H
I LL INO I
S
UNIVERSITY OF ILLINOIS AT URBANA-CHAMPAIGN
PRODUCTION NOTE
University of Illinois at
Urbana-Champaign Library
Large-scale Digitization Project, 2007.
UNIVERSITY OF ILLINOIS
ENGINEERING EXPERIMENT STATION
BULLETIN No. 65 JANUARY, 1913
THE STEAM CONSUMPTION OF LOCOMOTIVE ENGINES
FROM THE INDICATOR DIAGRAMS
By J. Paul Clayton, Assistant, Mechanical Engineering Department,
Engineering Experiment Station
CONTENTS
I. INTRODUCTION PAGE
1. Prelim inary ..................... ....... .............. 5
2. Development of a New Analysis of Cylinder Performance... 6
3. Application of the Analysis to Locomotives ............... 7
4. Sources of Test D ata............... ........ ....... 7
5. Results of the Analysis of Locomotive Diagrams........... 8
6. Acknowledgm ent . . . . . . ........ ........................ . 8
II. APPLICATION TO SIMPLE LOCOMOTIVES OF THE n-Xe
METHOD FOR DETERMINING STEAM CONSUMPTION
7. Operative Conditions and Method of Application to Tests... 9
8. Relations of x. and n for simple Locomotive Engines........ 10
9. Relations of x, and n for the Purdue Locomotive........... 10
10. Relations of x, and n for all Simple Locomotives Tested..... 10
11. Effect on the Relations of x, and n of Varying the Speed.... 15
12. Effect of Varying the Cut-off Pressure .................... 18
13. Effect of Varying the Size of Cylinders.................... 20
14. Effect of Various Types of Valves .......... . . . . . . . ........ 20
15. Effect of the Use of Saturated and of Superheated Steam..... 20
16. Effect of Varying the Length of Cut-off ................... 21
17. Effect of Varying the Back Pressure ...................... 21
III. APPLICATION OF THE n-x, METHOD TO COMPOUND
LOCOMOTIVES
18. Operating Conditions and Methods of Application to Tests.. 21
19. Relations of x, and n for Compound Locomotives .......... 22
20. Relations of x, and n for High Pressure Cylinders.......... 23
CONTENTS
PAGE
21. Effect of Varying the Speed ...... . . . . . . . . . . . . . . . . . . 24
22. Effect of Varying the Range of Pressure................ 25
23. Relations of x, and n for Low Pressure Cylinders........... 28
24. Effect of Varying the Speed ....... ... ............ 28
25. Effect of Varying the Range of Pressure................ 29
IV. ANALYSIS OF THE n-Xc RELATIONS
26. Causes which Affect the n-x, Relations................... 29
27. Effect on the Relations of x, and n of Varying the Range of
Pressure................... .......... .............. 31
28. Effect on the n-x, Relations of Varying the Speed ......... 31
29. Values of x ............... ....... ............... 36
30. Values of x. and n Found for Various Types of Locomotives-
Their Use in Design ................................ 36
V. DIRECTIONS FOR DETERMINING THE STEAM CONSUMPTION
OF LOCOMOTIVES FROM THE INDICATOR DIAGRAM
31. Preparation of Indicator Diagrams and the Application of
the n-x, Method to the Determination of Steam Con-
sumption ............ . . ........................ 36
32. Other Applications of the n-x, Method .................. 38
33. Application of the n-x. Methods to Compound Locomotives 40
34. The Degree of Accuracy Obtained by the Use of the n-x,
M ethod......... . . .......................... . 41
VI. APPLICATION OF THE LEAKAGE, CLEARANCE, AND LOCATION
OF CYCLIC EVENTS METHODS TO LOCOMOTIVE TESTS
35. Uses of the Method for Detecting Leakage ................ 41
36. Uses of the Method for Determining Clearance............. 41
37. Uses of the Method for Closely Locating the Cyclic Events.. 42
VII. CONCLUSIONS ........................................ 42
APPENDIX I
I. THE LOGARITHMIC DIAGRAM.
1. Description of Logarithmic Cross-section Paper ........... 44
2. Construction of the Logarithmic Diagram................ 44
3. Method of Obtaining the Value of z, from Representative
Indicator D iagram s ........ ............. .......... 46
4. Typical Indicator and Logarithmic Diagrams from the
TAP.AmAt~VP.Q T~~ted.............................
Lo om ti e Teste .. ............................
CONTENTS 3
APPENDIX II
I. THE TESTS PAG,
1. General Dimensions of the Locomotives Tested ........... 61
2. Logs of Tests .................. .................... 61
LIST OF TABLES
1. General Data from Simple Locomotive Tested...... .............................. 11
2. General Data from Compound Locomotives Tested ................................. 11
3. Construction of the Logarithmic Diagrams of Test 110 of the Purdue Locomotive....... 45
4. Principal Dimensions of the Locomotives Tested .................................... 62
5. Log of Testsa of Purdue Locomotive..................................... ........ 66
6. Log of Tests of Locomotive No. 1499................................. . ......... . 70
7. Log of Tests of Locomotive No. 734.................................. ......... . 70
8. Log of Tests of Locomotive No. 5266...... ....................................... 70
9. Log of Tests of Locomotive No. 7510 .......................... ...... .......... . 72
10. Log of Tests of Locomotive No. 3395................................. .. ........ . 72
11. Log of Tests of Locomotive No. 585.................................. . . ........ 74
12. Log of Tests of Locomotive No. 929 .......................... ...... . . ......... 74
13. Log of Tests of Locomotive No. 2512............................................. 74
14. Log of Tests of Locomotive No. 535.............. . ......................... 76
15. Log of Tests of Locomotive No. 3000.......................... ....... . .......... 76
16. Log of Tests of Locomotive No. 628............................................. 76
LIST OF FIGURES
1. General Relations between xc and n for the Purdue Locomotive....................... 12
2. Relations of xc and n for the Various Speeds at 200 lb. Gage Pressure from the Purdue
Locom otive ................................................................ 12
3. Relations of xc and n for All Simple Locomotives Tested............................. 14
4. Relations of xc and Speed from the Purdue Locomotive for the Constant Value of n = 1.000.. 16
5. Relations of xc and Speed from All Simple Locomotives for the Constant Value of n = 1.000 . 17
6. Relations of xc and Cut-off Pressure from the Purdue Locomotive for Constant Speeds and
the Value of n = 1.000 ...................................................... 18
7. Relations of Xc and Cut-off Pressure from All Simple Locomotives for Constant Speeds and
the Value of n = 1.000 . .................................... ................. 21
8. Relations of Xc and n for High Pressure Cylinders of Compound Locomotives........... 24
9. Relations of xc and Speed for High Pressure Cylinders of Compound Locomotives for
Constant Value of n = 1.000, and for Center of Tests Corrected to Average Line...... 25
10. Relations of Xc and Range of Pressure (Cut-off to Average Back Pressure) from Compound
Locomotives for Constant Speeds and the Value of n - 1.000...................... 27
11. Relations of Xc and n for Low Pressure Cylinders of Compound Locomotives........... 28
12. Relations of xc and Speed for Low Pressure Cylinders of Compound Locomotives for
Constant Value of n - 1.000, and for Center of Tests Corrected to Average Line...... 29
13. The Relation, for Simple Locomotives, between Speed and the Value of n for Constant
Quality of Steam in the Cylinder at Cut-off ........................ .............. 39
14a and b. Representative Indicator and Logarithmic Diagrams Respectively from Purdue
Locomotive Test No. 110..................... .......................... 49
15a and b. Same for No. 1499, Test No. 118.......................................... 50
16a and b. Same for No. 734, Test No. 203.......................................... 51
17a and b. Same for No. 5266, Test No. 917............................. ....... .... 52
18a and b. Same for No. 7510, Test No. 1613............................... .......... 53
19a and b. Same for No. 3395, Test No. 2413......................................... 54
20a and b. Same for No. 585, Test No. 308 ......................................... 55
21a and b. Same for No. 929, Test No. 408.................. ....... .............. . 56
22a and b. Same for No. 2512, Test No. 510................ . .... ....... ........... 57
23a and b. Same for No. 535, Test No. 603................. .............. ......... 58
24a and b. Same for No. 628, Test No. 711..................... ................... 59
25a and b. Same for No. 3000, Test No. 802 ........................................ . 60
THE STEAM CONSUMPTION OF LOCOMOTIVE ENGINES
FROM THE INDICATOR DIAGRAMS
I. INTRODUCTION
1. Preliminary.-Steam locomotives in service on the road are
tested from time to time to obtain data as to their capacity and effi-
ciency, both being matters of vital importance in the successful and
economical operation of trains. The tests are made for various pur-
poses, among which the most important are those for the determination
of the indicated or dynamometer horse power, the measurement of the
steam and coal consumption per horse power developed either in the
cylinders or at the tender drawbar, and the adjustment of the valve gear.
Two general methods of testing locomotives for economy and capacity
are in use: (1) On the test plant, where all quantities measured may
be ascertained with great accuracy for any given set of conditions and
where conditions can be controlled. (2) On the road in regular service
by measuring the total coal and water used for all purposes, and by
determining the power developed by the engine either in the cylinders
by means of the indicator, or at the tender drawbar through the aid of
a dynamometer car.
The first method is the only one which permits the accurate deter-
mination of the effects produced by the varying conditions of service,
including the steam consumption per indicated horse power hour de-
veloped at a given rate of power.
The second method is of use only to measure the capacity and
average economy over a given run or over a long period of time. The
steam consumed at the several rates of power cannot be segregated in
this method due to the continual change of profile, necessitating cor-
responding changes in the rates of power, and to operating restrictions
imposed by different service conditions.
The use of steam for auxiliaries such as the air pump, the train-
heating system, blower, electric train-lighting sets, and also the loss of
steam or water through the safety valves, blow-off valves, and boiler
leaks render impossible the determination of the actual steam consumed
per unit of power developed by the engines, since from 2% to possibly
15% or 20% of the steam generated is used by the auxiliaries, or is lost.
It is thus practically impossible under ordinary conditions to measure
the actual steam consumption of the engines.
While indicator diagrams are generally taken during a locomotive
test, the use of these diagrams has been limited to the determination
ILLINOIS ENGINEERING EXPERIMENT STATION
of the indicated horse power, the correctness of the adjustment of the
valve gear, the effect of the exhaust nozzle on the back pressure, and
the diagram factor as a guide for future engine design. It has been
considered impossible to obtain a reliable estimate of the steam con-
sumed by the engines from the diagrams, because of the variable and
unknown "initial condensation" of steam up to the point of cut-off.
Further, no data have been secured from the diagrams regarding pis-
ton and valve leakage, and it is practically impossible correctly to locate
on the diagram the events of the stroke, cut-off, release, true compres-
sion, and admission.
2. Development of a New Analysis of Cylinder Performance.-As
the result of an investigation of the forms of the expansion and com-
pression curves which occur in indicator diagrams, new methods were
developed for obtaining a measure of the actual steam consumption from
the diagram alone, for detecting leakage into or out from the cylinder
while the engine is in normal operation, for determining the amount
of the clearance displacement, and for determining the location of the
events of the cycle.
The development of these methods has been described in detail in
Bulletin No. 58 of the Engineering Experiment Station and in a paper1
before the American Society of Mechanical Engineers. A short r6sum=
of the results will be given here.
The investigation disclosed the fact that the indicator diagram con-
tains in itself the evidence necessary for an almost complete analysis
of cylinder performance, the results of which have not heretofore been
considered possible.
In obtaining these results the indicator diagram was transferred to
logarithmic cross-section paper and a figure constructed which is called
a logarithmic diagram. By the aid of this diagram it was found that the
expansion and compression curves of all elastic media used in practice
obey substantially the polytropic law PVn- C, or in other words that
the curves become straight lines on logarithmic paper. From this fact
there were developed rational methods of approximating the clearance
of a cylinder, of closely locating the cyclic events, and of detecting mod-
erate leakage with the engine in regular operation.
It was discovered that the value of n in the law PVnT C is con-
trolled directly in steam cylinders by the quality of the steam mixture
which is present at cut-off, called xc, and that the relation of x0 and n
is practically independent of cylinder size and of engine speed for the
same class of engine as regards jacketing and back pressure. This fact
1 A. S. M. E. Journal, p. 539, April, 1912.
CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES
enables us to determine the actual amount of steam and water present
in a cylinder at cut-off from the experimentally determined relations
of xc and n, and thus to determine from the diagram the actual steam
consumed. This method of determining steam consumption will be
called the n - xc method in subsequent discussion.
For details of the processes described and for the exhibit of the
facts leading to the results mentioned, the reader is referred to Bulletin
1No. 58.
3. Application of the Analysis to Locomotives.-In view of the dif-
ficulties of determining the actual steam consumption of locomotive en-
gines on the road, and of segregating the consumption at different rates
of power, the advantages to be derived from applying the new analysis
to locomotives are apparent.
For this application it is extremely fortunate that there are in exist-
ence several hundred complete tests of almost all common types of sim-
ple and compound locomotives. These tests were run on locomotive test
plants under laboratory conditions and were carried on with great care.
4. Sources of Data.-The tests which have been analyzed in this
investigation comprise the Purdue tests made by Dr. W. F. M. Goss, the
St. Louis tests made by the Pennsylvania Railroad System, and later
tests made at Altoona, Pennsylvania, by the Pennsylvania Railroad
Company.
The Purdue tests were run at the locomotive testing plant of Purdue
University, Lafayette, Indiana, on a 16 in. x 24 in. simple locomotive.
The first series of tests analyzed were made in 1904-1905 with saturated
steam under different pressures varying from 120 lb. to 240 lb. gage,
and are noted in "High Steam Pressures in Locomotive Service," by
Dr. W. F. M. Goss. In the second series of tests which are described
in "Superheated Steam in Locomotive Service," by the same author, a
Cole superheater giving about 1600 F. of superheat was used under
various pressures.
The St. Louis tests which are described in "Locomotive Tests and Ex-
hibits," published by the Pennsylvania Railroad Company, were run at
the Louisiana Purchase Exposition at St. Louis, Missouri, in 1904. The
test plant was built by the Pennsylvania Railroad System, and erected
in the Transportation Building of the Exposition. Two simple and six
compound locomotives were tested at this plant, and the results from all
of these tests have been analyzed.
The Altoona tests were run on the same plant as the St. Louis tests
after that plant had been removed to its permanent location at Altoona,
Pennsylvania. Of the tests made there since 1904, two simple locomotives
ILLINOIS ENGINEERING EXPERIMENT STATION
using saturated steam and one simple locomotive using steam super-
heated about 2500 F. were among those analyzed.
The locomotives from which the tests were obtained comprise prac-
tically all important types in use in America and Europe except the
Mallet compound locomotive. Six simple and six compound locomo-
tives are represented.
5. Results of the Analysis of Locomotive Diagrams.-The develop-
ment of the n - xc method of determining from the indicator diagrams
the actual steam consumed, and of the other methods relating to leakage,
clearance, and cyclic events results in enlarging the scope of locomotive
tests and in making more accurate and valuable the information to
be gained from them.
It also makes more valuable the application of the results of loco-
motive tests on test plants to the conditions obtaining upon the road.
The application of these methods to road tests accomplishes the follow-
ing results:
(1) The steam consumption of the engines may be obtained from
the indicator diagram alone to a degree of accuracy greater than that
obtained by most full road tests.
(2) The n - x0 method of accounting for the actual steam consump-
tion of the engines in connection with the regular road test will give
reliable information as to the amount of steam used by auxiliaries and
that lost and wasted, such information being exceedingly difficult to
obtain at the present time.
(3) The existence, and in some cases the amount of leakage through
valves and into and out from the cylinders may be ascertained; the
spring of valve gears may be determined from the logarithmic diagrams
as shown by the change in location of the cyclic events under various
conditions.
(4) The clearance may be determined from the diagram to a sat-
isfactory degree of accuracy.
6. Acknowledgment.-Acknowledgment is made to Dr. W. F. M.
Goss for the use of material from the tests which he conducted at Pur-
due University; to Purdue University through Dean C. H. Benjamin
for the use of the original indicator diagrams from the Purdue tests;
to the Pennsylvania Railroad Company through Mr. C. D. Young, En-
gineer of Tests, for the use of the original indicator diagrams and of
material from the St. Louis tests, and also from later tests made at Al-
toona.
Valuable suggestions have been received from Dr. W. F. M. Goss,
Professor C. R. Richards, and Mr. F. W. Marquis.
CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES
Thanks are also due to Mr. A. F. Westlund for his efficient services
in preparing the data, and in checking the manuscript.
II. APPLICATION TO SIMPLE LOCOMOTIVES OF THE n - Xo METHOD FOR
DETERMINING STEAM CONSUMPTION
7. Operating Conditions and Methods of Application to Tests.-All
of the tests of simple and compound locomotives analyzed were run with
the locomotive operating under approximately constant conditions of
speed, cut-off, and boiler pressure as shown by the laboratory designation.
The duration of tests was in most cases from two to three hours, although
some few were run for only 30 minutes. All readings except the weight
of coal, this weight not being used in this investigation, and the indica-
tor diagrams were taken every ten minutes.
All water lost from injector overflow was returned to the feed tank,
or was caught, weighed, and allowance was made; all steam lost from
safety valves, calorimeters, etc., was allowed for and subtracted from the
quantity used per hour by engines; correction was not made in the log
for the moisture carried by the steam, as the actual amount of steam and
water present was desired; allowance was made for differences in height
of water in the gage glass between the start and end of a test; there-
fore as far as can be ascertained, the weight of total steam and water
used by engines per hour was correct, barring boiler leakage and the
usual experimental errors incident to short boiler tests.
To represent the tests, one complete set of indicator diagrams taken
at the same reading was selected, with an average mean effective pres-
sure nearest to the average mean effective pressure of the whole test.
These readings were taken when the boiler pressure was not more than
4 lb. from the average pressure prevailing during the test. Almost all
of the sets of diagrams were within Y2 of 1% of the average mean ef-
fective pressure for the test, hence the set selected could be taken
fairly to represent the whole test.
From the set so selected logarithmic diagrams were constructed in
accordance with the method described in Appendix I. The average val-
ues for n, xc, and the absolute pressure at cut-off, called p, were deter-
mined from the logarithmic diagrams in the manner described in Appen-
dix I, Article 3.
For the purpose of obtaining reliable results the following conditions
were imposed:
(1) The steam pressure was maintained fairly constant. Tests
having bad "steam failures" were rejected.
ILLINOIS ENGINEERING EXPERIMENT STATION
(2) The feeding of water was regular for the very short tests, short
tests having irregular feeding were not used.
(3) Representative diagrams were chosen.
(4) Tests rejected by the Pennsylvania Railroad for evident in-
consistencies were not used.
(5) Boiler pressures which varied between wide limits were not
used. Only those diagrams were used which were taken when the boiler
pressure did not vary more than 4 lb. from the average for the test.
All tests not rejected for the conditions mentioned were analyzed and
used. The tests rejected amounted to 5% of the total number available.
8. Relations of xc and n for Simple Locomotive Engines.--The
relations of xc and n from the cylinders of six typical simple loco-
motives were examined. The tests gave data as to the effect on the
relation of change of cut-off pressure, speed, cylinder size, the use of
saturated and superheated steam, and of various types of valves as they
affected valve leakage and steam distribution.
A total of 189 tests was analyzed. The general classification of
the locomotives tested and the number of tests analyzed for each one is
given in Table 1. The principal dimensions of the six locomotives are
given in Appendix II.
The general logs of the 189 tests are given in Tables 5-10 in
Appendix II. Only those quantities are given which relate to the
water fed and the values of xc and n.
9. Relations of x, and n for the Purdue Locomotive.-The values
of Xc and n from the 104 tests of the Purdue locomotive are plotted
in Fig. 1. These tests were run at the boiler pressures of 120, 160,
180, 200, 220, and 240 lb., and for each pressure at speeds of 97.5,
146, 195, and 243.5 r. p. m. The points comprise 35 tests with super-
heated steam, and 69 tests with saturated steam. The cut-off varied
from 12% to 46% of the length of the stroke. In spite of the widely
varying conditions of pressure, speed, cut-off, and quality of steam used,
it is seen that the general relation of xc and n is well defined.
The values of xc and n for the 19 tests run at 200 lb. pressure are
plotted in Fig. 2, showing the effect of various speeds for tests run at
the same boiler pressure. This figure contains lines which will be ex-
plained in connection with the determination of the influence of speed
upon the relations of xc and n.
10. Relations of xc and n for all Simple Locomotives Tested.-All
of the values of xc and n from the 189 tests of the six locomotives were
plotted in Fig. 3. This figure proves the relation of xc and n for one
class of engine, and it also proves the comparative independence of this
CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES
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ILLINOIS ENGINEERING EXPERIMENT STATION
105
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FIG. 2. RELATIONS OF Xc AND n FOR VARIOUS SPEEDS AT 200 LB. GAGE PRESSURE.
FROM THE PURDUE LOCOMOTIVE.
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CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES
relation from the effect of unduly varying pressures, speeds, sizes, types
of valves, and quality of steam used.
In the tests shown, the speeds varied from 40 to 280 r. p. m.; the
boiler pressures from 120 to 240 lb.; the displacement of the cylinders
from 2.8 to 9.1 cu. ft. (the cylinder sizes varying from 16 in. x 24 in.
up to 27 in. x 28 in.); the quality of the steam from saturation to 2500
F. of superheat and the cut-off from 12% to 50% of the stroke.
The tests were made with locomotives having common slide valves,
balanced slide valves, and piston valves. Almost every condition which
is ever present in a simple locomotive cylinder is present except speeds
below 40 and above 280 r. p. m., and lengths of cut-off over 50%.
The conditions mentioned were not obtained for the following rea-
sons: Speeds below 40 r. p. m., which were made in general at the
limit of adhesion, were not attempted because of the very uneven rota-
tional speed which caused slipping. This was due to lack of sufficient
flywheel inertia effect, this effect being present on the test plant and not
on the road because on the road the whole mass of the locomotive and
train caused the wheels to revolve at a uniform rate. The torque exerted
by the brakes attached to the supporting wheels was fairly uniform, and
the speeding up and slowing down of the drivers during parts of a rev-
olution caused slipping, thereby necessitating the regrinding of the sur-
face of the supporting wheels.
Lengths of cut-off exceeding 50% were not attempted because of the
danger of slipping, as the coefficient of adhesion of the driving wheels
upon the supporting wheels of test plants is far less than the coefficient
for clean dry rails.
Speeds exceeding 280 r. p. m. were obtained, but the effect of the in-
ertia of the indicator pencil motion at speeds of 320 r. p. m. and over,
distorted the expansion curves so greatly that good values of n could
not be obtained from them.
In determining the curve to represent the general relations of xc and
n shown in Fig. 3, several factors must be examined. It will be seen
that as 55% of the tests were from one locomotive and if each test
were given equal weight, then this locomotive, although the smallest one
tested, would govern over one-half of the evidence on which the rela-
tions for all locomotives would be founded. The tests run on each lo-
comotive were numerous enough that the average value of xc and n
for each one could be closely determined for its entire range of action.
As the locomotives tested represented practically all of the typical de-
signs of simple engines in modern use as to size, pressure, and valves,
ILLINOIS ENGINEERING EXPERIMENT STATION
it was decided to locate the "center of gravity" of the tests for each lo-
comotive and to give equal weight to the tests from each.
The center of gravity, or average value of the values of xc and n
for each locomotive was obtained by averaging the co-ordinates of x,
and n, and plotting the result as a cross through the same kind of point
which was used to represent the tests of each locomotive.
After the center of gravity of the tests of each locomotive was ob-
tained, the location of the center of gravity for all the locomotives was
determined in a similar manner by using the centers found for each one,
the center for all tests being plotted as a large cross in Fig. 3.
41tALV OF n FROM E,41PAN5V CURVt
FIG. 3. RELATIONS OF Xc AND n FOR ALL SIMPLE LOCOMOTIVES TESTED.
A straight line was then drawn through the center of gravity of the
tests of all locomotives, and was made to pass through the center of
the tests of locomotive No. 3395.
A straight line was used from the following considerations: Pre-
vious experience1 with the relations of xo and n in Corliss engines had
shown that the relation is a natural straight line for any one engine,
and that the relations of other engines of the same class might differ
a small amount as to the exact values obtained but that the slope of the
line obthined was substantially the same. The relation of xc and n
'Bulletin No. 58, p. 12. Engineering Experiment Station.
CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES 15
for adiabatic expansion as developed in Bulletin No. 58, is also a
straight line having a different slope.
The line as drawn also represents the centers of the tests of all the
locomotives with an average deviation of 2.4%, measured from the zero
value of xc. The average deviation of the points above the curve is about
the same as that of the points below the curve.
The center of gravity of all tests is shown by a concentric circle
which is 2.4% higher than the curve, due to the fact that the Purdue
locomotive has 55% of all the tests, and is the highest point in distance
measured above the line.
The points shown which are drawn with a circle around them were
not considered in drawing the line, as they were undoubtedly subject to
certain inconsistencies in testing, the exact causes of which have not
been determined.
The equation of the line selected is xc = 1.620 n - 0.909. This
equation expresses the results of all tests (except the five encircled
points) to an average deviation of 5%, regardless of sign, and to a
normal maximum deviation of about 9%.
It must be remembered, however, that all the errors of very short
boiler tests are present and their effect is included in the values of xc
which have been found. For this reason it is believed that the errors
given are considerably larger than the true ones, and that the line given
represents the true value of xc for a given value of n much more closely
than appears from the errors given.
The points plotted in Fig. 3, of which the average condition is rep-
resented by the line drawn, were examined for the effect on the value
of xc, for constant values of n, of varying the speed, cut-off pressure,
back pressure, size of cylinder, the type of valves used as regards leakage,
the use of saturated and superheated steam, and the length of cut-off. The
seven variables given comprise all of the variables present in the tests of
the six engines examined 'and also in each engine under different condi-
tions of construction and of operation.
11. Effect on the Relations of xc and n of Varying the Speed.-
In locomotive service the speed of engines under sustained conditions of
operation varies from about 40 up to perhaps 320 r. p. m., the latter
speed corresponding to a piston speed of 1500 ft. per min. for a 28 in.
stroke of the piston.
In stationary practice the speed of engines having the same length
of stroke or longer is between 60 and 150 r. p. m., thus having a
range of speed of only 90 r. p. m. between limits. Locomotive 'engines,
however, have a range of speed of about 280 r. p. m. between limits,
ILLINOIS ENGINEERING EXPERIMENT STATION
showing that the range is three times that of stationary engines of
equivalent size or power. It may be expected, therefore, that varying
the speed would affect in some degree the relations of x, and n for loco-
motive engines.
The method employed to examine the effect of change of speed upon
the relations of xc and n is illustrated in Fig. 4, which is derived from
JP£D-REkVWUr~KO3 P£R MlNTr£.
FIG. 4. RELATIONS OF Xc AND SPEED FROM THE PURDUE LOCOMOTIVE FOR THE
CONSTANT VALUE OF n= 1.000
Fig. 2. Fig. 2 gives the points derived from all tests of the Purdue
locomotive run at 200 lb. boiler pressure. The center of gravity of
each group of tests run at one speed was obtained and was plotted as a
cross through a point representing the speed examined. The full line
representing the average relation for all locomotives is drawn as shown.
Through the center of gravity for each speed a line was drawn, parallel
to the full line, to the intersection of the line n = 1.000. The point of
intersection therefore gives the value of xc, for the constant value of
n 1.000, at the speed examined. The points of intersection thus
obtained were plotted in Fig. 4, and are represented by the triangles.
Points obtained from the tests at other pressures were also plotted in
Fig. 4. This figure represents the relation of xc and speed at the value
of n = 1.000 for the series of pressures used.
It is evident from the points plotted in Fig. 4 that there is a definite
tendency for a high value of xc to be obtained as the speed increases,
the value of n remaining the same.
CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES
The process just described was repeated for the tests of all the loco-
motives and, together with the centers of gravity of the Purdue tests,
was plotted in Fig. 5. A group of points was obtained which like Fig. 4
showed that the average effect of increasing the speed was to increase
the value of xc, for constant values of n.
To represent the average effect of change of speed upon xc, the points
were divided into two groups and the center of gravity of each one was
found as indicated by the crosses; a line was then drawn through the two
centers as shown. The average deviation of the points irrespective of
sign is 3.2% (measured from the zero of xc), each point being weighted
in proportion to the number of tests it represented, except the Purdue
tests, which were rated at 4 tests each.
From Fig. 3 it is seen that the line crosses the value n = 1.000 at
xc = 0.711. On drawing the line x. = 0.711 in Fig. 5 it is found to
I'
JPAZOD - RfErOwUrOVJ PE Mf'VUTE
FIG. 5. RELATIONS OF Xe AND SPEED FROM ALL SIMPLE LocoAOTIVEs Fia P nE
CONSTANT VALUE OF n= 1.000
intersect the line representing the relations of xo and speed at 143 r. p. m.
This intersection indicates that the average relation of xo and n rep-
resented by the line xc= 1.620 n-0.909 is true for a speed of between
140 and 150 r. p. m. It also indicates: (1) That the average points
obtained at speeds below 140 r. p. m. fall below the line; (2) That the
average points obtained at speeds above 150 r. p. m. fall above the line;
(3) That by making corrections for the speed at which the indicator
diagrams were obtained, the average deviation resulting from determin-
ILLINOIS ENGINEERING EXPERIMENT STATION
ing the value of xc by the equations given is lowered from 5.0% to 3.2%.
The equation xc = 1.620 n - 0.909 was modified therefore by adding
a corrective term for speed which expresses the relation of x, and speed
shown in Fig. 5. The modified equation is
xc = 1.620 n - 0.909 - 0.00037 (143 - S)
where S = speed in r. p. m.
The corrective term drops out at 143 r. p. m., it lowers the value
of xc for speeds below 143 r. p. m., and raises the value of xc for higher
speeds.
The causes which operate to produce the effect upon the value of xc
due to change of speed are discussed in Section IV.
12. Effect of Varying the Cut-off Pressure.-The effect on the value
of x, due to variation of the cut-off pressure of the diagram, speed
and n being constant, was first observed from the Purdue tests, which
include a wide range of cut-off pressures resulting from boiler pressures
varying from 120 to 240 lb.
The points used were plotted in Fig. 6 and were obtained from Fig. 4
CUr-Oar pReWsu1 -s PAeR 0so// AYOaUT7r
FIG. 6. RELATIONS OF Xc AND CUT-OFF PRESSURE FROM THE PURDUE LOCOMOTIVE
FOR CONSTANT SPEEDS AND THE VALUE OF n= 1.000.
as follows, the example being taken from the tests at 20 miles per hour;
the cut-off pressures for the tests run at 220 lb. pressure and at the speed
of 97.5 r. p. m. (20 miles per hour) were averaged and found to be
176 lb. absolute; hence for n=1.000 and speed S=97.5 r. p. m.,
the value of xc obtained is 0.704. In a similar manner the tests at
*o
CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES 19
200 lb. pressure gave an average cut-off pressure of 157 lb. absolute and
a value of 0.707 for xc. This procedure gave the relation of xe and
cut-off pressure at the constant speed of 97.5 r. p. m. and n = 1.000.
In like manner the points for the other speeds were plotted in
Fig. 6, thus giving the relation desired for a series of constant speeds.
The points obtained were divided into four groups of six points each
and the center of gravity of each group found as indicated. The
centers were joined by a smooth curve. The curve as drawn indicated
that the value of xc at constant values of S and n reached an average
maximum value for a cut-off pressure of about 105 lb. absolute, and
that above 125 lb. a straight line was obtained.
It appears therefore that as the cut-off pressure increases the value
of x, decreases for constant values of S and n.
The effect on the relations of xc and n, due to change of cut-off
pressure, was compared with the same effect found in the previous
tests' on a Corliss engine and the relations for this engine for the value
of n = 1.052 and the speed of 120 r. p. m. was drawn dotted as shown.
The result of this comparison is a striking corroboration of the
curve as drawn. The curves are almost exactly parallel in the range
common to both. Both have a maximum point only 5 lb. apart, and
both have about the same slope for pressures above 120 lb. The form
of the curve representing the effect of cut-off pressure is thus fairly
well established.
The points in Fig. 5 were examined for the effect of cut-off pressure
in a way similar to that described for the Purdue tests, and the results
are given in Fig. 7. The centers of gravity obtained in Fig. 6 were
transferred to Fig. 7 to represent the Purdue tests.
The points of Fig. 7 give the average relation for all locomotives
of xo and cut-off pressure for a series of constant speeds and for
n= 1.000. The group of points obtained shows the same trend as
the Purdue tests although the vertical displacement due to speed is
present and makes the relation somewhat indefinite.
It was assumed that the Purdue tests shown in Fig. 6, because of
their large range of cut-off pressures and similarity to previous rela-
tions, represented the form of the curve, but was placed too high on the
plot to represent the average relation for all locomotives. Therefore
the center of gravity of all the points of Fig. 7 was found and a curve
drawn through this center similar in form to the Purdue relation.
It is seen from Fig. 7 that the range of cut-off pressures in simple
locomotives is between 120 and 180 lb. absolute, while the majority lie
1 Bulletin No. 58, p.15, Engineering Experiment Station. Journal A. S. M. E., April, 1912, p. 550.
ILLINOIS ENGINEERING EXPERIMENT STATION
between 130 to 160 lb. The average cut-off is about 145 lb., this point
being close to the average value of xc = 0.711 for n = 1.000 given in
Fig. 3.
It is also evident that the difference in the value of x, for the
average cut-off, 145 lb., to an average high value, 165 lb., is only 1.6%,
while to an average low value, 125 lb., it is only 1.3%.
The effect of varying the cut-off pressure on the relation of xc
and n is so small of itself, and so much smaller than the effect due to
change of speed, that it need not be considered.
13. Effect of Varying the Size of Cylinders.-The size of the
cylinders varied from 16 in. x 24 in. up to 27 in. x 28 in., the latter
having a displacement of 3.25 times the smaller one. No effect on the
relation of xc and n was found that could be traced to any change of
size of the cylinders.
In applying the n - x, method to stationary engines, as noted in
Bulletin No. 58, the sizes varied from 10.5 in. x 12 in. up to 34.2 in. x
60 in., the latter having 53.5 times the displacement of the former.
No effect in the relation of xa and n was found from this cause.
14. Effect of Various Types of Valves.-The locomotive engines
tested were equipped with plain balanced D slide valves, balanced
double-ported slide valves, and piston valves. It was thought that there
might be some difference in the apparent relations of xc and n due to
the different types of valves allowing steam to leak at different rates
from the steam chest direct to the exhaust passage.
The results indicate that the locomotive having the least apparent
valve leakage had balanced D slide valves as did also the one having
the greatest valve leakage. The results of the two piston valves tested
indicate that they both leaked apparently at a rate intermediate between
the two extreme cases, their rate of leakage being close to the average
for all valves. None of the valves tested leaked materially into or
out from the cylinder.
The probable leakage occurring through the valves is discussed in
Section IV.
15. Effect of the Use of Superheated and of Saturated Steam.-
The use of superheated steam in cylinders in place of saturated steam
results in a higher value of xc for the same conditions of speed and
cut-off. The higher value of xc which is obtained results, in turn, in a
higher value of n. When the same value of xc is obtained at the same
speed with either saturated or superheated steam, the same value of n
has been found to result.
CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES 21
16. Effect of Varying the Length of Cut-off.-The length of cut-off
used in the tests varied from 12% to 50%. It has been found that,
other conditions being the same, if a given value of xo occurs in one test
at 12% cut-off, and in another test on the same locomotive at 46%
cut-off, the value of n resulting is the same, showing that the length
of cut-off has no measurable effect on the relation of x. and n.
CV T- O pRF&wRe- e Peff JI /IN ADJOu/17
FIG. 7. RELATIONS OF Xc AND CUT-OFF PRESSURE FROM ALL SIMPLE LOCOMOTIVES
FOR CONSTANT SPEEDS AND THE VALUE OF n= 1.000
17. Effect of Varying the Back Pressure.-The back pressure of
the steam in the cylinders varied from 15 to 36 lb. absolute, a range
of 21 lb. Varying the back pressure between these limits appears to
have no effect on the relation of xc and n.
When the back pressure is as high as 100 lb. absolute, however, as
in the high pressure cylinders of compound engines, the relation of xc
and n is changed considerably, other conditions being the same.
III. APPLICATION OF THE n - Xc METHOD TO COMPOUND LOCOMOTIVES
18. Operating Conditions and Methods of Application to Tests.-
The same general test conditions prevailed for the compound loco-
motives as for the simple locomotives.
The method of selecting a set of indicator diagrams to represent
the average conditions of a test was as follows: The average power of
the test was represented by a combined sum made up of the sum of
the values of the mean effective pressures for the low pressure cylinders,
after each was multiplied by the value of the cylinder ratio, plus the
ILLINOIS ENGINEERING EXPERIMENT STATION
sum of the values of the mean effective pressures for the high pressure
cylinders. The set chosen, taken at the same reading, was one in which
this combined sum was nearest to the sum of the test averages obtained
in the same manner, and in which the boiler pressure was not more than
4 lb. from the average pressure prevailing during the test. The method
of selection used eliminates any unequal division or work in the cylinders.
The desired condition was, in most cases, fulfilled to within an average
of 1/2 of 1% of the mean condition.
For the purpose of obtaining reliable and accurate results the follow-
ing conditions, in addition to those mentioned on page 9, were imposed:
(1) Expansion lines showing extreme effects of inertia or sticky
indicator pistons were not used, as fair values of n could not be obtained.
(2) The range of pressure from cut-off to release during expansion
exceeded 12 lb. for low pressure indicator diagrams and 60 lb. for high
pressure diagrams in order to provide a sufficient length of curve to be
able accurately to determine the value of n.
The tests rejected for the reasons outlined above and those given
on page 9 amounted to 10% of the total number available.
For the purposes of this investigation the high pressure and low
pressure indicator diagrams were treated as separate tests, each receiv-
ing, however, the same weight of steam per revolution from the boiler.
19. Relations of xc and n for Compound Locomotives.-Indicator
diagrams from six typical compound locomotives were examined to
determine the relations of xe and n. Data were obtained as to the effect
on the n - x, relation of change of speed, cut-off and back pressure,
the use of saturated and superheated steam, the type of valves employed,
and the effect of various rates of leakage of steam from the steam chest
directly under the valves to the exhaust passage without this steam
having entered the cylinder. This class of leakage in subsequent dis-
cussion will be called simply valve leakage.
The conditions existing during the tests varied between wide limits.
The speeds varied from 40 to 320 r. p. m. The boiler pressures varied
from 200 to 225 lb. The pressure in the receivers between the high and
low pressure cylinders varied from 25 to 95 lb. gage. The back pressure
in the low pressure cylinders varied from 1 to 20 lb. above the atmos-
phere. The cut-off varied from 25% to 65% of the length of the stroke.
The valves used included plain, balanced, and balanced double-ported
slide valves, plain piston valves, and special piston valves controlling
the steam distribution to both high and low pressure cylinders. The re-
ceiver capacity varied from 0.4 to 2.2 times the displacement of the low
pressure cylinders. The size of the high pressure cylinders varied
CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES
from 14.16 in. x 23.65 in. to 23 x 32 in.; the low pressure cylinders
varied from 22 in. x 23.65 in. to 35 in. x 32 in.
A total of 52 high pressure and 53 low pressure tests are presented.
For very serious inconsistencies, due apparently to excessive valve leak-
age amounting to as high as 18.5% of the total steam used, all tests of
locomotive No. 929 and all low pressure tests of No. 535 were not used
to obtain the general relation of xo and n. An analysis of the tests of
these locomotives in comparison with the other tests is given in
Section IV. After deducting the tests not used, there remained a total
of 43 tests from the high pressure cylinders of five locomotives and 34
tests from the low pressure cylinders of four locomotives.
The general classification of the locomotives tested and the number
of tests analyzed for each one are given in Table 2. The principal
dimensions of the six locomotives are given in Appendix II.
The general logs of the 105 tests are given in Tables 11-16 in
Appendix II. Only those quantities are given which relate to the
water fed and to the values of xc and n.
20. Relations of x, and n for High Pressure Cylinders.-The
values of x~ and n for all high pressure tests are plotted in Fig. 8.
The values obtained exhibit a much larger variation in position
than those obtained from the simple locomotives in Fig. 3. The large
variation obtained was found to be due to the addition of an important
variable not present in the simple locomotives, namely, widely varying
back pressures in the cylinders due to the varying receiver pressures em-
ployed in the different locomotives tested.
The center of gravity of the tests of each locomotive, the center of
all tests, and the center obtained from the centers for each locomotive
were all obtained in a manner similar to that fully described on page 13.
The center of tests for No. 929 was plotted, but was not used. It is
the point shown encircled in Fig. 8.
Unfortunately the range in the values of x, obtained was so small
relatively that a definite slope for a line to represent the average rela-
tions for all tests could not be obtained. It was decided, however, in
the light of previous experience that the relations for the high pressure
cylinders of locomotives possessed a slope similar to that obtained from
simple locomotives, as the same general design and conditions prevail
for both types.
A line was drawn, therefore, as shown in Fig. 8, to represent
the average relation obtained from the high pressure cylinders of typical
compound locomotives. The equation of this line is
=-- 1,620 n - 0.827,
ILLINOIS ENGINEERING EXPERIMENT STATION
The average deviation of all points from this line is 8.0%, while
the normal maximum deviation is 12.0%.
The crosses representing the center of the tests for each locomotive
are located at distances varying considerably from the average line due
to varying back pressures for the same cut-off pressures and also to
varying rates of valve leakage. The effect of both of these variables
is treated later.
21. Effect of Varying the Speed.-The effect of varying the speed
on the relations of xc and n was investigated by the same general method
as that employed for simple locomotives, except that, in order to elimi-
nate the vertical displacement of the center representing all the tests
for each locomotive, the values of xc for this center were each corrected
to the average line in Fig. 8.
The points obtained are plotted in Fig. 9. The method of correcting
for vertical displacement of the center for the tests of each locomotive
is as follows: A line was passed through this center parallel to the
average line for all tests and extended to the intersection with the value
of n= 1.000; the value of xc at the intersection was read off; the
amount in the value of xc that the center was above or below the line
FIG. 8. RELATIONS OF Xz AND n FOR HIGH PRESSURE CYLINDERS OF COMPOUND
LOCOMOTIVES.
7
CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES 25
was subtracted or added respectively to all readings for the intersec-
tions of the lines passed through the center of tests at each speed.
Thus if a center for the tests of one locomotive was located 0.06 in the
value of xc above the line, the value of 0.06 was subtracted from the
value at the intersection of each speed center at the value of n = 1.000.
The average effect of change of speed was determined as the straight
line in Fig. 9. The average deviation of the points from the line
is 3.4%. The result of accounting for the effect of speed on the equa-
tion expressing the relations of xc and n is as follows:
x,= 1.620 n - 0.827 - 0.00034 (150 - S)
where S=speed of engine in r. p. m.
The speed effect obtained is very similar to the same effect for simple
locomotives, but with a slightly different slope.
22. Effect of Varying the Range of Pressure.-It was found that
other conditions remaining the same, raising the back pressure in the
high pressure cylinder increased the value of xc for the same value of n.
It was also found that lowering the cut-off pressure, the back pressure
remaining the same, had the same effect, though to a smaller degree.
This last effect is corroborated by the same effect observed in the rela-
tions of xc and n for simple cylinders given in Fig. 7.
Since the effects of raising the back pressure and of lowering the
cut-off pressure each change the value of x. in the same direction, they
are cumulative and can be combined as the range of pressure from
cut-off to the average back pressure. It was also found after careful
examination that this range of pressure was the best measure of the
observed effects for both the high and low pressure cylinders.
The back pressure in the high pressure cylinders is taken from the
indicator diagrams as the average pressure at mid-stroke when the re-
ceiver capacity is large and the back pressure is therefore fairly uni-
form. When the receiver capacity is relatively small and the back pres-
sure therefore is extremly variable, it is obtained from the diagrams at a
point near the beginning of compression.
For the purpose of ascertaining the effect of varying the range of
pressure on the relation of x, and n, the effect due to change of speed
was removed from the values of xc obtained from the intersection of
the line extended from the center of tests at one speed.
To show the effect desired the points obtained are plotted in Fig. 10.
The corrections made for the effect of speed were obtained from Fig. 9.
The method used was as follows: The average speed of all the tests of
one locomotive was found and the value of Xc read off from the line
in Fig. 9 for this speed; the correction for speeds below the average
ILLINOIS ENGINEERING EXPERIMENT STATION
was made by adding to the value of xc obtained, the difference between
the value of xa taken from the line at this speed, and the value of xc
found for the average speed; the correction for speeds above the average
was inade by subtracting in a similar manner the difference obtained.
0 2O I.0 60 0 /W /20 /40 /60 /&0 ~00 W2602$0 0 360 -WO 320
SP££D- REVOLUtI/r/O,5 P26 MIfWT7
FIG. 9. RELATIONS OF Xc AND SPEED FOR HIGH PRESSURE CYLINDERS OF COMPOUND
LOCOMOTIVES FOR CONSTANT VALUE OF n=1.000, AND FOR CENTER OF TESTS
CORRECTED TO AVERAGELINE.
For example, if the average speed for the tests of one of the loco-
motives is 160 r. p. m., the average value of xc at n = 1.000 from
Fig. 9 is 0.796. If the center of tests at 80 r. p. m. be considered, the
average value of xc at 80 r. p. m. from Fig 9 is 0.769, being lower than
the value of xc at 160 r. p. m. by 0.027. The value of x, from the center
of tests at 80 r. p. m., after being increased by 0.027 to eliminate the
average effect of speed, would be plotted in Fig. 10.
In examining the effect under consideration it is apparent that the
relations of xc and n for simple cylinders and for the high pressure
cylinders of compound locomotives differ only in the effect produced
by different ranges of pressures; that is, if the back pressure in the
high pressure cylinder were lowered to about atmospheric pressure,
CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES
this cylinder would operate, under the same conditions, as a simple
cylinder and would therefore have the same relations of xc and n.
The effect of range of pressure for high pressure cylinders and for
simple cylinders is, therefore, a continuous one.
The centers of all tests of each locomotive, the centers of tests at
each speed for each locomotive, and two concentric circles and a cross
representing the average relation for all simple locomotives are plotted
RA/N6E OF PRfSUREZ FROM CW7-oF TO SACWPRe/M5/RE, Z.
FIG. 10. RELATIONS OF Xc AND RANGE OF PRESSURE (CUT-OFF TO AVERAGE BACK
PRESSURE) FROM COMPOUND LOCOMOTIVES FOR CONSTANT SPEEDS AND THE
VALUE OF n= 1.000
in Fig. 10. The center of all high pressure points plotted was obtained
and is plotted as a cross.
A line passing through the center of high pressure tests and the
center of simple tests was drawn to represent the average effect of range
of pressure on the relation of xc and n.
The equation after correcting for the average effect of range of
pressure takes the form
xo 1.620 n - 0.827 - 0.00034 (150 - S) + 0.0031 (102.5 - B)
where B = range of pressure from cut-off to the back pressure in lb.
per sq. in.
The average value of xc is obtained at 102.5 lb. range of pressure.
The value of x, is higher for ranges of pressure below 102.5 lb., and
K
K
K
K
ZZ~
ZOW' PRfJ'fCu CrtN/WOfR
I I
ILLINOIS ENGINEERING EXPERIMENT STATION
lower for ranges above 102.5 lb. The average deviation of the points
from the line is 6.2%. This large deviation apparently shows the
effects of varying rates of valve leakage as explained ii Section IV.
23. Relations of xc and n for Low Pressure Cylinders.-The
methods employed to obtain the general relations of xc and n for low
pressure cylinders, and the effect on this relation of change of speed
and range of pressure, were similar in all respects to the methods de-
scribed for the high pressure cylinders.
The values of x, and n obtained are all plotted in Fig. 11. The val-
VALUE Of n PF8OM PAAI(Y/6 CUL/£3V.
FIG. 11. RELATIONS OF X, AND n FOR Low PRESSURE CYLINDERS OF COMPOUND
LOCOMOTIVES.
9
ues obtained from locomotives No. 929 and No. 535 were not used on ac-
count of excessive valve leakage.
The line shown in Fig. 11 was drawn as outlined for the high
pressure cylinders, using the same slope as the line obtained for the
simple cylinders. The equation of the line is
xc = 1.620 n - 0.833.
The average deviation of all the points from this line is 7.8%.
24. Effect of Varying the Speed.-The points obtained which show
the effect of varying the speed on the relation of x0 and n are plotted
1
CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES
wo
K a7
k 076
074
^a^
707
oew
64
ae4
SP-EO - 1EYOl /T/OGyJ PR m/4'TE
FIG. 12. RELATIONS OF Xc AND SPEED FOR Low PRESSURE CYLIN DERS OF COMPOUND
LOCOMOTIVES FOR CONSTANT VALUE OF n = 1.000, AND FOR CENTER OF TESTS
CORRECTED TO AVERAGE LINE.
in Fig. 12. The equation after correcting for the effect of change of
speed is
x==1.620 n-0.833-0.00069 (154--S)
The average deviation of the points from this line is 4.5%.
25. Effect of Varying the Range of Pressure.-The points obtained
which show the effect on the relation of xo and n of changing the range
of pressure are plotted in Fig. 10. The equation as further modified
by this effect is
x = 1.620 n - 0.833 - 0.00069 (154 - S) + 0.0047 (30- R)
The average deviation of the points from this line is 3.3%.
This extremely close agreement shows that the effects of varying
the speed and range of pressure comprise all the important variables.
IV. ANALYSIS OF THE n - Xc RELATIONS
26. Causes Which Affect the n -x, Relations.-The data which
have been presented in the preceding pages will here be examined
critically as to the causes which affect the relation of xc and n due to
ILLINOIS ENGINEERING EXPERIMENT STATION
varying the range of pressure from cut-off to the back pressure and to
varying the speed of the engine. These two variables are the only ones
which cause an appreciable effect on the n - Xc relation for locomotive
engines.
It is well here to consider and compare the operating conditions of
pressure and speed obtaining in stationary and in simple locomotive
engines.
The boiler pressure of simple locomotives is always closely constant.
The great majority have pressures of about 200 lb. gage, although the
newer designs using highly superheated steam employ pressures of
from 165 to 190 lb. gage. Pressures of from 200 to 230 lb. are em-
ployed in compound locomotives. The pressure used in stationary
engines varies from 80 to 200 lb. gage.
The speed of locomotive engines in sustained operation varies from
about 40 to 320 r. p. m. The speed of simple stationary engines of
equal power varies from 60 to 150 r. p. m.
Relatively speaking, therefore, simple locomotive engines may be
classed as constant pressure and variable speed; while compound loco-
motive engines may be classed as variable pressure and variable speed.
Simple and compound stationary engines, however, may be classed as
constant speed and variable pressure types.
From this classification it is apparent that the effects on the n- xc
relation to be considered are as follows:
(1) In simple and compound stationary engines the effect of range
of pressure is important while speed may be neglected.
(2) In simple locomotive engines the effect of speed is important
while range of pressure may be neglected. (See Fig. 6 and 7.)
(3) In compound locomotive engines the effects of both range of
pressure and speed are important. (See Fig. 9, 10, 12.)
The valves of a locomotive engine, when compared with stationary
engines of the same size, are extremely large in proportion to the size
of the cylinder. This is due to the high speeds which it is necessary
to employ in order to obtain large specific capacities from the cylinders.
As much as 2500 indicated horse power has been obtained continuously
from two 27 in. x 28 in. cylinders. (See tests of No. 3395.) The
piston valves of this locomotive are 16 in. in diameter.
If it be true as stated by various experimenters that single valves
as a class leak steam directly under the valve from the steam chest to
the exhaust passage, without this steam having entered the cylinder,
then locomotive engines with their large valves might be expected seri-
ously to show the effects of valve leakage at low speeds.
CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES
In Corliss and four valve engines any steam that leaks from the
steam chest through the valves must leak into the cylinders.
27. Effect on the Relations of xo and n of Varying the Range of
Pressure.-The effect of lowering the range of pressure from cut-off
to the back pressure is always to give smaller values of n for the same
value of xc, other conditions remaining the same. This result is due
to the following reasons: For a given value of xc, the value of n is the
result of the volumes obtained by adiabatic expansion of the steam
and water present plus an increase of volume of steam due to the return
of heat from the cylinder walls and the consequent re-evaporation of
part of the water condensed during admission. The rate of re-evapora-
tion is controlled by the range of temperature due to the range of
pressure, and it is greater or less according as the range of pressure
decreases or increases respectively.
The effect of the range of pressure upon the n - xc relations for
simple locomotives is small, as will be seen in Fig. 6 and 7; it is larger
for the high pressure cylinders of compound locomotives, as is shown
in Fig. 10; it is still larger for low pressure cylinders, as is also shown
in Fig. 10. The slopes of the lines in these figures are 0.12, 0.76, and
1.17 respectively, showing the increasing effect of this variable as the
range of pressure decreases.
28. Effect on the n - x Relations of Varying the Speed.-The
effect on the relations of xc and n of increasing the speed is to give
higher values of xc for the same value of n, other conditions remaining
the same.
The relations of X, and n for Corliss engines did not show any
definite increase in the value of x, for speeds of from 90 to 150 r. p. m.
The effect on the value of x, due to increase of speed is well shown
for the relations of the Purdue locomotive in Fig. 4. In this figure
it is seen that the average value of xc increased from 0.735 at 100 r. p. m.
to 0.756 at 240 r. p. m., a change in value of 0.021.
The average effect due to changes of speed for all simple locomotives,
shown in Fig. 5, is from 0.695 at 100 r. p. m. to 0.747 at 240 r. p. m.,
an increase of 0.52, which is 25 times the increase found for the Purdue
locomotive.
It is apparent that the center of all tests of the Purdue locomotive,
which showed the least increase of xc for increase of speed, is relatively
the highest center plotted in Fig. 3. It will be seen also from Fig. 5
that the points of No. 1499 show the largest increase of x, for increase
of speed, and that its center of tests plotted in Fig. 3 is relatively the
lowest.
ILLINOIS ENGINEERING EXPERIMENT STATION
The only phenomenon which accounts consistently for the observed
effects due to speed is valve leakage. By valve leakage is meant the
leakage of steam directly through the valves without its having entered
the cylinder.
As has been stated, locomotives are peculiarly open to valve leakage
at low and moderate speeds because of their relatively large valves and
the use of very high pressures. The large valves expose a large surface
through which steam may leak while the high pressures employed tend
to increase the leakage to much larger amounts than those found in low
pressure stationary engines with small valves. The experiments1 which
have been made on valve leakage show that the leakage is proportional,
in a given engine, to the outside perimeter of the valve seat between
the steam chest and the exhaust passage and also to the difference of
pressure between these two regions. Varying the speed of operating
the valves was found to have no effect on the amount of leakage. It
was found also that although a valve might be perfectly tight while at
rest yet it would leak a large amount when in motion, due to the break-
ing up of the oil film and to condensation and re-evaporation from the
bridges and surfaces of the valve seat after they had been exposed first
to steam at the initial pressure and then to the exhaust pressure.
Since valve leakage is proportional only to the perimeter of the
valve seat and to the difference of pressure, it would, therefore, be a
constant weight per unit of time for any one engine. Hence it follows,
as valve leakage is constant per unit of time, that increasing the speed
of the engine and thus using more steam in the cylinders would lessen
the effect of valve leakage, measured as the per cent. of the total steam
used. For example, if an engine running 50 r. p. m. leaks 500 lb. of
steam per hour through its valve while receiving 4500 lb. per hour in
the cylinder, the leakage is 10% of the total steam supplied; on the
other hand, if it runs 150 r. p. m. and uses therefore three times the
steam in the cylinders, 13,500 lb., then the valve leakage is only 3.6%
of the total steam supplied.
All the evidence at hand shows that the existence of valve leakage
and its relatively diminishing amount with increase of speed are the
only conditions which account satisfactorily for the observed facts as
shown in Fig. 4, 5, 9, and 12. That is, it is probable that there is very
little if any effect on the n-x- relations of varying the speed, but the
existence of leakage and its increasing relative amount when speeds are
decreased lead to an apparent value of, x, which is lower than the real
value for the steam actually admitted to the cylinders. It is also
£ Leakage through a Piston Valve, by George Mitchell, Power, Oct. 11, 1910, p. 1805.
Callender and Nicholson'e Experiments on Valve Leakage.
CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES 33
probable that the value of xo for engines having the larger values of
valve leakage would increase faster with increase of speed than engines
having very small leakage, because the increase of speed would increase
the apparent value of x, at a much faster rate. This condition is
exactly the one which occurs, as is shown in Fig. 3, 4, 5, 9, and 12.
The slope of the line representing the effect of varying the speed
for any one locomotive is apparently the best index as to the amount of
valve leakage which exists.
It is probable that the relative location of the centers of tests in
Fig. 3 is also a reliable index to the amount of valve leakage. The
line drawn in Fig. 3 represents the average relation of the apparent
value of xe and the value of n. If a center of the tests for one loco-
motive lies above this line, then it apparently has a higher average
value of x0 for the same value of n; the reverse is true if the center lies
below the line. Since the effect of any leakage that may take place is
to decrease the value of xc for a given value of n, then the greater the
leakage the lower would be the value of xc.
The most striking case of the effects which have been described is
found in the tests of No. 929, having tandem compound cylinders.
The cylinders of No. 929 were almost exactly the same size as those
of No. 585, yet, at the same speeds, cut-offs, and pressures the steam
consumption of No. 929 averaged 19.6% more than that of No. 585.
As the conditions of the tests of these two locomotives were almost
exactly similar, they should have had practically the same steam con-
sumption. It is, therefore, almost absolutely certain that a large pro-
portion of the steam delivered by the boiler of No. 929 never entered
its high and low pressure cylinders, where it could be used in producing
power, but that it leaked directly through the valves. The effect of
any such leakage was charged to the value of xc which was obtained,
and this value in consequence appears to be very much smaller than
the values obtained from any of the other compound locomotives, al-
though all of them except the No. 585 had much smaller cylinders.
For instance, in the high pressure cylinders the average value of xc
obtained for the No. 929 is 0.662, while the average value of xc for all
other compounds is over 0.80. The same condition holds for the low
pressure cylinders, although to a lesser degree.
In the light of the facts which have been presented and also from
previous experience it is practically certain that the values of n obtained
for the No. 929 are accompanied by values of X, for the steam actually
present in the cylinders as shown by the line in Fig. 11. It is also
practically certain that had no leakage occurred, the steam consump-
ILLINOIS ENGINEERING EXPERIMENT STATION
tion of the No. 929 would have been practically the same as for the
No. 585 under the same conditions.
It was assumed, therefore, that the value of n obtained represented
the values of xc actually existing in the cylinders, and that the steam
consumption of the No. 929 for the steam actually used in the cylinders
was the same as for the No. 585.
The average steam consumption of No. 929 was 23.8 lb. per i. h. p.
hr., while that of No. 585 for the tests run at the same speeds was
19.9 lb., showing that No. 929 consumed 19.6% more steam than did
the No. 585 for the same conditions.
The average quality of xc in the high pressure cylinders of the
No. 929 was found to be 0.836, as computed from the values of n, 8,
and R, using the equation given on page 29. In a similar manner the
value of xc for the low pressure cylinders was found to be 0.817, making
the average value of xc for both the high and low pressure cylinders,
0.827.
The average apparent value of xc from the tests for both high and
low pressure cylinders was 0.674. Since this value of xc is lower than
0.827-0.674
0.827, more steam to the amount 0.827 18.5% was used
than was accounted for in the cylinders.
The results of these computations is a striking proof that not only
was large valve leakage taking place, but that its amount has been
established by two independent methods, which corroborate each other
to a marked degree of accuracy. No. 929 consumed 19.6% more steam
than the No. 585, while from the relations of x, and n it is seen that
18.5% more steam was used than that which was accounted for in the
cylinders. This analysis shows conclusively why the No. 929 had such
poor economy in steam consumption when compared with all the other
compound locomotives tested.
An examination of the design of the valves in No. 929 was made to
ascertain if there were any peculiar features present in these valves
which would account for the large valve leakage. The design is shown
in cross-section in the report of the St. Louis tests, page 390. It will
be seen that there are two annular passages containing live steam from
which the high pressure cylinder receives its supply. The high pressure
valve is in effect two inside admission piston valves made in one and it
is seen that the live steam has four possible avenues of leakage into
the receiver as against only two in the ordinary piston valve. These
four faces of the valve undoubtedly permit at least twice the leakage
which occurs through an ordinary piston valve with only two faces,
CLAYTON--STEAM CONSUMPTION OF LOCOMOTIVE ENGINES 35
and they are doubtless responsible for the enormous valve leakage which
has been shown to exist. The low pressure valve is an outside admission
piston valve, having only two faces which would permit of leakage. The
results show, however, that it leaked to about the same degree as the
high pressure valve, so that its surface on the valve bushing must not
have been in good condition or the piston rings were not yet worn to
a good bearing.
The only other locomotive which had valves similar in design to
those on the high pressure cylinders of No. 929 were the low pressure
cylinders of No. 535, shown on page 540 of the report of the St. Louis
tests. This locomotive has one valve which controls the steam distribu-
tion to both the high and low pressure cylinders. The portion of the
valve serving the high pressure cylinder is in effect a simple inside
admission piston valve, and as seen in Fig. 8 and 9 no unusual amount
of leakage was present in the high pressure portion of the valve. The
portion of the valve serving the low pressure cylinder is in effect two out-
side admission piston valves with four faces subject to leakage from
steam in the receiver direct to the two annular exhaust passages. The
values of xc and n from the low pressure cylinders show the effects of
very bad valve leakage at 80 r. p. m., becoming less in proportion at 160
r. p. m. and negligible at 240 r. p. m. The effects of the large valve
leakage at 80 r. p. m. are also apparent in the increased steam con-
sumption1 of No. 535 over that obtained in the other compound loco-
motives. At 160 r. p. m. the effects of leakage begin to grow propor-
tionately much less and at this and higher speeds the steam consump-
tion decreased to the amount generally consumed by compound loco-
motives having their valves in good condition.
The valve leakage found for No. 929 is corroborated by the actual
performance on the road of the class of locomotives to which No. 929
belongs. It was learned from an independent source that when one of
these locomotives is starting a full tonnage train, the "blow," or leakage
through the valves, is so great that a distinctive and continuous roar
of leaking steam is heard.
The analysis which has been given for the low points in Fig. 8 and
11 shows that the variations in the vertical distance of the center of
tests for each locomotive from the average line is almost certainly due
to the fact that the valves of each locomotive have their own rate of
leakage, the leakage for some valves being less than the average, while
that of others is greater.
The amount of valve leakage existing for a particular locomotive
I Locomotive Tests and Exhibits, pp. 707, 708, 710.
ILLINOIS ENGINEERING EXPERIMENT STATION
probably depends on the design and relative size of the valves, and also
on the condition of the surfaces of the valve seats, balance rings, and
balance plates for slide valves, and of the surfaces of the valve bushings
and piston rings for piston valves.
Referring to Fig. 3 the relatively high point of the Purdue loco-
motive and its flat speed effect curve in Fig. 4 probably means that its
valves were tighter than any of the others, due to its being kept in
laboratory condition. On the other hand, the low point of No. 1499
in Fig. 3 and its steep speed effect curve in Fig. 5 is probably due to
the fact that this locomotive was new and had not been broken in before
it was tested, consequently the valves had not worn to a good surface,
and the average leakage was larger than that for any of the other simple
locomotives tested.
29. Values of xc.-The assumption has been made throughout this
investigation that the steam saved in the cylinders in compression was
always dry saturated at the beginning of compression and the values
of Xe given were computed on this basis.
It is probable, however, in the simple locomotives, that the com-
pression steam is slightly wet for engines using saturated steam and is
superheated for engines using highly superheated steam.
If these two conditions exist the values of xc as given are slightly
wrong. Any error from this cause does not affect the results, however,
if the convention of dry steam at compression is uniformly followed.
The values of xc obtained by following this convention are comparable
though not absolutely correct.
30. Values of xc and n Found for V.arious Types of Locomotives-
Their Use in Design.-Fig. 3, 8, and 11 show the average values of xc
and n which are obtained from typical simple and compound loco-
motives. Where conventional indicator diagrams are laid out before the
locomotive is built, the data show the values of n which should be used
for the expansion curves. The value of n=1.0 still may be used for
the compression curves without serious errors.
The value of n for the expansion curves of locomotives using steam
superheated 2500 F. should be assumed as an average value of 1.3.
V. DIRECTIONS FOR DETERMINING THE STEAM CONSUMPTION OF
LOCOMOTIVE ENGINES FROM THE INDICATOR DIAGRAMS
31. Preparation of Indicator Diagrams for the Application of
the n-xo Method for Determining Steam Consumption.-Possibly 95%
of the locomotives in use in the United States and Canada are of the
type using simple cylinders. The compound locomotive, with the single
CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES 37
exception of the Mallet type, has dwindled in numbers and importance
since the introduction of the high superheat simple locomotive.
The directions for applying the n - x, method will therefore be
outlined in full for the simple type, and the change in the method for
its application to the compound type will be briefly mentioned.
Since the n - xo method depends entirely on the indicator diagram,
great care must be observed in taking these diagrams. The indicator
itself must be an accurate instrument in the best possible condition.
The indicator pipe connections must be large, short, direct, and well
covered with heat insulating material. An extensive investigation by
Dr. W. F. M. Goss' shows that long and indirect pipe connections
materially alter the form and character of the expansion curves. A
theoretically correct reducing motion, free from lost motion, must be
used so as to reproduce the actual expansion. Very short cords for the
indicator drum must be used to avoid cord stretch. The arrangement of
having one indicator at each end of the cylinder is always to be pre-
ferred if the road clearances allow it.
It is to be remembered that the method accounts for the actual
weight of steam and water present in one revolution only, as repre-
sented by the set of diagrams analyzed.
Since the method accounts for the consumption on the basis of one
revolution, indicator diagrams for road tests must be taken at regular
intervals of distance, perhaps Y2 or 1 mile apart. The mile post can
be used to indicate the time for taking diagrams. The rate of speed
must be observed as each set of diagrams is taken, as the speed has an
influence on the relations of xc and n.
After the test is over all diagrams are integrated and the average
horsepower obtained in the usual manner. To apply the n -xo
method the diagrams are divided into groups of similar lengths of
cut-off, four or more groups generally being sufficient for this purpose.
Since the effect of speed on the n - x, relations is a linear one, the
average speeds may be used without error. From each group as out-
lined above select two sets of diagrams, each taken at the same reading,
which are nearest in area to the average area of the group and which also
are nearest to the average speed which prevailed for the diagrams in
the group.
Construct logarithmic diagrams for each set as described in detail
in Appendix I. From these diagrams the average value of n for one
set of diagrams is determined.
1 Trans. Am. Society of M. E., Vol. 17, p. 398.
ILLINOIS ENGINEERING EXPERIMENT STATION
The relations of xc, n, and 8 for simple locomotives are plotted in
the chart of Fig. 13. The values of n and S are located on the chart
and the intersection of the lines representing them is located. The
intersection is then seen to lie between two lines of constant quality,
or value of xc, the exact value of x, being determined by interpolation.
The value of x, found gives the quality of the steam mixture at cut-off.
From the steam accounted for per revolution at cut-off by the indicator,
and the value of xa found for this steam, the actual weight of steam
and water in the cylinder is determined. The weight of dry steam
saved per revolution in compression is determined as described in
Appendix I. The total weight of steam and water per revolution found
to be present, less the weight of compression steam saved per revolution,
gives the weight of steam supplied per revolution by the boiler for
average conditons of valve leakage. Calculations similar to those de-
scribed but in the reverse order are given in detail in Appendix I.
Similar calculations are also given in Bulletin 58.
After all the sets chosen are analyzed the average consumption at
different values of cut-off is determined on the basis of consumption in
one revolution.
To determine the water consumed by the engine over a given run or
during a given time, the average steam consumption per revolution for
each group is multiplied, first by the number of sets of diagrams in
any one group of the different cut-off values, and second by the number
of revolutions that the drivers have made between the taking of cards.
In this manner, if diagrams are taken every mile, and the number of
revolutions made by an 80 inch driver would be 252, the calculation
described gives the total water consumed by one group. The consump-
tion for the other groups, after being computed in the same manner,
are all added and the total water used for the period is obtained.
Instantaneous rates of consumption in total weight of steam per hour
or per indicated horse power hour can be obtained from each set of
diagrams taken.
32. Other Applications of the n-xc Method.-If it is desired to
test an engine for valve leakage, the locomotive should be tested on a
test plant or under road conditions where the steam used for other pur-
poses is known. The steam used by the engines is accounted for by
the n - xc method, the total water fed to the boiler is measured, and
this includes the amount used in the cylinders; the amount that leaked
through the valves over the average leakage of the valves when in good
condition is accounted for by the difference between the two measure-
ments if the boiler is tight.
CLAYTON-STEAM CONSUMPTION OF LOCOMOTIVE ENGINES
z
o0
0
0
0
0
o
z
z
0