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Simplified Curve and
Switch Work

A Collection of Valuable Points
for the Supervisor and Foreman
and for College Instruction.

W. F. RENCH

Supervisor, Pennsylvania Railroad

MR. ELMER T. HOWSON

Civil Engineering Editor of the Railway Age Gazette

whose counsel and criticism

have been of much help.

This book is,

with his kind permission,

respectfully inscribed

by the author

365561

Railway Educational Press, Inc.,
Chicago, Illinois

TABLE OF CONTENTS.

Introduction.

PART I.

Curves
CHAPTER I

THE RELINING OF CURVES WITH A STRING 14

Art. 1. Definitions of Curve Functions. — Art. 2. Use
of String Method. — Art. 3. Geometrical Principles.

CHAPTER II
PRELIMINARY STUDY OF THE CURVE 23

Art. 4. The Test with a String.— Art. 5. The Study
of the Locality. — Art. 6. The Diagnosis of the
Curve.

CHAPTER III

THE SOLUTION OF STRING LINING PROBLEMS 28

Art. 7. Rules for Solving Curve Problems.— Art 8.
Examples in Curve Solution. — Art. 9. Application
of the Corrections.

CHAPTER IV

SUPERELEVATION OF CURVES 53

Art. 10. Approach and Run-off of Curves. — Art. 11.
Superelevation of Body of Curves. — Art. 32. An-
alysis of Lining and Elevation Corrections.

CHAPTER V

THE SPIRAL 64

Art. 13. The Spiral by Middle Ordinates— Art. 14.
The Spiral by the Instrument. — Art. 15. Advantage
and Cost of Spiraling Curves.

CHAPTER VI

THE VERTICAL CURVE.... 78

Art. 16. The Uses of the Vertical Curve in Main-
• tenance. — Art. 17. Computation of the Vertical Curve.
— Art. 18. Example of a Vertical Curve.

CHAPTER VII

ECONOMICS OF CURVES s:1,

Art. 19. Economics of Curve Location. — Art. 20.
Economics of Curve Maintenance.

SIMPLIFIED CURVE AND SWITCH WORK

PART II

Practical Switch Connections
CHAPTER VIII

ESSENTIAL ELEMENTS IN THE DESIGN OF SWITCH CON-
NECTIONS 96

Art 21. Elementary Principles. — Art 22. Defini-
tions.— Art. 23. Theoretical and Practical Considera-
tions in Design.

CHAPTER IX

RULES FOR COMPUTATING S WITCH DIMENSIONS 116

Art. 24. The Lead.— Art. 25. The Degree of Curve.—
Art. 26. The Frog Number.— Art. 27. The Frog
Angle and Switch Angle. — Art. 28. Distance between
^2-in. Frog Points in Crossovers. — Art. 29. Distance
between Frogs in Ladders. — Art. 30. Distance be-
tween ^2 -in. Frog Points in Slip Switches.
CHAPTER X

RULES FOR VARIOUS FUNCTIONS OF TURNOUTS 130

Art. 31. Lining the Turnout Curve. — Art. 32. De-
signing the Bill of Switch Ties. — Art. 33. Narrow
Gage Switch Connections. — Art. 34. Graphical
Method of Laying Out Switches. — Art. 35. Hints for
Layout.

CHAPTER XI

PRACTICAL CONSIDERATIONS IN INSTALLING TURNOUTS 148

Art. 36. Organization. — Art. 37. Special Tool Equip-
ment.— Art. 38. Details in the Design.
CHAPTER XII

METHODS IN INSTALLING AND MAINTAINING SWITCHES 156

Art. 39. Simple Connections. — Art. 40. Slip
Switches. — Art. 41. Maintenance of Switch Connec-
tions.— Art. 42. Practice in Operation.

PART III

Siding Location
CHAPTER XIII

SIMPLIFIELD FIELD WORK 172

Art. 43. Problems in Tape Line Layout. — Art. 44.
Problems in Instrumental Layout. — 'Art. 45. Problem
of 2-point Coincidence. — Art. 46. Practical Con-
siderations in Siding Layout.

CHAPTER XIV
SPECIAL PRACTICES.... .. 194

FOREWORD.

This work, as the title indicates, is a simplifica-
tion of methods for solving curve and switch prob-
lems. The principal object has been to reduce
the solutions to their simple arithmetical relations,
so that the large majority of track men may have at
their command a means of meeting such questions

The method of "throw and resultant" for realm-
ing curves has been in use on a number of rail-
roads for a period of about twenty years. The sup-
plementary rule announced in this book, wherein is
contained the relation of error to correction and by
which the proper throw may at once be ascertained,
will effect a large saving of time and labor in the
lining of curves by that method. The "diagnosis"
of the curve must be left for the investigator, al-
though certain suggestions are made that will prove
helpful, and the examples selected illustrate not
only typical cases but some that are unusual.

The placing of a speed limit upon all train move-
ments has rendered the determination of the proper
superelevation a matter of simple calculation by a
safe empirical rule. This plan will save greatly in
maintenance by avoiding the experimenting that
the engineer or supervisor knows is the method
usually employed. The rule given in this book has
been fully tested in the most widely varied service,
and is offered with the fullest confidence in its
usefulness.

SIMPLT.I'IKM _rUkVK_ \N1) SWITCH WORK

The addition of an easement to all curves operat-
ed at high speed, and to the sharper curves used at
moderate speed, is now considered not merely a
refinement, but an essential feature in the adjust-
ment of the line. The curve that is generally ac-
cepted as the ideal easement is the cubic parabola.
The easy method advanced herein for locating this
curve by the instrument should appeal to engineers
as requiring no reference data of any kind and only
the simplest of calculations. The method by mid-
dle ordinates should appeal to the track man as
supplying a ready means both for applying and
maintaining the curve in string lining.

The rules for switch connections are intended to
eliminate all need for tables or pocket memoranda,
and are designed to make possible the solution of
such problems by the more intelligent track fore-
men. The importance of the latter feature cannot
but appeal to maintenance officers, as tending to
render the track foreman's position a more attrac-
tive one.

No apology is thought necessary for the intro-
duction of matter pertaining to narrow-gage switch
work, since one-sixth of the total railroad mileage
of the world is of less gage than the standard, and
a widening interest centers in the industrial de-
velopment of South America where the narrow gage
predominates.

The examples in siding layout are those which
are of every day occurrence, and the aim has been
to confine the solutions to the simpler theorems of

FOREWORD

geometry, developing formulae that enable the lo-
cation to be made with appliances which are al-
ways at hand.

Neither in the item of switch installation, nor in
that of siding location, is the work intended to re-
place the much more comprehensive field books,
but rather to supply what these lack. The informa-
tion given represents the sum total of what the
engineer or supervisor needs to carry in his mind,
and with patient study it may all be learned by the
brighter track foremen.

To meet the acknowledged unequipment of most
newly graduated engineers in the particular field
of track maintenance, it seems desirable to impart
a fuller and more detailed instruction in the prac-
tical elements of curve and switch work. The va-
rious field books deal only with the theoretical
functions, and it is necessary for the young engi-
neer in practice to adjust his knowledge to actual
working conditions. This requires in most cases a
long apprenticeship, in which each separate prob-
lem must be encountered and its correct solution
determined by successive trials.

It is with a view of eliminating such experiments
that this book, embodying the conclusions of a wide
practical experience, has been designed. The author
has been continuously engaged in maintenance
work with the Pennsylvania for twenty-five years,
and within that period has handled a number of
times every problem referred to. It is confidently
believed that the methods, rules and suggestions

SIMPLIFIED CURVE AND SWITCH WORK

advanced will be found to represent the most re-
cent and approved practice.

The book is therefore Commended to the col-
leges as supplying profitable reading in the Civil
Engineering courses, especially that of Railway
Engineering, which, by reason of the heavier burden
being laid upon our transportation system, is as-
suming an ever-increasing importance in the tech-
nical world.

INTRODUCTION.

The two subjects, curve and switch work, em-
brace elements which are mainly technical in charac-
ter. They involve a certain amount of measuring and
figuring, necessary to correctness in design, and they
also include problems in execution, or the actual plac-
ing of the work. The only requisite of the tangent track
is that it shall be straight and level; but the adjust-
ment of curves, the installation of switches, and the
laying out of industrial tracks, require the use of
simple mathematics, as well as a knowledge of actual
track work.

Both subjects have heretofore been developed
principally for the engineer and almost wholly from
the theoretical standpoint. A knowledge of the
geometrical functions of curves is desirable, and an
understanding of the physical principles of curvi-
linear motion quite useful ; but the practical con-
ditions on even the best railroads make it impossi-
ble to use rules founded upon theory alone. It is
quite generally recognized that easements are nec-
essary to curves, and must be secured in some
way or other. The impracticability of employing
superelevation directly proportional to the degree
of curve is also fully appreciated.

The theory of turnouts is based upon the sup-
position that the switch and frog rails follow a
regular curve, but this is seldom true in practice.
While the stub switch, now a fast-disappearing,

SIMPLIFIED CURVE AND SWITCH WORK

feature in track construction, was the single type
in use, and frogs were only a few feet in length,
the difference in theory and practice was not great.
But the present use of point switches as long as 30
ft. and frogs of a similar length, has made necessary
a change in switch practice. When layouts were
not extensive and physical features such as the un-
dergrade bridge were few, leads could be made
the true practical length. Now such structures
frequently necessitate a departure from ideal de-
sign; and a knowledge of what measurements may
be varied without disadvantage, and of the permis-
sible extent of such variations, becomes quite es-
sential.

The proper adjustment of curves has become a
most important element in maintenance, because of
the higher standard in track structure imposed by
the heavier and faster traffic. The travel of today
demands a smoothly-riding track, and the larger
and stiffer equipment requires it, to insure the
movement being not only safe but expeditious.
Curves cannot be brought to or kept in smoothly-
riding condition, even with the most faithful main-
tenance, unless the needed adjustments of the
alinement and the superelevation are first made.

The correct spiraling of curves and the proper
placing of the easement and run-off are of just as
much importance as the lining of the main part
of the curve. A knowledge of the practical ele-
ments in location and maintenance are necessary
.that past errors may be avoided, and efficient meth-

INTRODUCTION

ods established to attain a high standard and to main-
tain it.

The subject of switch work is especially impor-
tant because of the increased length of the locomo-
tive wheel base, and because trains must frequently
be passed at high speed from one track to another,
not only with safety but with comfort to the pas-
senger. Correct design and construction are there-
fore of paramount importance. There are a num-
ber of rules, which it is important to know, and
which may be remembered easily. They are gen-
erally exact, sometimes empirical, but shoufd never
be "rules of thumb."

The hints for layout given in this book embrace
a number of special features which are likely to
arise in actual work, and the practical considera-
tions in installation, maintenance and operation of
switch connections discuss important points. They
are based upon the practice of several of the larger
railway systems, and should be of use in solving
problems of track work by methods which are
known to be efficient.

Six problems in siding location are given which
will be found convenient for cases of new siding
layouts, and they may also be applied with equal
facility to changes in main track alinement. Clear-
ance, grade and curvature must be carefully con-
sidered in planning new sidings because of a per-
sistent expansion in manufacturers, which is certain
to greatly increase with the readjustment of in-
dustrial conditions throughout the world.

PART I— CURVES

CHAPTER I.
THE RELINING OF CURVES WITH A STRING.

1. DEFINITIONS OF CURVE FUNCTIONS.

Curve and Tangent — A few of the terms that are
used in connection with curves should be under-
stood a,s a necessary equipment for the study of
curve adjustment or switch layout. The line of a
railroad is made up of straight lines and curves.
The straight lines are called tangents because they
are placed tangent to the curve. The curve is con-
considered as extending between the tangent points
where it meets the adjoining straight lines.

P. C. and P. T.— The first tangent point, or the
point where the curve may be regarded as com-
mencing, is the point of curve, and is designated by
the initials P. C. The second tangent point, or the
point where the curve ends, is the point of tangent,
and is designated by the initials P. T. These points
are only relative and depend upon the direction the
line is considered to take.

Simple Curve — A simple curve is a part of a cir-
cle joining two tangents. It is defined either by
its radius, R, or its degree of curve, D. The de-
gree of curve is the angle at the center subtended
by a chord of 100 ft., the chord being a straight line
joining two points on the curve. Degree of curve

I
RELINING CURVES WITH A STRING

is expressed in degrees and minutes, there being
60 min. in each degree. The foreman will better
understand the degree as the number of inches
measured between a curve and the middle of a 62
ft. string stretched along the curve.

Compound and Reversed Curves — A simple curve
has been defined as part of a circle joining two
tangents. When two or more circular curves are
included between two successive tangents, the
curve is known as a compound curve. When two
or more curves turn in opposite directions the curve
is called a reversed curve. If any tangent, no mat-
ter how short, occurs between two simple curves,
they do not form a compound or reversed curve.

True P. C. and P. T.— The true P. C. and P. T.
of a curve are seldom to be found at the actual
ends of the curve. There is always some easement
or spiral curvature at the ends of every operated
curve. The middle of this will generally be close
to the true P. C. and P. T. It is preferable to
speak of the ends of the curve as "beginning of
spiral" and "end of spiral," the direction in both
cases being considered toward the middle of the
curve. If correctly adjusted the point of no eleva-
tion would be the beginning of spiral and the point
of full elevation somewhat beyond the end of
spiral.

Curve Ordinate — The ordinate of a curve is the
right angle distance between the chord and the
curve. The middle ordinate is the one measured at
the exact middle of the chord. The quarter ordi-

SIMPLIFIED CURVE AND SWITCH WORK

nate, which is employed in switch work, is the off-
set at the points one-fourth the length of the chord
from each end. In this work for the sake of brevity
ordinate is always meant to be the middle ordinate,
unless distinctly stated otherwise.

Mean Ordinate, Throw and Resultant — The
''mean" ordinate of an entire curve, or of a selected
group of ordinates, is the average of all the ordi-
nates that are being considered at one time in any
part of the curve adjustment. Ordinarily it repre-
sents the general curvature either of the whole
curve or the part of the curve that is being studied.
For greater convenience the amount of throwing
done upon the curve is expressed by the simple
word "throw." It measures only the amount of
the change at the several points, and has nothing
to do with the throwing done between the several
points. The points should properly be called
"stations," and they are so designated generally
throughout this work. The word "resultant" is
used for the middle ordinate that would be meas-
ured after any particular throw at an adjoining
point. It is not necessary that the resulting ordi-
nate be actually measured, and in fact this is prac-
tically never done. The term ''half function of
throw" is^ used in several places, and means the
half corrections that affect the adjacent points after
a throw at the point between them.

& USP: OF STRING METHOD.

Many roads require the alinement of curves to
])(• maintained by using the string method. "While

RELINING CURVES WITH A STRING

it is usually intended that this shall apply par-
ticularly to the minor corrections which may be
called "detail lining," it will be found that this
method is equally useful in restoring the general
line, and is even superior in this respect to the en-
gineer's instruments. The general realining of a
curve, being an engineering problem, is not strictly
within the scope of the track foreman's duties. It
is even desirable that foremen who are not familiar
with the manner of realining an entire curve, shall
be prohibited from using the string for any other
purpose than detail lining, or, at the most, for ob-
taining the data necessary to a study of the curve
by the supervisor.

This method of lining takes advantage of the
well-known fact that a curve which is maintained
fairly well, but which lacks attention from the
engineers for a time, is likely to become a succes-
sion of elliptical curves, each of short length, but
some flatter and others sharper than the average
of the curve. It is necessary that a regular curve
be substituted for these, and the one should be ap-
plied which will require the least throwing of the
track.

Experience has shown that this cannot, as a rule,
be determined by the use of the engineer's instru-
ments, and in any event, the string method is much
less costly and is generally more accurate. This
method has the further advantage that the means
of performing the field work are always available,
and no special mathematical knowledge is neces-

SIMPLIFIED CURVE AND SWITCH WORK

sary for either the field work or the application of
the corrections. The method is rendered especially
easy by the rule stated in Article 7, so that the
entire study and correction of a curve may be made
by the brighter track foremen.

3. GEOMETRICAL PRINCIPLES.

Basis of Method for String Lining — The basis of
the system of curve adjustment by means of a
string is the geometrical principle, illustrated in
Fig. 1, that a line joining the midpoint of the two
sides of a triangle is equal to one-half the third
side. By a study of the figure it will be seen that
the string in the position AC, which it held when
the ordinate at B was first measured, forms one
side of the triangle. The position AC' or AC",
which the string would occupy if the amount of the
ordinate at B were measured after an outward or
inward throw at C, forms the second side. The
effect of the throwing at C upon the ordinate at
B, and of course upon that at D as well, would
be equal to one-half the throw at C, which forms
the third side of the triangle.

This method, while not absolutely exact, is suf-
ficiently so for all practical purposes. The error is
negligible for even the sharpest curve or the longest
length of string. When the effect of the throwing at
one point upon the two adjacent points is understood,
many foremen will realize why lining at successive
points, so as to have for the moment the selected aver-

RELINING CURVES WITH A STRING

si 5

II*
.!**

SIMPLIFIED CURVE AND SWITCH WORK

age ordinate, docs not result in the correction of the
defective line.

Referring again to the figure, the resultant at
C, after an inward throw of the extent shown by
CC', will plainly be the amount of the original ordi-
nate with the entire throw deducted. The re-
sultant at B will be the original ordinate at that
point with one-half the throw made at C added,
and the same will be true of the resultant at D.
This correction, which may be called the "half-
function of the throw," is equal to the line FF'. The
resultant at C would thus become the line C'G,
and at B the line BF'. On the other hand, if the curve
were shifted outward at C to include the point
C", the ordinate at C would be increased by the
full amount of the throw at that point, and the
ordinates at B and D would be decreased by half
the amount of this throw. The distance to be sub-
tracted from the ordinate at B or D is shown in
the figure as FF", and the resultant at C is the
line C"G, and at B is the line BF".

General Rule for the Effect of Throwing— The
general rule may now be stated and should be per-
fectly clear. Whenever the term "throw" is used
in this work it will mean the distance that the
curve is to be moved at any one point, and the
term "resultant" will mean the ordinate that would
result from a throw at an adjacent point. The
throwing of the curve at one point causes the ordi-
nate at that point to increase or decrease by the full
amount of the throw according as the throw is out-

RELINING CURVES WITH A STRING

7\.'ard or inward; and also causes the ordinates of the
tivo adjacent points to correspondingly decrease or
increase by half the amount of the throw, the effect
being an increase when the throw is inward and a
decrease when the throw is outward. In exceptional
cases, when the curve is badly out of line, the applied
inward throw or half -function of outward throw may
exceed the ordinatc or resultant, when the smaller
figure must be subtracted from the larger and a minus
value be given the resultant. This means that such
resultant must be subtracted where ordinarily it would
l^e added in any succeeding process.

Five Operations in String Lining — The relining
of a curve with a string consists of five successive
steps, which are as follows : 1st, the preliminary
test ; 2d, the study of the locality ; 3rd, the diag-
nosis; 4th, the solution; 5th, the application. All
these steps are important, and should be conducted
with care. Fine accuracy is not as essential as
the avoidance of distinct errors. The preliminary
test is made with a proper kind of string, which
should be as thin as will withstand drawing en-
tirely taut. The measurements should be taken
with care and no misreading made, as one false
ordinate will destroy the value of the adjustment,
at least for the group in which it occurs.

The study of the locality is not only important as a
safety measure to determine what can be done, but
it shows to the practical eye of the expert foreman
just what corrections appear to be necessary, although
of course it would not determine their extent. The

SIMPLIFIED CURVE AND SWITCH WORK

detailed study of the curve, which is called the diag-
nosis, bears the same relation to the curve adjustment
that the physician's study of a case does to the art
of healing. The solution is a practical means of de-
termining with the least expense of time and labor
the exact corrections necessary. The application gives
some hints as to the most convenient manner of per-
forming- the actual work of lining the curve.

CHAPTER II.
PRELIMINARY STUDY OF THE CURVE.

4. THE TEST WITH A STRING.

It is desirable in all cases that slight defects
in the line of the curve be corrected as far as possi-
ble by eye, before the string is used and the test
ordinates measured. This will not only lighten the
labor of the solution, but will facilitate the rinding
of the best solution. (If this is not done before-
hand, detailed adjustments may be made in the
original notes with the object of establishing groups
of ordinates that will form a practical solution.
But then care would have to be taken to correct
the resulting throws in accordance with the pre-
liminary adjustment.)

Accuracy — The ordinates should be measured
to the nearest one-eighth inch. In the solution,
when taking half the throw to apply as a correc-
tion at the adjacent points, if the throw should be
an odd number of eighths, as % or % in., it is proper
to use the nearest one-eighth above or below as
best suits the case. The engineer might prefer to
employ decimals of a foot, and the nearest one-
hundredth foot should then be used. It is generally
found preferable to adopt inches, because the ordi-
nates will nearly always be taken by the foreman,
and the lining of the curve done later by him, and
he can most easily make his measurements in
inches.

SIMPLIFIED CURVE AND SWITCH WORK

Length of String — The length of string may be
62 ft. for branch-line curves, and may vary between
62 ft. and 100 ft. for main-line curves. It is some-
times useful to fix the length of the string so that
a station may occur at each full elevation point.
Before the ordinates are measured, marks should
be made entirely around the curve at points one-
half ,the string length apart, these being consecu-
tively numbered for future use. The stations
should extend as far as there is any curvature,
since it is equally important to have the easements
or spirals in proper position.

Common Error — A common error of the inex-
perienced foreman is to take the ordinates by mov-
ing around the curve a full string length, instead of
a half string length at a time. This, of course, ren-
ders the test of no use. While measuring the ordi-
nates, notes should be made of the amount of the
superelevation and the points where it begins and
where the full elevation is reached; also of any
obstructions which would prevent lining the track
in either direction.

5. THE STUDY OF THE LOCALITY.

It is not only a distinct advantage, but desirable
as a safety measure, that the supervisor or road-
master, as well as the foreman, should observe con-
ditions at the curve before the solution is finished,
and preferably^ before it is begun ; in other words,
before the throws for the different stations have
been figured out and finally determined upon. On

PRELIMINARY STUDY OF THE CURVE

double- and multiple-track roads, especially those
with track centers close to 12 ft., the leeway should
be known so that the safety of the parallel move-
ments will not be endangered by the lining. On
many branch lines, particularly those that parallel
river courses, the present clearances with rock
bluffs are barely sufficient, and any encroachment
by the subsequent shifting might be more or less
dangerous. The physical features of the situa-
tion should be fully known, so that the necessary
adjustments can be provided for.

Very many of the simpler cases of curve adjust-
ment will be disposed of by the supervisor upon
the occasion of his regular trips to the various
points where his subdivision forces are engaged,
and the attentive foreman will thus observe the
direct application of the rules he has studied.

6. THE DIAGNOSIS OF THE CURVE.

Figuring the Mean Ordinates — The determina-
tion of the right treatment for a curve, which op-
eration may be called the "diagnosis," is the most
important part of the proceeding. The first step
in this determination is to ascertain the mean or
average ordinate for the body of the curve. Be-
fore this can be figured it is necessary to cut off
the ordinates at the ends of the curve, which
will plainly belong to the easements of the curve.
The remaining ordinates, which constitute the body
of the curve, are then carefully added together.
The sum divided by the number of ordinates added

SIMPLIFIED CURVE AND SWITCH WORK

will give the average or "mean" ordinate. If the
whole number in each of the ordinates is the same,
the fractions only need be considered. These may
all be reduced to eighths, and their sum divided by
the number of ordinates used will give the frac-
tion to place after the uniform whole number to
supply the mean ordinate.

Easement or Spiral — An easement or spiral must
next be designed or selected (See Article 13) to fit
the average ordinate, and the application of the
easement or spiral at the ends may then cause suf-
ficient change in the body of the curve to require a
different mean ordinate, and a consequent new de-
sign or selection of the easement or spiral. It will
nearly always be found preferable to dispose of
the adjustments necessary for the spiral before
those of the body of the curve are attempted. To
facilitate this the proposed ordinates for the ease-
ments should be written in beside the original or-
dinates with which they most nearly agree.

Sharp and Flat Places — The next step is to sep-
arate the curve into its sharp and flat places. These
several groups will consist essentially of ordinates
which on the ends are similar, and either less or
greater than the average ; and which between these,
or at the middle, are the direct opposite in value
of those on the ends. That is, each sharp spot
must have a flat spot either side of it to absorb
the effect of the inward throw necessary, and each
flat spot must have a sharp spot on either side to
receive the outward throw necessary. These sharp

PRELIMINARY STUDY OF THE CURVE

and flat places must have a mean which is in prac-
tical agreement with the general mean, and they
must be balanced in order to form a series that
will be possible of adjustment.

For example, if the sum of the errors of the
sharp place is 2 in., the sums of the errors of the
two accompanying flat places must be approxi-
mately equal and their combined sum equal to
2 in. When this exact balance of positive and nega-
tive error does not obtain, adjacent throw must be
had to render the series symmetrical. In testing a
series to see if the errors balance, it is useful to
write the several errors of each end of a selected
group with their sums, which should be equal or
nearly so ; and, separately, the errors of the middle
of the group with their sum, which should equal
the combined sums of the errors of the ends.

This examination of the curve is necessary to
disclose a general deficiency, which may appear at
first glance as merely a permissible inaccuracy in
detail. Thus, although the Vs nas been found to
furnish a satisfactory margin of correctness, a suc-
cession of ordinates y% in. in error, accompanied by
the requisite group on either side % in. in error in
the opposite direction, might require a substantial
throw for proper adjustment. A careful study of
the examples given will throw further light upon
this feature of curve solution.

CHAPTER III.
THE SOLUTION OF STRING-LINING PROBLEMS.

7. RULES FOR SOLVING CURVE PROBLEMS

The solution is based on the general proposition
that : for an assemblage of ordinates, wherein the
first and last ordinates are below the mean and
the middle ones above it, the throw is inward; and
where the first and last ordinates are above the
mean and the middle ones below it, the throw is
outward.

Rule for Determining Throw — While no exact
relation exists between error and correction, it will
be found that the throzv at the middle of a series is
approximately equal to the sum of the errors both
above and below the mean of the series; or to twice
the sum either of the errors above or of those below
the mean. If the sum of all the errors is employed
the working mean may be used ; if double the sum
of the errors one side or the other, the exact mean
must be used. This rule is practically exact when
the number of ordinates in a series is odd. When
the number of ordinates is even the throw will be
slightly more at the point next to the middle in the
half that requires the greater correction ; and in
the other half the throw will be slightly less.

After applying the computed correction to
the middle, the solution should progress to-
ward each end in turn, bearing in mind,

SOLUTION OF STRING-LINING PROBLEMS

first, that the sum of the throws at the two points on
. cither side of the middle must be equal to twice the
difference between the resultant at the middle and the
adopted mean; and then, that each succeeding throw
must be such as to make the resultant nearer the mid-
dle c'qual to this mean; and, finally, that the resultant
at the third station from either end of the group must
be approximately equal to the end ordinate, so that
the final throiv at the station between them will cor-
rect all three points at once.

Ideal Easement — In the course of the solution
due regard must be given to the easements of the
curve. The most satisfactory spiral is obtained by
diminishing the full ordinate a certain number of
units for the ordinate at the end station of the body
of the curve, and one unit less for the ordinate at
each successive station in turn. The detailed
method of determining the value of the unit is de-
scribed under the article headed "Spiral by Mid-
dle Ordinates." The maximum number of units
will depend upon the amount of superelevation and
its rate of decrease, and should be one less than
the number of stations in the run-off. The example
given below is from an actual case, (analyzed
farther on), and is for a 3 deg. curve and 100 ft.
chords. The maximum number of units is seven,
and each has a value of -fa in., producing ordi-
nates as follows: 8, 6, 4^4, 2%, ls/8, % and J4 in.
An example is also given of a spiral between the
two parts of a compound curve, taken from the
same case, in which a 3-deg. curve is joined to

SIMPLIFIED CURVE AND SWITCH WORK

a 1-deg. 50-min. curve, with resulting ordinates of:
8, 6J4, 5^4 and 4% in. In this case the maximum
number of units is three and the value of the unit

A in-
Practical Easement — These are examples of the
ideal easement, but it should be noted that the
spiral curve admits of some modification on its
lighter portion. An example is given of the ease-
ment in another actual case, which is that of a
main line curve carrying a daily traffic of 250 trains
at an authorized speed of 50 miles per hour. The
deflections are from a 75-ft. string and are as fol-
lows :

Degree 5' 10' 15' 20' 25' 30' 35'

Ordinate % l/4 3/s V* 5/s 3/4 7/s

Superelevation....^ Y4 l*/s iy2 17/8 2*/4 25/8

45' 1° 1°21' 1°47' 2°17' 2°52' 3°33' 4°19' 4°19'

1^ 1^ 2 25/8 33/8 4.y4 V/4 63/s W/8

3 33/6 33/4 4*/s 4y2 47/s V/4 5S/8 Q

The degree of curve at the several points on the ease-
ment is shown above the ordinates, and the superele-
vations are shown below them. It will be noted that
the full elevation is attained at a point on the body
of the curve two stations beyond the end of the ease-
ment. The run-off is carried through 16 stations at a
uniform rate of 1 in. to 100 ft.

Errors in Designing Easements — The worst possi-
ble error, and a not uncommon one, is to make the
ordinates in the easement decrease at a uniform rate.
This practice is responsible for the deficiencies notice-
able at the ends of curves which are otherwise per-
fectly alined and excellently maintained. The ordi-

SOLUTION OF STRING-LINING PROBLEMS

nates in the first of the above cases if designed in this
incorrect manner would be as follows: 7%, 6^4,
4}/2, 3%, 2%, lys in. A comparison of these figures
with the true spiral shows the wide variation of
the two. In the last case cited, the ordinates by the
false method would be the same as the figures for
superelevation. It is readily seen that at the point
where an ordinate of y% in. would occur, indicating
a curvature of 0 deg. 15 min., only y% in. of super-
elevation would obtain, and this certainly is insuffi-
cient for high speed. Farther on the spiral curve is
fully described and a method given for its applica-
tion both by the instrument and the string.

8. EXAMPLES IN CURVE SOLUTION.

The first five examples illustrate the elementary
principles in the string-lining of curves, and further
examples are given in all of which the various
processes of the solution are fully described. A
final example is given in which every feature of curve
adjustment is illustrated.

In the solutions the throw is distinguished by a
circle enclosing it; an arrow indicates the direction
of the throw, (to the left for inward throw and to
the right for outward throw) ; and a letter, when
used, indicates the order in. which the corrections
are applied, a hexagon enclosing the station number
indicates the full elevation point, and a rectangle the
level point.

Examples 1 to 4 — These examples are quite sim-
ple, and the successive steps will be minutely de-

SIMPLIFIED CURVE AND SWITCH WORK

scribed in order that every detail of the solution
may be fully understood. It is presumed the dia-
gram in Fig. 1 has been studied, and the terms
"throw" and "resultant," as used, are entirely clear.
An inspection of the group of five ordinates in
Examples 1 and 2 discloses that both form a perfect
series, in which the ordinates either side the middle
are exactly balanced; and a simple calculation
shows the mean of the ordinates to be 1^4 in. In
Example 1, the end ordinates are less and the
intermediate ordinate is greater than the mean, and the
indicated throw, therefore, inward; while in Ex-
ample 2 the end ordinates are greater and the inter-
mediate ordinate is less, and the indicated throw,
therefore, outward.

In Example 1, the average ordinate for the whole
curve is 1^4 in.; by comparing the actual ordinates
(column 2, example 1) with 1^4 in., the errors
are, in succession, ^4 in., 0, l/2 in., 0, l/+ in,, and
their arithmetical sum is 1 in., which is the throw
at the middle of the series. This inward throw at
Sta. 3 diminishes the ordinate at that station to a
resultant 1J4 in., and the effect of this inward
throw is to increase the ordinates at Sta. 2 and Sta.
4 one-half the amount of the throw, or l/2 in., and
the resultants at those two points thus become
2*/4 in.

The sum of the throws at Sta. 2 and Sta. 4 must
equal twice the difference between the resultant at
Sta. 3 (ll/4 in.), and the desired final ordinate
in-)> and will therefore equal 1 in.; and as
32

SOLUTION OF STRING-LINING PROBLEMS

both halves of the series are symmetrical, the
throws at Sta. 2 and Sta. 4 will be equal, and will
each be j£ in. Applying the inward throw of y2
in. at Sta. 2, the resultant 2^4 m- is reduced to
the desired mean, and the ordinate at Sta. 1 is in-
creased by one-half of J/£ in., or Y^ in., bringing
it to the desired mean and at the same time the first
resultant at Sta. 3 'is also increased by J4 m- to
a new resultant \y2 in. It will now be noted
that this resultant equals the last ordinate in the

EXAMPLE I

EXAMPLE 2.

Station

Ordinate

Solution

Station

Ordinote

Solution

}

2i<T>/J

lib®* 8

"(T)a/4 1*2 /j

a(T)+?} 2 /|

2i*(j)clj

/*C0*/J

EXAMPLE 3.

EXAMPLE 4.

Station

(Mule

Solution

Station

Ordinate

Solution

1-2

/4*(J)*-/|

^l^®!/!

</d>? /i

<J)^7/J /|

;| /|

2 /I

2J-»(J)^/|

lid®*!*

</>tf // /I

1L4

cQyti 2 n

^i<D^/l

/^«ffX/J

Examples 1 to 4, Problems in String Lining.

series, as should be the case, and the final inward
throw of y2 in. at Sta. 4 reduces the resultant at
Sta. 4 to the desired mean, and at the same time

SIMPLIFIED CURVE AND SWITCH WORK

increases the second resultant at Sta. 3 and the ordi-
nate at Sta. 5 to the desired mean.

The processes in Example 2 are exactly similar
except that the outward throws increase the suc-
cessive ordinates and resultants, and the effect is
to decrease the adjacent ordinates or resultants.
It will be noted that the errors in Example 2 are
also Y^ in., 0, Y-2 in., 0 and l/^ in., and the middle
throw 1 in., as in Example 1.

Examples 3 and 4 illustrate the case where an
adjacent throw is necessary to render the groups
Sta. 14 to Sta. 18 and Sta. 22 to Sta. 26 each a prac-
tical series. As will be seen readily it only needs
that the ordinate at Sta. 14 be reduced to lJ/£ in.,
and that at Sta. 22 increased to 2 in. to render both
an evenly balanced series.

The half function of an outward throw of l/2 in.
at Sta. 13, and of an inward throw of J-£ in. at
Sta. 21, reduces the ordinate at Sta. 14 and increases
the ordinate at Sta. 22 to the required resultants ;
and incidentally renders the resultants at Sta. 13
and Sta. 21 equal respectively to the ordinates at
Sta. 11 and Sta. 19, so that a final outward throw
of y* in. at Sta. 12 and inward throw of y2 in.
at Sta. 20 renders the first three resultants in each
example equal to the desired mean.

After this process the remaining members in the
two examples become identical with Examples 1
and 2 and their final solution is exactly similar.

If these four examples are now considered as
combined into one problem it will be seen how im-

SOLUTION OF STRING-LINING PROBLEMS

portant is the question of determining by the pre-
liminary study of the curve the treatment to be
accorded. The faculty of being able to do this
quickly is rapidly acquired by practice.

Example 5 — Example 5 has been selected because
it illustrates the making of a spiral for the ends and
because it contains a typical sharp and flat place.

tXAMPLL 5. (U^1)' Curve with 100' String.}

Sta

Ord.

Solution

Sta

Ord. Solution

Sta

Ord. Solution

Example 5. Problems in String Lining.

The spiral for a curve whose ordinate is 2 in. may
decrease by 5, 4, 3, 2 and 1 units, respectively, of
value y$ in. each, with final figures as obtained, viz. :
3, 1%, 7/s, T/2, K and y8 in.

The sharp place between Sta. 8 and Sta. 16 has
a total of positive errors of y% in., and the middle
throw at Sta. 12 is twice this, or 1% in. l"he sum
of the two throws at Sta. 11 and Sta. 13 must be
1^8 in. to make the final resultant at Sta. 12, 2 in.;
and the throw at Sta. 10 must be in. to make the

SIMPLIFIED CURVE AND SWITCH WORK

final resultant at Sta. 11, 2 in., and also to make the
resultant at Sta. 10 nearly equal to the ordinate at
Sta. 8. The throw must be ^s in. at Sta. 14 to
make the final resultant at Sta. 13, 2 in. and to make
the resultant at Sta. 14 equal to the ordinate at
Sta. 16. A final throw of $i in. at Sta. 9 and %
in. at Sta. 15 completes the correction of the series.
The flat place between Sta. 17 and Sta. 25 has a
total of positive errors of y± in. and the middle

Sta

Ord.

Solution

ii
n

Ik
-]

-I

Jfa

15
14
15
16

17
18

V
20
El
22
21
24

Ord

Solution

Example 6. 0 Deg. 20 Min. Curve with 10(

throw at Sta. 21 is twice this, or lV2 in. The sum
of the two throws at Sta. 20 and Sfa. 22 must be
2J/2 in. to make the final resultant at Sta. 21
equal 2 in. ; and the throws at Sta. 19 and Sta. 23

SOLUTION OF STRING-LINING PROBLEMS

must each be % in. to make the final resultants at
Sta. 20 and Sta. 22 equal 2 in., and to make the
resultants at Sta. 19 and Sta. 23 equal or nearly
equal to the ordinates at Sta. 17 and Sta. 25. A
final throw of ^ in. at Sta. 18 and Sta. 24 completes
the correction of the series.

The adjustment of the spirals involves only de-
tailed correction, and does not follow any set rule.
It is apparent there is a sharp place at Sta. 2 and

Sta. 3 and at Sta. 27 and 28,
and that there is similarity
a flat place at Sta. 5 and
Sta. 6 and at Sta. 30 and
Sta. 31.

Example 6 — Example 6
has been selected for solu-
tion as requiring the use of
all the above rules. A study
of this curve shows : that
the easement Sta. 1 to Sta.
3 is not quite a true spiral ;
that there is a sharp place
between Sta. 5 and Sta. 9;
that both an outward
throw on one side and an
inward throw on the other
will be necessary to elim-
inate this sharp place ; that there is a flat place be-
tween Sta. 8 and Sta. 17; that there is a flat place
between Sta. 18 and Sta. 25; that there is a sharp
place between Sta. 28 and Sta. 33 ; and that the cor-

Sta

Ord

Solution

2
6

*©

2
8

{j)

i
8

Ft. String.

SIMPLIFIED CURVE AND SWITCH WORK

rection of the latter must also restore the spiral fea-
ture between Sta. 33 and 35.

The average for the body of the curve is ^f
in., but in line with the adopted standard it will
be proper to work to either ^4 m- or ~/$ in. Evi-
dently since Sta. 3 and Sta. 4 are less than the mean,
while Sta. 5, Sta. 6 and Sta. 7 are greater, two other
stations below the mean are needed to complete the
series. But Sta. 8 and Sta. 9 will also be a part of
a series requiring outward throw. We must esti-
mate for the time being the value of the resultants
at Sta. 8 and Sta. 9 after the prospective outward
throws at Sta. 9 and Sta. 10, which resultants we
assume may become equal severally to the ordi-
nates at Sta. 3 and Sta. 4. The average of this
series is then % in. and, applying the rule, the
sum of the positive errors being 1/4 in., the correc-
tion at Sta. 6 is \y2 in.

It is apparent that the sum of the throws at Sta.
5 and Sta. 7 must be 2^4 'm-> and that the use of
1 in., at Sta. 5 and 1J4 m- at Sta. 7 will render
the resultant at these two points equal to the ordi-
nate at Sta. 3 and the resultant at Sta. 9, respec-
tively; and that the completed solution will attain
the desired average.

Noting that the resultants at Sta. 8 and 9, after the
inward throw of y2 in. at Sta. 8, are 1^ in. and
1^4 in-> we find that the mean of the series Sta.
8 to Sta. 18 is 24 m-> and that the sum of the posi-
tive errors is 1% in.; the throw should be twice
this or 2^4 in. at Sta. 13. The resultant at Sta.

SOLUTION OF STRING-LINING PROBLEMS

13 is 3y2 in., and the sum of the throws at Sta.
12 and Sta. 14 must be equal to 5J^ in. in order to
make the final resultant fy in. at Sta. 13.

As greater throw is evidently necessary for the
first half we try 2J/8 in. at Sta. 12 and 2ft at
Sta. 14. It is now easy to follow to the end ; the
next throw must be 2ft in. to reduce the resultant
at Sta. 12 to ^4 in., and the next 2ft in. to re-
duce the resultant at Sta. 11 to ^4 in. The resul-
tant at Sta. 10 now approximates the resultant at
Sta. 8, and a final throw of ft in. at Sta. 9 renders
the resultant at this station and also at Sta. 8 and
Sta. 10, % in., and confirms the correctness of
the resultants assumed for Sta. 8 and Sta. 9 in the'
beginning of the solution. We follow a similar
method between Sta. 14 and Sta. 18, when, the re-
sultant for Sta. 16 approximating the ordinate
at Sta. 18, the last throw of ft in. completes the cor-
rection.

The correction of the series from Sta. 18 to Sta.
25, the average ordinate of which is ft in. and sum
of positive errors -JJ in., with maximum correction
therefore I ft in., follows the general lines already
described.

The elimination of the sharp place, Sta. 28 to Sta.
33 presents the case of a series with an even num-
ber of members. The computed maximum throw
is 3/4 in., but as the higher stations require greater
correction, % in. is adopted for Sta. 31, and ft in.
for Sta. 30.

The resultant at Sta. 33 completes a practical

SIMPLIFIED CURVE AND SWITCH WORK

•33-

oo oo

'«iy H

-»f@

O . »OKO MOO 'OIOO

-0,0

SOLUTION OF STRING-LINING PROBLEMS

spiral, and a slight detail throw at Sta. 2 accom-
plishes the same result.

Example 7 — The problem of the reversed curve
in Example 7 is given because it illustrates the util-
ity of the string method in providing practical
easements in an extreme case. The location map
gives the following data for the curves : 1493+74.8,
P. C. 7-°R., 1498+42.8, P. T., 1499+78.5, P. C. 8°L,
1506+50, P. T. It will be observed that a tangent
length of but 135.7 ft. was provided between the
curves upon which to run off a superelevation of
5 in. for the one curve and 5^ in. for the other,
these being proper for the speed prescribed by the
time-table, namely, 40 miles per hour.

An effort had previously been made to adjust the
curves, with fair results as regards the body of the
curves, but without success for the easements be-
tween them. The run-off of the lighter curve had
been commenced at Sta. 16 and ended at Sta. 22
and the approach of the other curve started at this
point and completed at Sta. 33. The effect of this
was to establish at Sta. 18 and Sta. 28, where, as
the curves were then alined, the full elevation
should have occurred, elevations respectively of
%y2 in. and 3% m-> which virtually limited the speed
used to 30 miles per hour.

The general problems of the two curves are quite
similar and, as always occurs when easements not
provided for are added, necessitated the sharpen-
ing of the curves throughout, which in both cases
amounted to Y± of one degree, or 3 per cent of the

SIMPLIFIED CURVE AND SWITCH WORK

final degree. The further problem in each was to
utilize a sharp spot for throwing the curves out-
ward as much as possible, thus introducing a flat-
spot near the end of the main curve which was
needed to receive a heavy inward throw on the ends,
the effect of which would be to move the ends of
the main curve one station farther from the revers-
ing point. The advantage to be thus gained consist-
ed in providing additional length of easement needed
to modify the rate of the run-off, which was finally
established as 1 in. to 36 ft. for both curves.

The detailed corrections preceding Sta. 13 and
following Sta. 38 are general and need no expla-
nation. The necessary sharp place on the first
curve occurs at Sta. 13 and the outward throws
leave the resultant at Sta. 16 equal to 6^ in.,
which with the flat place at Sta. 23 permits of the
inward throw between these points. The easement
between Sta. 19 and Sta. 23 is readily designed with
a maximum of 6 units and a value of JJ in. for
the unit, and supplies ordinates as follows : 5 J^,
3J4 %*/&, 1, 3/8 in., the sum of which is 12ys in.
The sum of the resultant at Sta. 16 and the
seven original ordinates following is 35 in. The
test of whether the projected easement is pos-
sible will lie in this sum being approximately equal
to the sum of the ordinates in the easement and the
normal ordinates for the remaining- three stations,
which is found to be the case.

The ideal ordinates of the easement should be
placed opposite their respective stations, when the

SOLUTION OF STRING-LINING PROBLEMS

successive errors between Sta. 16 and Sta. 23 are
-ft — T/8 — KH-1&+'1,+J4 ,— */2 — ft in., the arith-
metical sum of which is 4^ in. As the number of
stations in the series is even, this will be the
correction at the exact middle of the series and the
use of 4% in. at Sta. 19 and 4^ in. at Sta. 20 is
seen to furnish satisfactory adjustment.

The required sharp place in the second curve is
found between Sta. 36 and Sta. 38. As the outward
throw found possible is considerable it will be in-
structive to trace the correction through the series.
Sta. 30, already flat, will plainly be the end of the
series of outward throw and the point to receive
the prospective inward throw preceding it. Since
Sta. 36 and Sta. 38 together have positive error
of y% in., it will be necessary for the inward throw
at Sta. 29 to be large enough to render the resul-
tant from this source at Sta. 30 equal to 8^4 in., or
there would otherwise not be a practical series for
the outward throw. The errors between Sta. 30 and
Sta. 36 are then : +^ ,— ft —ft — ft,+ft,+% in., the
arithmetical sum of which is 2% in., which is the
throw at Sta. 34. The resultant, 10 in., at this station
exceeds the desired final ordinate by 1^4 in.', which
last figure therefore represents the approximate
throw at the adjacent points. The resultants at Sta.
33 and Sta. 35 exceed the mean ordinate by J/£ in. and
ft in. respectively and the throws at Sta. 32 and Sta.
36 are twice these or 1^ in. and % in. Final throws
of ft in. at Sta. 31 and ft in. at Sta. 37 complete the
correction of the series, except that the resultant

SIMPLIFIED CURVE AND SWITCH WORK

at Sta. 30 is reduced to ll/2 in. The flat places at
Sta. 30 and at Sta. 23, Sta. 24 and Sta. 25 furnish
the desired opportunity to make the inward throw.

The easement for this case follows the same gen-
eral lines as for the preceding case except that the
ordinate being greater and the maximum number of
units the same, the value of the unit will be larger
and it is found to be 25/64 in. The ordinates of
the proposed easement are. %, Iji, %H> 3%> 5% in.
The sum of the ordinates between Sta. 23 and Sta. 29
and the resultant at Sta. 30 is 38% in., while the sum
of the three uniform ordinates and the ordinates of
the projected easement is also 38% in., and the ease-
ment is therefore practicable.

Placing the proposed ordinates for the easement
opposite the respective stations, the errors between
Sta. 23 and Sta. 30 are in their order — %, — J/g, — ]/%,
+%,+2I/i, — %, — J4, — 3A in-, and their arithmetical
sum is 5 in. But the number of stations again
being even this will be the correction for the exact
middle of the series and the corrections at Sta. 26
and Sta. 27 will lie above and below this figure.
The use of 3% in. at Sta. 26 and 5% in. at Sta. 27
and proper succeeding corrections, effects the de-
sired result.

At first thought it might seem that the presence
of a % in. ordinate at Sta. 23 for both easements
makes the two curves encroach upon each other;
but in fact the curve of each ends at this station
and the ordinate attaches to the curvature beyond
in each case.

SOLUTION OF STRING-LINING PROBLEMS

Referring back to the original notes of the aline-
ment, it is seen that the several adjustments, to-
gether with the utilization of the plain principles
of mechanics, which permits the full elevation to
be established two stations from the end of the
main curve, have resulted in an extension of the
available distance for running off the combined
superelevations from 136 ft. to 372 ft. This makes
possible the use of 5 in. and 5^ in. superelevation,
respectively, which can be run off at a safe rate of
1 in. to 36 ft. A speed of 40 miles per hour is then
both safe and comfortable, whereas the original
alinement, with full elevation at the P. C. and the
run-off made at nearly the same rate, would have
permitted a combined superelevation of but 5 in.,
and the curves would have been only fit for opera-
tion at 30 miles per hour.

Example 8 — The solution of the reversed curve
in Example 8 illustrates the utility of the string
method in effecting a considerable change whereby
a very unfavorable alinement at the point of reverse
was corrected and an increase in the supereleva-
tion made possible. These adjustments operated
to withdraAv a speed restriction of 15 miles per hour
which had always existed and which required con-
stant maintenance of slow signals. The improve-
ment was especially important because the point
was at one end of the ruling grade of the branch
road.

A careful study of the original ordinates will
show that, although some detailed correction was

SIMPLIFIED CURVE AND SWITCH WORK

— - C\J

r«i ro

•es?

0 —•

to,

SOLUTION OF STRING-LINING PROBLEMS

required upon the body of the curve, the principal
defect was the lack of sufficient easement between
the curves to properly run off the combined super-
elevation that the general branch speed of 40 miles
per hour required. The original alinement indi-
cates the degree of the one curve as 8 deg. and of
the other as '4 deg., with a tangent distance of but
105 ft. between them. Previous adjustments had
resulted in an extension of the available run-off
distance to a total of 6 stations, which allowed a
combined superelevation of 5 in. for the two curves.
Considering the maximum curvature of 10 deg. on
the one and of 5 deg. on the other, this would suf-
fice~for a speed of 28 miles per hour. In order, how-
ever, to provide for a speed of 40 miles per hour,
requiring combined superelevation of iy2 in. for the
two curves, it was necessary to extend the run-oft
distance two more stations.

It is plain that this cannot all be done by any
scheme of detailed correction at the immediate point
of reverse, but an extension of one station was thus
effected. The only way remaining is to sharpen
the curves, which would of course shorten the tan-
gent distance of each ; but the 8 deg. curvature is
already the maximum for 40-mile speed. It is thus
only possible to make this adjustment through the
lighter curve, and it is seen that a maximum throw
of 13^4 in. not only eliminates the sharp spot at
Sta. 19, but extends the available run-off one sta-
tion farther and completes the attainment of the
result that was sought.

SIMPLIFIED CURVE AND SWITCH WORK

EXAMPLE 9

Sta.

Ord

Solution

Thrws

7
8
9
10
II
12
15
14

/6
17
Id

Preliminary
Adjustment

EXAMPLE 10

sta

Qrz/.

Solution

Errors

24
25
26

28
29
50

52
55
54

5i
51

+ 2

+ 4+7 i

Station 30

-9

-2
-2

Examples 9 and 10. Preliminary Adjustment; Error and Correc-
tion.

SOLUTION OF STRING-LINING PROBLEMS

Example 9 — The problem of Example 9 is some-
what odd but by no means rare in curve adjustment,
especially where a rotighing-in of the line has not
been arranged for, before the test ordinates were
taken. It is plain that the presence of the flat spot
at Sta. 13 seriously interferes with the general ad-
justment of the curve, but that when the detailed
adjustment is made the general correction is quite
apparent. It will be noted that in the preliminary
correction the aim was to first draw the curve into
an ellipitical form, as that is the basic requirement
in this system of curve adjustment. The need for
this preliminary correction occurs more commonly
in light curves than in sharp ones. It is necessary
that care be exercised to add the partial throws to-
gether when they are in the same direction, or to
subtract them when in an opposite direction, to
obtain the final resultant correction.

Example 10 — The problem of this reversed curve
is instructive as showing the development of an
easement of the minimum practical length, permit-
ting a run-off at the safe rate of 1 in. to 36 ft.,
notwithstanding the exceedingly short extent of
tangent provided in the original alinement, which
was but 65 ft. between a 6 deg. and a 4 deg. curve.
It will be seen that 124 ft. of easement and 248 ft.
of run-off is available, which is sufficient to take
care of the combined superelevation of 7 in. required
by the curves. Before the adjustment, no more
than 6*4 in- of combined superelevation was prac-
ticable, and this was only enough for 35 miles per

SIMPLIFIED CURVE AND SWITCH WORK

hour; besides, the difference in ordinates at one
station of 3^4 in. gave the same effect as a 7 deg.
30 min. curve without easement, and such a con-
dition is improper.

9. APPLICATION OF THE CORRECTIONS.

When the various corrections have been figured
it only remains to make the several throws. Any
further use of the string is generally unnecessary.
The figures for the throws, if worked out by the
supervisor, may even be telephoned the foreman
with confidence that the result will be a correct
alinement.

Use of Pole — For recording the original position
of the track and for measuring the extent of the
throws, a method by the use of a pole is the most
generally satisfactory one. The pole should be of
white pine planed on the four sides and should be
about 11 ft. long. It is placed against the web 01
the rail of an adjoining track and at right angles
with the rail, and the position of the gage line is
then marked upon it. This is done for each of the
several points that are to be shifted. The number
assigned to the respective station is written over
these marks for identification during the course of
the lining. In order to avoid interference of the
several marks and throws, it is desirable to use both
ends of the pole, eight distinct markings being thus
possible. But since tracks are seldom exactly par-
allel, many more indications may be made without
confusion, and the record of an entire curve may

SOLUTION OF STRING LINING PROBLEMS

often be carried upon the pole at one time. It will
sometimes be found to render the method still more
convenient to add to the pole record, rnarks indicat-
ing the proposed as well as the present position of the
track.

Upon frequent trials with the pole the progress
of the lining will be noted, and the ultimate attain-
ment of the completed throw thus observed. The
pole record may be preserved for a day or two to
test the corrected line for slight defects that are
likely to occur while the track is becoming bedded
in its new position ; but when the throw is small
this will not be necessary.

Line Stakes — Sometimes stakes are set just in-
side the line of the high rail, being so placed that
upon completion of the realining the track will be
everywhere a uniform distance from the stakes.
This distance should not be less than 6 in. nor more
than 12 in. In the event of the solution being made
by the supervisor, he can give the foreman, in place
of figures for the throw at the various points, the
distances to set his stakes from the rail, adding 12
in. to the throws when they are inward, or sub-
tracting the throws from 12 in. when they are out-
ward.

The general use of stakes involves considerable
unnecessary labor, and has no advantage in any re-
spect over the pole method, except that on single
track stakes are indispensable. It is always per-
missible to use stakes if there is any question of
the correctness of the test ordinates, in order that

SIMPLIFIED CURVE AND SWITCH WORK

the proposed alinement may be proven with the
string before the lining is authorized. In special
cases, such as spike lining through switch connec-
tions or crossings, it is convenient to mark the
original position of the rail directly upon a tie from
which the spikes have been withdrawn. In such
lining the rule that quarter ordinates are three-
fourths the middle ordinate can be employed with
advantage.

CHAPTER IV.
SUPERELEVATION OF CURVES.

The matter of superelevation of curves is of
equal importance with the adjustment of the aline-
ment. The impracticability of employing a fixed
formula for superelevation has been demonstrated.
It is now recognized that the rule for equilibrium
gives too low an elevation for the lighter curves,
and too high an elevation for the sharper curves.
It is plainly desirable that the flanges of the wheels
shall be constantly in contact with the outer rail
of the track. If the motion on the curve were just
balanced, each slight irregularity in the line and
gage, or unevenness of the superelevation, would
cause the flanges to strike the inner and outer rail
alternately. This would introduce a decided dis-
comfort in riding. It is well known that the best
results are attained upon curves a little above 45
min., provided the line is good and the amount of
elevation just sufficient. This cannot be realized
upon the lighter curves, and it is for this reason
mainly that extremely light curves are unsatisfac-
tory.

The practical superelevation is developed for
both the easement and the body of the curve. As
the adjustment of the former by means of the spiral
is principally for the object of properly running off
the superelevation, the spiral is explained in the

SIMPLIFIED CURVE AND SWITCH WORK

next succeeding chapter. The method by ordinates
is relatively simple, but some practice is necessary
to be able at once to fit a working spiral to the
ordinates found, with the least possible throwing.
The method by the instrument will not be of direct
concern to the trackman, but the ease of its appli-
cation will leave the engineer no excuse for omit-
ting it in future locations.

The analysis of lining and elevation corrections
is of interest as showing the direct relation each
bears to the other. Remembering that light curves
require the greater comparative elevation, and ap-
preciating that the run-off must be made at some
regular rate, there is no alternative but to adopt
for the easements a curve that begins with flat
curvature and increases in a definite progression to
the full degree of curve.

10. APPROACH AND RUN-OFF OF CURVES.

After the curve has been realined and defective
easements corrected, it may be necessary to re-
surface the run-off; as the point of full elevation,
both from theoretical considerations and as a mat-
ter of experience, should generally be established
close to the station that is next to the last point
of full ordinate toward the middle of the curve,
provided the stations are not less than 30 ft. nor
more than 50 ft. apart. This is for the reason that
the force tending to throw the car outward, which
is called the centrifugal force, does not reach its
greatest effect until the car is wholly upon the

SUPERELEVATION OF CURVES

curve. It should be understood that the body of
the curve extends to the first station back of the
last point of full ordinate toward the ends of the
curve.

High-Speed Track — The approach and run-off of
curves in high-speed track should be placed in
proper relation with the curve of the easement, and
be so designed that the rate of increase or decrease
of elevation may be uniform and not greater than
y2 in. to 33 ft. The preferable rate is % in. to 33
ft., but for light curves l/\ in. to 33 ft. is quite satis-
factory.

Moderate Speed Track — The approach and run-
off in tracks operated at moderate speed, or in sid-
ings operated at low speed, may be made at a some-
what greater rate than y2 in. to 33 ft., but the rate
should never exceed 1 in. to 33 ft. Tests with mod-
ern equipment have shown that the side bearings
will foul when the rate is greater than 1^ in. to
33 ft., and the limit established provides for only
y2 in. defect in surface.

Limited-Speed Track — When a short run-off must
be used, and the speed is limited, a practical run-off
is obtained by making the elevation at the natural
point of curve one-half the full elevation. The
point of full elevation will then occur 30 ft. to 50
ft. beyond the point of curve, and the point of no
elevation will occur 30 ft. to 50 ft. back of the point
of curve. The elevation of the middle point back
of the point of curve should be slightly less than
one-fourth the full elevation, and that beyond the

SIMPLIFIED CURVE AND SWITCH WORK

point of curve slightly more than three-fourths
the full elevation. This will make the profile of the
elevated rail a vertical reversed curve and render
the run-off quite as easy for moderate speed as the
longer run-off is for high speed.

An example of a short run-off for a 2 deg. curve
with \y2 in. elevation, to be operated at 40 miles
per hour, is as follows : 0, level ; 0+20, J4 m- \
0+40 (P. C), # in.; 0+60, 1# in.; 0+80, lj£ in.

11. SUPERELEVATION OF BODY OF CURVES.

The maintenance of line on curves is dependent
upon a proper selection of superelevation both for
the body of the curve and for the easements. It is
not possible to make a formula that will apply alike
to all variations of curvature, for any theoretical
formula would apply only to the ideal curve. The
ideal curve is the one of greatest radius, or least
degree of curvature, wherein the slight changes due
to shifting under traffic are of minimum effect. For
high-speed main lines this is about 0 deg. 45 min.
and for branch lines about 1 deg. 30 min.

The distortion of a curve through traffic shifting
becomes greater as the degree of curve decreases.
Since superelevation should be adjusted to the cur-
vature that actually exists, manifestly a curve
should have the superelevation that would be prop-
er for the highest degree that might in fact be
found, instead of that which would be selected to
suit the assumed degree of the curve. Greater ele-
vation is therefore required by the lighter curves

SUPERELEVATION OF CURVES

than that determined by the theoretical formula of
mechanics.

Similarly, there is less superelevation needed for
the sharper curves than the theoretical formula
would indicate, because curves sharper than the
ideal suffer relatively less distortion under traffic
than lighter ones, and also because of the destruc-
tive effects from the slower traffic when the super-
elevation is excessive for such movement, and es-
pecially from theoretical considerations outlined in
the next paragraph.

Since the centrifugal force acts horizontally and
the component of this force along the plane of the
top of the rails diminishes as the degree of curve
(and with it the superelevation) increases; and
since, from the fact of the car body being pivoted
on supports near its ends, its center of gravity is
deflected inward, which deflection increases as the
degree of curve increases ; and since the component
of the centripetal force, which is developed by the
weight of the car and is the force tending to deflect
the car inward, increases with the degree of curve,
there is therefore by theory as well as experience
relatively less superelevation necessary for equili-
brium as the degree of curve increases.

Rule for Superelevation — An empirical rule has
been found which satisfies the requirements re-
ferred to and which has been amply tested in prac-
tice. Its usefulness depends upon the employment
of the actual measured degree, and not the some-

SIMPLIFIED CURVE AND SWITCH WORK

limes incorrectly recorded degree, and presumes
maintenance with reasonable fidelity.

In the table of superelevations there is shown a
series of arcs between 0 deg. 15 min. and 2 deg.,
in which the members increase progressively, the

TABLE

OF SUPERELEVATIONS.

Degree Constant Theo. Elev.

Prac. Elev. Max. Speed

15 min.

54 in.

1 in 70 miles per hour

20 min.

1 in.

154 in

70 miles per hour

30 min.

154 in.

2 in

70 miles per hour

45 min.

254 in

70 miles per hour

1 deg. 05 min.

354 in.

3 in

70 miles per hour

1 deg. 30 min.

5 in.

354 in

70 miles per hour

2 deg. 00 min.

654 in.

4 in

70 miles per hour

2 deg. 30 min.
3 deg. 00 min.

4
4

754 in.
(854) in.

454 in
5 in

68 miles per hour
65 miles per hour

3 deg. 30 min.

(9) in.

554 in

63 miles per hour

4 deg. 00 min.

(10) in.

6 in

61 miles per hour

4 deg. 30 min.

(1054) in.

654 in

60 miles per hour

5 deg. 00 min.

(1154) in.

7 in

59 miles per hour

TABLE OF PRACTICAL ELEVATIONS.

Degree

0° 15'

0° 20'

0° 25'

0° 30'

0° 35'

0° 45'

0° 55'

1° 05'

1° 30'

2° 00'

2° 30'

3° 00'

3° 30'

4° 00'

30'
00'
30'
00'
30'
00'
30'

8° 00'

\y2

2""

i"54'

15?

2*A

154

254

'iy2

254

2""

354

254

T~54"

354

254

„....

1 54

354

254

154

354

254

1 /4

3 ^a

2 54

354

254

454

354

254

354

454

354

first increment being 5 min. and each succeeding
increment 5 min. greater than the preceding one.
Opposite the smallest arc is placed the constant 10,
which represents so many ten-thousandths, and in

SUPERELEVATION OF CURVES

inverse order the numerals down to 4, which applies
to the largest arc in the series and to all curves
above 2 deg.

The proper superelevation in inches is obtained by
multiplying together the square of the limiting speed
in miles per hour, the degree of the curve and the con-
stant that applies, the nearest half-inch being used in
the final result.

The theoretical elevations in the appended table
were obtained by the use of the constant 6.6 for all
the degrees of curvature. This constant is derived
directly from the formula in mechanics, and is in
rather common use. The practical elevations were
obtained by the use of the several constants shown.
The apparent variance in result for the higher de-
grees of curvature really does not exist, since it is
customary to assume a lower rate of speed in figur-
ing for the sharper curves; but clearly such prac-
tice is objectionable because it lacks uniformity.
The empirical rule requires only that the limiting
speed shall be employed, which will always be fixed
by time-table rule. While the maximum speed
alone was used in the making of the first of the
two tables, it will be found that the empirical rule
furnishes equally satisfactory results for all speeds.
The second table shows the proper superelevations
in inches for various degrees of curve and for dif-
ferent limiting speeds in miles per hour.

Effect of Traffic — In determining the question of
superelevation full consideration should be given
the needs of the more important traffic. It may

SIMPLIFIED CURVE AND SWITCH WORK

sometimes be preferable, in the case of heavy-ton-
nage freight lines, to establish the superelevation
with reference to the slow traffic and limit the
movement of passenger trains or light engines to
the same rate of speed. On main lines carrying not
only high-speed passenger trains, but a considerable
number of freight trains, it is usual to confine the
freight traffic to separate tracks ; but as these tracks
must sometimes be used for passenger trains, a bal-
ance is obtained by restricting somewhat the speed
of the former and increasing that of the latter as
much as possible.

12. ANALYSIS OF LINING AND ELEVATION COR-
RECTION.

Example 11 is intended to show the application
of all the above methods in practice. The tangent
offsets have been computed for the average of the
curvature between each two adjoining stations, as
obtained from the respective middle ordinates of
those stations. It will be seen that in both ease-
ments the several offsets are in the approximate
ratios of the cubes of successive numerals, between
1 and 7 for the longer easement and 1 and 5 for
the shorter one. This satisfies the requirements of
the curve known as the cubic parabola considered
as being referred to coordinate axes. It will further
be noted that the arcs shown as average degree,
which are twice the deflection angles of the curve,
are in the ratios of the squares of successive numer-
als. This is a geometrical condition of the same

SUPERELEVATION OF CURVES

curve, and it is thus shown that the spiral whose
ordinates increase progressively is the cubic para-
bola. This curve has long been regarded as the
most efficient of all easement curves.

A comparison of the computed elevations with
those that would conform with a regular rate of
increase, confirms the correctness of the empirical
rule for superelevation. It will be noted that the
practical elevations are a mean of the computed
elevations on either side, as is proper from due con-
sideration of mechanical forces applied to a moving
railway car. The limiting speed for the curve
should be 65 miles per hour, and this requires that
the 3 deg. curve should have 5 in. elevation and the
1 deg. 50 min. curve 3J/2 in. elevation.

The curve of the spiral on the approach between
Sta. 2 and Sta. 4+50 increases in a regular progres-
sion by increments of 6^2 min. multiplied by the
numerals between 1 and 7 ; and the corresponding
ordinates increase regularly by increments of $% in.
multiplied by the same numerals, 1 to 7. The cur-
vature of the spiral between the two curves Sta.
7+50 to Sta. 8+50, increases by increments of
1, 2 and 3 times 12 min. respectively, while the or-
dinates increase by 1, 2 and 3 times T9g- in. The
curvature of the spiral on the run-off between Sta.
12+50 and Sta. 14 increases by 1 to 5 times iy2
min., while the ordinates increase by 1 to 5 times
T% in. These features further confirm the curves
as the cubic parabola. The rates of change in
curvature coordinate satisfactorily with the rates of

SIMPLIFIED CURVE AND SWITCH WORK

to Jo ON cvi ••-
O --» <\j IT} c\4

OOooOOOOoOO

C\i CVi -^ --,•-- . • — --.-~.~^--.~^

\O OQ OQ °o °O °O

to hr> f\j — .

lO Cvj f\|

ojOjfO»Oxl-sj-'^>iC)vS)vS)ls^N-oooo<rs<3\OO2;~^CNC^fr>

SUPERELEVATION OF CURVES

change in superelevation, which are 1J4 in- to 100
ft. on the ends, and 1 in. to 100 ft. between the
curves.

It will be noted in this example that the supple-
mentary rule which supplies the relation of error
to correction is equally applicable to the easements,
the only difference being that instead of a mean
ordinate being used, the proper final ordinates at
the respective stations are used.

The average error of this example before treat-
ment was 12 per cent, which would not be bad but
for the fact that two-thirds of the error occurs at
three points, which it is interesting to note are in
each case within the easements. Sta. 3+50 and
Sta. 74-50 are especially bad, and the easement Sta.
12+50 to Sta. 14 is generally deficient.

CHAPTER V.
THE SPIRAL.

13. THE SPIRAL BY MIDDLE ORDINATES.

As the string method of lining the body of curves
has replaced the instrumental method, so also will
the former method be found preferable for estab-
lishing the easement at the ends of curves or be-
tween the parts of a compound curve. The spiral,
which is desirable from the beginning, but is ac-
tually indispensable when the new railroad has set-
tled and become fit for high-speed operation, is a
refinement which is rarely provided in the original
location, and it must be obtained in the course of
maintenance by readjustment to some extent of the
body of the curve.

The prime requisite in the design of a spiral is
that it shall be in proper relation with the run-off
of the curve, which in turn is dependent upon the
amount of superelevation and its rate of decrease.
This rate, stated previously in a general way, may
be established for high-speed service somewhat as
follows : for curves under 45 min., y\ in. to 33 ft. ;
between 45 min. and 3 deg., % in. to 33 ft. ; over 3
deg., y2 in. to 33 ft.; and for slower speeds, not to
exceed 1 in. to 33 ft. While it is not always prac-
ticable, especially for the sharper curves, to obtain
the exact spiral desired, there are certain principles
which should be satisfied as far as possible. The

THE SPIRAL

important part of a spiral is the portion which con-
nects with the main curve or, in the case of a com-
pound curve, with the sharper curvature.

The ideal ordinates of the spiral curve should be
adhered to through two-thirds of its length, or gen-
erally to the point where 1^2 in. or less of super-
elevation obtains. Beyond that point the spiral
admits of some modification, and may be made more
flat if desired or if necessary in order to extend it
to the point of no .elevation.

The Unit Series for Designing the Spiral — In the
spirals of Example 11 it was observed that the
tangent offsets varied as the cubes of successive
numerals, and the deflection angles varied as the
square of the distance, which are characteristics of
the cubic parabola. It may be shown that these
conditions are present in all spirals whose members
increase by successive increments, which are them-
selves in arithmetical progression. Thus, the series
1, 3, 6, 10, 15, 21 in., etc., in which the maximum
number of units is 6 and the value of the unit 1 in.
may be taken as an example. The curvature be-
tween any two adjacent stations would be repre-
sented by a mean of the ordinates, the series indi-
cating the curvature thus becoming J^, 2, 4J/2, 8,
12*/2 and 18 in., in which it is seen that the ratios
of the several members to the first are the squares
of successive numerals ; the ratio of 2 to ^ being
4, which is the square of 2, the ratio of 4^ to J/£
being 9, the square of 3, etc.

The unit series extended as far as may be neces-

SIMPLIFIED CURVE AND SWITCH WORK

THE SPIRAL

sary is especially useful in designing an easement
for the sharper curves, and its employment in the
design of any easement reduces to a minimum
the labor required. The value of the unit will
be obtained by dividing the ordinate of the
body of the curve by the highest member of
the series found practicable of application. The
several ordinates of the easement will be obtained
by multiplying each member of the series by the
value of fche unit. Thus, if the ordinate is 8 in. and
5 stations of easement are found possible, dividing
8 in. by 21 gives ^ in. as the value of the unit;
and the several ordinates of the easement are found
to be % in., 1% in. 2J4 in-, 3^4 in., 55/s in.

Length of String for l/8 Spiral — In the solution
of most problems of main line curves operated at
the highest speed and requiring the longest ease-
ment possible, it will generally be found preferable
to adapt the length of string to the particular curve
that is being investigated. In such cases the T/g
spiral furnishes an ideal solution. The series in
which the value of the unit is ^ in. is as follows :
n/s, H, #, 1*4, % 2^, 3}4 4%, 554 6%, Sy4 in.,
etc.

By proper choice of a length of string the ordi-
nate of the body of the curve may be made to
coincide with the number of this series, which will
furnish the desired or practical length of easement.
If for any reason it is necessary or desirable to use
a different length of string than will provide this
agreement, it is only necessary to change the value

SIMPLIFIED CURVE AND SWITCH WORK

-HCM —KM — «\i — I<NJ

MS6

O io ^s N">

eq
le
sp

O O O O
tr> O K~) O

O fO O N^ O JO O

R R

0
OO

O C\j
°O OO

c\j xj- N- o |sr>

VQ V^) V,^ f^^. f^s.

C\j <\J

rv-t

N CQ ON O ^;

PJOIJO

I^KO ^100 -KVl

^^ <\4 ro

S i? S S §

fe-S

o o o o o o o

O O O O O
O to O K> O

THE SPIRAL

of the unit to some multiple of l/% in., which is found
by obtaining the ratio of the square of the chord
used to the square of that which would be ideal.
Use of the Table of Spiral Functions — A table
has been prepared which gives the computed values
of the functions pertaining to certain curves which
can be extended by offhand interpolations to in-
clude all curves. The question of superelevation
and rate of decrease having been established for
the known degree of curve, the proper length of
string may be selected from the ^table for use in
making a study of the curve and for designing the
easement. Or, conversely, the table may be used
to determine the value of the unit when a different
length of string is used.

ONE-EIGHTH SPIRALS FOR HIGH SPEED

OPERATION.
(Run-Off 1" to 100'— Chord 100'.)

1"30'

Superelevation . . . \l/2"

2y2"

Degree of Curve 20'

30'

45'

1°05'

Point of Full Elevation., ft
Point of Full Ordinate.... ft
End of Spiral fy%

Ift

154

25^
25/8

•^/^r
VA

1*A

l/S */S Y4 VA

ft 3/8 Y*

x ft

SPIRALS FOR 350 FT. RUN-OFF. ft

(Chord 100'.)

Speed ................................ 70 70 65 55 50

Superelevation ................ 3" 4" 5" 5" 5"

Degree of Curve .............. 1° 2° 3° 4° 5°

Point of Full Elevation.. 2$/s 5% ^7^ \Qi/2

Point of Full Ordinate.... 2$/8 5% 77/g iQi/2

End of Spiral .................... 1% 3^ 5S/8 iy2

iy4 zy2 33/4 5

3/4 V/2 VA 3

ft ft \ft V/2 V/8

Beginning of Spiral ........ ft ft ft y2 ^

Rate of Run-Off 1" in 117' 87^' 70' 70' 70'

SIMPLIFIED CURVE AND SWITCH WORK

SPIRALS FOR 2.17 FT. RUN-OFF.
(Chord 62'.)

Speed 48 46 44 42 40

Superelevation 3^" 4" 4^" 5" 5^"

Degree of Curve 4° 5° 6° 7° 8°

Point of Full Elevation.. 45678
Point of Full Ordinate.... 45678

End of Spiral 2^ 3^ 4^ 4^ 5^

1% 2^ 27/8 354 334

VA V/2 1^/4 2 2*/4

V* 3/4 7/8 1 1#

Beginning of Spiral Y4 % Y4 3/& 3/£

Rate of Run-Off l"in 60' 54' 48' 43' 40'

Thus, in Example 11, a chord of 100 ft. was used
for the 3 deg. portion of the compound curve as
well as for the 1 deg. 50 min. portion ; and the maxi-.
mum number of units found practical for the de-
sired easement of the 3 deg. curve was 7. By refer-
ence to the table it is found that the chord cor-
responding to a maximum of 7 units is 66 ft. The
proper value of the unit is found by multiplying
ys in. by the ratio of (100)2 to (66) 2, and it thus
becomes •£% in.

As another illustration, a perfect spiral between
a 3 deg. curve and a 0 deg. 20 min. curve would be
obtained by the use of a 92 ft. string, when the
ordinate of the sharper curve would be the tenth
member of the series and of the flatter curve the
third member. The 7 stations of easement, equiva-
lent to 9 stations of run-off, allow a decrease in
elevation between the 5 in. for the 3 deg. curve and
the \l/2 in. for the 0 deg. 20 min. curve, of % in.
in 33 ft. But it might not be practicable to apply
the preferred easement and the one attainable

THE SPIRAL

might only permit of a run-off at the rate of % in.
in 33 ft., which is the extreme limit for high-speed
operation. This would require that a 66 ft. string
be used, and the ordinate of the sharper curve
would become the 7th member of the series, and of
the flatter curve the second member; and the
length of easement thus would be reduced 2 sta-
tions. Any further reduction in the length of ease-
ment would require a greater reduction in speed.

Examples of Spirals — A typical spiral is given for
several light curves in high-speed operation; for
several average main-line curves with moderate run-
off; and for several sharp curves with minimum rate
of run-off for branch operation.

While the design of the spiral is only indirectly
related to the speed, and similarly no arbitrary
length of easement for certain groups of curvature
is practicable, these functions have been included in
the table for the convenience of those who may pre-
fer to give them consideration.

14. THE SPIRAL BY THE INSTRUMENT.

The type of easement that is most suitable for
general use is one that can be readily designed for
application with the instrument, and easily main-
tained by string lining. The cubic parabola fulfills
both requirements. While the engineer may. reason-
ably claim that it generally is an unnecessary refine-
ment to stake out the detailed spiral curve in the
preliminary location, it cannot be denied that provi-
sion should be afforded for such adjustment, and a

SIMPLIFIED CURVE AND SWITCH WORK

knowledge of the practical working limits, as de-
rived by a careful study of the operating require-
ments, becomes important.

Staking out the Curve between Offset Tangents
— A simple method for applying the easement curve
by the instrument is as follows : Stake out the cir-
cular curve as between imaginary tangents parallel
to, and a selected distance within, the lines of the
actual tangents; shorten the circular curve on each
end by the half length of the easement, and locate
points on the actual tangents at the same distance
in the opposite direction ; relocate the stakes mark-
ing the original ends of the circular curve a dis-
tance outward equal to one-half the selected offset dis-
tance. This location will enable the track-laying
forces to adjust the curves by eye with sufficient
precision for the purpose of the new construction
and will allow of the final detailed adjustment being
made later with nominal expense.

Relation of Offset to Length of Spiral— The
amount of the offset will depend upon the length
of easement desired, and this in turn will be gov-
erned by feasibility and the service required. The
least offset of practical utility is one whose length
in tenths of a foot is equal to the figure represent-
ing the degree of curve, and this will provide an
easement curve with the half length equal to 60 ft.
If a longer easement curve is desired and is not im-
practicable, the offset distance should be increased
in the ratio of the squares of the half-lengths.

For a very satisfactory adjustment upon a branch

THE SPIRAL

of medium traffic requirements, the half-length of
easement might be made 75 ft., and the offset dis-
tance would then be the number of tenths of a
foot equal to \y2 times the figure for the degree
of curve. If a run-off at a rate of J^ in. to 30 ft.
were desired for a 4 deg. curve, operated at 40 miles
per hour, with a superelevation of 3 in. attained 60
ft. upon the circular curve, the half-length of 60
ft. would be proper, and the offset distance would
be 0.4 ft. ; but if the same curve were part of an
important main line route to be operated at 55 miles
per hour, and the rate of the run-off necessary for
the 6 in. superelevation were desired to be 1 in. to
100 ft., a half-length of 250 ft. would be required
and the offset distance would be 7 ft.

Staking out the Easement Curve by Offsets — In
the latter case it would be necessary to stake out
the entire easement curve, preferably by 50-ft. sta-
tions, and the above described methods would ap-
ply ; or, if preferred the location might be made by
offsets, for one-half the easement curve from the
actual tangent, and for the other half by similar
offsets from the original circular curve. With this
method equal stations could be used, when the sev-
eral offsets would be 'the proportion of that at the
middle of the easement determined by the cube of
their relative distance from the ends of the ease-
ment. Thus, in the case cited, the first offset would
be l/125th of 3.5 ft. or 0.028 ft., and the several other
offsets, respectively, 8, 27 and 64 times this, or 0.22
ft., 0.76 ft., and 1.79 ft.

SIMPLIFIED CURVE AND SWITCH WORK

The same methods would of course apply to the
easement between two curves of considerably dif-
ferent curvature. The offset distance between the
imaginary tangents at the P. C. C. would then be
computed from the difference in the numbers repre-
senting the degree of the two curves. The several
offsets would be measured from the two circular
arcs. The unit middle ordinate would be obtained
by dividing the difference between the ordinates
of the two curves by the highest number of the series
applicable. The spiral ordinates then obtained would
each be increased by the amount of the ordinate of
the lighter curve.

15. THE ADVANTAGE AND COST OF SPIRALING CURVES.

Early Location Made Without Easements — It

was universally the practice in the early days of
railroads, as it very generally is today, to locate
a line as a succession of tangents with no provision
for present or future easements. Although opera-
tion is possible over such an alinement it must nec-
essarily be at a very moderate speed, and even
then accidents are of not infrequent occurrence.
While locomotives were small and the greatest
speed attainable was comparatively slow, the lack
of easements for the lighter curves was not felt;
but their absence from the sharper curves was al-
ways a source of trouble. Indeed, it is difficult to
conceive how operation was otherwise than pre-
carious upon many such curves that were devoid
of easements. The presence of superelevation pre-
74

THE SPIRAL

supposes curvature and the very fact of a tangent
track being several inches out of level, whether at
the approach to a curve or elsewhere, suggests the
possibility of accident. The records of most branch
roads contain the accounts of derailments occuring
at the ends of curves, the causes of which were
never satisfactorily ascertained. But the fact is
pertinent that such accidents become noticeably
fewer following the proper spiraling of the curves.
With the increase of speed in both passenger and
freight schedules the addition of easements has be-
come not merely a refinement for comfort, but a
necessity for safety.

Making Easements on Old Lines — Various meth-
ods have been used in providing present easements
on old lines. The first was usually to throw the
ends of the curve outward, which served to remedy
part of the defect, though the resulting protrusions
beyond the tangents were both unsightly and to
some extent uncomfortable. When adjoining curves
turned in the same direction and the tangent be-
tween was short, it readily appeared that a relining
of the entire tangent would effect the necessary
correction ; although in most cases the protrusion
was allowed to remain as the lesser of two evils.

As methods were evolved for the lining of curves
^the flat places developed by the outward throw of
the ends were eliminated by lining the entire body
of the curve inward, the throw being often as much
as 6 in. Finally, when such methods, at first crude,
were further improved, complete adjustment was

SIMPLIFIED CURVE AND SWITCH WORK

made on exact lines, the protrusions being removed,
a more efficient easement provided and finer detail
line of the curve attained. The last adjustment
nearly always consisted in making, first, an inward
throw of the ends, designed to remove the protru-
sions, which makeshift correction and the distorting
action of the traffic had produced, and also to flatten
the curve for the easements ; and second, an out-
ward throw throughout the entire remaining body
of the curve, varying in amount from 2 in. to 6 in.,
to absorb the sharp places which the preceding
throws had introduced at each extremity of the
remaining arc. The net result of the several changes
was a lengthening of the curve amounting to about
75 feet on each end and a sharpening of the circular
arc about 3 per cent of the initial degree.

Providing for Easement in Original Location — As
affecting the question of introducing easements into
the original location, or at least of providing the
means for such correction at a later time when the
roadbed shall have settled, it will be instructive to
study the cost of the relining necessary to attain
this end when no such provision has been made.
It will no doubt be thought that the value of the
labor thus spent is so indefinite as to be impossible
of even approximate estimation. But the record of
cost on a typical branch road of medium traffic and
maintenance is offered as a suitable criterion. The
road, which is cinder ballasted, is 44 miles in length
and the speed prescribed is 40 miles per hour. The
alinement follows the shore of a river through all

THE SPIRAL

its points and bays, and contains 185 curves, sev-
eral as sharp as 8 deg., the average of all being 3
deg. 20 min. It is safe to say that each has had the
three general lining adjustments referred to during
the 20 years of the road's operation, and a con-
servative estimate of the total cost of the several
adjustments is approximately lOc per foot of curve.
For this road, on which the curves compose 57 per
cent of the total length, the expense of adjustment was
$300 per mile of single track line. The labor neces-
sary for spiraling the curves thus amounted to no
less than $13,000, a considerable sum of which
would unquestionably have been largely saved if
ultimate addition of easements had been provided
for in the original alinement.

CHAPTER VI.
THE VERTICAL CURVE.

16. THE USES OF THE VERTICAL CURVE IN MAIN-
TENANCE.

The subject of vertical curves, which is discussed
in this chapter, is not strictly a part of the general
theme of curve adjustment, but concerns rather the
adjustment of gradients. It is, however, a very im-
portant feature in track maintenance and one which
is not always given the attention it deserves. Ad-
justments by the vertical curve are handled by the
engineer, and this subject is therefore of little in-
terest to the track foreman.

The method of designing the vertical curve as
a parabola is explained in the several field books,
and is probably in quite common use. Its utility
in modifying the sharp change at a grade intersec-
tion is generally recognized ; but its advantage in
replacing a succession of short, straight grades of
continually changing inclination may not be so fully
appreciated. It is just as necessary that the verti-
cal changes in motion shall be effected smoothly as
that the horizontal changes in direction shall be
made by means of regular curves.

Rate of Change — The importance of the vertical
deflections is well shown by the case of the run-off.
In times past a rate of y2 in. to 30 ft. was nearly
universal. It is now recognized that the maximum

THE VERTICAL CURVE

of comfort obtains when a run-off of one-half this
inclination is employed. Somewhat similar prin-
ciples enter into the design of a vertical curve, and
the proper length of curve to afford an easy pass-
age over a summit or across a depression is ob-
tained by an application of the features common to
the run-off.

Continuous Vertical-Curve Gradient — The prob-
lem of establishing a new gradient to fit one that has
been much distorted through years of track rais-
ing by the eye often presents two phases : one of
establishing a number of short grades and one of
merging the short grades into a continuous grade on
a curved line. The essential feature in grade refine-
ment is not that the grade shall be straight, but
that it shall be continuous. This becomes of the
greatest importance when the grade is coincident
with an interlocking or an extensive switch layout.

The method given for computing vertical curves
is of practical application to all grade intersections
that are commonly met with in railway practice,
and it can be employed for any length of vertical
curve. The method has been applied in the case
of a grade correction wherein a vertical curve a mile
in length resulted. The method will be found
equally advantageous in compromising the steep
gradients sometimes required in siding layout.

Vertical curves are not employed in siding con-
struction and maintenance to the extent their use-
fulness deserves, and many derailments may be
traced to lack of this feature. When the mean of

SIMPLIFIED CURVE AND SWITCH WORK

the elevation of two points 18 ft. apart differs more
than 1 in. from the elevation of the point midway
between them, a vertical curve is a necessity. The
difficulty of introducing a vertical curve for a sum-
mit after the track is completed is of course appre-
ciated.

17. COMPUTATION OF THE VERTICAL CURVE.

The simplest method of computing a vertical
curve is the orthodox one in which (1) the correc-

I ha mean of A and F. D' is midway between DandE.
D6-4of OD1 andBB'=3 of DG orj ofDD1. DH^ofDD1

Fig. 3. Geometrical Principle of the Vertical Curve.

tion at the grade intersection is one-half the differ-
ence between the elevation of the intersection and
a mean of the elevations of the assumed tangent
points, and (2) the corrections at the other points
are the fractions of the whole correction represented
by the square of their fractional distance from the
tangent points, the corrections being minus for a
summit and plus for a depression.

The geometrical principles are illustrated in Fig.
3. The method is the more nearly exact the smaller

THE VERTICAL CURVE

the intersection angle of the grades ; but this method
is sufficiently accurate for all grades that are prac-
tical to railroads. Vertical reversed curves or com-
pound curves follow the same general lines as
simple vertical curves. In the case of the former
the best arrangement is had by entirely eliminat-
ing the tangent common to both curves.

For vertical curves in high speed main lines the
assumed tangent points should be so remote from
the intersection that the correction 100 ft. from the
tangent points will not exceed ll/2 in. It is desir-
able that where possible this correction shall be as
little as 24 in. A too sudden change is similar in
effect to a run-off that is made at an excessive rate.

The practical limit for the adjustment of siding
grades is determined by the length of wheel base
of the locomotive operating over the siding. The
vertical curve should be flat enough to make the
middle ordinate, on a chord equaling in length the
wheel base, as little as 1 in.

18. EXAMPLE OF A VERTICAL CURVE.

An example on somewhat similar lines to the
figure will make the application of the principle
entirely clear. Assume the grade A to D to be as-
cending 1.1 per cent and D to F, descending 0.1
per cent; and that the elevation of A is 91.0, of the
intersection D, 94.3, and of F, 94.0. The elevation of
the middle point of the chord, or the point E, will
be a mean of the elevations at A and F, or 92.5.
One-half the difference between this grade and the

SIMPLIFIED CURVE AND SWITCH WORK

grade of the intersection will be equivalent to the
middle ordinate of the vertical curve. The value
thus obtained is 0.9 and this subtracted from the
elevation of the intersection will give the elevation
of the vertex of the curve, or 93.4. (If the verti-
cal curve were a depression instead of a summit,
the middle ordinate would have been added.)

The corrections at the several stations are ob-
tained by dividing the correction at the middle,
0.9, by the square of the ratio of distance from the
ends of the curve. Thus B is % the whole distance
from A, and the correction is 1/9 of 0.9, or 0.1; C
is Yz the distance and its correction 4/9 of 0.9, or
0.4. The tabular figures show the final results.
Station Tangent Grades Vertical Curve.

Elevation Elevation.

92.1

920

932

928

94.3

93.4

94.2

938

94.1 .

940

F ..

...94,0 .,

....94.0

CHAPTER VII.
ECONOMICS OF CURVES.

19. ECONOMICS OF CURVE LOCATION.

Speed on Main and Branch Lines — Generally
speaking, there are but two divisions of railways,
main lines to be operated at the now almost uni-
versal maximum limit of 70 miles per hour, and
branch lines to be operated at the commonly pre-
scribed maximum of 40 miles per hour. Upon the
former the passenger traffic is usually predominant ;
upon the latter the freight traffic. When the main
line is burdened with a considerable freight traffic
it is the rule for this traffic to be carried upon def-
initely assigned tracks; and since these tracks may
frequently be required for passenger movement
their adjustment must be coordinated with the av-
erage of the two speeds, or say 55 miles per hour. It
is now fully recognized that enginemen cannot reg-
ulate speed closer than 10 per cent, except when
speed indicators are provided; and that even with
faithful maintenance, depressions of % m- m main
lines and of J^ in. in branch lines and similar varia-
tions of alinement are unavoidable. The latter fig-
ures may therefore be considered the working lim-
its for the purpose of this discussion.

Light Degree Curves Unfavorable — One of the
most common errors in past location of main lines
has been the endeavor to obtain too light a degree

SIMPLIFIED CURVE AND SWITCH WORK

of curvature. Thus, 10 min. curves are sometimes
used, 15 min. not unusal and 20 min. quite common.
Experience has shown that a measurable increase
in cost of maintenance attaches to such selections.
The degree of curve may be considered as the num-
ber of inches a joint deflects from a cord held to
contact at the two adjacent joints. The exact
length of such a chord is 61 ft. 8 in., but the propo-
sition will serve for illustration. For a 15 min.
curve the deflection would be J4 m-> and such a
curve would theoretically require a superelevation
of 24 in. If a joint on the high side should become
54 in. low and through this cause shift outward
y^ in., as quite probably would be the fact, there
would result a curvature twice as sharp as the
normal degree, or 30 min., and the superelevation
of l/2 in. would be wholly inadequate, since such a
condition would require 2 in. This disadvantage
is partly overcome by employing a superelevation
somewhat greater than that determined by the the-
oretical formula of mechanics. For example, a
practical superelevation of l1/^ in. is used for a 20
min. curve although theoretically no more than 1
in. is necessary.

If, however, the curve was 45 min. and the same
errors should enter, the curvature would become 1
deg. and, if the proper superelevation of 21/o in. had
been used, the 2% in. obtaining would still be suffi-
cient for the increased curvature. A curve of this
degree may therefore be considered the ideal one,
and both theory and practice will indicate that the

ECONOMICS OF CURVES

desirable limit for the lighter curves is between 30
min. and 1 deg., with even closer limits between
40 min. and 50 min. to be preferred.

Maximum Curvature — The maximum limit of
curvature for important main lines to be operated
without speed reduction is 2 deg. 20 min., which
requires 5 in. superelevation. This amount should
be fixed as the limit of superelevation for high speed
tracks, not because any more is unsafe, but by rea-
son of the discomfort which results when a slower
speed is used. If the speed should become less
than 35 miles per hour at such a point the disad-
vantage in this respect would be quite marked, and
the destructive effects would be greater as the speed
was further reduced.

The determination of the practical limits for
branch line location is made similarly, and these are
in general three times those for main lines, or be-
tween 1 deg. 30 min. and 7 deg. The proper super-
elevation for a 45 min. curve at an authorized speed
of 40 miles per hour is 1 in. If this should become
1^2 in. through the low side settling and the curva-
ture thereby become as light as 15 min. a speed of
70 miles per hour would be required for comfort;
and if by the high side settling the superelevation
should become as little as % in. and the curvature
as sharp as 1 deg. 15 min., no more than 30 miles
per hour would be permissible. In the case of a 1
deg. 30 min. curve, however, requiring I1/? in. super-
elevation, a sharpening of the curve to 2 deg. by
reason of the superelevation diminishing to 1 in.

SIMPLIFIED CURVE AND SWITCH WORK

would not render the conditions unfavorable, and a
flattening of the curve to 1 deg. with the superele-
vation increased to 2 in. would not introduce any
element of discomfort.

As regards the maximum limit of 7 deg. for which
a superelevation of 5^ in., to provide for natural
deficiencies of line and surface and to allow for a
10 per cent increase of speed, would be necessary
where maintenance was of medium character, this
limit is based mainly upon a practical knowledge
that superelevation in excess of this figure is un-
desirable if not actually improper. When main-
tenance is of the best a curve as sharp as 8 deg. may
be operated at a speed of 40 miles per hour; but
a safer practice would be to restrict the speed to 35
miles per hour for which the limiting superelevation
of 5% in. would then be correct.

Location of Grade Intersections — Another error
in location, causing a serious disadvantage in main-
tenance that is reflected in operation, is the placing
of a grade intersection at the end of a curve. This
is especially troublesome upon lines of undulating
profile and with numerous curves, and these fea-
tures usually occur together. The problems of the
easement and of the vertical curve are simple
enough when considered separately, but when they
are in combination a question results which is much
too complicated for any but the accomplished phys-
icist. While it is possible to effect a practical ad-
justment of such conditions, the future maintenance
will severely try the ability of the most expert track

ECONOMICS OF CURVES

foreman. It is a matter of experience that no great-
er disadvantage to the riding qualities of a track
can be found than a dip in the grade just at the end
of a curve, and the same fact holds true in a less
degree of a summit. It requires some sacrifice to
adjust the line or the profile so that the two fea-
tures will be separated, but the advantages in main-
tenance which result fully justify the correction.
This question is of timely interest, because of the
tendency in making a compensation of the gradient
for curvature, to introduce the change exactly at
the end of the curve, which in the process of re-
fined adjustment become the center of the ease-
ment, and the error is thus cumulative.

Minimum Length of Tangents — When curves
are provided with proper easements there is the-
oretically no need for any tangent between the
curves, but with a due regard for the aesthetic re-
quirement and economically because it provides for
the addition of siding connections under more
favorable conditions, tangents should be provided at
proper intervals. The minimum length to satisfy
both needs would be 400 ft.

Widening Centers on Curves — In view of the great
importance of clearance, not only at the side but
between adjoining train movements, it becomes
quite essential that a factor be designed for widen-
ing the track centers on curves. Three elements
enter into the question, viz. : the design of the equip-
ment, the relative superelevation of the several
tracks and the degree of maintenance. The maxi-

SIMPLIFIED CURVE AND SWITCH WORK

mum truck centers may be assumed as the equiva-
lent in length of the chord which furnishes a middle
ordinate in inches equal to the degree of curve. The
overhang at the end is generally the same as that
at the middle and, as these two combine to decrease
the clearance, it may be stated that ideally the cor-
rection should be 2 in. per degree. When adjoin-
ing tracks are operated at different maximum
speeds requiring difference in superelevation, there
should be a further allowance of three times this
difference. If maintenance is good the extreme al-
lowance for swaying might safely be made 1 in. ;
if only fair as much as 2 in. would be required. Thus,
a well-maintained main line curve of 2 deg. 30 min.,
with inner tracks operated at 60, and outer tracks at
70 miles per hour, would require a correction of
10% in. in the track centers. Clearly the tracks
could not be made parallel throughout as this would
require a reverse at the ends. The proper solution
of such a case would be to adjust the difference
through the respective easements, of the several
tracks.

Special Curve Problems — With the advent of the
high island platforms for passenger service a nice
problem in curve economics is presented for solu-
tion. This structure is almost certain to occur
either wholly or in part upon curves. It is, of
course, essential that a uniform opening be estab-
lished and maintained between the car and the plat-
form. To attain this with the platform alined upon
a regular curvature ending in the tangents requires

ECONOMICS OF CURVES

that a reverse be introduced into the track curve,
which is not only unaesthetic but disadvantageous.
The importance of this will be fully appreciated
when it is considered that the difference in distance
of track from platform between tangent and a 2
deg. 30 min. curve, with 1 in. superelevation for
operation at 30 miles per hour, would be 3% in.
Such protrusion would unquestionably cause a very
deficient alinement. The trouble will be entirely
avoided by introducing proper easement curves into
the platform alinement, as well as that of the track.

20. ECONOMICS OF CURVE MAINTENANCE.

The order of correction for the various defects
of curves which are in poor line throughout should
be : First, a roughing-in of the line to render the
test with the string more effectual ; second, adjust-
ment of the line after a careful study of the ordi-
nates obtained; third, application of a proper super-
elevation, including the run-off, or correction of any
deficiency that may be found in the existing super-
elevation ; fourth, the re-gaging, which is readily ap-
parent after the line rail has been made true ; and
fifth, a fine detail lining.

Correction of Line Defects First — The general cor-
rection of the line is nearly always the first opera-
tion, for the fine surface would be disturbed if the
throws should be several inches, and in the event
that the established superelevation were excessive
for the curve when made regular, this amount of
elevation might be necessary even for safety at

SIMPLIFIED CURVE AND SWITCH WORK

points on the curve where sharp places exist. Fur-
ther, the proper superelevation and its limits, and the
approach and run-off can only be determined by
the line study of the curve. A careful examination
of the present features of the run-off is quite essen-
tial, as it is no unusual occurrence to find the run-
off improperly located, sometimes as much as sev-
eral hundred feet from where it should be.

Protrusions at Ends of Curve — A very common
defect, is the protruding of the ends of the curve
outside the line of the tangents. This defect arises
through the tendency of a curve to make its own
easement, and through the invariable practice of
maintainers lining out the ends of curves to obtain
the advantage of an easement. It is found that
when the curve is provided with proper easements
in the relining, natural shifting ceases and there is
no longer a tendency of the foreman to thus dis-
tort the line in endeavoring to make a seeming cor-
rection. The elimination of this defect should be
one of the main considerations in the preliminary
lining, as its presence precludes a proper adjust-
ment of the line.

Line and Surface Interdependent — The physical
requirements of the curve having been amply met
in perfect alinement and correct superelevation, and
the easement and run-off being in proper proportion
and location, the supervisor and foreman are con-
fronted with the duty of maintaining the excellence
of these features. It is well known that each is cor-
related writh the others. Perfect line will not con-

ECONOMICS OF CURVES

tinue if the surface becomes deficient; the surface
breaks down more quickly when the line is allowed
to deteriorate ; and the easement and the run-off suf-
fer if one or the other develops defects.

The maintenance of good surface is more neces-
sary on curves than on tangents. A ^4-in. varia-
tion in the level of a tangent, provided it is con-
tinuous, cannot be regarded as poor maintenance.
Such a condition might exist for some time and its
presence be undiscovered until a critical test was
made with the level board. In ordinary practice no
attempt would be made to level up a tangent track
having no greater variation than this until a raise
in face was being made, when, of course, the surface
would be made true. But on curves such a defect
would be immediately objectionable. While super-
elevation is generally chosen to the nearest half
inch, it is quite desirable in the case of light curves
that there should be excess rather than deficiency.

Selection and Maintenance of Superelevation-
Through past error of practice, many main-line
curves are of light curvature, 20 min. being most
common. Experience has shown that upon such
curves, when used at high speed, a half inch of
superelevation makes the difference between com-
fort and discomfort to the passenger. This differ-
ence being noticeable in the choice between two
superelevations, the difference would be much more
marked if, through breaking down of the surface,
the established superelevation should vary in places
as much as y2 inch. Bad maintenance would be

SIMPLIFIED CURVE AND SWITCH WORK

readily apparent both in the line and the surface.

Regularity of the superelevation is the most im-
portant element in curve maintenance. This re-
quirement can only be attained by consistent super-
vision. The track foreman is ordinarily quite faith-
ful in his use of the track level when surfacing is
being done, but he is not so apt to carry his level
with him to try his curves for this defect. If the
surface of the rail sights properly, the track is, in
his view, all right. A test under his eyes with the
level is the best lesson that can be given.

Maintenance of Line — The line having been made
correct, the maintenance of good surface is neces-
sary to its remaining correct. But even with faith-
ful maintenance there is a certain amount of slight
shifting under the traffic, which cannot be con-
trolled, and which requires periodical correction. If
neglected these slight detailed defects soon increase
to the extent of a general deficiency, and eventually
the line of the curve is lost and another relining with
the string is necessary. In no other feature of track
work is the old saw regarding the stitch in time more
aptly illustrated.

There is no permanent means of marking the cor-
rect line of a curve. Stakes are struck by dragging
parts of cars and only slightly disturbed after which
they are worse than useless. Steel pins, old rails,
even stone monuments are disturbed by frost, and
in any event their usefulness depends upon measure-
ment with a varying tape line held in every posi-
tion except the horizontal. Maintenance of the cor-

ECONOMICS OF CURVES

rect line by continued watchfulness is the better
practice.

Short Sags — The correction of the short sags,
often no more than two or three rail lengths in ex-
tent, is an important item in curve maintenance.
These dips are unfavorable at any point, as they
render fine lining impossible and, no matter how
perfect the work with the level, their presence pre-
vents fine results in surface. But they are par-
ticularly objectionable on curves. Doubtless in
theory they cause no defect if symmetrical with the
cross section. But the depressions in the two rails
are seldom directly opposite and a rolling of the
car is the inevitable result, which under extreme
circumstances may become a lurch. They should
be regarded as defects and carefully removed in the
general surfacing program.

Raise in Face — A raise in face is periodically nec-
essary for all main tracks, the intervals depending
upon the kind of roadbed and the character of the
traffic. When such raising is being done on curves,
it is customary for the low rail to be selected as the
grade rail, although a very distinct advantage may
be gained by using the opposite rail. In raising tan-
gents it is very desirable to raise both rails together
and usually against the current of traffic. But on
curves many foremen prefer to raise the high rail to
a proper grade, introducing for the time being added
superelevation, and to follow this by bringing the
low rail to the required grade, and this procedure is

SIMPLIFIED CURVE AND SWITCH WORK

usually the better one when the raise is no greater
than 2 in.

Maintenance of Ties — The basic requirement for
curve maintenance is an ample renewal of the cross-
ties to provide a firm bearing at all times. Generous
tie replacement is desirable in all kinds of road, but
it is essential on curves. This is not alone needed
for maintaining the gage, although that is the prime
consideration, but it is also necessary for preserving
the surface, which in turn contributes to per-
manence of the line. A main-line curve can hardly
be considered adequate track for heavy service un-
less it is well tied, with each tie protected by a tie
plate.

Correct Gage — The importance of correct gage on
curves cannot be over estimated. The supereleva-
tion of a curve is of course adjusted to just one
speed. If the movement is at a very much slower
speed, the wheels will press against the inside rail ;
if faster, against the outside rail; in either case a
variation in the gage becomes immediately notice-
able. The tendency of every curve to spread can
only be met by a full equipment of tie plates. No
matter what type of tie plate is preferred, they
should be provided with a shoulder to relieve some-
what the pressure against the outside spikes. The
tie plate should carry a third spike, and on curves
vvhere required a fourth spike, to draw the plate
close against the rail base and to help hold it in
place.

When tie plates are applied the gage should be

ECONOMICS OF CURVES

made correct according to the standards of the
road. The gage should only be widened when the
curvature exceeds 10 degrees, and should never be
made more than 4 ft. 9 in. The best means of de-
tecting imperfect gage by a casual inspection, is to
run the eye along both rails of the track. If an ir-
regularity shows upon one rail and not upon the
other, the trouble is surely in the gage. Even where
the track is plentifully equipped with tie plates there
is constant need of gage correction, and to this end
it is the practice on many divisions to keep a gaging
gang of three men constantly employed. If the
leader of this gang is efficient, the gage correction
may be made a means of correcting the detail line
as well.

PART II— PRACTICAL SWITCH
CONNECTIONS

CHAPTER VIII.

ESSENTIAL ELEMENTS IN THE DESIGN OF
SWITCH CONNECTIONS.

21. ELEMENTARY PRINCIPLES.

There is a certain information essential to the
correct installation of switch connections which it
is necessary for the supervisor, and quite desirable
for those of his foremen who must perform such
work, to have at their instant command. The super-
visor is required to lay out switch work on the
ground when access to tables may not be possible,
or to instruct his foreman when a resort to mem-
oranda would be inappropriate. The track foreman
cannot always have the benefit of the supervisor's
guidance ; and at any rate when equipped to pro-
ceed upon his own working knowledge he naturally
feels a greater degree of interest in the undertaking.
There are not a few track foremen who are quite
resentful of the intrusion of detailed directions for
specific cases, but who are entirely willing to be
instructed in the general rules necessary for nice
accomplishment. This is especially true of switch
connections, for which, unfortunately, there is much
misleading data extant. Heretofore only the mathe-
matically educated have been able to solve the va-

DESIGN OF SWITCH CONNECTIONS

SIMPLIFIED CURVE AND SWITCH WORK

rious problems of switch work, but through the dis-
covery of certain exact arithmetical relations among
the various functions of crossovers and ladders, and
by devising empirical rules for the dimensions that
do not require fine exactness, the field becomes open
to all intelligent track men. The data herein as-
sembled is offered therefore as a guide to all railroad
builders and maintainers.

It is presumed that the terms commonly em-
ployed for the various functions of switch connec-
tions are entirely familiar, but in order that there
may be no misunderstanding of them, their nomen-
clature is fully defined and their interpretation, as
used, clearly indicated in the diagrams. It must be
understood that the detailed design of switch and
frog members, which varies somewhat with dif-
ferent roads, materially affects certain functions,
and that it is therefore impossible to formulate rules
which will apply absolutely to all cases. The em-
pirical rules stated are for average practice, but it
will be found that for even the extremes of design
a relation obtains which only requires that proper
constants be selected. The lead and degree of
curve are the dimensions most affected by the
choice of switch length and by design of the frog;
but experience has shown that a slight variation
in the length of the lead causes no defect in the fin-
ished work, and the degree of curve is only of inci-
dental concern.

Theoretical leads are never directly employed in
railroad switch work. The nearest approach to such

DESIGN OF SWITCH CONNECTIONS

use is in the very sharp turnouts below No. 4, where-
in it is the practice to curve the turnout rail of the
frog, and as the straight switch point rail still is
used, the problem remains one of practical design.
A rigid construction of Section 2 of the Safety Ap-
pliance Act virtually requires discontinuance of
frogs below No. 5 in new work, and interest in
them is only one of present maintenance and ju-
dicious elimination as opportunity arises. The prob-
lem of lining the turnout curve at the heel of the
frog furnishes the one practical use for the theore-
tical formula for lead, and this use is only an indi-
rect application of the geometrical principle.

The function of distance between frogs, both in
crossovers and ladders, follows geometrical lines;
rules for its computation should be exact and care
should be taken, when applying the frogs, to use the
exact dimension. This is especially true of cross-
overs, for even though laid on precise lines the di-
mension will be found after a time to vary as much
as 2 in. through the creeping of the rails. This fact
alone condemns the use of a formula that is often
employed in computing published tables, which gives
results that are too long for all crossovers, but par-
ticularly for the lower numbers of frogs. As most
non-interlocked crossovers are trailing, the error
thus introduced is increased by the running of the
rails, the consequent tightening of the gage being
very undesirable.

It is unquestionably a duty to follow standard di-
mensions whenever possible, with the single excep-

SIMPLIFIED CURVE AND SWITCH WORK

tion that the lead may be varied somewhat, which
indeed local conditions will often necessitate. The
two dimensions especially which admit of no varia-
tion are the heel gage of the switch and the guard
rail gage. Adherence to the former avoids fatigue-
ing stresses in the switch rail and any deviation
from the latter invites accident.

22. DEFINITIONS.

The term switch connection embraces in a general
way turnouts, crossovers, ladder tracks and slip
switches. Derailing sivitches, used without a frog,
and double crossovers, formed by two simple cross-
overs in opposing directions which intersect, are two
less common items. The turnout may be defined as
the portion of track which forms the physical con-
nection between two separate tracks ; the crossover,
as the combination of two turnouts to effect a con-
nection between two thoroughfare tracks which are
generally parallel; the ladder track, as the diagonal
track from which one or more tracks diverge by sep-
arate turnouts ; and the slip switch, as a diagonal track
which crosses a thoroughfare track and has single or
double connections with the intersected track.

The essential function of the switch connection is
to enable trains to go from one track to another.
Thus, the turnout is frequently of use to allow one
train to turn aside in order to let a superior train
pass; the crossover, to divert trains to an adjoining
track used in the same or an opposing direction; the
ladder track to furnish a compact entrance to several

100

DESIGN OF SWITCH CONNECTIONS

tracks; and the slip switch to afford a route not only
crossing but connecting with another route.

The universal method of keeping car trucks upon
the track is by means of flanges on the wheels. These
impinge upon the inside lines of the rails, which are
thus known as the gage lines, and the distance be-
tween the gage lines is the gage of the track. For
deflecting the wheels from the track being traveled,
a device is employed which is called the switch, and
for continuing the wheels along the preferred track
when the rail of an intersecting track is met, a special
contrivance is used which is called the frog. For the
benefit of the student who has not had the oppor-
tunity to gain a practical knowledge of the various
members composing the switch connection, these will
be described in some detail.

The switch consists essentially of two point rails,
one or more rods to hold the points the correct dis-
tance apart and to keep them from rising, riser or
switch plates to support the point rails and maintain
the stock rails in position, rail braces to prevent the
rails pushing out or turning over and a switch stand
for throwing the switch when this is not done by a
power contrivance. The tapered end is called the
point of szmtch and it is usually ]/% in. thick. The
opposite end is called the heel of switch. Each one
of the point rails is known as a switch point. When
facing the point of switch, the point on the right
side is the right hand point and the point on the left
side is the left hand point. When the center frogs
of a crossing are replaced by point rails which move

101

SIMPLIFIED CURVE AND SWITCH WORK

for the two routes, as in slip switches, these points
are known as movable points.

The frog is the device used to pass the wheels run-
ning upon one rail of the track across a rail of another
track. The channel in which the flanges run is called
the flangeway. The point of frog, generally called
the y2 in. point, because it is ^ in. wide, is always
understood to be the actual point, and not the the-
oretical point which is the intersection of the gage
lines. The toe of frog is the end nearest the switch
and the heel of frog the end farthest away.

The simplest type of frog is the stiff or rigid frog,
in which all the parts are held firmly in position. A
frog having one rail which moves outward to let the
flanges pass, is known as a spring rail frog. If it
moves to the right when facing the point it is a right
hand frog, and if to the left it is a left hand frog. If
it has two rails which move, both to the right and left
hand, it is a sliding frog.

Frogs are designated by their number, (which is
the ratio of a bisecting line to the spread) ; by the
weight of the rail of which they are made, and
sometimes also by the different section of rail em-
ployed; and by the design, whether stiff, right or
left-hand, or sliding.

The guard rail is an adjunct of the switch connec-
tion, which is mainly used to keep the wheels from
striking or going to the wrong side of the point of the
frog, but is also occasionally used in advance of
switches to prevent the thin point being struck by the
wheels. The stability of this member depends upon

102

DESIGN OF SWITCH CONNECTIONS

its being properly secured by clamps and tie plate
fasteners, or by some other mode of reenforcement.

The various geometrical features of the switch con-
nection are plainly indicated in the diagram. The
lines represent the gage lines of the rails in all cases.

23. THEORETICAL AND PRACTICAL CONSIDERATIONS
IN DESIGN.

Relation Between Switch Angle and Frog Angle.
—The design of switch connections embraces the de-
termination of two distinct questions : First, the num-
ber of frog best adapted to the space available and
the service required; and, Second, the length of
switch most suitable for use with the selected num-
ber of frog. The former is largely an operating ques-
tion ; the latter can only be decided by a close ana-
lytical study of the mathematical functions. A purely
theoretical consideration of the question indicates that
the ideal relation exists when the switch angle is no
greater than one-fourth the frog angle; but experi-
ence has shown that quite satisfactory results are ob-
tained when this ratio is as low as 1 to 3^. It is
readily seen that any increase in the length of switch
employed with a particular frog tends to increase the
degree of curve of the turnout, and it is this fact
mainly which restricts the choice of switch length.

Ordinary Combination of Switch and Frog. — A
strict observance of the ideal relation would necessi-
tate the employment of a larger number of standard
lengths of switch than is actually required for prac-
tical results, and would add greatly to the. interest

103

SIMPLIFIED CURVE AND SWITCH WORK

expense for emergency stock. It has been found that
three or four chosen lengths answer all requirements.
These are somewhat different for different roads.
When no higher number of frog than No. 16 is em-
ployed the choice would be as follows : 10 ft. switch
for No. 4, 5 or 6 ; 15 ft. for No. 6, 7, 8 or 9 ; 24 ft.
for No. 10, 11, 12, 14, 15 or 16. If frogs as high
as No. 20 were employed the choice would then be
as follows : 10 ft. for No. 4, 5 or 6 ; 18 ft. for No. 6,
7, 8, 9, 10, 11, or 12; and 30 ft. for No. 12, 14, 15,
16, 18 or 20. It will be noted that in each case the
switch length is twice the middle number of the series.
When the extent and importance of the traffic war-
rants the use of a fourth length of switch, the first
series would obtain with the addition of the 30 ft.
length for use with the No. 18, 20 and 24 frogs. The
preferable combinations are discussed farther on.

Difference of Length, Lead and Turnout Rails. —
In the table of the principal functions for various
combinations, the lead has been modified within prac-
tical limits from the strictly theoretical dimension with
a view to the use of commercial lengths in the main
rail, or where this is not practicable, of such lengths
cut in two in the proportions necessary to make the
difference between the straight lead rail and the
curved turnout rail. This difference follows a regular
ratio, and is obtained in every case by dividing 12 in.
by the number of the connection, which it should be
noted is not always that of the frog employed, but is
the one which most nearly corresponds with the re-
sultant curvature.

104

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105

SIMPLIFIED CURVE AND SWITCH WORK

Classification of Switch Connections for Speed.—
By the uses to which they are applied connections are
divided into four general classes, viz. : siding con-
nections for low speed; main track and siding con-
nections for moderate speed; main track connections
for medium restricted speed, and main track connec-
tions for the greatest practicable restricted speed.

The general division embracing siding connections
consists of those over which road power cannot oper-
ate, and they are therefore less than No. 6. Because
of the menace they introduce such frogs should be
rigidly excluded from main tracks carrying passenger
traffic. The typical frog of this class is the No. 5,
which average practice fixes as the lowest number that
will satisfy the requirements of the Safety Appliance
Law. It requires no demonstration to show that the
proper length of switch to be used with this number
of frog is 10 ft. In fact, it is generally recognized
that this length of switch is the minimum that may be
employed with any connection.

Length of Switch With Frogs No. 6 to 9.— The
second classification includes by far the largest per-
centage of all frogs that are in use on American rail-
ways, embracing those between Nos. 6 and 9. Bear-
ing in mind the general use of these numbers it is
plain that the adoption of a common length of switch
for all is exceedingly desirable. Since each is of
frequent occurrence in main tracks, the ability to
cover all by a single length of switch is of unques-
tionable advantage.

The determination of the proper length of switch

106

DESIGN OF SWITCH CONNECTIONS

for use with this group concerns particularly the No.
6. This number must sometimes be used for main
track connections, through which road power, includ-
ing the modern types of passenger locomotives,
operates not only in drill service, but quite often in
main line movement. Practice permits the employ-
ment of any length of switch between 10 ft. and 18 ft.
with this number of frog ; but the 10 ft. length intro-
duces a too abrupt change in direction for comfortable
operation in passenger service, and causes a very con-
siderable shock with consequent wear upon the point
in the case of drill movement. On the other hand,
while the 18 ft. length supplies the requisite improve-
ment in the detour feature, the degree of curve is in-
creased nearly 10 per cent, and the minimum thus
created becomes somewhat precarious for road move-
ment.

A reference to the table shows that the use of a
15-ft. length does not unduly increase the degree of
curvature, while the switch angle is reduced one-third.
This length of switch therefore appears to be more
generally desirable for the No. 6 frog than either of
the other lengths. It will also be seen that in the case
of the No. 7 a curvature nearly equal to that with the
18-ft. switch results, and that the curvature of the
No. 8 and No. 9 with the 15-ft. switch is materially
less than that with the 18-ft. switch. The middle
ordinate of the chord of the turnout arc is uniformly
6% in., which practically may be used as 6 in. with
4^2 in. at the quarters. Thus exact line may be ob-
tained readily, which is an essential feature in switch

107

SIMPLIFIED CURVE AND SWITCH WORK

construction. This length is therefore recommended
as one of the standard lengths in preference to 18 ft.

Length of Switch With Frogs No. 10 to 16. —
The one objection to the 15-ft. switch is that this
length is not desirable with the No. 10 frog, which
is in very common use on many roads. This turnout,
however, more properly belongs with the class of
main line turnouts through which a medium restricted
speed is not only safe but comfortable, and a longer
switch even than 18 ft. is desirable. It will be ob-
served upon reference to the table that the use of a
24-ft. switch with a No. 10 frog only slightly in-
creases the curvature above that which obtains with
the 18-ft. switch, while the detour feature is again
one-third improved. This also applies to the No. 11
and No. 12 frogs, which are often employed in pref-
erence to the No. 10 when space for the No. 15 is
lacking. The 24-ft. length is quite desirable for the
No. 15 and No. 16 frogs, and in all of these the middle
ordinate is seen to be very close to 6 in.

Length of Switch With Frogs No. 18 to 24.—
There still remains the fourth class wherein detour
must be made at the greatest speed practicable, both
as a means of maintaining headway and of avoiding
loss of time while passing through the connection.
The former is the more important consideration, as
headway once lost usually requires a dozen miles to
regain, and if adverse grade is present it may require
a much greater distance. It will be conceded that a
conservative limit for the unbalanced elevation of a
curve is 1^ in. This fact considered alone would

108

DESIGN OF SWITCH CONNECTIONS

permit the operation of Nos. 18, 20 and 24 connec-
tions, whether of turnouts or crossovers, at a speed
of from 35 to 45 miles per hour. But it is neither
comfortable nor entirely safe to detour through the
angle made by a 30- ft. switch at a speed faster than
30 miles per hour, unless the alinement through the
switch is adjusted to furnish equal advantage to the
main track and the turnout routes, which would, of
course, require that the speed through both routes

Fig1. 5. P. R. R. Standard 18-Ft. Point Switch.

should be restricted alike ; when a speed of 35, 40 and
45 miles per hour, respectively, would be entirely
proper.

The 18-Foot Switch as a Compromise Length.—
It is recognized that the 18-ft. switch is extensively
used and by many of our best roads, and that it covers
a wide range of numbers, viz. : between No. 6 and
No. 12. It has been shown, however, that neither the
10-ft. nor the 18-ft. switch is desirable with the No.
6 frog, and, similarly, neither the 18-ft. nor the 30-ft.

109

SIMPLIFIED CURVE AND SWITCH WORK

in such
will be
drilling

length is adapted to the No.
12 frog. While the 18-ft.
length is quite satisfactory
with the No. 10 frog as re-
gards curvature, it is not
easy enough in the detour
feature to fully meet the
to needs of this number in
fc main line movement. The
| fact that by its use the
be number of working lengths
•c may be kept at three, with
K a saving in stock account,
1 1 has heretofore justified its
I g use ; but the increase in the
•£ size of both passenger and
* ti' freight locomotives warrants
^ the revision of standards to
k meet the new conditions,
» even though the fourth
|P length be introduced.

Selection of Frogs for
New Tracks. — The choice
of stock numbers of frogs
will probably always be a
matter of individual prefer-
ence, but a study of some of
the practical considerations
a selection will be of interest. The No. 5 frog
used where only drill power operates. If the
must be done by road power the No. 6 should

DESIGN OF SWITCH CONNECTIONS

be the minimum permissible. This number is almost
invariably chosen for wye tracks, not alone because of
the considerably less room required, but also because
the shorter length can be traversed in less time, an im-
portant item at terminal points. It is desirable on ac-
count of the natural shifting of the track beyond the
connection that the general radius be no less than 300
ft. in any case.

The No. 8 frog is the most frequently used of the
group of smaller numbers. It is a common selection
for main track connections with station sidings, with
private industry tracks, with set-off sidings for
crippled cars, and especially for yard ladders. The
feature that renders it desirable for this last purpose
is the fact that it is the lowest number that can be
used at 15 miles per hour, and thus the greatest con-
servation of room will obtain without sacrifice of
celerity in operation.

Nos. 10, 11 and 12 frogs are preferred for main
track crossovers where only a moderate speed is re-
quired, not alone because they are safer if greater
speed than the established limit should be used, but
because they encroach less upon the clearance with
the traffic running upon adjoining tracks, an import-
ant consideration with 12-ft. track centers. The Nos.
15 and 16 frogs are very useful where space is limited
and it is desirable to make movements with speed, or
where a fair degree of headway must be maintained.
The Nos. 18, 20 and higher frogs are preferable
where ample space is available and the highest speed
practicable must be used.

Ill

SIMPLIFIED CURVE AND SWITCH WORK

112

DESIGN OF SWITCH CONNECTIONS

The numbers
from No. 15 up-
ward are not in-
frequently very
useful to render
the curvature
favorable when
the turnout i s
from the inside
of a sharp curve ;
and, similarly,
the No. 10 and
No. 12 frogs sup-
p 1 y t h e needed
operating advan-
tages of the high-
er numbers when
the turnout is
from the outside
of a curve.

Frog Numbers
and Switch
Lengths for
Standard Use.—
The question of
what numbers of
frogs will best
serve the uses of a trunk line railroad can be de-
termined readily from the foregoing discussion.
They will be found to be Nos. o, 6, 8, 11, 15 and 20.
It will be noted that these numbers increase in a

113

regular progression, and
that in a general way the

- 1t 2 "P \o \o \o vo \o vo vo vo ve vo vo vo vo vo 1

degree of curve of all ex-
cept the second number is
just half that of the next
lower number. The sug-

M1 i tot^oa^H^

gested numbers will be

found to supply a regular-

ly increasing length for

crossovers, and they thus

furnish the means for eco- ^ g s s fc

nomical use of the space g |

available. The No. 15 and £75 g

^ 3

No. 20 turnouts, which are g '
much used in interlocking g
layouts, employ rails that j
vary 5 ft. in length and p
thus supply the required %
spacing for insulated joints . g

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without the introduction of "Sf f f v Tf v f v ^, , T°f

, fo 'Vt^fM^j-ONVoojaiVco^HOs^to^oJo

unusual lengths. O rfw^ftto*^*0k0lSSSS32

The use of the 10-ft. -W ^
switch with the No. 5, of « t. ___

<]q c«'-|'-<^-'^'^t^*^'^'''

the 15-ft. switch with the H ^
No. 6 and No. 8, of the 1

24-ft. switch, with the No. ^

11 and No. 15, and of the I
30-ft. switch with the No.

20, all give a uniform mid- ^

die ordinate of practically WJ^SfeSSi^^^wSS^

6 in. for the chord of the o^^oo^^wo^^roSo^?^

turnout arc. This feature
supplies the opportunity M

.. ... g c> ^•w-'O «^90^ o^N^-^vo ooo •*

for general use of a um- $%

DESIGN OF SWITCH CONNECTIONS

form rule in lining the turnout curve, which is a very
considerable advantage. It is well known that even
on main line divisions poor line through the turnout
arc is quite common, and this defect may be traced to
the practice of lining the curve by eye, or what is al-
most equally unsatisfactory, by a system of offset
measurements. In the rush of lining such connections
the simpler the process the better the result obtained.
Speed Twice the Frog Number. — The approxi-
mate speed in miles per hour that may be used
through connections, assuming the curvature to be at
least 50 per cent greater than will just pass the power
in question, is about double the frog number, and it
thus will be seen that the numbers recommended fur-
nish a regular progression in this respect also.

CHAPTER IX.

RULES FOR COMPUTING SWITCH DIMENSIONS.
24. THE LEAD.

The lead is the principle dimension of the turnout.
It is the distance measured along the main rail be-
tween the actual point of switch and the actual, or
^-in., point of frog. The proper lead is that one
which makes the tangents through the switch and the
frog meet at a point midway between these members.
This not only provides regular curvature, but the low-
est degree of curvature that is possible for the con-
nection. The function of the lead is therefore de-
pendent not only upon the number of the frog, but
upon the length of switch used and also upon the toe
length of frog. A turnout is almost equally satisfac-
tory with any one of several different lengths of
switch, provided in each case the proper lead is used.
Thus, a No. 6 turnout may have any length of switch
between 10 ft. and 18 ft., and a No. 12 any length
between 18 ft. and 30 ft. It is generally considered,
however, that the selection which renders the ratio of
switch angle to frog angle about as 1 to 4 is most
satisfactory. This in effect signifies that with 5^4 m-
heel gage the length of switch should be about twice
the frog number.

The frog length in the lead being generally the
same for all turnouts in the same class, the variable
part of the lead will be the length of rail between

116

COMPUTING SWITCH DIMENSIONS

the frog- and switch.
This may be expressed
in multiples of the frog
number, with sufficient
accuracy for general
use.

The empirical rule
given below will be
found quite in accord
with accepted stand-
ards when a toe length
between 6 ft. and 7 ft.
obtains. If a shorter
toe length is the rule,
the constants may read-
ily be changed to fur-
nish exact agreement
with the leads that are
proper for such reduced
toe length. In fact,
when this means of ex-
pressing the function of
the lead is adopted as a
memory aid, which is
its main purpose, the
constants should be
first adapted to the
practice that obtains on

the particular road.
Length of Track Rails in Lead. — The length of

rail in the lead is 5 times the number of the frog for

117

SIMPLIFIED CURVE AND SWITCH WORK

a 10 ft. switch, 5J/> times for a 15 ft. or an 18 ft.
switch, 5^4 times for a 24 ft. switch and 6 times for
a 30 ft. switch.

It is only necessary to add the switch length and
the toe length of frog to the figures thus computed to
obtain the practical lead. This rule is not only use-
ful as a memory aid, but it furnishes the means of
obtaining readily the proper lead in the event that
a frog of special number is employed, for which no
standard lead is announced.

The permissible variation from regular lengths of
lead is 2 ft. for a No. 6 connection and 8 ft. for a
No. 20 connection and a due proportion for inter-
mediate lengths. Provided these limits are not
passed, it is entirely proper to modify the length of
lead so that regular lengths of rail may be employed.
In the table which accompanies the discussion of
the essential elements of design it is shown how the
lead may be accomodated to the rail length.

Excepting only the case where a frog is the crotch
of two equal curves turning in opposite directions,
there is a regular ratio of difference between the
length of the lead rail and of the turnout arc, and this
difference will be obtained by dividing 12 inches by
the frog number. When the turnout is from a curve
the frog number to be used is the one that most
nearly corresponds with the resultant curvature of
the turnout.

25. THE DEGREE OF CURVE.

Margin of Accuracy, — For the purpose of the
supervisor and the foreman the degree of curve may

118

COMPUTING SWITCH DIMENSIONS

be defined as the number of inches the rail deflects
from the middle of a string 61 ft. 8 in. in length held
to contact at its two ends, fractions of the inch being
multiplied by 60 to supply the minutes of arc. The
degree of curve of a turnout does not figure in any
way in its installation and is only of consequence in
determining the class of power which may be per-
mitted to operate through it, or the limit of speed to
be prescribed, or the templates to be used in plotting
a switch layout. The motive power experts do not
assume to fix the limit of practical operation nearer
than 50 per cent above the curvature that may be*
just passed, and it is recognized that enginemen can-
not regulate speed closer than 10 per cent, and for
plotting the last margin is also ample. An em-
pirical rule, therefore, which enables the investigator
to approximate the curvature within 10 per cent will
satisfy all practical requirements.

Effect of Frog, and Switch Rail. — It is, of course,
understood that the degree of curve of a properly
designed turnout depends both upon the length of
switch rail and the toe length of frog. The shorter
these two members are the more nearly does the
curve approach the theoretical degree, which is, of
course, the minimum. The heel gage admits of little
variation from 5^ in., which provides about 3-in.
flangeway, and a reduction in the length of the switch
rail only increases the abruptness with which the
turnout deflects from the main track. It is recog-
nized that a 10 ft. length of switch point is the mini-

119

SIMPLIFIED CURVE AND SWITCH WORK

mum for the best service. Similarly, the toe length of
frog for modern hard-center construction can hardly
be less than 5 ft. for any frog, and must be for No.
8 and No. 10 frogs no less than 5 ft. 6 in. and 6 ft,
respectively, to avoid the use of filler blocks for the
joints. It may, therefore, be considered that the
combinations shown in the table represent good
practice, and it is upon those dimensions that the ap-
proximate ratios of curvature as given below are
laid.

It will be found, however, that the ratios of curva-
ture for different frog numbers will hold with no more
than 10 per cent error for the specified designs in
use on any particular road, and the value for the
basic turnout being determined the values for the
others will follow the same ratios in all cases. Thus,
the road that prefers short switch points and frogs
might have a value as low as 19 deg. 30 min. for the
cirrve of a No. 6 turnout, which would require the
use of 8 ft. point rails and 4 ft. 6 in. toe length of
frog. If turnouts of other numbers followed the
same general type, the ratios would produce the de-
grees of curvature for all cases.

Radius and Degree of Turnout Curve Leading
from Tangent. — The radius of a No. 6 connection
from tangent track is 250 ft. The radius of a No.
8 is tunce this, of a No. 10 three times, of a No. 11
four times, of a No. 13 five times, of a No. 14 sir
times, of a No. 15 seven times, of a No. 16 eight
times and of a No. 20 thirteen times. The degree of
curve of a No. 6 is 23 deg. and the degree of curve

120

COMPUTING SWITCH DIMENSIONS

of the other turnouts mentioned varies inversely in
the above ratios.

Degree of Turnout Curve Leading From Curved
Track. — To determine the degree of curve of a
turnout from curved track, it is only necessary to add
the degree of the main track curve to the normal de-
gree of the turnout when the connection is from the
inside and to subtract it from the normal degree when
the connection is from the outside. In the latter
case, if the subtrahend should be the greater, the re-
sult would be a minus quantity, and this would in-
dicate that the connection, instead of turning away
from the main track, curved in the same direction.
If in any case the radius were desired, it might be
obtained with a sufficient accuracy by dividing 5730
by the resulting degree.

26. THE FROG NUMBER.

The number of a frog is the ratio of the length of
a bisecting line to the spread at the end of such line.
This bisecting line must be measured from the
theoretical point of frog, or a proper allowance made
for the distance between the theoretical and practical
points. It is not correct to use the ratio of a length
along the sides of the frog point to the spread,
although for frogs of less angle than the No. 6 no
sensible error will result therefrom. If the spread
in such a case is measured as the equal segments of
a broken line, with each half at right angles with one
side of the frog, the process will be rendered exact.
This proposition furnishes a convenient and accurate

121

SIMPLIFIED CURVE AND SWITCH WORK

means of determining the frog number. The length
of frog is always measured along the running rails.
This length divided by the sum of the spread at the

Cotangent

Geometrical Principle of frog number (3)
Fig. 10. Diagram Showing Frog- Number and How Obtained.

two ends, measured between the gage lines and in the
manner indicated by the broken lines in Fig. 10, will
give the exact number of the frog.

27. THE FROG ANGLE AND SWITCH ANGLE.

It is not infrequently necessary to know the exact
frog and switch angle, especially for the purpose of
computing the precise degree of curve of the turn-
out. The degree of curve for turnouts from straight
track is found by subtracting the switch angle from
the frog angle and dividing the remainder by the
length of curve between the switch and the frog.

One of the necessary dimensions to be remem-
bered in all railroad engineering is the length of
radius of a 1 deg. curve, which, as is well known, is
5,730 ft. It happens that this dimension expressed
in chain lengths, or .what is equivalent, divided by
100, supplies the constant necessary to obtain the

122

COMPUTING SWITCH DIMENSIONS

frog angle. The frog angle in degrees and decimals
of a degree is found by dividing the constant 57.3
by the frog number The results by this rule are
practically exact for frogs above No. 6, and nearly
so for frogs of No. 6 and lower.

If the difference between the thickness of the switch
point, which is usually y% in., and the heel gage were
just 6 in., the same constant divided by twice the
length of switch would equal the switch angle. It is,
however, only necessary to compute a new constant
which will be to 57.30 as the actual difference is to 6.
This difference is 5^g with a 5^4 in. heel gage and the
constant is found to be 53.70. This figure divided by
twice the length of switch will give the switch angle
within a few seconds.

28. DISTANCE BETWEEN J/£ IN. FROG POINTS IN
CROSSOVERS.

An exact rule for calculating the distance measured
along the main track between the actual or */£ in.
points in a crossover, is as follows:

Subtract twice the gage from the track centers,
multiply by the number of the frog, subtract inches
equal to the number of the frog and further, sub-
tract the quotient obtained in dividing the track
centers by four times the frog number.

Thus this dimension for No. 6 crossover with 13
ft. centers is obtained as follows : 13 ft. 0 in. — 2
(4 ft. 8^ in.) = 3 ft. 7 in. x 6 = 21 ft. 6 in— 6 in.—

13 !*' QR—= 20 ft 5^ in- and for Na 8 cross'

T: X O

123

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124

COMPUTING SWITCH DIMENSIONS

over with 12 ft. 2 in. centers as follows : 12 ft. 2 in.
—2 (4 ft. Sy2 in.) = 2 ft. 9 in. x 8 = 22 ft. 0 in.

This rule is especially useful where a crossover is
to be installed between tracks that have a different
intertrack distance than the standard, or where frogs
of different numbers are to be combined in the same
crossover. In the latter case the multiplier is the
mean of the two frog numbers and the subtrahend
and item in the divisor the same mean figure.

The rule as generally given heretofore makes no
mention of the further correction, and the error
through this omission may readily be figured as 6^
inches for a No. 6 crossover with 13 ft. 0 in. centers
of tracks.

It is mistakenly thought by some that a different
distance between actual or J/£ in. points should be
used when the crossover is on a curve ; but all linear
dimensions for such a case remain the same. The
effect is merely to introduce between the frogs a
curve similar to the main track curve, and turning in
the same direction, in place of the usual tangent track.
29. DISTANCE BETWEEN FROGS IN LADDERS.

The problem of obtaining the distance between frog
points for ladder tracks to be measured along the
ladder involves tedious computation by tables that
the following simple rule which is exact will avoid :

Multiply the track centers by the number of the
frog and add the quotient obtained in dividing the
track centers by four times the frog number.

125

SIMPLIFIED CURVE AND SWITCH WORK

Thus this dimension for No. 10 frog and 15 ft.
0 in. track centers is obtained as follows : 15 ft. x 10 -f-

' m' = 150 ft. tyz in. ; and for No. 8 frog and

4: X -LU

13 ft. 0 in. centers as follows: 13 ft. 0 in. x 8 +

13 ft. 0 in. .

— — 104 ft. 5 in.

4x8

Curved Ladders. — The above method is cor-
rect whether the ladder is straight or curved. A
curved ladder is always proper when the main tracks
are on a curve, and the degree and direction of curva-
ture of the ladder will be exactly the same as those
of the tracks with which the ladder connects. A very
common error is to endeavor to introduce a straight
ladder for a system of curved tracks. If the degree
of curve is small the result may not be bad for the
first few frogs, but the error grows as tracks are
added and soon requires that another number of frog
be used, and may necessitate the employment of
special frogs. It is certain to furnish very imperfect
general results.

When designing a ladder for curved tracks, due
consideration must be given the fact that the curva-
ture, whether the turnout be from one side or the
other of the main-track curve, is no greater than the
difference between the normal degree for the
selected number of frog and the degree of the main
track curve. The advantage in recovery that ob-
tains in the case of a simple turnout from curved
track to a parallel siding does not obtain in a ladder.

Lining a Ladder. — The computed dimensions for
ladders furnish a ready means of aiming them and

126

COMPUTING SWITCH DIMENSIONS

are equally applicable whether the ladder connects
with tangent or curved track.

A convenient method of lining a new ladder track,
connecting either with a tangent or curved main track,
follows closely the definition of the frog number.
Equal distances may be laid off along the outside
rail of the main track from the theoretical point of
frog, which is one-half the frog number in inches

20'

tf 3x5*15 -0

Fig. 11. Method of Laying Out a Right Angle.

ahead of the ^2 in. point, and right-angle measure-
ments made to the near rail of the ladder. These
offsets will be obtained by dividing the distances by
the number of the frog. For convenience, the equal
distances may be made an even multiple of the frog
number, as 48 ft. for a No. 6, 8 or 12 ; when the first
offset would be 8, 6 or 4 ft. respectively, the second
one twice this, and so on.

A right angle may be accurately turned from a
tangent rail by stretching a metallic tape line taut
with the zero end held at the point to be turned, the
45 ft. mark held a: a point 15 ft. distant, the tape

137

SIMPLIFIED CURVE AND SWITCH WORK

line being grasped at
the 20 ft. mark. This
furnishes a right angle
triangle with the sides
in the ratio of 3, 4 and 5.

30. DISTANCE BETWEEN
1/2 IN. FROG POINTS
IN SLIP SWITCHES.
It is not so important
to remember the dimen-
sions which apply in
slip switches, as, ex-
cepting the distance be-
tween the l/2 in. points
of frogs, the dimensions
are largely dependent
upon details of design,
(such as the length of
the switch and the point
where the turnout curve
originates), and the
standard plan must nec-
essarily b e consulted.
It is well, however, to
know the following rule,
which is practically ex-
act, for obtaining the
distance between the

/2 in. points measured along the axis of tl\e slip.
It follows the same geometrical solution as in a plain
ladder, the difference being that the correction for l/2

128

COMPUTING SWITCH DIMENSIONS

in. points do not negative each other, but are addi-
tive; and twice the gage replaces the track centers
in the principal function and the further correction
applies only to the gage distance for the ladder track.
The distance between ^ in. points of frog in exten-
sion of the ladder to adjoining tracks should be ob-
tained by the rule for simple crossovers. To find the
distance between actual or y2 in. points in slip switches :

Multiply t^vice the gage by the frog number and
add inches equal to the number of the frog and
further, add the quotient obtained in dividing the gage
by four times the frog number.

Thus, this dimension for a No. 6 slip switch, with
4 ft. 9 in. gage is obtained as follows: 2 (4 ft. 9 in.)

x 6 + 6 in. + 4 *tj 9 m- = 57 ft. 8^ in.; and for

TT X 0

a No. 15 slip switch, with 4 ft. %l/2 in gage, as fol-
lows: 2 (4 ft. Sy2 in.) x 15 + 15 in. +-i^^
= 142 ft. 7 in.

129

CHAPTER X.

RULES FOR VARIOUS FUNCTIONS OF
TURNOUTS.

31. LINING THE TURNOUT CURVE.

The curve of the turnout should always be estab-
lished by the use of the string. It has been found
that for all turnouts from straight track no matter
what the frog number, if the adopted practical leads
are used, the middle ordinate of a string drawn be-
tween the heel of switch and toe of frog is 6 in., and
the ordinates at the quarter points of the string are
each 4*/2 in. For turnouts from the inside of a curve
the middle ordinate is 6 in., plus the ordinate of the
main track curve obtained with the same length of
string as used for the turnout; and for turnouts from
the outside of a curve the middle ordinate is 6 in.
minus the ordinate of the main track curve, the
quarter ordinates in both cases being computed as
three-fourths the resulting middle ordinate.

If the turnout is a very long one it is sometimes
useful, after fixing the position of the rail at the
middle and quarters, to draw the string to a contact
at the middle point, when by the principle that ordi-
nates vary approximately as the square of the chords,
the new ordinates at the original quarter points will
be found to be one-fourth the original middle ordi-
nate; and additional points may be established at the
quarters in each half by ordinates which are com-
puted as three-fourths of the middle ordinate from
the half string.

130

FUNCTIONS OF TURNOUTS

Lining Track Behind Frog. — The matter of lin-
ing the curve at the heel of the frog is almost in-
variably left to the eye of the foreman with the re-
sult that this part of the turnout is usually the most
irregular and the one incidentally where the greatest
number of derailments occurs, especially in the
sharper turnouts. When the curve at the heel is con-
tinuous with the curve of the lead, the line is some-
times established with the instrument at the time the
layout is made; or else the curve may be exactly
alined by a proper use of the method of ordinates.
But for turnouts which reverse into a parallel track
a rule can be stated that will apply to all cases, and
will furnish a direct method of establishing at once
both a regular curve and the one of largest radius
possible for the connection.

There is a mistaken impression, and it is even stated
as a rule for guidance in a book on switch work
which has considerable use, that in such lining the
frog tangent should be extended to the same length
as that obtaining in a crossover. This is not correct
because the shorter the tangent of the curve, the
greater will be the degree of curve, and if no limiting
features are present the curve should be made as
long as practicable, and it may even be desirable to
establish the P. C. at the heel of the frog. This is
especially important where the turnout is from the
outside of the curve. In such a case it may be es-
sential to use this advantage with the alternative cir-
cumstance that the turnout may enter a different class
for operation. Thus, if a No. 6 connection is limit-
ing for road power, such a connection from the out-
side of a 5 deg. curve, with the point of curve at the

131

SIMPLIFIED CURVE AND SWITCH WORK

heel of frog, would just remain within the limit.
Alined in the manner of a crossover, the curvature
would become 28 deg., or 207 ft. radius, and the con-
nection be open only to switch engines.

The suggested practice adds to the operating effici-
ency of the turnout without appreciable sacrifice of
standing room on the siding and is a maintenance ad-
vantage as well, because that part of 'the turnout, not
being secured as is the lead portion, is subject to
traffic shifting and requires a greater initial radius
to remain with even moderate supervision within the
required degree of curvature. This proposition being
accepted, the rule for lining when the P. C. is estab-
lished at the heel of the frog may be stated, which
follows a similar geometrical solution to that for
theoretical lead except that the item of gage is re-
placed by the off-set from the heel of the frog on the
turnout rail to the line of the near rail of the parallel
track. The computation, when any other point on
the frog tangent is used, follows an exactly similar
solution, but correction of the middle ordinate must
be made in the proportion of the squares of the
chords.

Rule for Lining the Curve Back of Frog. — From
the .distance between gage lines of the parallel tracks
subtract the spread at the heel of the frog and mul-
tiply by twice the number of the frog, which gives
the distance to be measured along the main track
from the heel of frog to the point at right angles
with the end of the curve, whether the turnout be
from straight or curved track. For turnouts from
straight track, measure from the middle of a string
drawn between this point and the heel of the frog an

132

FUNCTIONS OF TURNOUTS

ordinate of 20 in., and from the quarter points an
ordinate of 15 in., which will give three essential
points in the curve. For turnouts from curved track
the middle ordinate must be increased by the amount
of the ordinate of the main track curve, obtained
with the same length of string, when the turnout is
from the outside, and similarly decreased when the
turnout is from the inside of the main track curve;
the quarter ordinates will be three-fourths the re-
sulting middle ordinates in all cases.

Thus, for the No. 10 connection with a siding on
the outside of a 4 deg. curve, on 12 ft. 2 in. centers
with the main track, the distance to be measured from
the heel of the frog to the end of the curve would
be obtained as follows: 7 ft. 5^ in. — 10 in. =
6 ft. 7^ in. x 20 — 132 ft. 6 in. The middle ordi-
nate of a 4 deg. curve being 18 in. the ordinate to be
measured at the middle in lining the curve at the heel
is 20 in. + 18 in., or 38 in., and at the quarters,
three-fourth of 38 in., or 28^ in.

When the turnout is above No. 10 the use of the
string becomes inconvenient and a method by offset
measurements is generally preferable. The calcula-
tion for total length along the main track is the same.
This distance may be divided into three or four parts
and the offset from the imaginary parallel track will
be the proportion of the offset distance at the P. C.
represented by the square of the fractional distance
from the P. T. These may be made supplements of
the distance between the main track and the parallel
track and direct measurements be used to locate the
turnout curve. This method applies nearly as well
to the lower numbers of frog, and is correct whether

133

SIMPLIFIED CURVE AND SWITCH WORK

the main track is tangent or curve or in part both.
The resulting curve is not quite circular, but this is an
advantage both in operation and maintenance.

For lining the turnout curve and the tangent and
curve back of the frog, the maintenance standards of
some roads furnish offset distances from the main
rail at established intervals. These are very useful
provided care is taken that the measurements are
made exactly at right angles. It should be noted that
these offsets are identical for all different conditions
of layout whether the turnout is from tangent or
curve. The principal disadvantage is that the dimen-
sion data are not always at hand, and they are too
many to be remembered.

32. DESIGNING THE BILL OF SWITCH TIES.

It is very necessary that the supervisor shall be
able to instruct his foreman how to make up and
apply a set of switch ties, especially for new work,
so that when the switch work is completed the tim-
bers will line up on both sides accurately. The aver-
age foreman will err on the side of excess, probably
with the thought that timbers can be cut off but never
pieced out. This results in measurable loss, both for
the timber wasted and for the labor necessary to cor-
rect the error.

The published bill of material for various turnouts
and crossovers, which is practical enough for pur-
chasing department purposes, supplies no guide either
in selecting or applying the ties. Even if by clever
interpolations a working bill is made up from the
general bill it does not furnish any check upon its
installation.

134

FUNCTIONS OF TURNOUTS

The rule for lining the curves of turnouts furnishes
a practical means of calculating the lengths of the
switch ties for the middle and quarter points between
the heel of switch and toe of frog, and these are
found to be practically the same for all turnouts. The
length at the middle is 10 ft. 4 in., at the quarter
nearest the switch 9 ft. 5 in., and at the quarter near-
est the frog 11 ft. 5 in. The timber at the heel of
the switch is always 9 ft. 0 in., but that at the toe of
the frog varies according to the spread of the frog.
It is 12 ft. 9 in. for No. 24, No. 20 and No. 15 frogs,
12 ft. 8 in. for a No. 10 frog, 12 ft. 5 in. for a No.
8 frog and 12 ft. 2 in. for a No. 6 frog. It is, of
course, well known that the timber at the point of
frog of all turnouts is 13 ft. 3 in.

Ties Between Switch and Frog of Turnouts and
Crossovers. — There is thus at hand a practical
check upon the bill to be designed, as well as upon
the correctness of the installation. This bill may be
obtained off-hand by the following simple rule, which
is fairly accurate for all turnouts, either from straight
or curved track:

Determine first what number of ties will be required
between the heel of switch and the toe of frog and
divide this member by 3. Calculate the increase at
the frog by dividing 23 in. (or any other spacing
center to center of ties that may be preferred) by
the number of the frog. Beginning with 9 ft. 0 in.
set down lengths for the first third by adding suc-
cessively one-third the increase at the frog, and for
the second third by adding two-thirds of the increase

135

SIMPLIFIED CURVE AND SWITCH WORK

at the frog, and for the last third by adding the full
increase at the frog.

BILLS OF TIMBER BETWEEN HEEL OF SWITCH

AND TOE OF FROG.

(Ties 22^ Inch Centers.)

No. 5 Turnout or Crossover.

ft. in. ft. in. ft. in. ft. in.

90 94 10 0 10 10

91 96 10 3 11 3
93 99 10 6 11 7

No. 6 Turnout or Crossover,

ft. in. ft. in. ft. in. ft. in.

90 95 10 2 11 4

91 96 10 4 11 8

92 97 10 6 11 11

93 99 10 9 12 2
9 10 11 1

No. 8

Turnout

or Crossover.

ft.

in.

ft.

in.

ft.

in.

ft.

in.

No. 11

Turnout

or Crossover.

ft.

in.

ft.

in.

ft.

in.

ft.

in.

3 .

— • — 12 9

No. 15 Turnout or Crossover.

ft. in. ft. in. ft. in. ft. in.

90 96 10 4 11 6

90 96 10 5 11 7

136

FUNCTIONS OF TURNOUTS

«)

-12

—

No. 20 Turnout or Crossover.

ft. in. ft. in. ft. in. ft. in.

90 96 10 4 11 6

90 96 10 4 11 7

91 97 10 5 11 8
91 97 10 6 11 9

91 97 10 7 11 10

92 98 10 7 11 11

92 98 10 8 12 0

93 99 10 9 12 2
93 9 10 10 10 12 3

93 9 10 10 10 12 4

94 9 11 10 11 12 5
94 10 0 11 0 12 6

94 10 1 11 1 12 7

95 10 1 11 2 12 8

95 10 2 11 4 12 9

96 10 3 11 5

It will be found that the last tie in the last third
approximates the length computed for the toe of the
frog and that the ties at the middle and quarters are
practically the same lengths as was computed for
those points. To illustrate: The number of ties be-
tween the switch and frog of a No. 15 turnout is 47.
The increase at the frog is l*/2 in. The respective
increments are, therefore, % in. for the first 16 ties,
1 in. for the second 16 ties and \y2 in. for the last 15
ties. It will be instructive to write down the full bill
and note that the 12th tie is -9 ft. 5 in., the 25th tie

137

SIMPLIFIED CURVE AND SWITCH WORK

10 ft. 4 in., the 37th tie 11 ft. 6 in., and the 47th tie
12 ft. 9 in.

If the turnout leads to a parallel track, the length
of the switch ties through the frog and beyond, in-
creases to the last tie at the uniform rate calculated
for the increase at the frog. If the turnout con-
tinues to curve away from the main track the timbers
beyond the frog must be correspondingly lengthened.

Long Ties for Crossovers. — The rule will be
used in the same manner to obtain the lengths of the
short ties in a crossover. The length of the last short
tie will equal the track centers and the length of the
long ties will equal the track centers plus the standard
cross-tie length. It is then only necessary to deter-
mine the number of long ties that attach to a par-
ticular set, which in turn will indicate the limits with-
in which the long ties occur. For 12 ft. 7 in. centers
the number of long ties in a crossover is 2^/2 times the
number of the frog. This ratio is 2% for 12 ft. 2 in.
centers and 2% for 13 ft. 0 in. centers. As the last
short tie before reaching the No. 10 frog is 12 ft.
7 in. it will readily be seen that for those centers the
entire space between the toe of the two frogs will be
laid with a total of 25 long ties of a uniform spacing
of 23 inch centers. In a No. 15 crossover on the
same track centers there would be long ties not only
through the extent of the frogs but for three ties
either side the frog, or a total number of such ties
of 37. The ties under slip switches follow standard
designs of layout and the plans should be consulted
in selecting and applying the ties, as well as in the
other parts of the work.

138

FUNCTIONS OF TURNOUTS

Obtaining the Bill of Ties in Renewals. — When
renewal of an existing turnout or crossover is to be
made, it is a very simple procedure to measure the
distance between the gage lines of the two outside
rails over each tie, provided they are properly spaced,
and if not, then at the points where with proper
spacing ties would occur, and add to the figures thus
obtained the constant 3 ft. 10 in., which will give the
proper lengths of ties to be used. It is a still simpler
method to hold lining sticks outside the rails where
the new switch ties should be placed, and then mea-
sure the lengths for the ties from the end of one
stick to the other.

33. NARROW GAGE SWITCH CONNECTIONS.

Even though a sixth of the railroad mileage of the
world is of narrow gage, the introduction of matter
pertaining to such gage would perhaps not be alto-
gether appropriate here, were it not for the fact that
increased attention is being directed toward the in-
dustrial field of South America, where the narrow
gages, particularly meter gage, are in common use.
The subject is also of direct local concern through
the rather extensive employment of both the 3 ft.
0 in. and 3 ft. 6 in. gages in contractors' railways.

A broader gage than the standard, principally 5 ft.
6 in., is used quite extensively in certain sections of
the world and its total mileage approximates that of
narrow gage, but its use in America is not being ex-
tended and it thus has no direct interest.

As the distance between frogs in crossovers, lad-
ders and slips is a purely geometrical function, the
rules for its computation are equally applicable to all

139

SIMPLIFIED CURVE AND SWITCH WORK

gages and the ratios of curvature also remain the
same, but a different value attaches to the basic turn-
out. It is further necessary to design new constants

NARROW GAGE SWITCH CONNECTIONS.

No.

Factor

2.50

Lead Rail

15' 0"

Lead

37' 0"

Radius
115'

Degree

51° 30'

Mid. Ord.
3"

2.64

18' 6"

40' 6"

168'

34° 40'

2.75

22' 0"

44' 0"

236'

24° 30'

2.83

25' 6"

47' 6"

318'

18° 06'

2.88

28' 9"

50' 9"

420'

13° 40'

2.92

32' 0"

54' 0"

535'

10° 44'

Functions for 3' 0" Gage

3.2

19' 254"

41' 254"

155'

40° 25'

324

3.2

22' 5"

44' 5"

214'

28° 35'

354

3.2

25' 754"

47' 754"

265'

21° 00'

3.2

28' 9 54"

50' 9 54"

362'

15° 54'

3^/8

3.2

32' 0"

54' 0"

471'

12° 20'

354

3.2

35' 254"

57' 254"

594'

.A. /-«

9° 43'

35i

Functions for Meter Gage

4.3

25' 954"

47' 9y2"

192'

30° 12'

sy&"

4.3

30' 154"

52' 154"

269'

21° 25'

5/f

8
9

4.3

34' 4 24"
38' 854"

56' 4M"
60' 8 54"

367'
485'

15° 40'
11° 50'

4 ft"

4.3

43' 0"

65' 0"

626'

9° 10'

4 A",

4.3

51' 354"

73' 3 54"

860'

6° 40'

Functions for 3'

6" Gage

for the length of lead rail and for the middle ordi-
nate in lining.

Length of Switch Rail. — The choice of switch
length is more important in narrow gage than in
standard gage. Since the ostensible purpose in build-
ing a new railroad of narrow gage is economy in first
cost, however little this feature may be realized in
after operation, a variety of switch lengths is out of
the question and, indeed, a single length only is per-
missible. This length should not alone satisfy the
essential requirements of the connection, but should
be such that upon change of the gage to the standard
the points may continue in use.

As the 15 ft. length has been found quite suitable
for employment in standard gage with the entire

140

FUNCTIONS OF TURNOUTS

group of frogs that are in most general use, it is
proper to consider this length in its relation to narrow
gage connections. A thorough study of the resultant
degree of curve and of the middle ordinate for lining
will show that the 15 ft. length is entirely satisfactory.
A table is furnished giving the principal functions for
3 ft. 0 in., meter, and 3 ft. 6 in. gages. It will be noted
that for 3 ft. 0 in. gage a middle ordinate of 3 in. is
proper, for meter gage 3 y2 in. and for 3 .ft. 6 in. gage
434 in., and that these apply practically to all frogs,
as was to be expected from the preceding study of
standard gage functions.

Length of Lead. — The lead in narrow gage
switch work admits of little deviation from the ideal
lengths, and the multiplier to obtain the length of
track rail will therefore not be constant for the
different numbers of frog, although the variation is
not great. The use of the mean, which is 2T7D- for
3 ft. 0 in. gage, 3T30- for meter gage and 4^ for 3 ft.
6 in. gage, furnishes fair results in practice. It will
be observed that the difference in length between the
lead rail and the turnout arc is likewise the quotient
found in dividing 12 in. by the frog number that most
nearly represents the resultant degree of the con-
nection.

Degree of Curve. — The degree of curve in nar-
row gage turnouts follows the same ratios as in
standard gage, but the curve of the No. 6 connection
for 3 ft. 0 in. gage is 50 deg., for meter gage 40 deg.,
and for 3 ft. 6 in. gage 30 deg. The rules for lining
at the heel of the frog and for designing the bill of
timber may be readily adapted to use in the narrow
gage.

141

SIMPLIFIED CURVE AND SWITCH WORK

Where 11 ft. 0 in. centers of tracks obtains and
the equipment is as wide as 9 ft. 1 in. and of a total
length of 51 ft. 0 in., the use of curves greater than
40 deg., or 147 ft. radius, is undesirable and the No.
6 frog should therefore not be employed in less
than meter gage. The combined nosing and overhang
of such equipment while making parallel movements
through crossovers with curvature of that degree
would limit the track centers to 12 ft. 0 in. The
presence of one of these features alone would re-
duce the clearance on 11 ft. 0 in. centers to a bare
margin of safety.

Permissible Speeds. — The speed permissible
through standard gage connections has been deter-
mined as equivalent in miles per hour to double the
frog number, but by reason of the smaller bearing
area of the tie and the increased impact due to higher
center of gravity and greater oscillation in narrow
gage, a speed of no more than once the frog number
is allowable.

34. GRAPHICAL METHOD OF LAYING OUT SWITCHES.

It is practically impossible to establish a com-
plicated layout of switches upon the ground with the
transit instrument, and whenever such a feat is at-
tempted nice work is required on the part of the fore-
man to harmonize the arrangement. A much more
satisfactory solution of the problem is found in the
graphical method. With good templets a layout may
be plotted exactly to scale, and if the scale is large
enough, (but not so large that the radius of the
curves overruns the available scope of the curve
templets), scale measurements may be taken at in-

143 \

FUNCTIONS OF TURNOUTS

tervals across the
layout and from
these, and the lin-
ear measure-
ments for the prac-
tical lead, a fairly
correct location
can be made.

Even when turn-
outs as high as No.
20 are employed it
is possible to use
a scale as great as
1 in. to 16 ft., but
in most cases, if
the plotting is ex-
ceedingly a c c u -
rate, a scale of 1
in. to 32 ft. is suf-
ficient. The archi-
tect's scale is pref-
erable to the en-
gineer's scale for
this purpose, as di-
mensions for
switch c o n n e c -
tions are general-
ly, and should al-
ways be, in feet
and inches rather than tenths, especially because the
men who apply the switch material can best use inch

143

SIMPLIFIED CURVE AND SWITCH WORK

rule. The diagram shows a layout that was suc-
cessfully installed by means of measurements scaled
from a plan drawn to a scale of 1 in. to 32 ft.

35. HINTS FOR LAYOUT.

A specific arrangement, which by a proper
selection of location may often be made to ap-
ply for such important points as the end of double
track, or the ends of passing sidings, is the estab-
lishing of the point of switch of the turnout at
the beginning of a curve, when there will be con-
tinuous simple curvature for both sides of the con-
nection and the superelevation will be common to
both tracks. This is of very great advantage to the
operating efficiency of the turnout.

In congested districts it is not always possible to
employ a simple ladder and resort may be necessary
to lap connections. This should never be three-throw
switch work, which is in the nature of special design
requiring interest charges for infrequently used dup-
licates. Lap connections can always be designed
which will employ regular stock patterns of frog and
switch material.

It is often advantageous, particularly when the
crossover is on a curve or partly on a tangent, to plan
the crossover with dissimilar frogs. If, for example,
the available space on a 3 deg. 30 min. curve will per-
mit of no longer crossover than a No. 10, a better
alinement will be obtained by the use of a No. 8 turn-
out from the outside and a No. 12 turnout from the
inside of the curve, the resultant curvature being 8

144

FUNCTIONS OF TURNOUTS

deg. for both ends ; whereas one end of the No. 10
crossover would otherwise have been 11 deg. This
plan eliminates the tangent between the frogs, but for
low speed movement this is not important. The ar-
rangement, however, has limitations, as it is not pos-
sible in ordinary track centers to mate any frog with
one that has a number more than 60 per cent, greater ;
that is, a No. 8 and a No. 12, a No. 10 and a No. 15,
a No. 15 and a No. 20, or a No. 15 and a No. 24 are
limiting combinations.

In deciding what number of frog to employ it is
necessary to consider not only the general question of
curvature but also the question of clearance with ad-
jacent tracks. Thus, a No. 6 connection in tangent
track adjoining a main track with 12 ft. centers is
hardly a safe selection. The "nosing" of the longest
passenger equipment while passing through such
turnouts furnishes bare clearance with the traffic
running on the adjacent track, and if curvature and
superelevation enter there may be actual interference.

A similar question is involved where two switches
leading from a double track are placed exactly op-
posite. In such a case when simultaneous move-
ments are being made from the main line into both
turnouts the clearance is doubly affected. To avoid
this disadvantage the location of the switches should
be staggered at least 10 ft. By reason of the vital
need for ample clearance in all train movements and
because of the maintenance difficulty as well as the
commercial scarcity and consequent high price of

145

SIMPLIFIED CURVE AND SWITCH WORK

timbers above 22 ft. in
length, the practice of
placing crossovers for
parallel movements ex-
actly opposite is being
d i s c o n t i nued. They
should be so located that
each will have independ-
ent long timbers.

It is usually considered
objectionable to locate
crossovers on a curve but
there are advantages
which weigh well with
the disadvantages. Thus,
a No. 20 crossover on a 1
deg. 40 min. curve is a 3
deg. 20 min. curve on
one end and tangent on
the other. Although the
curvature is twice as
sharp as for a No. 20
from straight track,
there is the compensat-
ing feature of the super-
elevation of the main
track curve, which being
designed for high speed
on the main track is ample for the reduced speed
through the sharper curve of the turnout.
Diversion to Parallel Position. — The theoretical
140

FUNCTIONS OF TURNOUTS

design of a crossover may be employed for the rather
common case wherein a track is diverted to a par-
allel position, usually the regular distance for track
centers, although the distance may be a different one.
Exact theoretical lead will be employed, which is equal
to twice the gage multiplied by the number of the
frog, and the rule for distance between the frog
points will apply except that it will not be reduced by
inches equal to the frog number. The lining of the
curves may be done by offsets in the manner else-
where explained ; or, alternately, by drawing a string
between the theoretical point of switch and point of
frog and lining the track with an ordinate of 14^4 in.
at the middle and ^ of this or 10^4 in. at the quar-
ters. Proper correction would need to be made if
the proposed layout were on a curve. In that event
the principal point to be observed would be the de-
signing of the crossover with dissimilar frogs, which
might even be of unusual numbers, so that the cur-
vature of the two parts of the arrangement would be
equal.

For a diversion through 13 ft. 2 in. distance be-
tween parallel tangents the equivalent of a No. 24
crossover with 90 feet of tangent between the curves
is quite favorable. The curvature is 1 deg. 05 min.,
and with the use of lJ/£ in. superelevation, which may
be run off one-half on the curve and one-half on the
tangent at a rate of y2 in. to 30 ft., a speed of 50
miles per hour might be established.

147

CHAPTER XI.

PRACTICAL CONSIDERATIONS IN INSTALLING
TURNOUTS.

36. ORGANIZATION.

Training Gangs for Switch Work. — The correct
and expeditious placing of switch connections re-
quires special qualifications, and any important opera-
tion of that character should be assigned to a gang
expert in such work. The foreman should be one
whose ability and taste in the refinements of switch
installation have been demonstrated beyond question,
and it is almost equally important that the major part
of the gang should be capable workmen, since every
operation requires not only skill but despatch.

Each supervisor's division should have at least one
such gang available and other gangs should be in
process of development to undertake such work when
the occasion arises. For this object the simpler items
of switch construction, such as new switches in pri-
vate industry tracks, unimportant spurs in isolated
situations, etc., should be delegated to the less ex-
perienced gangs, and their efforts should receive
greater assistance from the supervisor. An unskilled
gang can often be combined with an expert one in a
switch operation, with excellent advantage to the
former and without detriment to the general result.

Number of Men Required.— The number of men
needed to constitute an efficient gang for the expedi-

148

PRACTICAL INSTALLATION OF TURNOUTS

tious application of a switch connection, in a busy
main line over which passenger traffic is carried at
speed and in considerable volume, is not far from 24,
exclusive of the foreman and his assistants. A less
number is not able to handle the heavy work period-
ically necessary, and a greater number cannot labor to
advantage in the restricted space. Two of the labor-
ers should be men qualified to act as flagmen ; a third,
whose dependability is unquestioned, should watch for
the approach of trains and convey proper warning;
a fourth is needed to carry water and look after the
tools; at least ten should be capable spikers and all
should be useful in general lines of work. Each in-
dividual of the gang should have a specific duty to
perform when the rush is on after the use of track
has been given. The entire gang should fall into
their allotted duties naturally and without the neces-
sity of a preliminary line-up.

Developing Quickness of Action. — The men who
flag should be alert to display the warning signal the
moment the need is communicated, and should be
trained to hold the banner against trains until unmis-
takably recalled. The waving of a red flag by the
foreman at the immediate location of the work should
be the notice for the men to start the work, and should
also be the signal for the distant flagman to act.

Only when its movements are automatic and instan-
taneous can the gang be regarded as well organized.
Any members who are slow or awkward or inclined
to run into the way of danger should be promptly
eliminated. The efficient foreman is able to indicate

149

SIMPLIFIED CURVE AND SWITCH WORK

his instructions with a word, even a gesture, and he
should exact instant obedience. With the conscious-
ness that his practice is founded upon correct rules,
he proceeds unerringly and his confidence inspires
efficient co-operation from his men.

37. SPECIAL TOOL EQUIPMENT.

Besides the ordinary stock tools, the switch gang
should have a rail dolly to move rails quickly from
place to place ; a rail saw to cut rails of proper length,
(a very frequent necessity in extensive interlocked
switch work carrying specific locations of insulated
joints) ; pneumatic tie tampers and rail drills for use
whenever access to a compressed air line is possible;
a hydraulic rail bender to break rails for temporary
connections, to bend stock rails for accurate adjust-
ments with the switch rail, and in certain cases to
bend the rails to conform with the curve of the
sharper turnouts; and, not least in importance, a tool
which may be called the pick adze, because generally
made in the blacksmith shop from an ordinary tamp-
ing pick, which is exceedingly useful in respiking for
cutting about spikes to facilitate their withdrawal.

The track gages employed should be only those
whose accuracy has been tested and a steel tape
divided into twelfths is practically a necessity for
nice work. A metallic tape is good enough for meas-
uring the lengths of the switch ties or for laying off
their places in the connection, which should always
be done by continuous measurement, particularly in
slip switch work. A ball of twine for lining should

150

PRACTICAL INSTALLATION OF TURNOUTS

not be lacking. As the switch gang is a floating one
a substantial tool box is required.

38. DETAILS IN THE DESIGN.

Avoiding Unusual Lengths of Rail. — The prac-
tical length of lead having been determined so as to
employ whole stock lengths of rail wherever pos-
sible, the turnout arc should be made of the exact in-
creased length necessary by cutting a longer stock
length. This practice is important because the pres-
ence of unusual lengths of rail in the main track is
very undesirable, and because the cutting of a rail if
not properly done introduces an elevation of the sur-
face which is noticeable in riding. However, this
latter objection may be overcome by using the rail
saw, or by scoring only the perimeter of the base in
cutting, which nearly invariably furnishes a square
break with the smoothness of the rail surface undis-
turbed. It is a distinct advantage to make the rail
units in the turnout arc as few in number as pos-
sible, especially in the sharper turnouts. The signal
requirement for a 5 ft. staggering of block joints can
usually be met by proper selection from the odd stock
lengths of rail available.

Arrangement of Joints. — One of the essential de-
tails in switch work is a nice arrangement of the
joints. Whether housing of the switch points is ap-
proved or not, the joints in advance of the point rails
should follow a uniform standard. The joints in the
two stock rails admit of little staggering, but this
should be such that each joint has independent tie

151

SIMPLIFIED CURVE AND SWITCH WORK

support. With the longer switch points no inter-
mediate ties between the joints are possible unless
long stock rails are used, the utility of which is
doubtful.

Assuming 33 ft. stock rails and a 30 ft. switch,
the joint on the main stock rail should be the one
nearer the point of switch, because this will enhance
the efficiency of the joint at the other end of this rail,
which is a part of the main track structure. The dis-
tance in advance of the point of switch to this joint
should be 4 ft. 11 in., which allows sufficient space
ahead of the switch for the splice bar, and spaces the
joint at the reverse end of the rail one tie-interval
from the heel of the switch. The joint of the turn-
out stock rail should be 8 ft. 3 in. in advance of the
point, which spaces the other end of this stock rail
three tie-intervals from the heel of the switch. The
preservation of this uniform arrangement is desir-
able even though it may generally require the intro-
duction of shorter rails into the main track, and even
though, if space be limited, it may necessitate a re-
sort to the shortening of the lead within the allowable
limits. This uniformity is of course a necessity when
stock rails housed at the mills are employed. As
switches which occur together are usually part of a
route across multiple track systems, the suggested ar-
rangement would bo duplicated for the adjoining
switch with the result that the two switches would be
separated 13 ft. 2 in., or 46 ft. 2 in., which unques-
tionably are very favorable distances.

152

PRACTICAL INSTALLATION OF TURNOUTS

The elimination of joints from guard rails, desir-
able at all times but essential with the employment
of guard rail clamps and their fillers, is a well known
requirement of nice work. The further arrangement
of joints should be such as to use the shorter, odd
lengths of rails supplied with all rail orders to the
usual amount of 10 per cent, the presence of which
at other points is undesirable. To obtain the best
line, no rail length less than 15 ft. should be employed.
All rails should be drilled and the joints full bolted
and tightened before final line is established.

Bend in Stock Rail — The point at which to in-
troduce the angle in the turnout stock rail is one con-
cerning which practice varies. A computation of the
distance from the actual to the theoretical point of
switch, assuming the former to be generally J/s in.
thick, shows it to vary between 3 in. for a 10 ft.
switch and 8 in. for a 30 ft. switch. It is not pos-
sible to bend a rail to an exact angle at any point
and the proper location of the bend, for the bending
apparatus available, is readily found by trial for each
length of switch. This distance will usually be de-
termined as 6 in. for a 10 ft. switch, 9 in. for an 18
ft. switch and 12 in. for a 30 ft. switch. The set
should be made in the stock rail leading to the less
important track, even though this would normally be
the tangent from which the turnout seemingly
springs. The important feature is to provide a
smooth route for the faster or higher class traffic.

Spacing of Ties — The spacing of the switch ties
is a detail which should have careful attention. In

153

SIMPLIFIED CURVE AND SWITCH WORK

main running tracks carrying fast-passenger or
heavy-freight traffic with timbers of about 9-in face,
a spacing center to center of 22 % in. should be em-
ployed, which is equivalent to 18 ties to a 33 ft. rail,
and is equal in bearing area to 20 ties of a width
averaging 8 in. This spacing is a convenient one be-
cause in the application of the rule for computing the
bill of switch timber the increments become even
fractions of an inch for the three most used of the
higher numbers of frog, viz., $£ in., ^4 m- and l/^
in. for a No. 20; % in., 1 in. and 1J^ in. for a No. 15

and J4 m-> l/^ m- and 2*4 m- ^or a No. 10.

While this spacing would appear somewhat diffi-
cult of application by continuous measurement for
some foremen, facility may be acquired readily in
adding 2 ft. and dropping back \y2 in. each tie space.

In private sidings and yards a spacing center to
center of 27 in. is sufficient, which is equivalent to
15 ties to a 33 ft. rail or equal in bearing area to 17
ties of a width averaging 8 in. While this may seem
excessive for such places from the standpoint of sup-
port for the rail, it is none too much to fully meet
the requirements in maintaining the alinement. This
spacing renders the increments in computing the bill
1% in. 2^4 in. and 3^ in. for No. 8 and 1^ in., 3
in. and 4^ in. for No. 6. It is, of course, quite a
simple procedure in laying out the spaces to go for-
ward 2 ft. 3 in. each time. The spacing in both
cases would have to be modified in the event that
hewn switch ties were employed.

Location of Switch Lever — It is desirable that

154

PRACTICAL INSTALLATION OF TURNOUTS

non-interlocked switches in main running tracks
should have the ground lever so placed that when set
for the main track the rod connecting the switch
with the switch stand is in tension. For switches
that connect ordinary sidings, the switch stand, if
possible, should be on the right-hand side of the
switch in facing the connection. Wherever a siding
connects with a main track a derail should be in-
stalled in the siding at the clearance point to prevent
cars being moved beyond that point by the wind, by
error of train crews or by malicious persons, when no
lamp or other indication would warn a train approach-
ing on the main track of the danger.

155

CHAPTER XII.

METHODS IN INSTALLING AND MAINTAINING
SWITCHES.

39. SIMPLE CONNECTIONS.

The location of the connection having been selected
and the details of the design determined, the main
points of the lay-out should be marked upon the rail.
These include not only the point of switch and */2 in.
point of frog, but all the joints proposed throughout
the lead. Preliminary establishment of the joints is
essential to the placing of the switch timbers in their
correct positions, avoiding the need for respacing.

The Guard Rail — The timber having been in-
stalled, the main-track guard rail should be applied.
It should be well secured and the proper width of
flangeway provided. This width is 1-j/I in. when the
gage of the track is 4 ft. Sl/2 in. and 2^J in. when
the gage is 4 ft. 9 in. Frogs of No. 6 and lower usu-
ally have the 4-ft. 9-in. gage. After the frog is
placed care should be taken that the guard rail gage
of 4 ft. 6^4 in. is observed. This is the distance from
the gage line of the frog to the gage line of the guard
rail. It does not vary in amount for different gages
of the track. For convenience the guard rail gage
should be measured upon some part of the track gage.

For the greatest effectiveness, a full equipment of
guard rail clamps and guard rail tie plates is neces-
sary. The tie plate guard rail fastener is another

156

INSTALLING AND MAINTAINING SWITCHES

useful accessory in the support of the guard rail. No
variation in guard rail gage is permissible, and the
longitudinal position of the guard rail should follow
the standard closely.

The Frog and Lead Rails — Along with the frog
the full lead rail including the switch point is usually
applied. When the main track point only is in place
it should be both spiked down and clamped to the
stock rail and when both points are in, but not con-
nected to the switch stand, the turnout point should
also be wedged away from the main rail. If the ex-
act heel gage is preserved and the bend made in the
stock rail at the proper place, the switch point will
set up close to the stock rail through the whole length
of the tapered section. When the switch is thrown
the corresponding point will similarly be in contact
with the main rail.

Mating of Switch Rail and Stock Rail — Acci-
dents have resulted from foremen making the mis-
take of putting in a switch point of different section
or weight than the rail in the track. A much worn
switcli point in combination with a full section stock-
rail might also cause an accident. The stock rail
should never be chipped with the cutter to make the
point set up close, as this practice renders the rail
more liable to fracture.

When Protection is Required — There are cer-
tain rules for renewing ties and rails in main tracks
which must always be observed, and these apply
equally in the installation of frogs and switches. The

157

SIMPLIFIED CURVE AND SWITCH WORK

rule specifies that any condition which interferes with
the safe passage of trains at full speed is an obstruc-
tion and must not be attempted without full protec-
tion in both directions.

An obstruction is considered to exist when more
than one tie in face is removed, or more than four
ties are removed in any rail length, or the ties ad-
jacent to the one removed are not fully spiked and
tamped. Also when the spikes are withdrawn from
more than every other tie on both sides of the rail, or
the joints have less than two bolts in place with either
one of these not fully tightened. An inferior com-
promise joint or one not properly applied, which al-
lows a drop in the surface or an offset in the gage of
more than ^ in., would constitute an obstruction. A
tightening of the gage more than ^ m- or a widen-
ing more than ^4 m- from the standard would re-
quire protection. In regaging when more than every
other tie is unspiked and the spikes removed on the
inside from more than four consecutive ties there is
an unsafe condition. In all work care should be
taken that trains are passed with an ample margin of
safety.

40. SLIP SWITCHES.

As the various parts composing a slip switch are
made to the exact dimensions prescribed by a stand-
ard plan, the utmost care is necessary in applying the
material to assure correctness in every detail. The
linear measurements, particularly for the longer slips,
must always be made with a steel tape and for the

158

INSTALLING AND MAINTAINING SWITCHES

nicest work the tape should be one that has been
tested for its accuracy. It is not too great a refine-
ment to adjust the measurements for temperature
variation. Steel tapes are not infrequently as much
as }/2 in. in error, and extremes of temperature may
balance this error or introduce a further error, which
in a No. 20 slip nearly 200 feet long might cause a
total error of 4 in., which would of course be inad-
missible.

Measuring Dimensions — Axis of Slip — All linear
dimensions should be measured along the axis of the

-Distance between $" points in slips

Movabk point frogs
Fig. 15. Diagram of Slip Switch.

slip, a line connecting the theoretical points of the
end frogs. It will be found useful to sketch this
axial line accurately upon the ties for the triple pur-
pose of laying off the detailed linear dimensions, for
squaring the switch ties as they are applied and for
lining the ends of the timbers, which for a double
slip crossing will be symmetrical about this line.

The position of one of the connections leading to
the slip will determine the location of the adjacent
end frog. While the standard plan will indicate the
distance between the end frogs, measured along the
axis, a somewhat more convenient determination is
possible. By multiplying twice the gage by the frog

15!)

SIMPLIFIED CURVE AND SWITCH WORK

number the distance between theoretical points of the
end frogs measured along the main rail is obtained.
The second frog may thus be located readily, proper
care being necessary in squaring across the track.

The alinement and gage of the track being cor-
rect, the axis may then be established and its middle
point will be the center of the slip. From this point
all measurements in both directions will be made to
locate the points of the movable point frogs, the
points of the slip switches and the several timbers of
the slip.

Tie Spacing — The distances between centers of
ties are given consecutively, but to attempt to lay off
these by successive measurements would introduce
cumulative error which at the ends of the slip might
amount to several inches, and, this again would be
out of the question. The distances from the center of
the slip to each tie should be calculated and the loca-
tion made by continuous measurement along the line
previously laid down for the axis of the slip.

As the ties that properly belong with the slip vary
in length only between the limits of 10 ft. 0 in., which
is the nominal length of the tie at the middle of the
slip, and a length which equals the track centers, and
while the number of ties within these limits for each
half varies from 17 for a No. (5 to 55 for a No. 20,
the increments will be nearly uniform and the ends
on both sides practically in a straight line ; thus ncr-
difficulty whatever need be experienced in applying
the necessary timber for any slip set. It should be

160

INSTALLING AND MAINTAINING SWITCHES

noted that the last short tie has a similar location
with reference to the end frog in the slip that it holds
in reference to the frog of a plain crossover.

Main-Track Alinement — In the installation of
any switch connection the importance of obtaining a
correct alinement fcr the main track is well known,
but the absolute necessity for this precaution in the
placing of slip switch work cannot be too strongly
stated. While a perfect alinement of the slip ladder
is desirable and will follow if the installation is cor-
rect in all its details, the essential feature is to pre-
serve the integrity of the main-track alinement. If
the line is a tangent, it should be established by the
engineer and this determination be faithfully fol-
lowed. If the slip is on a curve, the method of ordi-
nates should be used in the lining, first with a 100-ft.
string to correct the general line and then with a 50-
ft. string to obtain a fine detail line. This will be a
final determination because the timbers having been
placed in their exact permanent locations no shifting
or other work causing distortion will be necessary.

As mechanical work cannot in the nature of things
be perfect, some detailed adjustments may be neces-
sary even with the most faithful adherence to the
standard plan in the application of the material. This
correction should not be attempted until a final sur-
facing has been given, as frequently defects that ap-
pear as line are really caused by imperfect surface.

Slip Switch Accessories. — Since accuracy in the
installation is unavailing without the means of main-

161

SIMPLIFIED CURVE AND SWITCH WORK

taining the exact relations of the parts, heel blocks
should be provided, with the bolts connecting both
lines of rail; anti-creeping straps should be supplied,
anchoring the heels of the slip switches and the heels
of the movable points against creeping in either di-
rection; and every track leading to the slips should
be amply equipped with anti-creeping devices.

A better practice has developed in the matter of
applying the adjustable rail braces used in connection
with the bridle plates. It formerly was the practice
to secure the braces to the bridle plates by lag screws
let into the switch tie, but the hold was not sub-
stantial and the screws frequently worked loose. It
is now the practice to use screws which enter the
bridle plates where additional thickness of metal has
been provided, to admit which the tie must be dapped
or adzed out about 1 in. It is necessary to fit the
plate neatly into its seat so that moisture may be ex-
cluded as far as possible.

Gradient — A very distinct error in switch eco-
nomics, and one which as a rule is not fully appreciat-
ed, is the placing of an extended layout upon a broken
grade. This is particularly disadvantageous when the
layout is at the marked depression made by two sharply
changing gradients and the effect is most adverse in
the case of a slip ladder by reason of its greater length.
The ideal location of an interlocking is with a single
grade continuous throughout its limits. The saving in
maintenance, both to the signal and track forces,
through the ideal arrangement, is quite measurable.

162

INSTALLING AND MAINTAINING SWITCHES

The aesthetic feature is likewise greatly enhanced by
such provision.

41. MAINTENANCE OF SWITCH CONNECTIONS.

Removing the Ballast — Whether preliminary to
the installation of a new connection or to the renewal
of the timbers in the old, it is of decided advantage
to remove the ballast entirely to the bottom of the
ties throughout the length of the connection. In no
other way can economy of time be effected in the
general respacing of ties that occurs both in the or-
iginal application and in renewal. An exception might
be made when spotting of switch timbers only is be-
ing done; but this excellent and generally prescribed
rule for renewal is seldom practicable, as the timbers
are almost certain to be in a fairly uniform state of
wear and decay. The entire removal of the old ballast
assures a cleanly ballasted track, which is of great
benefit both to the riding of the connection and to the
life of the ties.

Surfacing — The tamping should receive especial
attention, as the comfortable riding of switch connec-
tions is the exception rather than the rule. The
pneumatic tie tamper will be found of especial utility
in such surfacing. The practice of elevating the
switch rail for safety introduces a very neat problem
for the expert maintainer. A plotted profile of a
succession of closely bunched switches in a main track
is calculated to instill despair of fine results in riding,
but it is well known that such results can be attained.
In general, the joints at the heel of switches and block

163

SIMPLIFIED CURVE AND SWITCH WORK

joints require the hardest tamping and the most fre-
quent surfacing.

Lining — Proper line seldom obtains through
main track switch connections because enough pains
were not taken in the original installation. Correction
can sometimes be made by separating the main track
and the turnout between the switch and frog into in-
dependent units by unspiking the respective tracks
upon alternate ties, and throwing with the bars, com-
pleting the adjustment by careful spike lining. The
latter should always be done by widening the gage
rather than narrowing it. Care must be taken at the
frog to preserve the correct guard-rail gage at all times
that service is permitted.

Accurate line through the connection having been
secured by careful attention to the rules given, the
preservation of perfect line can be assured only by a
faithful use of tie plates, and the rule should be
made imperative that every switch tie should be
plated. It is doubtful whether treated switch ties,
which are frequently of inferior soft woods, are safe,
for a single train movement, in connections of heavy
service, without the addition of tie plates. The use
of white oak for all switch ties is a desirable, but pro-
bably unattainable, ideal. The troublesome mainten-
ance question caused by the running of switches can
be largely met by a generous use of anti-creeping de-
vices, both throughout the connections and for some
distance along the main track in the opposite direction
to that of the traffic.

Attention to Slide Plates — The cleaning and lubri-

164

INSTALLING AND MAINTAINING SWITCHES

cation of the plates and other bearing surfaces of
switches and of movable point and spring rail frogs,
is a very important item of maintenance. The pre-
vention of sanding over switch connections relieves
the maintainer of much useless labor, and the road of
much unnecessary expense for oil consumed. At the
approach of freezing weather it is generally customary
to remove the ballast from the tie spaces at frogs,
switches and guard rails to facilitate the removal of
snow and ice.

Inspection and Test — Frequent inspection of
switches, both by the track foreman and signal
maintainer, is necessary to guard against lack of
adjustment, which might result in accident. These
inspections should be made monthly for general
condition, bi-weekly for detail defects and daily
whenever possible to detect small irregularities
which might assume dangerous degrees in brief
time. The limit of safe wear is a variable one, but
as regards the frog, is about reached when the half-
inch point is worn J^ in. below the original top sur-
face of the frog. As regards the switch, the limit
of safe wear can only be determined by the judg-
ment of the inspector. Stock rails represent only
nominal maintenance expense and should be kept
in first class condition at all times.

The condition of the various members that com-
pose the switch connection and the adjustments
maintained are of such vital importance that de-
tailed tests are prescribed on all roads and, in order
that these tests shall not be perfunctory, it is cus-

165

SIMPLIFIED CURVE AND SWITCH WORK

ternary to require that they be conducted jointly
by a representative of the signal department and of
the track department and that they be made on or
about certain dates.

To facilitate the rendering of the periodical reports
each switch or crossover in a given interlocking is
numbered and each switch rail distinguished by a
letter. The opening at switch points is prescribed by
the standards of the road and is usually 5 in. The
opening at which the switch lock will foul when the
switch is closed is fixed by the signal practice of the
road and is generally T3^ in. Terms are indicated to
describe the condition of the switch points, stock
rails and ties as good, fair, bad. The gage is measured
and any other features are noted under the head of
remarks. The signal department's responsibility is in
the adjustment of the interlocking connections, that
of the track department in the condition and general
maintenance details of the several members of the
switch connections. As the signal department does
not have any concern with the frogs or guard rails,
these are covered in another test made by the track
foreman alone.

The switch test develops the exact condition of the
switches and their connections at intervals, which for
the best practice is every two weeks, and not only
safeguards the traffic but supplies an excellent de-
fense in the event of an accident from some obscure
cause. These tests by the signal and track maintainers
are invaluable, but there is still necessary the occa-

166

INSTALLING AND MAINTAINING SWITCHES

sional inspection by the signal supervisor and the more
frequent detailed inspection by the track supervisor.

The inspections by the supervisor of track should
take in the physical characteristics of the entire lay-
out, and his notes should be full and be recorded in
permanent form. He should especially observe the
points of frogs to note if they are being touched by
passing wheels as indicating a loose guard rail gage,
and he should then try the gage and order the neces-
sary correction. This test is especially important at
crossings which require constant attention to gage.
The condition of all switch points should be noted and
also, as far as possible, their adjustments when thrown
for a movement. The two rails should be sighted to
discover any tight gage that may have developed, as
the movement of the rails through creeping sometimes
introduces a tightening of as much as -f$ in.,
whereas ^ in. is the most that is entirely safe. It
should be observed particularly whether the joints at
the heel of the switches and the insulated joints are
properly surfaced, and whether the full complement
of bolts is inserted at the rail joints. Any points un-
favorably reported by the maintainers should be ex-
amined.

The inspections made by the higher officers are
usually by proxy, many divisions having a special-
duty man who makes such tests for the division of-
ficer ; and there is an occasional test by the representa-
tive of the engineer maintenance of way. The di-
vision superintendent and his staff make superficial

167

SIMPLIFIED CURVE AND SWITCH WORK

observations of the interlocking layouts about once in
every three months when the various towers are being
inspected as to their sanitary condition.

The record of switch inspection and test is very inv
portant in view of the insistence of the road and civil
authorities for exact information in the investigation
of derailments. One has but to walk over a few
miles of railroad to note the many parts of cars that
drop off in passage, and to wonder that so few of
them drop into the throats of frogs and switches.
Cases where such obstructions have caused derail-
ment are not rare, but the proof of the occurrence is
seldom found and the record of the exact condition
of the switch connection may be the needed evidence
to clear the maintenance department.

42. PRACTICE IN OPERATION.

Speed Through Main Track Turnouts — The im-
portant question of what classes of power should
be permitted to operate over certain numbers of
switch connections and what speed such opera-
tion should carry is best determined from the de-
gree of curvature. A speed of 30 miles per hour
has been found entirely satisfactory through No.
15 turnouts from tangent track or from the inside
of very light curves, but the resultant curvature
for such operation should not exceed 3 deg. 30
min. This allows a theoretical unbalanced eleva-
tion of 2 in. which is only permissible in switch
connections where the effect of traffic shifting is
practically eliminated by the character of the track

168

INSTALLING AND MAINTAINING SWITCHES

structure. This speed will be indicated by the middle
arm of the signal.

With the increased use of higher numbers of frog
than No. 15, it is desirable that the increased speed
made possible be fully realized. The design of the
switch operates to restrict the speed except through
the route that is given preference in the adjustment of
the stock rail. If the two routes are given equal ad-
vantage, a speed of 40 and 45 miles per hour, re-
spectively, may be permitted through No. 20 and
24 connections. For such use the top arm would
be given and a general order would prescribe the
limiting speed, and some type of speed indication
board would be placed to call attention to the re-
stricted point.

Speed in Yards — As the curvature through yards
will vary greatly, the only safe rule is to limit opera-
tion to the highest speed that the sharpest connections
allow. In ladders, which are usually No. 8 but oc-
casionally No. 10, the allowable speed might be fixed
at 15 miles for the first and 20 miles for the second,
provided the presence of a curved main line did not
adversely affect the curvature too greatly. In the
case of interlocked crossovers it is customary to regu-
late the speed by the signal indication. As the lowest
arm permits a speed as great as 15 miles per hour,
it is necessary when movement should be made at a
slower speed to indicate by legend upon a standing
sign board the speed that may be used.

The limit of curvature that may be passed by the

169

SIMPLIFIED CURVE AND SWITCH WORK

common types of road engine is the curve of a No. (>
connection from tangent track, or 250 ft. radius. Some
types of road locomotives may be forced around a
very much sharper curve, but it is generally recog-
nized that a margin of at least 50 per cent is proper
for absolute safety.

Location of Switch Lamps — The location of the
switch lamp is of direct concern in operation. Its
distance from the track is important as a safety con-
sideration. Whenever practicable it should be at
least 4 ft. 7 in. distant from the gage of the nearest
rail. If placed closer its height should be such that a
brakeman clinging to the car would not have his
clothing caught and possibly be dragged down with
serious result. This is usually accomplished by hav-
ing the lamp stand separate from the switch stand.
Such an arrangement has a still further advantage as
affecting safety in operation, because the lamp would
then more certainly indicate the position of the
switch. In the event that the switch stand were
damaged the lamp, if attached to it, would generally
give no indication of the defect.

Numbering Switches — In long- ladders a great
advantage in operation is secured by a plain designa-
tion of the switch leading to each individual track.
Time is frequently lost in seeking the right switch,
and not infrequently even more time is wasted in cor-
recting a false drill movement occurring through error
in choosing the switch. This may be avoided by the
addition of a target to the switch stand carrying a

170

INSTALLING AND MAINTAINING SWITCHES

designating number or letter, so placed that the light
from the switch lamp will fall upon it, and slightly in-
clined so the brakeman riding the car will receive
information as to the track he is about to go upon.
The banner should not be a fixed board that one might
stumble over, but should be integral with the switch
stand.

Care of Switch Lamps — The degree of care used
in attending to switch targets and lamps is of great
consequence in operation. The targets require re-
painting at least every six months, and should be kept
bright and clean by washing as may be necessary in
the intervening time. The lampman should always
make sure that there is enough oil in the fonts to keep
them burning the required time. When the lamps are
lighted it should be seen that the wicks are properly
adjusted at the proper height to give a good light with-
out smoking, and that the lamps are lined to give the
best possible indication to trains.

171

PART III— SIDING LOCATION

CHAPTER XIII.
SIMPLIFIED FIELD WORK.

The supervisor frequently has need of a simplified
method for laying out the curves of a siding, either at
the time the preliminary survey is made, or later when
the siding is about to be constructed. In the first case
the layout may be required to immediately show the
applicant the main features of the alinement, in the
second case the service of the engineer may not be
available, or the use of an instrument be unobtainable.
In either event a tape line location may be the only
one possible.

Doubtless some cases will require instrumental
work, and it is then useful to know how the processes
can be simplified, for the corps will usually consist of
the supervisor or his assistant and a trackman or two.
The problems in instrumental layout are, of course,
not intended for the track foreman.

It is believed that many of the simpler cases of sid-
ing location can be met by the foreman himself with
the use only of a tape line. Most foremen, as well as
supervisors, carry with them at all times a 5 ft. ex-
tension rule and 50 ft. tape line, and many also carry
a 100 ft. length of string to correct the general line
of curves. By the aid of the simple rules of geometry
and with the accessories mentioned it will be possible

172

SIDING LOCATION

for the foreman to dispose of many cases and often
avoid the necessity of the supervisor making a special
visit to the location. For this object the first two
problems which follow are explained in greater detail,
and examples are given to illustrate the several rules.

The matter is greatly simplified by the fact that the
right-of-way line is nearly always parallel with the
tracks, and the building which fixes the location of the
siding is also usually parallel, and the siding therefore
either parallel or at right angles with the track. But
even for those cases where the siding is not parallel
or at right angles with a tangent main track, a special
solution is possible which is not unduly complicated
and which can be comprehended by many track fore-
men. It is not claimed that any new theorems have
been developed, but it is claimed that the solutions
offered are not to be found in any of the field books.

It will perhaps be thought by some that in neglecting
the tangents introduced into the siding curve by the
straight switch and frog, accuracy is being sacrificed ;
but it will be found that for turnouts above No. 5
(and those below have been practically eliminated by
the operation of the Safety Appliance Law), no sensi-
ble error will result from this source. Stakes need not
be set at either the point of switch or the point of frog,
but the location of these should be indicated by marks
on the rail, and care should be taken that the J/£ in.
point of frog is always understood.

43. PROBLEMS IN TAPE-LINE LAYOUT.
Problem 1 — The simplest case is that of a siding

173

SIMPLIFIED CURVE AND SWITCH WORK

parallel with a tangent main track and fronting a
building, the location of which fixes the maximum
offset distance. There is no practical need, nor is
there usually the space, to introduce any tangent be-
tween the curves. In order to render the physical con-
ditions as favorable at the point of reverse as at the
beginning and end of the reversed curve, it is quite
an advantage to make the two curves somewhat flatter
at the reversing point and this may be done by using
the formulae of the parabola. While this increases
the length of the curve somewhat, the extension is not
more than a few feet even for an extreme case.

P
The formulae symbolized are : p = — and 1 =

V 2 p R, or expressed in words signify that for a
chosen distance from the point of curve along the
tangent, the offset is equal to the square of the dis-
tance divided by twice the radius; or, conversely, for a
chosen offset from the tangent, the linear distance is
equal to the square root of the product of the offset
multiplied by tzvice the radius. (The field books em-
ploy these formulae for staking out a circular curve
by offsets from the tangent and chords produced. The
value of the offset from the chord produced is twice
that from the tangent, and the distance used is mea-
sured as a chord of the curve, instead of a length
always laid off along the tangent. The method is
unsatisfactory because the operation of successively
producing the chords renders the process subject to
cumulative error.)

174

SIDING LOCATION

By the use of the formulae in the manner first in-
dicated, the distance from the end of the curve to the
reversing point, and from the reversing point to the
point of switch may be obtained at once. These dis-
tances will be equal, if the two curves are of equal
radii, and the reversing point will be midway between
the line of the main track and of the siding. (Whether
the curves be of equal radii or otherwise, this point
will lie in a line joining the two tangent points.)

Any number of intermediate points on both curves
may be set after computation of the offsets. The off-

x Main

Fig. 16. Problem 1, Siding Layouts.

sets from the main track for the second curve will be
obtained by subtracting the offsets calculated for the
first curve from the whole distance between the siding
and main track. Thus all the measurements will be
made from an actual base line and every source of

175

SIMPLIFIED CURVE AND SWITCH WORK

error in the field work eliminated. It should be noted
that the several offsets vary as the square of the linear
distance. If the distances selected are in a simple
ratio, the square of this ratio multiplied by the first
offset will supply the other offsets with a considerable
saving in computation.

For example, assume that the building is located
15 ft. beyond a right of way 50 ft. wide on a double
track railroad, and that a curve of 500 ft. radius is
to be used. The distance from the center line of the
main track to the center line of the siding would then
be 51 ft. The offset distance to the reversing point
would be one-half this, or 25 ft. 6 in. By the formula,
1 = V 2 P R, we find 1 = 160 ft. It will be con-
venient to divide this distance into 4 equal parts of
40 ft. each. By the rule, the first point being % the
whole distance, its offset will be -^ of 25 ft. 6 in., or
1 ft. 7y& in. ; the offset at the 2d point will be 2
squared or 4 times 1 ft. 7^ in., or 6 ft. 4^4 in.; the
offset at the 3rd point will be 3 squared or 9 times 1
ft. 7^$ in., or 14 ft. 4^ in. ; the 4th offset will be, of
course, 25 ft. 6 in. ; the 5th offset will be 51 ft. 0 in.
minus 14 ft. 4^6 in., or 36 ft. 7% in.; the 6th offset
will be 51 ft. 0 in. minus 6 ft. 4^ in., or 44 ft. 7^ in. ;
the 7th offset will be 51 ft. 0 in. minus 1 ft. 7T/s in., or
49 ft. 4% in. ; and the last offset will be the full dis-
tance, 51 ft. 0 in.

The longer offsets should be laid out at an exact
right angle by knotting the string at a length of 80 ft.
and holding the ends of this length at adjacent points,
grasping the string at a point 30 ft. from the point

176

SIDING LOCATION

being turned and drawing it taut. This plainly fur-
nishes the 3, 4 and 5 proportion, the main rail being
the 40 side, the offset the 30 side and the diagonal, or
hypotenuse, the 50 side.

This simple solution furnishes a curve which varies
but slightly from a true circle, and the length of the
two curves is only increased 4 ft. 6 in. It will be
noted that the selection of a 500 ft. radius makes the
offset 4 ft. 9 in. for a linear distance of 69 ft. Thus
a No. 8 frog may readily be placed in the new curve.

When the length of radius is not absolutely deter-
mined by limiting conditions, as indeed seldom is the
case, that one should be chosen which will make the
offset at the point of frog equal to the gage plus J/£ in.
This radius will be about 5 per cent larger than the
actual radius obtaining through the lead ; but this ad-
vantage-is quite desirable both from the maintenance
and operating standpoints.

The above solution may be used for the case of a
crossover between two tracks which are parallel, but
which are so far separated that tangent between the
frogs is impracticable. If it is preferred to make the
reversed curves circular rather than parabolic, the
formulae outlined in Problem 2 for a continuous cir-
cular curve should be employed.

Problem 2 — The problem of locating a siding at
right angles with the main track may likewise be met
by the use of offsets and with as great accuracy as the
average engineering instrument will supply. It is
necessary in any event to adjust the detail line of

177

SIMPLIFIED CURVE AND SWITCH .WORK

178

SIDING LOCATION

the curve when finally laid, and this can best be done
with the string. The formulae for offsets employed
in the preceding case will not answer for the cir-
cular curve required, and the proper formulae for
such cases are the following: p = R — \/~R.2—\2 and

P).

These symbols signify that for a chosen distance
from the point of curve along the tangent, the offset
is equal to the radius minus the square root of the
difference between the radius squared and the linear
distance squared; or, conversely, for a chosen offset
from the tangent, the linear distance is equal to the
square root of the product of the offset multiplied by
the difference between twice the radius and the offset.

This may be used for the offsets from either end
to the middle of the curve, for which point it should
be noted that the linear distance is equal to the radius
divided by the square root of 2, which is 1.414, and
the offset is equal to the difference between the radius
and this linear distance.

As an example let us assume that it is desired to
connect a siding at right angles with the main track
by a 500 ft. radius curve. The length of a circle with
radius of 500 ft. is 3 1/7 times 500 ft., or 1,572 ft.
One fourth of this is 393 ft., and this will be the true
length of the siding curve. The linear distance
(either measured along the main track or siding tan-
gent) to the offset from the middle of the curve is
500 ft. divided by 1.414 or 354 ft. The offset itself
is 500 ft. minus 354 ft. or 146 ft.

It will be convenient to lay out the curve by offsets
179

SIMPLIFIED CURVE AND SWITCH WORK

180

SIDING LOCATION

70 ft. apart. By the formulae, p = R - - V R2 — ^>
we have : p = 500 - - V 250000 — 4900 = 4' 11" ;
p = 500 — V 250000 — 19600 = 20' 0" ; p = 500 -
V 250000 — 44100 = 46' 3" ; p = 500 — V 250000 -
78400 = 85' 9"; p— , by preceding process, 146' 0".

These may be laid off from the main track by
squaring carefully with the 3-4-5 triangle method.
The siding tangent may then be produced backward
by the aid of the string. The point of tangent, which
is the beginning of the back measurements, will be
500 ft. from the main track. The above distances may
then be laid off in the same order, and the curve will
be fully established. The length measured around
the curve through the stakes will be a few inches less
than 393 ft., which is the exact length of the curve.

Problem 3— The problem when the line of the
siding either converges toward or diverges from the
line of the main track may appear to be quite com-
plicated, but when understood becomes fairly simple.
The field work necessary for the solution of such a
case consists only in measuring the angle of diverg-
ence and the offset distance at the point of tangency.
The problem then is to determine the position of a
tangent parallel with the main track, which will make
the curve with the chosen radius pass through the
point desired, and be tangent to the line of the sid-
ing at that point.

The field books develop, with great interest to the
mathematically inclined, the problem of finding the
equal radii for a known position of the line joining

181

SIMPLIFIED CURVE AND SWITCH WORK

the two ends of the reversed curve. But as the ef-
fect of such a proposition is to establish a curvature
that will generally necessitate the use of special frogs
it is clearly not of much use in the solution of the
practical track problem.

The angle may be obtained with the tape line by-
laying down equal distances along the two sides of the
angle and measuring the spread at the ends of such
distance, (care being taken that the measurement is
along a broken line as, previously explained), and by
dividing the constant 57.3 by the ratio of these meas-
urements, which, it will be noted, is the same prob-
lem as used in measuring the angle of a frog.

The length of chord subtending a central angle of
this computed value may be found with sufficient ac-
curacy by dividing the angle by the degree of curve.
The tangent offset for this chord will be obtained
from the formulae in Problem 1, and the linear dis-
tance by a solution of the right-angled triangle in
which the chord is the known hypotenuse and the
tangent offset the other known side. The position
of the parallel tangent, and the linear distance to the
point of curve, are now known and the solution of
the problem becomes simply that of Problem 1, ex-
cept that for the diverging line a portion of the com-
puted curve is imaginary, and for the converging line
a portion of computed curve will be duplicated be-
yond the point of tangency with the imaginary par-
allel line.

182

SIDING LOCATION

44. PROBLEMS IN INSTRUMENTAL LAYOUT.

Problems 4 and 5 — The problem of establishing
a connection from curved main track requires instru-
mental work in measuring the angle between the sid-
ing tangent and the tangent to the main track curve
at the point of intersection and of deflecting for the
several stations, after computing the length of curve
between the point of intersection and the P. C. of the
siding curve and the distance on the siding tangent
between the main track curve and the P. T. of the
siding curve. The distance from the main track
curve to a possible point of tangent for the siding
curve should be measured as a check on the selec-
tion of radius for the siding curve. The choice of
curves is limited to those which will permit of the
use of a regular number of frog and will thus be the
degree of curve of some regular connection plus or
minus the degree of the main track curve, depending
upon whether the siding is from the inside or out-
side of the curve.

There are six cases of this one general problem of
which two that most commonly occur are given. The
other cases include two more from the outside, in
both of which A is greater than 90 degrees and R1
either greater or less than Rcos A, and two more from
the inside in both of which A is less than 90 degrees
and R1 either greater or less than Rcos A. Each case
supplies variations which the mathematical skill of
the engineer will readily differentiate.

The solution of all is rendered more facile by ex-

183

SIMPLIFIED CURVE AND SWITCH WORK

<L Siding

D K' £.

Fig. 19. Problem 4, Instrument Layouts.

184

SIDING LOCATION

tending the siding tangent to a line normal to it which
passes through the center of the main track curve
and intersects a line parallel with the siding tangent
through the center of the siding curve. This brings

K W

Fig-. 20. Problem 5, Instrumental Layouts.

the measured angle A, which it will be noticed is in-
cluded between the radius of the main track curve
and the normal to the siding tangent, into direct geo-
metrical relation with the two known radii. The

185

SIMPLIFIED CURVE AND SWITCH WORK

solution indicated for the two cases may be applied
with apparent modification to all the cases, when the
angle between the siding tangent and the radii passing
through the P. C. of the siding curve may be ob-

Fig. 21. Problem 6, Instrumental Layouts.

tained, as well as the central angle of the siding curve,
and the distance to the actual P. T. of the siding
curve, when a test of the correctness of the assumed
radius will be had upon comparison with the tentative
measured distance.

186

SIDING LOCATION

When it is not necessary to immediately establish
the siding curve, the work may be greatly simplified
by taking scale measurements from an accurately
plotted plan, and these will answer every purpose if
the original survey was correct and the drawing made
to a scale as large as 1 in. to 40 ft., or preferably 1 in.
to 32 ft.

45. PROBLEM OF 2-POiNT COINCIDENCE.

Problem 6 — The problem of locating a siding on
a continuous simple curve which shall pass through
two definite points is of very frequent occurrence, as
when a property corner must be avoided and farther
on a corner of a building cleared. The finite problem
is capable only of theoretical solution, when the re-
sult will be a curve which may or may not approxi-
mate that of some regular connection, but it will gen-
erally be possible to change one or both points so that
the curve of the nearest regular number of frog may
be employed.

The theoretical solution is readily made by means
of the geometrical relations indicated in the diagram
and furnishes the two following formulae by which
the radius may first be computed and if this an-
swers the practical requirement, the distance from the
point of curve to the foot of the perpendicular through
the nearer point.

It will be noted that the formula for obtaining the
radius has been reduced with a view of establishing
the function R in its simplest form, which will be
found to facilitate greatly the detailed solution. In-

187

SIMPLIFIED CURVE AND SWITCH WORK

deed, without this simplification the solution is im-
measurably tedious.

a+b e c

R- — V2bR — b2

2 2 (a — b) a — b

*= Vb(2R — b)

The factor preceding the square root sign need
only be carried to two decimal places, and to the same
degree of accuracy when squared. The remaining
members may be used throughout of the nearest even
whole number.

When the radius found is not of practical applica-
tion, as when a radius of 375 ft. results which lies
midway between the curve of a No. 6 and of a No. 8,
No. 7 not being used, the problem becomes one of ad-
justment within the limits that are possible for
changes in the two assumed points. The quarters will
seldom be so close that a change of a few feet will
not be practicable and in such event the choice will
lie between a compounded curve and a special frog.

A solution of the extreme case mentioned will af-
ford some hints that will tend to simplify the solutions
of other problems. It should be noted that a radius
within 50 ft. will furnish practical results in the use
of any particular frog. Thus a radius of 300 ft. will
answer for a No. 6 or 450 ft. for a No. 8, but, upon
the determination of the radius, the distance should
be computed to the point where the offset distance is
equal to the gage plus y2 in. and this point used for
the point of frog, and a proper lead laid off to deter-
mine the point of switch which need not be exactly
at the point of curve.

188

SIDING LOCATION

Let a = 137, b = 51, c=100; then, R— 152=1.16 V 102 R— 2,601
R2 — 304 R -f 23,104 = 138 R — 3,511
(138) (25,737)

R2 _ 442 R _j_ 48,841 = 22,226

(diff. 25,737)

R — 221 = 149, or R = 370.
Changing to a = 1.32, b = 56, c = 100, R— 160 =

1.32 V112R — 3,136
R2 _ 320 R -f 25,600 = 196 R — 5,456
(196) (40,904)

R2_ 516 R -j- 66,564 = 35,508

(diff. 40,964)
R — 258 = 189, or, R = 447 ft, which permits the use of

No. 8.

Changing to a = 144, b = 44, c = 100, R — 144 = V88 R — 1,936
R2 — 1 288 R -f 20,736 = 88 R — 1,936
(88) (14,608)

R2 — 376 R -J- 35,344 = 12,672

(diff. 14,608)
R —188 = 113, or R = 301 ft, which permits the use of

No. 6.
46. PRACTICAL CONSIDERATIONS IN SIDING LAYOUT.

Clearance — The feature of clearance in siding
layout is a basic one because it concerns not only the
movement but affects also the question of safety to
persons. Some roads prescribe the minimum distance
from the track for structures and a few require that
this limit shall be followed in the case of movable
obstructions. But the addition to this minimum made
necessary by the nosing, overhang or tilt of the cars,
which is a variable one, is not generally stated. As-
suming that the widest car which moves in regular

189

SIMPLIFIED CURVE AND SWITCH WORK

traffic is 10 ft. 9 in., a limit of 4 ft. 7 in. from the
gage line of tangents for all obstructions would al-
low a margin of 1 ft. 7 in. without any correction for
accidental unevenness of elevation or for swaying of
the car while in motion and with a fair degree of
maintenance this would render the operation entirely
safe.

Car design is such that in a general way the nosing
nearly equals the overhang on cu-ves that are with-
out superelevation. The corrections may be readily
computed for cars with 30-ft. truck centers by tak-
ing one-fourth the degree of the curve as inches of
overhang, and assuming that the nosing is no more
than that figure, and adding or subtracting whatever
may be proper for the superelevation employed. If
this is \l/2 in. as suggested farther on, the tilt at the
eaves of box cars would add or subtract 4^2 in. from
the correction as the low or high side were in ques-
tion; but for vertical obstructions the correction on
the high side would be \y2 in. at the hand hold.

The overhead clearance limit is conveniently fixed
at 16 ft. above the top of rail, which meets the require-
ments of all present equipment and probably is ample
for all future design. As this clearance will not pass
a man riding a car, tell-tales should be placed. The
least overhead clearance that will safely pass train-
men standing upon the highest cars is 20 ft. 9 in. above
the top of rail.

The fact should not be overlooked that at the end
of the curve a correction should also be made which

190

SIDING LOCATION

is one-half that for the body of the curve. The dis-
tance beyond the point of tangent to the point where
correction no longer applies is about 18 feet.

Alinement — The considerations of alinement,
grade and superelevation are other important ele-
ments in a siding layout. As a general proposition
if space is available, no shorter radius should be em-
ployed than can be operated practically by any class
of engine. For most roads this is the curve of a No.
6 turnout from tangent which is 23 deg. or 250 ft.
radius. This requirement is not practical in congested
districts, and it will often be necessary to modify the
curvature to just what a due consideration for safety
in coupling cars will permit. This radius has been
variously determined, but probably is close to that of
a No. 5 turnout from tangent or a 162-ft. radius.
Where sharp curvature and maximum gradient are
both involved, insistence should be had upon the best
possible feature for each.

Gradient — The allowable maximum gradient for
siding connection for the best service is 2 ft. in 100
ft., and the maximum for track upon which cars stand
for unloading 1 ft. in 100 ft. It is possible to operate
sidings with a gradient of as much as 4.7 ft. in 100
ft., but the best drill engines cannot handle more than
three loaded cars on such a gradient and the opera-
tion is therefore unprofitable. The danger of wrecks
from cars running away, with the possibility of foul-
ing the main line even when derails are provided, ren-
ders such a gradient highly objectionable. It is very

191

SIMPLIFIED CURVE AND SWITCH WORK

important that all radical changes of grade in siding
connections shall be eased by vertical curves, as the
absence of such advantage is a frequent source of
accident.

The general feature of gradient concerns the ap-
proaches to coal trestles more particularly, and is one
where the road must often take a firm stand against
the insistence of the applicant for greater headroom.
The adoption of a limiting gradient by the road many
times would supply the means of combating such de-
mands. If more headroom is required it can nearly
always be had by excavating the site. Any less clear
height than 6 ft. 6 in. below the stringers will not
permit of a horse being driven through and any
greater headroom than 14 ft. will break the coal or
grind a measurable amount of it into dust with a
considerable loss to the dealer.

Superelevation — The question of superelevation
is one concerning which authorities differ. It will be
argued that no superelevation is possible through the
connection and therefore none is necessary beyond the
connection. But the difference is that the track
through the extent of the switch timbers is more
rigidly secured in line and surface, and gage as well,
if tieplates be used on the timbers, and there is less
chance for distortion. It will be found that a super-
elevation of 1^2 in. for all siding curves is a decided
maintenance advantage

Maintenance — The importance of good line and
surface is not fully appreciated. In very many obscure

193

SIDING LOCATION

cases of siding derailment, wherein the cause is given
as "truck failing to curve," it is really irregular line or
uneven elevation. The matter of run-off of the sup-
erelevation is a vital one in modern operation. To
safely pass all types of equipment the run-off should
not be made at a greater rate than 1 in. to 33 ft. If
through poor maintenance the rate should become
greater than 1^2 in. to 33 ft., derailment would be
likely to result.

To spend money in siding maintenance is much
better than spending it for small wrecking, with its
annoying interruption to drill work or the possibility
of injury to men. The best maintenance of sidings
can only be attained by constant inspection and super-
vision. The trackwalker should go over every siding
once every day. The foreman should inspect each
siding in his territory twice a week. The supervisor
should make a careful examination of his sidings and
switches once every month and make permanent notes
of what he finds. He should also require a report
every two weeks from his foreman stating that he
has made his inspections and calling attention to any
specified repairs that may be necessary requiring ma-
terial that he lacks. For the best results the fore-
man should not be overburdened with siding repson-
sibility. Probably 30 siding switches are the most that
one foreman can look after if he has main track duties
also.

193

CHAPTER XIV.
SPECIAL PRACTICES.

Staggered-Point Switches — Considerable econ-
omy is effected in the wear of switch points in yards
at places where the service is extreme, by moving the
point of lesser wear back a distance of 26 in., so that
the first lug of the one point and the second lug of
the other are opposite; and by adding a guard rail
9 or 10 ft. long curved sharply through 12 in. at the
end nearest the switch and in the standard manner
at the other end. The guard rail is set close to the
switch, which permits 12 in. of 2-in. flangeway op-
posite the point receiving the greatest lateral thrust
from the traffic loads.

This greatly increases the life of the point and is
an excellent protection against derailment as well.
The two opposite lugs must be connected with the
standard head rod, and for entire safety each lug
should be connected with the one diagonally opposite.
If made on a standard plan these rods may be of
regulation design, but if resort must be had to make-
shift design, a flat rod of 2% in. by y± in. material is
quite satisfactory. Care should be taken that the heel
gage of the shortened point is widened to maintain
proper gage. As the guard rail is subjected to a
severe strain it should be braced by anchor clamps
and at least one tie plate guard rail fastener.

This arrangement has been used in a number of

194

SPECIAL PRACTICES

locations where the service is extreme, but the sav-
ing at one point will serve for illustration. Two
switches follow each other closely and spring from
the inside of a 17 deg. curve. Approximately 30
movements are made over the switches every day.
At each one of the switches the high side point of
new 100-lb. material formerly lasted just two months,
it being a matter of actual knowledge that 12 switch
points were consumed at the two places in one year.
Besides, it was the rule for a derailment to herald the

Fig. 22. Staggered Switch Points.

time for renewal of the worn points. Since the points
have been protected by this method they have lasted
fully five years. Sixty switch points are thus saved
in this period and derailments have also been elim-
inated.

It is doubtful if any other device or method in
switch work is capable of effecting one-tenth the sav-
ing in expense for maintenance as the one described.

Making a Crossing with Switch Points— The
sketch illustrates a means of effecting a crossing by
the use of switch points. It is plain that the points

195

SIMPLIFIED CURVE AND SWITCH WORK

merely serve the purpose
of movable point frogs.
A narrow-gage track is
shown intersecting a
standard-gage track, be-
cause that is probably the
principal combination
likely to occur. Each
switch point may be
thrown by an independent
lever, or they can all be
pipe-c onnected and
thrown by one operation.
The points composing
each separate frog are
placed a distance apart in
inches equal to one-fourth
the ratio between the
length of the point and
the heel gage, for points
Y% in. thick at the point
of switch, or y2 the ratio
for points *4 in. thick.
For a straight crossing
the distance between the
heels of the end switches
is equal to the difference
of the gages plus twice

the heel gage multiplied by the tangent of the switch

angle.

Shifting Connections Endwise — When it becomes

196

SPECIAL PRACTICES

necessary to move a connection or crossover to a new
location within certain limits there are usually two
alternatives, viz., to build a new connection or to shift
the old one by mechanical means. When the distance
to be moved is less than 100 ft. it will generally be
preferable to move it bodily, especially if a locomotive
or steam derrick pull is possible. The joints at the
ends of the connection are broken, all ballast is cleaned
from the cribs, and a flat bed level with the bottom of
tie prepared at the new location. The ties about the
switch are apt to give trouble, but this may be over-
come by spiking them in place beforehand. A con-
nection may thus be moved by a large force of men
with bars. The saving in expense by shifting rather
than rebuilding is quite considerable.

Renewing Slip Switches with Steam Derrick —

When the old material in a slip that is in service is
considerably worn it is hardly safe to attempt to re-
new the slip piecemeal. The difficulty of properly
compromising the old work with the new is practically
prohibitive. There are few points where the main
track and the slip can both be dispensed with while a
new set is being installed. It has become a nearly
standard practice to rebuild the slip complete beside
the tracks, and, at a convenient time between regular
trains, set it in place with steam derricks or cranes,
holding it by each end. If the slip is larger than No.
8 it will be necessary to furnish longitudinal rein-
forcement. It is quite important to provide a margin
of 1 in. at each end for the joining of the rails. A

197

SIMPLIFIED CURVE AND SWITCH WORK

No. 8 slip may be thus renewed in as short a time as
15 minutes.

Avoiding a Facing Point Switch — The problem
of avoiding a facing point switch usually is solved
by building a parallel siding on regular track centers
with the main track, and turning the spur from such
siding. If a bridge or other structure prohibits the
placing of the siding in this manner it may be laid as
a gauntlet with the main track.

The main point to be observed is that the gauntlet
distance shall be such as to employ for the cross-
ing of the spur with the first rail the next larger frog
to the one used for crossing the second rail. It is
also an advantage to separate the J/£ in. points a dis-
tance equal to the length of the frogs. With a No.
8 and No. 10 frog the gauntlet distance would be 20
in.; with a No. 6 and No. 8 frog it would be 26 in.
When the distance is over 10 in. the ties should be
relined.

Advancing the Point of Switch — It is sometimes
impracticable to place a switch at the point required
by the adopted location of the frog. An existing
structure may prevent it, or the need of drawing the
switch closer to the power system may be imperative.
The solution of such a case is to employ as long a
switch as possible and extend the switch tangent to a
point where a regular curve will connect with the
frog tangent.

198

INDEX.
A

PAGE

Advancing point of switch — .. 198

Alinement in siding location 191

Approach and run-off of curves 54

B
Bill of switch ties 134

Clearance in siding location 189

Computation of vertical curve 80

Connections, shifting endwise 196

Connections, simple 156

Corrections in curve lining, applying 50

Corrections to curves, analysis of lining and elevation 60

Crossing with switch points 195

Crossovers, long ties for _ 138

Curvature, light degree . 83

Curvature, maximium 85

Curve adjustment, preliminary 49

Curve, degree of in narrow gage turnouts 141

Curve, diagnosis of 25

Curve lining, applying corrections 50

Curvet lining, back of frog _ ., 132

Curve maintenance, economics of 89

Curve ordinate * 15

Curve problems ~ ^ 88

Curve — see also "vertical curve."

Curve solution, examples 31

Curve throw, measuring with pole 50

Curved ladders 126

Curves, accuracy in measuring ordinates 23

Curves, approach and run-off 54

Curves, definitions of 14

Curves, degree of in turnouts 118

Curves, economics of 83

Curves in switch connections 163

Curves, protrusions at ends of 90

199

SIMPLIFIED CURVE AND SWITCH WORK

PAGE

Curves, staking out between offset tangents ^.._ 72

Curves, study of the locality 24

Curves, superelevation of body 56

Curves, superelevation of _ 53

Curves, testing with a string 23

Curves, vertical 78

Curves, widening centers on 87

Definitions of curve terms 14

Definitions, switch connections 100

Design of switch connections 96

Of turnouts, practical „ 151

Theoretical and practical considerations, in switch

connections _ 103

Diagnosis of the curve -. 25

Easement or spiral curves 26

Easement curves, staking out by offsets 73

Errors in designing _ *... 30

Ideal ~ 29

Practical 30

Easements, early location made without 74

On new lines 76

On old lines ->. 75

Economics of curves - 83

Elevations, tables of _ _ 58

Errors in designing easements 30

In string lining 24

Examples in curve solution 31

Examples of spirals 71

Pace, raise in - 93

Facing point switch, avoiding 198

Field work, simplified for siding location 172

Flat places in curves _ 26

Foreword 7

Frog and lead rails, maintaining 157

Frog and switch rail, effect of 119

Frog angle 122

200

INDEX.

PAGE

Frog angle and switch angle, relation between — 103

Frog number - 121

Frog points in crossovers, distance between 123

Frogs, distance between in slip switches 1

Frogs, maintaining 157

Frogs, Nos. 6 to 9 - 106

Frogs, Nos. 10 to 16 108

Frogs, Nos. 18 to 24 - 108

Frogs, selection for new tracks 110

Functions of turnouts, rules for 130

Gage, correct - 94

Gradient, continuous vertical curve 79

In siding location - 191

In slip switches 162

H
High-speed track, superelevation — . 55

Ideal easement 29

Inspection and test of switches 165

Installing and maintaining switches...* . 156

Installing turnouts, practical considerations in 148

Intersection of grade lines, location 86

Introduction ,. 11

Instrumental layouts, siding 183

J
Joints in turnouts 151

Ladder, lining a 126

Ladders, curved 126

Layout, hints for 144

Layouts for siding » 173

Layouts with the instrument, siding 183

Lead and turnout rails, difference in length 104

Lead rails, length 117

201

SIMPLIFIED CURVE AND SWITCH WORK

PAGE

Lead rails, maintaining : 157

Leads for narrow gage switches 141

Leads for switches 116

Length of lead and turnout rails, difference in 104

Light degree of curvature 83

Limited-speed track, superelevation 55

Line and surface of curves interdependent 90

Line defects, correction of 89

Line, maintenance of 92

Line stakes _ 51

Lining a ladder , 126

Lining switch connections 164

Lining track behind frog 131

Location made without easements..., 74

Location of grade intersections 86

Location, providing for easement in 76

Location siding 172

Maintenance of line 92

Sidings 92

Superelevation 91

Ties - 94

Switch connections 163

Main-track alinement at slip switches <. 161

Maximum curvature 85

Mean ordinate, throw and resultant » 16

Mean ordinates, figuring 25

Men, number required in installing turnouts fc 148

Methods of installing and maintaining switches 156

Minimum length of tangents 87

Moderate speed track, superelevation..— 55

N
Narrow gage switch connections 139

Offset, relation to length of spiral 72

Offset tangents, staking out curves between 72

Offsets, staking out the easement curves by ,. 73

Old lines, making easements on 75

One hundred-ft. string for lining 0. deg. 20 min. curve 36

202

INDEX.

PAGE

Operation of switches „ 168

Ordinate, curve 15

Ordinates, figuring mean 25

Point of switch, advancing _ 198

Pole used for measuring curve throw 50

Practical considerations in installing turnouts 148

Practical considerations in siding layout 189

Practical easement 30

Practical switch connections 96

Preliminary curve adjustment 49

Quick action in putting in turnouts 149

Rail, lengths used in practical turnouts 151

Raise in face 93

Relation of offset to length of spiral 72

Renewals, turnout, bill of ties for 139

Resultant throw in curve lining 16

Reversed curve, lining with 62-ft string 46

Reversed curve, spirals for 40

Run-off and approach of curves 54

Sags, short 93

Selection and maintenance of superelevation 91

Sharp and flat places in curves 26

Short sags 93

Siding layouts, practical considerations 189

Siding location 172

Sixty-two-ft. string for lining reversed curve 46

Slide plates, attention to 164

Slip switch accessories 161

Slip switches, distance between frogs 128

Slip switches, installing 158

Slip switches renewed with steam derrick 197

Solution of examples in curve lining 31

Special practices 194

203

SIMPLIFIED CURVE AND SWITCH WORK

PAGE

Speed as related to curve superelevation 55

Speed in yards 169

Speed on main and branch lines * 83

Speed, permissible in narrow gage turnouts 142

Speed through main-track turnouts «~~ 168

Spiral by middle ordinates 64

Spiral or easement curves 26

Spiral curves 64

Spiral, relation of offset to length of 72

Spiral, string to use for l/% 67

Spiral, unit series for designing 65

Spiral functions, use of table 69

Spiraling curves, the advantage and cost of 74

Spirals, examples of 71

Spirals for reversed curves _ 40

Staggered-point switches 194

Stakes, line 51

Staking out curves between offset tangents 72

Staking out the easement curve by offsets 73

Steam derrick used for renewing slip switches 197

Stock rail, bend in 153

String, length to use for l/% spiral - 67

100-ft., for lining 0. deg. 20 min. curve 36

Length used in lining curves 24

String lining, basis of method 18

Errors in 24

Five operations 21

General rule for the effect of throwing 20

String method of lining curves _ 16

Surfacing switch connections „ 163

Switch, advancing point of.— 198

Switch angle _ 122

Switch angle and frog angle, relation between 103

Switch, avoiding facing point 198

Switch connections, classification for speed 106

Switch connections, definitions 100

Switch connections, design of 96

Switch connections, elementary principles. — 96

Switch connections, maintenance of 163

Switch connections, narrow gage 139

Switch connections, practical 96

Switch dimensions, rules for computing 116

Switch lamps, care of 171

Switch lamps, location of 170

Switch length with frogs Nos. 6 to 9 106

204

INDEX.

PAGE

Switch length with frogs Nos. 10 to 16 , 108

Switch lengths with frogs Nos. 18 to 24 108

Switch lever, location of 154

Switch points used for crossings 195

Switch rail for narrow gage 140

Switch ties, designing bill of » 134

Switch ties, tables ~ 136

Switch timbers 136

Switch work, inspection and tests 165

Switches, graphical method of laying out 142

Switches, installing and maintaining 156

Switches, numbering *. 170

Switches, shifting endwise 196

Switches, staggered-point 194

Superelevation, effect of traffic on 59

Superelevation in siding location 192

Superelevation of body of curves 56

Superelevation of curves 53

Superelevation, maintenance of 91

Superelevation, rule for „ 57

Superelevation, selection and maintenance of 91

Superelevation, tables of 58

Surface and line of curves interdependent 90

Tables of elevations _ 58

Table of spiral functions 68, 69

Tables of switch ties 136

Tangent, definition of ~T ^ 14

Tangents, minimum length of *. 87

Tape-line layout, problems in siding location 173

Tape-line layouts, siding _ 173

Testing curves with a string » 23

Throw, pole used for measuring 50

Throw, rule for determining in curve lining 28

Tie spacing in slip switches 160

Ties, maintenance of _ 94

Ties, spacing of in turnouts 153

Tool equipment for putting in turnouts „ 150

Turnout curve, degree leading from curved track 121

Turnout curve, lining „.„ 130

Turnout curve, radius and degree in tangent track 120

Turnout dimensions _ 105

Turnout renewals, obtaining bill of ties 139

205 •

SIMPLIFIED CURVE AND SWITCH WORK

PAGE

Turnouts, practical considerations in installing 148

Turnouts, rules for various functions of — . 130

Turnouts, speed through main-track 168

Turnouts to parallel tracks 146

U
Unit series for designing the spiral 65

Vertical curve, computation of 80

Vertical curve, example , 81

Vertical curve gradient, continuous 79

Vertical curves ~ 78

Vertical curves, rate of change 78

Vertical curves, use in maintenance..... 78

Yards, speed in 169

206

The Trackman's Chance

What has been done for the trackman?

Track work has been classed as unskilled labor.
It will always be so classed until the trackman, him-
self, changes the order of things.

The professional man has his instructive library;
for the guidance of the engineer there are volumes
packed with technical information and absolute data;
today there are books that teach even the grocer
and the butcher the most approved modern methods
of running their businesses and show them how to
double their earnings.

What is there for the trackman?

Track work calls for unlimited patience, great en-
durance, good judgment, quick thinking, dexterity.
It » skilled labor and the RAILWAY EDUCATIONAL
PRESS is trying to show trackmen a way in which
they may prove this to the world. The RAILWAY
EDUCATIONAL PRESS is emphasizing the impor-
tance of the trackman's work, so that the construc-
tion and maintenance of track shall be given the
standing rightfully due them — shall be elevated to the
dignity of a profession.

Practical Track Work and PRACTICAL TRACK
MAINTENANCE are the first two completed vol-
umes of a series of books on track work.

These books, the ones which are described in the
following pages, and others, will form a snug little
library, and they will tell everything there is to tell
on the great and important subject of track work.

With the aid of this library, any trackman has it
in his power to become an expert worker. Expert
workers in any line are well paid; they have stand-
ing; they demand recognition and they get it.

RAILWAY EDUCATIONAL PRESS. Inc.

Fourteen East Jackson Boulevard

Chicago : : : : : Illinois

Practical Track
Maintenance

(Price $1.60 Postpaid)
By KENNETH L. VAN AUKEN

Table of Contents

Chapter I — The Big Problem —
Labor.

Chapter II — Developing Track
Foremen.

Chapter III — How to Handle
Laborers.

Chapter IV — Renewing Ties.

Chapter V — Relaying Rail.

Chapter VI — Ballasting and Sur-
facing.

Chapter VII — Reports and Ac-
counts.

Chapter VIII— Spring Work.

Chapter IX — Summer Work.

Chapter X— Fall Work.

Chapter XI— Winter Work.

Chapter XII— Track Work in the
Tropics.

Chapter XIII — Yard Mainten-
ance.

Chapter XIV — Rapid Improve-
ment of a Section.

Chapter XV Track Materials,

Tools and Appliances.

"/ know of nothing ever put in print of
such value."

— Engineer Maintenance of Way

RAILWAY EDUCATIONAL PRESS. Inc.

Fourteen East Jackson Boulevard

Chicago : : : : : Illinois

208

Practical Track Work

Or* How to Build Track and Switches

(Price $1.60 Postpaid)
By KENNETH L. VAN AUKEN

An intensely practical and interesting book on methods of
doing track and switch work. Written from fourteen years'
practical experience.

The author of "PRACTICAL TRACK WORK" was, him-
self, a track worker. He has worked ten hours a day in all
kinds of weather; he has been foreman of a construction

gang of foreigners — he knows the trials such foremen under-
go. He knows the hard, driving work they do, often unap-
preciated, always underpaid. He knows all about it for he
has been there himself.

J. W. Powers, Supervisor of Track on the New York Cen-
tral says: "I congratulate you most heartily on being the
author of "PRACTICAL, TRACK WORK," a book devoid
of abstract problems and useless theories; but written in a
plain, common-sense, and masterly manner and complete
in its general detail of practical information."

Every man who wants to advance and who wants to know
how to construct as well as maintain track, will find
"PRACTICAL TRACK WORK" indispensable.

RAILWAV EDUCATIONAL PRESS. Inc.

Fourteen East Jackson Boulevard

Chicago : : : : : Illinois

Maintenance Methods

(Price $1.60 Postpaid)
By EARL STIMSON

Engineer Maintenance of Way, Baltimore & Ohio
Railroad

This book is a pioneer in its field. It dis-
cusses the different methods of organizing
maintenance work and gives detailed meth-
ods for getting the most work done with the
least amount of labor. It gives the track
foreman many specific instances of methods
he can easily apply to increase the work of
his gang.

Promotion comes to the track man who
maintains his track in the best shape at the
least expense. This book tells the track man
how to increase his ability and the amount
of work done by his gang so that he may
attract the favorable attention of higher offi-
cials.

A twentieth century track book, giving
the very latest and best ideas on main-
tenance methods.

(Manuscript under preparation}

RAILWAY EDUCATIONAL PRESS, Inc.

Fourteen East Jackson Boulevard

Chicago : : : : : Illinois

210

Winter Track Work

(Price $1.60 Postpaid)
By E. R. LEWIS

Assistant to General Manager, D. S. S. & A. Ry.

A thorough and practical book, tell-
ing the track man just how to handle
his winter work, from shimming to op-
erating a snow-bucking train.

E. R. Lewis, the author, has had 30
years' railroad experience, starting in at
the bottom where he had charge of a
few miles of track, and holding various
positions up to his present position
where he has charge of track main-
tenance and construction on the entire
system.

The book lives up to all you would
expect from such a prominent, prac-
tical man.

RAILWAY EDUCATIONAL PRESS, inc.

Fourteen East Jackson Boulevard

Chicago : : : : : Illinois

211

The Autocrat at the Lunch Table

(Price $1.60 Postpaid)
By BRUCE U. CRANDALL

The only book published which takes up the rela-
tion between railway supply men, and railway com-
panies and officials; written in an interesting conver-
sational style and containing much information useful
to both railway and supply man.

P. I_. Maury, sales manager of The Sherwin-Wil-
liams Company, says: "I received the copy of The
Autocrat at the Lunch Table and have enjoyed it so
much and found it so good that I am having our
purchasing agent send you an order for twelve copies.
I would like to have this order cover the one copy
which you sent me, leaving a balance of eleven copies,
which I wish you would send to me also as soon as
possible. I desire these for our railway representa-
tives, for I think that your book contains a lot of good
common horse sense that all of us can read and
thereby profit from."

RAILWAY EDUCATIONAL PRESS. Inc.

Fourteen East Jackson Boulevard

Chicago

Illinois

212

THE TRACK PRIMER

(Price $1.60 Postpaid)
By CHARLES L. VAN AUKEN

Written for the benefit of the track
laborer, assistant foreman and foreman; a
carefully detailed description of how to do
all the little jobs in track maintenance.

This book is written in exceptionally sim-
ple English, so that it can be understood by
a green track laborer or by any foreign
laborer who understands the English lan-
guage.

Questions are given at the end of each
chapter for the reader to answer and the
book is in every way equal to a correspond-
ence course — at one-twentieth the price.

(Manuscript under preparation. Vol-
ume, 1 will be ready for distribution
January /, 1917. Volume. 2 will
be ready for distribution June /, 1917)

RAILWAY EDUCATIONAL PRESS. Inc.

Fourteen East Jackson Boulevard

Chicago : : : : : Illinois

213

Inspecting Track and
Roadway

(Price $1.60 Postpaid)
By STEPHEN J. EVANS

Good track inspection, like good
track drainage, is the foundation of
good maintenance. Further, it is the
basis of safety.

For these reasons this volume on in-
spection, written by a man who has had
experience as track laborer, foreman,
general track foreman and roadmaster,
will be in demand with every live track-
man.

A trackman must know everything
contained in this volume if he expects
to maintain his track in high class shape
and to merit promotion.

(Manuscript under preparation; ready
for distribution January /, 1917)

RAILWAY EDUCATIONAL PRESS. Inc.

Fourteen East Jackson Boulevard

Chicago : : : : : Illinois

214

ROADBED AND TRACK
DRAINAGE

(Price $1.60 Postpaid)
By KENNETH L. VAN AUKEN

The basis of good track maintenance is a
good foundation; and a good foundation is
possible only with good drainage.

ROADBED AND TRACK DRAINAGE,
therefore, fills a long-felt want. It discusses
subgrade conditions and gives the trackman
information from which he can determine
whether or not his drainage is defective, and
then gives practical methods for bettering it.

This book explains why track frequently is
hard to maintain, even though there is plenty
of ballast and no apparent reason for its con-
stant settling.

There is nothing of greater importance in
track maintenance than track drainage and
every trackman who buys this thoroughly prac-
tical book will be greatly benefited by it.

(Now under preparation; ready for dis-
tribution January /, 1917)

RAILWAY EDUCATIONAL PRESS. Inc.

Fourteen East Jackson Boulevard

Chicago : : : : : Illinois

215

THIS BOOK IS DUE ON THE LAST DATE
STAMPED BELOW

AN INITIAL FINE OF 25 CENTS

WILL BE ASSESSED FOR FAILURE TO RETURN
THIS BOOK ON THE DATE DUE. THE PENALTY
WILL INCREASE TO SO CENTS ON THE FOURTH
DAY AND TO $1.OO ON THE SEVENTH DAY
OVERDUE.

ren 29

rB 1087'

*%•

3C5561

UNIVERSITY OF CAUFORN1A LIBRARY

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