UC-NRLF
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\y/' H S I T Y OF ILLINOIS BULLETIN
ISSUED WEEKLY
\ifr ' ' SEPTEVIBER 18. 1916 NO. 3
(Entered a? second-class matter Dec. 11, 1912, at Urbaaa, 111., under the Act of August 24, 1912.]
THE TRACTIVE RESISTANCE ON
CURVES OF A 28-TON
ELECTRIC CAR
BY
EDWARD C. SCHMIDT
AND
HAROLD H. DUNN
BULLETIN NO. 92
ENGINEERING EXPERIMENT STATION
PUBLISHED BY THE UNIVERSITY OF ILLINOIS, URBANA
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PRICE: TWENTY-FIVR CENTS
EUROPEAN AGENT
CHAPMAN AND HALL, LTD., LONDON
UNIVERSITY OF ILLINOIS
ENGINEERING EXPERIMENT STATION
BULLETIN No. 92 SEPTEMBER, 1916
THE TRACTIVE RESISTANCE ON CURVES OF A
28-TON ELECTRIC CAR
BY
EDWARD C. SCHMIDT
Professor of Railway Engineering,
and
HAROLD H. DUNN
Assistant in Railway Engineering, Engineering Experiment Station
CONTENTS
PAGE
I. INTRODUCTION 5
II. SUMMARY 5
1. The Car, The Track, etc 6
2. Methods 6
3. Results 7
III. MEANS EMPLOYED IN CONDUCTING THE TESTS 7
4. The Test Car 7
5. The Track 9
IV. TEST CONDITIONS AND TEST METHODS 10
6. Test Conditions 10
7. The Selection of the Track 11
8. General Methods 11
V. THE IMMEDIATE RESULTS OF THE TESTS. . 13
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VI. THE FINAL RESULTS OF THE TESTS 21
9. The Resistance Due to Curvature 21
10. The Relation of Curve Resistance to Curvature 21
11. The Relation of Curve Resistance to Speed 25
12. The Concurrent Relations of Curve Resistance, Curva-
ture, and Speed 27
13. Conclusion 28
Appendix I. The Track 30
Appendix II. Test Methods and Methods of Calculation 34
Methods Used in Producing the Curves of Figs. 3 to 13 ... 34
Methods of Calculation 34
Appendix III. The Immediate Results of the Tests 37
CONTENTS 3
LIST OF TABLES
PAGE
1. Data Kelating to the Seven Curves 9
2. A Summary of Test Conditions on the Curves and on Their Corresponding
Tangents 10
3. Values of Eesistance on the Curve, Eesistance on the Tangent, and Re-
sistance Due to Curvature for Each of the Seven Curves at Various
Speeds 22
4. Values of Curve Resistance of Various Curvatures and Speeds 28
5. The Immediate Results of the Tests on the 2°-0' Curve 38
6. The Immediate Results of the Tests on the 2°-50' Curve 40
7. The Immediate Results of the Tests on the 3°-40' Curve 42
8. The Immediate Results of the Tests on the 5°-0' Curve 44
9. The Immediate Results of the Tests on the 6°-30/ Curve 46
10. The Immediate Results of the Tests on the 8°-0' Curve 48
11. The Immediate Results of the Tests on the 14°-30' Curve 50
LIST OF FIGURES pAGE
1. The Test Car 7
2. Plan and Cross Section of the Test Car 8
3. The Relation of Resistance to Speed on the 2°-0' Curve 14
4. The Relation of Resistance to Speed on Tangent W, Which Pertains to
the 2°-0' Curve 14
5. The Relation of Resistance to Speed on the 2° -50' Curve 15
6. The Relation of Resistance to Speed on Tangent S, Which Pertains to
the 2°-50' Curve 15
7. The Relation of Resistance to Speed on the 3°-40' Curve 16
8. The Relation of Resistance to Speed on Tangent R, Which Pertains to
the 3°-40', the 5°-0', the 8°-0', and the 14°-30' Curves 16
9. The Relation of Resistance to Speed on the 5°-0' Curve 17
10. The Relation of Resistance to Speed on the 6° -30' Curve 18
11. The Relation of Resistance to Speed on Tangent D, Which Pertains to
the 6°-30' Curve 18
12. The Relation of Resistance to Speed on the 8°-0' Curve 19
13. The Relation of Resistance to Speed on the 14°-30' Curve 20
14. The Relation of Resistance to Speed on All the Curves and on Their
Corresponding Tangents 23
15. The Relation Between Curve Resistance and Curvature at Various Speeds 24
16. The Relation Between Curve Resistance and Curvature at Various Speeds 25
17. The Relation Between Curve Resistance and Speed for Curves of Various
Curvature 26
18. The Concurrent Relations Between Curve Resistance, Speed, and Curva-
ture '. 27
19. Profile and Alignment Diagram of the Track on the 2°-0' Curve 30
20. Profile and Alignment Diagram of the Track on the 2°-50' Curve 31
21. Profile and Alignment Diagram of the Track on the 3°-40' Curve 31
22. Profile and Alignment Diagram of the Track on the 5°-0' Curve 32
23. Profile and Alignment Diagram of the Track on the 6°-30' Curve 32
24. Profile and Alignment Diagram of the Track on the 8°-0' Curve 33
25. Profile and Alignment Diagram of the Track on the 14°-30/ Curve 33
26. Reproduced from a Portion of One of the Test Car Charts 35
347264
THE TRACTIVE RESISTANCE ON CURVES OF A
28-TON ELECTRIC CAR
I. INTRODUCTION
The tractive resistance of cars running on curved track is greater
than their resistance on straight track of like grade and construction.
This excess is generally termed curve resistance or resistance due to
curvature. A knowledge of its magnitude is needed in many problems
which present themselves in connection with steam and electric rail-
way design and operation. While these problems are more important
and more numerous on steam roads, they are not unimportant nor
infrequent on electric roads. Nearly all the existing information re-
garding curve resistance has arisen from tests and experience with
trains on steam railways, and it is doubtful whether the values of
curve resistance thus derived are valid for the single self-propelled
cars used on electric lines. Such considerations led the Railway
Engineering Department of the University of Illinois to make the
tests, the results of which are presented in this bulletin.
The tests were undertaken to measure) the curve resistance of a
28-ton electric car, owned by the department, with the view of deter-
mining its value at various speeds and on as great a variety of curves as
were available on the lines of the Illinois Traction System, upon which
the experiments were conducted. The results established for this car
the; relations between curve resistance and speed and between curve
resistance and rate of curvature.
The test conditions, test methods, and final results are presented
in the body of the bulletin, while the details concerning the apparatus,
test data, methods of calculation, and intermediate results are given
in the appendixes. Throughout the bulletin the term ' * curve resis-
tance" or "resistance due to track curvature" means the tractive
force needed by the car on curves in excess of the force needed to move
it over straight track. This tractive force is the force required at the
wheel rims to keep the car moving at uniform speed on level track
and in still air. It is expressed in pounds per ton of car weight.
Acknowledgment is gratefully made of the interest and coopera-
tion of the officers of The Illinois Traction System, which rendered it
possible to conduct the tests on that road; and to Mr. D. C. Faber,
formerly a Fellow in the Department of Railway Engineering, who
was in charge of the test car during some of the tests and who made
some of the preliminary calculations.
5
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"ILLINOIS'" ENGINORERING EXPERIMENT STATION
II. SUMMARY
At the expense of some duplication there is presented at this point
a summarized statement of the conditions, methods, and results of the
tests, which may serve to provide a general view of the work and to
facilitate an understanding of the more detailed explanations which
follow.
1. The Gar, Track, and Equipment. — The tests were made with
a car such as is commonly used on interurbaii electric roads; it
has a body 45 feet long of the double-end type with round vestibules.
This body is carried on four-wheeled trucks which are spaced 23 feet
3 inches from center to center and which have a wheel base of 6 feet
4 inches. The car is equipped with four 50-horsepower motors and
weighs approximately 28 tons.
The tractive resistance of this car was determined when running
upon each of seven curves whose curvature varied from 2 to 14%
degrees, and also when running upon adjacent tangent track. The
superelevation of the outer rail on the curves varied from 0.75 inches
on the 2-degree curve to 5.9 inches on the 14%-degree curve. The
track was laid with 70-pound rails on ties spaced about 24 inches be-
tween centers in gravel or cinder ballast. Judged by the standards
which prevail on electric interurban roads built for moderate speed,
the track was well constructed and well maintained. It was surveyed
especially for the purposes of the tests. With a few exceptions the
tests were made on dry rail in fair weather. The average air temper-
ature varied during the tests from 25 to 65 degrees F. and the maxi-
mum average wind velocity was 18 miles per hour.
2. Methods. — In making a test, the test car was run first in one
direction and then in the other over one of the curves and its adjacent
tangent. During each such pair of runs the car speed was maintained
as nearly constant as possible. Similar pairs of runs were then made
at other speeds, until sufficient data had been accumulated to define
the resistance at various speeds on the curve and on its corresponding
tangent. Under this procedure each pair of runs results in two values
of resistance: one with such wind as prevailed helping the car, the
other with the wind opposing it. From the final curves which define
the mean between these values, the influence of the wind is, therefore,
nearly, if not quite, eliminated, and the results relate to movement in
still air. The results of the tests provide mean values of resistance
on each curve and on its tangent. The difference between these values
of resistance is the desired resistance due to track curvature.
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR 7
3. Results. — The tests demonstrate that for the car in question
curve resistance varies directly with both track curvature and speed.
For a particular speed, the curve resistance increases as the curvature
increases and in direct ratio with the curvature, as shown in Fig. 16.
This implies that at a particular speed the curve resistance, when
expressed in pounds per ton per degree of curve, is a constant for
all curvatures; a relation which is in accord with the results of
previous experiments. On the other hand, the value of curve resis-
tance expressed in pounds per ton per degree is shown to be different
at each different speed, and it varies in such a way that for a curve
of a particular curvature the curve resistance increases in direct ratio
with the speed, as shown in Fig. 17. The concurrent relations between
curve resistance, track curvature, and speed are shown in Fig. 18, and
they are defined by the formula:
Rc = 0.058 8 C,
in which Rc is the curve resistance expressed in pounds per ton, 8 is
the speed in miles per hour, and C is the degree of curve. Values de-
rived by means of this equation appear in Table 4.
III. MEANS EMPLOYED IN CONDUCTING THE TESTS
4. The Test Car. — The car used for the tests is owned by the
Railway Engineering Department of the University. It is a standard
45-foot car similar to those commonly used on interurban roads built
for moderate speed. Its general design is shown in Figs. 1 and 2.
FIG. 1. THE TEST CAR
The car weighs 55,150 pounds, although during the tests this weight
was subject to certain corrections due to changes in equipment and in
the number of passengers. The sectional area of the car body and
trucks is 90 square feet.
8
ILLINOIS ENGINEERING EXPERIMENT STATION
The trucks are of the standard Motor Truck Company's C-60
type and weigh 7,824 pounds each, without the motors. The truck
journals are 4*4 by 8 inches, the wheel diameter is 33 inches, and the
5-11
FIG. 2. PLAN AND CROSS SECTION OF THE TEST CAR
truck wheel base is 6 feet 4 inches. One of the trucks is equipped with
rolled steel wheels and the other with chilled cast iron wheels, all of
which have standard Master Car Builders ' tread and flange contours.
During these tests the car was equipped with ball-bearing center
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR
plates. Each truck is provided with two Westinghouse 101-D, 500-
volt, direct current motors, which have a commercial rating of 50
horsepower each. The motors are mounted on the axles and geared
to them in the ratio of 22 to 62. They are controlled by the Westing-
house unit switch system of multiple control.
An especially designed recording apparatus within the car offers
a means for measuring and recording the current consumed, the volt-
age, speed, time, distance traversed, location on the road, and brake
cylinder pressure. Continuous graphical records of these data are
drawn upon a chart which is made to travel at a rate proportional
either to time or to the distance traveled by the car. A more complete
description of the car and of this recording apparatus appears in
Bulletin 74 of the University of Illinois Engineering Experiment Sta-
tion. In addition to the data above enumerated, there were recorded
for each run the average wind velocity and direction, air temperature,
rail condition, and the gross' car weight.
5. The Track. — The tests were made on the lines of the Illinois
Traction System between Danville, Urbana, Champaign, Decatur, and
Springfield. The oldest/ portions of this track were laid in 1903, the
latest in 1907. Judged by the standards which prevail on interurban
electric roads built for moderate speed, the track was well constructed
and well maintained. On both the curves and the tangents used in
the tests, the track was laid with 70-pound A. S. C. E. section rails
carried on hard-wood ties spaced about 24 inches between centers.
The ballast was either gravel or cinders.
The curves chosen were seven in number varying in curvature
from 2 to 141/2 degrees, as great a range in curvature as was presented
by the track available for test purposes. The gauge on all but the 8-
degree and the 14%-degree curves was 4 feet 8% inches, while on
these two curves it was 4 feet 9 inches. A summary of the facts relat-
ing to the seven curves is given in Table 1. All the track used for
TABLE 1
DATA RELATING TO THE SEVEN CURVES
Average
Curvature
Length of
Track
Section
Superelevation
Grade
Weight
of Rail
Average Maximum Minimum
Difference
in Elevation
Degrees
Feet
Inches
Inches
Inches
Feet
Lb. per Yd.
2°-0"
2°-50'
3°-40'
5°-0'
6°-30'
8°-0'
14°-30'
500
1737
1125
714
365
176
276
0.7
3.0
1.9
2.8
4.5
5.3
5.9
1.2
4.1
3.3
3.8
5.4
5.5
6.9
0.0
1.3
0.2
0.4
2.2
5.0
5.0
1.47
8.52
4.81
0.15
3.22
0.65
0.17
70
70
70
70
70
70
70
10
ILLINOIS ENGINEERING EXPERIMENT STATION
the tests was surveyed especially for the test purposes, and the results
of these surveys are presented in Appendix I, together with further
details.
IV. TEST CONDITIONS AND TEST METHODS
6. Test Conditions. — The tests were all made in moderate
weather. The lowest air temperature recorded during any test was
15 degrees F., and the lowest average temperature throughout the
duration of any test was 25 degrees. The corresponding highest tem-
peratures were 70 degrees and 65 degrees, respectively. With five ex-
ceptions the tests were made on dry rails. The highest average
velocity of the wind prevailing during1 any of the tests was 18 miles
per hour, whereas the maximum component of this velocity parallel
TABLE 2
A SUMMARY OF TEST CONDITIONS ON THE CURVES AND ON THEIR
CORRESPONDING TANGENTS
1
2
3
4
5
6
7
Curve
or
Tangent
Test
Number
Degree
of
Curve
Weight of
Car and Load
Approx.
Average
Air Temp.
Rail
Condition
Average
Wind
Velocity
Pounds
Deg. P.
M.P.H.
117-118
2«-0'
56200
25
Wet
12.0
123-124
2°-0'
56750
30
Dry
4.0
117-118
56200
25
Wet
12.0
123-124
56750
30
Dry
4.0
119-120
2°-50'
56750
45
Dry
3.5
121-122
2°-50'
56750
30
Dry
3.0
119-120
56750
45
Dry
3.5
121-122
56750
30
Dry
3.0
125-126
3°-40'
57350
35
Dry
15.0
Curve
127-128
3°-40'
57500
25
Wet
0.0
129-130
3°-40'
57350
65
Dry
15.0
125-126
57350
35
Dry
15.0
127-128
57500
25
Wet
0.0
Tangent R
129-130
57350
65
Dry
15.0
141-142
57800
40
Dry
3.8
153-154
57900
60
Dry
0.0
125-126
5°-0'
57350
35
Dry
15.0
Curve
127-128
5°-0'
57500
25
Wet
0.0
129-130
5°-0'
57350
65
Dry
15.0
Tangent R
*
Curve
133-134
6°-30'
57300
35
Wet
7.5
109-110
56950
55
Wet
18.0
Tangent D
111-112
56350
55
Wet
18.0
113-114
56200
55
Dry
10.0
141-142
8°-0'
57800
40
Dry
3.8
153-154
8«-0'
57900
60
Dry
0.0
Tangent R
*
141-142
14°-30'
57800
40
Dry
3.8
153-154
14°-30'
57900
60
Dry
0.0
Tangent R
*
* Same tangent as for 3°-40' Curve
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR 11
to the tangent track or to a chord connecting the ends of the curve
was 15 miles per hour. The wind velocity and direction were obtained
by means of a portable wind vane and an anemometer set up beside
the test track. A summary of the conditions for each test is given
in Table 2.
7. The Selection of the Track. — The primary consideration in
the selection of the curves was to have them include as great a variety
and range in degree of curvature as the circumstances would permit.
When available, those curves were chosen which had at either end a
long and comparatively level stretch of straight track, in order1 that
the resistance on the curve and on the tangent might be measured
simultaneously and, therefore, under like conditions of wind and
weather. In three out of the seven cases, however, the straight track
adjacent to the curve was, by reason of its construction or mainte-
nance, or by virtue of the operating conditions which there prevailed,
unsuitable for the purposes of the tests, and in these instances the
tangent track was chosen elsewhere. In such cases the determination
of tangent resistance was made as far as possible under conditions
similar to those which obtained during the tests on the related curve.
The curves chosen were fairly regular in curvature, and all the track
on both the curves and the tangent sections was well ballasted.
8. General Methods. — By means of the data which were recorded
during each run and which have been enumerated in Chapter III, it
is possible to calculate the gross resistance offered to the motion of
the car over a given track section. This gross resistance is composed
of the resistance due to grade, that due to acceleration, that due to
wind,* the net resistance on level straight track at uniform speed, and,
on the curved track, the resistance due to curvature. The purposes
of the tests require the elimination of the first three of these five
elements of gross resistance. The grade and acceleration resistances
may be easily eliminated by calculation, but the wind resistance is
neither controllable nor to be eliminated by calculation from the data
at hand. The elimination of wind resistance may, however, be accom-
plished by the method of making the tests, and with this end in view
the following method of test was used.
Over each track section the car was run in one direction at a
predetermined speed which was maintained as nearly uniform as pos-
sible. It was then immediately run over the same section at the same
speed, but in the reverse direction. Where curved and tangent track
* Throughout the bulletin wind resistance is distinguished from the resistance due to
still air, the latter being an inseparable part of inherent or net resistance.
12 ILLINOIS ENGINEERING EXPERIMENT STATION
were adjacent they were both included in each of these runs. This
process was repeated at various speeds until enough data had been
accumulated to define for this track section the relation between resis-
tance and speed up to the maximum speed of operation. The whole
group of these pairs of runs constitutes what is designated in the
report as a test.
The wind in one case opposes and in the other helps the motion of
the car, and each pair of such runs results, when grade and accelera-
tion resistance have been eliminated, in two values of resistance ; one
value equal to net resistance* plus such resistance as was offered by the
wind, the other equal to net resistance minus the resistance offered
by the wind. In runs in which the direction of the wind was parallel
to* the direction of motion of the car, a properly determined mean be-
tween these two values is the net resistance itself with the influence
of wind entirely eliminated. In runs in which the direction of the
wind made an angle with the direction of motion of the car, only that
portion of wind resistance due to the component of wind velocity
parallel to the track would disappear from the mean value of resis-
tance, and there would remain embodied in this meant a certain resis-
tance due to the increased wheel-flange friction caused by that com-
ponent of wind velocity which is normal to the direction of motion of
the car. All the resistance curves resulting directly from the tests
represent the mean between paired values determined in the way just
described. The curves themselves, therefore, define values of resistance
in which there remains only that effect of the wind produced by its
velocity component normal to the track ; that is, they are in error by
only a slight excess in flange friction. Under the low wind velocities
which prevailed this error is small, and doubtless much less than the
casual variations which occur in inherent resistance itself. These con-
clusions apply to the immediate results of the tests ; that is, to the re-
sistance-speed curves shown in Figs. 3 to 13, inclusive. For reasons
stated in the next paragraph the error referred to does not, however,
appear in the final results.
The simultaneous operation of the car over the curve and its
adjacent tangent ensures that the resistances on the curve and on the
tangent were obtained under practically identical wind conditions.
Whatever error or excess in mean resistance arises from the normal
component of wind velocity is, consequently, likewise identical on the
*As used in this connection the term net resistance is assumed to include on the curves
the resistance due to curvature.
tThe method of determining this mean is explained in Appendix II.
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR 13
curve and on the tangent. Since, however, the final result sought,
the resistance due to curvature, is the difference between the total
resistance on the curve and the resistance on the tangent, this error,
by the process of subtraction, disappears from the final results of
the tests. In those cases in which tangent resistance had to be meas-
ured on track not adjacent to the corresponding curve, the wind condi-
tions were nearly the same as during tests on the curve, and the same
conclusion, therefore, holds in these instances also.
From the data recorded in the test car the gross resistance was
first determined for each run over each track section. This was then
corrected for acceleration by means of data provided by the car
records, and next for grade resistance by reference to the track profiles.
The methods of making these calculations are stated in Appendix II,
together with further details concerning the car records and the test
methods.
V. THE IMMEDIATE EESULTS OF THE TESTS
The calculations made for each run result, for the track section
under consideration, in a value of car resistance at a particular speed.
For all the runs these resistance values, together with the correspond-
ing speeds, are set forth in the tables given in Appendix III. Using
these values as coordinates, the points shown in Figs. 3 to 13 have
been plotted; each point defines the resistance-speed relation during
one run, and the whole group of points in each figure characterizes
this relation for a particular track section. By a method which is
explained in Appendix II, a line has been drawn among the points
of each of these figures which represents the mean resistance discussed
in Chapter IV, and which in each case has been accepted as defining
the relation existing between resistance and speed for the track section
in question. Figs. 3 to 13, inclusive, constitute the immediate results
of all the tests.
The points indicated by circles in these figures pertain to runs in
which the wind opposed the motion of the car, while those represented
as black dots pertain to runs in which the wind helped the car motion.
The few cases in which there was no wind are represented by circles
half filled in. Under the test procedure previously outlined, there
should appear in each figure equal numbers of circles and dots. This
condition, however, is not exactly met in any of these figures, because
during the process of calculation a few points were rejected on
account of discrepancies or inadequacy in the record. In general,
however, the balance implied by the test procedure is substantially
realized.
14
ILLINOIS ENGINEERING EXPERIMENT STATION
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SPEED— MILES PER HOUR
FIG. 3. THE RELATION OF RESISTANCE TO SPEED ON THE 2°-0' CURVE
30
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SPEED— MILES PER HOUR
FIG. 4. THE RELATION OF RESISTANCE TO SPEED ON TANGENT W, WHICH PERTAINS
TO THE 2°-0' CURVE
There is considerable variation among the points in these figures
and also a considerable variation from the mean defined by the curves.
Some of this is due to the influence of wind, but even among the points
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR 15
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FIG. 5. THE EELATION OP EESISTANCE TO SPEED ON THE 2°-50' CURVE
30
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SPEED— MILES PER HOUR
FIG. 6. THE RELATION OF RESISTANCE TO SPEED ON TANGENT S, WHICH PERTAINS
TO THE 2°-50' CURVE
16
ILLINOIS ENGINEERING EXPERIMENT STATION
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FIG. 7. THE RELATION OF RESISTANCE TO SPEED ON THE 3°-40' CURVE
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FIG. 8. THE RELATION OF RESISTANCE TO SPEED ON TANGENT R. WHICH PERTAINS
TO THE 3°-40', THE 5°-0', THE 8°-0', AND THE 14°-30' CURVES
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR 17
relating to like, wind conditions there is similar disagreement. Part
of this variation may be due to accumulated errors in instruments or
in the calculations; but, since every precaution was taken to avoid
such errors, they are undoubtedly rare and .small in amount. The
reasons for the differences referred to must be sought chiefly in the
casual changes which occur in such elements of inherent resistance
as flange friction, journal friction, and gear friction, and perhaps also
in instantaneous changes in wind velocity and direction. The discor-
dance shown is not greater than that usually encountered in measure-
ments of car or train resistance.
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SPEED— MILES PER HOUR
FIG. 9. THE EELATION OF EESISTANCE TO SPEED ON THE 5°-0' CURVE
All the figures show a continuous increase of resistance with speed,
except Fig. 13, applying to the 14°-30' curve. In this case the
resistance decreases until a speed of about 12!/2 miles per hour is
reached and then increases as the speed is increased beyond this point.
This peculiarity, which showed itself during the earliest runs on this
curve, led to repetitions of the tests, but always with the same result,
and Fig. 13 must be accepted as representing the facts in the case.
The superelevation on this curve is 5.9* inches, and the component of
car weight parallel to the plane of the rails amounts to about 5,800
pounds. It was assumed that perhaps this component, up to the
18
ILLINOIS ENGINEERING EXPERIMENT STATION
14
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FIG. 10. THF RELATION OF RESISTANCE TO SPEED ON THE 6°-30' CURVE
30
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SPEED — MILES PEE HOTTE
FIG. 11. THE RELATION OF RESISTANCE TO SPEED ON TANGENT D, WHICH PERTAINS
TO THE 6°-30' CURVE
RESISTANCE ON CURVES OP A TWENTY-EIGHT TON ELECTRIC CAR 19
speed of minimum resistance, had produced an excessive flange fric-
tion on the inner rail and had bound the trucks by keeping the inner
side bearings in continuous contact. Since this component is opposed
by the centrifugal force developed by the car in rounding the curve,
these effects should continuously diminish as the centrifugal force
increases up to the speed where this component of car weight equals
the centrifugal force. Here the point of minimum resistance would
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SPEED — MILES PEE HOUR
FIG. 12. THE KELATION OF EESISTANCE TO SPEED ON THE 8°-0' CUEVE
be expected to occur. Calculations for this case, however, show this
speed to be at 16 instead of at 12% miles per hour. This discrepancy
is not in itself enough to discredit the assumption ; but investigation
of the other curves shows that this speed, at which the centrifugal
force and the weight component are in balance, occurs at from 23 to
26 miles per hour, and, if the assumption were valid, similar minimum
points should occur at these speeds in the resistance curves for these
cases. No such minimum points occur, however, in any of the other
figures, and the explanation on these grounds must consequently be
abandoned. The condition presented in Fig. 13 is accepted as unex-
plained by the information at hand.
From the results shown in Figs. 3 to 13, grade and acceleration
resistance have been eliminated, and, as previously explained, the
effect of the component of wind velocity parallel to the track has also
20
ILLINOIS ENGINEERING EXPERIMENT STATION
been eliminated; the influence of the normal component of wind
velocity, on the other hand, is still embodied in these results. The
resistance defined by the line drawn in Fig. 3, for example, which
relates to the 2-degree curve, consequently comprises net resistance on
level track at uniform speed, resistance due to the component of wind
velocity normal to the track, and the resistance due to curvature.
The resistance defined by the line in Fig. 4, which relates to the tan-
SPEED — MILES PER HOUR
FIG. 13. THE EELATION OF EESISTANCE TO SPEED ON THE 14°-30' CURVE
gent adjoining the 2-degree curve, comprises net resistance on level
track at uniform speed and the resistance due to the normal component
of wind velocity. The ordinates of the curves in these two correspond-
ing figures, therefore, differ only by an amount equal to the resistance
due to curvature on the 2-degree curve. Similar statements apply to
the curves in Figs. 5 to 13.
In the further consideration of Figs. 3 to 13 it will be convenient
to keep in mind their relationship. The 2°-0', 2°-50', 3°-40', and
6°-30' curves (Figs. 3, 5, 7, 10) have each their own tangent (Figs. 4,
6, 8, 11), the diagram for which immediately follows the diagram for
the corresponding curve. The 5°-0', 8°-0', and 14°-30' curves (Figs.
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR 21
9, 12, 13) have all the same tangent as the 3°-40' curve. The relation
between these figures is as follows :
Fig. 3, the 2°-0' curve, is used with Fig. 4, Tangent W.
Fig. 5, the 2°-50' curve, is used with Fig. 6, Tangent S.
Fig. 7, the 3°-40/ curve, is used with Fig. 8, Tangent R.
Fig. 9, the 5°-0' curve, is used with Fig. 8, Tangent R.
Fig. 10, the 6°-30' curve, is used with Fig. 11, Tangent D.
Fig. 12, the 8°-0' curve, is used with Fig. 8, Tangent R.
Fig. 13, the 14°-30' curve, is used with Fig. 8, Tangent R.
VI. THE FINAL RESULTS OF THE TESTS
9. TJie Resistance Due to Curvature. — The resistance-speed
curves of Figs. 3 to 13, properly paired, are all brought together in
Fig. 14 in which seven pairs of lines appear, one for each of the
seven curves. The first pair of lines in Fig. 14 relates to the 2-degree
curve, the upper line marked C shows the relation between resis-
tance and speed on the curve, while the lower line marked T shows
this relation on the adjacent tangent. These lines are reproduced
from Figs. 3 and 4, respectively. Fig. 14 presents also six additional
pairs of curves similarly marked pertaining to the six remaining
curves, and all reproduced from Figs. 5 to 13.
As has been stated in Chapter V the difference between the ordi-
nates of these pairs of lines at any speed is the value of curve resis-
tance at that speed for the curve in question. For example, for the
2-degree curve (see Fig, 14) the resistance on the curve at 20 miles
per hour is 14.0 pounds per ton, and the resistance on the tangent
is 11.3 pounds per ton. The difference between these values, 2.7
pounds per ton, is the curve resistance at 20 miles per hour on the
2-degree curve. At speeds varying from 10 to 40 miles per hour the
values of resistance on the curve, resistance on the tangent, and curve
resistance have been thus determined for each of the seven curves
and set forth in Table 3. This table summarizes, therefore, the direct
results of the tests as presented in Figs. 3 to 14, inclusive, and it
presents also the derived values of curve resistance whose determina-
tion was the immediate purpose of the tests. The values of curve
resistance given in the table are accepted as the average values at the
various speeds. As has been previously explained these values are
nearly, if not quite, freed from any effect of wind.
10. TJie Relation of Curve Resistance to Curvature. — For each
of the speeds in Table 3 there appears for each of the seven curves a
22
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 3
VALUES OF EESISTANCE ON THE CURVE, RESISTANCE ON THE TANGENT, AND RESIS-
TANCE DUE TO CURVATURE FOR EACH OF THE SEVEN CURVES AND AT VARIOUS
SPEEDS. THESE VALUES ARE DERIVED DIRECTLY FROM FIGURES 3 TO 13
INCLUSIVE. THEY ARE EXPRESSED IN POUNDS PER TON
Curve
Speed— M.PH.
10 | 15 | 20 I 25 | 30 | ,35 | 40
2<>-0'
7.50
10.78
14.00
17.45
21.00
24.70
28.70
Res. on Curve
6.95
9.00
11.30
13.93
16.88
20.25
24.15
" " Tang.
0.55
1.78
2.70
3.52
4.12
4.45
4.55
Curve Res.
20-50'
12.20
13.40
15.05
17.30
20.00
23.25
27.00
Res. on Curve
6.95
8.55
1044
12.75
15.30
18.21
21.50
" " Tang.
5.25
4.85
4.61
4.55
4.70
5.04
5.50
Curve Res.
30-40'
8.00
10.50
13.25
16.40
20.50
26.20
33.00
Res. on Curve
5.80
8.02
10.60
13.45
16.70
20.47
24.50
" " Tang.
2.20
2.48
2.65
2.95
3.80
5.73
8.50
Curve Res.
5°-0'
12.25
15.00
18.33
22.30
26.83
31.62
36.70
Res. on Curve
5.80
8.02
10.60
13.45
16.70
20.47
24.50
" " Tang.
6.45
6.98
7.78
8.85
10.13
11.15
12.20
Curve Res.
6°-30'
10.60
14.65
18.75
23.00
27.50
32.05
36.55
Res. on Curve
6.87
8.62
10.55
12.65
15.00
17.80
20.95
" " Tang.
3.73
6.03
8.20
10.35
12.50
14.25
15.60
Curve Res
8°-0'
10.80
14.05
17.55
21.60
26.25
31.75
Res. on Curve
5.80
8.02
10.60
13.45
16.70
20.47
" " Tang.
5.00
6.03
6.95
8.15
9.55
11.28
Curve Res.
140-30'
19.70
24.60
34.45
Res. on Curve
8.02
10.60
13.45
" " Tang.
11.68
14.00
21.00
Curve Res.
value of curve resistance. At 15 miles per hour, for example, there
are given in the third column of the table seven values of curve resis-
tance : 1.78 pounds per ton on the 2-degree curve, 4.85 pounds per ton
on the 2°-50' curve, and so on. These values are plotted in the second
diagram of Fig. 15 as seven points which show the relations existing
during the tests between curve resistance and curvature at the speed
of 15 miles per hour. Using the remaining values from Table 3, similar
groups of points have been plotted in Fig. 15 which show this relation
at the other speeds.
An inspection of the points in Fig. 15 discloses at all speeds a
fairly regular relationship between curve resistance and curvature.
With perhaps the exception of the first, pertaining to 10 miles per
hour, these diagrams show for each speed an increase in curve resis-
tance which is approximately directly proportional to the increase in
curvature. There have been drawn among the points in these dia-
grams straight lines which have been accepted as defining the average
of the relations between curve resistance and curvature represented
by the points derived from the individual tests. For obvious reasons
these lines are all made to pass through the origin of coordinates.
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR
23
At speeds up to 25 miles per hour the points in Fig. 15 which
relate to the 2°-50' and to the 5-degree curves lie above the mean values
represented by the lines, while at higher speeds they correspond closely
with the mean. At speeds up to 25 miles per hour the points for the
3°-40' and for the 8-degree curves correspond well with the mean, but
2*-0
2—50'
ti#mt
6°-30"
14°— 30'
FIG. 14.
SPEED — MILES PEE HOUR
THE EELATION OF EESISTANCB TO SPEED ON ALL THE CURVES AND ON
THEIR CORRESPONDING TANGENTS
lie below it at higher speeds. The test data offer a probable explanation
of these variations only in the case of the 5-degree curve, whose poorer
construction might be assumed partially to account for its high resis-
tance. In the other cases, however, no such explanation is available.
In drawing the lines in Fig. 15 due consideration was given to the
relative weight of the points there plotted; that is, to the number of
tests represented by the various points.
24
ILLINOIS ENGINEERING EXPERIMENT STATION
The lines drawn in Fig. 15 are brought together and reproduced
to a larger scale in Fig. 16, in which, as before, each line defines for
a particular speed the average or general relation between curve resis-
tance and curvature. The whole group defines this relation for the
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TRACK CURVATURE— DEGREES
FIG. 15. THE RELATION BETWEEN CURVE RESISTANCE AND CURVATURE AT
VARIOUS SPEEDS
entire series of tests. For each speed curve resistance increases in
direct proportion with the curvature. At 15 miles per hour, for
example, the curve resistance expressed in pounds per ton is 4.35,
8.70, and 13.05, for curves of 5, 10, and 15 degrees, respectively. This
implies at this speed a constant curve resistance of 0.87 pounds, when
expressed in pounds per ton per degree. The direct proportionality
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR 25
between curve resistance and curvature exhibited in Fig. 16 is in
accord with the results of previous experiments and with current
practice.
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TRACK CURVATURE— DEGREES
FIGm is. — THE EELATION BETWEEN CURVE EESISTANCE AND CURVATURE, AT VARIOUS
SPEEDS. THE LINES SHOWN ARE ASSEMBLED FROM FIG. 15
11. The Relation of Curve Resistance to Speed. — The lines of
Fig. 16 present values of curve resistance for seven speeds which cover
the speed range of the experiments. The figure offers, therefore, a
means of determining the general relation between curve resistance
and speed. If in Fig. 16 the ordinates of the seven lines are measured
at a curvature of 5 degrees, seven values of curve resistance are
obtained: 2.90, 4.35, 5.80, 7.25, 8.70, 10.15, and 11.60 pounds per ton,
which correspond respectively to speeds of 10, 15, 20, 25, 30, 35, and
40 miles per hour. These corresponding values of resistance and speed
are plotted in Fig. 17 as the seven points there shown for a curvature
of 5 degrees. These points are found to lie on a straight line as shown
26
ILLINOIS ENGINEERING EXPERIMENT STATION
in the figure. The two other straight lines corresponding to 10
degrees and 15 degrees curvature were obtained by a like process.
That the lines connecting the points in Fig. 17 are straight is due,
of course, to the relation which exists between the lines in Figs. 15
and 16 ; that is, to their relative slope. It is proper to explain that
the lines originally drawn in Figs. 15 and 16 did not precisely satisfy
this condition in the derived lines of Fig. 17. They did so so nearly,
however, that, for the sake of the resulting simplicity, it seemed justi-
fiable to modify them, and the slopes of a few of the lines in Fig. 15
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SPEED— MILES PEE HOUR
FIG. 17. — THE EELATION BETWEEN CURVE EESISTANCE AND SPEED FOR CURVES OF
VARIOUS CURVATURES
were adjusted so that the lines connecting the derived points in Fig.
17 would be straight. An inspection of Fig. 15 shows, it is believed,
that this adjustment has done no violence to the experimental data.
It has, on the other hand, resulted in a simplicity of the relations
shown in Fig. 17 and of the formula given beyond, which seems amply
to warrant it.
The lines drawn in Fig. 17 apply to curvatures of 5, 10, and 15
degrees, and by the process above explained similar lines for other
rates of curvature might have been included. Fig. 17 is derived
directly from Fig. 16 and, like it, presents the average results of the
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR 27
whole research. From Fig. 17 it is obvious that for constant curva-
ture, curve resistance was directly proportional to speed; that is, on
any given curve the resistance due to curvature varied in these experi-
ments directly with the speed. On the 5-degree curve, for example,
its average value at 10 miles per hour was 2.90 pounds per ton, and
at 30 miles per hour 8.70 pounds per ton, three times as much. In
previous experiments there has been occasional evidence that curve
resistance might be greater at high than at low speeds, although in
some discussions of the subject the contrary is held to be true. Neither
opinion has had definite or adequate support, and there has hitherto
been no conclusive experimental evidence of any definite relation be-
SPEED— MXLES PER HOUR
FIG. 18. THE CONCURRENT RELATIONS BETWEEN CURVE RESISTANCE, SPEED,
AND CURVATURE
tween curve resistance and speed. In practice the influence of speed
has been generally ignored.
12. The Concurrent Relations of Curve Resistance, Curvature,
and Speed. — For the car used in the tests curve resistance varies
directly with both curvature and speed, the rate of variation in each
case being as shown in Figs. 16 and 17. These two figures have been
combined in the diagram of Fig. 18, which exhibits the concurrent
relations of the three variables. These relations are also defined by
the equation :
Rc = 0.058 8C (1)
in which Rc is the curve resistance on level track at uniform speed
expressed in pounds per ton, S is the speed in miles per hour, and C
is the degree of curve. This formula represents exactly the mean
28
ILLINOIS ENGINEERING EXPERIMENT STATION
relations between curve resistance, speed, and curvature, which are
denned by the lines drawn in Figs. 15, 16, and 17, and it embodies,
consequently, the generalized results of all the tests.
By means of Formula 1 there have been calculated the values
of curve resistance which are presented in Table 4. The values are
given for curves varying from 1 to 15 degrees and for speeds ranging
from 10 to 40 miles per hour, corresponding approximately to the
range in curvature and in speed during the tests. Inspection of Table
4 shows curve resistance to vary from 0.58 pounds per ton on a 1-
TABLE 4
VALUES OF CURVE RESISTANCE AT VARIOUS BATES OF CURVATURE AND AT VARIOUS
SPEEDS. THESE VALUES ARE DERIVED FROM FORMULA 1 AND
REPRESENT THE FINAL RESULTS OF THE TESTS
Curvature
Degrees
Curve Resistance — Pounds Per Ton
Curvature
Degrees
Column Headings Indicate Speed in Miles Per Hour
10 | 15
20
25
30
35
40
1
0.58
0.87
1.16
1.45
1.74
2.03
2.32
1
2
1.16
1.74
2.32
2.90
3.48
4.06
4.64
2
3
1.74
2.61
3.48
4.35
5.22
6.09
6.96
3
4
2.32
3.48
4.64
5.80
6.96
8.12
9.28
4
5
2.90
4.35
5.80
7.25
8.70
10.15
11.60
5
6
3.48
5.22
6.96
8.70
10.44
12.18
13.92
6
7
4.06
6.09
8.12
10.15
12.18
14.21
16.24
7
8
4.64
6.96
9.28
11.60
13.92
16.24
18.56
8
9
5.22
7.83
10.44
13.05
15.66
18.27
20.88
9
10
5.80
8.70
11.60
14.50
17.40
20.30
23.20
10
11
6.38
9.57
12.76
15.95
19.14
22.33
25.52
11
12
6.96
10.44
13.92
17.40
20.88
24.36
27.84
12
13
7.54
11.31
15.08
18.85
22.62
26.39
30.16
13
14
8.12
12.18
16.24
20.30
24.36
28.42
32.48
14
15
8.70
13.05
17.40
21.75
26.10
30.45
34.80
15
degree curve at 10 miles per hour to 34.8 pounds per ton on a 15-
degree curve at 40 miles per hour. Expressed in pounds per ton per
degree of curve, curve resistance varies from 0.58 at 10 miles per hour
to 2.32 at 40 miles per hour. Although for the sake of exact corre-
spondence between the table and Formula 1 and Figs. 16 and 17 the
tabular values are given to the second decimal place, it should not be
assumed that the last figures are significant.
13. Conclusion. — The final results of the tests are summarized
in Formula 1 and in Table 4, which present mean or average values
of curve resistance at various rates of curvature and at various speeds.
They apply to the particular car tested under conditions of weather
and track which have been fully defined. They are useful for predict-
ing the curve resistance to be expected from similar cars running
under like conditions, but if they are so used these conditions should
be borne in mind. It is probable that the formula applies to cars
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR 29
whose weight varies considerably from the weight of the test car;
but if the truck wheel base is materially different, the formula should
be used with caution. Its use should probably not be extended to
speeds much in excess of 40 miles per hour. How far the formula is
applicable beyond a curvature of 15 degrees cannot be stated, but
it is significant that it represents the actual test results on the 14%-
degree curve with considerably greater accuracy than on some of the
curves of lower curvature. Whether the results apply closely to other
than self-propelled cars is open to question.
Formula 1 and Table 4, as well as Figs. 16 and 17, are general-
izations which define only average values of curve resistance. They
are derived by processes which preclude their precise agreement even
with all the test values themselves, as is disclosed by an examination
of Fig. 15. Consequently, in an individual case their use in pre-
dicting curve resistance cannot reasonably be expected to give results
which correspond with the actual resistance any more exactly than
do the averages upon which these generalizations rest correspond with
the results of the individual tests; no closer correspondence, that is,
should be expected than exists between the mean curves and the points
of Figs. 3 to 13 which are fundamental to the whole process. Such
limitations are common to all generalizations of train or car resistance
and do not seriously impair their usefulness for the purposes for which
they are generally employed.
Bulletin 74 of the Enginering Experiment Station gives the re-
sults of experiments in which the resistance of this car was determined
when running on level tangent track at uniform speed. This resis-
tance is given by the formula :
Rt = 4 + 0.222S + 0.00181— S* (2)
By combining this equation with Formula 1 above, we obtain for this
car the following formula which gives its total resistance when run-
ning on a level curve at uniform speed.
R = Rt + Rc = 4 + 0.222S + 0.00181 ^S2 + 0.058 SC (3)
In Formula 3, R is the total resistance expressed in pounds per ton,
8 the speed in miles per hour, C the curvature in degrees, A the
cross-sectional area of the car in square feet, and W its weight in
tons. If the car is on a grade and its speed changing, the usual cor-
rections for grade and acceleration must be applied to Formula 3.
30
ILLINOIS ENGINEERING EXPERIMENT STATION
APPENDIX I
THE TRACK
Information regarding the track has been given in Chapter III.
This appendix is intended to supplement Chapter III by the presenta-
tion of further details concerning the track on the curves.
The results of the track surveys are presented in Figs. 19 to 25,
inclusive, in which are given for each curve the profile on each rail,
elevations having been taken every 100 feet; the superelevation of
the outer rail, also at 100-foot intervals; and the degree of curva-
ture. For the 2°-0', 2°-50', 3°-40', and 5°-0' curves the curvature
was determined at 50-foot intervals by measuring mid-ordinates, for
the 6°-30' curve it was determined at 50-foot intervals by measuring
deflection angles, and for the 8°-0' and' 14°-30' curves by measuring
deflection angles at intervals of 25 feet. Each curve has been desig-
nated by the average of these values of curvature. Distances are
shown in the figures by means of stations which were 100 feet apart.
In the tables given in Appendix III the section limits are defined by
trolley line pole numbers. The location of each pole is indicated on
the alignment diagrams of Figs. 19 to 25 by means of a short dash
beside which is recorded its distance in feet from the preceding station.
For example, Pole 20, Fig. 19, is located 80 feet from Station 23.
<?
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FIG. 19. PROFILE AND ALIGNMENT DIAGRAM OF THE TRACK ON THE 2°-0' CURVE
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR
31
FIG. 20. PROFILE AND ALIGNMENT DIAGRAM OF THE TRACK ON THE 2°-50' CURVE
FIG. 21. PROFILE AND ALIGNMENT DIAGRAM OF THE TRACK ON THE 3°-40' CURVE
32
ILLINOIS ENGINEERING EXPERIMENT STATION
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FIG. 22. PROFILE AND ALIGNMENT DIAGRAM OF THE TRACK ON THE 5°-0' CURVE
FIG. 23. PROFILE AND ALIGNMENT DIAGRAM OF THE TRACK ON THE 6°-30' CURVE
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR 33
-
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2
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FIG. 25. PROFILE AND ALIGNMENT DIAGRAM OF THE TRACK ON THE 14°-30' CURVE
34 ILLINOIS ENGINEERING EXPERIMENT STATION
APPENDIX II
TEST METHODS AND METHODS OF CALCULATION
This appendix is intended to supplement what has been stated in
Chapter IV concerning the test methods and to present also certain
details concerning the methods used in calculating the values of resis-
tance and speed which constitute the immediate results of the tests.
Methods Used in Producing the Curves of Figs. 3 to 13. — As has
been previously explained, the points in Figs. 3 to 13 occur in pairs,
one point in each pair relating to a run in which the wind helped the
car, the other to a run in which the wind opposed the car. The curves
drawn in the figures define the mean of the values represented by these
points. If wind resistance varied directly with speed, an arithmetical
mean or average of the values represented by the points would define
a point on this curve. Since wind resistance varies, however, about
as the square of the speed, a mere arithmetical mean of these values
does not serve exactly to define the mean curve ; but this mean must
be established by another and somewhat more elaborate process. Such
a process has been set forth on page 34 of Bulletin 74 of the University
of Illinois Engineering Experiment Station. When the wind veloci-
ties are low, the difference between the curves defined by taking an
arithmetical mean and by this more exact process is negligible. Dur-
ing these tests the wind velocities were generally low, and the points
representing runs with and against the wind are generally closely
interwoven. For this reason the mean curves in Figs. 3 to 13 were all
produced by taking the arithmetical mean of the resistance values
represented by the points in the figures. Preliminary to drawing these
curves, the average coordinates of various groups of points in each
figure were determined, and these average coordinates were then plot-
ted as auxiliary points through which the curve was passed as nearly
as possible.
Methods of Calculation. — The data recorded during these tests are
enumerated in Chapter III. All the data which pertained directly to
car operation were graphically recorded upon the test car charts. A
portion of the chart obtained during Test 121 is reproduced as Fig.
26, upon which the section limits and certain explanatory lettering
have been added.
When the track sections were surveyed, markers were placed be-
side the track at the ends of the curves and tangents, and during a
test the positions of these numbered markers were recorded upon the
chart. In this way the chart made during a run over the test track
was divided into two or more sections as illustrated by Fig. 26. That
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR
35
Q
]
j
'
11
1
0
&•
DATUM L.I
CURRENT
]
TIME -5
1
3
r
VOLTAGE
DATUM L,
ELECTRIC
LOCATION
DISTANCE -
3
m
1
01
BRAKE CV
DATUM LIN
:
Z
PI
J
REC.O
IP
m
-o
0
-2
ni
RECOT
2
SPEE
J
1
s
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g
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0
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UNDER
tn
A
4
d
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D INTERVAL-S
0
N
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POLE 12
>T INTERVAL-S -
INTERVALS -^
3
n
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36 ILLINOIS ENGINEERING EXPERIMENT STATION
part of the chart lying between the poles numbered 12 and 29 was
produced during a run over a section of curved track, while that por-
tion lying between the poles numbered 4 and 12 was made during a
run over a section of tangent track. In making the calculations only
those chart sections were considered over which there were no brake
applications, no large variation of the current or voltage from the
average value, and no large difference in the speed of the car. It has
been found desirable to choose both track and chart sections so that
the energy consumed by grade and acceleration will be as small as
possible, and the errors in their calculation will have slight effect on
the accuracy of the values of average net car resistance. When the
variation in speed is large the energy required to produce accelera-
tion is alone frequently greater than that required to overcome all
other resistances combined. In all the tests reported in this bulletin
the variations in speed in passing the track sections have exceeded 2
miles per hour in only 11 per cent of the total number of resistance
determinations, and in only 3 cases out of 392 has this speed variation
exceded 5 miles per hour. The maximum variation over any section
was less than 10 miles per hour.
The result desired from each chart section is a value of average
net car resistance. These values are given in Column 18 of Tables 5
to 11 in Appendix III. Full explanations of the significance of the
various items in these tables and of the methods by which they were
derived are presented in Appendix II of Bulletin 74 of the Engineer-
ing Experiment Station.
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR 37
APPENDIX III
THE IMMEDIATE RESULTS OF THE TESTS
This appendix presents in tabular form the fundamental data,
some of the intermediate results, and the final values of car resistance
and speed for each of the curves. The corresponding data for tangents
D, W, S, and R, are given in Tables 9, 10, 11, and 12, respectively, of
Bulletin 74 of the Engineering Experiment Station. The items in
these tables have all been derived by the processes explained in Ap-
pendix II. The points in Fig. 3 to 13 were plotted by using as
coordinates the values of resistance and speed which appear in Col-
umns 18 and 19 of these tables.
38
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 5
THE IMMEDIATE EESULTS OF THE TESTS ON THE 2°-0/ CURVE, GIVING THE RESULTS
OP RESISTANCE AND SPEED USED IN PRODUCING FIG. 3
1 2
Section
Grade
Motor
Data
Wind
Limits
Rise or
Length
Time
•
Item
No.
Test
No.
Opposing
or
Trolley
Fall Over
Section
of
Track
to Run
Over
Number
in Use
Efficiency
of Motors
Helping
Line Pole
Section
Section
and
and
Numbers
+Up
Connection
Gears
— Down
*
O orH
Feet
Feet
Sec.
1
Per cent
1
124
H
16-21
—1.47
500
9.8
4M
73.1
2
123
O
21-16
+
14.8
48
73.0
3
123
O
21-16
+
27.6
70.0
4
124
H
16-21
10.5
4M
72.2
5
123
O
21-16
+
9.5
81.4
6
124
H
16-21
11.3
• >
77.6
7
124
H
16-21
— .
10.6
»»
69.8
8
123
0
21-16
+
14.2
48
71.5
9
124
H
16-21
14.6
67.1
10
117
H
21-16
+
12.7
"
77.9
11
124
H
16-21
27.6
"
64.7
12
123
0
21-16
+
28.6
»
66.5
13
124
H
16-21
16.1
»»
72.7
14
123
0
21-16
+
23.3
» »
68.4
15
124
H
16-21
27.6
"
63.8
16
118
O
16-21
.
10.5
4M
83.2
17
118
O
16-21
— .
19.1
48
76.7
18
117
H
21-16
+
9.9
4M
85.2
19
118
O
16-21
9.9
"
85.7
20
117
H
21-16
+
8.7
"
85.0
21
118
O
16-21
9.2
"
85.6
22
117
H
21-16
-f
8.2
• '
84.3
23
118
O
16-21
8.7
»»
84.4
24
117
H
21-16
+
8.6
' '
84.5
= Series-Multiple. M = Multiple.
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR
39
TABLE 5 (Continued)
THE IMMEDIATE EESULTS OF THE TESTS ON THE 2°-0/ CURVE, GIVING THE RESULTS
OF EESISTANCE AND SPEED USED IN PRODUCING FIG. 3
10 I
31
12
13 14
15
16
17
18
19
Speed
Energy Imparted to the Car
Net Car
Average
Item
At
At
Average
Average
By the
Resis-
Speed
No.
Entrance
Exit
Voltage
Current
By the
Change in
By the
tance
Over tho
to the
from the
Current
Kinetic
Grade
Section
Section
Section
Energy
M.P.H.
M.P.H.
Volts
Amp.
Ft. Lb.
Ft. Lb.
Ft. Lb.
Lb. per
Ton
M.P.H.
1
33.84
33.84
358
103.0
194820
0
+ 83420
19.61
34.79
2
23.40
22.50
270
57.6
247840
+ 84690
17.56
23.03
3
10.80
11.34
142
55.7
225410
—24510
__ i»
8.28
12.35
4
32.94
32.76
354
100.0
197920
+ 24240
+ ;;
21.54
32.47
5
33.66
33.66
445
134.8
342130
0
18.23
35.88
6
29.70
30.96
378
119.6
292370
—156690
~+ ||
15.44
30.17
7
32.94
32.40
342
94.3
175980
+ 72330
23.38
32.16
8
23.58
22.86
268
53.9
216320
+ 68550
— "
14.20
24.01
9
23.04
23.04
229
46.8
154830
0
+ "
16.79
23.35
10
27.00
26.10
592
53.0
228960
+ 97010
— 82610
17.32
26.84
11
11.16
12.78
121
46.6
148550
—79510
+ 83420
10.75
12.35
12
11.34
11.34
126
49.4
174630
0
— "
6.43
11.92
13
19.98
20.70
245
57.6
243600
— 60040
+ ;;
18.82
21.17
14
14.40
14.22
157
51.1
188650
+ 10560
8.16
14.64
15
10.80
12.42
122
45.4
143890
— 77110
+ "
10.59
12.35
16
32.04
33.48
470
148.4
449390
— 191530
+ 82610
24.23
32.47
17
18.18
19.08
405
55.1
241150
— 68070
+ ;;
18.20
17.85
18
35.82
36.18
541
168.4
566700
— 52620
30.71
34.43
19
34.02
36.00
552
182.8
631350
— 281440
+ ;;
30.78
34.43
20
40.14
40.68
592
157.4
508190
— 88590
23.99
39.18
21
36.36
38.34
573
168.5
560760
— 300250
+ ||
24.42
37.05
22
42.48
42.12
586
143.6
429000
+ 61830
29.05
41.57
23
39.60
40.32
562
150.8
458950
—116810
+ ||
30.23
39.18
24
39.96
40.14
565
151.4
458440
—29270
24.67
39.64
40
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 6
THE IMMEDIATE EESULTS OF THE TESTS ON THE 2°-50' CURVE, GIVING THE EESULTS
OP EESISTANCE AND SPEED USED IN PRODUCING FIG. 5
1 •••! § I f • 1 4 |5|6|7|8|9
Section
Grade
Motor
Data
Wind
Limits
Rise or
Length
Time
Item
Test
Opposing
Fall Over
of
to Run
Number
Efficiency
No.
No.
or
Trolley
Section
Track
Over
in Use
of Motors
Helping
Line Pole
-,
Section
Section
and
and
Numbers
+Up
Connection
Gears
— Down
*
O orH
Feet
Feet
Sec.
Per cent
1
119
H
29-12
— 8.52
1737
39.2
4M
77.4
2
120
O
12-29
+
38.1
4M
83.7
3
120
O
12-29
+
41.0
4M
78.4
4
120
0
12-29
+
46.0
4M
78.9
5
119
H
29-12
35.4
4M
67.8
6
120
0
12-29
+
42.6
4M
82.5
7
119
H
29-12
38.3
2M
77.6
8
120
O
12-29
+
49.4
2M
85.3
9
119
H
29-12
49.2
2M
78.2
10
120
O
12-29
+
54.5
2M
83.1
11
119
H
29-12
48.8
4 S
67.5
12
120
O
12-29
+
61.9
48
82.1
13
119
H
29-12
50.1
4 S
69.7
14
120
O
12-29
+
57.7
4S
82.0
15
119
H
29-12
47.7
4S
72.4
16
120
O
12-29
+
41.3
4M
80.3
17
120
0
12-29
+
46.0
2M
85.7
18
120
O
12-29
45.9
2M
85.5
19
119
H
29-12
-
46.0
4 S
71.2
20
120
O
12-29
+
59.2
48
80.7
21
121
O
29-12
51.3
48
62.8
22
122
H
12-29
+
57.2
4 S
77.9
23
121
0
29-12
52.5
48
61.6
24
122
H
12-29
+
64.3
4 S
76.8
25
121
0
29-12
35.3
4M
65.1
26
121
O
29-12
.
36.6
4M
72.0
27
122
H
12-29
+
61.2
4Sw
76.0
28
121
0
29-12
59.0
4Sw
55.6
29
121
O
29-12
— .
71.3
2M
73.4
30
121
0
29-12
— .
56.0
4 S
64.9
31
122
H
12-29
+
77.2
48
75.1
32
121
0
29-12
56.9
48
64.1
33
121
O
29-12
_
32.7
4M
77.7
34
122
H
12-29
+
34.4
4M
83.8
35
121
O
29-12
30.1
4M
73.8
36
122
H
12-29
+
78.2
48
75.4
37
121
0
29-12
83.9
C
—
38
121
O
29-12
—
106.5
c
—
= Series-Multiple. M = Multiple. Sw — Switching. C — Coasting.
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR
41
TABLE 6 (Continued)
THE IMMEDIATE EESULTS OF THE TESTS ON THE 2°-50' CURVE, GIVING THE EESULTS
OP EESISTANCE AND SPEED USED IN PRODUCING FIG. 5
10
11
12
13 14
15
16
17
18 19
Speed
Energy Imparted to the Car
Net Car
Average
Item
At
At
Average
Average
By the
Resis-
Speed
No.
Entrance
Exit
Voltage
Current
By the
Change in
By the
tance
Over the
to the
from the
Current
Kinetic
Grade
Section
Section
Section
Energy
M.P.H.
M.P.H.
Volts
Amp.
Ft. Lb.
Ft. Lb. | Ft. Lb.
Lb. per
Ton
M.P.H.
1
26.96
32.18
358
123.2
987020
— 632860
+ 483510
17.00
30.21
2
30.38
31.46
436
159.9
1639720
—136910
—
20.68
31.08
3
31.10
29.12
365
127.8
1105890
+ 244430
—
17.59
28.89
4
26.42
26.06
340
139.2
1266870
+ 38730
—
16.68
25.75
5
31.82
33.08
330
90.1
526250
— 167640
+
17.09
33.46
6
26.78
27.86
397
152.3
1567090
— 120970
—
19.53
27.80
7
31.10
31.10
380
59.5
495590
0
+
19.87
30.92
8
23.90
24.62
417
119.2
1544830
— 71620
20.08
23.97
9
22.46
25.88
325
69.3
639000
— 338910
+
15.90
24.07
10
22.46
21.02
355
101.5
1203440
+ 128350
17.21
21.73
11
23.54
25.52
425
41.7
430480
— 199130
+
14.50
24.27
12
19.58
19.76
488
67.8
1240200
— 14520
15.06
19.13
13
22.10
24.98
438
43.5
490600
—277960
+
14.13
23.64
14
21.92
21.38
516
65.9
1186400
+ 47930
15.24
20.53
15
23.72
26.06
472
46.1
554210
— 238790
+
16.22
24.83
16
30.02
29.12
378
138.9
1284060
+ 109110
18.46
28.68
17
24.98
26.24
458
121.1
1612430
— 132300
—
20.22
25.75
18
25.16
25.52
443
114.3
1465370
— 37400
—
19.16
25.80
' 19
23.54
26.60
482
44.5
518120
— 314530
+
13.94
25.75
20
21.38
19.76
488
62.7
1078150
+ 136630
14.84
20.01
21
22.10
22.10
196
42.4
394880
0
+
17.82
23.09
22
20.84
20.48
278
75.3
1375940
+ 30490
18.72
20.70
23
21.56
21.74
189
41.4
373260
— 15980
+
17.06
22.56
24
18.86
18.50
239
74.3
1293620
+ 27570
—
17.00
18.42
25
33.26
33.08
288
86.5
422170
+ 24480
+
18.87
33.55
26
31.64
32.54
327
104.3
662910
+ 118410
+
20.86
32.36
27
18,50
17.78
223
71.8
1098370
+ 53550
—
13.56
19.35
28
19.76
19.94
160
37.2
287900
+ 14650
+
15.36
20.07
29
14.90
17.06
203
61.3
480140
— 141520
+
16.68
16.61
30
19.58
20.84
200
44.6
478180
— 104400
+
17.39
21.15
31
15.08
15.62
200
69.5
1188680
— 33980
13.62
15.34
32
19.58
20.48
194
43.8
457010
— 73910
+
17.58
20.81
33
35.24
36.50
420
113.8
895690
—185300
+
24.22
36.22
34
34.34
32.72
479
155.7
1585580
+ 222710
26.88
34.43
35
38.30
38.66
407
98.9
659400
— 56800
+
22.04
39 35
36
12.74
14.18
203
71.1
1255410
— 79470
14.05
15.14
37
16.34
13.46
0
+ 175940
+
13.38
14.12
38
13.10
11.30
! ! 0 ' + 90040
+
11.64
11.12
42
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 7
THE IMMEDIATE RESULTS OF THE TESTS ON THE 3°-40' CURVE, GIVING THE RESULTS
OF RESISTANCE AND SPEED USED IN PRODUCING FIG. 7
2
8
9
Section
Grade
Motor
Data
Item
No.
Test
No.
Wind
Opposing
or
Limits
Trolley
Rise or
Fall Over
Section
Length
of
Track
Time
to Run
Over
Number
in Use
Efficiency
of Motors
Helping
Line Pole
Numbers
+UP
— Down
Section
Section
and
Connection
*
and
Gears
i
OorH
Feet
Feet
Sec.
Per cent
1
126
H
27-38
+ 4.81
1125
25.3
4M
78.0
2
125
0
38-27
__
24.1
» »
66.6
3
125
0
38-27
25.2
»»
71.0
4
126
H
27-38
+
28.2
• »
79.8
5
126
H
27-38
+
24.7
»»
83.5
6
126
H
27-38
+
23.8
»»
84.2
7
126
H
27-38
+
38.0
48
75.5
8
125
o
38-27
29.7
71.5
9
126
H
27-38
+
34.6
»»
75.7
10
128
27-38
+
36.2
4M
78.1
11
127
38-27
75.6
23.5
12
128
27-38
+
48.7
48
71.7
13
129
H
38-27
29.9
48.7
14
130
0
27-38
+
38.1
"
75.3
15
129
H
38-27
40.8
"
35.0
16
130
O
27-38
+
43.1
"
74.2
17
129
H
38-27
20.3
4M
63.3
18
130
0
27-38
+
23.9
"
82.3
19
129
H
38-27
21.1
"
26.7
20
130
0
27-38
+
24.7
' '
78.1
21
130
O
27-38
+
25.4
"
78.2
22
129
H
38-27
25.7
"
30.5
23
130
O
27-38
+
23.4
"
83.7
24
129
H
38-27
26.9
' '
64.2
25
130
O
27-38
+
23.7
' >
80.6
26
129
H
38-27
55.6
4S
53.3
*S= Series-Multiple. M=Multiple.
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR
43
TABLE 7 (Continued)
THE IMMEDIATE EESULTS OF THE TESTS ON THE 3°-40' CURVE, GIVING THE BESULTS
OP RESISTANCE AND SPEED USED IN PRODUCING FIG. 7
10 I
11
12 13 14
15
16
17
18 | 19
Sp<
>ed
Energy
Imparted to
the Car
Net Car
Average
Item
At
At
Average
Average
By the
Resis-
Speed
No.
Entrance
Exit
Voltage
Current
By the
Change in
By the
tance
Over the
to the
from the
Current
Kinetic
Grade
Section
Section
Section
Energy
M.P.H.
M.P.H.
Volts
Amp.
Ft. Lb.
Ft. Lb.
Ft. Lb.
Lb. per
M.P.H.
Ton
1
32.56
29.68
344
131.1
656380
+ 371050
—275850
23.30
30.32
2
33.64
32.20
275
90.7
295220
+ 196260
+ "
23.79
31.83
3
30.58
30.40
294
104.8
406550
+22720
+ ;;
21.86
30.44
4
28.42
26.62
340
147:0
829490
+ 205080
23.52
27.20
5
31.84
32.02
407
162.0
1002830
—23790
— "
21.80
31.05
6
32.56
32.56
449
166.9
1107550
0
— "
25.78
32.23
7
21.04
20.32
239
67.5
682800
+ 61640
— »»
14.52
20.19
8
25.18
26.44
262
54.0
443210
— 134640
+ ||
18.12
25.83
9
23.02
20.86
264
66.2
675120
+ 196200
18.46
22.17
10
20.28
20.46
280
152.4
889700
— 15220
— 276580
18.49
21.19
11
9.66
8.94
91.8
40.4
48610
+ 27790
+ ;;
10.91
10.15
12
17.94
16.68
173
58.4
520450
+ 90510
10.34
15.75
13
26.28
25.02
155
33.1
110180
+ 133800
+ 275850
16.12
25.65
14
20.52
20.52
236
66.9
668180
0
"
12.16
20.13
15
18.54
18.18
93.6
26.5
52240
+ 27360
+ ||
11.02
18.80
16
18.90
18.18
207
64.4
628790
+ 55260
12.65
17.80
17
39.24
37.62
304
81.8
235690
+257740
+ ||
23.85
37.79
18
32.04
30.78
395
151.0
865310
+ 163850
23.35
32.09
19
38.52
36.00
151
43.3
27170
+ 388730
+ ||
21.44
36.35
20
33.30
31.50
344
132.0
646040
+ 241440
18.96
31.05
21
30.24
28.98
270
156.3
618180
+ 154460
— "
15.40
30.20
22
30.24
28.44
140
47.1
38100
+218640
+ ||
16.51
29.85
23
32.58
32.58
436
160.4
1010100
0
22.76
32.78
24
28.80
29.16
222
86.8
245430
— 43190
+ ||
14.82
28.51
25
34.74
32.40
383
139.9
754830
+ 325210
24.93
32.36
26
11.16
14.76
103
36.5
164350
—193160
+ "
7.66
13.80
44
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 8
THE IMMEDIATE EESULTS OF THE TESTS ON THE 5°-0' CURVE, GIVING THE RESULTS
OF RESISTANCE AND SPEED USED IN PRODUCING FIG. 9
Grade
Motor
Data
Section
Wind
Limits
Rise or
Length
Time
Item
Test
Opposing
Fall Over
of
to Run
Number
Efficiency
No.
No.
or
'Trolley
Section
Track
Over
in Use
of Motors
Helping
Line Pole
Section
Section
and
and
Numbers
+Up
Connection
Gears
— Down
*
0 orH
Feet
Feet
Sec.
Per cent
1
125
O
24-14
— 0.15
714
14.0
4M
82.9
2
126
H
14-24
+
15.2
4M
80.5
3
126
H
14-24
+
17.4
4M
83.1
4
125
0
24-14
15.6
4M
77.3
5
126
H
14-24
+
15.6
4M
85.3
6
126
H
14-24
+
14.7
4M
83.4
7
126
H
14-24
+
13.6
4M
85.8
8
126
H
14-24
+
24.8
48
76.5
9
125
0
24-14
19.0
4S
70.3
10
126
H
14-24
+
21.4
4S
76.3
11
127
24-14
25.0
4M
74.9
12
128
. .
14-24
+
23.9
4M
75.8
13
127
. .
24-14
47.3
4S
70.8
14
128
. .
14-24
+
30.4
4S
73.4
15
129
H
24-14
19.9
4S
68.7
16
130
0
14-24
+
23.7
4S
74.6
17
129
H
24-14
27.9
48
69.9
18
130
O
14-24
+
31.0
4S
75.0
19
130
O
14-24
+
15.4
4M
85.5
20
130
0
14-24
+
14.9
4M
79.0
21
129
H
24-14
12.4
4M
83.4
22
130
0
14-24
+
16.0
4M
85.1
23
130
O
14-24
+
14.6
4M
82.8
*S= Series-Multiple. M= Multiple,
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR 45
TABLE 8 (Continued)
THE IMMEDIATE RESULTS OF THE TESTS ON THE 5°-0' CURVE, GIVING THE RESULTS
OF RESISTANCE AND SPEED USED IN PRODUCING FIG. 9
10
11
12
13
14
15
16
17
18
19
Speed
Energy Imparted to the Car
Net Car
Average
Item
At
At
Average
Average
By the
Resis-
Speed
No.
Entrance
Exit
Voltage
Current
By the
Change in
By the
tance
Over the
to the
from the
Current
Kinetic
Grade
Section
Section
Section
Energy
..;•
M.P.H.
M.P.H.
Volts
Amp.
Ft. Lb.
Ft. Lb.
Ft. Lb.
Lb. per
Ton
M.P.H.
1
34.72
35.26
462
146.7
580160
— 78220
+ 8600
24.93
34.77
2
33.10
32.02
383
138.6
479000
+ 145580
30.09
32.03
3
28.42
28.24
387
164.6
679280
+ 21110
—
33.79
27.98
4
32.74
31.84
354
123.2
387840
+ 120310
+
25.24
31.21
5
30.22
32.20
460
196.4
886580
— 255830
30.39
31.21
6
32.74
32.56
436
155.8
614200
+ 24330
30.77
33.12
7
33.82
35.08
524
195.9
883380
— 179700
.
33.95
35.80
8
19.60
20.32
243
71.9
488880
— 59500
.
20.55
19.63
9
26.26
24.82
245
51.8
250010
+ 152260
+
20.07
25.62
10
22.30
22.30
268
68.1
439530
O
21.05
22.75
11
18.84
19.56
221
131.9
402550
— 57370
+ 8630
17.23
19.47
12
20.10
19.56
245
136.5
446780
+ 44440
23.51
20.37
13
10.74
10.92
121
59.8
357380
—8090
+
17.44
10.29
14
16.32
16.68
189
62.7
390010
— 24650
17.38
16.01
15
24.30
23.76
220
49.3
218690
+ 53720
+
13.73
24.46
16
19.98
19.80
230
64.3
385700
+ 14820
— 8600
19.14
20.54
17
17.64
18.54
166
54.0
257880
— 67400
+
9.72
17.45
18
16.02
16.74
194
69.9
465020
— 48830
19.91
15.70
19
30.06
32.58
480
199.6
930380
—326760
.
29.06
31.61
20
33.48
31.86
380
128.4
423550
+ 219110
30.97
32.67
21
39.06
38.88
482
150.6
553640
+ 29040
+
28.88
39.26
22
27.54
30.24
441
194.1
859580
— 322930
25.79
30.43
23
34.02
33.66
431
150.0
576390
+ 50440
—
30.20
33.34
46
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 9
THE IMMEDIATE RESULTS OF THE TESTS ON THE 6°-30' CURVE, GIVING THE EESIJLTS
OF RESISTANCE AND SPEED USED IN PRODUCING FIG. 10
3
Section
Grade
Motor
Data
Wind
Limits
Rise or
Length
Time
Item
No.
Test
No.
Opposing
or
Trolley
Fall Over
Section
of
Track
to Run
Over
Number
in Use
Efficiency
of Motors
Helping
Line Pole
Section
Section
and
and
Numbers
+Up
Connection
Gears
— Down
*
O orH
Feet
Feet
Sec.
Per cent
1
133
H
1155-1151
H-3.22
365
18.3
48
73.1
2
134
O
1151-1155
., .
13.4
38.0
3
133
H
1155-1151
+
25.1
74.5
4
134
O
1151-1155
17.7
49.8
5
133
H
1155-1151
+
16.5
74.5
6
134
O
1151-1155
12.7
45.1
7
133
H
1155-1151
+
17.0
75.9
8
134
0
1151-1155
12.1
49.3
9
133
H
1155-1151
+
20.2
75.6
10
133
H
1155-1151
+
15.0
78.3
11
134
0
1151-1155
9.1
4M
57.0
12
133
H
1155-1151
+
9.9
83.5
13
134
O
1151-1155
7.9
54.1
14
134
O
1151-1155
.
7.9
76.3
15
134
O
1151-1155
.
13.0
4S
53.7
16
133
H
1155-1151
+
20.9
75.6
17
134
O
1151-1155
14.4
62.2
18
133
H
1155-1151
4-
12.9
78.4
19
134
O
1151-1155
11.4
50.9
20
133
H
1155-1151
+
25.7
75.2
21
133
H
1155-1151
4-
13.6
77.4
rS— Series-Multiple. M=Multiple.
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR
47
TABLE 9 (Continued1)
THE IMMEDIATE EESULTS OF THE TESTS ON THE 6°-30' CURVE, GIVING THE RESULTS
OP RESISTANCE AND SPEED USED IN PRODUCING FIG. 10
10
11
12
13
14
15
16
17
18
19
Sp
wd
Energy
[mparted to
the Car
Item
No.
At
Entrance
to the
Section
At
Exit
from the
Section
Average
Voltage
Average
Current
By the
Current
By the
Change in
Kinetic
Energy
By the
Grade
Net Car
Resis-
tance
Average
Speed
Over the
Section
M.P.H.
M.P.H.
Volts
Amp.
Ft. Lb.
Ft. Lb.
Ft. Lb.
Lb. per
Ton
M.P.H.
1
14.59
12.38
173
63.2
215730
+ 123080
— 184510
14.75
13.60
2
18.84
18.84
106
13.2
10510
0
+ "
18.65
18.57
3
9.49
10.00
146
78.4
315710
—20530
10.58
9.91
4
13.23
14.08
97.2
34.6
43730
— 47940
+
17.24
14.06
5
15.61
14.25
202
66.3
242830
+ 83860
13.60
15.08
6
18.84
19.52
149
31.4
39530
—53870
+
16.27
19.60
7
14.93
14.25
202
74.4
286030
+40980
13.63
14.64
8
19.69
20.03
140
33.7
41510
—27890
+
18.95
20.57
9
12.04
11.53
182
77.5
317720
+ 24820
15.11
12.32
10
16.29
16.46
248
84.5
363020
—11500
—
15.97
16.59
11
27.17
27.17
225
73.8
63500
0
+
23.71
27.35
12
24.45
24.11
380
180.0
417000
+ 34090
25.49
25.14
13
31.76
31.42
230
69.8
50600
+44360
+
26.72
31.50
14
31.59
31.93
365
115.8
187890
— 44600
+
31.35
31.50
15
18.84
19.18
158
35.9
58400
— 26690
20.68
19.14
16
11.19
11.19
184
77.2
331060
0
14.01
11.91
17
16.12
17.48
169
42.4
94670
—94360
+
17.68
17.28
18
19.69
19.18
282
77.9
327710
+40940
17.61
19.29
19
20.71
21.05
169
34.1
49320
—29320
+
19.56
21.83
20
9.49
11.53
157
83.4
373260
—88550
9.58
9.68
21
18.67
17.82
256
75.6
300490
+ 6405C
—
17.21
18.30
48
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 10
THE IMMEDIATE EESULTS OF THE TESTS ON THE 8°-0' CURVE, GIVING THE EESULTS
OF EESISTANCE AND SPEED USED IN PRODUCING FIG. 12
Item
No.
Test
No.
Wind
Opposing
or
Helping
Section
Limits
Trolley
Line Pole
Numbers
Grade
Length
of
Track
Section
Time
to Run
Over
Section
Motor Data
Rise or
Fall Over
Section
+ Up
— Down
Number
in Use
and
Connection
*
Efficiency
of Motors
and
Gears
O orH
Feet
Feet
Sec.
Per cent
1
142
O
1735 -1737.5
+ 0.65
176
6.7
4S
80.3
2
142
0
1735 -1737.5
+
6.4
"
66.8
3
141
H
1737.5-1735
6.2
» >
41.2
4
142
O
1735 -1737.5
+
13.9
»
73.3
5
142
O
1735 -1737.5
+
8.1
> >
64.8
6
142
0
1735 -1737.5
+
6.7
> '
78.0
7
141
H
1737.5-1735
4.9
4M
21.5
8
142
O
1735 -1737.5
T
4.9
65.4
9
142
0
1735 -1737.5
+
4.5
»»
72.3
10
142
0
1735 -1737.5
+
5.3
"
73.9
11
141
H
1737.5-1735
8.1
4S
33.0
12
142
O
1735 -1737.5
+
8.8
4M
74.0
13
141
H
1737.5-1735
7.7
48
28.2
14
141
H
1737.5-1735
— .
10.3
21.2
15
142
O
1735 -1737.5
+
7.7
4M
75.9
16
141
H
1737.5-1735
7.95
4S
49.6
17
142
0
1735 -1737.5
+
15.3
70.1
18
141
H
1737.5-1735
6.1
»
52.8
19
142
0
1735 -1737.5
+
4.5
4M
85.2
20
141
H
1737.5-1735
9.4
4S
56.4
21
141
H
1737.5-1735
.
6.5
59.1
22
141
H
1737.5-1735
.
6.1
»
62.5
23
142
0
1735 -1737.5
+
5.6
411
69.7
24
142
0
1735 -1737.5
+
3.5
86.1
25
142
0
1735 -1737.5
4-
5.6
> >
74.6
26
141
H
1737.5-1735
8.3
48
59.7
27
141
H
1737.5-1735
.
10.7
C
28
142
0
1737.5-1735
+
5.4
4M
69.6
29
142
0
1735 -1737.5
+
9.4
' '
73.4
30
153
1737.5-1735
12.2
48
28.5
31
153
1737.5-1735
.
9.0
43.8
32
154
„
1735 -1737.5
+
6.8
> »
74.0
33
154
.
1735 -1737.5
+
11.7
"
74.7
34
153
1737.5-1735
7.8
> >
66.8
35
153
. .
1737.5-1735
—
7.4
"
40.4
36
153
. .
1737.5-1735
—
6.2
»»
51.5
37
154
1735 -1737.5
+
7.5
»»
76.1
38
153
1737.5-1735
7.46
' '
37.3
39
153
1737.5-1735
6.2
> >
54.8
40
153
1737.5-1735
—
12.2
' '
46.7
"8 = Series-Multiple. M = Multiple. C = Coasting.
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR 49
TABLE 10 (Continued)
THE IMMEDIATE EESULTS OF THE TESTS ON THE 8°-0' CURVE, GIVING THE RESULTS
OF RESISTANCE AND SPEED USED IN PRODUCING FIG. 12
10
11
12
13
14 | 15
16
17 | 18 | 19
Speed
Energy Imparted to the Car
Item
No.
At
Entrance
to the
At
Exit
from the
Average
Voltage
Average
Current
By the
Current
By the
Change in
Kinetic
By the
Grade
Net Car
Resis-
tance
Average
Speed
Over the
Section
Section
Section
Energy
M.P.H.
M.P.H.
Volts
Amp.
Ft. Lb.
Ft. Lb.
Ft. Lb.
Lb. per
Ton
M.P.H.
1
17.52
18.96
290
94.9
218390
— 109530
—37570
14.02
17.91
2
18.78
17.88
203
46.7
59780
+ 68790
17.89
18.75
3
19.32
19.32
401
24.1
36420
0
+
14.55
19.35
4
7.62
9.06
128
71.4
137360
— 50080
9.77
8.63
5
16.26
15.18
162
45.5
57060
+ 70800
— -
17.75
14.81
6
17.88
18.42
260
79.3
158950
— 40870
—
15.83
17.91
7
25.26
24.90
117
43.1
3920
+ 37650
+
15.56
24.49
8
26.34
25.26
236
89.2
49750
+ 116190
25.24
24.49
9
27.06
26.52
301
109.7
79230
+ 60330
— .
20.05
26.67
10
21.12
20.58
258
120.3
89660
+ 46950
— .
19.47
22.64
11
14.82
14.28
86
27.7
9440
+ 32760
-f
15.68
14.81
12
13.92
13.56
171
136.4
112000
+ 20630
— .
18.69
13.64
13
16.08
15.72
59
26.2
4980
+ 23870
+
13.06
15.58
14
11.76
11.40
56
22.6
4060
+ 17380
+
11.60
11.65
15
15.54
15.54
212
145.3
132750
0
—
18.71
15.58
16
15.90
15.90
110
34.3
21960
0
+
11.70
15.09
17
7.26
8.16
108
58.8
100460
— 28940
—
6.67
7.84
18
20.40
20.04
166
35.3
27840
+ 30350
+
18.83
19.67
19
25.26
26.34
432
204.6
249930
— 116190
—
18.91
26.67
20
13.02
13.02
97
38.9
29560
0
+
13.20
12.77
21
19.68
19.68
169
39.8
38110
0
+
14.88
18.46
22
20.04
20.04
169
42.7
40570
0
+
15.36
19.67
23
22.74
22.20
236
101.3
68830
+ 50600
16.09
21.43
24
34.08
34.44
539
208.3
249520
— 51430
—
31.56
34.29
25
21.48
20.94
243
126.7
94860
+ 47760
—
20.65
21.43
26
14.28
14.28
112
41.2
33730
0
+
14.02
14.46
27
11.94
11.40
0
0
0
+ 26280
+
12.55
11.21
28
23.10
22.56
262
100.0
72620
+ 51410
— •
17.00
22.22
29
12.66
12.66
171
130.0
113120
0
—
14.85
12.77
30
10.04
9.68
57
26.3
7690
+ 14800
+ 37640
11.80
9.84
31
13.64
13.64
107
31.6
19650
0
+
11.24
13.33
32
17.42
17.42
220
62.5
102060
0
—
12.64
17.65
33
10.22
11.66
153
78.1
154050
— 65690
—
9.96
10.26
34
15.08
15.62
165
48.1
60980
— 34570
+
12.57
15.38
35
16.52
15.80
130
29.9
17130
+ 48520
+
20.27
16.22
36
20.66
20.12
179
34.3
28920
4- 45910
+
22.07
19.35
37
15.62
15.62
207
75.4
131410
0
—
18.40
16.00
38
16.16
15.98
116
28.9
13750
+ 12060
+
12.45
16.09
39
20.12
19 76
165
36.6
30270
-f 29930
+
19.20
19.35
40
9.86
9.50
68
33.5
19160
-J- 14530
4- -
14.00
9.84
50
ILLINOIS ENGINEERING EXPERIMENT STATION
TABLE 11
THE IMMEDIATE EESULTS OF THE TESTS ON THE 14°-30' CURVE, GIVING THE
EESULTS OF EESISTANCE AND SPEED USED IN PRODUCING FIG. 13
Grade
Motor Data
Section
— — —
Item
No.
Test
No.
Wind
Opposing
or
Limits
Trolley
Rise or
Fall Over
Section
Length
of
Track
Time
to Run
Over
Number
in Use
__. j
Efficiency
of Motors
Helping
Line Pole
Numbers
+ UP
Section
Section
Connection
*
and
Gears
— Down
O or H
I?eet
Feet
Sec.
Per cent
1
141
O
1735-1732
— 0.17
276
10.1
4 S
74.2
2
142
H
1732-3735
*
10.7
' '
72.9
3
141
O
1735-1732
9.0
' '
60.7
4
142
H
1732-1735
-f
9.9
' '
78.4
5
141
O
1735-1732
9.9
' '
61.7
6
142
H
1732-1735
+
22.7
' '
72.4
7
141
O
1735-1732
8.7
"
74.4
8
141
0
1735-1732
9.1
1 >
60.0
9
142
H
1732-1735
+
10.7
> >
75.0
10
142
H
1732-1735
11.6
"
77.2
11
141
O
1735-1732
— .
7.1
4M
84.2
12
142
H
1732-1735
+
7.2
1 '
83.0
13
141
O
1735-:i732
10.2
48
72.0
14
142
H
1732-1735
+
8.8
4M
80.0
15
141
0
1735-1732
9.2
4S
76.8
16
142
H
1732-1735
+
27.5
"
72.2
17
141
0
1735-1732
13.2
» »
70.3
18
141
O
1735-1732
—
12.7
» >
60.6
19
141
0
1735-1732
— .
12.0
' '
69.3
20
142
H
1732-1735
+
25.0
' '
72.9
21
141
0
1735-1732
9.2
> '
75.7
22
141
O
1735-1732
— .
11.5
1 •
76.8
23
142
H
1732-173o
4-
7.6
4M
78.2
24
141
0
1735-1732
—
8.1
4S
73.8
25
141
O
1735-1732
.
14.1
' '
69.2
26
141
O
1735-1732
— .
9.6
' '
73.9
27
141
O
1736-1732
— .
9.6
' '
75.0
28
142
H
17*2-1735
+
38.1
"
71.7
29
141
0
1735-1732
9.8
"
72.9
30
141
O
1735-1732
— .
9.5
> >
77.7
31
141
O
1735-1732
— .
14.5
' '
66.5
32
142
TJ
1732-1735
+
5.6
4M
86.1
33
141
b
1735-1732
12.6
4S
68.7
34
142
H
1732-1735
+
21.1
1 '
75.2
35
141
O
1735-1732
9.3
1 '
74.7
36
142
H
1732-1735
4-
8.4
4M
83.8
37
142
H
1732-1735
+
7.6
' '
79.9
38
153
1735-1732
— .
8.6
4S
74.5
39
154
1732-1735
+
9.0
' '
77.4
40
153
1735-1732
11.7
"
63.2
4J
153
[ *
" '
1735-1732
— .
12.6
M
75.1
42
153
1735-1732
— .
29.0
»»
67.7
43
153
[ \
1735-1732
— .
9.7
' '
71.6
44
153
1735-1732
— .
10.3
"
70.8
45
153
1735-1732
:
8.5
' '
67.7
46
153
1735-1732
8.1
' »
77.0
47
153
1735-1732
.
22.3
J'
68.2
48
153
1735-1732
,
9.0
*' '
75.9
49
15b
\ '
1735-1732
28.9
"
48.9
50
15S
1735-1732
—
15.4
' '
64.7
- Series-Multiple. M = Multiple.
RESISTANCE ON CURVES OF A TWENTY-EIGHT TON ELECTRIC CAR 51
TABLE 11 (Continued)
THE IMMEDIATE RESULTS OF THE TESTS ON THE 14°-30' CURVE, GIVING THE
EESULTS OF RESISTANCE AND SPEED USED IN PRODUCING FIG. 13
10
11
12
13 14
15
16
17
18
19
Speed
Energy Imparted to the Car
Item
At
At
Average
Average
By the
Net Car
Average
Speed
No.
Entrance
Exit Voltage
Current
By the
Change in
By the
Resis-
Over the
to the
from the
Current
Kinetic
Grade
tance
Section
Section
Section
Energy
M.P.H.
M.P.H.
Volts
Amp. | Ft. Lb.
Ft. Lb.
Ft. Lb.
Lb. per
Ton
M.P.H.
1
18.96
18.96
224
63.2
156470
0 +9830
20.85
18.63
2
18.24
17.52
194
60.1
134150
+ 53680
. > >
22.32
17.59
3
21.48
20.22
167
41.1
55320
+ 109550
+ "
21.90
20.91
4
18.60
18.78
260
82.4 245280
— 14030
, *"
27.76
19.01
5
19.32
18.06
420
35.9
135870
+ 98200
+ "
30.58
19.01
6
7.62
7.62
112
67.9
184360
0
— "
21.88
8.29
7
21.66
21.48
268
61.2
156580
+ 16190
+ "
22.89
21.63
8
21.12
19.50
178
40.3
57780
+ 137200
_l_ >
25.68
20.68
9
18.60
17.88
225
66.4
176840
+ 54760
>
27.80
17.59
10
14.28
15.18
227
80.2
240470
— 55280
»
21.98
16.22
11
26.16
26.52
383
202.7
342260
— 39540
_i_ >
39.18
26.50
12
26.34
26.34
383
164.5
277660
0
. »
33.58
26.14
13
19.32
18.78
193
57.5
120240
+ 42900 ,
_j_ •
21.69
18.45
14
21.30
21.12
312
164.3
266140
+ 15920
. »
34.13
21.38
15
19.86
20.04
260
71.6
194000
— 14970
_|_ »
23.68
20.45
16
5.82
5.82
91.8
70.9
190650
0
>
22.67
6.84
17
14.28
13.38
142
56.4
109640
+ 51900
_l_ •
21.48
14.26
18
15.72
13.56
113
42.0
53860
+ 131870
_l_ »
24.52
14.82
19
15.90
15.00
164
52.7
106040
+ 57980
+ ' '
21.80
15.68
20
6.00
7.26
106
75.4
214790
— 34840
»
21.33
7.53
21
20.04
19.86
247
67.8
172010
+ 14970
_j_ >
24.67
20.45
22
16.98
17.52
220
78.3
224390
— 38840
_l_ »
24.49
16.36
23
26.52
25.26
290
150.0
190670
+ 136030
. »
39.72
24.76
24
22.74
22.38
264
59.8
139180
+ 33870
i »
22.93
23.23
25
13.02
12.66
140
54.0
108800
+ 19280
i »
17.29
13.35
26
19.68
19.32 230
61.4
147760
+ 29270
i i
23.43
19.60
27
19.68
19.32 243
65.2
168270
+ 29270
_j_ >
26.00
19.60
28
3.48
4.02
93.6
67.2
253450
— 8440
. »
29.48
4.94
29
19.14
19.14
218
59.0
135510
0
_l_ f
18.22
19.20
30
20.04
20.04
264
76.7
220480
0
_l_ »
28.87
19.81
31
13.38
12.30
128
49.2
89600
+ 57830
_j_ »
19.72
12.98
32
33.90
34.08
573
194.7
396700
— 25510
>
45.30
33.60
33
14.28
14.28
164
51.4
107630
0
_j_ >
14.73
14.93
34
6.18
9.96 151
88.6
313150
— 127200
»
22.08
8.92
35
20.22
20.40 243
63.8
158880
— 15240
_|_ »
19.24
20.23
36
21.48
23.10 370
199.1
382450
— 150580
»
27.84
22.40
37
24.00
23.64 318
149.1
212320
+ 35760
»
29.87
24.76
38
21.56
21.56 266
61.6
154840
0
+ 9840
20.61
21.88
39
21.56
21.74
279
72.3
207240
— 16250
_^ ' »
22.67
20.91
40
17.06
15.44
144
44.1
69260
+ 109780
+ "
23.64
16.08
41
13.82
15.26
189
71.8
189400
— 87310
+ "
14.01
14.93
42
8.06 ! 5.18
75
54.7
118880
+ 79500
+ "
26.06
6.49
43
20.12
19.76 226
55.0
127340
+ 29930
+ ' '
20.92
19.40
44
18.86
18.32 223
53.5
128320 i + 41860
_j_ »
22.53
18.27
45
22.46
21.20 217
47.7
87850
+ 114700
_j_ »
26.58
22.14
46
22.10
21.74 300
68.0
187670
+ 32910
_[_ »
28.83
23.23
47
8.96
8.60
96
54.2
116760
+ 13180
_[- »
17.49
8.44
48
20.66
20.30
272
66.5
182270
+ 30740
-|- »
27.89
20.91
49
9.68
0.00
49.5
34.8
35960
+ 195370
+ »
30.18
6.51
50
13.64
11.66
120
46. 5
82010
+ 104450
+ '
24.57
12.22
52 PUBLICATIONS OF THE ENGINEERING EXPERIMENT STATION
Bulletin No. 1. Tests of Reinforced Concrete Beams, by Arthur N. Talbot. 1904. None
available.
Circular No. 1. High-Speed Tool Steels, by L. P. Breckenridge. 1905. None available.
Bulletin, No. 2. Tests of High-Speed Tool Steels on Cast Iron, by L. P. Breckenridge
and Henry B. Dirks. 1995. None available.
Circular No. a. Drainage of Earth Roads, by Ira O. Baker. 1906. None available.
Circular No. 3. Fuel Tests with Illinois Coal (Compiled from tests made by the Tech-
nologic Branch of the U. S. G. S., at the St. Louis, Mo., Fuel Testing Plan, 1904-1907), by
L. P. Breckenridge and Paul Diserens. 1909. Thirty cents.
Bulletin No. 3. The Engineering Experiment Station of the University of Illinois, by
L. P. Breckenridge. 1906. None available.
Bulletin No. 4. Tests of Reinforced Concrete Beams, Series of 1905, by Arthur N. Tal-
bolt. 1906. Forty-five cents.
Bulletin No. 5. Resistance of Tubes to Collapse, by Albert P. Carman and M. L. Carr.
1906. None available.
BuUetin No. 6. Holding Power of Railroad Spikes, by Roy I. Webber, 1906. None
available.
Bulletin No. 7. Fuel Tests with Illinois Coals, by L. P. Breckenridge, S. W. Parr, and
Henry B. Dirks. 1906. None available.
Bulletin No. 8. Tests of Concrete: I, Shear; II, Bond, by Arthur N. Talbot. 1906.
None available.
Bulletin No. 9. An Extension of the Dewey Decimal System of Classification Applied to
the Engineering Industries, by L. P. Breckenridge and G. A. Goodenough. 1906. Revised
Edition 1912. Fifty cents.
Bulletin No. 10. Tests of Concrete and Reinforced Concrete Columns. Series of 1906,
by Arthur N. Talbot. 1907. None available.
Bulletin No. 11. The Effect of Scale on the Transmission of Heat through Locomotive
Boiler Tubes, by Edward C. Schmidt and John M. Snodgrass. 1907. None available.
Bulletin No. 12. Tests of Reinforced Concrete T-Beams, Series of 1906, by Arthur N.
Talbot. 1907. None available.
Bulletin No. 13. An Extension of the Dewey Decimal System of Classification Applied
to Architecture and Building, by N. Clifford Ricker. 1907. None available.
Bulletin No. 14. Tests of Reinforced Concrete Beams, Series of 1906, by Arthur N.
Talbot. 1907. None available.
Bulletin No. 15. How to Burn Illinois Coal Without Smoke, by» L. P. Breckenridge.
1908. None available.
Bulletin No. 16. A Study of Roof Trusses, by N. Clifford Ricker. 1908. Fifteen cents.
Bulletin No. 17. The Weathering of Coal, by S. W. Parr, N. D. Hamilton, and W. F.
Wheeler. 1908. None available.
Bulletin No. 18. The Strength of Chain Links, by G. A. Goodenough and L. E. Moore.
1908. Forty cents.
Bulletin No. 19. Comparative Tests of Carbon, Metallized Carbon and Tantalum Fila-
ment Lamps, by T. H. Amrine. 1908. None available.
Bulletin No. 20. Tests of Concrete and Reinforced Concrete Columns, Series of 1907,
by Arthur N. Talbot. 1908. None available.
Bulletin No. 21. Tests of a Liquid Air? Plant, by C. S. Hudson and C. M. Garland.
1908. Fifteen cents.
Bulletin No. 22. Tests of Cast-Iron and Reinforced Concrete Culvert Pipe, by Arthur
N. Talbot. 1908. None available.
Bulletin No. 23. Voids, Settlement, and Weight of Crushed Stone, by Ira O. Baker.
1908. Fifteen cents.
*Bulletin No* 24. The Modification of Illinois Coal by Low Temperature Distillation,
by S. W. Parr and C. K. Francis. 1908. Thirty cents.
Bulletin No. 25. Lighting Country Homes by Private Electric Plants, by T. H. Amrine.
1908. Twenty cents.
Bulletin No. 26. High Steam-Pressures in Locomotive Service. A Review of a Report
to the Carnegie Institution of Washington, by W. F. M. Goss. 1908. Twenty-five cents.
Bulletin No. 27. Tests of Brick Columns and Terra Cotta Block Columns, by Arthur
N. Talbot and Duff A. Abrams. 1909. Twenty-five cents.
Bulletin No. 28. A Test of Three Reinforced Concrete Beams, by Arthur N. Talbot.
1909. Fifteen cents.
Bulletin No. 29. Tests of Reinforced Concrete Beams: Resistance to Web Stresses,
Series of 1907 and 1908, by Arthur N. Talbot. 1909. Forty-five cents.
*Bulletin No. 30. On the Rate of Formation of Carbon Monoxide in Gas Producers, by
J. K. Clement, L. H. Adams, and C. N. Haskins. 1909. Twenty-five cents.
* Bulletin No. 31. Fuel Tests with House-heating Boilers, by J. M. Snodgrass. 1909.
Fifty-five cents.
Bulletin No. 32. The Occluded Gases in Coal, by S. W. Parr and Perry Barker. 1909.
Fifteen cents.
Bulletin No. 33. Tests of Tungsten Lamps, by T. H. Amrine and A. Guell. 1909.
Twenty cents.
*Bulletin No. 34. Tests of Two Types of Tile-Roof Furnaces under a Water-Tube Boiler,
by J. M. Snodgrass. 1909. Fifteen cents.
Bulletin No. 35. A Study of Base and Bearing Plates for Columns and Beams, by
N. Clifford Ricker. 1909. Twenty cents.
*A limited number of copies of those bulletins which are starred are available for free
distribution.
PUBLICATIONS OF THE ENGINEERING 'E^ERIMEN^T STATION ' 53
Bulletin No. 36. The Thermal Conductivity of Fire-Clay at High Temperatures, by
J. K. Clement and W. L. Egy. 1909. Twenty cents.
Bulletin No. 37. Unit Coal and the Composition of Coal Ash, by S. W. Parr and W. F.
Wheeler. 1909. Thirty-five cents.
*Bulletin No. 38. The Weathering of Coal, by S. W. Parr and W. F. Wheeler. 1909.
Twenty-fire cents.
^Bulletin No. 39. Tests of Washed Grades of Illinois Coal, by C. S. McGovney. 1909.
Seventy-five cents.
Bulletin No. 40. A Study in Heat Transmission, by J. K. Clement and C. M. Garland.
1910. Ten cents.
* Bulletin No. 41. Tests of Timber Beams, by Arthur N. Talbot. 1910. Twenty cents.
* Bulletin No. 42. The Effect of Keyways on the Strength of Shafts, by Herbert F.
Moore. 1910. Ten cents.
Bulletin No. 43. Freight Train Resistance, by Edward C. Schmidt. 1910. Seventy-
fire cents.
Bulletin No. 44. An Investigation of Built-up Columns Under Load, by Arthur N. Tal-
bot and Herbert F. Moore. 1911. Thirty-five cents.
* Bulletin No. 45. The Strength of Oxyacetylene Welds in Steel, by Herbert L. White-
more. 1911. Thirty-five cents.
* Bulletin No. 46. The Spontaneous Combustion of Coal, by S. W. Parr and F. W.
Kressman. 1911. Forty-five cents.
*Bulletin No. 47. Magnetic Properties of Heusler Alloys, by Edward B. Stephenson,
1911. Twenty-five cents.
*Bulletin No. 48. Resistance to Flow Through Locomotive Water Columns, by Arthur
N. Talbot and Melvin L. Enger. 1911. Forty cents.
*Bulletin No. 49. Tests of Nickel-Steel Riveted Joints, by Arthur N. Talbot and Herbert
F. Moore. 1911. Thirty cents.
*BuUetin No. 50. Tests of a Suction Gas Producer, by C. M. Garland and A. P. Kratz.
1912. Fifty cents.
Bulletin No. 51. Street Lighting, by J. M. Bryant and H. G. Hake. 1912. Thirty-five
cents.
*Bulletin No. 52. An Investigation of the Strength of Rolled Zinc, by Herbert F. Moore.
1912. Fifteen cents.
*Bulletin No. 53. Inductance of Coils, by Morgan Brooks and H. M. Turner. 1912.
Forty cents.
*Bulletin No. 54. Mechanical Stresses in Transmission Lines, by A. Guell. 1912.
Twenty cents.
*Bulletin No. 55. Starting Currents of Transformers, with Special Reference to Trans-
formers with Silicon Steel Cores, by Trygve D. Yensen. 1912. Twenty cents.
*Bulletin No. 56. Tests of Columns: An Investigation of the Value of Concrete as
Reinforcement for Structural Steel Columns, by Arthur N. Talbot and Arthur R. Lord. 1912.
Twenty-five cents.
*Bulletin No. 57. Superheated Steam in Locomotive Service. A Review of Publication
No. 127 of the Carnegie Institution of Washington, by W. F. M. Goss. 1912. Forty cents.
*Bulletin No. 58. A New Analysis of the Cylinder Performance of Reciprocating En-
gines, by J. Paul Clayton. 1912. Sixty cents.
*Bulletin No. 59. The Effect of Cold Weather Upon Train Resistance and Tonnage
Rating, by Edward C. Schmidt and F. W. Marquis. 1912. Twenty cents.
Bulletin No. 60. The Coking of Coal at Low Temperatures, with a Preliminary Study
of the By-Products, by S. W. Parr and H. L. Olin. 1912. Twenty-five cents.
* Bulletin No. 61. Characteristics and Limitation of the Series Transformer, by A. R.
Anderson and H. R. Woodrow. 1913. Twenty-five cents.
Bulletin No. 62. The Electron Theory of Magnetism, by Elmer H. Williams. 1913
Thirty-five cents.
Bulletin No. 63. Entropy-Temperature and Transmission Diagrams for Air, by C. R.
Richards. 1913. Twenty- five cents.
*Bulletin No. 64. Tests of Reinforced Concrete Buildings Under Load, by Arthur N.
Talbot and Willis A. Slater. 1913. Fifty cents.
* Bulletin No. 65. The Steam Consumption of Locomotive Engines from the Indicator
Diagrams, by J. Paul Clayton. 1913. Forty cents.
Bulletin No. 66. The Properties of Saturated and Superheated Ammonia Vapor, by G. A.
Goodenough and William Earl Mosher. 1913. Fifty cents.
Bulletin No. 67. Reinforced Concrete Wall Footings and Column Footings, by Arthur
N. Talbot. 1913. Fifty cents.
*Bulletin No. 68. Strength of I-Beams in Flexure, by Herbert F. Moore. 1913
Twenty cents.
*Bulletin No. 69. Coal Washing in Illinois, by F. C. Lincoln. 1913. Fifty cents.
Bulletin No. 70. The Mortar Making Qualities of Illinois Sands, by C. C. Wiley. 1913.
Twenty cents.
Bulletin No. 71. Tests of Bond between Concrete and Steel, by Duff A. Abrams. 1914.
One dollar.
* Bulletin No. 72. Magnetic and Other Properties of Electrolytic Iron Melted in Vacuo,
by Trygve D. Yensen. 1914. Forty cents.
* Bulletin No 73. Acoustics of Auditoriums, by F. R. Watson. 1914. Twenty cents.
*Bulletin No. 74. The Tractive Resistance of a 28-Ton Electric Car, by Harold H. Dunn.
1914. Twenty-five cents.
*A limited number of copies of those bulletins which are starred are available for free
distribution.
54 PUBLIC AriONS t)F I'HE ENGINEERING EXPERIMENT STATION
Bulletin No. 75. Thermal Properties of Steam, by G. A. Goodenough. 1914. Thirty-
five cents.
*Bulletin No. 76. The Analysis of Coal with Phenol as a Solvent, by S. W. Parr and
H. P. Hadley. 1914. Twenty-five cents.
*Bulletin No. 77. The Effect of Boron upon the Magnetic and Other Properties of
Electrolytic Iron Melted in Vacuo, by Trygve D. Yensen. 1915. Ten cents.
*Bulletin No. 78. A Study of Boiler Losses, by A. P. Kratz. 1915. Thirty-five cents.
*Bulletin No. 79. The Coking of Coal at Low Temperatures, with Special Reference to
the Properties and Composition of the Products, by S. W. Parr and H. L. Olin. 1915.
Twenty-five cents.
*Bulletin No. 80. Wind Stresses in the Steel Frames of Office Buildings, by W. M. Wil-
son and G. A. Maney. 1915. Fifty cents.
* Bulletin No. 81. Influence of Temperature on the Strength of Concrete, by A. B. Mc-
Daniel. 1915. Fifteen cents.
*Bulletin No. 82. Laboratory Tests of a Consolidation Locomotive, by E. C. Schmidt,
J. M. Snodgrass and R. B. Keller. 1915. Sixty-five cents.
*Bulletin No. 83. Magnetic and Other Properties of Iron-Silicon Alloys, Melted in
Vacuo, by Trygve D. Yensen. 1915. Thirty-five cents.
*Bulletin No. 84. Tests of Reinforced Concrete Flat Slab Structure, by A. N. Talbot
and W. A. Slater. 1916. Sixty-five cents.
*Bulletin No. 85. Strength and Stiffness of Steel Under Biaxial Loading, by A. T.
Becker. 1916. Thirty-five cents.
* Bulletin No. 86. The Strength of I-Beams and Girders, by Herbert F. Moore and
W. M. Wilson. 1916. Thirty cents.
*Bulletin No. 87. Correction of Echoes in the Auditorium, University of Illinois, by
F. R. Watson and J. M. White. 1916. Fifteen cents.
*Bulletin No. 88. Dry Preparation of Bituminous Coal at Illinois Mines, by E. A. Hoi-
brook. 1916. Seventy cents.
*Bulletin No. 89. Specific Gravity Studies of Illinois Coal, by Merle L. Nebel. 1916.
Thirty cents.
Bulletin No. 90. Graphical Methods in Electric Motor Car Calculations, by A. M. Buck.
1916. Free upon request.
Bulletin No. 91. Subsidence Resulting from Mining, by L E. Young and H. H. Stoek.
1916. Free upon request.
Bulletin No. 92. The Tractive Resistance on Curves of a 28-Ton Electric Car, by E. C.
Schmidt and H. H. Dunn. Free upon request.
*A limited number of copies of those bulletins which are starred are available for free
distribution.
00278
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