i
.00238
.0048
.0071
.0095
.0119
.0143
.0167
.0190
.0214
i*
.00269
,0054
.0081
.0107
.0134
.0161
.0188
.0215
.0242
1A
.00288
.0058
.0086
.0115
.0144
.0173
.0202
.0230
.0259
H
.00301
.0060
.0090
.0120
.0151
.0181
.0211
.0241
.0271
i*
.00336
.0067
.0101
.0134
.0168
.0201
.0235
.0268
.0302
11
.00343
.0069
. 0103
.0137
.0172
.0206
.0240
.0274
.0309
a
.00372
.0074
.0112
.0149
.0186
.0223
.0260
.0298
.0335
Ift
.00402
.0080
.0121
.0161
.0201
.0241
.0281
.0322
.0362
iA
.00410
.0082
.0123
.0164
.0205
.0246
.0287
.0328
.0369
If
.00450
.0090
.0135
.0180
.0225
.0270
.0315
.0360
.0405
U
.00466
.0093
.0140
.0186
.0233
.0280
.0326
.0373
.0419
1&
.00492
.0098
.0148
.0197
.0246
.0295
.0344
.0393
.0443
H
.00535
.0107
.0161
.0214
.0268
.0321
.0375
.0428
.0482
1*
.00581
.0116
.0174
.0232
.0291
.0349
.0407
.0465
.0523
if
.00609
.0122
.0183
.0244
.0305
.0365
.0426
.0487
.0548
if
.00628
.0126
.0189
.0251
.0314
.0377
.0440
.0503
.0566
ift
.00678
.0136
.0203
.0271
.0339
.0407
.0474
.0542
.0610
1A
.00688
.0138
.0206
.0275
.0344
.0413
.0482
.0550
.0619
If
.00729
.0146
.0219
.0292
.0364
.0437
.0510
.0583
.0656
U
.00771
.0154
.0231
.0308
.0386
.0463
.0540
.0617
.0694
iff
.00782
.0156
.0235
.0313
.0391
.0469
.0548
.0626
.0704
11
.00837
.0167
.0251
.0335
.0418
.0502
.0586
.0669
.0753
A
.00859
.0172
.0258
.0344
.0430
.0515
.0601
.0687
.0773
m
.00893
.0179
.0268
.0357
.0447
.0536
.0625
.0715
.0804
2
.00952
.0190
.0286
.0381
-0476
.0571
.0666
.0762
.0857
2tV
.01012
.0202
.0304
.0405
.0506
.0607
.0709
.0810
.0911
2A
.01050
.0210
.0315
.0420
.0525
.0630
.0735
.0840
.0945
2i
.01074
.0215
.0322
.0430
.0537
.0645
.0752
.0860
.0967
2&
.01139
.0228
.0342
.0456 ! .0569
.0683
.0797
.0911 .1025
2i
.91152
.0230
.0346
.0461 ; .0576
.0691
.0806
.0921 .1036
2*
.01205
.0241
.0361
.0482
.0602
.0723
.0843
.0964
.1084
2&
.01259
.0252
.0378
.0504
.0630
.0755
.0881
.1007
.1133
2A
.01273
.0255
.0382
.0509
.0636
.0764
.0891
.1018
.1145
2 f
.01342
.0268
.0403
.0537
.0671
.0805
.0940
.1074
.1208
2!
.01371
.0274
.0411
.0548
.0686
.0823
.0960
.1097
.1234
2^
.01414
.0283
.0424
.0566
.0707
.0848
.0990
.1131
.1273
2*
.01487
.0297
.0446
. 0595
.0744
.0892
.1041
.1190 1 .1339
2&
.01563
.0313
.0469
.0625
.0781
.0938
.1094
. 1250 . 1407
2|
.01609 .0322
.0483
.0644
.0805
.0965
.1126
. 1287 . 1448
2|
.01640 .0328
.0492
.0656
.0820
.0984
.1148
.1312
.1476
2H
.01719 .0344
.0516
.0688
.0860
. 1031
.1203
.1375
.1547
2^
.01735 .0347
.0521
.0694
.0868
.1041
.1215
.1388
. 1562
2!
.01800
.0360
.0540
.0720
.0900
.1080
.1260
.1440
.1620
2*
.01866
.0373
.0560
.0746
.0933
.1120
.1306
. 1493
.1679
2H
.01883
.0377
.0565
.0753
.0941
.1130
.1318
.1506
.1694
2*
.01967
.0394
.0590
.0787
.0984
.1180
.1377
.1574
.1770
2A
.02002
.0400
.0601
.0801
.1001
.1201
.1401
.1602
.1802
2M
.02054! .0411
.0616 .0821
.1027
.1232
.1438
.1643
.1848
108
THE STEAM ENGINE INDICATOR
TABLE III Continued
HORSE-POWER PER POUND OF MEAN EFFECTIVE PRESSURE
(Area X piston speed) -f- 33.000.
Diameter
of
Cylinder
or Rod,
Inches.
PISTON SPEED IN FEET PER MINUTE.
100
200
300
400
500
600
700
800
900
3
.02142
.0428
.0643
.0857
.1071
.1285
.1499
.1714
.1928
fcV
.02287
.0457
.0686
.0915
.1144
. 1372
.1601
.1830
.2058
3 F
.02324
.0465
.0697
.0930
.1162
.1395
.1627
.1859
.2092
3|
.02437
.0487
.0731
.0975
.1219
.1462
.1706
.1950
.2193
31-
.02514
.0503
.0754
.1006
.1257
.1508
.1760
.2011
.2262
ST%
. 02592
.0518
.0778
.1037
. 1296
. 1555
. 1814
.2074
.2333
3f
.02711
.0542
.0813
.1084
.1355
. 1627
. 1898
.2169
,2440
3f
.02751
.0550
.0825
.1100
.1376
.1651
.1926
.2201
.2476
3*
.02915
.0583
.0875
.1166
.1458
. 1749
.2041
.2332
.2624
31
.03085
.0617
. 0926
.1234
.1543
.1851
.2160
.2468
.2777
3|
.03128
.0626
.0938
.1251
.1564
.1877
.2189
.2502
.2815
37
To
.03258
.0652
.0977
.1303
.1629
. 1950
.2281
.2606
.2932
3|
.03347
.0669
.1004
. 1339
.1673
. 2008
.2343
.2678
.3012
si
.03437
.0687
.1031
.1375
.1719
. 2062
.2406
.2750
.3093
31
.03574
.0715
.1072
.1429
.1787
.2144
.2502
.2859
.3216
3&
.03620
.0724
.1086
.1448
.1810
.2172
.2534
.2896
. 3258
4
.03808
.0762
.1142
.1523
.1904
.2285
.2666
.3046
.3427
4^
.04001
.0800
. 1200
.1600
.2001
.2401
. 2801
.3201
.3601
4
. 04050
.0810
.1215
.1620
.2025
.2430
.2835
.3240
.3645
4i
.04198
.0840
.1259
.1679
.2099
.2519
.2939
.3358
.3778
4}
.04300
.0860
.1290
.1720
.2149
. 2579
.3009
.3439
.3869
4
.04401
.0880
.1320
.1760
.2201
.2641
.3081
.3521
.3961
41
.04555
.0911
.1367
.1822
.2278
.2733
.3189
.3644
.4100
4|
.04608
.0922
.1382
.1843
.2304
. 2765
.3226
.3C86
.4147
- 4*
.04819
.0964
.1446
.1928
.2410
.2892
.3374
. 3856
.4337
4|
.05036
.1007
.1511
.2014
.2518
.3022
.3525
.4029
.4532
4|
.05091
.1018
.1527
.2036
.2545
.3055
.3564
.4073
.4582
4A
.05257
.1051
.1577
.2103
.2629
.3154
. 3680
.4206
.4731
4|
.05370
.1074
.1612
.2149
.2686
.3223
.3760
.4298
.4835
4|
.05484
.1097
.1645
.2194
.2742
.3290
.3839
.4387
.4936
4|
.05656
.1131
. 1697
.2262
.2828
.3394
.3950
.4525
.5090
4^
.05714
.1143
.1714
.2286
.2857
.3428
.4000
.4571
.5143
5
.05950
.1190
.1785
.2380
.2975
.3570
.4165
.4760
.5355
5f
.06251
.1250
.1875
.2500
.3126
.3751
.4376
.5001
.5626
51
.06560
.1312
.1968
.2624
.3280
.3936
.4592
.5248
.5904
4
.06876
.1375
.2063
. 2750
.3438
.4126
.4813
.5501
.6188
5^
.07200
.1440
.2160
.2880
.3600
.4320
. 5040
.5760
.6479
5|
.07530
.1506
.2259
.3012
.3765
.4518
.5271
.6024
.6777
51
.07869
.1574
.2361
.3148
.3934
.4721
. 5508
.6295
.7082
5i
.08215
.1643
.2465
.3286
.4108
.4929
.5751
.6572
.7394
6
.08569
.1714
. 2570
.3427
.4284
.5141
. 5998
.6854
.7711
61
.09297
.1859
.2789
.3719
.4648
.5578
.6508
.7438
.8367
6
. 10055
.2011
.3017
.4022
.5028
.6033
.7039
.8044
.9050
61
. 10844
.2169
.3253
.4338
.5422
.6506
.7591
.8675
.9760
.11662
.2332
.3499
.4665
.5831
. 6997
.8163
.9330
.0496
71
.12510
.2502
.3753
.5004
.6255
.7506
.8757
.0008
. 1259
. 13388
.2678
.4016
.5355
.6694
.8033
.9371
.0710
.2049
7f
. 14295
.2859
.4288
.5718
.7147
.8577
1 . 0006
.1436
.2865
8
. 15232
.3046
.4570
.6093
.7616
.9139 1.0662
.2185
.3709
8i
.16199
.3240.
.4860
.6480
.8099
.9719 1.1339
.2959
.4579
8^
.17195
.3439
.5159
.6878
.8598
1.0317 1.2037
.3756
.5476
81
. 18222
.3644
. 5467
.7289
.9111
1.0933 1.2755
.4577
1 . 6400
COMPUTING THE HORSE-POWER
109
TABLE III Continued
HORSE-POWER PER POUND OF MEAN EFFECTIVE PRESSURE
(AreaXj>iston speed) -h 33,000.
Diameter
of
Cylinder,
or Rod.
Inches.
PISTON SPEED IN FEET PER MINUTE.
100
200
300
400
500
600
700
i
800 900
9
. 19278
.3856
.5783
.7711
.9639
1.1567 1.3495
1.5422
1.7350
9}
.20364
.4073
.6109
.8146
1.0182
1.2218
1.4255
1.6201
1.8328
9*
.21479
.4296
.6444
.8592 1.0740
1.2888
1 . 5036
1.7184
1.9331
9|
.22625
.4525
.6788
.9050
.1313
1.3575
1 . 5837
1.8100
2 . 0362
10
.23800
.4760
.7140
.9520
.1900
1.4280: 1.6660
1.9040
2.1420
1<H
.25005
.5001) .7502
.0002
.2503
1.5003 1.7504
2.0004
2.2505
10*
.26239
.5248
.7872
.0496
.3120
1 . 5744 1 . 8368
2.0992
2.3615
lOf
.27504
.5501
.8251
. 1002
.3752
1.6502 1.9253
2.2003
2.4754
11
.28798
.5759
.8639
.1519
.4399
1 . 7279
2.0159
2 . 3038
2.5918
Hi
.30122
.6024
.9037
.2049
.5061
1.8073
2.1085
2.4098
2.7110
Hi
.31476
.6295
.9443
.2590
.5738
1.8885
2.2033
2.5181
2.8328
11|
.32858
.6572
.9857
.3143
.6429
1.9715
2.3001
2.6286
2.9572
12
.34273
.6855
1.0282
.3709
.7136
2.0564
2.3991
2.7418
3.0845
12
.37188
.7438
.1156
.4875
1.8594
2.2313
2.6032
2.9750
3.3469
13
.40221
.8044
.2066
.6088
2.0111
2.4133
2.8155
3.2177
3.6199
13*
.43376
.8675
.3013
. 7350
2.1688
2.6026
3.0363
3.4701
3.9038
14
.46648
.9330
.3995
1.8659
2 . 3324
2.7989
3.2654
3.7319
4 . 1984
14*
. 50039
.0008
.5012
2.0016
2.5020
3.0023
3.5027
4.0031
4 . 5035
15"
.53548
.0710
. 6065
2.1419
2.6774
3.2129
3.7484
4.2839
4.8194
16
.60927
.2185
.8278
2.4371
3.0464
3.6556
4.2649
4.8742
5.4835
17
.68782
.3756
2.0635
2.7513
3.4391
4 . 1269
4.8147
5.5025
6.1904
18
.77112
.5422
2.3134
3.0845
3.8556
4.6267
5.3978
6 . 1690
6.9401
19
.85918
.7184
2.5775
3.4367
4.2959
5.1551
6.0143
6.8735
7.7326
20
.95200
.9040
2.8560
3.8080
4.7600
5.7120
6.6640
7.6160
8.5680
21
1.04957
2.0991
3.1487
4 . 1983
5.2479
6.2975
7.3470
8.3966
9.4462
22
.15191
2.3038
3 . 4557
4.6076
5.7595
6.9115
8.0634
9.2153
10.3672
23
.25903
2.5181
3.7771
5.0361
6.2952
7.5542
8.8132
10.0722
11.3313
24
.37087
2.7417^ 4.1126
5.4835
6.8544
8.2253
9 . 5962
10.9670
12.3379
25
.48748
2.9750J 4.4625
5.9499
7.4374
8.9249
10.4124
11.8999
13 . 3874
26
.60887
3.2177
4.8266
6.4355
8.0444
9.6533
11.2622
12.8710 14.4799
27
.73503
3.4701
5.2051
6.9401
8.6752
10.4102
12.1452
13.8802 15.6153
28
.86591
3.7318
5.5977
7.4636
9.3295
11.195513.0614
14.9273
16.7932
29
2.00157
4.0031
6.0047
8.006310.0079
12.009514.0110
16.0126 18.0142
30
2.15988
4.3198
6.4796
8.6395110.7994
12.9593
15.1192
17.2790 19.4389
31
2.28718
4.5744
6.8615
9.1487 11.4359
13.7231
16.0103
18.2975
20.5846
32
2.43712
4.8742
7.3114
9.748512.1856
14.6227
17.0598
19.4970
21.9341
33
2.59182
5.1836
7.7755
10.367312.9591
15.5509 18.1427
20.7345
23.3264
34
2.75127
5.5025 8.2538
11.0051 13.7564
16.5076 19.2589
22.0102
24.7615
35
2.91548
5.8310
8.7465111.661914.5774
17.492920.4084
23.3239
26.2394
36
3.08455
6.1691
9. 2535i 12. 3379 15. 4224
18.506921.5914
24.6759
27.7604
37
3.25818
6.5164
, 9.774613.032816.2911
19.549322.8075
26 . 0657
29.3239
38
3.43667
6.8733
10.3101 13. 7468J 17. 1835
20.6202124.0569
27.4936
30.9303
39
3.62000
7.2400
10.860014.480018.1000
21.720025.340028.960032.5800
40
3.80788
7.6158
11.423615.231519.0394
22.8473
26.6552
30.463034.2709
41
4.00091
8.0018
12.0027 16.0036:20.0046
24.0055
28.006432.0073
36.0082
42
4.19818
8.3964
12. 5945! 16. 7927;20. 9909
25.1991
29.387333.5854
37.7836
43
4.40061
8.8012
13.201817.602422.0030
26.4036
30.804235.2048
39.6055
44
4.60758
9.2152
13.8227 ! 18.430323.0379
27.6455
32.253136.8606
41.4682
45
4.81939 9.6388
14. 4582; 19. 2776 24. 0970
28.9163
33.735738.5551
43.3745
46
5.0360610.0721
1 15. 1082 21. 1442 25. 1803
30.2164
35.2524140.2885 45.3245
47
5.25727
10.5145
15. 7718 21. 0291 : 26. 2863 31. 5436
36.800842.0582
47.3154
48
5.48364
10.9673
16.450921.934627.4182132.9018
38.3815
43.8691
49.3528
110 THE STEAM ENGINE INDICATOR
TABLE III Continued
HORSE-POWER PER POUND OF MEAN EFFECTIVE PRESSURE
(AreaX piston speeds 33, 000.)
M I 72
-,3
C O
.Stf
8
PISTON SPEED IN FEET PER MINUTE.
100
200
300
400
500
600
700
800
900
49
5.71424
11.4285
17.1427
22.8570
28.5712
34 . 2854
39.9997
45.7139
51.4282
50
5.95000
11.9000
17.8500
23.8000
29.7500
35.7000
41.6500
47.6000
53 . 550C
51
6.19030
12.3806
18.5709
24.7612
30.9515
37.1418
43.3321
49 . 5224
55.7127
52
6.43545
12 . 8709
19.3604
25.7418
32 . 1773
38.6127
45 . 0482
51.4836
57.9191
53
6 . 68535
13.3707
20.0561
26.7414
33.4268
40.1121
46 . 7975
53.4828
60.1682
54
6.94000
13.8800
20.8200
27.7600
34 . 7000
41.6400
48 . 5800
55 . 5200
62.460C
55
7 . 19939
14.3988
21.5982
28.7976
35.9970
43 . 1963
50.3957
57.5951
64.7945
56
7.46364
14.9273
22.3910
29.8547
37.3183
44.7820
52.2457
59.7093
67.173C
57
7.73273
15.4655
23.1982
30.9309
38.6637
46 . 3964
54.1291
61.8618
69 . 5946
58
8.00636
16.0127
24.0191
32.0254
40.0318
48 . 0382
56.0445
64 . 0509
72.0572
59
8.28485
16.5697
24 . 8546
33 . 1394
41.4243
49.7091
57.9940
66.2788
74.5637
60
8.56788
17.1358
25.7036
34.2715
42.8394
51.4073
59.9752
68.5430
77.1109
61
8.85606
17.7121
26 . 5682
35.4243
44.2803
53 . 1364
61.9924
70.8485
79 . 7045
62
9 . 14879
18.2976
27.4464
36 . 5952
45.7440
54.8927
64.0415
73.1903
82.3391
63
9.48364
18.9673
28.4509
37.9346
47.4182
56.9018
66 . 3855
75.8691
85.3528
64
9.74848
19.4970
29.2454
38.9939
48.7424
58.4909
68.2394
77.9878
87 . 7363
65
10.05545
20.1109
30.1664
40.2218
50.2773
60.3327
70.3882
80.4436
90.4991
66
10.36727
20.7345
31.1017
41.4690
51.8362
62.2035
72.5707
82.9379
93 . 3052
67
10.68394
21.3679
32.0518
42.7358
53.4197
64 . 1036
74.7876
85.4715
96.1545
68
11.00515
22.0103
33 . 0155
44.0206
55.0258
66 . 0309
77.0361
88.0412
99 . 0464
69
11.33121
22.6624
33.9936
45 . 3248
56.6561
67.9873
79.3185
90.6497
101.9809
70
11.66212
23 . 3242
34 . 9864
46.6485
58.3106
69.9727
81.6348
93.2970
104.9591
71
11.99758
23.9952
35.9927
47.9903
59.9879
71.9855
83.9831
95.9806
107.9782
72
12.33788
24.6758
37.0136
49.3515
61.6894
74.0273
86.3651
98.7030
111.0409
73
12.68303
25.3661
38.0491
50.7321
63.4152
76.0982
88.7812
101.4642
114.1473
74
13.03273
26.0655
39.0982
52 . 1309
65.1637
78.1964
91.2291
104.2618
117.2946
75
13.38758
26.7752
40.1627
53 . 5503
66.9379
80.3255
93.7131
107.1006
120.4882
76
13.74697
27.4939
41.2409
54.9879
68.7349
82.4818
96.2288
109.9758
123.7227
77
14.11091
28.2218
42.3327
56.4436
70.5546
84.6655
98 . 7764
112.8873
126.9982
78
14.48000
28.9600
43.4400
57.9200
72.4000
86 . 8800
101.3600
115.8400
130.3200
79
14.85364
29.7073
44 . 5609
59.4146
74.2682
89.1218
103.9755
118.8291
133.6828
80
15.23182
30.4636
45.6955
60.9273
76.1591
91.3909
106.6227
121.8546
137.0864
81
15.61515
31.2303
46.8455
62.4606
78.0758
93.6909
109.3061
124.9212
140.5364
82
16.00303
32.0061
48.0091
64.0121
80.0152
96.0182
112.0212
128.0242
144.0273
83
16.39576
32.7915
49.1873
65.5830
81.9788
98.3746
114.7703
131.1661
147.5618
84
16.79333
33 . 5867
50.3800
67.1733
83.9667
100.7600
117.5533
134.3466
151. HOC
85
17 . 19545
34.3909
51 . 5864
68.7818
85.9773
103.1727
120.3682
137 . 5636
154.7591
86
17.60242
35.2048
52.8073
70.4097
88.0121
105.6145
123.2170
140.8194
158.4218
87
18.01424
36 . 0285
54.0427
72.0570
90.0712
108.0854
126.0997
144.1139
162.1282
88
18.43061
36.8612
55.2918
73.7224
92.1531
110.5837
129.0143
147.4449
165.8755
89
18.85182
37 . 7036
56.5555
75.4073
94.2591 113.1109
131.9627
150.8146
169.6664
90
19.27788
38.5558
57.8336
77.1115
96 . 3894
115.6673
134.9452
154.2230
173.5001
91
19 . 70879
39.4176
59.1264
78.8352
98 . 5440
118.2527
137.9615
157.6703
177.3791
92
20.14424
40.2885
60.4328
80.5771
100.7214
120.8656
141.0099
161.1542
181.2985
93
20.58455
41.1691
61.7537
82 . 3382
102.9228
123 . 5073
144.0919
164.6764
185.261C
94
21.02970
42.0594
63.0891
84.1188
105.1485126.1782
147.2079
168.2376
189 . 2673
95
21.47940
42.9588
64.4382
85.9176
107.3970
128.8764
150.3558
171.8352
193.3146
96
21.93394
43.8679
65.8018
87.7358
109.6697
131.6036
153.5376
175.4715197.4055
97
22.39333
44 . 7867
67.1801
89.5735
111.9668
134 . 3642
156.7535
179. 14691201. 5403
98
22.85758
45.7152
68.5727
91.4303
114.2879
137.1455
160.0031
182.8606205.7182
99
23 . 32626
46.6525
69.9788
93.3050
116.6313
139.9576
163.2838
186.6101209.9363
100
23.80000
47.6000
71.4000
95.2000
119.0000
142.8000
166.6000
190.4000214.200C
COMPUTING THE HORSE-POWER
111
in the crank-end. The effective pressure at an}' time in the forward
stroke is the pressure in the head-end at that instant minus the pressure
in the crank-end, and to get the proper mean effective pressure during
the forward stroke we should take the mean pressure on the head-end
less the mean back pressure on the crank-end. This would make no
difference in the computed power of the engine as a whole, for what was
lost on one end would be gained by the other, but it would, if the back-
pressure lines were different, affect the amounts of power indicated
at the different ends, and comes into the question of balancing the load
equally. In New England factories it is common to run an engine one-
half condensing, that is, to have a separate exhaust pipe for each end,
one running to the condenser and the other end exhausting, perhaps
FIG. 100.
under a back pressure for heating, etc. The diagrams from such an engine
would be like Fig. 100. Obviously the load would not be equally divided
between the two ends of the cylinder when the areas of the diagrams
were equal. When the piston is on the line A B and moving in the direc-
tion of the arrow there is a pressure urging it forward proportional to
the height of A and the back pressure is proportional only to the height
of B, so that the effective pressure is A B, although if we take the back-
pressure line of the head-end diagram it will appear to be only AC. The
diagram from the crank-end would appear, taken by itself, to have an
effective pressure proportional to EF when the piston was at that point
in the stroke, but since the piston is moving against a back pressure
proportional to the height of D the effective pressure at that point is
DE. The effort of both ends upon the crank pin cannot be balanced by
making the area of the crank-end diagram equal to that of the head-end.
112
THE STEAM ENGINE INDICATOR
The work actually done upon the crank when the piston is moving for-
ward is found by combining the back-pressure line of the crank-end
FIG. 101.
diagram with the forward-pressure line of the head-end diagram as in
Fig. 101, and vice versa for the backward strokes as in Fig. 102. The
FIG. 102.
work will be equalized between the two ends when the area of these
reconstructed diagrams are equal, proper allowance being made for the
piston rod.
CHAPTER XIV
MEAN EFFECTIVE PRESSURE AND POINT OF CUT-OFF
BY COMPUTATION
THE mean effective pressure of steam working between given limits
of pressure and with a given ratio of expansion may be calculated
upon the assumption that the product of its volume and pressure remains
constant (see chapter on expansion), and such calculation is of use in
designing, selecting or estimating the horse-power of an engine.
In Fig. 103 let vertical distances represent pressures, and horizontal
distances volume, as in the ordinary indicator diagram. Let OX be the
Aa
^
1
:
2
FIG. 103.
line of absolute zero of pressure and OA the zero of volume. If we
start with the volume AB of steam of a pressure OA and expand it in the
usual unjacketed cylinder through the usual range, the expansion line
will follow more or less closely the curve BC, which passes through
points so located that the product of the pressure and volume is constant.
For instance, if the volume is doubled, the pressure will be halved, and
the line will pass through 6, which is twice as far from the line of zero
volume, but only one-half as far above the line of zero pressure as the
point B.
113
114 THE STEAM ENGINE INDICATOR
Suppose AB to be the steam line, and BC the expansion line of a
diagram from a steam engine cylinder. The average height of the dia-
gram would be the average forward pressure during the stroke on the
scale to which it is drawn. Since the area is the average height multi-
plied by the length, the area divided by the length is the average height,
which represents the average pressure.
It is easy to see that with the expansion curve following the definite
law the area BCX1 will be a definite proportion of the area A BIO
for any particular ratio of expansion. For four expansions, for example,
i.e., when the final volume is four times the initial volume, which is
what is meant by a "ratio of expansion" of four, the area under the
expansion line is 1.3863 times that under the steam line to whatever
scale the diagram is drawn. Table IV at the end of the volume gives
the proportion between these two areas for other ratios of expansion
under the title of " Hyperbolic Logarithms."
If we make OA equal one pound pressure and 01 one unit of volume,
then the area ABIO will be 1X1=1, and the area BCXl will be 1.3863
(for four expansions). The total area then in these units will be 2.3863,
and the length in the same units 4, so that the average height on the
scale selected for the expression of one pound would be 2.3863 divided
by 4, and this would be the average or mean forward pressure.
To FIND THE MEAN FORWARD PRESSURE PER POUND OF
INITIAL
RULE. Divide 1 plus the hyperbolic logarithm of the ratio of the ex-
pansion by that ratio; the quotient will be the mean forward pressure per
pound of initial.
The logarithms will be found in Table IV at the end of the volume.
The column headed 0% in Table V was calculated in this way, and
gives the mean forward pressure per pound of absolute initial pressure,
expanded in a cylinder without clearance. When the piston does not
pass through the full length of the cylinder, or more properly does not
displace the full volume of the expanding steam, we would have the
volume AB expanding into the volume OX, while the piston moves
only through the distance oX and is displaced only through the volume
aB by the entering steam. In order to take care of the clearance, the
formula becomes that printed above the table, and with this formula
the remaining columns of the table are calculated. By its use the mean
forward pressure of the ideal diagram may be easily calculated for any
initial pressure, ratio of expansion and clearance.
EXAMPLE. What would be the mean effective pressure in an engine
having 3 per cent clearance, with an initial pressure of 90 pounds gage,
MEAN EFFECTIVE PRESSURE AND POINT OF CUT-OFF 115
TABLE V
MEAN PRESSURE PER POUND OF INITIAL, WITH DIFFERENT
CLEARANCES AND POINTS OF CUT-OFF
Fraction of
Stroke
Complete at
Cut-off.
PERCENTAGE OF CLEARANCE
0%
1%
1.5%
2%
2.5%
3%
3.5%
4%
4.5%
5%
5.5%
6%
v,o
.1
3303
3439
3505
3568
.3630
.3690
.3750
.3808
.3864
.3919
.3974
.4027
l / 9
.111
3549
3677
3738
3798
.3856
.3913
.3968
.4022
.4075
.4129
.4178
.4227
*/
.125
3849
3966
4023
4078
.4132
.4187
.4237
.4287
.4338
.4386
.4433
.4480
y,
.143
4213
4320
.4370
4420
.4471
.4518
.4565
.4612
.4655
.4699
.4743
.4788
.15
4346
4447
4497
4546
.4794
.4639
.4684
.4729
.4774
.4816
.4860
.4901
Ye
.167
4662
4757
4802
4844
.4890
.4933
.4973
.5014
.5056
.5096
.5134
.5173
3 Ae
.188
5013
5097
5138
5181
. 5217
.5259
.5295
.5332
.5367
.5405
.5440
.5474
'/
.20
5219
5298
5336
5376
.5414
.5449
.5482
.5517
.5556
.5588
.5623
.5656
.21
5376
5453
5489
5523
.5560
.5595
.5628
.5664
.5698
.5730
.5760
.5795
.22
5533
5602
5639
5673
.5704
.5740
.5773
.5804
.5834
.5868
.5900
.5931
.23
5681
5750
5781
5815
.5848
.5878
.5913
.5940
.5971
.6001
.6029
.6063
.24
5827
5891
5922
5952
.5986
.6012
.6042
.6071
.6106
.6131
.6162
.6184
'A
.25
5966
6025
6059
6090
.6120
.6148
.6174
.6207
.6229
.6258
.6286
.6312
.26
6105
6162
6190
6218
.6251
.6274
.6304
.6332
.6359
.6385
.6408
.6430
.27
6232
6294
6319
6350
.6370
.6398
.6424
.6448
.6480
.6501
.6531
.6549
.28
6363
6416
.6445
6471
.6496
.6520
.6551
.6572
.6600
.6618
.6644
.6669
.29
6491
6545
.6569
6592
.6613
.6642
.6660
.6686
.6712
.6736
.6759
.6780
3 AO
.30
6609
6663
.6684
.6712
.6729
.6755
.6779
.6803
.6825
.6845
.6864
.6882
Vie
.313
6760
6805
.6830
.6855
.6878
.6899
.6919
.6938
.6956
.6985
.7000
.7026
.32
6851
6891
.6914
.6935
.6956
.6974
.7004
.7021
.7035
.7062
.7074
.7099
Vs
.333
6988
.7029
.7047
.7076
.7092
.7106
.7132
.7144
.7168
.7190
.7212
.7219
.34
7067
.7115
.7130
.7145
.7171
.7183
.7207
.7230
.7238
.7259
.7279
.7298
.35
.7178
.7220
.7232
.7256
.7266
.7288
.7310
.7330
.7350
.7368
.7370
.7402
.36
.7281
. 7316
.7338
.7346
.7367
.7386
.7405
.7422
.7439
.7454
.7468
.7482
y
.375
.7433
.7458
.7476
.7494
.7510
.7525
.7539
.7569
.7582
.7593
.7603
.7630
.38
.7475
.7512
.7528
.7544
.7559
.7573
.7586
.7615
.7626
.7636
.7662
.7670
.39
.7566
.7613
.7627
.7640
.7653
.7664
.7691
.7700
.7708
.7734
.7740
.7764
Vs
.40
.7665
.7691
.7719
.7729
.7738
.7765
.7772
.7778
.7802
.7806
.7829
.7831
7/
/16
.438
.8000
.8024
.8030
.8044
.8063
.8068
.8079
.8096
.8104
.8115
.8127
.8138
.45
.8089
.8127
.8130
.8141
.8158
.8165
.8176
.8187
.8199
.8210
.8221
.8231
Vi
.50
.8466
.8484
.8492
.8503
.8513
.8522
.8530
.8539
.8548
.8556
.8565
.8573
.55
.8733
.8792
.8810
.8817
.8824
.8831
.8838
.8844
.8851
.8858
.8864
.8871
%6
.563
.8868
.8875
.8882
.8888
.8895
.8901
.8908
.8914
.8920
.8926
.8932
.8938
3 /5
.60
.9064
.9076
.9081
.9087
.9092
.9097
.9102
.9107
.9112
.9117
.9122
.9127
V,
.625
.9188
.9194
.9201
.9206
.9210
.9215
.9220
.9224
.9228
.9233
.9237
.9241
.65
.9300
. 9308
.9312
. 9316
.9320
.9323
.9327
.9331
.9335
.9338
.9342
.9340
V 3
.667
.9371
.9378
.9382
.9385
.9389
.9392
.9396
.9399
.9402
.9405
.9408
.9411
U /ie
.688
.9451
.9457
.9460
.9463
.9466
.9469
.9472
.9475
.9478
.9480
.9483!. 9486
7 Ao
.70
.9497
.9502
.9505
.9508
.9511
.9513
.9516
.9518
.9521
.9524
.9526
.9528
3 A
.75
.9657
.9661
.9663
.9665
9667
.9668
.9670
.9672
.9674
.9675
.9677
.9679
116 THE STEAM ENGINE INDICATOR
TABLE V Continued
MEAN PRESSURE PER POUND OF INITIAL, WITH DIFFERENT
CLEARANCES AND POINTS OF CUT-OFF
PERCENTAGE OF CLEARANCE
Fraction of
Stroke
Complete at
Cut-off.
6.5%
7%
7.5%
8%
8.5%
9%
9-5%
10%
.4409
10.5%
11%
11.5%
12%
.4076
.4126
.4176
.4225
.4271
.4320
.4366
.4453
.4498
.4540
.4580
Vio
.1
.4278
.4326
.4373
.4417
.4462
.4507
.4549
.4593
.4633
.4676
.4715
.4757
'/
.11
.4527
.4571
.4615
.4657
.4700
.4740
.4782
.4821
.4858
.4897
.4938
.4973
Vs
.12
.4827
.4871
.4908
.4951
.4987
.5026
.5062
.5101
.5138
.5173
.5205
.5242
1 A
.14
.4939
.4978
.5020
.5059
.5096
.5131
.5169
.5204
.5237
.5274
.5309
.5342
.15
.5210
.5245
.5283
.5318
.5352
.5389
.5417
. 5457
.5488
.5517
.5551
.5583
Ye
.16
.5511
.5546
.5579
.5610
.5639
.5673
.5705
.5736
.5764
.5791
.5825
.5848
Vi,
.18
.5687
.5716
.5750
.5782
.5812
.5841
.5868
.5901
.5924
.5954
.5982
.6009
y
.20
.5821
.5853
.5882
.5910
.5944
.5968
.5998
.6028
.6055
.6081
.6106
.6129
.21
.5959
.5986
.6011
.6043
.6073
.6101
.6128
.6154
.6177
.6199
.6230
.6249
.22
.6087
.6118
.6138
.6166
.6192
.6225
.6248
.6270
.6300
.6318
.6345
.6371
.23
.6212
.6239
.6264
.6297
.6319
.6340
.6369
.6397
.6413
.6438
.6462
.6485
.24
.6336
.6359
.6390
.6410
.6438
.6465
.6480
.6505
.6528
. 6550
.6570
.6602
y<
.25
.6460
.6479
.6507
.6533
.6548
.6571
.6594
.6626
.6646
.6665
.6682
.6711
.26
.6576
.6601
.6626
.6649
.6670
.6691
.6710
.6728
.6757
.6772
.6799
.6812
.27
.6692
.6714
.6735
.6755
.6773
.6803
.6818
.6833
.6859
.6885
.6895
.6918
.28
.6800
.6819
.6849
.6865
.6880
.6906
.6919
. 6943
. 6967
.6990
.6997
.7018
.29
.6911
.6927
.6954
.6966
.6991
.7002
.7024
.7046
.7067
.7087
.7107
.7125
Vio
.30
.7039
.7063
.7073
.7096
.7117
.7138
.7157
.7176
.7194
.7211
.7226
.7241
5 / lti
.31
.7123
.7131
.715$
.7173
.7193
.7211
.7229
.7245
.7261
.7275
.7289
.7319
.32
.7239
.7257
.7275
.7292
.7308
.7323
.7353
.7366
.7378
.7389
.7417
.7426
Vs
.33
.7316
.7333
. 7349
.7364
.7378
.7391
.7421
.7432
.7442
.7469
.7477
.7484
.34
.7417
.7432
.7445
.7457
.7468
.7496
.7506
.7514
.7540
.7546
.7571
.7575
.35
.7511
.7523
.7533
.7543
.7569
.7577
.7602
.7608
.7632
.7636
.7658
.7660
.36
.7639
.7646
.7671
.7676
.7700
.7711
.7725
.7739
.7752
.7766
.7779
.7792
3 /8
.37
.7677
.7702
.7707
.7730
.7733
.7755
.7767
.7781
.7794
.7807
.7820
.7832
.38
.7768
.7791
.7793
.7815
.7824
.7837
.7850
.7862
.7875
.7888
.7900
.7912
.39
.7853
.7874
.7880
.7892
.7905
.7918
.7930
.7942
.7954
.7966
.7978
.7990
V 5
.40
.8149
.8161
.8172
.8182
.8193
.8204
.8214
.8224
.8235
.8244
.8254
.8264
7 A.
.43
.8242
.8252
.8263
. 8273
.8283
.8293
.8303
.8312
.8322
.8331
.8341
. 8350
.45
.8582
.8590
.8598
.8606
.8614
.8622
.8629
.8637
.8644
.8652
.8659
.8667
Y 2
.50
.8877
.8883
.8890
.8896
.8902
.8908
.8914
.8920
.8925
.8931
.8937
.8942
.55
.8944
.8950
.8956
.8962
.8968
.8973
.8979
.8984
.8989
.8995
.9000
.9005
Vli
.56
.9132
.9136
.9141
.9146
.9150
.9155
.9159
.9164
.9168
.9173
.9177
.9181
3 /5
.60
.9245
.9,249
.9253
.9257
.9261
.9265
.9269
.9272
.9276
.9280
.9284
.9288
Vs
.62
.9349
.9352
.9356
.9359
.9363
.9366
.9369
.9373
.9376
.9379
.9382
.9385
.65
.9415
.9418
.9421
.9424
.9427
.9430
.9433
. 9436
.9438
.9442
.9444
.9447
2 /3
.66
.9489
.9491
.9494
.9497
.9499
.9502
.9505
.9507
.9509
.9512
.9514
.9517
"A.
.68<
.9531
.9533
.9536
.9538
.9541
.9543
.9546
.9548
.9550
.9552
.9554
.9557
7 Ao
.70
.9680
.9682
.9684
.9685
.9687
.9688
.9690
.9691
.9693
.9695
.9696
.9698
3 /4
.75
MEAN EFFECTIVE PRESSURE AND POINT OF CUT-OFF
117
cutting off at one-quarter stroke, and exhausting at atmospheric
pressure?
By the table, the mean pressure per pound of absolute initial
for 3 per cent clearance and one-quarter cut-off is 0.6148 of the
initial pressure. The absolute initial is 90 + 14.7 = 104.7 Ibs. The
Absolute Zero of 1'ressure
FIG. 104.
mean pressure of the ideal diagram is therefore 104.7X0.6148=64.37
pounds. This is the mean effective pressure represented by the dia-
gram ABODE in Fig. 104. Since there is 14.7 pounds back pressure
above absolute zero, this must be subtracted, giving 64.3714.7=49.67
as the mean effective pressure represented by the area ABCFG. If
FIG. 105.
FIG. 106.
the engine were condensing we would subtract the absolute back pres-
sure corresponding with the vacuum, roughly one pound for each two
inches of vacuum short of 30 inches, i.e., one pound for 28 inches, two
pounds for 26 inches, three pounds for 24 inches, etc.
More accurate values may be found in a table of the Physical Prop-
erties of Steam.
118
THE STEAM ENGINE INDICATOR
But no engine makes a diagram like ABCFG; the steam line is apt
to fall away, the points of cut-off and release to be rounded, the line of
counter-pressure to hang up in places, and the compression takes out
considerable area. The actual mean effective pressure will be to the
mean effective calculated above as the actual diagram which the engine
would make is to the ideal area. This relationship is indicated for three
typical cases in Figs. 105, 106, and 107 by diagrams which give the
percentages which the realized area bears to the ideal. If in the above
example we may expect the engine to realize about 90 per cent of the
FIG. 107.
ideal area, we may say the probable M.E. P. equals about 49.67X0.9=44.7
Ibs.
To FIND THE MEAN EFFECTIVE PRESSURE FROM THE
TABLE
RULE. Multiply the tabular value opposite the given point of cut-off
and in the column of the given clearance by the absolute initial pressure;
subtract the absolute back pressure and multiply by the proportion of the
ideal area probably realized.
The initial pressure means the pressure which gets into the cylinder,
and may be very different from the boiler pressure, especially with
a throttling governor.
CHAPTER XV
STEAM CONSUMPTION FROM THE DIAGRAM
KNOWING the cubic capacity of the cylinder and the number of times
it is filled and emptied per hour, we could, if the entire contents of the
cylinder remained as steam all the time, compute the cubic feet of steam
passing through the engine in that time. Knowing from the diagram
the pressure of this steam we can find in a steam table the weight per
cubic foot, and thus the weight of steam passed per hour. The dia-
gram also gives us a measure of the horse-power, dividing by which
we get the number of pounds of steam accounted for by the diagram
per hourly horse-power. This will be always less than the actual amount
of steam supplied to the engine, because a considerable proportion of such
steam is condensed on its entrance to the cylinder, and is not re-evaporated
until after the valve opens for exhaust, so that it does not show as steam
upon the diagram at all. The computation is of use, however, for pur-
poses of comparison, and as a measure of the minimum amount of steam
which the diagram would allow per horse-power, and should be under-
stood by one who desires to attain proficiency with the indicator.
Let A =area of piston in square inches,
S= length of stroke in feet,
N = number of strokes per minute,
P=mean effective pressure, indicated by diagram.
V= volume generated by the piston per hour.
V=~ XSXGON, ........ (1)
the area in square inches divided by 144 to reduce to square feet, multi-
plied by the length of the stroke, gives the cubic feet per stroke, and
by 00 times the number of strokes per minute gives the number of cubic
feet passed through by the piston per hour.
The horse-power is 33 Q QQ . (2)
Dividing equation (1) by equation (2) we get the number of cubic feet
passed through by the piston in an hour for each horse-power. As the
119
120
THE STEAM ENGINE INDICATOR
area, length of stroke, and number of strokes per minute are used i]
calculating both the volume and the horse-power they cancel each othe
in the division, and the formula becomes
PANS
33000
.460A T 33000_ 13750
144PANS ~P~'
or in plain language, 13,750 divided by the mean effective pressure wil
give the cubic feet of piston displacement per hour for each horse
power generated by any engine, whatever its size or speed. Substitut
ing for P the common abbreviation of the mean effective pressure w<
have
13700
= volume generated per hour per horse-power. . .
(3
If the engine had no clearance nor compression and the release di(
not occur until the end of the stroke, we could measure the pressure o
FIG. 108.
the steam at the point a, Fig. 108, find in a steam table the weight o
steam of that pressure per cubic foot, multiply the volume per horse
power by that weight, and find the weight per horse-power per hour
As the quantities in the steam tables are usually given in pounds absolut
it is better to measure from the zero line ox, or to add 14.7 pounds to th'
measurement from the atmospheric line. Or we could equally we!
measure the. pressure at any other point after the cut-off valve closes
and take such proportion of the volume given by formula 3, based 01
the whole stroke, as the portion of the stroke completed by the pistoi
up to the point chosen bears to the full stroke. If we measure the volum
at a we have had so many complete cylinderfuls of steam at that pres
sure, and formula (3) will give the volume per horse-power. If we measur
STEAM CONSUMPTION FROM THE DIAGRAM 121
the volume at half-stroke 6 we have had only one-half the volume at this
higher pressure, and formula must be multiplied by 0.5 to give the num-
ber of cubic feet per horse-power per hour, of this higher pressure steam.
Likewise if we measure the pressure at one-quarter stroke c we shall
have had but one-quarter of the volume, and must multiply the for-
mula by 0.25, and so for any other fraction of the stroke. If the amount
of steam in the cylinder v/ere constant throughout the expansion the
weight per horse-power per hour would be the same whether we meas-
ured it at cut-off or at release, or at any point between, but condensa-
tion and re-evaporation are going on, so that there is more steam in the
cylinder later in the stroke than immediately after the cut-off, and there
will usually be found to be a greater amount of steam accounted for
per horse-power per hour the nearer the measurements are made to the
point of release. Call the fraction of the stroke completed at the point
chosen F, and the weight of steam per cubic foot at that pressure w f ,
then under the simple conditions assumed
137 =lbs. steam per H.P.H (4)
M.E.P.
when the pressure is measured at the end of the stroke, as at a, F becom.es
unity or one, and the formula becomes
=lbs. steam per H.P.H. ..... (o)
^.i .
We have yet to determine the amount of steam required to fill the
clearance, and the amount left in the c}dinder when the exhaust valve
closes. As we cannot exhaust into a perfect vacuum there will always
be some such steam, even when there is no compression. Suppose
the engine to have five per cent clearance, then when the piston was
at a instead of having the volume swept through by the piston behind
it we should have 1.05 times that volume. When the piston was at
half-stroke we should have instead of 0.5 of the piston displacement
0.55 of that volume, and generally for any fraction F of the stroke com-
pleted at the point chosen for measurement we should have F +c of
the piston displacement behind it, c being the clearance in fractions
of the stroke, and the steam per horse-power per hour becomes
13750 Wf . (6)
M.E.P.
Suppose in Fig. 109 the exhaust valve to close at e when the return
stroke is 0.8 completed. The volume of steam shut in would be the area
122
THE STEAM ENGINE INDICATOR
of the piston in square feet multiplied by the fraction of stroke uncom-
pleted plus the five one-hundredths of the stroke, included in the clearance,
that is, 0.2+0.05=0.25; or generally, calling the portion of the stroke
uncompleted at the compression x, the volume inclosed would be, per
hour,
A
** / . \ s*s~i IT /^7\
144
40 Scale
M.E.P.47.6 Ibs.
Steam Consumption = 18.08 Ibs.
per h.pJi.
8.6 inches
4 inches
FIG. 109.
PANS
and this divided by the horse-power f to give the volume saved
ooOUO
per horse-power, and multiplied by the weight w x of steam per cubic
foot at the pressure obtained at the point x would be
13750
M.E.P. (aH *
Subtracting this from formula (6) we have
(8)
(9)
Where c= clearance in fractions of the stroke;
F= fraction of stroke completed at point chosen on expansion line:
x= fraction of stroke uncompleted at point chosen on compres-
line
it> =wt. per cu.ft. of steam at pressure measured at F\
w x =v/t. per cu.ft. of steam at pressure measured at x;
Q=steam accounted for per H.P. per hour.
STEAM CONSUMPTION FROM THE DIAGRAM 123
RULE. To the fraction of the forward stroke completed at the point
chosen add the clearance, also in fractions of the stroke, and multiply the
sum by the weight per cubic foot of steam of the pressure measured at this
point. (Product 1.}
To the fraction of the return stroke uncompleted at the point chosen on
the compression line add the clearance, expressed as before, and multiply
the sum by the weight per cubic foot of steam of the pressure measured at
this point. (Product 2.}
Multiply the difference between products 1 and 2 by the quotient of 13,750
divided by the M.E.P.; the final product will be the number of pounds vf
steam per hour per horse-power accounted for by the diagram.
As an assistance in working with the above rule or formula Table VI
gives the value of 13,750 divided by mean effective pressures of from
10 to 100 pounds. The first column under zero gives the quotients for
even pounds, the succeeding columns for additional tenths of pounds.
Thus the quotient of would be found in the horizontal line with
oo.o
35 and in the column under 6 to be 386.23.
EXAMPLE. The diagram shown in Fig. 109 shows with a 40 scale a
M.E.P. of 47.5 pounds; clearance 5 per cent. How much steam is
accounted for per horse-power per hour?
Let us select the points F and x from which to make our measure-
ments. The whole length of the diagram is 4 inches, the length to the
point F, 3.5 inches. The fraction F of the stroke completed at this
point is therefore '-j- =0.875. The distance xa equals 0.4 of an inch,
0.4
and the fraction of the return stroke uncompleted at the point x is ^- =0.1.
The pressure (absolute) at F is 32 pounds, at x 19 pounds. The
weight of steam per cubic foot at 32 pounds is 0.0789, at 19 pounds
0.0483.
then c-0.05
7^=0.875
x=0.l
w f =0.0789
w x = 0.0483
and M.E.P. = .47.5
The steam accounted for per horse-power per hour is
x[(0.875 + 0.05)0.0789- (0.1 +0.05)0.0483].'
47.5
124
THE STEAM ENGINE INDICATOR
From the table we find the value of -p=-v- to be 289.47, and we have
47.5
289.47X[(0.925X0.0789) -(0.15X0.0483)] -19.03 pounds of steam per
hour for each horse-power.
It is not necessary that the point X, at which the pressure of the steam
saved by compression is measured, shall be at the commencement of
compression. It may be located at any point upon that line or upon
.05 >
\
\
X2\J
FIG. 110.
the dotted continuation of that line into the clearance space. In Fig.
110, representing the compression corner of a diagram on a large scale
let the vertical divisions represent hundredths of the stroke, the clearance
C being five per cent or five hundredths, and the exhaust valve closing
at X when ten one-hundredths of the stroke are uncompleted. When
the exhaust valve closes we have a volume of steam inclosed equal to
C+X =0.05 +0.10 =0.15 of the displacement at the pressure X, or if
we measure at X 1 , when 0.08 of the stroke remain to be completed, we
shall have 0.05 + .08 =0.13 at the pressure X, 1 or 0.10 at the pressure X 2 ,
or 0.05 at the pressure X 3 , 0.03 at X 4 , etc., so that so long as we measure
VALUES OF
STEAM CONSUMPTION FROM THE DIAGRAM
TABLE VI
13750
125
M.E.P.
FOR COMPUTING STEAM CONSUMPTION
1
2
3
4
5
6
7
8
9
10
1375.00
1361.39
1348.04
1334.95
1322.15
1309.52
1297.17
1285.04
1273.14
1261.46
11
1250.00
1238.74
1227.68
1216.81
1206.13
1195.65
1185.34
1175.19
1165.25
1155.46
12
1145.83
1136.36
1127.05
1117.88
1108.87
1100.00
1091.11
1082.67
1074.21
1062.01
13
1057.69
1049.62
1041.66
1033.83
1026.12
1018.51
1011.03
1003.64
996.38
989.21
14
982.14
975.18
968.31
961.54
954.86
948.29
941.78
935.37
929.00
922.82
lo
916.67
910.60
904.61
898.69 893.05
867.09
881.41
875.79
870.25
864.77
16
871.87
854.04
848.76
843.55
838.41
833.33
828.31
823.35
818.45
813.61
17
808.82
804.09
799.42
794.79
790.23
785.71
781.25
776.84
772.47
768.15
18
763.89
759.67
755.49
751.36
747.28
743.24
739.24
735.29
731.38
727.51
1!'
723.68
719.89
716.15
712.43
708.76
705.13
701.53
697.99
694.44
690.95
20
687.50
683.08
680.69
677.34
674.02
670.73
667.47
664.25
661.06
657.84
21
654.76
651.66
648.58
645.54
642.52
639.53
636.57
633.64
630.73
627.85
22
625.00
622.17
619.37
616.59
613.94
611.11
608.41
605.72
603.07
600.43
23
597.83
595.24
592.67
590.12
587.61
585.11
582.62
580.16
577.73
575.31
24
572.92
570.54
568.18
565.84
563.52
561.22
558.94
556.67
554.43
552.21
25
550.00
547.81
545.64
543.47
541.33
539.21
537.11
535.02
532.94
530.88
26
528.85
526.82
524.81
522.81
520.83
518.87
516.91
514.98
513.06
511.15
27
509.26
507.38
505.51
503.66
501.82
500.00
498.11
496.39
494.60
493.19
2S
491.07
489.32
487.55
485.86
484.15
482.45
480.76
479.09
477.43
476.12
29
474.14
472.51
470.89
469.28
467.68
466.10
464 . 53
462.89
461.40
459.86
30
458.33
456.81
455.30
453.79
452.30
450.82
449.34
447.88
446.42
444.98
31
443.55
442.12
441.99
439.30
437.83
436.51
435.12
433.75
432.39
431.35
32
429.69
428.35
427.01
425.69
424.38
423.07
421.77
420.49
419.21
417.93
33
416.67
415.41
413.85
412.91
411.67
410.44
409.22
408.01
406.80
405.60
34
404.41
403.22
402.05
400.87
399.71
398.55
397.39
396.25
395.11
393.98
35
392.84
391.73
390.63
389.51
388.41
387.32
386.23
385.15
384.08
383.01
36
381.94
380.89
379.83
378.78
377.75
376.71
375.68
374.66
373.64
372.62
37
371.62
370.62
369.62
368.63
367.65
366.66
365.69
364.72
363.75
362.79
38
361.84
360.89
359.94
359.00
358.07
357.40
356.22
355.29
354.38
353.47
39
352.56
351.64
350.77
349.87
348.98
348.10
347.22
346.34
345.47
344.11
40
343.75
342.89
342.32
341 . 19
340.34
339.51
338.67
337.83
337.01
336.18
41
335.36
334.55
333.74
332.92
332.12
331.32
330.52
329.71
328.94
328.16
42
327.38
326.36
325.83
325.06
324.26
323 . 50
322.77
322.01
321.35
320.51
43
319.77
319.02
318.29
317.55
316.82
316.09
315.36
314.64
313.92
313.21
41
312.50
311.79
311.09
310.38
309.68
308.98
308.29
300.61
306.92
306.23
45
305.55
304.88
304.20
303.55
302.86
302.19
301.53
300.87
300.22
299.34
46
298.91
298.26
297.62
296.97
296.33
295.48
295.06
294.43
293.80
292.96
47
292.55
291.93
291.31
290.61
290.08
. 289.47
288.86
288.26
287.65
287.05
4N
286.46
285.86
285.26
284.66
284.09
283.50
282.92
282.34
281.76
281.18
49
280.61
280.04
279.47
278.09
278.34
277.77
277.21
276.66
276.10
275.55
50
275.00! 274.45
273.90
273.35
272.82
272.27
271.73
271.20
270.67
270.13
51
269.61 269.08
268.55
268.03
267.51
266.99
266.47
265.95
265.44
264.93
52
264. 43 1 263.91
263.41
262.91
262.40
261.90
261.40
260.91
260.41
258.03
63
259.43
258.94
258.45
257.97
257.49
257.00
256.53
256.05
255.57
255.10
54
254.63
254.16
253.69
253.22
252.75
252.29
251.83
251.37
250.91
250.47
55
250.00 249.54
249.09
248.64
248.19
247.74
247.30
246.86
246.41
245.97
126 THE STEAM ENGINE INDICATOR
TABLE VI Continued
VALUES OF ~ FOR COMPUTING STEAM CONSUMPTION
1
2
3
4
5
6
7
8
9
56
244 . 64
245.10
244.66
244.22
243.79
243.36
242.93
242.50
242 . 07
241.65
57
241.23
240.80
240.38
239.26
237.80
239.13
238.71
238.30
237 . 88
237.47
58
233.62
236 . 66
236.25
235.84
235.44
235.04
234.64
234 . 22
233 . 84
233.44
59
237.07
232.64
232 . 26
231.87
231.84
231.09
230.71
230.31
229 . 93
229.54
60
229.17
228.79
228.41
228.03
227.65
227 . 27
226.89
226.52
226.15
225.78
61
225.41
225.04
224.67
224.30
223.92
223.57
223.21
222.85
222.49
222.13
62
221.71
221.42
221.06
220.67
220.35
220.00
219.64
219.29
218.93
218. 6C
63
218.25
217.91
217.56
217.21
216.87
216.53
216.19
215.06
215.51
215.18
64
214.84
214.50
214.17
213.99
213.50
213.17
212.69
212.51
212.19
211.86
65
211.54
211.21
210.88
210.56
210.44
209.92
209.60
209 . 28
208.96
208.64
66
208.31
208.01
207.70
207.39
207.08
206.70
206.45
206.14
205.83
205.53
67
205.22
204.91
204.61
204 . 31
204.00
203 . 70
203.40
203.10
202.80
202. 5C
68
202.20
201.91
201.61
201.32
201.04
200.73
200.43
200.14
199.85
199.56
69
199.27
198.98
198.69
198.41
198.12
197.84
196.12
197 . 56
196.99
196. 7C
70
196.43
196.14
195.86
195.59
195.31
195.03
194.75
194.34
194.21
193.93
71
193.66
193.39
193.12
192.84
192.57
192.31
192.03
191.77
191.50
191.23
72
190.97
190.71
190.44
190.17
189.91
189.65
189.39
189.13
188.87
187.24
73
188.36
188.10
187.84
187.58
187.33
187.07
186.82
186.56
186.31
186. oe
74
185.80
185.56
185.30
185.06
184.81
184 . 56
184.31
184 . 07
183.82
183.57
75
183.34
183.09
182.84
182.60
182.36
182.11
181.87
181.63
181.39
181. 1C
76
180.92
180.68
180.45
180.21
179.97
179.73
179.50
179.27
179.03
178. 8C
77
178.57
178.34
178.11
177.87
177.65
177.42
177.19
177.09
176.73
176.51
78
176.28
176.05
175.83
175.61
175.38
175.16
174.81
174.71
174.49
174.27
79
174.05
173.83
173.61
173.39
173.17
172.95
172.73
172.52
172.18
172.
80
171.87
171.66
171.45
171.23
171.02
170.81
170.59
170.38
170.17
169.96
81
169.75
169.54
169.33
169.12
168.91
168.71
168.50
168.29
168.09
167. 8
82
167.68
167.47
167.27
167.07
166.86
166.67
166.46
166.26
166 . 06
165. 8e
83
165.66
165.46
165.26
165.06
164 . 86
164.67
164.47
164.27
164.09
163. 8
84
163.69
163.49
163.30
163.11
162.92
162.72
162.52
162.22
162.14
161. 9e
85
161.76
161.57
161.38
161.19
161.01
160.82
160.63
160.44
160.25
160.07
86
159.88
159.70
159.51
159.33
159.14
158.73
158.77
158.59
158.41
158. 2
87
158.04
157.86
157.68
157.50
157.32
157.14
156.96
156.78
156.61
156.44
88
156.25
156.07
155.89
155.71
155.54
155.36
155.19
154.01
154.84
154.66
89
154.49
154.32
154.14
153.97
153.80
153.63
153.46
153.29
153.12
152.94
90
153.78
152.61
152.44
152.27
152.10
151.93
151.76
151.60
151.54
151. 2(
91
151.09
150.93
150.77
150.60
150.43
150.27
150.11
149.94
149.77
149.61
92
149.45
149.29
149.13
148.97
148.81
148.64
148.48
148.32
148.16
148. 0(
93
147.85
147.58
147.53
147.25
147.21
147.05
146.90
146.73
146.59
146 . 4 r
94
146.27
146.12
145.96
145.81
145.65
145.50
145.34
145.19
145.04
144 . 8<
95
144.73
144.58
144.48
144.28
144.13
143.98
143.82
143.67
143.52
143.3^
96
143.23
143.08
142.93
142.67
142.63
142.48
142.34
142.19
142.04
141. 9(
97
141.75
141.61
141.46
141.31
141.17
141.02
140.88
140.73
140.59
140.4^
98
140.31
140.17
140.02
139.87
139.73
139.59
139.46
139.31
139.17
139.(X
99
138.88
138.74
138.61
138.46
138.33
138.19
138.05
137.91
137.77
137.6;
100
137.50
137.36
137.22
137.09
136.95
136.81
136.68
136.54
136.41
136.2'
STEAM CONSUMPTION FROM THE DIAGRAM
127
the pressures and volumes accordingly X may be located anywhere on the
compression curve, or even on the dotted extension of that line inside
the clearance space. The compression after the piston has reached the
end of its stroke will go on by the admission of the higher pressure steam.
Suppose in Fig. Ill the exhaust valve closes at E, shutting in a volume
proportional to the line OE, of exhaust steam. When the piston reaches
the end of its stroke on the line A a the clearance will be full of steam
raised by compression to the pressure B. The admission valve being
now opened, live steam rushes in and raises the pressure to that of the
steam line AC, by which process the steam saved by compression and
which occupied the whole clearance at a pressure B before admission
g h is compressed to a volume proportional to
the line gh, corresponding with the pressure
to which it is subjected. At this pressure,
it will be seen, it occupies three-sevenths
of the clearance space, and the remain-
ing four-sevenths must be supplied from
the boiler. The amount of new steam
supplied up to the point of cut-off
then is proportional to the line
hC. When the pencil reached
D the compression steam had
B ^ expanded to a volume
FIG. 111.
proportional to ed, corresponding with that pressure, and the new
steam involved in the stroke is proportional to the line Dd, and
this is true of any line drawn horizontally across the diagram
between the expansion and compression line, or the continuation
of the latter into the clearance. This fact, when the compression
is such that a horizontal line from the point which we wish to use on
the expansion line will cut the compression line, as Fx, gives a simple
process for finding the steam accounted for by the indicator corrected
both for clearance and compression. It will be remembered that the
formula when the whole volume of the displacement was involved and
the pressure taken at the end of the stroke t was by formula (5),
13750w
M.E.P.'
128 THE STEAM ENGINE INDICATOR
where w was the weight per cubic foot of steam at the terminal pressure.
If instead of measuring the pressure at the terminus of the stroke t,
we take any other time point, as F or D, the volume involved will be
to the whole displacement volume as xF or dD is to the length of the
diagram ay. If as before F =the fraction of the stroke completed at
the point chosen for measurement, as F, Fig. Ill, and X=the portion
of the return stroke uncompleted at the point chosen on the com-
pression line, then F X (i.e., jF jX, Fig. Ill) will be the fraction
of the whole length of the diagram occupied by the line XF, included
between the expansion and compression lines. Substituting for w in
formula (5) w/ = the weight per cubic foot at the pressure measured
at point F, and multiplying by the fraction F X, we get the steam
accounted for per horse-power and per hour, reducing the complete
formula to
13750 .
RULE. From the fraction of the stroke completed at the point chosen
on the expansion line subtract the fraction of the stroke uncompleted at
the point on the compression line which is in the same horizontal line. Mul-
tiply the difference by the weight per cubic foot of steam at the pressure
measured at the points chosen and by the quotient of 13,750 divided by the
mean effective pressure. The final product will be the weight of steam
accounted for per horse-power per hour.
When the terminal pressure is so high or the compression is so small
that a horizontal line would cut the admission rather than the com-
pression line, the point X will be independently located and formula (9)
used rather than to construct the extension of the compression line into
the clearance, though the simple method just described would still be
used on speculative or theoretical work. If the horizontal line intersects
the junction of the compression and admission lines as at B, the portion
X of the stroke uncompleted at this point becomes zero. If the hori-
zontal line crosses the admission line, as at Dd, X becomes minus, and
the .distance from the admission line A a to the point d where the hori-
zontal crosses the compression line must be added to F. The value
FX, however, would in this case be more easily arrived at and may
be found in any case by dividing the length of the horizontal line, as
dD, included between the expansion lines, by the length of the diagram ay.
RULE. Draw a line across the diagram parallel with the atmospheric line.
Divide the length of that portion of this line included between the expansion
and compression lines by the extreme length of the diagram, and multiply
the quotient by the weight per cubic foot of steam at the pressure indicated
by the height of the horizontal line. Multiply this product by the quotient
STEAM CONSUMPTION FROM THE DIAGRAM 129
of 13,750 divided by the mean effective pressure, and the result will be the
pounds of steam accounted for per horse-power per hour.
This rule is identical with the other, the proportion of the line of
quantities to the length of the diagram being arrived at differently.
It can be deduced from the formula algebraically as follows: When
the points F and X are at the same height w x =w f , and the formula
becomes
STEAM ACCOUNTED FOR BY MULTIPLE-CYLINDER DIAGRAMS.
We have seen that the amount of steam in the cylinder is different
at different points in the stroke, increasing by re-evaporation as the
stroke progresses. The same thing holds true in a multiple-cylinder
engine. A portion of steam is measured off by the cut-off valve of the
high-pressure cylinder. This portion in passing through the series of
cylinders develops a determined amount of power. If the quantity of
steam remained constant the quantity per horse-power hour would be
the same whether measured immediately on the closure of the high-
pressure cut-off valve or just before its final release in the low-pressure
cylinder. But its quantity is constantly changing and more steam will
be found to be accounted for per horse-power hour at the terminal end
of the low-pressure than at any other point, under ordinary conditions.
The steam accounted for may be computed at any point between cut-off
and release on a diagram from any cylinder by the same rules and
formulas used for simple engines, but in order that the area, stroke
and number of revolutions may cancel, as shown, that M.E.P. must be
used which would be equivalent in effect in the cylinder with which
we are working to the aggregate of the several mean effectives in their
respective cylinders.
The effect of a given mean effective pressure is proportionate to the
displacement per unit of time of the cylinder in which it works. A
given mean effective pressure will produce twice the power in* a cylinder
having twice the area, with the same piston speed. So if it is wished
to find how much M.E.P. would be necessary to develop an amount
of power in the low-pressure cylinder equivalent to that developed by a
given M.E.P. in the high, the M.E.P. must be divided by the ratio of the
displacements between the high- and low-pressure cylinders. To find
this ratio multiply the square of the diameter, the stroke, and the revolu-
tions per minute of each cylinder together, and divide the product from
the larger cylinder by that from the smaller. As in ordinary multi-
130 THE STEAM ENGINE INDICATOR
cylinder engines all the cylinders have the same length of stroke an
number of revolutions per minute, these factors cancel, and the oper;
tion is reduced to dividing the square of the diameter of the larg(
cylinder by the square of the diameter of the smaller, or dividing tl
larger by the smaller diameter and squaring the quotient.
RULE. To refer the mean effective pressure of one cylinder to anothe
multiply the given M.E.P. by the ratio between the cylinder displacemen
if the cylinder to which it is to be referred is smaller, or divide if it is i\
larger.
EXAMPLE. In a compound engine having cylinders 12 and 24 inch
in diameter, running at the same piston speed, the diagrams show \
pounds of M.E.P. in the high-pressure and 9.18 pounds in the low. Ref
the mean effective pressure to the low-pressure cylinder.
The ratio between the cylinders is
(24 -5-12) 2 =4.
Then 38 pounds in the high-pressure cylinder would be equaled 1
38-^4=9.5 pounds in the low pressure. Add this to the 9.18 poun
shown by the low-pressure diagram and we have 9.5 +9.18 18.68 poun
of mean effective pressure which would be required to do in the lo 1
pressure cylinder alone the work of 38 in the high and 9.18 in the lo
In working out the steam accounted for per horse-power per hour fro
the low-pressure diagram therefore the M.E.P. used would be 18. '
pounds.
When working from the high-pressure diagram the M.E.P. of t
low-pressure diagram must be referred to the smaller cylinder. (
account of the smaller displacement, it would require four times
much pressure (4 is the ratio between the cylinder displacements)
do the work in the high-pressure cylinder as in the low, so that to <
the work of 9.18 pounds M.E.P. in the low-pressure cylinder wou
require 4X9.18 =36.72 in the high. Add to this the 38 pounds indicati
by the high-pressure diagram and find 36.72+38=74.72 pounds as t]
M.E.P. to be used in the formula when the steam accounted for
computed from the high-pressure diagram. With a triple- or quadrupl
expansion engine proceed the same way.
With this aggregate M.E.P. proceed as though the diagram we
from a single-cylinder engine. When the mean effective is referred
the high-pressure cylinder it is liable to become much larger than ai
actually obtained, and to exceed the limit of the values given in Table V
We therefore publish Table VII, taken from the Ashcroft book of instru
tions for the Tabor indicator (a continuation of that table), giving tl
13750
values of ., _, _. for mean effective pressures from 100 to 250 pounds.
STEAM CONSUMPTION FROM THE DIAGRAM
131
If instead of making a table of
13750
for various mean effective
M.E.P.
pressures we make one of I3,7o0w for various values of w, we avoid
using a table to find the weight per cubic foot of steam. Such a table,
computed by J. W. Thompson, M.E., is printed on page 132. Finding
in this table the value for the pressure at the point chosen for measure-
ment, divide it by the M.E.P. and multiply the quotient by F X, or
by the ratio of the horizontal line across the diagram to the total length
of the diagram. When points on the expansion and compression lines
are at different heights the other process will be more convenient.
TABLE VII
13750
VALUE OF
M.E.P.
M.E.P.
Lbs.
13750
M.E P.
Lbs.
13750
M.E.P.
M.E.P.
Lbs.
13750
M.E.P.
Lbs.
13750
M.E.P.
Lbs.
13750
M.E.P.
M.E.P.
M.E.P.
M.E.P.
101
136.1
131
104.9
161
85.4
191
71.9
221
62.2
102
134.8
132
104.1
162
84.8
192
71.6
222
61.9
103
133.4
133
103.3
163
84.3
193
71.2
223
61.6
104
132.2
134
102.6
164
83.8
194
70.8
224
61.3
105
130.9
135
101.8
165
83.3
195
70.5
225
61.1
106
129.7
136
101.1
166
82.8
196
70.1
226
60.8
107
128.5
137
100.3
167
82.3
197
69.7
227
60.5
108
127.3
138
99.6
168
81.8
198
69.4
228
60.3
109
126.1
139
98.9 !
169
81.3
199
69.0
229
60.0
110
125.0
140
98.2
170
80.8
200
68.7
230
59.7
111
123.8
141
97.5
171
80.4
201
68.4
231
59.5
112
122.7
142
96.8
172
79.9
202
68.0
232
59.2
113
122.6
143
96.1
173
79.4
203
67.7
233
59.0
114
120.6
144
95.4
174
79.0
204
67.4
234
58.7
115
119.5
145
94.8
175
78.5
205
67.0
235
58.5
116
118.5
146
94.1
176
78.1
206
66.7
236
58.2
117
117.5
147
93.5
177
77.6
207
66.4
237
58.0
118
116.5
148
92.9
178
77.2
208
66.1
238
57.7
119
115.5
149
92.2
179
76.8
209
65.7
239
57.5
120
114.5
150
91.6
180
76.3
210
65.4
240
57.2
121
113.6
151
91.0
181
75.9
211
65.1
241
57.0
122
112.7
152
90.4
182
75.5
212
64.8
242
56.8
123
111.7
153
89.8
183
75.1
213
64.5
243
56.5
124
110.8
154
89.2
184
74.7
214
64.2
244
56.3
125
110.0
155
88.7
185
74.3
215
63.9
245
56.1
126
109.1
156
88.1
186
73.9
216
63.6
246
55.8
127
108.2
157
87.5
187
73.5
217
63.3
247
55.6
128
107.4
158
87.0
188
73.1
218
63.0
248
55.4
129
106.5
159
86.4
189
72.7
219
62.7
249
55.2
130
105.7
160
85.9
190
72.3
220
62.5
250
55.0
132
THE STEAM ENGINE INDICATOR
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STEAM CONSUMPTION FROM THE DIAGRAM
133
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CHAPTER XVI
DIAGRAMS FROM COMPOUND ENGINES, CLEARANCE
NEGLECTED
So far as taking the diagrams from a compound engine, figuring
the horse-power, the water accounted for, etc., the directions already
given will suffice. The diagram will be taken just as though the cylinder
operated upon were the only one concerned, the selection of the spring
being governed by the range of pressures in that cylinder and con-
venience in reducing the diagrams to a common scale, as will be explained.
The indicated horse-power is found by computing the horse-power of
each cylinder in the ordinary manner from its own diagrams and adding
the indicated horse-power of the several cylinders for the total power
of the engine. The steam accounted for per horse-power per hour is
obtained by referring the mean effective pressures of the several cylinders
to the cylinder in which the pressure used for the computation is measured,
as explained in the chapter on steam consumption from the diagram.
Each diagram is a representation of the distribution and use of steam
in the conditions of its own cylinder, and may be studied in connection
with a theoretical diagram for these conditions, just as a diagram from
a single cylinder engine would.
In order to study the action of the steam in the engine as a whole,
however, and to compare it with an ideal expansion of steam through
the range adopted, the diagrams must be studied in their relation to one
another, and this involves their reconstruction in several particulars.
In the first place, to be comparable, the diagrams must be upon the same
scale. For the high pressures used in the initial cylinder of compound
engines a stiff spring must be used. In order to get a large diagram
on the low-pressure cylinder a spring of lower scale is used. When we
wish to compare the resulting diagrams we must reduce them to the
same scale, and as we can work more accurately upon a large than a
small scale, it is preferable to increase the height of the high-pressure
diagram to that which it would have been if taken with the same spring
as the other.
Suppose we have a compound engine with the low-pressure cylinder
twice the diameter of the high, cutting off at a quarter stroke in both
cylinders, with a boiler pressure of 160 pounds absolute and 26 inches
134
DIAGRAMS FROM COMPOUND ENGINES, CLEARANCE NEGLECTED 135
of vacuum, the stroke of both cylinders being equal; and that from
this engine we had got the diagrams, Fig. 112, with an 80 scale, and
Fig. 113, with a 20 scale. ; Neglecting for the present the influence of
clearance, let us combine them so as to show the continuous action of
the steam in the whole engine.
If the high-pressure diagram had been taken with a 20 instead of
an 80 spring every point upon it would have been g-=4 times as high
above the atmospheric line as the diagram
shows it. The first step, therefore, is to re-
draw this diagram four times its present height.
Divide the diagram into a convenient
number of equal parts and erec
\
High
Pres
SCAL
X 1
10
13
FIG. 112.
15 16
etr.N.T.
ordinates upon the divisions. In Fig. 112 sixteen spaces have been
used, as they are easily obtained by successive halvings; or the spacing
may be done by using the scale diagonally across the diagram, as in
Fig. 74. Measure the distances from the atmospheric line to the forward-
and backward-pressure lines of the diagram on each ordinate, and transfer
these distances, multiplied by four, to the cor-
responding ordinate upon the larger diagram.
On ordinate 8, for example, the distances
A B and AC in Fig. 114 are four times
the distances ab and ac on the cor-
Low Pressure
20 SCALE
FIG. 113.
i
responding ordinate in Fig. 112. A pair of proportional dividers will be
found convenient for this work. Drawing a line through the points thus
indicated, we obtain the diagram shown in Fig. 114. AVhere sudden
changes of pressure occur, so that it would be difficult to draw the line
correctly between points so far apart, additional ordinates may be put
136
THE STEAM ENGINE INDICATOR
"~ -~^
4^ in, as at x, Fig. 112, putting an ordinate in th
\
X
\
same position on the reconstructed diagram.
\ We can now consider the diagrams
somewha
1 in their relation one to another by placin
\ them together, as shown in
Fig.
114
, where t
\ the low-pressure diagram
is just
as it wa
\ drawn by the indicator.
The
steam is e*
\ panded to about 40 pounds,
exhausts int
\
the receiver, and the space between th
\
back-pressure line of
the
high-pressui
\ l diagram and the steam line of
the
lo\\
1
pressure shows the loss in
going throug
i
i
the ports and receiver between the tw
i
i
k
cylinders.
But even now we are not able to corr
\pare the diagrams
with a
theoretics
i
diagram showing the expansion
of th
1
steam from the initial
pressure to th
,
terminal in the
low-pressure
cylir
\
\
\ der. To do this they must
be re
\
\ duced to the same scale of volume
V
c
If the area of the hi^
;h-pressui
\
\ piston was
one square
foo
\
then every
foot of
movemer
\
\ of that piston would expan
I
1
\
the
steam
behind
\
Si
one cubic
foo
\
\
s x s
x
\
\
\
I \
\
e
~\
E
H,
v ^_
d
B
^^
/
/
^ :
_--'
^^.
^
A
FIG. 114.
DIAGRAMS FROM COMPOUND ENGINES, CLEARANCE NEGLECTED 137
If the low-pressure piston has twice the diameter of the high
it would have four times the area, and each foot of movement
of the low-pressure piston would add four cubic feet to the
volume of the steam. One foot of movement of the low-
pressure piston is equal, then, to four feet of the high; and
since the movement of the piston is represented by the length
of the diagram, the high-pressure diagram, to be comparable
to the low, should be only one-fourth the length of the low-
pressure diagram.
This calculation has been made on the assumption that
the larger cylinder had twice the diameter of the smaller and
that the strokes were equal. In general the diagrams should
be to each other in length as the volumes of their respective
cylinders. The volume of the cylinder (clearance neglected)
is the cross-sectional area multiplied by the length of the
stroke; the area is the square of the diameter multiplied by
0.7854. Then letting
d= diameter high-pressure cylinder;
D= low-pressure cylinder;
/ = length stroke high-pressure cylinder;
L= low-pressure cylinder;
the ratio of the lengths of the diagrams would be
d 2 X 0.7854 Xl
D 2 X 0.7854 XL'
The decimals cancel, and as the stroke is ordinarily the
same in both cylinders the lengths usually cancel also, so
that usually the ratio of the diagram length is
In our case we found this ratio to be J, that is,
the high-pressure diagram must be \ as long as
the low.
Lay off on the admission end of the
enlarged diagram, Fig. 114, a length
^s,
ATMOSPHERIC
ABSOLUTE ZERO
FIG. 115.
138 THE STEAM ENGINE INDICATOR
equal to J- the length of the low-pressure diagram, divide it int<
as many spaces as the original diagram was at first divided, 16 ii
this case, and erect ordiriates as shown. Then transfer the pressure;
on the ordinates of the large diagram to the corresponding ordinate;
of what will be the shortened diagram. For instance, we made a do
d on the last ordinate of the shortened diagram at the same height ai
the point D, where the line touches the last ordinate of the large diagram
another at e on the second ordinate; counting from the right, at the sami
height as E on the corresponding ordinate of the large diagram; am
so on for both the forward and back pressure lines upon all the sixteei
ordinates. Connecting these points we get the diagram shown by thi
dotted line, as though it had been taken with a 20 spring and only one
quarter the movement to the paper barrel that the low-pressure diagran
had. If this diagram is placed above the low-pressure diagram, as ii
Fig. 115, we have a representation of the continuous action of the stean
and can draw about it the theoretical diagram, as shown by the dotte(
line, showing how much of the inclosed area is covered by the diagram;
from the engine, and how nearly perfect the utilization of the stean
has been.
CHAPTER XVII
DIAGRAMS FROM COMPOUND ENGINES, CLEARANCE
CONSIDERED
IN the last chapter was described the combination of diagrams from
the various cylinders of a compound engine so as to be comparable with
an equivalent action of the steam in a single cylinder.
Clearance was neglected for the sake of simplicity, but it
now becomes necessary to proceed to the consideration of
the effect of clearance in such a combination. Its treat-
ment is shown in Fig. 116 for a two-cylinder engine in
which the diameters of the cylinders are as 2 to 1, making
the volumes for equal strokes as 4 to 1. In the low-
pressure cylinder the clearance is -fa, or 8J per cent of
the displacement. Draw the line of zero pressure, per-
fect vacuum OX, Fig. 116, and at a distance ab (=-^3-
the length of the low-pressure diagram) from the ad-
mission line erect the line OA of zero volume. Then
set the reconstructed high-pressure diagram at such a
distance from the line OA that the clearance space cd
shall be the proper percentage of the length de of that
diagram. In other words, add the clearance line in the
usual manner to the reconstructed diagrams, and in
combining make the clearance lines coincide.
Let us consider a little further the action of steam
in compound engines, using for the purpose con-
ventional or theoretical diagrams drawn upon
the same scales
for both cylin-
ders. Let us
take first the en-
gine with no re-
ceiver but with
the high-pressure
exhausting directly into the low, and the pistons moving together, as in a
tandem, or with equal opposite movements, as with a cross-compound the
cranks of which are opposite. Suppose the cut-off to take place in the
139
FIG. 116.
140
THE STEAM ENGINE INDICATOR
high-pressure cylinder at one-quarter stroke, C, Fig. 117, in which case
the steam would be expanded to the terminal pressure T, say 30 pounds.
Now suppose a valve as at A, Fig. 118, between the two cylinders, to open,
and the pistons to commence to move toward the left. As the area of
the low-pressure cylinder is four times as great as that of the high, every
inch of movement will add four times the volume in the low-pressure
cylinder that is taken up by the forward movement of the high-pressure
piston. When, for instance, the pistons have made one-quarter of their
c\ c \
-
FIG. 117.
stroke, and are in the position shown, the steam will still have three-
quarters as much room to occupy in the high-pressure cylinder as it
had before the return stroke was commenced, and in addition it will
have one-quarter of the low-pressure cylinder. As the low-pressure
has four times the volume of the high, the steam will have in one-quarter
of the low-pressure as much room as it had in the high-pressure cylinder
at the end of the forward stroke, besides the three-quarters of its original
volume, still left in the high-pressure cylinder. Its volume has, there-
fore, at the point under consideration, been expanded to If that at the
DIAGRAMS FROM COMPOUND ENGINES, CLEARANCE CONSIDERED 141
termination of the forward stroke, and knowing that the pressure is in-
versely as the volume (see Chapter on Expansion Line), we divide the
terminal pressure 30, by If, and find a little over 17 pounds as the pres-
sure at the point e, Fig. 117. Locating the pressure at the other points
in the same manner, we find that the back pressure on the high-pressure
piston, which in this case would also be the forward-pressure on the low-
FIG. 118.
pressure, would follow the line TA, Fig. 120, with an uninterrupted pas-
sage of the steam between the cylinders throughout the stroke.
If the point of cut-off in the high-pressure cylinder were to change,
it would change the terminal pressure T in that cylinder, and correspond-
ingly increase or diminish the initial pressure in the low. Instead of
cutting off at (7, Fig. 117, one-quarter of the stroke, the steam were cut
Low Pressure
1 Vol.
FIG. 119.
off at c, one-third of the stroke, the terminal pressure would be t instead
of T, and the back-pressure line of the high-pressure diagram, which is
at the same time the steam line of the low-pressure diagram, would be
ta. If, on the other hand, the cut-off is earlier in the high-pressure,
the initial for the low-pressure will be lowered and less work will be done
in that cylinder.
142
THE STEAM ENGINE INDICATOR
Now suppose that instead of remaining open, the valve A, Fig. 118,
between the cylinders, closed at quarter stroke, giving a one-quarter
cut-off in the low-pressure cylinder as well as in the high. This would
carry the expansion line of the low-pressure along the line eE, but it
would shut up the exhaust of the high-pressure cylinder, and compres-
sion would commence at e, running the back-pressure line rapidly up
in the direction ef.
Now suppose that instead of exhausting directly into the low-pressure
FIG. 120.
cylinder the high-pressure exhausts into a receiver or reservoir, from
which the low-pressure takes its supply, as in Fig. 119.
This receiver can be so large in proportion to the cylinders that the
fluctuations in the quantity of steam taken from and delivered to it
during the stroke will affect the pressure but little. Understand that
the low-pressure cylinder must take out of the receiver as much steam
as the high-pressure delivers to it. It is obvious that it cannot con-
tinuously take out more and if it does hot take out as much the steam
would accumulate in the receiver and raise the pressure until the volume
DIAGRAMS FROM COMPOUND ENGINES, CLEARANCE CONSIDERED 143
taken by the low-pressure contained as much steam as the high-pressure
was delivering. Suppose the capacity of the receiver to be ten times
that of the high-pressure cylinder. At the beginning of the stroke there
will be one volume in the high-pressure cylinder and ten volumes in the
receiver of steam at the terminal pressure y=30 pounds, 11 volumes
in all. At quarter stroke, Fig. 118, there will be three-quarters of a volume
in the high-pressure, ten volumes in the receiver, and one volume in the
low, one-quarter of the low-pressure cylinder being equal to the whole
FIG. 121.
volume of the high, llf volumes in all. The pressure will have fallen-
then to only TT-~ of the original 30, or to a little over 28 pounds, as at
1 1 . /o
g, Fig. 120, instead of to 17, as at e, Fig. 117. Suppose now the valve
A, Fig. 118, to close, i.e., cut-off to occur on the low-pressure cylinder.
The expansion in that cylinder would follow the line gh, Fig. 120, while
the high-pressure cylinder would continue to exhaust into the receiver,
and at the end of the stroke would have taken back that excess of three-
quarters of a volume which it had when cut-off occurred on the low-
144 THE STEAM ENGINE INDICATOR
pressure, and brought the pressure back from 28 to 30 pounds, the coun-
ter-pressure following the line gi.
Suppose a heavier load to come on the engine, changing the point
of cut-off from one-quarter to one-third stroke. First let us consider
the effect with a fixed cut-off on the low-pressure cylinder, which we
will allow to remain at one-quarter stroke. The. result is shown by the
dotted diagram in Fig. 120. The greater portion of the increase of load
is taken by the low-pressure cylinder, on which the cut-off has not changed,
the area gained by the later cut-off in the high-pressure cylinder being
largely offset by the loss of area due to the increase of back pressure
through the higher terminal. Notice also that with the low-pressure
cut-off set at one-quarter, the volume which the low-pressure cylinder
takes out of the receiver each stroke just equals the volume delivered
to it by the high-pressure, so that whatever the terminal pressure, the
high-pressure diagram will end in a point.
Suppose now there had been an automatic cut-off on both cylinders,
and that the low-pressure cut-off changed to one-third stroke too. The
low-pressure cylinder has four times the volume of the high. One-third
of the low would have JX4 = 1J times the volume of the high, so that
for every cubic foot of steam that the high-pressure cylinder delivers
to the receiver the low-pressure cylinder takes out 1J cubic feet. Since
there is a greater volume going out of the receiver than there is going
into it, the pressure will fall until the greater volume taken out by the
low-pressure cylinder contains only the same quantity or weight of
steam as that delivered in a smaller volume by the high-pressure cylin-
der. In other words, the receiver pressure will fall until the cylinderful
of steam delivered to the receiver at 40 pounds will expand to 1J times
its volume in the receiver, which should require a receiver pressure of
40 -r- 1^=30 pounds. We should therefore have a diagram like Fig. 121,
where the dotted lines represent both cylinders cutting off at one-quarter
stroke, the full lines, both cylinders cutting off at one-third stroke.
CHAPTER XVIII
ERRORS IX THE DIAGRAM
IN treating of the reducing motion we have described in kind the
various errors to which it is liable. It now remains to consider them
in degree. Fig. 122 shows the error which would result from taking
\
FIG. 122.
the motion from a pin on a lever like Fig. 123, vibrating through about
90. A diagram which should follow the full line would be distorted
by this arrangement to that shown by the dotted lines. The cut-off
would appear too early, the expansion line would hold up too much for
the apparent cut-off, but would be below its proper position in the first
of the stroke, crossing the correct line at the center, and making the ter-
minal appear higher than it should be. It makes the release and com-
pression appear late and reduces the area of the diagram, and hence
the apparent indicated horse-power. Both the right- and left-handed
diagrams, i.e., those from the head and the crank end, are affected the
same way. When you see a diagram which resembles the dotted one
in Fig. 122, look over the reducing motion.
145
146
THE STEAM ENGINE INDICATOR
As just stated, Fig. 122 was drawn upon the assumption that tin
lever vibrated through 90. This is excessive. It is recommended t<
use a lever not less than one and a half times the length of the stroke
This gives a vibration between 35 and 40. In Fig. 124 is shown th<
distortion due to using a lever like Fig. 123, one and a half times th<
length of the stroke, taking the motion from a pin in the lever, and {
cord led off parallel to the guides.
The distortion is much less than with the shorter lever, and th<
purpose for which the diagram is taken must determine whether thi
amount can be tolerated for the sake of simplicity in the reducing
motion. When we measure for a carpet we do not take into accoun
FIG. 124.
the fractions of an inch, and when we weigh coal we do not pay atten
tion to the ounces. In ordinary indicating to see that the valve gea
has not become deranged, to make a rough cast of the power for pur
poses of record, etc., we need not be so precise as though we were testing
a cruiser, when the difference of one pound mean effective pressure wouh
mean ten thousand dollars to the builders; or a steam plant where i
few horse-power more or less would determine for or against the guar
antee; or when with Hirn, we undertake to trace from the diagran
the distribution and disposition of the heat units going through the
plant. This is when the indicator and its user must get right dowr
to extreme accuracy, and after every precaution is used the results wil
still be too far from the truth. This motion cannot be corrected b}
ERRORS IN THE DIAGRAM
147
the use of a brumbo pulley, for the pulley would not move through equal
arcs for equal movements of the cross-head. It would pull the cylinder
a distance equal to 4', 5', Fig. 122, in the middle of the stroke, and
only that equal to 1', 2', etc., at the ends, so that instead of being
equally divided for equal movements of the piston the diagram would
be divided irregularly, as are the spaces on the arc. If this arc were
straightened out, reduced to the length of the diagram without dis-
turbing the proportion of the spacing, corresponding ordinates, as 3'/,
erected, and the pressure transferred to these from the proper ordinates,
as from B to /, we should get the diagram represented by the broken
FIG. 125.
line, showing that the use of the arc is productive of greater accuracy
in this case. With a lever of constant length, as in Fig. 125, however,
the use of the arc introduces an error. (See chapter on reducing
motions.)
Leading the cord away from the reducing motion in any other direc-
tion than parallel with the guides introduces an error. Let us see how
much. Suppose we have a pantograph, as in Fig. 126, or a reducing
wheel, as in Fig. 127, and that instead of leading the cord off in the
direction AB parallel with the guides, we led it off in the direction shown,
the angle being 30 when the cross-head is nearest to the cylinder.
148
THE STEAM ENGINE INDICATOR
The resulting distortion of the diagram will be that shown in Fig. 128.
When the piston has traveled one-eighth of its stroke the pencil, which
should be at A, will be a, and so on for the other ordinates. Notice
that this makes the apparent cut-off earlier on the head-end and later
on the crank-end. At all times and in both directions the travel of
the paper-drum is less than it should be, altogether it looks to be more
when traveling to the right. Thus, starting with at the right the
pin on the pantograph, when the engine cuts off at quarter stroke, will
have moved a distance equal to 02, but the movement of the paperr
drum will be equal to OC only. When the stroke is completed the
pantograph pin has traveled through a distance equal to 08, but the
paper-drum has traveled through OD, the comparative movement of
the pantograph pin and the paper-drum for successive eighths of fche
FIG. 126.
stroke, being shown by the bold-faced figures 1, 2, 3, etc., and the dotted
ordinates to the right of them. The full-line ordinates are placed upon
the equal eighths of the shortened diagram OD. Starting at D back-
ward the pantograph pin would move in the first eighth of the stroke
to 1, in the second eighth to 2, etc. The corresponding position of the
pencil on the paper would be at the dotted ordinates as before, a less
distance, it will be seen, than the actual movement in every case; but
when we come to erect the full-line ordinates on the even eighths of the
shortened diagram they fall behind the dotted lines, showing how we
can get an apparently excessive movement on the crank end with a
movement really less than it should be. Notice that the distortion due
to this cause tends to throw the card out of balance, affecting the dia-
ERRORS IN THE DIAGRAM
149
grams from the head- and crank-ends in different directions, not in the
same way as did the distortion of the lever motion in Fig. 122.
Another source of error in the diagram, briefly referred to before, is
that due to a long and indirect passage from the cylinder to the indicator.
The errors introduced are: less realized pressure, lower compression
and higher terminal. This subject has been discussed in the various
technical papers, and varying opinions have been elicited. In order
to determine this question, the author, in connection with Mr. A. C.
Lippincott, undertook the tests resulting in the diagrams shown in Figs.
129 to 138. We designed the apparatus shown in Fig. 129.
A a
Crank
End
Head End
SCc 6
FIG. 128.
rr, A". JT.
Our first test was made on an 11X11 Ball & Wood engine at the
Roosevelt Building, New York, through the courtesy of Mr. Thomas
Murphy, the engineer in charge. The engine was running at 270 revolu-
tions per minute, driving an electric generator with a very constant load,
so constant that when the pencil was held on for 20 revolutions the line
of the diagram was scarcely thickened. Three and a half feet of half-
inch pipe connected the cross F with the tee G, and a similar length was
used between E and H J the right and left nipple I being about 7 inches
long. This pipe was thoroughly heated and drained before each card
was taken, by turning the three-way cock, so that steam could issue
150
THE STEAM ENGINE INDICATOR
through the little escape orifice, opening the drips and the cock B, the
engine running continuously.
Having taken a diagram with the direct connection, the three-way
cock was reversed and the cock B opened, compelling the steam to travel
through the loop of about 8 feet of |-inch pipe and fittings to the indicator.
The result is shown in Fig. 130. The pencil was allowed to pass over
the card 20 revolutions as before, to insure that the diagram was not
erratic or exceptional. This experiment was repeated over and over
again. Whenever we switched to the direct connection we got Fig.
To Cylinde
FIG. 129.
131, whenever with the direct connection we opened the connection to
the piping, we got Fig. 132; and when the steam was compelled to pass
around to the further side of the three-way cock to get to the indicator
we got Fig. 130. The passages through the pipes and fittings were
perfectly clear, and ordinary |-inch plug cocks, half-inch fittings and the
three-way cock regularly supplied with the indicator were used. The
nipple A is screwed into the hole in the cylinder ordinarily provided
for the indicator cock. When the handle of the three-way cock is
ERRORS IX THE DIAGRAM
151
thrown to the right, as in the drawing, the steam enters the cock from
the left and has a direct passage to the indicator, and if the plug cock
FIG. 130.
FIG. 131.
FIG. 132.
B is closed the steam has no access to the extraneous piping, and the
indicator is about as directly connected as it would be with the usual
152
THE STEAM ENGINE INDICATOR
nipple elbow and single cock. The plug cock C is open and D is closed,
so that when B is opened steam can pass clear around the loop and enter
the three-way cock at the right, as it must do to get to the indicator
when the handle of the three-way cock is swung the other way. Any
sort of a circuit of piping, steam hose, or fittings may be connected at
EF for the steam to pass through on its way to the indicator. The handle
of the three-way cock can also be left so as to give the steam a direct
passage to the indicator and the cock B left open so as to obtain the
effect of the addition to the clearance without the friction of the
pipe.
Fig. 129 shows the apparatus as applied to a cylinder tapped at the
side as are engines of the Corliss type. For engines tapped on top of
FIG. 133.
the cylinder it is turned as shown in Fig. 133, which will explain the
necessity of the cocks C and D.
Fig. 134 is a card on which all three diagrams were taken as quickly
as the cocks could be shifted. Through the kindness of Mr. Gillespie,
in charge of the steam plant of the Young Women's Christian Associa-
tion Building, we were able to repeat the experiment on a 12X12 New
York Safety engine, which also ran at 270 revolutions, but was more
heavily loaded. This load was also electrical and very steady, Fig.
135 being its diagram with the direct connection and 35 passages of the
pencil.
Fig. 136 shows very prettily the effect of added clearance obtained
by opening the cock B, leaving the passage to the indicator still direct.
ERRORS IN THE DIAGRAM
153
Fig. 137 shows the diagram obtained with the indirect connection,
the pencil passing 25 times over.
Puwr, K.T.
FIG. 134.
FIG. 135.
FIG. 136.
Fig. 138 shows all three diagrams on the same card.
Seven or eight feet of pipe is of course excessive for an indicator
connection, though not much more so than 6 feet of steam hose. If
154
THE STEAM ENGINE INDICATOR
such a difference as this exists with 8 feet there should be a visible dif-
ference with 4r| feet, or even with the ordinary side pipe on a long cylinder.
Fig. 131 is a photographic reproduction of the diagram obtained from
the first engine with the direct connection, the pencil passing over it
FIG. 137.
fully twenty times. A new card was placed upon the paper-barrel and
another diagram taken under the same conditions as Fig. 131. Then
leaving the three-way cock so that the steam passed directly to the in-
dicator, the cock B was opened, adding the pipe to the volume of the
Power, .y.,T
FIG. 138.
clearance, and another diagram was drawn upon the same card. The
result is shown in Fig. 132, and is as would have been expected less
realized pressure, lower compression, and higher terminal. For greater
distinctness, we have dotted the line of the first diagram, which will
be seen to be identical with Fig. 131.
CHAPTER XIX
MEASURING THE CLEARANCE
THE clearance of a steam engine includes not only the space between
the piston face and cylinder head, but all of the port or ports up to the
valve face when the engine is on the dead center. It is necessary to
know its amount whenever any accurate calculations are made con-
cerning the action of the steam. It is usually expressed as a fraction of
the volume displaced by one stroke of the piston, or what is equivalent
to this, a percentage of the length of the stroke.
Fig. 139 shows a single-valve engine with the steam chest at the
side of the cylinder, and the closely shaded portion represents the
FIG. 139.
clearance. If the valve and piston are tight, the amount of the clear-
ance may be found both easily and accurately as follows:
Put the engine carefully on the dead center in the usual manner
and set the valve so that it covers the port, blocking it, if necessary,
to hold it up against the seat. Make a fine mark aa on the cross-head
and guides.
Remove the indicator plug P and pour in enough water to fill the
clearance space up to the under face F of the plug, which is the highest
point of the clearance. Measure or weigh carefully the amount of water
poured in and make a note of it.
155
156
THE STEAM ENGINE INDICATOR
Now turn the engine over until the cross-head has moved 3 or 4
inches of its stroke and pour in a second quantity of water exactly equal
to that required to fill the clearance space. Then back the engine up
until the water rises again to the original level F. The cross-head and
piston will now be in the position shown in Fig. 140 and the shaded
portion will be filled with water. Make a second mark b on the guides
opposite the mark a on the cross-head. The dotted line XY, Fig. 140,
represents the original position of the cross-head, and the space to the
right of it will be that occupied by the second quantity of water and
will represent a volume equal to the clearance. The fraction of the
stroke occupied by this equivalent volume will be the distance ab on
the guides, and all that is needed to find the clearance in decimal parts
s
! A
1 \ i
i \^ ^/
i
3
K
)
1
FIG. 140.
of the stroke is to measure in inches the distance ab and divide it by
the length of the stroke in inches.
For instance, if in an engine of 15 inches stroke the distance ab was
found to be 1& inches (1.1875), the clearance would be _i__- =0.0791
lo
or 7-j 9 ^ per cent of the stroke.
In engines of the Corliss type, however, the indicator opening is not
on top of the cylinder, but usually at the side, as shown in Fig. 141.
This objection can be overcome by screwing into the indicator elbow a
short, vertical piece of pipe just long enough to bring the top end to
the level of the valve face as in the figure. Then pour in the water until
it overflows the top end of this pipe, leaving the steam valve open about
as for lead to prevent entrapping air at the highest point. If this air
were not allowed to escape, it would be compressed until its pressure
equaled the slight head of water and it would not be possible to fill the
entire clearance space with water.
MEASURING THE CLEARANCE
157
The distance ab on the guides is then found as before by pouring
in a second quantity of water and bringing it to the original level. It
is well to note here that if the second pouring is exactly equal to the
first, we shall have put in too much by the quantity contained in the
short piece of pipe from P to T, Fig. 141. This amount may be obtained
FIG. 141.
by measurement before the pipe is screwed into place and should be
deducted from the second pouring in order to correctly locate point 6,
Fig. 142. In the above method, it is not necessary to measure or weigh
the quantity of water in any particular units; a mark on a bucket, any
FIG. 142.
known number of canfuls or a balancing weight of unknown value will
give two equal quantities.
If a vessel graduated in U. S. liquid measure, i.e., quarts, pints, and
gills, be used to measure the first pouring, the second operation, by
which mark b was located, may be omitted and the clearance found by
a simple calculation.
158 THE STEAM ENGINE INDICATOR
Suppose it required- 3 quarts 1 pint and 2 gills of water to fill the
clearance of an engine 15 inches diameter by 15 inches stroke. In U. S.
liquid measure
4 gills =1 pint
2 pints = 1 quart
4 quarts = 1 gallon
Since 1 gallon =231 cubic inches,
1 gill = 7.22 cubic inches
1 pint =28.88 cubic inches
1 quart =57. 75 cubic inches
The volume of the clearance is then
3 quartsX57.75 = 173.25
1 pint X 28.88= 28.88
2 gills X 7.22= 14.44
Total =216.57 cu. in.
The cylinder area is 15 2 X0.7854 = 176.71 square inches, and thi
piston displacement for one stroke is 176.71X15=2650.7 cubic inches
Therefore the clearance is 216.6-^2650.7=0.0817 or 8.17 per cent o
the stroke.
P.]ven if the measuring apparatus is not graduated finer than pints
it is possible to estimate with reasonable accuracy to quarter pints
so that the error will not be serious.
There is another good way to find the clearance without locating
point 6 on the guides: it requires only the use of a pair of avoirdupois
scales, such as grocers use, and a bucket holding two or more time;
the water required to fill the clearance.
To illustrate more clearly we will work out an example. Fill thi
bucket with water and weigh it carefully; let us assume that the bucke
and water weigh 20 pounds. Now fill the clearance space from the bucket
taking care to spill none of the water, and again weigh the bucket am
the remaining water; suppose that it now weighs 12 pounds and 2 ounces
It has then required 20 pounds 12 pounds 2 ounces =7 pounds 14 ounce
= 7-} or 7.88 pounds of water to fill the clearance space. The volum<
of a pound of water at the temperature of the usual room is 27.7.
The volume of the clearance is 7.88X27.7=218 cubic inches. Th
percentage of clearance is then found as before by dividing the clearance
volume by the product of the piston area and stroke, i.e., by the pistoi
displacement.
MEASURING THE CLEARANCE
159
In engines having indicator openings on the side, a correction must
be made for the short piece of pipe, as previously mentioned.
We now have three methods of finding clearance :
1. By linear measure, using two equal quantities of water.
2. By liquid measure.
3. By weight.
There is still another method, which is as simple as any; it is shown
in Fig. 143. A bucket or other vessel is suspended above the cylinder
and a constant supply of water is furnished it by means of a hose or pipe.
From the bottom or side of the bucket a small rubber hose or J-inch
pipe leads the water to the cylinder. The head of the water on the dis-
charge end of the small pipe must be kept constant either by regulating.
Supply
FIG. 143.
the supply to the bucket so as to keep the water level constant, or bjr
allowing the bucket to overflow continually. If the latter is done, the
overflowing water must not follow along the small pipe and so get into
the cylinder. This can be prevented by using a siphon to supply the
cylinder. The operation is as follows: Put the engine on the dead center
and note the time in seconds required to fill the clearance space. Shut
off the supply to the cylinder and put the engine on the other center.
Then through the same pipe and under the same head fill the entire
cylinder and clearance space up to the original level, noting separately
the time in seconds required to fill the cylinder.
Since the quantity of water flowing through a constant opening
under a constant head is exactly proportional to the time, the clearance-
is equal to the first period of flow divided by the second period.
160 THE STEAM ENGINE INDICATOR
For example, suppose it requires 1 minute and 25 seconds (85 seconds)
to fill the clearance space and 28 minutes and 20 seconds (1700 seconds)
to fill the cylinder. The clearance is then '=0.05 or five per cent
of the stroke.
The smaller the supply pipe to the cylinder, the longer it will take
to fill the clearance space and the less the percentage of error in obser-
vation.
Various modifications of the details will suggest themselves for
vertical engines, locomotive engines and others. In every case it is
important to leave an opening for the escape of air at the highest point.
Suppose that instead of having plugs in the indicator openings the
engine were provided with a j-inch standard indicator pipe and 3-way
cock, as shown by the dotted lines in Fig. 139. The clearance space
would then include that portion of the indicator pipe from the face of
the 3-way cock to the cylinder connection. For a 15X15 inch engine,
this additional amount would be about 11 J inches of J-inch standard
pipe. The internal area or this pipe is 0.53 of a square inch, and the
added clearance volume due to it is 0.53X11J=6.10 cubic inches. In
finding the clearance of an engine equipped thus, the water should be
poured in through the indicator connection until it is just visible from the
top. When the side pipe is used and it is necessary to use a riser the
contents of the riser must be found separately and deducted.
The publication of the foregoing direction for measuring clearance,
prepared by Mr. C. G. Robbi s of the editorial department of Power,
called out the following suggestion from Prof. John E. Sweet:
The engine valve and piston must be made tight and the engine set
on the dead center as in any case. Set upon a platform or counter scale
a pail of water and an empty pail, and balance them by the weight on
the scale. Fill the clearance space from the pail of water, and then from
outside source put enough water in the empty pail to again balance
the scale. Mark the cross-head and guide, turn the engine forward
a little way and put the water in the second pail in the cylinder, and turn
the engine back until the water comes up in the indicator hole, and again
mark the cross-head as was clearly explained in the foregoing.
In the case of a Corliss engine where a stand pipe is necessary to
fill through the indicator hole, after the scale has been balanced with
the pail of water, and empty pail as above described, take off the stand
pipe, fill it with water and put it in the pail of water, then after putting
on the stand pipe proceed as before.
So far we have in a simple way obtained two marks on the guide
which truly represent the distance the piston has to travel to equal
the clearance, and whether the result is in even inches, which would
MEASURING THE CLEARANCE
161
render it simple to determine the per cent, or in fractions, which would
complicate the problem, the following graphic method answers equally
well, and is readily performed by anyone who can use a rule.
Draw a horizontal line as in Fig. 144, and lay off the stroke of the
engine AB } and draw the vertical line from B; at C draw another vertical
line the same distance from A as the two lines marked on the guide.
From A with 100 units of any comvenient length measure up on the
line #, that is to say, if the stroke of the engine be 11 inches, measure
up from A to some point on the line F to D 12J inches, which is a hundred
Length of Stroke -
FIG. 144
C "deanncoJA.
units of J inch each, then from D to A strike the straight line E and as
many J inches as there are from A to F, so much will be the per cent
of clearance in the engine. If the stroke of the engine is between 13
and 18 inches, 18} inches may be used for the line E when ^ of an inch
will be the unit, or if from 18 to 24 inches, then 25 inches for the line X
with J inch as a unit and so on.
Of course this is not the mathematicians' way of doing things, but
it eliminates many sources of error, is quick, easy to understand, and
just as accurate as the man who does it is able to work, and that is the
measure of accuracy in about everything.
TABLE I. HYPERBOLIC LOGARITHMS.
X.
Loga-
rithm.
X.
Loga-
rithm.
X.
Loga-
rithm.
X.
Loga-
rithm.
.OI
00995
1-57
.45108
2.13
.75612
2.69
.98954
.02
.01980
1.58
45742
2.14
. 76081
2.70
99325
03
.02956
i.59
46373
2.15
76547
2.71
99695
.04
.03922
i. 60
.47000
2.16
.77011
2.72
.00063
05
.04879
1.61
.47623
2.17
77473
2.73
.00430
.06
.05827
1.62
.48243
2.18
77932
2.74
.00796
.07
.06766
1.63
.48858
2.19
78390
2.75
.01160
.08
.07696
1.64
.49470
2.20
. 78846
2.76
01523
.09
.08618
1.65
.50078
2.21
79299
2.77
.01885
.IO
09531
1.66
.50681
2.22
79751
2.78
.02245
.11
.12
. 10436
II333
i 68
.51282
2.23
2.24
.80200
.80648
I'K
.02604
.02962
13
. 12222
1.69
52473
2.25
81093
2.81
03318
.14
.13103
1.70
53063
2.26
81536
2.82
.03674
.15
13977
1.71
53649
2.27
.81978
2.83
.04028
.16
.14842
1.72
.54232
2.28
.82418
2.84
.04380
.17
.15700
1-73
.54812
2.29
82855
2.85
.04732
.18
16551
1.74
.55389
2.30
.83291
2.86
.05082
.19
17395
1.75
55962
2.31
83725
2.87
05431
.20
.18232
1.76
56531
2.32
84157
2.88
5779
.21
. 19062
1-77
57098
2-33
-84587
2.89
.06126
.22
19885
1.78
.57661
2-34
85015
2.90
.06471
23
.2O70I
1.79
.58222
2-35
85442
2.91
.06815
.24
.21511
.80
58779
2.36
.85866
2.92
.07158
25
.22314
.81
59333
2.37
.86289
2-93
.07500
.26
.23111
.82
.59884
2.38
.86710
2.94
.07841
.27
.23902
.83
. 60432
2.39
.87129
2.95
.08181
.28
. 24686
.84
.60977
2.40
87547
2.96
.08519
.29
25464
.85
.61519
2.41
.87963
2-97
.08856
30
.26236
.86
.62058
2.42
.88377
2.98
.09192
.31
.27003
.87
62594
2.43
.88789
2-99
.09527
.32
.27763
.88
63127
2.44
.89200
3.00
.09861
33
.28518
.89
63658
2.45
.89609
3.01
.10194
34
.29267
.90
.64185
2.46
.90016
3-02
.10526
35
.30010
.91
.64710
2.47
.90422-
3.03
.10856
1.36
30748
.92
65233
2.48
.90826
3.04
. i i i 86
1.37
.31481
93
65752
2.49
.91228
3.05
.11514
1.38
.32208
.94
.66269
2.50
.91629
3.06
.11841
L39
.32930
.95
.66783
2.51
.92028
3.07
.12168
1.40
33647
.96
.67294
2.52
.92426
3.08
12493
1.41
34359
97
.67803
2.53
.92822
3.09
.12817
.42
.35066
.98
.68310
2.54
93216
3.10
.13140
43
35767
99
.68813
2.55
.93609
3. II
.13462
44
36464
2.00
69315
2.56
.94001
3.12
13783
45
37156
2.01
.69813
2-57
94391
3.13
.14103
.46
37844
2.02
.70310
2.58
94779
3.14
.14422
47
38526
2.03
. 70804
2.59
.95166
3.15
.14740
.48
.39204
2.04
7 I2 95
2.60
95551
3.16
15057
.49
.39878
2.05
.71784
2.61
95935
3.17
15373
.50
.40547
2.06
.72271
2.62
96317
3.18
.15688
51
.41211
2.07
72755
2.63
.96698
3.19
. 16002
.52
.41871
2.08
73 2 37
2.64
.97078
3.20
16315
53
42527
2.09
737i6
2.65
97454
3.21
.16627
54
43178
2.10
.74194
2.66
97833
3.22
.16938
55
43825
2. II
. 74669
2.67
.98208
3.23
1.17248
.56
.44460
2.12
.75142
2.68
.98^82
3.24
I.T7SS7
162
TABLE I. Continued. HYPERBOLIC LOGARITHMS.
X'
Loga-
ja
Loga-
N.
Loga-
X.
Loga-
rithm.
HI
rithm.
rithm.
rithm.
!
3-25
17865
3.81
1.33763
4-37
1.47476 i
4-93
59534
3-26
.18173
3.82
1-34025
4.38
I-47705
4.94
59737
3-27
18479
3-83
1.34286
4-39
1-47933 !
4-95
59939
3-28
18784
3.84
1-34547
4.40
1.48160 ]
4.96
.60141
3-29
19089 i
3-85
1.34807
4.41
1.48387 1
4-97
60342
3-30
19392
3.86
1-35067
4.42
1.48614
4.98
60543
3-31
3.87
I-35325
4-43
1.48840 j
4.99
.60744
3-32
19996
3-88
I-35584
4.44
1.49065 |
5.OO
.60944
3-33
. 20297
3.89
1-35841
4.45
1.49290 j
5.01
.61144
3-34
20597
3.90
1.36098
4.46
I-495I5
5-02
61343
3.35
. 20896
I-36354
4-47
-49739
5.03
.61542
3-36
.21194
3-92
1.36609
4.48
i . 49962
5.04
.61741
3-37
.21491
3-93
i . 36864
4.49
1.50185
5.05
.61939
3-38
.21788
3-94
1.37118
4.50
i . 50408
5.06
62137
3-39
.22083
3-95
4.51
i . 50630
5.07
62334
3-40
.22378
3.96
1.37624
4.52
1.50851
5.08
62531
.22671
3.97
I-37877
4.53
1.51072
5.09
.62728
3-42
. 22964
3.98
1.38128
4-54
i 51293
.62924
3-43
3-44
.23256
23547
3-99
4.00
I.38379
i .'38629
ts
5.12
.63120
63315
3-45
23837
4.01
1.38879
4.57
-5I95I
5.13
63511
3-46
.24127
4.02
1.39128
4.58
1.52170
5.14
63705
3-47
.24415
4.03
1-39377
4-59
1.52388
5.15
.63900
3-48
-24703
4.04
1.39624
4.60
1.52606
5.16
.64094
3-49
- 24990
4.05
1.39872
4.61
1.52823
5.17
. 64287
3-50
25276
4.06
1.40118
4.62
L53039
5.18
.64481
3-5 1
4.07
i . 40364
4.63
1-53256
5.19
64673
3-52
.25846
4.08
1.40610
4.64
5.20
. 64866
3-53
.26130
4.09
1.40854
4-65
i "-53687
5.21
. 65058
3-54
.26412
4.10
1.41099
4-66
i 53902
5.22
65250
3-55
-26695
4.11
1-41342
4.67
54n6
5.23
.65441
3-56
.26976
4.12
1-41585
4-68
-54330
5.24
.65632
3-57
27257
4.13
1.41828
4-69
^- 54543
5.25
.65823
3.58
2/536
4.14
i .42070
4.70
i 54756
5.26
.66013
3-59
-27815
4-15
1.42311
! 4-71
i 54969 i
5.27
. 66203
.28093
4.16
1-42552
! 4.72
1.55181 1
5.28
66393
3*6i
28371
4-17
1.42792
i 4-73
1-55393 !
5.29
. 66582
3-62
.28647
4.18
1-43031
i 4-74
-55604 |
5.30
.66771
3.63
.28923
4.19
1-43270
4-75
1.55814
5.31
.66959
3.64
.29198
4.20
4.76
-56025
5-32
67147
29473
.29746
4.21
4.22
I-43746
1.43984
4-77
4.78
1-56235 :
1.56444
5.33
5.34
67335
67523
3.67
.30019
4-23
1.44220
4-79
1-56653 ,
5.35
.67710
3-68
.30291
4.24
I-4445 6
4.80
1.56862
5.36
.67896
3.69
4-25
i . 44692
4.81
1.57070
5.37
.68083
3-70
30833
4.26
1.44927
4.82
^57277
5.38
.68269
4-27
1.45161
4.83
1-57485
5.39
68455
3.72
31372
4.28
1-45395
4.84
1.57691
5.40
. 68640
3-73
.31641
4.29
1.45629
4.85
: 1-57898
.68825
3-74
.31909
4.30
1.45861
4.86
! 1.58104
5.42
.69010
3-75
.32176
4-31
1.46094
4-87
1-58309
5.43
.69194
3.76
32442
4.32
i .46326
4.88
I 1-58515
5.44
.69378
3.77
32707
4-33
I-46557
4^89
1.58719
5-45
.69562
3.78
.32972
4-34
1.46787
1 4.90
1.58924
5.46
69745
3-79
33237
4.35
i .47018
4.91
1.59127
5-47
.69928
3.8o
4.36
1.47247
u 4.92
I-5933I
5.48
1 .70111
163
TABLE I. Continued. HYPERBOLIC LOGARITHMS.
X.
Loga-
rithm.
N.
Loga-
rithm.
1
N.
Loga-
rithm.
N.
Loga-
rithm.
5-49
1.70293
6.05
i . 80006
6.61
1.88858
7.17
1.96991
5-50
1 - 70475
6.06
1.80171
6.62
1.89010
7.18
1.97130
5-5i
1.70656
6.07
1.80336
6.63
1.89160
7.19
1.97269
5-52
i . 70838
6.08
1.80500
6.64
1.89311
7.20
1.97408
5-53
i .71019
6.09
i . 80665
6.65
1.89462
7.21
J -97547
5-54
1.71199
6.10
1.80829
6.66
1.89612
7.22
1.97685
5-55
1.71380
6. ii
1.80993
6.67
1.89762
7.23
1.97824
5-56
1.71560
6.12
1.81156
6.68
1.89912
7.24
1.97962
5-57
1.71740
6.13
1.81319
6.69
1.90061
7.25
i .98100
5-58
1.71919
6.14
1.81482
6.70
1.90211
7.26
1.98238
5-59
i . 72098
6.15
1.81645
6.71
1.90360
7.27
1.98376
5-6o
1.72277
6.16
i. 81808
6.72
i .90509
7.28
5.6i
! 72455
6.17
1.81970
6.73
1.90658
7.29
1.98650
5.62
1.72633
6.18
1.82132
6.74
i . 90806
7.30
1.98787
5.63
I.728II
6.19
1.82294
6.75
1.90954
7.31
1.98924
5.64
I . 72988
6.20
1.82455
6.76
i .91102
7.32
1.99061
5.65
I.73I66
6.21
1.82616
6.77
1.91250
7-33
1.99198
5.66
! 73342
6.22
1.82777
6.78
1.91398
7-34
J - 99334
5.67
!- 73519
6.23
1.82937
6.79
I-9I545
7-35
1.99470
5.68
I 73695
6.24
1.83098
6.80
i .91692
7.36
i . 99606
5.69
1.73871
6.25
1.83258
6.81
1.91839
7-37
1.99742
5.70
I . 74047
6.26
1.83418
6.82
1.91986
7-38
1.99877
5-71
1.74222
6.27
I-83578
6.83
1.92132
7-39
2.00013
5.72
! 74397
6.28
I-83737
6.84
1.92279
7.40
2.00148
5-73
J-7457 2
6.29
i . 83896
6.85
1.92425
7.41
2.00283
5-74
1.74746
6.30
1.84055
6.86
1.92571
7.42
2.00418
5-75
i . 74920
6.31
1.84214
6.87
1.92716
7-43
2.00553
5-76
i . 75094
6.32
1.84372
6.88
1.92862
7-44
2.00687
5-77
1.75267
6.33
1.84530
6.89
1.93007
7-45
2.00821
5.78
i . 75440
6-34
1.84688
6.90
I-93I52
7.46
2.00956
1-75613
6.35
1.84845
6.91
1.93297
7-47
2.01089
5.80
1.75786
6.36
1-85003
6.92
1.93442
7.48
2.01223
5.8i
I-7595 8
6.37
1.85160
6-93
1.93586
7-49
2-01357
5-82
1.76130
6.38
I-853I7
6.94
1-93730
7-50
2.01490
5-83
i . 76302
6-39
I-85473
6.95
1.93874
2 .01624
5|4
1.76473
6.40
1.85630
6.96
1.94018
7.52
2.01757
i . 76644
6.41
1.85786
6.97
1.94162
7.53
2.01890
5-86
1.76815
6.42
1.85942
6.98
I-94305
7-54
2.02022
5.87
1.76985
6.43
1.86097
6-99
i . 94448
7-55
2-02155
5-88
1.77156
6.44
1.86253
7.00
I-9459I
7.56
2.02287
5.89
1.77326
6-45
1.86408
7.01
1-94734
7-57
2.02419
5.90
! 77495
6.46
1-86563
7.02
1.94876
7.58
2.02551
1.77665
6.47
1.86718
7.03
1.95019
7-59
2 .02683
5-92
! 77834
6.48
1.86872
7.04
1.95161
7.60
2.02815
5-93
i . 78002
6-49
i .87026
7.05
1-95303
7.61
2.02946
5-94
1.78171
6.50
1.87180
7.06
1-95444
7.62
2.03078
5-95
i 78339
6.51
1.87334
7.07
1.95586
7.63
2.03209
5.96
1.78507
6.52
1.87487
7.08
1.95727
7.64
2.03340
5-97
1.78675
6.53
1.87641
7.09
1.95869
7.65
2.03471
5.98
i . 78842
6.54
1.87794
7.10
i . 96009
7.66
2.03601
5-99
i . 79009
6.55
1.87947
7.11
1.96150
7.67
2.03732
6.00
1.79176
6.56
i . 88099
7.12
1.96291
7.68
2.03862
6.01
i . 79342
6.57
1.88251
7.13
1.96431
7.69
2.03992
6.02
i . 79509
6.58
1.88403
7.14
1.96571
7.70
2.04122
6.03
1.79675
6.59
1.88555
7.15
1.96711
7.71
2.04252
6.04
i . 79840
6.60
1.88707
7.16
i .96851
7.72
2.04381
164
TABLE I. Continued. HYPERBOLIC LOGARITHMS.
X.
Loga-
rithm.
X.
Loga-
rithm.
X.
Loga-
rithm.
X.
Loga-
rithm.
7-73
2.04511
8.30
2.11626 :
8.87
2.18267
9.44
2.24496
7-74
2 . 04640
8.31
2 . 1 1 746
8.88
2. 18380
9.45
2.24601
7-75
2.04769
8.32
2.II866
8.89
2.18493
9.46
2.24707
7.76
2.04898
8.33
2.II986
8.90
2.18605
9.47
2.24813
7-77
2.05027
8.34
2. I2I06
8.91
2.18717
9.48
2 . 24918
7-78
2-05156
8-35
2.12226
8.92
2.18830
9.49
2.25024
7-79
2.05284
8.36
2.12346
8-93
2.18942
9.50
2.25129
7 .8o
2.05412
8-37
2.12465
8.94
2.19054
9.51
2.25234
7.81
2.05540
8.38
2-12585
8.95
2.19165
9.52
2-25339
7.82
2.05668
8-39
2.12704
8.96
2.19277
9.53
2.25444
7.8 3
2-05796
8.40
2.12823
8.97
2.193 8 9
9.54
2.25549
7.84
2.05924
8.41
2. 12942
8.98
2.19500
9-55
2-25654
7.85
2.06051
8.42
2.I306I
8.99
2.19611
9.56
2.25759
7.86
2.06179
8.43
2.I3I80
9.00
2.19722
9-57
2.25863
7.87
2 . 06306
8.44
2.13298
9.01
2.19834
9.58
2.25968
7-88
2-06433
8-45
2.I34I7
9.02
2.19944
9-59
2.26O72
7.89
2.06560
8.46
2-13535
9.03
2.20055
9.60
2.26176
7.90
2 . 06686
8.47
9.04
2 .20166
9.61
2.26280
7.91
2.06813
8.48
2.I377I
9.05
2. 20276
9.62
2.26384
7.92
2 . 06939
8-49
2.13889
9.06
2.20387
9.63
2.26488
7.93
2.07065
8.50
2.14007
9.07
2.20497
9.64
2.26592
7-94
2.07191
8.51
2. I4I24
9.08
2 .20607
9.65
2.26696
7-95
2.07317
8.52
2.14242
9.09
2.20717
9.66
2.26799
7.96
2-07443
8.53
2-14359
9.10
2.20827
9.67
2.26903
7-97
2.07568
8.54
2.14476
9.11
2.20937
9.68
2 . 27006
7.98
2.07694
8.55
2-14593
9.12
2.2IO47
9.69
2.27109
7-99
2.07819
8.56
2.14710
9.13
2.2II57
9.70
2.27213
8.00
2.07944
8.57
2.14827
9.14
2 .21266
9.71
2.27316
8.01
2.08069
8.58
2.14943
9.15
2-21375
9.72
2.27419
8.02
2.08194
8.59
2. 15060
9.16
2.21485
9-73
2.27521
8.03
2.08318
8.60
2.15176
9.17
2.21594
9.74
2.27624
8.04
2.08443
8.61
2.15292
9.18
2.21703
9-75
2.27727
8.05
2.08567
8.62
2.15409
9.19
2. 2l8l2
9.76
2.27829
8.06
2.08691
8.63
2.15524
9.20
2. 21920
9-77
2.27932
8.07
2.08815
8.64
2. 15640
9.21
2.22O29
9.78
2.28034
8.08
2-08939
8.65
2.15756
9.22
2.22138
9-79
2.28136
8.09
2 . 09063
8.66
2.15871
9-23
2.22246
9.80
2.28238
8.10
2.09186
8.67
2.15987
9.24
2.22351
9.81
2.28340
8. ii
2.09310
8.68
2. l6l02
9.25
2 . 22462
9.82
2.28442
8.12
2.09433
8.69
2. 16217
9.26
2.22570
9-83
2.28544
8.13
2-09556
8.70
2.16332
9-27
2.22678
9.84
2.28646
8.14
2.09679
8.71
2-16447
9.28
2.22786
2.28747
8.15
2.09802
8.72
2. 16562
9.29
2.22894
9.86
2 . 28849
8.16
2.09924
8.73
2. 16677
9.30
2.23001
9-87
2.28950
8.17
2.10047
8.74
2. 16791
9-31
2.23109
9.88
2.29051
8.18
2. 10169
8.75
2.16905
9-32
2.23216
9.89
2.29152
8.19
2.I029I
8.76
2 . I7O2O
9-33
2.23323
9.90
2-29253
8.20
8.21
2.I04I3
2-10535
8-77
8.78
2.I7I34
2.17248
9-34
9-35
2.23431
2.23538
9.91
9-92
2.29354
2-29455
8.22
2.10657
8-79
2.17361
9.36
2.23645
9-93
2.29556
8.2 3
2.10779
8.80
2.17475
9-37
2.23751
9.94
2.29657
8.24
2.10900
8.81
2.17589
9.38
2.23858
9-95
2.29757
8.25
2. II02I
8.82
2.17702
9-39
2.23965
9.96
2.29858
8.26
2. III42
8.83
2.17816
9.40
2.24071
9-97
2-29958
8.27
2.II263
8.84
2.17929
9.41
2.24177
9.98
2.30058
8.28
2.11384
8.85
2.18042
9.42
2.24284
9.99
2.30158
8.29
2.U505
8.86
2.l8l5S
9-43
2 . 24390
INDEX
ACCURACY of reducing motions, 14.
Accuracy of the spring, 5.
Action of the steam shown by the diagram,
41.
Adjustment of the cord, 34.
Admission line, 44.
Allowance for piston rod, 104.
Angularity of cord affecting diagram, 147.
Apparatus for testing for the effect of long
indicator piping, 150, 152.
Assembling the instrument, 36.
Attachment of the indicator, 28..
BACK pressure line, 67.
Balancing the effort, 111.
Brumbo pulley, 13.
Brumbo pulley affecting diagram, 147.
Buckeye reducing motion, 24.
CARE of the instrument, 1.
Care of the instrument after using, 39.
Cause of drop in steam line, 47-50.
Centering the diagram, 34.
Change of load affecting distribution in
compound engine, 141.
Clearance affecting compression, 72.
Clearance; effect on combined diagrams
from compound engines, 141.
Clearance line located from expansion
curve, 61.
Clearance, measurement of, 155.
Coffin averaging instrument, 94.
Combining diagrams from compound en-
gines, 135.
Compound-engine diagrams, clearance con-
sidered, 139.
Compound-engine diagrams, clearance neg-
lected, 134.
Compression affected by clearance, 72.
Compression and clearance loss, 74.
Compression in condensing engine, 71.
Compression line, 70.
Computing horse-power, 96.
Connection of reducing lever to cross-head,
14, 15, 16.
Connection of reducing motion to the in-
strument, 32.
Conventional steam chest diagram, 49.
Cord, 33.
Cord adjustment, 34.
Corrected diagrams for head and crank
end, 112.
Correcting theoretical M.E.P. for departures
from the ideal, 118.
Counterpressure line, 67.
Cushioning effect of compression, 73.
Cylinder condensation, 50, 76.
DEFECTS of pendulum reducing motion,
14.
Determination of leakage, 63.
Determination of the point of cut-off, 60.
Diagram, the ideal, 41.
Diagrams for head- and crank-end, 112.
Diagrams from compound engines, clear-
ance considered, 139.
Diagrams from compound engines, clearance
neglected, 134.
Diagrams taken with excessive indicator
piping, 153.
Direction of lead of cord for pendulum
reducing motion, 13.
Dirt and scale in indicator piping, 31.
Distortion of diagram due to shortness of
pendulum lever, 15.
Distortion of diagram varying with man-
ner of attachment of cord, to the cross-
head, 16, 17.
Drawing the theoretical expansion curve, 55.
Drop in compression line, 75.
Drop in steam line, 47.
Drum-spring tension, 5.
EARLY release, 65.
Economy of expansion, 53.
Effect of brumbo pulley on diagram errors,
147.
Effect of change of load in compound engine,
144.
Effect of clearance on compression, 72.
167
168
INDEX
Effect of clearance on M.E.P., 114.
Effect of compression on clearance loss, 74.
Effect of condensation and re-expansion, 61.
Effect of long indicator piping, on diagram,
149.
Effect of quality of steam on expansion
line, 61.
Effect of receiver capacity on the com-
bined diagram, 142.
Effect of small exhaust pipe on back pres-
sure, 67.
Effect of small ports on back pressure, 67.
Effect of a variable cut-off in low-pressure
cylinder, 142.
Effect on diagram of angularity of cord, 147.
Effect on diagram of length of reducing
lever, 15.
Errors in the diagram, 145.
Expansion, ratio of, 114.
Experiments with excessive piping, 149.
Exhaust line, 67.
/"^ RAPHIC method of determining clear-
\J ance, 61, 161.
HATCHET planimeter, 92.
Horse-power constant, 100.
Table of, 107.
Horse-power corrected for piston rod, 104.
Horse-power (definition), 96.
Horse power developed by oaoli separate
stroke, 106.
IMPROPER connection of the instru-
ment, 29.
Indicator piping affecting diagram, 149.
Indicator piping experiments, 149.
Interchangeable (right- and left-hand) in-
dicators, 31.
LAW of expansion of steam, 55.
Leads, 9.
Leakage, 63.
Length of diagram, 12, 89.
Location of indicator connection, 27.
Loop at release, 65.
Loop in compression line, 75.
Loss of pressure between boiler and steam
chest, 47.
Lost motion in the indicator, 3.
Lubrication of the instrument, 10.
M
.E.P. affected by clearance, 114.
Mean effective pressure (definition),
77.
Mean effective pressure by computation,
113.
Mean effective pressure from diagram, 77.
Mean pressure of the ideal diagram, 115.
Mean pressure per pound of initial, 115.
Table of, 115.
Measuring clearance, 155.
Measuring loops, 82.
Measuring loops with planimeter, 88.
Measuring ordinates on the diagram, 77.
Measuring scales, 9, 79.
Methods of drawing the theoretical ex-
pansion curve, 55.
N
EGATIVE loop, 82-88.
PANTOGRAPH, 18.
Pantograph table, 19.
Paper suitable for cards, 10.
Paper, putting on, 37.
Parallelism, 3.
Parallel rules, 81.
Pencil holders, 6.
Pendulum lever, 11.
Piping affecting diagram, 149.
Piping experiments, 149.
Piston rod area allowance, 104.
Piston speed, 97.
Table of, 101, 102.
Planimeter, 83.
Plotting the expansion curve, 55.
Point of "cut-off, 60.
Point of release, 64.
Proportional movement of pencil, 4.
RATIO of expansion, 114.
Reading the planimeter, 85.
Reading the vernier, 85.
Receiver capacity affecting distribution, 142.
Reducing motion, 11.
Reducing wheels, 26.
Reduction of compound engine diagrams to
correct scales for combining, 135.
Relation of pressure and volume, 55.
Release, 64.
Removal of dirt and scale in indicator
piping, 31.
Right- and left-hand instruments, 31.
Rod connection for reducing lever, 16.
Rule for horse-power, 96.
Rule for mean effective pressure, 118.
Rule for mean pressure, 114.
Rule for steam accounted for by indicator,
123.
s
CALES, 9, 79.
Selection of an indicator, 1.
INDEX
169
Separate diagrams for head- and crank-
end, 112.
Setting the pantograph, 19.
Slotted connection for reducing lever, 14, 15.
Spacing ordinates on the diagram, 78.
Springs, 5, 6, 7, 8, 36.
Steam accounted for by the indicator, 119.
Steam-chest diagrams, 49.
Steam consumption from the diagram, 119.
Steam consumption in compound engine,
129.
Steam line, 47.
Sweet's method for measuring clearance,
160.
TABLE for computing mean and initial
pressures, points of cut-off and ratios
of expansion, 115.
Table for computing steam consumption
values of 13750 W, 132.
Table for computing steam consumption
13750
values of 100 to 250 pounds, 131.
Table for computing steam consumption
values of
E p up to 100 pounds, 125.
Table for using the pantograph, 19.
Table of horse-power constants, 107.
Table of hyperbolic logarithms, 1G2.
Table of ideal mean effective pressures, 115.
Tapping the cylinder, 27.
Test for accuracy of reducing motion, 26.
Testing the spring, 5.
VACUUM springs, 7.
Variable cut-off on low-pressure cyl-
inder, 142.
Variations of compression with back pres-
sure, 72.
Vernier, 85.
Volume of steam per hour per horse-power,
table of 125-131.
W
IRE, used as indicator cord, 33.
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