A NEW ANALYSIS OF THE CYLINDER PERFORMANCE
OF RECIPROCATING ENGINES
INTRODUCTION
Preliminary.The cylinder performance of a reciprocating
engine using an elastic fluid for the working medium may be con
sidered from two points of view: (1) the performance as a heat
engine, or the efficiency of transformation of the available heat
into indicated work; and (2) as a mechanism, or the measure of
perfection attained in the distribution of the working fluid, and
in preventing its leakage past the valves, piston, or piston rods.
Our knowledge of cylinder performance is obtained almost
entirely from indicator diagrams. These diagrams provide a
measure of the work performed in one cycle of operation, thus
giving a means for determining what proportion of the heat avail
able has been transformed into work, this proportion being ex
pressed as a thermal, potential or other efficiency.
The results of methods used at present in the analysis of cyl
inder performance may be divided into two classes: (1) those
which are relatively exact and satisfactory; and (2) those which
are relatively inexact and unsatisfactory. Under these two
headings the following results may be enumerated:
CLASS 1.
1. Indicated work.
2. Aid in valve setting.
3. Rough location of cyclic events.
4. Hirn's analysis for steam cylinders.
5. Measure of initial condensation in steam cylinders.
6. Detection of leakage, if very large, during expansion or
compression of any elastic medium.
7. Measure of the diagram factor for the purposes of design.
CLASS 2.
1. Accurate approximation of clearance volume from all cyl
inders using elastic media.
2. Close location of cyclic events.
3. Reliable detection and approximation of moderate leak
age with the engine in regular operation.
4. Measure of the actual steam consumption from steam
diagrams.
ILLINOIS ENGINEERING EXPERIMENT STATION
5. Separation of the initial condensation and leakage in
steam cylinders.
6. Division of feed between the two ends of a steam cylinder
for the application of Hirn's analysis.
It has generally been thought by engineers that a satisfac
tory solution of these lastmentioned problems is impossible be
cause the indicator diagram has not been supposed to contain in
itself the evidence necessary for their solution.
The investigation described in this bulletin is the result of
an extensive analytical and experimental study of the forms of
the expansion and compression curves which occur in indicator
diagrams. The analytical study was carried on by means of
transferring the indicator diagram to logarithmic crosssection
paper and then drawing a figure which will be called the loga
rithmic diagram.
It is wellknown that the equation of the polytropic curve
PV" = C becomes a straight line when plotted on logarithmic
crosssection paper. Conversely, when the expansion or com
pression curve of an indicator diagram becomes a straight line in
the logarithmic diagram, the curve is of the form PV" = C, the
value of n being the slope of the line.
By means of the logarithmic diagram, it has been found that,
free from certain abnormal influences, expansion or compression
of an elastic medium takes place in the cylinders of reciprocating
engines substantially according to the law PV" = C.
From the fact that the law PVP' = C holds for expansion
and compression curves from practice, there have been developed
rational methods of approximating the clearance volume, of
closely locating the cyclic events, and of detecting moderate leak
age when the engine is in regular operation. These methods ap
ply, however, only to those indicator diagrams which are taken
from the cylinders of reciprocating engines using any elastic fluid
for the working medium and having, as a part of the cycle, an
expansion or compression of the medium.
It has been discovered that the value of n for the expansion
curves of steam diagrams bears a definite relation in any given
cylinder to the proportion of the total weight of steam mixture
which was present as steam at cutoff. This proportion or
quality will be called Xc in this investigation, and its value will be
expressed in parts of unity. The relation of the value of n to the
value of xc for the same class of cylinder as regards jacketing has
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE 5
been found to be practically independent of engine speed and of
cylinder size.
The practical significance of finding this relation is that there
is now available an accurate method of approximating the value
of Xc and therefore the actual weight of steam and water present
at cutoff from the indicator diagram alone. As a result, a new
analysis of cylinder performance has been developed.
Acknowledgments.Acknowledgment of valuable assistance is
made to Dean W. F. M. Goss, Professor G. A. Goodenough
Professor 0. A. Leutwiler, Mr. C. M. Garland, to Purdue Univer
sity, and to various firms which furnished indicator diagrams and
tests for analysis.
PART I. THE APPROXIMATION OF THE ACTUAL STEAM
CONSUMPTION FROM INDICATOR DIAGRAMS
I. PRELIMINARY WORK
1. Study of Indicator Diagrams.The preliminary work con
sisted of an examination of the nature and form of the expansion and
compression curves of the indicator diagrams from a number of
steam engines. This work was accomplished by means of trans
ferring the indicator or PVdiagram to logarithmic crosssection
paper, and thus drawing a figure which will be called the log
arithmic diagram. It was found, after repeated experiments,
(see p. 55) that free from certain abnormal influences, expan
sion or compression of steam takes place in cylinders substanti
ally according to the law, PV11 = C. The values of n which were
obtained, however, exhibited a large range of variation, the
range being from 0.70 to 1.34. The engines from which the
values were obtained differed in type, size, speed, steam pres
sure, ratio of expansion and back pressure. Obviously, com
parisons could not be made of these examples because of the
number and magnitude of the variables.
Indicator diagrams taken from the same cylinder, with dif
ferent cutoff positions, showed that the value of n was higher as
the cutoff was lengthened. There was a large variation in the
value of n where the conditions of cylinder size, speed, steam
pressure, and steam distribution were the same. The only variable
shown by the diagrams was the length of the cutoff. It was
thought that there might be some relation, in any one cylinder,
between the value of n for the expansion curve and the quality of
the steam mixture at cutoff, as this quality was known to be
higher as the length of cutoff increased. One fact that seemed to
ILLINOIS ENGINEERING EXPFRIMENT STATION
confirm this hypothesis was that with superheated steam (under
the same general conditions, except the kind of steam used), when
the quality at cutoff was high, the value of n for expansion was
always much higher than with saturated steam. The only im
portant variable between the use of saturated and superheated
steam to account for the change in the value of n was the quality
of the steam mixture at cutoff, or the proportion of the total
weight of mixture in the cylinder which was present as steam at
cutoff. This quality or proportion will be called xc in this in
vestigation, and its value will be expressed as decimal parts of 1.
All cases examined of engines using superheated steam at
normal cutoff showed n to be higher than 1.0, and as high as
1.34; and all cases of small engines using saturated steam showed
n to be lower than 1.0 and as low as 0.70. These facts led to the
conclusion that the value of xc was the most important single fac
tor in the accompanying value of n. Tests were, therefore,
planned in which the effort was made to vary the value of xc be
tween the widest practicable limits.
II. LABORATORY TESTS
2. Equipment.A singlecylinder longrange cutoff, 12 in.
x 24 in.Corliss engine, located in the Mechanical Engineering
Laboratory of the University of Illinois, was selected for the
tests. A Corliss engine was selected because of the fact that
in this type all the steam used passed through the cylinder.
3. Plan of Tests.It was planned to observe the effect upon
the value of n of varying the value of xa under different conditions
of pressure and speed. The value of Xc was varied through a
large range by the use of saturated and superheated steam, in
conjunction with different lengths of cutoff, under the same con
ditions of pressure and speed. The values of xc obtained ranged
from 0.413 to 0.943, covering the range usually found in practice
with the type of engine used.
The values of n for the expansion curves were obtained by
means of the logarithmic diagram (see Appendix 1). The value of
xc given in the log is the average of the results obtained from one
set of headend and crankend diagrams for each test. The unit of
measurement, therefore, was the revolution, as the values of Xc for
the head and crankends cannot be measured separately when one
exhaust pipe is used for both ends of the cylinder. The value of n
given for one test is the average of the separate values from the
expansion curves of the headend and crankend diagrams, taken
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
from the set of diagrams already mentioned.
4. Number of Tests.Seventy five tests in 16 series were run.
Of this number, 60 tests in 14 series were selected as fulfilling
the requirements decided upon to give reliable data. Each series
consisted of 4 to 5 separate tests, differing from each other only
in the length of cutoff, with the same conditions of pressure and
speed. All tests were run with the steam exhausting from the
cylinder at about atmospheric pressure into a surface condenser.
The length of cutoff was varied in nearly uniform steps from
about 5 per cent to 45 per cent of the length of the stroke, and was
the means of varying the value of Xc when using either saturated
or superheated steam.
The 14 series were divided into 2 divisions of 7 series each;
one division being run with saturated steam, and the other with
steam superheated to 5000 F. at the superheater. Each division
consisted of 5 series run at different gauge pressures at constant
speed, and 2 series run at different speeds with constant pressure.
The steam pressures used were 57.5, 76.5, 95, 113, and 132 lb. gauge
with the engine running at 120 r. p. m. The other speeds employed
were 90 r. p. m. and 150 r. p. m. at the gauge pressure of 113 lb.
Each division, therefore, gave the effect of the use of 5 steam pres
sures at constant speed, and 3 speeds at constant pressure.
The governor changespeed device was always set to give
the desired speed with the engine running at noload. As the load
was increased, the speed decreased through the action of the
governor in about the same proportion for all initial speeds.
Whenever speed is mentioned, the noload speed is the one re
ferred to, the exact speed for any one test being given in the
general log.
The general log of the 29 tests run with saturated steam is
given in Table 1. Table 2 contains the results of the 31 tests
run with superheated steam. Table 3 gives the averages of simi
lar series, called groups, run at the same pressure and speed,
with both saturated and superheated steam. For any one group
of the two series of tests, as has already been pointed out, the only
variables are the length of cutoff, and the value of x,.
1. Values of n obtained under different conditions from the same
engine cylinder.All the simultaneous values of xc and n obtained
from the 60 tests were plotted in Fig. 1. A study of this figure
shows beyond question that as Xc increases in value, n increases
also. The values all lie in a region which has a definite trend to
wards higher simultaneous values of Xc and n. Observing the
ILLINOIS ENGINEERING EXPERIMENT STATION
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CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
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ILLINOIS ENGINEERING EXPERIMENT STATION
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CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE 11
general trend, it is seen that there is no exception to this general
relation. No value of n below 1.00, for instance, is found for
values of xc above 0.80, and no value of n above 1.10 is found for
values of x, below 0.72.
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V050 cf n '/?O EXP24A/'§S2/A TX
FIG. 1. GENERAL RELATIONS BETWEEN QUALITY AT CUTOFF AND THE VALUE OF Al
FOR. VARIOUS PRESSURES AND SPEEDS
It is also apparent that the points with long cutoff, obtained
from saturated steam for given values of Xc and n, are in the same
region occupied by the points with short cutoff obtained from
superheated steam for the same given values of xc and n.
Examining the region of n=0.901.00 and of Xc =0.500.70, it
may be seen that the points obtained with long cutoff
with saturated steam, and with short cutoff with superheated
steam, lie together indiscriminately. This shows conclusively,
in a general way, that the value of n is practically independent of
the length of cutoff, even though this length may vary from 5
per cent to 45 per cent, and that n depends solely on the value of
xc, the only other variable.
The points shown in Fig. 1 occupy a relatively wide region
until they are separated into the various groups of similar pres
sures and speeds. The points for each group were plotted sep
arately, and separate curves were determined for each condition.
From preliminary plotting, the relations between n and Xc were
found to be expressed closer by straight lines than by any other
ILLINOIS ENGINEERING EXPERIMENT STATION
family of curves. The method used to draw these lines will be given
for group F, which includes series 8, with 4 tests, and series
16 with 4 tests. This group is shown in Fig. 2. All points
K4
K
9/t/E OF n F/O/ OXPMWS/OV C/JRVE
FIG. 2. RELATION OF QUALITY AND THE VALUE OF M FOR TESTS RUN AT 111
POUNDS ABSOLUTE PRESSURE OF CUTOFF AND 150 R. P. M.
were given equal weight. The average of all the coordinates,
or the "center of gravity" was found and the condition imposed
that the line pass through this center as an axis, and that the
slope be determined by the position of the points. The points in
group F were divided into four logical pairs or groupings, and the
center of gravity found for each grouping. The line was then
drawn as shown. Where points were located so that a logical
grouping was in doubt, various groupings were made, and each
given weight in determining the slope.
The equation of the curve selected is xc =1.258 n0.614.
The average deviation of the points from this line is 2.6 per
cent (measured from the zero of x ) and the maximum deviation
is 4.6 per cent. This average deviation, 2.6 per cent, is smaller
than that for most of the groups. The straight line, in most cases,
represents the points found as closely as any other curve that
could be employed, and has the merit of simplifying greatly the
subsequent use made of the relations for the different groups.
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
The values of n for group F were also plotted to the various
accompanying cutoff positions at which each test was run. This
is shown in Fig. 3. The points in Fig. 3 show that for each initial
condition of steam, the value of n increased as the cutoff was
lengthened, and that with any given cutoff, different values of n
were obtained according as saturated or superheated steam was
used. Thus, at a cutoff of 15 per cent, the value of n obtained is
0.950 with saturated steam, and 1.084 with superheated steam.
The only variable present in these two cases is xc, the value of
which is higher with superheated steam than with saturated
steam. A definite relation between n and cutoff occurs only when
a given cutoff is accompanied by the same value of xc, i. e., the
value of n bears a direct relation to xc but not to cutoff. Fig. 3
taken in conjunction with Fig. 2, proves that the value of n de
pends directly only upon the value of Xc, and that the relation ofn
ItZ/F f n /Tra , PA/5AN CeURVZE
FIG. 3. RELATIONS OF PER CENT OF CUTOFF AND THE VALUE OF n FOR TESTS RUN
AT 111 POUNDS ABSOLUTE PRESSURE AT CUTOFF AND 150 R. P. M.
and xc is practically independent of the length of cutoff within the
limits of the tests.
(a) Effect of varying the steam pressure at constant speed.The
relations of xc and n were determined separately for all groups by
the method outlined for Fig. 3. The lines for the five pressures
used, comprising the results of groups A, B, C, D, and G, were
replotted as shown in Fig. 4. This figure also contains other
curves that are discussed in Appendix 1. The lines shown give
ILLINOIS ENGINEERING EXPERIMENT STATION
the relations of Xc and n for various absolute pressures at cutoff,
all obtained with a speed of 120 r. p. m.
These curves were then examined to find the effect of vary
ing the absolute pressure at cutoff (designated as p) on the rela
tions of Xc and n. In Fig. 4, the constant pressure curves were
intercepted at constant values of n, and the coordinates of xc and
p for the points of intersection plotted in Fig. 5. This process
was repeated at intervals of 0.05, for the values of n from 0.850
to 1.250. The curves were adopted as shown. The method used
was as follows: the maximum value, from the evidence of Fig. 4, was
assumed to be at the value, p = 95; the values of p = 61 and p = 78
were combined, and the center of the line connecting each pair
used as one point; with these assumptions the curves were drawn.
M ,VUL/r,2 n ./fK zX/P'w/ cwV'
FIG. 4. RELATIONS AT CUTOFF BETWEEN QUALITY AND THE VALUE OF f FOR
VARIOUS PRESSURES AT CONSTANT SPEED
Since the relation of Xc and n at constant speed and pressure is a
straight line, the curves of Fig. 5 were drawn by interpolation to
increments in the value of n to 0.01.
This procedure gave a series of relations between xc and p for
constant values of n. Since, however, the independent variables,
in any actual curve under examination, are n and p, the coordi
nates of the curves of Fig. 5 were changed so as to show the rela
tions of n and p at constant values of X . These relations are
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
shown in Fig. 6.
The effect of a change of pressure on the relations of xc and n
is not great between the limits of 75 to 150 lb. An approximate
equation has been worked out, therefore, which represents the
*.5 00 70. M M oA4 //o IZO /30 /40 ./S0
S076
4972
OX4
K 0.60
0.56
05Z
0.44
____ I
1 084
V
50 e, 71 I0 Io /9o00 I0 /0 /I0 /41 /100 /
sa'(Wzrf CE'/W(W ST ,ro," a9 L.B h5 w
FIG. 5. CHART SHOWING THE RELATION AT COTOFF BETWEEN QUALITY AND
PRESSURE FOR CONSTANT VALUES OF n FROM EXPANSION CURVE
I
 ,,o
i
r 1 ý 
I _.,,_
ILLINOIS ENGINEERING EXPERIMENT STATION
relations of Xc and n at an average pressure between the limits
mentioned. The equation corresponds to the relations at 129 lb.
and is of the form
x, = 1.245 n  0.576.
(b) Effect of varying the speed at constant pressure.Groups D,
E, and F, were run at speeds of 120, 90 and 150 r. p. m., respect
ively, with the average cutoff pressure on the diagrams constant
at 111 lb. absolute. The regulation of the governor was very
poor, there being about a 10 per cent drop in speed from no load
to full load. For this reason, the relations of Xc and n with va
rious speeds at constant pressure were affected by considerable va
riation of the speed itself for each group. The relations for each
group were found as already described, and the curves plotted in
Fig. 7. The relation of speed (designated as s) and Xc for con
stant values of n was derived from Fig. 7, and is given in Fig. 8.
The apparent relations of Xc, s, and n, obtained by drawing a
smooth curve through the three points obtained for each value
of n, are not satisfactory, owing to insufficient data and the change
of the speed itself in the three groups due to poor regulation.
The drop in the speed, for one group, does not seriously affect,
however, the relations of Xc and n for the various pressures at
constant speed.
2. Relation of the value of n to the quality of the steam mixture
at cutoff.From the evidence obtained from these tests, it may be
stated that, for any one engine, running at a given pressure and
speed, there is a definite relation between Xc and n which is
practically independent of the cutoff position within the limits ex
amined. This relation is apparently a linear one. It may also
be stated that the relation of Xc and n is dependent, to some ex
tent, on the absolute pressure at cutoff, and on the speed of the
engine.
It remained to compare the relations of xe and n for the en
gine tested with the relations for other engines. This comparison
is made in the next section.
An investigation of the value of k for adiabatic expansion,
(see page 83, Appendix 1) shows that there is a relation between
the initial quality x, and the value of k which, like the experiment
ally determined relation, is also a linear one. The adiabatic re
lations of x and k are plotted in Fig. 4, for the pressures used in
the tests.
Acknowledgment is made of the assistance rendered, in running these tests, by the follow
ing senior students, viz.. Messrs, Jacobsen, Schuster, Parmely. Hodgson. Janda, Butzer and
Wood, Class of 1910, and Messrs. Hasberg, Hagedorn, Allen, Herrcke, Cobb and Ponder, Class
of 1911.
4'
K
02
K
N
K
K
N
02
K
02
V//Z/f O  n , O/PO' ZX19/VSIOAV C(6RVE
FIG. 7. R LATIONq OF QUALITY AT CUTOFF ANt) THE VALUES OF n FOR VARIOUS
SPEEDS AT THE CONSTANT CUTOFF PRESSURE OF 111 POUNDS
k,
K
k
/00
060
085
080
07S
070
0.65
0.60
043
w., 0~
001
^5SS
FIG. 8.
,nt
Cons,
n v


4
'/00
7l~63
0900
~1
100
0.95
090
0.85
080
075
0.70
0.65
060
0S65
050
045
040
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
l60    
095 
090
0 so
05  
0.60    ^ ^          
050 
/'  
Srest af/0O/°PP/
_ o Test &t/SOP5
4 850 03 09.50 /000 1/5,9 I 0 19 //56 1200 2/3
J6o 40UU 44u 48U 2 S60 5o00 6 o
PISTON SPEED FEET PE/ MN//W/T
90 /00 I/0 120 130 140 /50 160
S/EE0 TPEVOL TI/70/S P/TP M/A/fNTE
RELATIONS AT CUTOFF BETWEEN QUALITY AND SPEED FOR CONSTANT
VALUES OF n AT CONSTANT PRESSURE
~0
'
ILLINOIS ENGINEERING EXPERIMENT STATION
III. THE APPROXIMATION OF THE ACTUAL STEAM
CONSUMPTION FROM INDICATOR DIAGRAMS
5. Engine Tests.The most reliable method of determining
the steam consumption of an engine is to measure or weigh the
water directly, preferably by means of a surface condenser. This
method necessitates an elaborate test, which disturbs the routine
of the plant tested, and is very costly for long tests of large
engines. The objections to tests of this kind are many, and a few
of them will be stated. When the boiler feed is measured, both
the engine and the boilers serving it have to be entirely discon
nected from other units, sometimes necessitating shutting down
the rest of the plant. Almost all tests, where there is more than
one unit, necessitate changes in heavy and permanent piping.
Boilers are apt to leak in service, and the measurements of the
leaks are unsatisfactory. One serious objection to long time tests
is that the different rates of steam consumption cannot be segre
gated. The ideal method of testing a steam engine would be a
method analagous to that used with electrical machines, i. e., to
measure instantaneous rates of consumption instead of the water
consumed over a long time.
6. The Missing Quantity.On account of the cost and dif
ficulties of making a test, many engineers have devised methods
of approximating the steam consumption without actually meas
uring it.
When indicator diagrams were first obtained, the loss from
initial condensation, or the existence of the "missing quantity",
was not suspected. The opinion, therefore, was that the con
sumption could be measured from the steam shown by the dia
gram at cutoff. After Clark' and Isherwood2 made their tests the
existence and amount of this initial condensation were revealed.
The very great difference in the proportion that this initial con
densation bears to the +otal weight of mixture present, either at
cutoff or during the expansion, that is found in different types and
sizes of engines has prevented any reliable determinations of the
actual steam consumption by this method. The steam consumption
computed from the diagram, when using saturated steam, is gen
erally from 15 per cent to 50 per cent below the actual consumption.
The devising of an accurate method of measuring the actual
weight of steam consumed from the diagram has therefore been
1 Railway Machinery
2 Engineering Researches.
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
regarded as impossible. Thurston' states that "the steam or water
consumption of an engine cannot be exactly ascertained by the
use of the indicator" for the reasons mentioned. Most other
writers on the subject have expressed similar views.
7. Approximation of the Initial Condensation..Methods of com
puting the weight or proportion of the "missing quantity", from
the dimensions, type, and speed of the engine considered, as shown
by the results of large numbers of tests, have been devised by
Thurston4, Escher', Marks5, Fourier, English6, Bodmer', Cotterill8,
Heck', and others. The results obtained from these methods
have not been uniform, and do not agree closely enough with the
test results to be used with confidence. Moreover, none of these
methods is applicable when superheated steam is used. Profes
sor Heck10 states that the steam consumption computed by the use
of his formula should ordinarily show not more than 10 per cent
difference from the test results.
8. The Relation of xc and n.The relation of xc and n, for the
same engine, has been shown to be very definite under
the same conditions of pressure and speed. This relation, or
dependence, of n upon xc , however, is not seriously affected
by changes of pressure and speed, within the limits of the tests.
The ordinary speeds of similar typ es of engines, 70 to 120 r. p. m.,
do not affect the relation seriously enough to be taken into ac
count when examining such cases, because of the twofold char
acter of speed in its influence upon the action of the cylinder walls.
The engine experimented upon was operated at 120 r. p. m.,
and had a stroke of 2 ft. Other engines of this class run at speeds
as low as 70 r. p. m., but have strokes of 5 or 6 ft. Cylinder con
densation is not dependent upon rotative speed alone, but is also
influenced by the piston speed, as determined by the length of
the stroke. On account of different lengths of stroke, different
engines cannot be compared on the basis of rotative speed. Thus
while the small engine tested has a rotative speed of 120 r. p. m.,
its piston speed is only 480 ft. per minute. In large engines,
while the rotative speed may be only 70 r. p. m., yet, with strokes
of 6 ft., the piston speed is 840 ft. per minute. What the smaller
engine gained by higher rotative speed, the large engine made up
in a measure by higher piston speed.
3 Engine and Boiler Trials, p. 237. 7 Engineering (London), Mar. 4,1892, p. 299.
4 A Manual of the Ste am Engine, p. 517. 8 The Steam Engine, p. 339.
4 Engineer (London), 1882. [p. 206.] 9 The Steam Engine, p. 109.
5 Relative Proportions of the Steam Engine, 10 The Steam Engine, p. 119.
Proceedings of the Brit.Inst. of M. E., Oct, 1889.
ILLINOIS ENGINEERING EXPERIMENT STATION
After taking into account the two parts of which speed is
composed, it is found that the speeds of stationary engines of the
type tested are in substantially the same range. On account of
this fact, only the results of the tests run at 120 r. p. m. have been
used in the applications made at present.
The relation of xc and n has been found to be practically
independent of cylinder size. This statement is true for non
jacketed cylinders and for pressures in the range examined. This
is shown in a general way in the following discussion for satu
rated steam.
9. The Phenomena Occurring in the Cylinder.Castiron is uni
versally used for steam cylinders. The greatest source of loss
in the cylinder is due primarily to the use of a metallic structure,
from practical considerations. The skin surface of this metal,
which is a fairly good conductor of heat, must be heated once every
cycle from the temperature acquired from contact with the ex
haust steam, up to nearly the temperature of the admission steam,
this heating being accomplished by the condensation of some of
the incoming steam. The amount of this condensation, measured
as the proportion of the mixture present, varies with the size,
valve design, relative roughness of the interior surface, tempera
ture range, length of cutoff, speed, location of ports and port
passages, quality of the steam supplied, and the jacketing and
lagging. It can easily be seen, from the number and relative
magnitude of these variables, that the computation of the weight
of condensation, by means of a formula which will take these vari
ables into account, can never be an accurate operation.
After many examinations into the cases of different types and
sizes of engines, with nonjacketed cylinders in good order, and
with pressure limits similar to those used with the tests, it has
been found that while the initial condensation is subject to the
action of ten or more variables, yet the value of n resulting from
a given value of xc is almost always substantially the same. A
few of the applications showing this point will be found in Table
4. Here the cylinder sizes vary from 10½ in. x 12 in. to 34.2 in.
x 60 in., the speeds from 48 to 263 r. p. m., and the types include
slowspeed Corliss, high speed, and locomotive engines. The
possibility of calculating accurately the weight of condensation
in these different cases may be easily imagined.
The phenomena caused by the presence of the cylinder walls,
in the class of engines discussed, have been found to be divided
into two natural classes: those occurring before cutoff, and those
CLAYTON NEW ANALYSIS OF CYLINDER PERFORMANCE
occurring after cutoff. The phenomena occurring before cutoff
are controlled by the action of the ten or more variables already
mentioned, and therefore are subject to all the variation that may
occur in any individual case to be examined. For this reason,
any method of computing the condensation accurately from the
physical facts surrounding the case is open to objection. This
method also cannot allow for the use of superheated steam, an
increasingly important condition. The phenomena occurring af
ter cutoff are practically independent of all variables except
xc, and initial pressure and speed. Of these variables, only the
value of xc and the initial pressure have proved to be of material
importance in the applications made thus far. This may be
summed up by stating that the value of Xc, in any particular
case, is subject to the action of many important variables, but
that the relation of xc and n is practically independent of these
variables within the limits examined in this investigation.
10. The Phenomena of Condensation and Reevaporation during
Expansion. When adiabatic expansion of initially dry saturated
steam takes place, a part of the steam is condensed as the pres
sure is lowered, the condensed steam giving up its latent heat
which is converted into work. When superheated steam is ex
panded adiabatically, the steam loses its superheat until satura
tion is reached, after which condensation takes place as in the
case of initially dry steam.
When, however, the steam is initially composed of a large
proportion of water, both being at the same temperature, adia
batic expansion may take place without additional condensation
and may even be accompanied by reevaporation. This fact is
due to the large amount of heat contained in the water, a part of
which flashes into steam as the pressure is lowered, thus supply
ing and neutralizing the loss of steam volume by condensation
which takes place with steam initially dry. Adiabatic expansion
is accompanied by condensation when the initial quality is above
the value 0.50 at an initial pressure of 240 lb. per sq. in. absolute,
but below the value of 0.50, it is accompanied by reevaporation.
An examination of Table 20 will show the values of the initial
quality which form the line of demarcation of condensation and
reevaporation during the adiabatic change of state.
In the actual engine using saturated steam, as has already
been pointed out, some of the incoming steam is condensed in
warming up the surface of the cylinder walls to approximately
the temperature of the incoming steam. When the admission of
22 ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 5
CONDENSATION AND REEVAPORATION OF STEAM DURING EXPANSION
E xam ple N o....... .... .......... ............... .......... .... ......... 1 2
Initial Quality, Parts of Unity......................................... 0.540 0.950
PRESSURES, LB. PER SQ. IN. ABSOLUTE
Initial ............ .......... ...... ...... .... ......................... 145.0 145.0
F inal........................ ... . ............................ ......... 20.0 20.0
VALUE OF a IN EQUATION PVn=C
Adiabatic expansion, from Table 20. ................................... 1.082 1.133
Actual expansion in engint, tested, from Fig, 6 ................... ... 0.900 1.230
VOLUME OF STEAM PRESENT, CU. FT. (VOLUME OF WATER NEGLECTED)
Final, adiabatic expansion................... ....................... . 6.24 5.75
Final, curve of constant steam 'weight ............... ................ 6.44 6.44
Final, actual expansion in engine tested .......................... 9.04 5.00
WEIGHT OF STEAM PRESENT, LB.
Inital, plus water.................... .. ... ... . ............. .... 0.594 0,338
Initial, steam only...... .......... .............................. 0.321 0.321
Final, adiaoatic expansion..... ...... ................................. 0.311 0.287
Final, curve of constant steam weight...................... ........ 0.321 0.321
Final, actual expansion in engine tested....... ....................... 0.450 0.249
QUALITY OF STEAM AT FINAL PRESSURE, PARTS OF UNITY
Adiabatic expansion ............... ............. ................. . 0.524 0.849
Curve of constant steam weight ..................................... 0.50 0.950
Actual expansion in engine tested............... .. ........... ........ 0.757 0.736
CONDENSATION OR REEVAPORATION, PARTS OF UNITY
Apparent reevaporation....................... ....... .......... ...... 0.217
R eal reevaporation .............................................. .... . 0.233
Apparent condensation ................. .................. ........... 0.214
Real condensation ........ ..... .... ................................. 0.113
steam is cut off and expansion commences, the condensation, due
to the presence of the cylinder walls, continues in general until,
at some point during expansion, the water on the cylinder walls
begins to reevaporate at such a rate that the weight of steam
present at the end of expansion is greater than that which was
present at cutoff.
To show the effects and extreme values of condensation and
reevaporation during expansion, there have been prepared in
Table 5 two examples, using the average results of tests which
have been run on the engine tested (see Appendix 2).
CLAYTONNEW ANALYSIS OF CYLINDER PFRFORMANGF
S1. Examples.Example 1 is a condition which obtains in
the engine tested when using saturated steam at about 140 lb.
gauge pressure with a length of cutoff of about 3 per cent. All
values of the qualities mentioned are portions of the total weight
of mixture in parts of unity. The value of Xc is 0.540, a low
value, yet one which often obtains in small engines. If this
steam were expanded adiabatically to the back pressure, 20 lb.
absolute, the resulting quality would be 0.524, giving a condensa
tion of 0.016. The expansion which actually takes place in the
engine tested under these conditions results in a final quality of
0.757, showing that the apparent reevaporation from the value
of Xc has been 0.217. However, the steam mixture in expanding
did expand adiabatically in order to give up heat to work, but the
actual or what might be called the gross expansion, was changed
in character by the reevaporation of a large proportion of the
water present, due to the return of heat from the cylinder walls
and the consequent flashing into steam of part of the water when
the pressure and the temperature were lowered. The real
reevaporation, measured by its effect upon adiabatic expansion,
has been the difference between 0.757 and 0.524 or 0.233.
The actual expansion in this case has been the result of two
factors which worked simultaneously; adiabatic expansion, and
the return of heat from the cylinder walls to the mixture. The
first factor, adiabatic expansion, as already explained, is itself
the result of two neutralizing or opposing conditions, i. e., the
condensation of initially dry steam during expansion, and the
relatively smaller amount of reevaporation of water initially in the
mixture due to the liberation of its excess of heat when the pres
sure and temperature were lowered. The net result of the two
conditions of thL adiabatic expansion, however, was a condensa
tion. The second factor is the large amount of reevaporation
due to the return of heat from the surface of the cylinder walls
to the condensed steam, amounting in example 1 to 0.233, or,
roughly, there has been reevaporated during expansion I of the
entire weight of mixture present.
Example 2 shows conditions which obtain in the engine tested
when served with steam at about 140 lb. gauge pressure, super
heated about 125° F. with a length of cutoff of about 45 per cent.
The value of xc is 0.950, a very high value for this class of en
gine. The quality after adiabatic expansion would be 0.849, a
condensation of 0.101. Where values of xc are as high as 0.950,
however, no reevaporation takes place in practice, but condensa
ILLINOIS ENGINEERING EXPERIMENT STATION
tion continues throughout expansion. After expansion in the
engine tested, the quality would be 0.736, showing much greater
condensation than that due to adiabatic expansion alone. The
apparent condensation has been 0.214, but the real condensation,
measured by its effect upon adiabatic expansion, has been 0.113.
The actual expansion in example 2, as in example 1, has been
the result of two factors; adiabatic expansion, and the further
abstraction of heat during the whole expansion by the cylinder
walls. Heat is abstracted during expansion by the cylinder in
the engine tested at all values of x, above 0.85, thus giving
values of n higher than the adiabatic value k.
The phenomena of condensation and reevaporation during
expansion are the causes of the relations existing between xc and
n in the cylinders of steam engines. The two examples given
show values obtained in extreme cases which illustrate very well
the effect of xc upon the character of the expansion, and there
fore upon the value of n, and show the range of values that n
assumes in one engine due to a change in the value of xc.
12. The New Method of Approximating the Value of xc.The
fact that the value of n depends upon the value of Xc and that the
values have definite relations under definite conditions, makes it
possible to reverse the order of procedure followed in obtaining
the relation and to approximate the value of Xc (and, therefore,
the actual steam consumed) from the value of n.
It appears, therefore, that this method of approximating the
value of xc at cutoff from experimentally determined relations,
and thus accounting for the "missing quantity", is upon much
surer ground than any method of computing condensation from
the physical facts surrounding the case. It approaches the prob
lem from the side where the phenomena occurring are practically
independent of all the variables mentioned.
13. Advantages of the Method. This method is free from sev
eral objections to which tests are open. It measures the consump
tion in one revolution, and is, therefore, practically measuring a
rate instead of a quantity. The only data needed for an approxi
mation are one set of indicator diagrams, taken simultaneously,
the constants of size and clearance, and the speed of the engine
tested. No interruption of any kind in the routine of a plant is
caused, and the expense incurred is not to be compared with that
of an equally accurate test. The method is accurate enough for
almost all purposes except guarantee tests subject to bonus and
forfeit contracts. In the case of locomotives on the road, it is
CLAYTONNEW ANALYSIS OF CYLINDFR PERFORMANCE
the only possible method of approximating the steam consump
tion of the main engines, due to the use of steam by the airpump,
trainheating system, blower, generator sets, safety valves,
whistle, blowoff valves, and leaks. The same is true of marine
engines, where many auxiliaries are supplied with steam from the
same boilers, and exhaust into the same surface condensers. The
method is especially useful for noncondensing engines, where the
boilerfeed measurement method is the only practicable one.
Steam consumption may be obtained as often as is desired instead
of probably once in an engine's life.
14. LimitationsThe relations of Xc and n given in chapter
II are applicable, however, only to nonjacketed cylinders ex
hausting at very close to atmospheric pressure. When the back
pressure is raised to 30 lb. absolute, for instance, there is a new
series of relations existing for the same initial pressure, due to a
different temperature range in the cylinder and the consequent
alteration of the phenomena occurring after cutoff. Steam
jackets also alter the phenomena occurring after cutoff, and
therefore have to be examined separately for the relations of
Xc and n. The steam used in the jackets and in reheaters has of
course to be collected and weighed as heretofore.
Since this method rests entirely on the indicator diagram,
great care must be observed in taking these diagrams. The indi
cator itself must be an accurate instrument in the best possible
condition. The indicator connections must be short and direct.
An extensive investigation by W. F. M. Goss" shows that the
long and indirect pipe connections materially alter the form and
character of the expansion curves. A correct reducing motion,
free from lost motion, must be used so as to reproduce the actual
expansion. The arrangement of having one indicator at each end
of the cylinder is always to be preferred.
The applications of this method must be made with judgment
and care. If large leakage exists, only an approximate solution
can be obtained, as certain assumptions have to be made. The
various steps involved in the use of the method must be thor
oughly comprehended to give satisfaction.
15. Application of the Method. The relations of Xc and n, as
determined for various pressures at constant speed from the en
gine described (see Appendix 2,) were plotted in the form of the
chart shown in Fig. 6.
The next step was to examine, with certain restrictions, the
11Trans. A. S. M. E. XVII, p. 398.
26 ILLINOIS ENGINEERING EXPERIMENT STATION
tests of other engines, and to compare the relations of xc and n
with those given in Fig. 6. The restricting conditions imposed
were: (1) that the tests should come from reliable sources; (2) that
the data supplied should be complete enough to be able to com
pute the quantities needed for comparison; (3) that the cylinders
should be nonjacketed; (4) that the diagrams furnished should be
representative of average conditions; (5) that the back pressure
in the cylinder examined should be practically atmospheric; (6)
that no large leaks should exist.
The values of xc., n and p were first found from the set of
diagrams to be examined. Next, the values of n and p were located
in Fig. 6 and the corresponding value of xc found, as obtained in
the tests given in chapter II. The value of xc obtained from the
chart and that obtained from the test examined were compared,
and the steam consumption, as computed by the value of xc taken
from the chart, was obtained.
The results of tests which fulfilled the conditions imposed
are given in Table 4. Four distinct classes of engines were
examined. These include simple Corliss, twovalve and four
valve types, the high pressure cylinders of compound engines,
the intermediate pressure cylinders of triple expansion engines,
high speed, and simple locomotive engines. The sizes range
from 10i in. x 12 in. to 34.2 in. x 60 in., and the speeds from 263
to 47.98 r. p. m.
The final results, given in columns 24, 29, 31 and 36 of
Table 4 were averaged (analysis 201 excepted) and the averages
are given in the following table:
APPROXIMATION FROM CHARTFIG. 6
Difference from Test Results Value of Actual Steam Con
Average Difference from Test Results per cent sumption
per cent
Irrespective of Sign ..................... ..... .... .... 3.06 3.72
Higher (+) or Lower () than Tests Results ............. 1.93 +2.50
APPROXIMATION FROM EQUATION Xc = 1.245n 0.576
Irrespective of Sign .................. .... ................. 3.32 3.98
Higher (+) or Lower () than Test Results...............
+I.9t
TABLE 4
Approximation of the Actual Steam Consumption From Indicator Diagrams Taken From NonJacketed Steam Engines
Class of Engine
2 
Date of
Test
6
Approximation from Chart
on from Equation Xl= 1.245 n 0.576
..
S
at'
Os
016
0570
...tsR
0'
ni~
U
10
+5t. 49
~ l707s
o½ §1
gla '?5
^13 O
sa0 0'
5OS .5
SI S
30
N
SIMPLE CORLISS. 2VALVE. AND
4VALVE, NONCONDENSING ENGINES
101 Corllss. Single Cylinder Not ascertained
021 Corlsi, Single Cylinder Not ascert'ined
103 Corliss. Single Cylinder Not ascertained
404 DoubleValve. 2Cylinders Not ascertained
105 FourValve. Single Cylinder Not aueertoined
Iidway t1)ynani
106u ourValve. Stngle Cylinder Engine Co.
00b Same Engine as 106a
40c Same Engine as 106a
4664 Same Engine as 106a
07 Corliss, 2 Cylinders Not ascertained
084 FourValve. Single Cylinder Not ascertained
108b Same Engine as Ia (Clondensing)
409 Corliss. 2 Cylinders 1I Cond'nsing) Not asertainrd
10 Csorliss. I Cylinder (I enId I(ondrensii') Not, ascertained
III1 Corliss. 2Cylindters(l Cond'cnsini' Not asertuined
!Not ascertaini d
INot ascertained
Not aseertained
Not ascertainrd
Not ascertained
d Makers Work.
Not ascertaintd
Not ascertained
SNot ascerlained
Not ascertained
Geo. H. Barrus
uGe. H. BirIus
(ie. H. B.rrus
ie. SI. 4.esu.
'('o H. Btrrus
G ee. H, i~arrus
Ae. H. BaN us
Ie ,. Barrus
io. H Burrus
Not ascertained
Not ascertained
Not acertuIned
Not ascertained
Not ascertained
101010
Not ascertained
Not ascertained
Not ascertained
Not ascertained
:Engine Tests". No. 1
"1oinol Tests", No. 2
"En ineTests". No. 7
F"Engine Tests", No. 10b
Engine Tests". No. 11
Makers
S'Engine Tests". No. 31b
Engine Tests", No. 17a
'Engine Tests", No. 17b
"Engin Tests". No. 15
"Engine Tests". No. 4
'Engine Tests", No. 29
73 X60
2H8 x 59Y.
2.i3, x 4X
I: x 241. 2
167 x 32
10%.s 12
47 n2,.
16 X 42
18 x Atd
73 nCAh
34.2 x &I
28 X60
74.7 4482 1.890
64.8 3888 3,362
64.7 3882 1.736
152.9 9174 0.8670
79.8 4788 0,3915
263 15780 0.1491
258 15480 0,1213
260 1560M 0 0.639
263 15780 0.0439
84.9 5094 1.742
165.6 9936 0.4735
164,4 9864 0.6137
61 3660 3602
50.3 3198 3.63
60.27 3616.2 3,953
0.167 3.529
0 116 1.852
0.0635 0.9305
0.0607 0.4532
0.0242 0.1733
0,0160 041373
00260 0.08990
0.0351 0.0790
0.041 1.783
00330 0.5065
0.0712 0.66849
0.080 3 682
0.093 35,26
0.250 4.203
0.825 1.098 65
0.801I 108 75
0.757 .051 75
0784 .131 70
0,603 0.964 60
0.794 .076 i 120
0.69 1.034 115
0.598 0.931 25
0.509 0.86 120
0.797 1.077 95
0.768 1.09.5 63
0.826 1.116 63
0.853 1,149 80
0.701 .071 74
0.680 1.0048 68
2.172 2.042 9160
3.551 3.384 13150
1.915 1.799 6985
0.8935 0.8309 7615
0.465 0.41058 1941
0.1791 0.1549 2440
0.1337 01.1177 1822
0.0915 0.0655 1021
0.0787 0.0436 60
1.8:5 1.7914 9140
0.5125 0.4705 4703
0.72D2 0.6490 6402
3.682 3602 13187
3.70 3.6i92 11810
4.033 3.7M 13685
30.00 +6.1 0.793
25.96 0.7 0801
30.06 +30 0.73i
24.53 4,,2 0.833
3809 +433 0 O24
294.9 +3.7 0.76
2301 30 .71
24.50 +24 W .5:
2B.68 0 .7 050
26069 43.0 0.5
22.37 +1,2 ,780
30.(0 +5.8 0 84
21 44 +i11. 0.854
..7 +1.7 0..75
24.33 4.3 0.729
4.2 10o 1.980 StW ,i4
+1 : 3.52 !3.345 . 30'3 2557
3 2 1 91, 14 797 B9, ;W.i
+6t. 0.8752 0.8117 744, 4.(oI
+3. 0.4381 0.3774 4i01.7 13.101
:. 0.102 0.1560 246t 2:.,15
+1. 0.1349 0.1I189 1810 232
 25 0.0921 0.0661 105Y1 24.701
1. 0.0796 0.0447 705 27732
_40 056 I1.815 9275 07.0A
231 0.)4937 04007 4577 2145
1 5 0.69407 0.6235 650 29:40
+0 ,1 3.677 3...597 130 W .40
0.4 3 740 3.647 116,5 22.28
+7.2 3.922 3.673 132) 23.02
leproductions of diagrams used. said to be representatie
leproduetions of diagrams used, said to bi representatite
epIroducions of diagrams used. said to be representative
iteproducIons of diagrams used, said to be representatie
leprodue tions of diagrams used, said to be eprescntutlve
1,lueprint of tracings furnished, said to be representatie
nueprint of tracings furnished, said to be represontative
liluaprint of traciags furnished, said to be representatin
ilueprint of tracings furnished, said to be representative
teproductions of diagrams used. said to be represelative
Reprodurtions of diagrams used, said to Oe representatio
ieprodictlons of diarams used, said to be representatie
Reproductions of diagrams used, said to be representative
iteproductions of diagrams used. said to be representative
Reproductions of diagrams used, said to be representative
15 Cotr iss ross 'con pound
152 iiitset' rrossomlnpound
1543 COiss 'Crossiionound
VatLs C'lmtieil Co.
lukyEngiineCo
Co 1. Corliss
'Thos. Oubs & Co G. A. Otakes.. MW . MWhite
Siloo) lleld. N. J.
huatton & Tro El. Rs Co Saroent & Lun0y
'aTirtuket Water Winrks Win. Rent. D. . Jacobus
Po tubm't 1. 4.
201 CorlisT (slow spe'd .t.. pin . enl Nes .sNertained National Tnsit Co. I uk' .IJ. . Dento
ton.lad.
COMPOUND CONDENSING ENGINESH. P. CYLINDERS
12003 Makers 20 x 36 x36 3 3.5 6740 433.5 15.00 75.83 4550 1.481 1,244 0.1012 1.582 0.786 1.079 100 0.777 1.1 1.600 1.498 6820 15.73 +1.2 0.767 2.4 1.621 1.5198 6915 15.95 +2.6 C Blueprint of tracing furnished, and was representative
5 602 Makers 18I x36 x3:6 3% 4.3 b675 639.2 14.20 123.3 7398 1.173 1.023 0.1490 1.322 0.774 1.060 120 0749 32 1.366 1.2170 9005 14.09 +38 0.744 39 1375 1.226 70 .19 +4.6 C lueprint of tracing furnished, and wasrepresentatve
51 91 TrannsA. SM E. XIII. 176 15 x 30% x 30 2 4.0 2007 140.78 14926 47.99 2879 0 6970 0.5492 0.0218 0.7188 0.764 1,047 130 0.72 1.7 0.742 07324 2109 14.97 +5.1 0.728 4.7 0.72 0.7324 109 14.97 +5.1 C &E Reproductions f diagrams used, said to be representatlve
TRIPLE EXPANSION CONDENSING ENGINESI. P. CYLINDERS
45 93 Tran A M E. XIV. 340 24% x 34 x 5 36 4 2.10 462 328 05 14.09 27.66 1659.6 2.787 1.432 0.031 2818 0.508 0.914 3.5 0.470 7.5 3.08 3.017 5003 15.25 +8.2 0562 +10.6 2.550 2.519 4180 12.74 9.6 C Rpd ionsonf ddiagramssaidto b reprsentavee Speed
I ,~ and Cutoffpressure. outside the limufsof Investigation.
1o1 Piston valve. Single Cylinder
in Singl'e valve'. Single Cylinder
l 'iluTw Cylndee Slide Valdet
HIGH SPEED SINGLEVALVE. NONCONDENSING ENGINES
A,. L. hde Sons 'Not ... re.u.. is l Not . sre .i. d Not is.setain(d M .kers 10 . . 6 2% 13.15 4820 184.6 2.35 253.4 15204 0.3109 0.3060 0.0948 0.444 07.9 1.027 140 0,710 3.0 0.4:31i 0.33362 .i O7.70. +6.1 0.703
Not nacrtaintd No' ,i artaned <e. H. a''rue tt 4 i ssiTe Not scti d. 13 14 x 13 2 10.0 1710 N053 32.61 '46 176 0 O178 0.4117 0.8643 0.4702 0.660 0.970 8 i 047 4,0 0.1871) 0.4aM 1070 1 35.40 +7.5 0.14
Nol ascertland Not as tantd . H. irus Not sceraine Engine Tes". No. 24 3 2t 12.0 8.6 7 3.71 24.4 404 01353 0.314 0.5 47 0.675 095 74 0 5.0 0.25 1.14 2170 35. 75 0.50
SIMPLE LOCOMOTIVE ENGINES
Setenrotatls loitu. Poedue Inis 1~alioeutoet XV. 40 56, 4 usc
ivneks l~afat its,'. 100
4.9 0.4352 0.3944 5478 3002 +7.4 C B .luepei.ts of tracingsafurnished, said to be .epresonttire
0.> 0.898 0.425 I97 35.61 40..' C ReIteroductions of diagrams used. said to be representative
3 7 0 3021 0.4 2. 47 31. .48 54.'> W Reproductions of diagram used. said to he representative
73.05 High Steam Presues in 16xt 2 C 7180 252.79 2840 97.08 5824.8 1.232 1.0164 0.1947 1.42167 0.711 1.003 100 0.683 3.9 1.488 1.29 7540 29.83 +5.0 0.673 5.3 1.5110 1.3163 7675 30.38 +69 C Originaldiagran furnished asrepresentative
Loeomotive Servicer No. H 7.44 7168
208120 L 7.34 7.63
10 17 II I1
Makers
Where Tested
21 22
By Whonm
Tested
Source of Dia
nramts and
Test Results
Cylinder
Dimen
sions
8h
Il II 34 II 10 3'!
15
9
REMARKS
31
23 2t 25 2 27 1 2
I I I I I
I
o and
CLAY TONNEW ANALYSIS OF CYLINDER PERFORMANCE
Analysis 201 shows an application the conditions of speed
and cutoff pressure of which are far outside of the limits exam
ined. The values given were obtained by extrapolating as
straight lines the lower portions of the curves of constant value
of Xc in the chart of Fig. 6. Although the speed is only 27.66
r. p. m. and the cutoff pressure only 38.5 lb. absolute, the value of
xc by chart was determined as 0.470, while the value by test is
0.508, a difference of 7.5 per cent based on the test value of xe . This
application is given to show that an extrapolation of the method
to unusual conditions of speed and cutoff pressure does not lead
to absurd results, although it is not nearly as accurate as the ap
plications to speeds higher than 50 r. p. m.
The results of the applications made up to the present time,
with the restricting conditions imposed, tend to show that the
steam consumption of engines may be approximated from the in
dicator diagram to within an average difference of less than 4
per cent from the test results. Individual examples, however,
may show as much as 8 per cent difference in rare cases.
16. Directions for Applying the Method to Engine Testing.The
manner of applying the method to the class of engines tested is
best illustrated by taking an actual case and tracing the steps
necessary to a determination of the steam consumption. It is to
be remembered that the method accounts for the actual weight
of steam and water present in one revolution only as represented
by the set of diagrams analyzed.
The set of diagrams to be analyzed is selected in different
ways, according to the test conditions. If the load on the engine
to be tested is fairly uniform, and if the average steam consump
tion over a period of time be desired, one set of diagrams
taken simultaneously is selected after the manner described in
detail in Appendix 3, p. 97. This method briefly is as follows: all
diagrams taken over a period of time at equal intervals are in
tegrated and the mean effective pressure of each diagram obtain
ed. The combination of one set of diagrams is sought nearest to
the average mean effective pressure and taken at the average
steam pressure. This set is taken to represent the mean condi
tion of power and is the set to be analyzed. If the load is ex
tremely variable, the diagrams must be separated into groups of
similar cutoff values, and one set from each group analyzed as
outlined for the uniform load condition.
If it be desired to obtain a waterrate curve, the engine is
operated under various loads, ranging from noload to fullload,
ILLINOIS ENGINEERING EXPERIMENT STATION
and one set of diagrams, taken simultaneously is obtained at each
load. Each set is analyzed and the result used to obtain the
usual waterrate curve. In this case, no average diagrams are
necessary as only the steam consumed at each load is desired.
It is now assumed that the set of diagrams to be analyzed is
selected, that they are taken from a singlecylinder nonjacketed
noncondensing Corliss engine, 28iin. x 591 in., the engine se
lected as an example being analysis 102 in Table 4.
Logarithmic diagrams of both indicator diagrams are con
structed as described in detail in Appendix 1. The average value
of n from the expansion curves of the headend and crankend
diagrams is then found to be 1.108, and the average cutoff pres
sure 75 lb. per sq. in. absolute.
The next step is to examine Fig. 6 and locate the intersection
of the vertical line for the value of n= 1.108 with the horizontal
line for the value of the absolute cutoff pressure of 75 lb. This
intersection is seen to be halfway between the "lines of constant
quality" of 0.79 and 0.80, giving a value of 0.795. This means
that the steam accounted for by the indicator as being present in
the clearance and displacement spaces up to cutoff is pres
ent at a quality of 0.795, or that it contains water to the amount
of 0.205.
From the logarithmic diagram, it is found that the headend
of the cylinder contains 8.57 cu. ft. of steam at the average cut
off pressure of 75 lb. absolute, while the crankend contains 7.83
cu. ft., making a total of 16.40 cu. ft. From the Marks and Davis
steam tables, the specific value of steam at 75 lb. pressure is 5.81
cu. ft. per lb., thus accounting for 2.822 lb. of dry steam. This
weight at the quality of 0.795 equals 3.551 lb., the total weight
of steam and water present per revolution. In a similar man
ner, from the logarithmic diagram, as described in Part II, chap
ter X, it is found that the total weight of dry steam retained in
the compression in both ends equals 0.167 lb. This compression
steam is present in the amount accounted for at cutoff so that the
net weight of steam passing through the cylinder per revolution
is 3.5510.137, or 3.384 lb. As the engine is running at 64.8 rev
olutions per minute, or 3888 revolutions per hour, the total steam
consumed per hour equals 3888 x 3.384 = 13150 lb. From
the diagrams, the indicated horsepower is found to be 506.5, thus
the steam consumption is determined at 25.96 lb. per i. h. p.
hour, while the condenser test of this engine from which these
diagrams were taken shows a steam consumption of 25.80 lb.
per i. h. p. hour, a difference of 0.6 per cent.
4p80 .g0 950 1000 14960 I 00 /./150 z 200 A ?0
",l l II /,5
1.50 0.55 00. O0 Oi _O 0.6' 0.<0 0.90
so \ / ' , " I I\ s
.83, ,90 , , , 950 /.0 / !rs ! / /I / / /F . 0 ,
V ^S^/EAOStS^ ' FO E'I.F "
IAO
/'C,
, . I , , tV ^ , ,v IS ^ i l,!VvS   I
/00[
, , l I ! I , I , I N
50 1 ' ' ' 1Iý 'S 1\ I I , I\ t\
, ! I . ýw .I '1 10.T
^~~~~ ,, ,^ ^Z^ /___. S^ X ^^  ^S < _ \K ^  ^J . .^ ^A
I050 1800I
a e
\ \ 6, CHART SH0W\ . \TERIAOBTWN _ S 9UHX \ Tr AD LEOnFCN \ _A \NT \o AT CUTOFF
\ \ \'^~v .^ ^ \ ,^^^ \ Y^^ J\ ,^ \'SI  \^S ^ l _^ S\ _ \ \ V A
   \N _v \_S _ _ '^^ s S ^ S v \^  ^ ^   \DS ^ ^   '  '^
______ ____, .\ ,,^. ^ .,, ^ ,,5 \Y ^ ^ ^ S v ,, \ ,\ .\ \ , \ , \ ,< "' \ S \ \o_
\, \ _ __ __. \ , ", ,\, \ \ ,, \ ^ ^ ^l ^ \N \!" ^ ^ K . ^ S .,S ', \ \ ,, ' "., _S^ , \ '\ _\ \ _S ,
" ,' \ ,' \ '__ _    ^ X \ " \ ' X \,,I X ,,.\ X, \ \ \ \ \l. <
O.S \fff \ . .5 7 ., .P09509 <
4 0, ,, ,. ,, ,,,' ,                 _ _ __ ,,__ , \
0.8SO 0.90 0.95 ' .O , ..S \.Q i.f0 \.O \ ', \
\~~~V9V ,.\' \ ",PO \//^/ \ ,, ,, \\ \ ,' , ,, ,
\ ,, , \ . \ . CHAK \HWB ' ~ ',AIO ",WI! Pa»» AT \1tO~ 'B ,A.ni o\ n \O \OUTH Qn\T ,,CT
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
IV. CONCLUSIONS
The following conclusions have been drawn from the results
of this investigation, as applicable to nonjacketed steam cylin
ders in good condition exhausting at or near atmospheric pres
sure, and with the limitations imposed as given in Part I.
1. At a given initial pressure and speed of engine, there is
a definite relation existing between Xc and n, in any one cylin
der, which is practically independent of the cutoff position.
2. This relation is practically independent of cylinder size
and of engine speed; it is therefore applicable to other cylinders
of the same type.
8 By means of the experimentally determined relations of
Xc and n, the value of xe may be approximated from the aver
age value of n obtained from the expansion curves of one set of
indicator diagrams, taken simultaneously; therefore the actual
weight of steam present in one revolution may be approximated.
4. The actual steam consumption may be obtained by this
method from the indicator diagram to within an average of 4 per
cent of the amount consumed as measured by test.
5. This method has the following advantages not possessed
by tests: it is more accurate than the average test, and is the
most accurate method available for testing certain classes of en
gines; it virtually measures an instantaneous rate instead of an
average quantity over a long time, and thus enables a large num
ber of points to be obtained for a waterrate curve; it permits of
making tests at frequent intervals instead of once in the en
gine's life; the expense is not to be compared with that of an
equally accurate test; it involves no change in the routine of the
plant tested.
PART II. THE LOGARITHMIC DIAGRAM APPLIED TO ALL
ELASTIC MEDIA
V. THE LOGARITHMIC DIAGRAM
17. 7he Indicator Diagram Plotted on Logarithmic Crosssection
Paper.The logarithmic diagram is obtained by transferring the
indicator or PVdiagram to logarithmic crosssection paper. The
method of transfer is as follows. The coordinates of the PVdia
gram are proportional to pressure and stroke, the latter being pro
portional to the volume displaced by the piston. The coordinates
of from 10 to 30 points on the PVdiagram are found in terms of
ILLINOIS ENGINEERING EXPERIMENT STATION
absolute pressures, preferably in lb. per sq. in., and of absolute
volumes, preferably in cu. ft. These points are plotted on log
arithmic cross section paper and are connected by a smooth
curve, forming a figure which will be called the logarithmic dia
gram. Fig. 9 shows the logarithmic diagrams derived from the
PVdiagrams of Fig. 15.
0
z
IL
_j
C
I,)
0~
U
It)
VI
0.
I
AS5OLUTE VOLUMECU. FT.
FIG. 9. LOGARITHMIC DIAGRAMS PLOTTED FROM FIG. 15
18. The Form of Expansion and Compression Curves from Prac
tice. About 300 PV diagrams from engines using steam, gas, air,
and ammonia have been examined to investigate the form and
character of the expansion and compression curves. As a re
sult, it may be stated that, free from certain abnormal influences,
expansion or compression of an elastic medium takes place
in the cylinders of reciprocating engines substantially according
to the law, PlYT =C.
19. Mathematical Relations of the Law, PVn =C.The equa
tion of the polytropic curve, PV/ '= C, when plotted on rectangu
lar crosssection paper, gives a curve depending for its form and
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
position on the values of P, V, n, and C. When this curve is
plotted on logarithmic paper, it becomes a straight line, depend
ing for its slope on the value of n and for its position upon the
value of C. The relations for such curves follow.
Given
PVn= C
Taking the logarithm of both terms
log P + n log V = log C
Transposing
log P =n log V+log C ........(1)
This equation is of the form of the straight line
y mx + b
where
y = log P
m= n
x = log V
b = log C
Thus m = n, the slope; or measure of inclination of the
line to the axis, log V. In Fig. 9, for example, at a point X on
the line
log P=  n log V + log C,
draw OX parallel to the axis log P, and draw OY parallel to the
axis log V. The slope of the line will be the value of the ratio
O  = n. OY is negative, being measured to the left, giving
OY
n its negative sign.
20. Use of the Logarithmic Diagram.The logarithmic dia
gram forms the basis of the methods of analyzing the cylinder
performance of reciprocating engines which are developed in de
tail in the following pages. These methods apply only, how
ever, to the logarithmic diagrams derived from the cylinders of
reciprocating engines using an elastic fluid for the working med
ium, and having, as a part of the cycle of operation, an expan
sion, a compression, or both. The figures of one set of indicator
diagrams and the corresponding set of logarithmic diagrams are
numbered the same, but the letters a and b are used in addition
to the figure number to denote the indicator and logarithmic dia
grams, respectively.
ILLINOIS ENGINEERING EXPERIMENT STATION
VI. RATIONAL METHOD OF APPROXIMATING CLEARANCE
21. In the cases of the great majority of the PVdiagrams
which were examined, the expansion and compression curves be
came straight lines in the logarithmic diagram, showing that the
law PV = C was applicable, or in other words, that n was a con
stant for one curve. The clearances furnished with the diagrams
examined had been carefully found by the displacement method.
It was desired to see what forms the lines assumed when the
clearance was taken larger or smaller than the measured quan
tity. The diagram shown in Fig. 10a, taken from a 42 in. x 60 in.
gas engine, was used for this purpose. The true clearance, mea
sured as 18.0 per cent, was used in the full logarithmic diagram
of Fig. 10b. Trials were made with clearances assumed as 14.0,
16.0, 20.0 and 22.0 per cent of the piston displacement. With the
true clearance of 18.0 per cent, the curves became almost perfectly
straight lines, while with the values of clearance less than 18.0
per cent, it is seen that the lines become bent to the left, and
with values of over 18.0 per cent, the lines become bent to the
right. Hence the straight line for the value of 18.0 per cent is the
transition between the family of curves bending to the left, rep
resenting a clearance smaller than the real value, and the family
of curves bending to the right, representing a clearance larger
than the real value.
The practical significance of this fact is that there is now
available a rational method of approximating the clearance of
any cylinder using an elastic medium, which has, as a part of the
cycle of operation, an expansion or a compression. This method
is based on the fact, already mentioned, that, in practice, all
elastic media, except under certain exceptional conditions, obey
substantially the law P V" = C, when subject to change of state,
and therefore become straight lines in the logarithmic diagram.
22. Graphical Method of Approximating Clearance.The
graphical method of approximating clearance requires only the
scale of the indicator spring to be known, and the atmospheric
line to be drawn, in order to locate the zero line of pressure. The
exact order of procedure necessary to make a trial, and the de
gree of accuracy obtained in any given case, is shown in detail in
page 35 for a 251 in. x 37J in. gas engine. All that is necessary is
to assume different values of clearance, and to plot the logarithmic
diagram for each assumed value. The straightline position of
the curves is found by trial and error, to lie between the two di
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
FIG. 10a (SCALE160 LB.)
I
(0
10
U)
Id
C
0
10
ABSOLUTE VOLUME  CU FT
FIG. 10l. TOD 42IN. x 60IN. GAS ENGINE, BLAST FURNACE GAS
ILLINOIS ENGINEERING EXPERIMENT STATION
verging families of curves representing too small and too large
clearance.
It follows also from the curves shown by Fig. 10b that the
clearance being known, the scale of the spring used may be ob
tained in the same manner if the atmospheric line is given.
23. Mathematical Method of Approximating Clearance.The
results obtained from the graphical method of trial and error
may also be accomplished by the use of the purely mathematical
process upon which the method depends.
When the law PV" = C holds, n is a constant for any part of
the curve. When the wrong clearance is used, the law PV = C
does not hold, and n varies from point to point. In the graph
ical method, trials of various values of clearance are made, until
the curve becomes approximately a straight line; this resultant
straight line is, therefore, the law PV' = C, in which n is a con
tant for all parts of the curve. The one condition necessary to be
fulfilled, therefore, is that n be constant for all parts of the curve,
but not of any particular value.
24. Application of the Mathematical Method.To illustrate the
use of the mathematical method in Fig. 10b, let us assume several
points, P1V1, P2V2, P3VF, and P4V4 at various intervals on one of
the curves, as on the compression curve at the clearance value 14.0
per cent. It is desirable for convenience to locate the points at
about equal intervals as shown. The law PVI' = C is assumed to
hold. Then, for two points, P1 V and P2V2, called group a, we
have
Pyin = C
P, = C
Equating these, we obtain
p2V n  p V n
Transposing and dividing
V2 1 P
(T1, P
Taking logarithm of both sides
n(log V,  log V1) = log Pi  log P2
whence
_ log P1  log P
na log 2  log V1......................(1)
In the same manner for the points P V3 and P4V4 called group
b, we obtain
log P3  log P4
n  log V4 log V...........................(2)
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
For the correct value of clearance, the following condition must
be fulfilled by trial and error
na : .b ..... . . . .........................(3)
The values of the logarithms of the coordinates of all points
are then found, and the values of na and nb computed. If the
points are located in the order shown, then with too small a clear
ance, na is lower in value than n b. A larger value of clearance
is then assumed, the operation being merely to add a constant
number to the values of VT, V2, 1V, and V4. The process is re
peated until the value of na becomes practically equal to rb.
When the clearance is assumed too large, na becomes higher in
value than nb , indicating that the true value has been passed.
25. Comparison of the Two Methods.The trial by the mathe
matical method is neither as accurate nor as short as the graph
ical method. It is not as accurate because the points assumed
may not be representative. When this is the case, the graphical
method allows judgment to be exercised in selecting the straight
line position, thereby eliminating irregularity of points.
The question arises as to whether the form of the lines due
to wrong clearance can be distinguished from the form due to leak
age or to "hooks", on the logarithmic diagram. This case is
treated in chapter IX.
The curve of the PVdiagram nearest the clearance space,
or the compression curve in Fig. 10b, is generally the better
guide in the graphical trials. This is well shown in Fig. 10b. A
given difference in the values of clearance used for trial causes
more horizontal variation in the position of the compression
curve than in the expansion curve. This fact allows closer lo
cations of the straightline transition region to be made from the
compression curve than from the expansion curve.
26. Examples. It was desired to determine the clearance
of the diagram shown in Fig. 1a. From general knowledge of
this class of engines, a trial by the graphical method was made
in Fig. 11b with the clearance assumed as 12.4 per cent, a value
purposely assumed as being too small. This value is seen, by the
bending of both curves to the left, to be much too small. Trials
were, therefore, made with the clearance assumed as 13.8, 15.1.
and 16.0 per cent of the piston displacement. The values of 15.1
per cent gave practically perfect straight lines for both the ex
pansion and compression curves, while the value of 16.0 per cent
shows that the lines have begun to bend to the right, indicating
too large a clearance. By inspection, it will be seen that the re
ILLINOIS ENGINEERING EXPERIMENT STATION
FIG. lla. (SCALE180 LB.)
1.0 £.0 3.0 4.0 5.0 6.0 70 8.09.010 0o
ABSOLUTE VOLUME  CU. FT.
FIG. llb. KOERTING FOURCYCLE 25%IN. X 37%IN. PRODUCER GAS ENGINE
900
400
300
1200
t 90
go
80
S 70
^40
I
to 30
20
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE 37
gion of fairly straight lines may be located as lying between the
values of about 14.5 per cent to 15.5 per cent. The clearance is,
therefore, selected as 15.0 per cent, a value which may be high
or low by not more than 4 per cent in this case. This clearance
value, 15.0 per cent, is a common value for engines of this class.
The graphical method is more accurate for large clearances,
measured in per cent of the piston displacement, than for small
ones. The closeness of location of the straightline region, lying
between the two families of diverging curves, will be found to be
within 5 per cent to 10 per cent of the clearance volume, for val
ues of clearance between 20 per cent and 2 per cent, respectively,
of the piston displacement.
VII. RATIONAL METHOD OF LOCATING THE STROKE
POSITION OF CYCLIC EVENTS
27. It is often desirable to know at what part of the
stroke the cyclic events occur. This knowledge can be best ob
tained from the PVdiagram. For ordinary purposes, these events
can be closely located in most cases by inspection on the PVdia
grams themselves; thus, on a diagram from a Corliss engine, cut
off may generally be located to within 116 in., measured along
the length of the diagram.
The actual beginning of true compression, however, can
never be accurately located on the PVdiagram. True compres
sion, unaffected by leakage, begins after the exhaust valve, in
closing, has acquired enough seal to prevent leakage. The point
of the beginning of true compression is generally at least 5 lb.
above the back pressure. The point at which leakage ceases can
not be located on the PVdiagram because the curve of true com
pression, and the curve during the time the valve has insufficient
seal, are of the same direction of curvature, and are not reverse
curves as in the general case of admission and expansion.
The fact that expansion and compression of a constant weight
of medium take place according to the law, PV" = 0, thus becom
ing straight lines in the logarithmic diagram, enables us to locate
cyclic events very closely, even in cases where they cannot be de
tected at all in the PVdiagram.
28. Application.An example is shown in Fig. 23a, contain
ing locomotive PVdiagrams taken at short cutoff and high
speed. The events of cutoff, release, compression, and lead
are very difficult to locate on such diagrams. These events
ILLINOIS ENGINEERING EXPERIMENT STATION
are located on the logarithmic diagram in Fig. 23b by noting
when the expansion and compression curves become straight, in
dicating a constant weight of steam mixture.
A sufficient number of points are plotted to show clearly the
direction of the diagram near the events desired. Thus these
events, even though obscure in the PVdiagram, may be located
to well within about 116 in. in the logarithmic diagram, this
length being equivalent to about 132 in. when retransferred to
the PVdiagram itself.
The use of this method has one great advantage in that it
largely eliminates the variable element of personal judgment. It
is a common occurrence to see PVdiagrams where two persons
have located an event such as cutoff, * in. apart, each location be
ing the best judgment of the person doing the work. The loga
rithmic diagram will at all times give closer locations of events
for these reasons than will the PVdiagrams.
The method also allows the point of true compression to be
located, the location of which is practically impossible in the PV
diagram.
VIII. RATIONAL METHOD OF DETECTING LEAKAGE
The law PV" = C is applicable only to cases where the weight
of the working medium remains practically constant during any
expansion or compression. When this weight changes materially,
either by leakage into, or out from, the cylinder containing the
medium, the resulting expansion or compression no longer obeys
the law, and it becomes a curve on logarithmic crosssection
paper. This fact is very clearly shown in the curves of the log
arithmic diagram derived from cylinders in which large leaks
were known to exist.
29. Examples of Known Leakage. (a) Gas Engine.The
first case, shown in Fig. 12b, occurred in a 10 in. x 19 in. gas
engine, intended for producer gas, but using illuminating gas
at high compression. The piston, a singleacting trunk type,
allowed a large leak, clearly detected by the noise of escaping
gas, at the beginning of the stroke. Both the compression and
expansion curves show the effect of this leak in a clear manner
when transferred to the logarithmic form. After that portion of
the stroke was reached where no sound of leakage was heard, the
two curves became straight lines. This indicated very clearly
that the effect of leakage, if appreciable, may be detected in the
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
30C
Z
CL
i 90
: 80
v) 7C
f 60
50
Ld
f 4C
S3C
20
IOC
ABSOLUTE VOLUME  CU.FT
FIG. 12b. 10IN. X 19IN. GAS ENGINE (ILLUMINATING GAS)
ILLINOIS ENGINEERING EXPERIMENT STATION
form of the curves of the logarithmic diagram.
(b) Steam Engine.The second case, shown in Fig. 13b, is
from a 14 in. x 35in. Corliss engine. The knowledge of the leaky
condition of the piston and valves came from the engineer in
charge.
The expansion and compression lines indicate by their form
at the upper ends, a large leak from the cylinder, or through the
exhaust valve. The lines also sho'v, by the rising of the curves
at the lower ends, a considerable addition to the steam in the
cylinder during expansion and compression. This steam could
come only from a large leak in the steam valve. The seven other
diagrams taken from this same engine all show the effect of leak
age in a similar manner.
(c) A.mmonia Compressor.The third case of known leakage,
shown in Fig. 14b, is from an 11 1 in. x 22in. doubleacting am
monia compressor. This cylinder was known to be in very bad
condition as regards wear and leakage of piston and valves. The
reexpansion curves, by the enormous amount of reexpansion
shown, indicate large leakage into the cylinder during this oper
ation. The lower part of the compression curves, by rising, in
dicates leakage into the cylinder, either past the piston or
through the discharge valves. The upper part of these curves
indicates leakage from the cylinder, either past the piston or
through the suction valves. These three examples show abnor
mal conditions which are comparatively rare.
Very smooth curves may be obtained in the PVdiagram even
if there is large leakage taking place. This is seen by referring
to Fig. 13a, both the expansion and compression curves being
fairly regular. The logarithmic diagram, however, shows clear
ly, in connection with the discussion and the examples shown,
that large leakage of two kinds was taking place during expan
sion and compression. Leakage which occurs during admission
or during exhaust has no effect upon the lines of the diagram as
the weight of the medium is continually changing.
30. Method of Detecting Leakage.It is seldom found,
when leakage occurs in a cylinder, that only one source of leak
age exists. Leakage is usually the result of wear, which affects
most of the possible sources of leakage in about an equal propor
tion. As a result, several leaks are generally affecting the
curves. This is the case in Fig. 13b and 14b. In Fig. 13b,
leakage was taking place both into and out from the cylinder.
In discussing leakage, it must be kept in mind that difference
GLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
FIG. 13a. (SCALE40 LB.)
A55OLUTE VOLUME  CU. FT.
FIG. 13b. 14IN x35IN. CORLISS ENGINE
ILLINOIS ENGINEERING EXPERIMENT STATION
FIG 14a (ACALE168LB.)
AI5bUtLUfL VULUML  CU. FT.
FIG. 14t. 141/I. x 2 .IN. AMMONIA COMPRESSOR
in pressure between two regions is the cause of this phenomenon.
In the steam engine, there are three pressures which must be
considered, i. e., the pressure in the steam chest, in the cylinder
at the point discussed, and in the exhaust passage. Leakage,
being due to difference of pressure, becomes material only when
this difference becomes considerable. Thus leakage into, or out
from a steam cylinder has been found to occur, in most cases, only
when the pressure difference is over about 20 lb. In Fig. 13b, the
leakage into the cylinder, shown by the lower parts of the lines,
begins to occur at about 25 lb. absolute, or 35 lb. lower than the
pressure at admission. The leakage out from the cylinder,
shown by the upper parts of the lines, ceases to occur at a pres
sure of about 40 lb. absolute for the expansion curve, and be
gins to occur at about 25 lb. absolute for the compression curve.
The difference of pressure between the steam in the cylinder and
that in the exhaust passage is about 35 lb. in the first case, and
about 20 lb. in the second case.
31. Division of the Lines of Expansion and Compression.
This fact, found on many diagrams analyzed, enables us to divide
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
the expansion and compression lines roughly into three equal
parts on the logarithmic diagram (when these lines extend from
the initial pressure to nearly the back pressure): (1) the upper
third, influenced by leaks out from the cylinder; (2) the middle
third, practically uninfluenced by leakage; (3) the lower third, in
fluenced by leakage into the cylinder. Thus fairly reliable values
of n, free from the effect of leakage, may be obtained from the
middle third of the lines,
Returning to Fig. 13b, both the lines indicate leaks out from
the cylinder. This can occur either past the piston or through
the exhaust valves. The piston generally becomes leaky sooner
than Corliss exhaust valves, and, in this particular engine, one
of the piston rings was found to be broken upon examination.
When diagrams from both ends of the cylinder are available, pis
ton leakage causes nearly an equal effect on the expansion
curves of both ends. The leakage into the cylinder can come
from only one source which can influence the curves, i. e., the
steam chest. The effect of this leak is seen in both lines in the
lower thirds.
In Fig. 14b, both forms of leakage are shown in the ammo
nia compression curves. The lower thirds show leakage into the
cylinder, either through the discharge valves or past the piston.
The upper thirds of the lines show large leakage from the cyl
linder, caused by the condition of either the suction valves or the
piston. Ordinarily, it is not possible to distinguish between two
leaks occurring in the same third of the curves.
32. Approximation of the Volume That Leaked.Fig. 12b
is an example where only one kind of leakage is present. Here,
the piston alone leaked badly at the commencement of the stroke.
The effect of this leak is seen in the upper third of both lines.
When only one kind of leakage exists, it is possible to com
pute with fair accuracy the volume of leakage taking place dur
ing expansion or compression. The lines are extended, as shown
in Fig. 12b, giving the lines of constant weights of the medium.
The volume of gas that had leaked during compression, up to
100 lb. absolute pressure, is then seen to be 0.014 cu. ft., or 6.3
per cent of the volume remaining. The volume of gas, measured
at the pressure of 450 lb. absolute, that leaked after combustion
during expansion, is seen to be 0.032 cu. ft., or 18.7 per cent of
the volume remaining after the leakage stopped.
The leakage that took place during combustion at the end of
ILLINOIS ENGINEERING EXPERIMENT STATION
the stroke cannot be computed, but it can be estimated by mak
ing the assumption that this leakage was proportional to the
mean rate of leakage shown by the two curves, and that its dura
tion was the time interval occurring between the point A and the
point B.
The important result that is attained by this method is not,
however, the approximation of leakage, but the knowledge that it
is taking place, so that it can be located and stopped.
33. The Use of the Method in Testing for Maximum Economy.
Many engines are sold and their prices fixed on the basis of their
test performances. The importance to the manufacturer of being
able to eliminate leaks during this test does not have to be em
phasized. The engineer in charge of the test should know
whether or not the engine is tight under regular operating con
ditions. All of our present knowledge of leakage is an in
ference drawn from the leakage "standing". Nobody knows
whether an engine that is tight "standing" leaks when in opera
tion, or viceversa. This method should be applied to all engines
about to undergo any test where maximum economy is the object
desired.
34. Knowledge as to When General Repairs of the Cylinder and
Valves Are Necessary.Leaks are caused by wear, poor design, and
accidents. The accidents include scoring of cylinders and valves,
cutting of valves, and cracks in the cylinder. Most leakage is
the result of wear and tear due to long and hard use. After the
wear and tear has become marked, it is the custom to rebore the
cylinder and to resurface the valves and valve seats.
Several methods are in use for determining when general
repairs are necessary for steam cylinders. One of these methods
is to judge the time from the general appearance of the parts on
inspection. Cylinders are rebored by some engineers when they
have worn "out of round" by a given amount. In small plants,
the most general method seems to be to wait until the leakage is
so large as to become clearly noticeable either by the reduced
capacity of the unit, or by the effect upon the coal pile. Some
railroad campanies overhaul the cylinders and valves of locomo
tive cylinders at regular intervals of, for instance, 150 000 miles
of travel. Some cylinders in stationary plants are rebored at
equal time intervals of some four or five years each.
As a pure question of economy, other things not considered,
general repairs of cylinder and valves should take place when the
extra annual cost of fuel and water due to leakage equals the
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
annual interest on the money necessary for general repairs. The
total cost of general repairs is composed of several items: the ac
tual cost of the repairs, the cost of losing the unit from service,
the interest on the cost of the extra capacity that may have to be
installed to take the load when units are out of service, and the
interest on the money invested in the unit out of service.
The existing methods of determining when general repairs
are necessary are not standardized as regards economy, and the
personal judgment of the man making the decision may be liable
to great variation. The method of detecting leakage from the lo
garithmic diagram offers a more rational solution of this impor
tant question.
35. Leakage of Engines.The results of an analysis made in
connection with this investigation by means of logarithmic dia
grams of 296 PVdiagrams taken from the cylinders of 47 engines
indicate that the majority of engines, in good condition, are prac
tically tight as regards leakage into or out from the cylinder.
IX. INTERPRETATION OF THE LOGARITHMIC DIAGRAM
In the discussions upon the effect of wrong clearance, leakage,
and excessive condensation upon the lines of the logarithmic
diagram, it was assumed, for the sake of clearness, that only one
of these effects existed at one time. The examples were selected
so as to illustrate only one of these effects in each case.
Cases occur where sev eral of these effects exist at one time
in the same diagram. The separation of one effect from another
is not an exact process. However, the character of the curves
showing excessive condensation, wrong clearance, and leakage is
quite different. For instance, wrong clearance affects the lines
throughout their length. Excessive condensation, in the cases of
the steam diagrams examined, always affects only the upper parts
of the curves. Leakage, as has been mentioned, affects ma
terially only the upper and lower thirds of the lines, where these
lines extend from the initial pressure to nearly the back pres
sure. When excessive condensation and large leakage exist to
gether, no close approximation of the clearance can be made.
An adequate treatment of the segregation of these various
effects, when found together, is beyond the scope of this bulletin.
The treatment is long and complicated. It has been found, how
ever, that experience in the use of logarithmic diagrams enables
one to separate these effects qualitatively, in some cases, from
the form of the expansion and compression curves.
ILLINOIS ENGINEERING EXPERIMENT STATION
The logarithmic diagram is more useful for analysis than any
other form of diagram because of the natural limitations of the
human mind. We do not possess the power to distinguish be
tween curves. We are, however, able to see clearly the
difference in these curves after they have been transformed into
straight lines, which fact alone makes these new methods of
analysis possible. We are now enabled in their straightline
form, to comprehend curves which we have always seen, but
could not distinguish one from another in their original form.
X. COMMON ERRORS MADE IN ANALYZING STEAM INDICATOR
DIAGRAMS
36. The Use of the Equilateral Hyperbola as a Standard of
Comparison.The values of n for the expansion curves of steam
indicator diagrams are not closely constant but are subject to a
very wide range of variation. The range of variation found in
the present investigation is from 0.70 to 1.34.
The range of values in the engine tested was from 0.835 to
1.234. The average values were 0.947 for the tests run with sat
urated steam, 1.056 for the tests run with superheated steam, and
1.004 for all tests.
The values of n for most engines of ordinary size using sat
urated steam at normal cutoff is between 0.95 and 1.05, while for
superheated steam, the range is usually from 1.00 to 1.30. For
saturated steam, the value of n = 1.0 is about an average value.
The explanation of the value n = 1.0 can be seen from the
results of the tests given on pp. 11 and 20. The only meaning
that the average value of n = 1 ever possessed is that the av
erage value of Xc , in the class of engines examined, lies in the
range between 0.60 and 0.70.
The law of Boyle or Mariotte, or the law of isothermal ex
pansion of a perfect gas, has no bearing of any kind whatsoever
on the expansion of steam in a cylinder. The equilateral hyper
bola sometimes occurring in steam cylinders is only a special
case of expansion according to the polytropic law PV7 = 0, while
Boyle's law is another special case which never occurs in steam
engine practice.
Because of the agreement in form between Boyle's law and
the equilaterial hyperbola (the special case of the law, PV"= C,
where n = 1.0), this latter curve has been called the ideal or
theoretical curve of expansion to which curves in practice are
CLAYTONNEW ANALYSIS OF CYLINDER PFRFORMANCE
supposed to approach as a measure of practical perfection in the
use of steam. The equilateral hyperbola is in no sense whatso
ever an ideal or theoretical curve, and its use for the purposes of
comparison is an empirical or arbitrary convention only. It
should be called the conventional expansion. It has ever been
contended that because an expansion curve did not coincide with
the equilateral hyperbola, some grave fault exists in the engine.
A value of n may be as low as 0.60 with no graver fault than very
excessive initial condensation, while a value of 1.35 may be found
from no graver fault than that of using steam superheated
about 2500 F.
The only rational use of applying the equilateral hyperbola
to steam PVdiagrams is to act as a guide to see whether n is
greater or less than 1.0. If the actual curve is not close to this
hyperbola, if no faults exist, and if the cylinder is nonjacketed,
then this fact means that the value of xc for the case examined
is less than about 0.60 or greater than about 0.70. The assump
tion that n = 1.0 as a standard of expansion is equivalent to as
suming that the value of xc is standard at about 0.65; however, no
engineer would seriously propose that the value of xc of 0.65
should be selected as a standard of economy. The elaborate
theory of analysis built on the assumption that n = 1.0 is the
natural result of the use of averages in any art where the actual
facts have never been investigated.
The use of the equilateral hyperbola to predict the form of
PVFdiagrams for the purposes of design is satisfactory in the
case of ordinary sizes of engines using saturated steam. When
steam superheated over 1000 F. is used, the value of n should be
assumed at between 1.10 and 1.25. The high values of n ob
tained with highly superheated steam in large engines alter
materially the division of work and the tangential forces acting
from those obtained when n is assumed to be 1.0. This fact
should be considered in the design of engines to use superheated
steam.
The use of the equilateral hyperbola to obtain the ratio known
as the "diagram factor" has no rational basis, but its use for
this purpose gives results which are valuable for the purpose of
design.
37 The Graphical Method of Approximating the Clearance. If
n has the value 1.0 on a PVdiagram, the clearance may be found
by locating the zero of volume on the zero line of pressure. This
process is performed graphically by reversing the method used
ILLINOIS ENGINEERING EXPERIMENT STATION
in constructing the equilateral hyperbola.
In actual expansions, however, n is almost never exactly
equal to 1.0, but is greater or less as already explained. The ac
curacy of the result by this method is dependent on how close the
value of n approximated 1.0. The clearance obtained by this
method may be as much as 100 per cent larger or smaller than
the actual clearance volume in ordinary cases, while errors of 25
per cent and 50 per cent are very common. Where errors of
this size are possible, the method is of no use for important work.
A rational method of approximating the clearance cannot be
based upon the assumption that n = 1.0, but only upon the fact
that it be of a constant value, the value itself being immaterial.
38. Combined Steam Indicator Diagrams.Very little of value
is obtained from the combined PVdiagrams of steam engines,
except the measure of the diagram factor for the purpose of
design.
One of the uses that has been made of the combined diagram
is to see whether continuity of expansion exists. It has been
assumed by various writers that continuity of expansion should
exist.
A study of the relations of xc and n shows that continuity of
expansion does not and should not exist except under very
special conditions.
39. Division of Feed for Applying Hirn's Analysis.One of the
requirements of Hirn's analysis is that we know exactly how
much steam was admitted to each end of a cylinder. These
amounts are not usually equal in practice, so an assumption must
be made to cover the needs of the case.
The usual assumption is to divide the feed between each end
of a cylinder in the ratio of the values of the mean effective pres
sure shown by the P Vdiagrams from the two ends. This as
sumption is probably not far from the actual division in most
cases, and is the best that can be done under the circumstances.
In the light of the facts presented in this investigation, this
feed may now be divided on a more rational basis. It has been
found that the presence of the piston rod in only one end of the
cylinder has no appreciable effect upon the value of n. This fact
enables us to divide the feed according to the volumes filled and
the values of xe as determined by the resulting values of n. This
method is believed to be the closest solution obtainable in the
case where the supply for each end of the cylinder cannot be
separately measured.
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
40. Computing the Weight of Steam Retained in Compression.
A carefully made investigation indicates, 1 when saturated steam
is used, that the steam in the cylinder is dry or even very slight
ly superheated at the closure of the exhaust valve. As shown
by the logarithmic diagrams, leakage of the steam in compression
continues until the exhaust valve, in closing, has acquired con
siderable seal.
The point which is selected to compute the volume of steam
retained in compression generally lies between the points A to B,
and 0 to D of Fig. 9. As the weight of steam retained is yet de
creasing, the point selected nearly always accounts for more
steam than was actually retained. In other words, we do not find
the value of xc to be as high as it actually is.
The following method shown in Fig. 9 has been adopted in
the present investigation. The straight line of the compression
curve on the logarithmic diagram, or the line of constant weight
of steam mixture, is prolonged dotted as shown to the back pres
sure. The intersection of this prolonged line with the back pres
sure line extended is taken as the volume of dry steam retained
in compression.
This method almost always gives less steam retained in com
pression than the ordinary method, and is believed to be rational
in the present state of knowledge of this subject.
XI. CONCLUSIONS
1. The indicator diagram, taken by means of a correct re
ducing motion and with a reliable indicator, contains the evidence
necessary for a complete and useful analysis of cylinder perform
ance.
2. The logarithmic diagram, derived from the indicator
diagram, discloses a new and complete analysis of cylinder per
formance.
3. Free from the influences of leakage, wrong clearance,
wrong location of the line of zero pressure, and excessively low
speed (principally in steam engines), expansion or compression
of an elastic medium takes place substantially according to the
law, PVn = C.
4. The clearance of cylinders may be found by graphical
trial on logarithmic crosssection paper to within 5 per cent to 10
per cent of the clearance volume, depending as the clearance it
] George Duchesne, Revue de Mecanique, July, 1899, quoted in Power, (Jan. 10, 1911, P. 71).
50 ILLINOIS ENGINEERING EXPERIMENT STATION
self varies from 20 per cent to 2 per cent, respectively, of the
piston displacement.
5. Thae cyclic events, even though entirely obscure in the
indicator diagram, may be located on the logarithmic diagram
(when plotted on logarithmic paper of 5 in. per square) to within
 in., this quantity being the equivalent of about  in. when re
transferred to the indicatordiagram.
6. Leakage (if appreciable) may be reliably detected from
the logarithmic diagram, and may, in some cases, be approximated
in volume.
7. The weight of steam retained in compression should be
obtained from the logarithmic diagram by prolonging the line of
constant weight of steam mixture to the back pressure line ex
tended; the intersection of these two extended lines is the volume
of steam which is retained.
APPENDIX 1
THE LOGARITHMIC DIAGRAM
ILLINOIS ENGINEERING EXPERIMENT STATION
APPENDIX 1
METHOD OF CONSTRUCTING THE LOGARITHMIC DIAGRAM
1. Description of Logarithmic Crosssection Paper. Logarithmic
crosssection paper differs from rectangular crosssection paper
in that the distances from the origin are proportional to the log
arithms of the numbers to be plotted instead of to the numbers
themselves. This system of coordinates gives an uneven scale
similar to that on a slide rule. The numbers of the divisions on
logarithmic paper are placed opposite the lines corresponding to
their logarithms, as on a slide rule, instead of to the values of the
logarithms of the numbers. This fact aids in plotting, as the log
arithms are employed without having to ascertain their values.
The logarithmic cross section paper used in this investigation
consists of four squares arranged two each way. These squares
are five inches each way, making the four squares together ten
inches each way. The use of four squares enables values to be
plotted ranging from 0.1 to 10.0, 1.0 to 100.0, etc., thus giving a
range of ten times the values obtainable if only one square were
used.
2. Construction of the Logarithmic Diagram.The coordinates
of the PVdiagram are proportional to pressure and stroke, the
latter being proportional to the volume displaced by the piston.
The coordinates of several points on the PYdiagram are found in
terms of absolute pressures, preferably in pounds per square inch,
and absolute volumes, preferably in cubic feet. The scale
of units employed is not material as long as it starts at the line of
zero pressure, or of zero volume. However, the units are more
easily manipulated afterwards if they are the same as those in
the steam tables.
The method of transferring the PVdiagram to the logarith
mic form is described in detail for the diagrams of test 30, given
in Fig. 15. The method of drawing the pressure ordinates is
shown on Fig. 15, crank end. The diagram is shown in outline by AB
YX. Perpendiculars QB and EX are drawn to the atmospheric line
EQ, and pass through the extreme stroke positions of the diagram.
The distance EQ is then the length of the diagram. OMis laid off
perpendicular to the atmospheric line EQ (extended) which was
drawn by the indicator pencil. OM is the line of zero volume, and
is drawn at a distance FE from the admission end EX of the di
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
agram, the distance FE being the same length in per cent of the
line EQ, or length of the diagram, as the proportion that the per
cent of clearance, or waste space, of the cylinder bears to the pis
ton displacement. In this case, the length of the diagram is 3.99
in., and the clearance is 7.01 per cent. The length FE is therefore
0.0704 x 3.99, or 0.281 in. ONis the line of zero pressure and is
drawn a distance FO below the atmospheric line, to the scale of the
spring used in obtaining the P Vdiagram. This distance is propor
tional to the barometer reading, coriected for temperature, pre
vailing at the day and place of the engine test. In this case, the
133.0
I13.4
95.0
76.3
STI
38.9
29.4
19.5
14.5
0.0
134.3
115.3
96.3
77.3
58.1
3&.7
29.1
19.5
14.5,
0.0
FIG. 15. HEAD END (SCALE 77.0 LB.)
x_ y
H\
G Q
fl L
FIG. 15. CRANK END (SCALE79.0 LB.)
corrected barometer reading is 14.2 lb. per sq. in. absolute,
14.2
hence, the distance FO is .0 , or 0.180 in.
From ON, points are laid off on QR and EX corresponding to the
absolute pressures at the intervals where it is desired to read off
the corresponding volumes. Fine lines are drawn connecting sim
ilar pressure points, as 19.819.8, 29.129.1, etc. The volumes
GA, GB, HD, HC, etc., are read off in hundredths of an inch
to the nearest halfhundredth. The tabular form used in this in
vestigation is given in Table 6 for the diagrams of Fig. 15 taken
I
0
54 ILLINOIS ENGINEERING EXPERIMENT STATION
in test 30. Thus the length GA is read off as 0.66 in., and is
given under the column for 19.8 lb. pressure headed Comp., mean
ing the compression curve, for the crank end diagram. The vol
umes in inches are then multiplied by the constant ratio which
one inch of length of the diagram bears to the displacement of the
piston. From Table 6, it is seen that the piston displacement of
the crank end is 1.523 cu. ft., and the length of diagram 3.99 in.;
1.523
hence, the ratio is. , or. 0.382 cu. ft. of piston displacement
per inch of diagram length. The length GA in cu. ft. of displace
ment now becomes 0.66 in. X 0.382 cu. ft. per in., or 0.252 cu.
ft., the volume of steam present at this point. This process is
repeated at intervals until the coordinates of from ten to thirty
points are determined. In the diagram shown in Fig. 15, the
coordinates of 18 points were found in each diagram.
The coordinates of P and V are then plotted, on logarithmic
crosssection paper, as shown in Fig. 9, which are the logarithmic
diagrams derived from the PVdiagrams of Fig.15. The points
plotted in Fig. 15 are taken from the columns headed cu. ft. at the
pressures shown. A smooth curve is drawn through the points
thus plotted, and the diagram is in shape to be studied.
TABLE 6
CONSTRUCTION OF THE LOGARITHMIC DIAGRAMS OF TEST 301
Head End Crank End
Volumes
Absolute inches cu. ft.
No. Pressures
lb. per.
sq. in. Comp.2l Exp.2
XtoA 2 to B
133.0 0.39 1.18
113.4 0.31 1.36
95.0 0.31 1.625
76.3 0.31 2.02
57.1 1 0 31 2 705
38.9 0.375 4.03
29.4 0.48 4.22
19.5 0.70 4.26
15.0 1.10 3.06
Comp. Exp.
0.156 0.470
0.124 0.5425
0.124 0.649
0.124 0.8055
0.124 1.080
0.150 1.610
0.192 1.685
0.279 1.699
0.439 1.220
Volumes
Absolute inches
lb. per
sq. in.
131.3
115.3
96.3
77.3
58.1
38.7
29.1
19.8
15.0
Length of indicator diagram......................... .. ........
Ratio of clearance to piston displacement. same end .... .......
Length on diagram proportional to clearance ratio..............
Length of diagram plus clearance................................
Piston displacement (cylinder 12.02'X21')........................
Clearance volum e........................... .. ...................
Displacement plus clearance, total volume.......................
Ratio, cu. ft. per inch of length on diagram................ ......
Scale of indicator spring per inch of ordinate ....................
1Letters refer to Fig. 15, crank end........ ....... ........
2Final results given in Table 1....... .....................
Comp. Exp.
0.30 1.205
0.28 1.39
0.28 1.65
0.28 2.06
0.295 2.76
0.385 4.12
0.485 4.26
0.66 4.20
0.93 3.77
H E.
3 95 in.
0.0789
0.312 in.
4.26 in.
1.575 cu.ft.
0.124 cu. ft.
1.699 cu.ft.
0.399 cu. ft.
77.0 lb.
cu. ft.
Comp.
0.115
0.107
0.107
0.107
0.113
0.147
0.185
0.252
0.355
CR. E.
3.99 in.
0.0704
0.281 in.
4.27 in.
1.523 cu.ft.
0.107 cu ft.
1.630 cu. ft.
0.382 cu. ft.
79.0 lb.
2
3
4
5
6
7
8
9
Exp.
0.4605
0.531
0.6305
0.7875
1.055
1.572
1.626
1.600
1.440
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
APPLICATION OF THE LAW PVn = C TO CURVES
FROM PRACTICE
3. Does the Law PVn = C Hold for Curves from Practice? It
has long been known that adiabatic expansion or compression of
any elastic medium takes place substantially according to the law
PVn = C. The values of n are different for different media, and
sometimes vary for the same medium with different conditions of
the initial state. These values, for media commonly used in re
ciprocating engines, are given on page 38 et seq.
In practice, however, expansion is never adiabatic, but is
changed in character by the presence of the metal surrounding
the working medium, and by imperfection of mechanism. Since
the actual change of state is not adiabatic, the question arises how
it has been changed in character, and whether this modified ex
pansion still obeys the law P V' = C.
Many investigators, Zeuner,1 Leloutre,' Luders,3 and Perry4,
have examined the curves from actual diagrams to clear up this
point for steam. They find that expansion in steam cylinders
takes place substantially according to the law PV' = C, but that
n varies in value between wide limits in different cases.
An examination was made of the curves of 296 diagrams from
the cylinders of 47 different engines using steam, gas, air and
ammonia to investigate this point. As a result, it may be stated
that, in the cases of the great majority of engines using elastic
media, expansion and compression take place substantially ac
cording to the law PVnF = C. Certain exceptions, however, have
been found, and the causes studied. These causes are treated in
the next section.
4. Examples of Logarithmic Diagrams from Various Types of
Engines.The logarithmic diagrams, obtained by plotting the
indicator diagrams as described on p. 52, are of a distinctly
different form from either the PVdiagrams or the temperature
entropy diagram. While the various typical forms of PVdiagrams
assume rather different forms after plotting, yet the resultant fig
ures retain in a general way the peculiar characteristics of each
PVtype, except that these peculiarities are exaggerated.
Various typical PVdiagrams are given in Fig. 1629.
They include examples from many types of engines, using steam,
1 Technical Thermodynamics II. p. 111.
2 Recherches experimentals, Bulletin de la Societe industrielle du Nord de la France, 1874.
3 Zur Theorie des Indikator diagrammes, Zivilingenieur, 1881, Vol. XXVII, p. 225.
4 The Steam Engine, p. 106.
56 ILLINOIS ENGINEERING EXPERIMENT STATION
FIG. 16a. CRANKEND (SCALE50 LB.)
U I
z
it
In'
III
u
Z
1
U)
D.
Id
i.
a
hi
ABSOLUTE VOLUME ClUFT.
FIG. 16b. GREENE 18MIN. x 43IN. STEAM ENGINE
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
FIG. 17a. (SCALE80 LB.)
ABSOLUTE VOLUME  CU. FT
FIG. 17b. IDE 16IN. X 16IN. HIGH SPEED STEAM ENGINE
58 ILLINOIS ENGINEERING EXPERIMENT STATION
FIG. 18a. HIGH PRESSURE (SCALE80 LB.)
FIG. 18a. Low PRESSURE (SCALE20 LB.)
z
g
Ia
u
Id
hi
10
'a
FIG. 18b. BUCKEYE 18,IN. X36IN. X 86IN. STEAM ENGINE
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE 59
FIG. 19a. RICE AND SARGENT 16IN. X 28IN. X42IN. SUPERHEATED STEAM
ENGINE (SCALE64.6 LB.)
40
z
L
0i
1.J
LJ
I.
J
0
i)
,C
0.03 004 05 .106.07.08.09 0.1 0.? 0.3 a4 C.5 o 0.7 0.9 1.0 Z.0 3.0
LENGTH OF DIAGRAM  INCHES
(PROPORTIONAL TO ABSOLUTE VOLUME)
FIG. 19b. RICE AND SARGENT 16IN. x 28IN. x42IN. STEAM ENGINE USING HIGHLY
SUPERHEATED STEAM
ILLINOIS ENGINEERING EXPERIMENT STATION
FIG. 20a. (SCALE162 LB.)
0.3 .04 0.01 M.007.JoO. 0.2 Q3 04 0.5 0.6 A70a801910 .0
LENGTH OF DIAGRAM INCHES
(PROPORTIONAL TO ABSOLUTE VOLUME)
FIG. 20h. STUMPF 23)IN. x 31%IN. UNIDIRECTIONALFLOW STEAM ENGINE USING
SUPERHEATED STEAM
'00 m~#~ 1Mill I
H =. o44_ A n . 9
Av n = .os7
== ::::::::rm ^^ m ^ :::::\=
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
FIG. 21a. (SCALE80 LB.)
0.3 0.4 0.5 0.6 0.7 0.9 .0 2.0 3.0 40
ABSO.LUTE VOLUMECU. FT
FIG. 21b. WESTINGHOUSE SINGLEACTING 13IN. X 22IN. X 13IN. STEAM ENGINE
gp    T_ _  . _ 
Th  ._    l
100
o    
ILLINOIS ENGINEERING EXPERIMENT STATION
FIG. 22a. H. P. TOP (SCALE100 LB.)
FIG. 22a. H. P. BOTTOM (SCALE100 LB.)
FIG. 22a. I. P. TOP (SCALE20 LB,)
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE 63
FIG. 22a. I. P. BOTTOM (SCALE20 BL.)
FIG. 22a. L. P. TOP (SCALI10 LB.)
FIG. 22a. L. P, BOTTOM (SCALE10 LB.)
ILLINOIS ENGINEERING EXPERIMENT STATION
'NI '&S 43.d "1  3inSS3ad 3.LniOaV
a
<!
z
E<
a
L
N
Lit
N1
oz
Il2
Nc
N
8
I C
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
FIG. 23a HEAD END (SCALE150 LB.
ABSOLUTE VOL.UME.CU.FT
FIG. 23b. PURDUE 16IN. x 24IN. SUPERHEATED STEAM LOCOMOTIVE
)
ILLINOIS ENGINEFRING EXPFRIMENT STATION
FIG. 24a. HEAD END (SCALE100 LB.)
FIG. 24a. CRANK END (SCALE100 LB.)
6
*0. C
cw H
0 
1.16
N
I
0.4 0o 0.C t7 0 V .y Z. 0v WJ.
ABSOLUTE VOLUME CU.FT
PURDUE 16IN. x 24IN SUPERHEATBD STEAM LoCOMOTIVE
0.3
rn
100
90
60
To
60
50
40
30
o20
FIG. 246.
N
ft
1
^
)
1
0
^
J
a
«
lllý
CR
L.L
IN P T
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
FIG. 25a. (SCALE 160LB.)
z
V)
Itoo
S90
80
U) 60
a 50
0.
S40
J
0
0
ABSOLUTE VOLUME CU. FT.
FIG. 25b. TOD 42IN X 60IN. GAS ENGINE BLAST FURNACE
ILLINOIS ENGINEERING EXPERIMENT STATION
FIG. 26a. (SCALE 400 LB.)
~ Ve_____
~ _  ___  
\ I
n \ ilco
_____ __ n _ _ _ _ _ \ _ _ 
I I i ti. !n
r77 " 
II__ _ _ \ \_  _
rrz ^=r::::::::: \ \ =
,,,__ __. ....... \_ 4 _
_ _ _ _ _ _ _ _ .... _ _S _ _ _
: ~ ~: :::::::: "J:
.u0 4".u
T700oo
600
500
400
300
J00
S90
go 80
. 60
S50
I
it
I
0.
0.2 0.3 0.4 0.5 0,6 7 0.8 0.9 1.0 2.0
AB5OLUTE VOLUME  CU. FT
FIG. 26b DIESEL 16IN. X 24IN. OIL ENGINE USING CRUDE OIL
I
n n o
m
G
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
FIG. 27a HIGH PRESSURE (SCALE120 LB.)
FIG. 27a Low PRESSURE (SCALE40 LB.)
rrrrnT11TT~r yr ri rrrfFT 1TrTFvr I I fli
Av 1.1 3
CR H
100 '1 4
501 1 1
H nV. 092 _
40 H  _____ Av.31 45
    :.    ""T  
Av r .4  1431
20 
10 
10 .. . . . .. _      ..     _ .. .
,00.0.009.lo
FIG. 27b
0200 0.030 0.04 s05 o06 r 0 8.09 0.1 0.2 0.3
AB50LUTE VOLUME  CU. FT
PORTER AIR LOCOMOTIVECOMPOUND 5IN. x 10IN. X 10IN
.4 0.5 06 90T
FIG. 28a. HEAD ENDLOW PRESSURE (CALE 17.0 LB.I
FIG. 28a. CRANK ENDLOW PRESSURE (SCALE21.6 LB.)
FIG .28a. HIGH PRESSURE (SCALE50 LB.)
D: 60
50 1
40
30   C
la0
. n   _  ^  _      
77
0.01 0.0 0.03 0.04 .05 .06 07.0.09 01 0.2 0.3 0.4 0.5 06 07 8 0 1.0 Z.0
ABSOLUTE VOLUME  CU.FT
.28b FIG. INGERSOLL SERGEANT 123IN. X 18,IN. 12IN TWO STAGE AIR COMPRESSOR
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
FIG. 29a. (SCALE136LB.)
FIG. 29b.
09 U 0. 05 0.6 T. 0.8 0.9 1.0
ABSOLUTE VOLUME  CUXT.
YORK SINGLEACTING 122IN. x 18IN. AMMONIA COMPRESSOR
00
 I
S
'S
I
N
F 
IrI~i
I I I I I' L 
7
En^
* 
7
i,
i
'S
L
r
r
k.
*
^
s
s>
:>
i
I
I II
__LI
j
I
] i I It I]
0 03 004 ROS A 1
ILLINOIS ENGINEERING EXPERIMENT STATION
gas, air and ammonia as the active media. The values of n for
the curves are given in each figure. The types of steam engines
represented include Corliss, high speed, auxiliary cutoff, poppet
valve, single acting, pumping and locomotive engines. The gas
engine diagrams include two four cycle types, one using blast
furnace gas, and the other a Diesel engine using crude petroleum.
The air diagrams contain one set from a compound air locomotive,
and one set from a twostage air compressor.
These figures show most of the typical forms of diagrams
that are obtained in practice. At first sight, the logarithmic dia
grams look distorted, but after the meanings of the different lines
become clear, they begin to seem as natural as the PVdiagram.
These logarithmic diagrams show how closely the law PV" = C
holds in actual curves from a great variety of engines using dif
erent media.
5. Cases Where the Law PVn = C Does Not Hold.The curves
of expansion and compression, obtained from PFdiagrams, do
not always follow the law PV" = C. This fact is due to several
causes, some of which have been definitely determined. These
causes will be treated separately.
a. Wrong Clearance, or Wrong Location of the Zero Line of
Pressure.The law PV" = C, is true only where P and V are mea
sured in absolute units. The clearance must be accurately deter
mined in order to give absolute values of V. The scale of the
spring, for the PVdiagram analyzed, must be known, and the
atmospheric line drawn by the indicator, in order to locate the
zero line of pressure. The units used for P or V may be of any
denomination, but they must be measured from the zero of P and V.
When a curve, PV" = C, is plotted on logarithmic paper, the
resultant curve is a straight line. The value of n, as already
explained, is the slope of this line, measured from any two points.
When the values of P and V are not absolute values, this curve is
no longer a straight line, but becomes a curve of the second degree.
The value of n being the slope obtained from two points on this
curve, is no longer constant for all parts of the curve, but varies
from point to point. Therefore, when P Vdiagrams are trans
formed to logarithmic diagrams, the values of both P and V must
be measured in absolute units. When these values are not in
absolute units, the resulting curve is not of the form, PV" = C,
and therefore is not a straight line on logarithmic paper. The
form of the curve obtained, when the values of V alone are not in
absolute units, is given in Fig. 10b.
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
b. Leakage.The law PVFn =C, is applicable only to cases
where the weight of the working medium remains practically
constant during any expansion or compression. When this
weight changes materially either by leakage into, or out from,
the cylinder containing the medium, the resulting curve no longer
obeys the law, and it becomes a curve in the logarithmic diagram.
This fact is very clearly shown in the curves of the logarithmic
diagram derived from cylinders in which large leaks were known
to exist. The examples showing this condition are shown in
pp. 39, 41, 42.
c. Low Speed in Steam Engines.Very low speeds of rotation,
together with very low piston speeds, will cause the compression
curve to deviate from the law PVy = C. The most common cases
of this effect are seen in the "hook", or excessive condensation,
near the upper end of compression curves. These "hooks" are
found almost altogether in small engines having very low piston
speeds, and in larger engines with small clearance, having very
low rotational speeds, as in pumping engines.
Diagrams containing "hooks" in the compression curves have
been published by Professor DwelshauversDery1 from the exper
imental engine at Liege. This is an example of a very low speed
in a small engine. The size was 12 in. x 24 in. and the speed
from 30 to 60 r. p. m. That this hook was caused by low speed
and consequent excessive condensation was proved in a measure
in the case of the engine described on page 88. This engine was
also 12 in. x 24 in., but was operated at from 90 to 150 r. p. m.
In no case was a hook in the compression curve obtained during
the tests, although some 1600 diagrams were taken. A set of
diagrams from these tests is shown in Fig. 15 and shows no sign
of a hook. On one occasion, however, the diagram shown in Fig.
30 was obtained. This was taken just after the engine was start
ed from cold, and had been brought up to a speed of 120 r. p. m.
In conjunction with the other diagrams obtained from this engine
in regular operation, this hook is believed to be due to excessive
FIG. 30. TAKEN WHILE STARTING FROM COLD
1 Power, June 2SS, 110, p. 1165.
ILLINOIS ENGINEERING EXPERIMENT STATION
condensation while the cylinder was comparatively cold.
Diagrams with the hook present in the compression curves
have been obtained from two other engines; one was an 8% in. x
12 in., running 110 r. p. m., and the other, 5 in. x 6 in., running
140 r. p. m.
This excessive condensation at the end of compression, or
near the dead center, seems to be due to the fact that the dele
terious surface effect of the cylinder walls is so enormous, com
pared with the weight and volume of steam present at this point.
The three causes treated above are believed to be the import
ant conditions that cause the curves in practice to depart materi
ally from the law PVn = C. Sometimes only one of these condi
tions is present, while in the other cases, a combination of these
may influence the resulting curves. The separation of these
conditions by their effect on the curves is treated in page 45.
VALUES OF n FROM PRACTICE.
6. Steam Engines.The values of n for the expansion and
compression curves of indicator diagrams are subject to a wide
variation. Zeuner1 gives the values of n found by several early
investigators. These values were taken mostly from the dia
grams of small and slowspeed engines. Leloutre found that the
value of n was practically constant for any one case, but varied
greatly in different engines, according to the initial pressure and
ratio of expansion. LUiders found values ranging from 0.903 to
0.535. Zeuner found values of from 0.900 to 0.436 from diagrams
taken by Hallauer from a Corliss engine. In none of these cases
was n found to be as high as 1.0. Zeuner concludes that the
value is generally close to 1.0, and does not vary much either way.
Heck' shows diagrams from the cylinders of compound Cor
liss engines, locomotives, pumping engines, and marine engines,
all using saturated steam. The values of n for saturated steam
from the expansion curves of the h. p. cylinders of these engines
are all close to 1.0. The values for the 1. p. expansion curves are
generally less than 1.0, ranging from about 0.95 to 0.90. The
values for the compression curves shown do not depart far from
1.0.
A large number of curves have been examined by the graph
ical method described on page 52. These examples, shown in Ta
ble 714, may be classed as follows:
1 Technical Thermodynamics, II. p. 111.
2 The Steam Engine, II. p. 476.
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
Class A. Corliss, fourvalve, and ridingcutoff types, all simple expan
sion
B. Same, compound.
C. Same, triple expansion.
D. Gridiron valve type, compound, steam jacketed.
E. Poppet valve type.
F. High speed engines, single valve types.
G. Singleacting engines.
H. Locomotive engines.
These classes cover the values derived from 138 diagrams
taken from 36 separate engines. On page 8, are given the values
obtained from 60 sets of diagrams taken from a 12 in. X 24 in.
Corliss engine.
The values given in Tables 714 are the average values from
both ends of one cylinder, and, in the case of twocylinder simple
engines, from both ends of both cylinders. In many cases only
the expansion curves were examined.
These diagrams were taken from cylinders ranging in size
from 11H in. x 13 in. up to 80 in. x 60 in., and in speed from 300
r. p. m. down to 23.6 r. p. m. Most of the cylinders were unjack
eted. Examples of both saturated and superheated steam are
shown. It will be seen, therefore, that the range of the exhibit
is very broad.
It is evident that the values of n are subject to extremely
wide variations, the range being from 0.436, found by Zeuner, up
to 1.341, found in this investigation in the case of an engine us
ing highly superheated steam. It is true, however, that the av
erage of all the values cited is not far from 1.0.
7. Gas Engines.The values of n for the curves of gas en
gine diagrams have a smaller range of variation than that found
in steam diagrams.
Gtildner' finds that the value of n for the compression curves
varies from 1.30 to 1.38, with an average of about 1.35, but he
mentions rare values higher than the adiabatic value, due to high
temperature of cylinder walls, and the consequent addition of
heat to the gas during compression. He finds that n for expan
sion2 varies normally from 1.35 to 1.50, but cites lower values
than 1.35 due to leakage, and higher values than 1.50 due to ex
cessive temperature of cylinder walls from poor cooling.
1 Internal Combustion Engines, p. 34.
2 Internal Combustion Engines, p. 38.
ILLINOIS ENGINEERING EXPERIMENT STATION
Wimperis' gives the values found by Professor Burstall from
diagrams taken during 10 tests on the same engine, presumably.
Professor Burstall finds n for expansion to vary from 1.199 to
1.344, with an average of 1.288. The values of nfor compression
vary from 1.345 to 1.364, with an average of 1.352.
The examination of 17 diagrams from 5 separate engines
gave values for expansion and compression as given in Table 15.
These values given show that the variation of n for expansion is
ordinarily from 1.10 to 1.37, while for compression it is from
TABLE 7
VALUES OF n FROM CLASS A STEAM ENGINES
Value of a No. of
Size Diagrams Make Remarks
inches Expansion Compression Examined
18i x 43 0.952 1.007 2 Greene Saturated steam
0.998 1.115 2
15i x 24 1.049 1.170 2 Buckeye
26% x 36 0.928 1.063 2
0.823 1.036 2
0.996 1.121 2
20 x 30 0.624 0.985 . 2
1. 024 0.992 2
18 x 42 1.047 0.994 2 Unknown
16 x 32 1 .065 1.154 2 Buckeye
S1.11 1.341 2
16% x 32 0.964 2 Unknown
26ie x 48 1.051 2
17x24.2 1.131 4
23 x 60 1.098 2
28% x 59% 1.108 2
11 Engines Total34 Diagrams
TABLE 8
VALUES OF n FROM CLASS B STEAM ENGINES
Expansion Compression No. of
Sizne 1. I Diagrams Make Remarks
inches h.p. 1 p. .p. 1. p. Examined
18% x 36 x 36 1.060 0.896 4 Buckeye Saturated steam
15 x 404 x 27 0.955 2 Fleming
20 x 36 x 48 1.055 0.973 0.973 0.742 4 Watts Campbell
21 x 42 x 36 1.068 0.987 4 Gaskell
25 x 50 x 37 0.841 0.879 0.850 8 Worthington
22 x 40 x 60 1.070 1.009 1.018 1,272 4 HarrisCorliss Cyls. jacketed
20 x 36 x 48 1.079 0.977 4 Watts Campbell " nonjacketed
16 x 40 x 48 1.090 0.950 4 Cooper Corliss
1.048 1.116 4 " " Cyls. jacketed
8 Engines Total38 Diagrams
3 The Internal Combustion Engine, p. 73.
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
TABLE 9
VALUES OF n FROM CLASS C STEAM ENGINES
Expansion No. of
Size No. of
Size Diagrams Remarks
inches h. p. . p. 1. p. Examined
28 x 54 x 80 x 60 0.987 1.112 0.984 6 Cylinders acketed
Compression
28 x54x80 x60 0.964 0.416 0.972
1 Engine Total6 Diagrams
TABLE 10
VALUES OF n FROM CLASS D STEAM ENGINES
Expansion No. of
Size Diagrams Make Remarks
inches h. p. 1. p. .Examined
28 x 58 x 48 1.046 1.070 2 McIntosh Superheated steam
23 x 48 x 48 0.955 0.969 2 Seymour & Co. Jackets not used
1.108 1
0.905 0.925 2
1.119 1.075 2
29 x 60 x 56 1.231 1
29x60x56 1.172 1
18 x 38 x 42 1.170 0.925 2
18 x 38 x 42 1.118 1.087 2
31 x 64 x 48 1.024 0.973 2
7 Engines Total17 Diagrams
TABLE 11
VALUES OF n FROM CLASS E STEAM ENGINES
Expansion Corn
Size _ Make Remarks
inches h. p
h.p 1. p. h.p. l.p.
16x28 x42 1.341 1.141 0.720 1.048 2 Rice and Sargent Highly superheated steam
1.260 1.180 1.262 1.210 2 ,.
1.293 1.152 0.980 0.989 2 "
" 1.033 1.011 0.710 1.060 2 Saturated steam
23% x 31% 1.197 1.057 2 Stumpf Straight Flow Hithly superheated steam
2 Engines Total10 Diagrams
TABLE 12
VALUES OF n FROM CLASS F STEAM ENGINES
Expan No. of
Sic Expansion Diagrams Make Remarks
inches h. p. Examined
14%1 x 13 0.970 2 Unknown Saturated steam
16 x 16 1.027 2 Ide
11 x 18% 0.706 2 Unknown
3 Engines Total6 Diagrams
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 13
VALUES OF n FROM CLASS G STEAM ENGINES
Expansion No. of
inchSize Diagrams Make Remarks
nches h. p. 1. p. Examined
13 x 22 x 13 1.073 0.874 2 Westinghouse Saturated steam
1.054 0.863 2
1,062 1
1 Engine Total5 Diagrams
TABLE 14
VALUES OF n FROM CLASS H STEAM ENGINES
SNo. of
Size Expansion Copres Diagrams Make Remarks
inces son Examined
16 x 24 1.003 4 Schenectady No. 2 Saturated steam
22 x 30 0.985 0.987 2 I. C. No. 940
0.981 2
22 x 30 0. 975 0.970 2 I. C. No. 920
1.006 1.125 2
16 x 24 0.974 1.208 2 Schenectady No. 3 Superheated steam
1.124 1.179 2
1.167 1.195 2
1.046 1.188 2
1.149 2
3 Engines Total22 Diagrams
TABLE 15
VALUES OF n FROM 4CYOLE GAS ENGINES
Size No. of
Size Expansion Compression Diagrams Make Gas Used
inches Examined
10 x 19 1.36 1.19 1 Otto Illuminating
1.37 1,09 1
1.27 1.26 1
1.21 1.35 1
1.26 1.35 1
1.25 1.74 1
1.30 1.43 1
1.16 1.27 1
1.21 1.43 1
42 x 60 1.16 1.32 1 Tod Blast furnace
1.16 1.30 1
1.09 1.32 1
32 x 42 1.18 1.34 1 AllisChalmers Producer
25% x37% 1.12 1.21 1 Koerting
16 x 24 1.10 1.20 1 Diesel Petroleum
1.11 1.22 1
1.02 1.22 1
5 Engines Total17 Diagrams
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
TABLE 16
VALUES OF n FROM COMPRESSED AIR LOCOMOTIVES
Size Expansion No. of
i  Diagrams Make
inches h. p. 1. p Examined
5 x 10x10 1.123 1.354 4 Porter
6 x 10 1.369 4
2 Engines Total 8 Diagrams
TABLE 17
VALUES OF n FROM AIR COMPRESSORS
Compression No. of
Sizes Diagrams
inches h. p 1. p. Examined
124 x 18% x 12 1.336 1.219 4
1.266 1.254 4
1 Compressor Total 8 Dia,
Make
Remarks
IngersollSargent Small amt. of cooling water
' I Large " I "
TABLE 18
VALUES OF n FROM AMMONIACOMPRESSORS
No bof
Compression Diagrams
Examined
1.148 1
1.186 2
1.235 2
Total 5 Diagrams
Make Remarks
York Dry comp. sing. acting
' " Doub. '
Wet compression
TABLE 19
VALUES OF n FROM GAS COMPRESSORS
Size Compressi
inches
28x 24 1.140
" 1.145
1 Compressor
on
No, of
Diagrams
Examined
Make
Remarks
2 IngersollSargent Illuminating gas
2 4
Total 4 Diagrams
Size
inches
12%'x 18
12% x 18
2 Compressors
ILLINOIS ENGINEERING EXPERIMENT STATION
about 1.20 to 1.40, leaving out of account very high values due to
imperfect cooling and very low values due to leakage and to cool
walls during the period of "starting up." The values of n are
low for expansion in large cylinders with lean gases, being about
the same as those found in steam cylinders using superheated
steam.
8. Compressed Air Engines. Very few data have been found
concerning the values of n from diagrams taken from compressed
air engines. Locomotives comprise the large part of this class
which use air expansively.
Curves were examined from eight diagrams taken from the
four cylinders of two locomotives, one a compound, and the other
a simple expansion type. The results are given in Table 16.
The expansion curves of these diagrams were very satisfac
tory, but the compression curves were all irregular, and no val
ues were obtained from most of them. This irregularity was
probably due to the vibration that is present in most locomotives
under running conditions. The values for expansion range from
about 1.12 to 1.37.
9. Air Compressors.Only 8 diagrams from one twostage
compressor were available for examination. The values of n for
compression are given in Table 17. No values for reexpansion
were obtained.
The values for compression in air compressors do not vary
much, and will generally fall between 1.20 and 1.35.
10. Ammonia, Compressors.The examples available of this
type of compressor were limited to 5 diagrams from 2 compres
sors. The compression curves were very satisfactory, but the re
expansion curves were quite irregular. These values will be found
in Table 18. The values found fall between about 1.15 and 1.24,
very little variation being observed.
11. Gas Compressors.This class refers to compressors used
to raise the pressure of illuminating gas in order to send it to
distant points in small pipes. The analysis of the gas compressed
in the single case examined is given on page 86. Values of n
were obtained for the compression curves only. These values are
given in Table 19. Although taken at different conditions of the
speed and the discharge pressure, these values show substantial
agreement, but are considerably lower than the values obtained
for air compression.
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
THEORETICAL VALUES OF k FOR ADIABATIC EXPANSION
The relations of P and V during adiabatic expansion of steam
and gases may be closely represented by the equation for the
polytropic curve PV/ = 0.
The value of k for steam depends upon the initial state, while
for gases k is equal to the ratio 
12. Values of kc for Steam.
(a) Saturated Steam. Rankine1 gives the value of k as 10
9
or 1.111, applicable to all initial states.
Grashof' examined the condition of initially dry saturated
steam and gives the value of k as 1.140.
Zeuner' examined the condition generally occurring in engi
neering practice, where the steam is initially composed of a mix
ture of vapor and water, and gives the relation 0
k= 1.035 +0.1 x.
He found the influence of initial pressure to be negligible.
Mr. E. H. Stone' examined the condition of various initial
states of pressure and quality, using the tables of Marks and
Davis, and gives the relation
k = 1.059  0.000315P + (0.0706 + 0.000376P) x.
Table 20 was computed from this equation and expresses the
relations of P and V with an average error of less than 0.2%.
(b) Superheated Steam. Zeuner5 gives the value of k as con
4
stant at , or 1.33?. Several conditions have been examined for
the initial state of 200 lb. absolute pressure with the superheat
varying from 800 to 530°. The relations of P and V were com
puted from Professor G. A. Goodenough's characteristic equa
tions6 for superheated steam.
It has been found, after many trials, that these relations are
closely expressed by the equation
P(V+ 0.088)15= C.
This equation expresses the relations of P and V with an average
error of about 0.5 per cent. The initial pressure and the degree
1 The Steam Engine, p 385.
2 Zeitschrift des Vereins deutscher Ingenieure. Vol. VIII. p 151.
8 Technical Thermodynamics II, p.83.
4 Thesis, University of Illinois, 1910.
5 Technical Thermodynamics, II, p. 223.
6 Principles of Thermodynamics, p. 203.
ILLINOIS ENGINEERING EXPERIMENT STATION
of superheat have very little effect upon the value of k for the
ranges commonly used in practice.
13. Values for Gases.The values of k for gaseous mixtures
commonly used in gas engines exhibit considerable variation due
to the variation in the relative proportion of the constituents.
The value of k for any gas is the value of the ratio ' and its
C'V
constancy depends on the relative constancy of the value of C,
and C, at different temperatures. It seems certain, from experi
ments of Mallard and Le Chatelier, that the values of C, and Cv in
crease with increase of temperatures, but that the ratio  ' at tem
Cv
peratures common to actual gas engine cycles, is very closely
constant.
Most of the following data on the value of k for gases has
been taken from Guldner'. The value of k depends, in any par
ticular mixture, upon the relative proportion of the constituents.
This may be seen from the values of k for different gases given in
Table 21, from Guldner. This table shows that by different pro
portions of these gases in a mixture, values of k may be obtained
between the extreme limits of 1.210 and 1.418. Thus k for illum
inating gas alone, for example, may have a value of 1.332, while
for a mixture of this gas with air in the proportion of 1 to 12, the
value rises to 1.402, or very nearly the value of pure air. After
combustion, the analysis of the gas changes, causing a change of
k, the effect being a lowering of its value because of the increase
in proportion of CO2 and H20O. Thus for the mixture cited above
the value of k after combustion is 1.387, a drop of 1.1 percent.
This, in a hypothetical case of an ideal gas engine cycle, would
cause an appreciable difference in the form of the expansion curve.
Table 22 gives all the data necessary to compute the value of
k for the case of one sample of illuminating gas without air. The
case of this same illuminating gas with varying ratios of air is
gas
given in Table 23. This table gives the data for the same gas
with the varying combustible ratios of air such as would obtain in
gas engine practice.
Table 24 gives the data and values after combustion of the
different mixtures of Table 23.
The value of k for any particular gas or gaseous mixture is
found as in Table 22. In general, rich gases, such as illuminat
lInternal Combustion Engines.
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
TABLE 20
ADIABATIC VALUES* OF k FOR VARIOUS INITIAL
STATES OF PRESSURE AND QUALITY
Initial Pressure
lb. per sq. in. abs.
60 80
1.133 1.134
1.128 1.129
1.124 1.124
1.119 1.119
1.114 1.114
1.110 1.109
1.105 1.104
1.101 1.099
1.096 1.094
1.092 1.089
1.087 1.084
100 120
1.136 1.137
1.131 1.131
1.126 1.125
1.120 1.120
1.114 1.114
1.109 1.108
1.104 1.102
1.098 1.096
1.093 1.091
1.087 1.085
1.082 1.079
140
1.138
1.133
1.127
1.119
1.113
1.107
1.101
1.095
1.089
1.083
1.077
160
1.139
1.132
1.126
1.119
1.113
1.106
1.100
1.093
1.087
1.080
1.074
180
1.141
1.134
1.127
1.120
1.113
1.106
1.099
1.092
1.085
1.078
1.071
200
1.142
1.135
1.127
1.120
1.113
1.105
1.098
1.091
1.084
1.076
1.069
220
1.143
1.135
1.128
1.120
1.112
1.104
1.097
1.089
1.081
1.074
1.066
*Values calculated by equation k=1.0590.000315 P+ (0.0706 + 0.000376 P) x
TABLE 21
ADIABATIC VALUES OF k
FOR VARIOUS GASES
Gas Value of k
TABLE 22
ADIABATIC VALUES OF k FOR AN AVERAGE
GERMAN ILLUMINATING GAS
Composition by
Volume I Weight
Cp
0.485 0.0846 3.430
0.350 0.4855 0.593
0.070 0.1703 0.245
0,045 0.1093 0.400
0.020 0.0765 0.200
0.0025 0"0070 0.217
0.0275 0.0670 0.245
Cv
2.430
0.468
0.174
0.330
0.155
0.153
0.174
Total
0.6955
k= 0.52 1.330
0.5231
ax Cii
GXCv
0.2890 0.2050
0.2880 0.2270
0.0416 0.0296
0.0437 0.0360
0.0153 0.0119
0.0015 0.0019
0.0164 0.0117
0.6955 0.5231
Initial
Quality
1.00
0.95
0.90
0.85
0.80
0.75
0.70
0.65
0.60
0.55
0.50
240
1,145
1.137
1.129
1.121
1.112
1.104
1.096
1.088
1.080
1.072
1.064
Gases
H
CH4
CO
C2H4
C02
0
N
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 23
ADIABATIC VALUES OF k FOR ILLUMINATING GAS OF'
TABLE 22 WITH VARIOUS RATIOS AIR
GAS
Ratio air by vol. V 6 8 10 12
gas
Ratio air by wt. G 15 20 25 30
gas
Wt. per e.u ft. of Mix lb. 0.0732 0.0748 0.0757 0.0769
CO 0.2667 0.2595 0.2556 0.2527
Cv 0.1914 0.1858 0.1828 0.1803
k 1.393 1.397 1.399 1.402
TABLE 24
ADIABATIC VALUES OF k FOR GAS GIVEN
IN TABLE 21, AFTER COMBUSTION
Volume Ratio a.r 6 8 10 12
gas
CO2 0.530 0.530 0.530 0.530
Combustion of H20 1.275 1.275 1.275 1.275
Burned Gses 0 0.150 0.570 1.000 1.410
volumes N 4.768 6.348 7.928 9.508
Constants for vp 0.2787 0.2674 0.2623 0.2566
Burned Gases
from 1 lb. Cv 0.2035 0.1940 0.1894 0.1851
k 1.370 1.380 . 1.385 1.387
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
ing gas or natural gas, require very large ratios of air and there
gas
fore the resulting mixtures have values of k very near the value
for pure air, 1.405. In the case of lean gases, as blast furnace
gas, or producer gas, requiring small ratios of air the value of k
gas
is lower or nearer the value k for the gas alone. The limits for
ordinary gases and mixtures are between the values of 1.320 and
1.405, while after combustion these values are lowered somewhat,
in general about 1 to 2 per cent. The range of values for gaseous
mixtures is not nearly so large as with steam.
14. Values for Air Compressors.The proportion of the con
stituents of air is almost always constant, so that the values
<Co and C,, are always constant if we are discussing them in tem
peratures in the range of compressor practice. This makes the
ratio of k constant. The value of k for air has been determined
many times by different investigators in different ways. The
degree of variation in determining this constant will be seen from
Table 25. Zeuner' after discussing all the values and the exper
iments supporting them, concludes that the value 1.410 most
clearly fits the case of pure dry air. Zeuner also shows that in
cases of water injection in compressors, used to keep down the
temperature, the value of /i does not change materially from
1.410. The true value seems to lie between 1.405 and 1.410.
15. Values for Compressed Air Engines.The temperatures
existing in the engines using compressed air for the active med
ium are not far below that existing in compressors. Within the
range covered by both, the value of k is, as far as can be ascer
tained, practically constant.
16. Values for Ammonia.The properties of ammonia have
not been so thoroughly investigated experimentally as those of
air and the vapor of water. The value of k, depending on the value
CV
other working media given. Various determinations place the
value of k as between 1.30 and 1.333, these values being some
what similar to those of superheated steam.
17. Values for Illuminating Gas and C02.Illuminating gas
is often compressed to send it to outlying districts in cities, and
there its pressure is reduced for distribution. The value of k
here depends in each case on the value of the ratio C from the
ITechnical Thermodynanmics, I, p. 121.
ILLINOIS ENGINEERING EXPERIMENT STATION
analysis of the particular gas compressed. The analysis and
values of the gas, made by the New Orleans Gas Company, New
Orleans, La., which is compressed to send it to outlying districts
of New Orleans, is given in Table 26.
The value of k for this gas, 1.349, is considerably higher than
the value of the gas given in Table 22, 1.332. This is due to the
very much larger proportion of CO in the gas of Table 26, and
illustrates well the variation of this value with gases of similar
heating value, but with a different proportion of the same constit
uents. Lummer and Pringsheim give the value of k for CO2 as
1.2961 from their experiments. Guldner gives the value as 1.293.
TABLE 25
ADIABATIC VALUES OF
k FOR AIR OBTAINED
BY VARIOUS EX
PERIMENTERS
Experimenter Value
La Place 1.403
Dulong 1.421
Wullner at 320 1.4053
at212° 1.4029
Clement 1.356
Masson 1.419
Hirn 1.384
Weisbach 1.402
Cazin 1.410
Rontgen 1.405
Lummer and
Pringsheim 1.4015
TABLE 26
ADIABATIC VALUES OF k FOR AN ILLUMINATING GAS
I II III IV V VI
Constituents Per Cent Wt. of 1 cu. Wt. in 1 cu. ft. Ratio kv IV xV
Weight ft. lb. of This Gas, b. kv
CO2 2.40 0.12267 0.00295 1.293 0.00381
C2 H4 9.00 0.07809 0.00703 1.210 0.00851
0 0.60 0.08921 0.00045 1.418 0.000635
CO 31.00 0.07807 0.02420 1.408 0.0341
H 35.20 0.00559 0.00197 1.412 .0.00278
CH4 18.50 0.04464 0.00827 1.270 0.01050
N 3.40 0.07831 0.00266 1.408 0.00375
Total 0.04753 0.06409
0.06409
0.04753
APPENDIX 2
DESCRIPTION OF THE PLANT
ILLINOIS ENGINEERING EXPERIMENT STATION
APPENDIX 2
DESCRIPTION OF THE PLANT
APPARATUS USED
The engine used for the tests given in Part I is of the Corliss
type, and is a part of the equipment of the Mechanical Engineer
ing Laboratory of the University of Illinois. The plant comprises
the engine and various auxiliaries which are used in connection
with the engine. These auxiliaries consist of a throttle valve in
the steampipe line, an independently fired superheater, a direct
current generator with a water rheostat, a surface condenser,
scales, and a tank. The instruments used consist of indicators,
steam pressure gauges, thermometers, ammeters, a voltmeter,
and a continuous revolution counter.
The general arrangement of the plant, with the exception of
the superheater and the steam piping, was the same for both sat
urated and superheater steam tests. Steam was obtained from
the main boiler plant of the University, located about 150 ft. away
from the engine. Two pipe lines, one of 6in. pipe for saturated
steam and the other of 4in. pipe for superheated steam, traverse
the laboratory, and each is connected to the steam pipe of the
engine tested.
The steam exhausts from the engine through 30 ft. of 5in.
pipe to the condenser, where the exhaust steam is condensed, and
is then weighed in a large tank on a platform scales. The engine
is connected by a belt to the generator, which furnishes the load.
This generator is loaded upon a water rheostat located close by.
1. The Eng.ine.The engine is a small welldesigned Corliss
engine of a standard type built for heavy duty service. Its prin
cipal dimensions are given in Table 27. A view of the right side
of the engine is shown in Fig. 31, and a view of the left side is
given in Fig. 32.
The cylinder is not steamjacketed on the ends, but is partly
jacketed on the barrel by the steam chest, the latter covering
about onesixth of the barrel surface. The exhaust passages are
separated from the lower part of the cylinder barrel by a dead
air space formed in cylinder casting. The cylinder is shown in
section in Fig. 34.
The engine is fitted with separate eccentrics for actuating the
exhaust and the steam valves, thus enabling the steam valve gear
to cutoff up to about 50% of the length ofjthe stroke. The two
separate eccentrics and the two wrist plates are well shown in
Fig. 31.
CLA FOONNEW ANALYSIS OF CYLINDER PERFORMANCE
TABLE 27
PRINCIPAL DIMENSIONS OF CORLIss ENGINE
1. TypeHorizontal singlecylinder, double eccentric. noncondensing, variable speed, heavy
duty frame, Reynolds Corliss Engine.
2. ClassBelt drive for mill work.
3. MakerAllis Chalmers Co, Milwaukee, Wisconsin
4. Rated Power of Engine100 h. p. at 115 lb. initial pressure above atmosphere on indicator
diagram, : cutoff, and 120 r. p. m.
5. Cylinder dimensions:
(a) Bore kmeasured while hot) ............... 12.02in.
(b , S troke .......................... ..............24.00 in .
(c) Diameter of pistoD rod....................... . 2 ij in.
6. Clearancein per cent of volume displaced by piston per stroke
(a, Head end......................... ............7.89 per cent
(o) Crank end ............ ... .......... ..7.04 per cent
7. SpeedControlled by flyball governor with variable gear ratio between main shaft and
governor, giving any engine speed from 20 to 160 r. p. m Usual speed 120 r p. m.
(a) Speed Control.The speed of the engine is controlled by
a flyball governor acting on the cutoff cams of the steam valve
gear. Variable speed is obtained by varying the gear ratio
between the main shaft and the governor. This gear ratio change
is accomplished by the mechanism shown to the left of the fly
wheel in Fig. 31. The mechanism is operated as follows: The
belt from the main shaft drives the concave disc to the left which is
loose on the shaft; this disc drives by friction three fiber rimmed
idlers which are mounted between two discs on frames supported
by a stationary frame in a manner which permits the plane
of the idlers with respect to the shaft to be changed; the concave
disc to the right is frictiondriven by the three idlers and is keyed
to the shaft which is connected through bevel gears to the gov
ernor. The discs arekept in contact with the idlers by an end
thrust provided by a helical spring (surrounding the shaft) which
is located between the right disc and the outboard bearing; the
left disc is loose on the shaft but works against a collar formed by
the sleeve carrying the shaft; the spring, therefore, acting against
the outboard bearing, forces the right disc against the idlers and
the left disc against its collar. The hand wheel shown in the
figure, by a gear and sector device not shown, changes the plane
of the idlers with respect to the shaft, and therefore changes the
ILLINOIS ENGINEERING EXPERIMENT STATION
gear ratio between the two discs. This device permits any speed
from 20 to 160 r. p. m. to be obtained. A leakage test of all
valves and the piston, the engine being at rest, showed that these
parts were fairly tight.
2. The Superheater.The superheater is of the Foster sep
aratelyfired type,and is rated at 2000 F. of superheat for a flow
of 4500 lb. of steam per hour. The draft is induced by an engine
driven fan.
3. The CondenserThe condenser is of the Worthington sur
face type having 362 sq. ft. of condensing surface. Two pumps
are provided; one a Worthington circulating pump drawing its
water from a creek about 40 ft. away, the other, a Blake wet air
pump, discharging into a tank on a platform scales. Tests at fre
quent intervals showed that the condenser was practically with
out leakage.
4. The Generator and Water Bheostat.The engine was
loaded on a generator and water rheostat shown in Fig. 33. This
generator is of the Edison bipolar type, and is rated at 100 kw.
at 140 volts, thus giving a full load current of 715 amperes. The
field was separately excited for the tests, the current being ob
tained from the laboratory 220volt direct current supply.
Fig. 33 shows the arrangement of the loading part of the plant.
The generator output was conducted through cables in the conduit
shown to the main switch on the switchboard: here connections
were made to the plates of the water rheostat. Voltmeter and am
meter connections are made on the back of the switchboard. The
table shown to the right of Fig. 33 contains the voltmeter and
millivoltmeter for the main load current, and the field ammeter
and rheostat for controlling the voltage. The water rheostat
consists of three watertight wooden barrels, each containing two
iron plates, one positive and one negative. The connections of
all the barrels are in parallel. Referring to Fig. 33, and describ
ing only one barrel, a plate connected to the negative terminal is
placed on the bottom of the barrel; the positive terminal is con
nected through the looped wire, shown to the front, to a movable
plate suspended by a rope from the long shaft hung under the
frame carrying the conductors. This long shaft is turned by
means of the handwheel and worm device shown. The rope hold
ing the upper plate is tied through a hole in the shaft, so that
when the shaft is turned, the rope is wound up, or vice versa, as
desired. The desired load as shown by the millivoltmeter is ob
tained by regulating the distance between the plates and by throw
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
ing salt in the water to obtain the desired resistance. An over
flow from the top of each barrel is provided at the back, so that
when the water boils, cold water is admitted so that the heat is car
ried away in the overflow water instead of by the boiling of the
water. All the upper plates are lowered simultaneously by means
of a long shaft. An almost absolutely constant load is maintained
by this rheostat.
5. The Instruments.The various instruments used were care
fully calibrated.
INDICATORS
The indicators and the indicator rig are shown in positions
in Fig. 32. Two Crosby inside spring indicators in very good
condition were used for the tests. The pipe connections consist
of 5 inches of Iin. pipe for each indicator. The reducing motion
is a wooden pantagraph mounted as shown. The lost motion in
the indicator rig was less than .01 in.
Great care was observed in the indicator work, since the in
dicator diagrams themselves formed the basis of the results to be
obtained. The pistons were oiled at intervals of about one hour.
The springs were calibrated by steam in the indicators used, by
a Cooley fluid scales tester, using a method which duplicated al
most exactly the conditions under which the indicators were used
during the tests.
ILLINOIS ENGINEERING EXPERIMENT STATION
FIG. 31.
FEG.32
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE 93
FIG, 33.
%4 ILLINOIS ENGINEERING EXPERIMENT STATION
(N
0
a
z
0
0
aI
0
0
u
0
I
U
z
< 0
z
o
I 7
IU g
0
;4
,n
).4
APPENDIX 3
TEST METHODS
ILLINOIS ENGINEERING EXPERIMENT STATION
APPENDIX 3
TEST METHODS
1. Preliminary.The object of the investigation given in
Part 1 was to examine the values and relations of the exponent n
obtained from the expansion curve of the indicator diagrams
under different conditions of pressure, speed, and cutoff. The
effect of changing one of these variables was studied while keep
ing the other two constant. The method of testing was planned
therefore with a view to maintaining the conditions of pressure,
speed, and cutoff as constant as was possible during any one test.
2. Length of Tests.Tests may be very short when a surface
condenser is used and constant conditions are maintained. Prior
to running a test, the engine was operated for about one hour.
It was found that after the operating conditions for one test had
been maintained constant for ten minutes that the steam con
densed per unit of time was almost exactly constant. After the
conditions had become constant, it was found that 30 minutes of
operation gave a length of test which produced trustworthy and
consistent results. All observations and diagrams were taken
every three minutes in response to a signal given on the even
minute. Six observers were required to maintain the desired
conditions of load, pressure, superheat, and to take the readings.
3. Control of Steam Pressure and Temperature.The steam
pressure was closely controlled by an observer, who throttled the
steam in the main, before it reached the engine, to the pressure
desired as shown by a gauge at the valve. Ordinarily this pres
sure was maintained to within three pounds of the pressure
desired. It was decided to keep the steam temperature for the
superheated steam tests constant at 500° F. at the superheater.
The superheater was operated by an observer who was guided by
the indication of a thermometer placed in the pipe carrying the
steam leaving the superheater. Ordinarily, the temperature of
the steam was kept within the limits of 4900 to 510° F. The
temperature variation at the steam chest of the engine did not ex
ceed 20 or 3° F. during one test. The load was kept to within
about 1 per cent variation from the average load during one test.
A back pressure of about i lb. above the atmosphere was main
tained at the engine by keeping the vacuum at the condenser at
1.5 in. of mercury, this vacuum being controlled by an observer who
regulated an air leakage valve on the condenser.
4. Plan of Tests.The testing crew became expert in control
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
ling the conditions so that the variations from constant conditions
were remarkably small for test work. When the conditions of
one test varied for any reason more than the amounts given, this
test was not used for the purposes of the investigation.
The tests were designated in the laboratory by a symbol in
dicating the conditions to be maintained. Thus, test 500°10052
120 indicated that the steam was to be superheated to 5000 F. at
the superheater; that 100 lb. gauge pressure was to be maintained
at the engine throttle; and 52 kw. load was to be put on the gen
erator; and that the speed was adjusted to be 120 r. p. m, measured
at no load.
5. Data for Test 52.All the readings to Test 52 (5000 100
52120) are given in Table 28. A study of these readings
shows the constancy of conditions that was attained.
METHOD OF SELECTING ONE SET OF INDICATOR DIAGRAMS
TO REPRESENT THE AVERAGE CONDITIONS OF ONE TEST
After a test was run, the constancy of the conditions of pres
sure, superheat, load, the number of revolutions and the weight of
the condensate for each 3min. reading was examined. If the va
riations of these conditions were within the limits selected, the
test was worked up in the usual manner. It was generally found
that the area of each of the indicator diagrams for each end of
the cylinder was within 3 per cent of the mean area. The gauge
pressure for each reading at which the diagrams were taken was
found in general to vary less than 3 lb. from the average. To rep
resent the average conditions of one test, the simultaneous com
bination of a gauge pressure reading nearest to the average and
of one set of diagrams which had an area nearest to the mean
area, was sought. This combination gave one set of diagrams,
taken at the average pressure, which represented the average
area of all the diagrams. This mean combination condition could
generally be satisfied to within I of 1 per cent of the average
area.
The value of the average quality of the steam mixture pre
sent in the cylinder at cutoff, and the average value of n for both
expansion curves were obtained from this set of diagrams (trans
ferred to the logarithmic form) selected as representative average
conditions. The unit of measurement of both quality and n was
therefore the revolution.
The manner of selecting the representative diagrams is illus
ILLINOIS ENGINEERING EXPERIMENT STATION
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CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
trated in Table 28. The areas of the diagrams are given in
columns 14 and 15. The pair taken at 2:44, the time of reading
No. 9, was chosen. The steam pressure for this reading is 99.5
lb. at the throttling valve, while the average is 99.4 lb. The pres
sure at the engine throttle was 94.1 lb., while the average was
95.1 lb. This last pressure, 94.1 lb., was always read some time
after the signal for readings, while the pressure at the throttling
valve was always read at the time of the signal.
The area of the crankend diagram of the pair selected is
2.70 sq. in., while the average is 2.714 sq. in.; the area of the head
end diagram is 3.05 sq. in., while the average is 3.055 sq. in. The
crankend diagram is 0.5 per cent lower in area than the average;
the headend diagram is 0.2 per cent lower than the average; both of
them considered together are 0.35 per pent below the average.
This figure, 0.35, may be taken to show the average difference, and
shows that no material error is introduced by this method.
6. Methods of Computation.The manner of computing the
value of xc and n is given for test 30, the representative indicator
diagrams of which are given in Fig. 15, and the logarithmic dia
grams in Fig. 9. The results of the computations for all tests are
given in Tables 1 and 2.
The absolute pressure of cutoff was determined from the indi
cator diagrams at a point located by inspection, as was also the
per cent of cutoff, the latter, however, not being involved in this
investigation. The cutoff pressures for all the tests constituting
one group were averaged and this average was used to obtain all
values of xc for one group. Test 30 belongs to group G, com
prising series 6 and 14, and the average absolute pressure at cut
off was 129.0 lb.
The logarithmic diagrams of test 30, shown in Fig. 9, are the
basis of the calculations for the value of xc. The calculations
which follow are given in detail in the same form as they were
made for all tests.
COMPUTATION FOR THE VALUES OF Xc AND n FOR TEST 30.
(VOLUMES OBTAINED FROM FIG. 9.)
Steam present at cutoff pressure of 129.0 lb. absolute
Volume of steam present, head end ...........0.482 cu. ft.
Volume of steam present, crank end.......... 0.478 cu. ft.
Total, head and crank end ...........0.960 cu. ft.
Specific volume' of steam at 129.0 lb. absolute = 3.478 cu. ft. per lb.
IMarks and Davis Steam Tables.
ILLINOIS ENGINEERING EXPERIMENT STATION
0.960
Weight of steam present at cutoff 3.478 =0.2760 lb.
Steam regained in compression at 15.0 lb. absolute
Volume of steam present, head end .......... 0.350 cu. ft.
Volume of steam present, crank end ............0.322 cu. ft.
Total, head and crank ends ...........0.672 cu. ft.
Specific volume of steam at 15.0 lb. absolute=26.27 cu. ft. per lb.
0.672
Weight of steam retained in compression  0.0256 lb.
From Table 1, the weight of steam and water supplied = 2796 lb. per hour
Revolutions per hour.................................... 6840
Pounds of steam and water supplied per revolution = 96=0.4087 lb.
6840
Total weight of mixture present per revolution
0.4087 lb. supplied
0.0256 lb. retained in compression
0.4343 lb. total present
Xc = 0.2760 0.635, or 63.5% present as steam.
0.4343
Value of n from point 0, Fig. 9.
Head end Length OX= 1.575 in.
OY= 1.56 in.
n, head end = 1.575 =1.010
1.56
Similarly:n, crank end= 1.535 = i.006
1.525
Average value of n = 1.008
When the actual cutoff pressure was less than 129.0 lb., the
line of constant weight of steam mixture on the logarithmic dia
gram was extended to this pressure, and the calculations made.
7. Compression Steam. The point of compression was selected
in the following manner from Fig. 9 for the reasons explained fully
on page 49. The straight line of the compression curve on the
logarithmic diagram, or the line of constant weight of steam mix
ture, was prolonged dotted as shown to the back pressure. In
these tests the average back pressure was about 15.0 lb., and
this back pressure was used to calculate all steam retained in
compression. The intersection of the compression line, pro
longed, with the back pressure line (15.0 lb.), extended, was
taken as the volume of dry steam retained in compression. This
method generally gives less steam retained than the ordinary
method.
APPENDIX 4
BIBLIOGRAPHY
ILLINOIS ENGINEERING EXPERIMENT STATION
APPENDIX 4
1. BIBLIOGRAPHY
The following references are given for the benefit of readers
who may wish to investigate further the various sources of infor
mation on this subject.
1. Application of the Law PVn = C to Curves From Practice.
Zeuner, Technical Thermodynamics (Klein), Vol. II, pp. 111, 119.
Leloutre, Bulletin de la Societ4 Industrielle du Nord de la
France, 1874.
Leloutre, Bulletin de la Soci6t6 Industrielle de Mulhouse, 1873,
(quoted in Thurston, A Manual of the Steam Engine, Vol.
I, p. 690.)
Luders, Zivilingenieur, 1881, Vol. XXVII, p. 225.
DwelshauversDery, Power, June 28, 1910, p. 1164.
Creighton, The Steam Engine, p. 115.
Perry, The Steam Engine, p. 106.
Rankine, The Steam Engine, p. 402.
Peabody, Thermodynamics of the Steam Engine, pp. 66, 103.
Thurston, A Manual of the Steam Engine, pp. 410, 690, 718.
Thurston, Trans. A. S. M. E., Vol. II, p. 203.
Wood, Thermodynamics, pp. 150, 191.
2. Theoretical Values of k for Adiabatic Expansion.
(a) Steam
Rankine, The Steam Engine, pp. 385, 432.
Zeuner, Technical Thermodynamics (Klein), Vol. II. pp. 83, 233,
277.
Grashof, Zeitschrift des Vereins deutscher Ingenieure, Vol. VIII,
p. 151.
Goodenough, Principles of Thermodynamics, pp. 191, 220.
Ennis, Applied Thermodynamics, p. 220.
(b) Other Elastic Media
Zeuner, Technical Thermodynamics (Klein), Vol. I, p. 121.
Guldner, Internal Combustion Engines (Diederichs), pp. 539, 540,
541.
Goodenough, Principles of Thermodynamics, p. 97.
Wood, Thermodynamics, pp. 77, 80.
Ennis, Applied Thermodynamics, p. 33.
Rankine, The Steam Engine, p. 249.
CLAYTONNEW ANALYSIS OF CYLINDER PERFORMANCE
3. Curve of Constant Steam Weight
Zeuner, Technical Thermodynamics (Klein) Vol. II, p. 37.
Rankine, The Steam Engines, p. 402.
4. Values of nfrom Practice
(a) Steam
Zeuner, Technical Thermodynamics (Klein), Vol. II, p. 111.
Lilders, Zivilingenieur, 1881, Vol. XXVII, p. 225.
(b) Other Elastic Media
Gildner, Internal Combustion Engines (Diederichs), pp. 34, 88.
Ennis, Applied Thermodynamics, pp. 99, 102, 120, 175.
Wimperis, The Internal Combustion Engine, p. 73.
Wood, Thermodynamics, p. 258.
5. Form of Steam Expansion Curves from Practice.
Thurston, A Manual of the Steam Engine, Vol. I. pp. 396, 410,
718, 719, 720.
Ripper, Steam Engine Theory and Practice, p. 100.
Ennis, Applied Thermodynamics, pp. 260, 268.
Spangler, Greene, and Marshall, Elements of Steam Engineering,
p. 195.
Pray, Twenty Years with the Indicator, p. 277.
Buchetti, Engine Tests and Boiler Efficiencies, (Russell), p. 79.
Zeuner, Technical Thermodynamics (Klein), Vol. II, p. 116.
Beaumont, The Steam Engine Indicator, p. 73.
Houghtaling, The Steam Engine Indicator, p. 119.
Wolff and Denton, Trans. A. S. M. E., Vol. II. p. 175.
Heck, Power, December 27, 1910, p. 2271.
Pullen, Experimental Engineering, pp. 295, 296.
Booth, Superheat, Superheating and Their Control, pp. 13, 14.
Hutton, Heat and Heat Engines, p. 245.
Burgh, The Indicator Diagram, p. 49.
Day, Indicator Diagrams, pp. 41, 43.
Hemenway, Indicator Practice and Steam Engine Economy, p. 55.
LeVan, The Steam Engine Indicator, pp. 53, 131.
Porter, Richard's Steam Engine Indicator, p. 84.
Robinson, Proc. British Inst. C. E., Vol. CXIV. p. 57.
6. Quality of Steam at End of Exhaust.
Duchesne, Power, January 10, 1911, p. 71.
Peabody, Thermodynamics of the Steam Engine, p. 229.
Carpenter, Trans. A. S. M. E., Vol. XII, p. 811.
Hallauer, Bulletin de la Soci6t6 de Mulhouse, Vol. XLVII, 1877.
Zeuner, Technical Thermodynamics (Klein), Vol. II, p. 431.
ILLINOIS ENGINEERING EXPERIMENT STATION
7. Hirn's Analysis.
Hirn, Th4orie MWcanique de Chaleur.
DwelshauversDery Revue Universelle de Mines, de Li6ge.
Thurston, A Manual of the Steam Engine, I. p. 526.
Carpenter, Trans. A. S. M. E., Vol. XII, p. 790.
Carpenter, Experimental Engineering, p. 545.
Creighton, The Steam Engine, p. 170.
Peabody, Trans. A. S. M. E., Vol. XII, p. 740.
Peabody, Thermodynamics of the Steam Engine, pp. 205, 223.
8. Formula for Computing Weight of Cylinder Condensation
at Cutoff
Thurston, A Manual of the Steam Engine, I, p. 517.
Escher, Engineer, (London), 1882.
Marks, Relative Proportions of the Steam Engine, p. 206.
Marks, The Steam Engine, p. 190.
English, Proc. Inst. M. E., October, 1889.
Bodmer, Engineering (London), March 4, 1892, p. 299.
Cotterill, The Steam Engine, p. 339.
Heck, The Steam Engine, Vol. I, p. 109.
9. Effect of Length and Form of Pipe Connection on the Form of
Indicator Diagrams.
Goss, Locomotive Performance, p. 281.
Low, The Steam Engine Indicator, p. 150.