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>ook»s 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 loss — 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 oft7 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 X4 2° =40. 2 X2 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 wrill 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 wrould 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 ef 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 0 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
\
0
|
<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 wrill 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 0 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 0 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 0 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 -
» 0
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 6E1, 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 0 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 0 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, 0 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 0 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 4.69—1.42=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. 242X.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 <