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Railway Track Design

Basic considerations and guidelines to be used in the establishment
of railway horizontal and vertical alignments.

he route upon which a train travels and the track is constructed is defined as an

alignment. An alignment is defined in two fashions. First, the horizontal
alignment defines physically where the route or track goes (mathematically the

XY plane). The second component is a vertical alignment, which defines the elevation,
rise and fall (the Z component).

Alignment considerations weigh more heavily on railway design versus highway design
for several reasons. First, unlike most other transportation modes, the operator of a

train has no control over horizontal movements (i.e. steering). The guidance
mechanism for railway vehicles is defined almost exclusively by track location and thus

the track alignment. The operator only has direct control over longitudinal aspects of
train movement over an alignment defined by the track, such as speed and

forward/reverse direction. Secondly, the relative power available for locomotion
relative to the mass to be moved is significantly less than for other forms of

transportation, such as air or highway vehicles. (See Table 6-1) Finally, the physical
dimension of the vehicular unit (the train) is extremely long and thin, sometimes

approaching two miles in length. This compares, for example, with a barge tow, which
may encompass 2-3 full trains, but may only be 1200 feet in length.

These factors result in much more limited constraints to the designer when considering
alignments of small terminal and yard facilities as well as new routes between distant

locations.

The designer MUST take into account the type of train traffic (freight, passenger, light

rail, length, etc.), volume of traffic (number of vehicles per day, week, year, life cycle)
and speed when establishing alignments. The design criteria for a new coal route

across the prairie handling 15,000 ton coal trains a mile and a half long ten times per
day will be significantly different than the extension of a light rail (trolley) line in

downtown San Francisco.

Chapter

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curves as D (degrees per 20 meter arc). However, there does not seem to be any
widespread incorporation of this practice. When working with light rail or in metric

units, current practice employs curves defined by radius.

As a vehicle traverses a curve, the vehicle transmits a centrifugal force to the rail at the

point of wheel contact. This force is a function of the severity of the curve, speed of
the vehicle and the mass (weight) of the vehicle. This force acts at the center of gravity

of the rail vehicle. This force is resisted by the track. If the vehicle is traveling fast
enough, it may derail due to rail rollover, the car rolling over or simply derailing from

the combined transverse force exceeding the limit allowed by rail-flange contact.

This centrifugal force can be

counteracted by the application of
superelevation (or banking), which

effectively raises the outside rail in the
curve by rotating the track structure

about the inside rail. (See Figure 6-6)
The point, at which this elevation of the

outer rail relative to the inner rail is such
that the weight is again equally

distributed on both rails, is considered
the equilibrium elevation. Track is

rarely superelevated to the equilibrium
elevation. The difference between the

equilibrium elevation and the actual
superelevation is termed underbalance.

Though trains rarely overturn strictly
from centrifugal force from speed
(they usually derail first). This same

logic can be used to derive the overturning speed. Conventional wisdom dictates that
the rail vehicle is generally considered stable if the resultant of forces falls within the

middle third of the track. This equates to the middle 20 inches for standard gauge
track assuming that the wheel load upon the rail head is approximately 60-inches apart.

As this resultant force begins to fall outside the two rails, the vehicle will begin to tip
and eventually overturn. It should be noted that this overturning speed would vary

depending upon where the center of gravity of the vehicle is assumed to be.

There are several factors, which are considered in establishing the elevation for a curve.

The limit established by many railways is between five and six-inches for freight
operation and most passenger tracks. There is also a limit imposed by the Federal

Railroad Administration (FRA) in the amount of underbalance employed, which is
generally three inches for freight equipment and most passenger equipment.

Figure 6-6 Effects of Centrifugal Force

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Underbalance limits
above three to four

inches (to as much as five
or six inches upon FRA

approval of a waiver
request) for specific

passenger equipment may
be granted after testing is

conducted.

Track is rarely elevated to

equilibrium elevation
because not all trains will

be moving at equilibrium
speed through the curve.

Furthermore, to reduce
both the maximum

allowable superelevation along with a reduction of underbalance provides a margin for
maintenance. Superelevation should be applied in 1/4-inch increments in most

situations. In some situations, increments may be reduced to 1/8 inch if it can be
determined that construction and maintenance equipment can establish and maintain

such a tolerance. Even if it is determined that no superelevation is required for a curve,
it is generally accepted practice to superelevate all curves a minimum amount (1/2 to

3/4 of an inch). Each railway will have its own standards for superelevation and
underbalance, which should be used unless directed otherwise.

The transition from level track on tangents to curves can be accomplished in two ways.
For low speed tracks with minimum superelevation, which is commonly found in yards

and industry tracks, the superelevation is run-out before and after the curve, or through
the beginning of the curve if space prevents the latter. A commonly used value for this

run-out is 31-feet per half inch of superelevation.

On main tracks, it is preferred to establish the transition from tangent level track and

curved superelevated track by the use of a spiral or easement curve. A spiral is a curve
whose degree of curve varies exponentially from infinity (tangent) to the degree of the

body curve. The spiral completes two functions, including the gradual introduction of
superelevation as well as guiding the railway vehicle from tangent track to curved track.

Without it, there would be very high lateral dynamic load acting on the first portion of
the curve and the first portion of tangent past the curve due to the sudden introduction

and removal of centrifugal forces associated with the body curve.

There are several different types of mathematical spirals available for use, including the

clothoid, the cubic parabola and the lemniscate. Of more common use on railways are
the Searles, the Talbot and the AREMA 10-Chord spirals, which are empirical

approximations of true spirals. Though all have been applied to railway applications to

Figure 6-7 Overbalance, Equilibrium and Underbalanced

UNDERBALANCE

Superelevation

Centrifugal

Force

Gravity

Resultant

Center of

Gravity

EQUILIBRIUM

Superelevation

Centrifugal

Force

Gravity

Resultant

Center of

Gravity

OVERBALANCE

Superelevation

Gravity

Resultant

Centrifugal

Force

Center of

Gravity

0007

max

= Maximum allowable operating speed (mph).
= Average elevation of the outside rail (inches).
= Degree of curvature (degrees).

max

Amount of
Underbalance

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6.4 Alignment Design

In a perfect world, all railway alignments would be tangent and flat, thus providing for

the most economical operations and the least amount of maintenance. Though this is
never the set of circumstances from which the designer will work, it is that ideal that

he/she must be cognizant to optimize any design.

From the macro perspective, there has been for over 150 years, the classic railway

location problem where a route between two points must be constructed. One option
is to construct a shorter route with steep grades. The second option is to build a longer

route with greater curvature along gentle sloping topography. The challenge is for the
designer to choose the better route based upon overall construction, operational and

maintenance criteria. Such an example is shown below.

Figure 6-9 Heavy Curvature on the Santa Fe - Railway Technical Manual – Courtesy of BNSF

Suffice it to say that in today’s environment, the designer must also add to the decision

model environmental concerns, politics, land use issues, economics, long-term traffic
levels and other economic criteria far beyond what has traditionally been considered.

These added considerations are well beyond what is normally the designer’s task of
alignment design, but they all affect it. The designer will have to work with these issues

occasionally, dependent upon the size and scope of the project.

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On a more discrete level, the designer must take the basic components of alignments,
tangents, grades, horizontal and vertical curves, spirals and superelevation and

construct an alignment, which is cost effective to construct, easy to maintain, efficient
and safe to operate. There have been a number of guidelines, which have been

developed over the past 175 years, which take the foregoing into account. The
application of these guidelines will suffice for approximately 75% of most design

situations. For the remaining situations, the designer must take into account how the
track is going to be used (train type, speed, frequency, length, etc.) and drawing upon

experience and judgment, must make an educated decision. The decision must be in
concurrence with that of the eventual owner or operator of the track as to how to

produce the alignment with the release of at least one of the restraining guidelines.

Though AREMA has some general guidance for alignment design, each railway usually

has its own design guidelines, which complement and expand the AREMA
recommendations. Sometimes, a less restrictive guideline from another entity can be

employed to solve the design problem. Other times, a specific project constraint can
be changed to allow for the exception. Other times, it’s more complicated, and the

designer must understand how a train is going to perform to be able to make an
educated decision. The following are brief discussions of some of the concepts which

must be considered when evaluating how the most common guidelines were
established.

A freight train is most
commonly comprised of

power and cars. The
power may be one or

several locomotives
located at the front of a

train. The cars are then
located in a line behind

the power. Occasionally,
additional power is placed

at the rear, or even in the
center of the train and

may be operated remotely
from the head-end. The

train can be effectively
visualized for this

discussion as a chain lying
on a table. We will assume for the sake of simplicity that the power is all at one end of

the chain.

Trains, and in this example the chain, will always have longitudinal forces acting along

their length as the train speeds up or down, as well as reacting to changes in grade and
curvature. It is not unusual for a train to be in compression over part of its length

Figure 6-10 Automatic Coupler

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(negative longitudinal force) and in tension (positive) on another portion. These forces
are often termed ‘buff’ (negative) and ‘draft’ (positive) forces. Trains are most often

connected together with couplers (Figure 6-10). The mechanical connections of most
couplers in North America have several inches (up to six or eight in some cases) of

play between pulling and pushing. This is termed slack.

If one considers that a long train of 100 cars may be 6000' long, and that each car

might account for six inches of slack, it becomes mathematically possible for a
locomotive and the front end of a train to move fifty feet before the rear end moves at

all. As a result, the dynamic portion of the buff and draft forces can become quite
large if the operation of the train, or more importantly to the designer, the geometry of

the alignment contribute significantly to the longitudinal forces.

As the train moves or

accelerates, the chain is pulled
from one end. The force at

any point in the chain (Figure
6-11) is simply the force

being applied to the front end
of the chain minus the

frictional resistance of the
chain sliding on the table

from the head end to the
point under consideration.

As the chain is pulled in a straight line, the remainder of the chain follows an identical

path. However, as the chain is pulled around a corner, the middle portion of the chain
wants to deviate from the initial path of the front-end. On a train, there are three

things preventing this from occurring. First, the centrifugal force, as the rail car moves
about the curve, tends to push the car away from the inside of the curve. When this

fails, the wheel treads are both canted inward to encourage the vehicle to maintain the
course of the track. The last resort is the action of the wheel flange striking the rail and

guiding the wheel back on course.

Attempting to push the chain causes a different situation. A gentle nudge on a short
chain will generally allow for some movement along a line. However, as more force is

applied and the chain becomes longer, the chain wants to buckle in much the same way
an overloaded, un-braced column would buckle (See Figure 6-12). The same theories

that Euler applied to column buckling theory can be conceptually applied to a train
under heavy buff forces. Again, the only resistance to the buckling force becomes the

wheel/rail interface.

Figure 6-11 Force Applied Throughout the Train - ATSF Railroad Technical

Manual - Courtesy of BNSF