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Simplified Curve and 
Switch Work 

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



Supervisor, Pennsylvania Railroad 



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 


Copyright 1916 

Railway Educational Press, Inc., 
Chicago, Illinois 






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


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



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



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



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



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. 



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



Practical Switch Connections 


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



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. 


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 



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


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


Siding Location 


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. 



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 


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 

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 


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 


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. 



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, 



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- 

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- 



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. 





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 



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 

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- 



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. 


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



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 

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- 



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. 


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- 



si 5 



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- 



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 



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. 



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 



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. 


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 



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. 


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 



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 



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. 




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 

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, 



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 



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....^ Y 4 l*/ s iy 2 17/ 8 2*/ 4 25/ 8 

45' 1 121' 147' 217' 252' 333' 419' 419' 

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

3 33/6 33/ 4 4*/ s 4y 2 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- 



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 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. 


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- 



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 (l l /4 in.), and the desired final ordinate 
i n -)> an d will therefore equal 1 in.; and as 


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 y 2 
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 \y 2 in. It will now be noted 
that this resultant equals the last ordinate in the 




















lib* 8 



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



a(T)+?} 2 /| 



































</d>? /i 



<J)^7/J /| 



;| /| 



2 /I 









</>tf // /I 


1 L 4 

cQyti 2 n 













Examples 1 to 4, Problems in String Lining. 

series, as should be the case, and the final inward 
throw of y 2 in. at Sta. 4 reduces the resultant at 
Sta. 4 to the desired mean, and at the same time 



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., 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 y 2 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- 



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.} 





Ord. Solution 


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 y 8 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 



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 


























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

throw at Sta. 21 is twice this, or lV 2 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 



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- 








































Ft. String. 


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 \y 2 in. 

It is apparent that the sum of the throws at Sta. 
5 and Sta. 7 must be 2^4 ' m -> an d 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 y 2 in. at Sta. 8, are 1^ in. and 
1^4 i n -> 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. 



13 is 3y 2 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- 

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 

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 





oo oo 

'iy H 







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. 8L, 
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 
%y 2 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 



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 12y s 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 



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 



at Sta. 30 is reduced to l l / 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, ]/%, 
+%,+2 I /i, %, J4, 3 A 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. 



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 

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





- C\J 

ri ro 






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 iy 2 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. 





























+ 2 

+ 4+7 i 

Station 30 



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



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 



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. 


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 

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 



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 

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- 

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 



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 


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- 

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 



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. 


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 



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 

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 
y 2 in. to 33 ft. The preferable rate is % in. to 33 
ft., but for light curves l /\ in. to 33 ft. is quite satis- 

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 y 2 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 
y 2 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 



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 \y 2 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. 


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 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 



than that determined by the theoretical formula of 

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- 



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

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



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. 


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 










1 05' 

1 30' 

2 00' 

2 30' 

3 00' 

3 30' 

4 00' 


8 00' 











\y 2 
















'iy 2 


















1 54 














1 /4 



3 ^a 


2 54 


























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 



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 



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. 


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 



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 T 9 g- in. The 
curvature of the spiral on the run-off between Sta. 
12+50 and Sta. 14 increases by 1 to 5 times iy 2 
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 



to Jo ON cvi - 
O -- <\j IT} c\4 


C\i CVi -^ --,-- . --.-~.~^--.~^ 

\O OQ OQ o O O 

to hr> f\j . 

lO Cvj f\| 


ojOjfOOxl-sj-'^>iC)vS)vS)l s ^N-oooo<rs<3\OO2;~^ CNC ^ fr > 


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

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. 



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., y 2 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 



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- 




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%, Sy 4 in., 

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 



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

C\j <\J 


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I^KO ^100 -KVl 

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S i? S S 


o o o o o o o 

O O O O O 
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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. 


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



Superelevation . . . \ l / 2 " 


2y 2 " 


Degree of Curve 20' 





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









l /S */S Y4 VA 

ft 3/8 Y* 

x 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 iy 2 

iy 4 zy 2 33/4 5 

3/4 V/2 VA 3 

ft ft \ft V/2 V/8 

Beginning of Spiral ........ ft ft ft y 2 ^ 

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



(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 Y 4 % Y 4 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 
y s 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 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 deg. 20 min. curve, of % in. 
in 33 ft. But it might not be practicable to apply 
the preferred easement and the one attainable 



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. 


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 



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 



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 \y 2 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. 



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. 


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- 


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 



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 



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. 




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 y 2 in. to 30 ft. was nearly 
universal. It is now recognized that the maximum 



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 



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- 


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 OD 1 andBB'=3 of DG orj ofDD 1 . DH^ofDD 1 

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 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 l l / 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. 


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 



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. 















94.1 . 


F .. 

...94,0 ., 





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 



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 -> an d 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 l 1 /^ 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 2 1 /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 



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 I 1 /? in. super- 
elevation, a sharpening of the curve to 2 deg. by 
reason of the superelevation diminishing to 1 in. 



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 



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- 



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 

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 



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. 


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 



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 w r ith the others. Perfect line will not con- 



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 y 2 inch. Bad maintenance would be 



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- 



rect line by continued watchfulness is the better 

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 



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 

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 

When tie plates are applied the gage should be 



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. 





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- 





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 



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- 



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. 


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 



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 



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 y 2 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 



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. 


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 



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. 



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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 



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- 

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 



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 



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 

Fig 1 . 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 

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. 



in such 
will be 

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 



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. 





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 


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 

t i . j , r OOO v Or-iO\COu-i^-\oOi-iOO 

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

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

unusual lengths. O rfw ^ ftto *^* 0k0l SSSS32 

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- $% 



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. 


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 



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

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 



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. 


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



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- 



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 

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 



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. 


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 



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 


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. 


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 



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. 


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. in. 2 
(4 ft. 8^ in.) = 3 ft. 7 in. x 6 = 21 ft. 6 in 6 in. 

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

T: X O 


> f: TJ- Tfr ft ro 

,-1 ,_, ^H T-l 1-1 ^H O) 


* CE oo ON -i i>) 


rX - "-I 

12 2 


S w ^ 

^ ^ 

w I 

CQ ^ 








o got^oooNO-icgn- 



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

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. 



Thus this dimension for No. 10 frog and 15 ft. 
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. in. centers as follows: 13 ft. in. x 8 + 

13 ft. in. . 

104 ft. 5 in. 


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 



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 



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 



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. 

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 



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 y 2 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 


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





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. 



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 



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 

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 



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 



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. 


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 



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. 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. 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 



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



(Ties 22^ Inch Centers.) 

No. 5 Turnout or Crossover. 

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

90 94 10 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 


or Crossover. 























































No. 11 


or Crossover. 








































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 













































































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 

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 11 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 \y 2 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 



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. 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. 



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. 


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. 
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 



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 






Lead Rail 

15' 0" 


37' 0" 



51 30' 

Mid. Ord. 



18' 6" 

40' 6" 


34 40' 




22' 0" 

44' 0" 


24 30' 




25' 6" 

47' 6" 


18 06' 




28' 9" 

50' 9" 


13 40' 

3 " 



32' 0" 

54' 0" 


10 44' 


Functions for 3' 0" Gage 



19' 254" 

41' 254" 


40 25' 




22' 5" 

44' 5" 


28 35' 




25' 754" 

47' 754" 


21 00' 



28' 9 54" 

50' 9 54" 


15 54' 




32' 0" 

54' 0" 


12 20' 




35' 254" 

57' 254" 


.A. /- 

9 43' 


Functions for Meter Gage 



25' 954" 

47' 9y 2 " 


30 12' 




30' 154" 

52' 154" 


21 25' 

5 /f 




34' 4 24" 
38' 854" 

56' 4M" 
60' 8 54" 


15 40' 
11 50' 

4 ft" 



43' 0" 

65' 0" 


9 10' 

4 A", 



51' 354" 

73' 3 54" 


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 



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. in., meter, and 3 ft. 6 in. gages. It will be noted 
that for 3 ft. in. gage a middle ordinate of 3 in. is 
proper, for meter gage 3 y 2 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 2 T 7 D - for 
3 ft. in. gage, 3 T 3 - 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- 

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. 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 



Where 11 ft. in. centers of tracks obtains and 
the equipment is as wide as 9 ft. 1 in. and of a total 
length of 51 ft. 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. in. The 
presence of one of these features alone would re- 
duce the clearance on 11 ft. 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. 


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 \ 


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 



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. 


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 



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 



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 


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 

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 y 2 in. to 30 ft., a speed of 50 
miles per hour might be established. 





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- 



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 



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. 


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 



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


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 



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 

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. 



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 



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 - an d l/^ 
in. for a No. 20; % in., 1 in. and 1J^ in. for a No. 15 

and J4 m -> l/^ m - an d 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 \y 2 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 



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. 





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. S l / 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 



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 



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 


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 



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- 

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 



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. 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 



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- 



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. 



The aesthetic feature is likewise greatly enhanced by 
such provision. 


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 



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- 



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- 



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 T 3 ^ 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- 



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- 

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 



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. 


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 



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 



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 



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 

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. 




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 



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. 

Problem 1 The simplest case is that of a siding 



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. 

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.) 



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 



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. in. 
minus 14 ft. 4^6 in., or 36 ft. 7% in.; the 6th offset 
will be 51 ft. in. minus 6 ft. 4^ in., or 44 ft. 7^ in. ; 
the 7th offset will be 51 ft. in. minus 1 ft. 7 T /s in., or 
49 ft. 4% in. ; and the last offset will be the full dis- 
tance, 51 ft. 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 



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 





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 


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 




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 



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. 




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 R 1 
either greater or less than Rcos A , and two more from 
the inside in both of which A is less than 90 degrees 
and R 1 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- 



<L Siding 

D K' . 

Fig. 19. Problem 4, Instrument Layouts. 



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 



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. 



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. 


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- 



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

a+b e c 

R- V2bR b 2 

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 y 2 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. 



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

R 2 _ 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 
R 2 _ 320 R -f 25,600 = 196 R 5,456 
(196) (40,904) 

R 2 _ 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 
R 2 1 288 R -f 20,736 = 88 R 1,936 
(88) (14,608) 

R 2 376 R -J- 35,344 = 12,672 

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

No. 6. 

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 



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 

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 \y 2 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 



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 



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 

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 



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 



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 



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- 

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 



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 y 2 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 


Shifting Connections Endwise When it becomes 



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 



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 

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. 




Advancing point of switch .. 198 

Alinement in siding location 191 

Approach and run-off of curves 54 

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 

Curve t 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 




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 




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 

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 

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 




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 

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 




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 




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 




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 




Turnouts, practical considerations in installing 148 

Turnouts, rules for various functions of . 130 

Turnouts, speed through main-track 168 

Turnouts to parallel tracks 146 

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 


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. 


Fourteen East Jackson Boulevard 

Chicago : : : : : Illinois 

Practical Track 

(Price $1.60 Postpaid) 

Table of Contents 

Chapter I The Big Problem 

Chapter II Developing Track 

Chapter III How to Handle 

Chapter IV Renewing Ties. 

Chapter V Relaying Rail. 

Chapter VI Ballasting and Sur- 

Chapter VII Reports and Ac- 

Chapter VIII Spring Work. 

Chapter IX Summer Work. 

Chapter X Fall Work. 

Chapter XI Winter Work. 

Chapter XII Track Work in the 

Chapter XIII Yard Mainten- 

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 


Fourteen East Jackson Boulevard 

Chicago : : : : : Illinois 


Practical Track Work 

Or* How to Build Track and Switches 

(Price $1.60 Postpaid) 

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. 


Fourteen East Jackson Boulevard 

Chicago : : : : : Illinois 

Maintenance Methods 

(Price $1.60 Postpaid) 

Engineer Maintenance of Way, Baltimore & Ohio 

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- 

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

(Manuscript under preparation} 


Fourteen East Jackson Boulevard 

Chicago : : : : : Illinois 


Winter Track Work 

(Price $1.60 Postpaid) 

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 

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


Fourteen East Jackson Boulevard 

Chicago : : : : : Illinois 


The Autocrat at the Lunch Table 

(Price $1.60 Postpaid) 

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." 


Fourteen East Jackson Boulevard 





(Price $1.60 Postpaid) 

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- 

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) 


Fourteen East Jackson Boulevard 

Chicago : : : : : Illinois 


Inspecting Track and 

(Price $1.60 Postpaid) 

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- 

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) 


Fourteen East Jackson Boulevard 

Chicago : : : : : Illinois 



(Price $1.60 Postpaid) 

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


Fourteen East Jackson Boulevard 

Chicago : : : : : Illinois 





ren 29 

rB 1087'