RR LRT Highway-Comparison-Geometric Policies 2007
Transcript of RR LRT Highway-Comparison-Geometric Policies 2007
AREMA Annual Conference and Exposition 2007
PROPOSED TECHNICAL PAPER ABSTRACT
Submitted: December 20, 2006 via fax
Principal Contact: Greg Toth, (312) 803-6511, [email protected]
Title: Railroad, LRT and Highway – A Comparison of Geometric Policies
Author: Greg Toth, P.E., PB
Abstract:
A comparison of geometric design practices for railroads, LRT and highway will be covered. This paper
addresses the differences in design policies between rail/LRT and highways covering horizontal alignment,
spirals, superelevation attainment calculation and application, a discussion of grade establishment and
design policies for vertical curves. Additional horizontal and vertical issues along with clearance
considerations will also be covered. The comparison will be based on existing FRA, FTA, AASHTO, and
State DOT criteria along with current railroad standard practices and AREMA policies.
The purpose of this paper is to familiarize highway engineers with railroad and LRT design. With railroads
reducing their engineering staffs and LRT becoming a more attractive alternative to driving in metropolitan
areas, more and more railroad and LRT design work is being passed on to the private sector where it may,
in many cases, be designed by highway engineers with little or no railroad or LRT experience. Therefore, a
basic understanding of railroad and LRT design and comparison to highway design would be beneficial to
the experienced highway engineer.
GEOMETRICS
RAIL vs.
HIGHWAY
By: Greg Toth, PE PB Americas, Inc.
Presented to the 2007 AREMA Annual Conference September 11, 2007
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Table of Contents A History Lesson …………………………………………………………………………… Comparing Rail and Highway Designs……………………………………………………… Degree of Curve……………………………………………………………………………... Spirals………………………………………………………………………………………... Grades………………………………………………………………………………………... Vertical Curves………………………………………………………………………………. Classification / Designation……………………………………………………………….…..Horizontal Alignment………………………………………………………………………… Additional Horizontal Issues…………………………………………………………………. Vertical Alignment…………………………………………………………………………… Vertical Curves………………………………………………………………………….…….Typical Roadway Sections…………………………………………………………………… Clearances……………………………………………………………………………………..Variances from the Norm…………………………………………………………………….. Conclusions……………………………………………………………………………………
List of Figures Figure 1 – Spiral Curve……………………………………………………………………….. Figure 2 – Vertical Curves…………………………………………………………………….Figure 3 – Single Track (Timber Tie Construction)…………………………………………..Figure 4 - Double Track (Concrete Tie Construction)………………………………………... Figure 5 – 115RE and 140RE Rail Sections………………………………………………….. Figure 6 – Direct Fixation Typical Section……………………………………………………Figure 7 – Embedded Track Typical Section…………………………………………………. Figure 8 – 2-Lane Roadway Typical Section…………………………………………………. Figure 9 – 4-Lane Divided Roadway Typical Section………………………………………... Figure 10 – Clearance Outline…………………………………………………………………Figure 11 – Maximum Vehicle Dynamic Envelope…………………………………………... Figure 12 – CTA ‘Clearance Car’ circa 1983………………………………………………….Figure 13 – ‘Tehachapi Loop’ Aerial Photograph…………………………………………….. Figure 14 – Camas Prairie Railroad (Great Northwest Railroad) 2nd Sub Track Chart……….. Figure 15 – Bridge #22 at MP22 Camas Prairie Railroad 2nd Sub……………………………..Figure 16 – Bridge #22.1 at MP22 Camas Prairie Railroad 2nd Sub…………………….….….
List of Tables Table 1 – Track Classification……………………………………………………….………… Table 2 – Maximum Relative Gradients…….….….….….….….….………………………….. Table 3 – Adjustment Factor for Number of Lanes Rotated…………………………………… Table 4 – Design Controls for Vertical Curves…………………………………………………
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Geometrics – Rail vs. Highway
A History Lesson
Years ago I was approached by my supervisor asking me if I had done any highway
design, and of course I said yes. Having done a lot of surveying over the years and also
having taught construction surveys in the Army where roadway design was a major
portion of the curriculum and also teaching in two State sponsored survey apprenticeship
programs in Maryland and Virginia amounting to about six years, I felt comfortable in
my abilities. I was then asked if I had ever done any railroad design and I had to tell him I
had not. His response was something like, “well… railroads are a lot like highways
except you have ballast, ties and rails instead of pavement.” Thus started my ‘new’ career
in railroad design.
I was introduced to an old retired railroad engineer who had worked for the ‘Great
Northern Railway’ for over forty years and had been hired as a part-time employee whose
job was to ‘teach me the ropes’. He would come in once or twice a week and answer any
and all questions I might come up with or had written down. Most questions related to
whether you could or couldn’t do a specific thing in design and for the most part I got the
answer, ‘No, because the train would fall off the tracks.” Then he would enlighten me
with a story of someone who had tried it and failed with the usual result of a derailment.
Some of the stories were quite amusing and often remarkable and we would both have a
good laugh about the ‘ineptitude’ of some ‘experts’ - but learn I did. This was the
beginning to what is approaching a thirty year experience in highway, railroad and transit
design – and boy what a ride it has been...
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Comparing Rail and Highway Designs
To begin with, as most people who have done both rail and highway design would agree,
usually the first and major difference mentioned - as far as horizontal alignment is
concerned - is that railroads use the ‘chord’ definition and highway designers use the
‘arc’ definition for determining the radius of a curve. Both measurements relate to the
‘degree of curvature’ (D) which is defined by a 100 foot length along the curve in
question. However, they are different due to how and where the measurement is taken.
Degree of Curve
By ‘chord’ definition, the degree of curve is the angle measured along the length of a
section of curve, subtended by a 100-foot chord. The following is the equation used to
define or calculate the radius.
R = 50 / sin (D/2)
For a curve that has a D(chord) of 1o, the radius is 5729.65 ft.
The degree of curve by ‘arc’ definition is defined as the angle measured along the length
of a section of curve, subtended by a 100-foot arc. The equation used in this case is:
R = 5729.58 / D
Where the constant 5729.58 is derived from the following ratio and usually rounded off
to hundredths.
D / 360o = 100 / 2πR
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In older books and publications one may find this number as simply 5730.
For a curve that has D(arc) of 1o, the radius is 5729.58 ft.
As one can see, the difference is small for a 1-degree curve but increases as the degree of
curve increases or the radius decreases as for a 4o curve, where R is 1432.69 and 1432.39
for the chord and arc definitions, respectively. This is a relatively small difference but
could result in a substantial difference over the length of an alignment by impacting
stationing, especially if the alignment is extremely long.
An Exception
One exception to rail design is in Light Rail Transit (LRT) systems, where in many cases
the system’s design criteria will use the arc definition to define the degree of curvature of
a horizontal curve. This was explained to me many years ago by an old engineer who told
me that when most of the earlier transit systems were started, highway or roadway
engineers were used to do the design since most if not all of the railroad engineers that
were around at that time were employed by the various railroads, of which there were
many.
There will be further discussions relating to the horizontal alignment later in this
document comparing common variables used in each type of design.
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Spirals
The second most common difference between railroad and highway design is that
railroads will almost always use spirals in the horizontal layout along the mainline,
whereas highway agencies such as the many state departments of transportation find the
use of spirals is not necessary. In my years of working with various states in the East and
Midwest, I found that most State DOT’s prefer not to use spirals although I have come
across some that do. This could be due to the fact that a vehicle (car, truck or bus)
following a lane on a road or highway through a simple curve can follow a suitable
transition path (something resembling a spiral) within the lane width whereas a train on a
railroad track has a set path with which it must follow. Also, simple curves are easier to
design, survey and construct.
Spirals are introduced where the tangent and curve meet along the alignment and are
determined to transition over a set calculated distance from the tangent section where the
radius is ‘infinity’ to the actual radius of the curve as defined by D or degree of curve.
They are placed such that approximately half the spiral is along the tangent section and
the other half is along the curve section. Spiral lengths are calculated from any number of
spiral definitions with the most common being the ‘Barnett Highway Spiral’ for
highways and the ‘AREMA Spiral’ for railroads. Both accomplish the same need to
transition from tangent to curve over a set distance and at a rate that is relatively
unnoticeable to passengers on trains or vehicles on highways.
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The second purpose of the spiral is to distribute the superelevation that is also calculated
by set equations for railroad, LRT and highway design as defined by AREMA (American
Railway and Maintenance-of-Way Association), FTA (Federal Transit Administration)
and AASHTO (American Association of State Highway and Transportation Officials),
respectively. Superelevation, or the difference in elevation between the two rails on a
railroad or LRT system, or the two edges of pavement on a highway, is a value that is
calculated that opposes the centrifugal forces going through a curve and is a function of
both speed and degree of curvature or radius.
Regarding spirals in highways, I had heard that many highway authorities did not use
them due to their difficulty in being staked out in the field, not to mention the complexity
in calculating them. Since spirals are a means to introduce superelevation into curves, for
those states where spirals are not used, the superelevation is placed such that anywhere
from 60-80% of the superelevation is placed on the tangent and the remainder on the
curve, with the common ratio in many states requiring 2/3 on tangent and 1/3 on curve.
Governing agencies such as AASHTO and State DOT’s have criteria that specify how the
superelevation is to be applied where spirals are not used. Figure 1 on the next page
shows a spiral with its associated variables noted.
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Figure 1 – Spiral Curve
Where,
TS = Point of Tangent to Spiral SC = Point of Spiral to Curve PI = Point of Intersection CS = Point of Curve to Spiral ST = Point of Spiral to Tangent CC = Center of Curve (also called the Radius Point) Dc = Degree of Curvature R = Radius ∆c = Delta Curve (Central Angle of Simple Curve) ∆s = Delta Spiral (Central Angle of Spiral) I-Angle = Delta (Total Central Angle of Curvature, where I-Angle = ∆c + 2∆s)
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Ls = Length of Spiral Lc = Length of (Simple) Curve Ts = Length of Tangent of Spiral Curve (TS to PI) Es = External of Spiral Curve
The previous figure represents a spiral that can be found and used in railroad, transit and
highway design.
I know from my surveying days that many a surveyor I had talked to who had to stake out
spirals preferred not to stake them out because they claimed they never fit properly and
that they ended up staking them out from both ends and left the ‘slop’ (which there
apparently always was) in the middle. And since when staking out spirals the deflection
angle at any given point is always different and needs to be calculated individually, I can
understand how this could cause problems and take additional time having to recalculate
each deflection at any given point on the spiral (Note: This was before everyone had a
calculator or started using total-station survey equipment).
A point to consider is that for highway design, AASHTO does not demand the use of
spirals but suggests that in some cases spirals may be beneficial, whereas for railroad
design, AREMA recommends the use of spirals while most railroads require them on at
least mainline and usually secondary tracks. In LRT design many authorities’ design
criteria normally require spirals on the mainline where radii are less than 10,000 ft.
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The differences in determining spiral lengths and superelevation attainment for railroads,
LRT and highways will also be covered later in this document.
Grades
Now that the horizontal alignment has been discussed to some degree, one of the
variables that is a major impact to both railroad and highway design is the grades that
must be designed in the vertical alignment which are shown in the profile.
Generally, grades are defined as a rate of change in the vertical and are usually measured
in percent (%) or a decimal of ‘feet per foot’ value. Both refer to the change in grade
normally measured over a 100 foot length. A 1-foot difference in elevation over a 100-
foot length would be either 1% or as the ratio of 0.01 ft/ft. In many cases the
measurements are taken to hundredths (0.01) or thousandths (0.001) of a percent and
thousandths or ten-thousandths (0.0001) if measured in feet per foot. Railroads and LRT
systems refer to the elevation set on the profile as the ‘top of rail’, whereas in highway
design it is referred to as the ‘profile grade line’, which is normally set at the centerline of
the roadway for undivided roads and either along the inside edge of pavement or an inner
lane line on divided highways.
One of the differences in comparing railroad and highway profiles is the magnitude of the
grade (percent (%) will be used in discussing grades). Generally, grades found on
railroads rarely exceed 1% on mainline tracks and are often as low as 0.3% as per many
governing railroad’s standards or design criteria, whereas grades of up to 4% are common
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on highways and as much as 6% on ramps in interchanges and 8% on county roads. Two
dictating factors in most all cases are matters concerning physics and economy (the cost
of fuel). The acceptable values for minimum and maximum grades can be found in some
railroad standards and all DOT and transit authority’s design criteria or standards. When
designing for a railroad, it may sometimes be necessary to obtain these values by directly
contacting the engineering department (or Chief Engineer’s office) and inquiring what
the values should be for that particular design.
LRT systems will normally allow grades of up to a maximum 6% with a maximum
sustained grade of 4%, and as high as 10% for shorter distances although approval will
normally be required by the governing authority. The steeper grades are possible due to
much lighter train weights and a higher horsepower per ton ratio on typical LRT vehicles.
Grades through platform areas of stations are normally flat with maximum values set by
the governing authority.
Grades through storage tracks or yards for both railroads and LRT systems generally
have a sag in the middle of the alignment to prevent cars/vehicles from rolling to either
end or onto the mainline. On stub ended tracks, the profile should slope to the stub end of
the track with a suitable stopping device at the end of the track such as a bumper.
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Vertical Curves
Closely tied to ‘grades’ are ‘vertical curves’ which allow one to negotiate a change in
grade without leaving one’s stomach in one’s throat or at one’s ankles. Railroads, LRT
and highways have set equations that are used to determine acceptable lengths.
Generally one will find longer vertical curve lengths on railroads than highways but
shorter lengths for transit lines. Recently AREMA has re-determined the design
parameters of calculating vertical curves which will be covered later in this document.
Classification / Designation
The type of railroad or highway classification or designation will dictate variable values
required to design the alignment, from design speed and degree of curvature or radius, to
maximum and minimum grades and vertical curves, and of course superelevation.
For railroads, the classification of the alignment is based on the class of track, which is
based on maximum operating speed limits. Table 1 on the next page illustrates the speeds
associated with the class of track and differentiates between freight and passenger service
for each class.
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rack Class Maximum allowable operating speed (mph) for freight trains
Maximum allowable operating speeds (mph) for passenger trains 1
Excepted track 10 N/A Class 1 track 10 15 Class 2 track 25 30 Class 3 track 40 60 Class 4 track 60 80 Class 5 track 80 90 Class 6 track 110 110 1 Class 7 track 125 125 1 Class 8 track 160 160 1 Class 9 track 200 200 1
1 Freight may be transported at passenger train speeds if specific conditions are met.
Table 1 – Track Classification
The table above was developed by the FRA (Federal Railroad Administration) and is
strictly enforced on all U.S. operating railroads. It can be seen that passenger speeds are
between 5 to 20 mph higher up to Class 5 Track. Class 6 track and above are considered
‘High Speed’ rail and follow a more restrictive set of requirements to maintain and
operate. The differences in Class 5 Track and below will have a bearing on determining
superelevation on tracks that carry both freight and passenger service and will be
discussed later in this document. As far as types of track are concerned, there are
mainline, siding, industry, branch and yard track, to name a few.
Highway design, on the other hand, has a more complex classification of roadways.
They can be urban or rural, classified as arterial or minor arterial, be designated as
interstate, freeway, or expressway, be divided or undivided, can also be designated as
collector roads and local roads or collector streets and local streets – and if there is an
interchange, there will be ramps and possibly frontage roads. Each classification has its
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own set of minimums and maximums, but all are based on the design speed. No simple
table could cover all the various types listed above. For those who are interested in such
tables, they can be found in AASHTO “A Policy on Geometric Design of Highways and
Streets” or in any State DOT Design Manual.
Horizontal Alignment
Other than the use of ‘chord’ vs. ‘arc’ definition for determining the radius of horizontal
curves, design speed and superelevation are two key factors in establishing the maximum
degree of curvature.
Railroads normally use degree of curve in determining the curvature and will usually
have a maximum of 2o for mainline mid-speed designs and 4o for mainline low-speed
designs. High-speed tracks are more restrictive and normally restricted to 1o or less along
the mainline, depending on the operating speed. The limiting factor on determining the
maximum degree of curve will normally be the design speed and be dictated by the
amount of superelevation used.
Highway designs normally use the radius for determining curvature and will allow for
wider ranges depending on whether the design is for freeways or expressways, urban or
rural, and of course will be dictated by the design speed. The minimum radius of any
given curve for a freeway or expressway can range from as low as 1340-ft radius (D =
4.28o) for a 60 mph design speed to 2050-ft radius (D = 2.79o) for a 70 mph design speed
(taken from Illinois DOT Figure 44-5D and Figure 45-4C).
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Light Rail Transit systems may allow a minimum radius on mainline tracks to be 500 ft
in embedded or on aerial track, 300 ft for ballasted at-grade track and a desired minimum
of 115 ft for main line embedded track. For yard and embedded main line track the
absolute minimum can be as low as 82 ft provided the vehicle specifications state that the
car can negotiate such a tight radius. Before selecting the minimum radius for any system
the engineer must obtain the vehicle specifications to determine what the minimum radius
can be. In most cases the controlling authority will have set the minimum and will require
approval before allowing any smaller radius to be used.
Once the radius for either type of design is set at each location, it must be determined
what the superelevation will be for that particular degree of curve or radius and the
design speed at which it is being designed.
For railroad design, the following equation is used in determining the equilibrium
superelevation and can be found in the AREMA “Manual for Railway Engineering”.
(1) E e = 0.0007 V2D
Where, E e = the equilibrium elevation in inches between the inner and outer rails V = the speed in miles per hour (mph) D = the degree of curve
Once this value is determined the length of spiral can be calculated.
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There are three equations AREMA specifies for use in determining spiral length, two of
which are based on what is known as ‘unbalanced’ superelevation and one which is based
on ‘actual’ superelevation.
(2) L = 1.63 E u V (3) L = 1.22 E u V (4) L = 62 E a
Where, L = the desirable length of spiral in ft. E u = unbalanced superelevation in inches E a = actual superelevation in inches V = train speed in mph The Transportation Research Board (TRB) has developed additional equations for use
with LRT design:
(5) L = 31 E a (6) L = 0.82 E u V (7) L = 1.10 E a V
These values were developed based on shorter and lighter transit cars which allow for
shorter lengths of curve to be designed.
Before going over the equations, one must first understand the concept and application of
‘unbalanced’ and ‘actual’ superelevation.
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As mentioned earlier, any given railroad alignment may have both freight and passenger
service and by looking at Table 1, one sees that there are different maximum operating
speeds, V, for each class of track. It can be seen that using equation (1) would result in
two different E e values between Class 1 and Class 5 Track based on the speeds shown.
To resolve the issue of different E values, it can be determined that by introducing an
unbalance in the superelevation, E u, that an actual superelevation, E a, could be used that
would satisfy both types of service at two different speeds. Over the years it was
determined that using a maximum E a of 5 inches and a maximum E u of 3” could not be
exceeded which yielded the equation where,
(8) E e = E a + E u, where E e = 8”
It was also determined that by introducing an E u, it gave the railroads the opportunity to
run trains at different speeds through the curves provided E u did not exceed 3”.
Another benefit for introducing an E u allows railroads to run trains at higher speeds and
not exceed the maximum E a of 5”.
An example being, if V = 40 mph and D = 4o, the maximum E e determined from
equation (1) would be approximately 4.5”. By adding an additional E u of 3” to this value,
one could set the E e to 7.5” and by rearranging the terms in the equation, determine that a
train could theoretically go through the curve at 50 mph. However, due to the wear and
tear on tracks with a high unbalance, most railroads prefer to maintain an E u of between
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1 and 2 inches. And since track maintenance is a high capital cost item, railroads will
tend to minimize the costs by either adjusting the radius to meet the speed requirement or
by increasing the E a if it can be increased, thereby reducing E u. Another option would be
to reduce speed which would impact operations and could result in lost revenue.
Getting back to the equations for determining the length of spiral, equation (1) is
generally used for new construction or total reconstruction while equation (2) is used
where existing track is to be realigned or where right-of-way is limited. Both these
equations are based on using E u while equation (3) is based on using E a. Once equations
(1) or (2) are determined, they must be compared with the results of equation (3) with the
larger value being used for the design. Normally the length is rounded up to the nearest
10’, but can be rounded up to any value provided there are no other impacts.
It should be noted that in some railroad standards, the constant ‘62’ in equation (3) is
often times a variable with values for it ranging from the low 40’s to over ‘100’ for
different speed increments. The constant may also have a small range between
‘preferable’ and ‘minimum’ values for each speed increment.
Superelevation on railroads is always applied to the rail on the outside of the curve and is
referred to as the ‘high’ rail, whereas the rail on the inside of the rail is referred to as the
‘low’ rail and is the location where the ‘top of rail’ profile is held.
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There are however, locations where spirals and superelevation are not used, specifically
in yards and on some sidings and industrial tracks.
In LRT design the length of spiral is determined by calculating the values for equations
(5) through (7) and using the largest value rounded to the nearest 5 ft to set the length of
spiral. Ranges of E a can range from 8 to 10 inches, but it is more common for it to be
limited to 6 inches with an E u of 4.5 inches.
Highway superelevation, on the other hand, is determined using a different equation
which includes a ‘side friction factor’ for different speeds. The simplified version
follows.
(9) (0.01e + f) / (1 – 0.01ef) = V2 / 15R
Where, e = rate of roadway superelevation, % f = side friction (demand) factor V = vehicle speed, mph R = radius of curve measured to a vehicle’s center of gravity, ft In highway design, there are also different rates of superelevation that can be used in the
design process that sets the maximum superelevation acquired between 4% and 12% with
increments of usually 2%. The maximum rates are normally set for different types of
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roadway design. Examples would be in setting the maximum of 6% for the main roadway
and 8% for ramps found in interchanges. In urban areas 4% maximum is often used in
freeways and expressways due to the amount of superelevation required for multiple
lanes, thereby reducing earthwork and also possibly minimizing right-of-way or the need
for retaining walls if there are constraints within the alignment.
The side friction factor, f, is a value that varies not only with the speed, but also with the
maximum superelevation rate used for the design.
The runoff length for superelevation and superelevation required for any given radius are
normally found in tables found in AASHTO and State DOT design manuals. All one
needs is the design speed and maximum superelevation allowed to determine any given
superelevation and runoff length for any given radius.
There is also a table provided by AASHTO and can be found in State DOT Criteria that
lists ‘maximum relative gradients’ for specific design speeds. Table 2 on the following
page from AASHTO (Exhibit 3-30) illustrates the ‘US Customary’ (English Unit) values
for determining runoff lengths.
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Design Speed (mph)
Maximum Relative
Gradient (%)
Equivalent Maximum
Relative slope 15 0.78 1:128 20 0.74 1:135 25 0.70 1:143 30 0.66 1:152 35 0.62 1:161 40 0.58 1:172 45 0.54 1:185 50 0.50 1:200 55 0.47 1:213 60 0.45 1:222 65 0.43 1:233 70 0.40 1:250 75 0.38 1:263 80 0.35 1:286
Table 2 - Maximum Relative Gradients
This table can be used to determine the runoff length for any given set of variables using
the following equation.
(9) Lr = (wn1) ed (bw) / ∆ Where, Lr = minimum length of superelevation runoff, ft ∆ = maximum relative gradient, percent n1 = number of lanes rotated bw = adjustment factor for number of lanes rotated w = width of one traffic lane, ft (typically 12 ft) ed = design superelevation rate , %
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The factor for number of lanes rotated can be found in AASHTO (Exhibit 3-31) and is
shown in Table 3 below.
Number of Lanes
Rotated
Adjustment Factor
bw
Length Increase Relative to One-Lane Rotated
(= n1 bw) 1 1.00 1.0
1.5 0.83 1.25 2 0.75 1.5
2.5 0.70 1.75 3 0.67 2.0
3.5 0.64 2.25
Table 3 – Adjustment Factor for Number of Lanes Rotated The use of Tables 2 and 3 will allow the designer to determine any length of runoff for
any speed with any number of lanes. However, one must realize that the length
determined will only cover the runoff from the full superelevation to where the slope
along the lane(s) is flat or 0%. To determine the full amount to obtain normal crown, one
must also determine the tangent runout length required to go from flat or 0% to normal
crown. The equation for this follows.
(11) Lt = eNC Lr / ed Where, Lt = minimum length of tangent runout, ft eNC = normal cross slope rate, % Lr = minimum length of superelevation runoff, ft ed = design superelevation rate, %
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Once the total transition length is calculated the location of the transition can be set,
normally placing the runoff such that between 60-80% falls on the tangent and the
remainder on the curve as noted earlier. Once that is done, the runout is placed at the end
of the runoff along the tangent.
Another variable that needs to be addressed in highway design is calculating the
transition lengths based on the location of the ‘point of rotation’. The point of rotation is
normally set at the centerline of an undivided roadway or at either the inside edge of
pavement or a lane edge for multi-lane divided highways. This is the point where the
grade line is normally set and is commonly referred to as the ‘profile grade line’. Placing
the location of this point on a divided highway design is critical since its location
determines how long the runoff length will be.
Additional Horizontal Issues
Another issue that commonly comes up in design for railroads, LRT and highways is the
minimum length of curve.
In railroad design, the minimum length of the simple curve is accepted to be 100 ft,
which does not include the lengths of the spirals. I say this because it is not always a
documented value and often times requires contacting the engineering department of the
railroad to obtain the “desirable” or “minimum” value.
In LRT design, the minimum length is determined by the following equation:
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(12) L min = 3V Where, L min = minimum length of curve in ft V = design speed in mph The minimum length of curve in highway design is a far easier value to obtain since it is
stated in the AASHTO design manual and can normally by found in State DOT standards
or criteria. According to AASHTO, curves should be at least 500 ft long for a central
angle of 5o and should be increased in length by 100 ft for each 1o decrease in the central
angle. The minimum length on main highways should be 15 times the design speed (in
mph) and for high-speed facilities should be 30 times the design speed.
Also, many times there will be occasions where the alignment requires reverse
movements over a short distance. In both railroad and highway design a tangent section is
required but not always for the same reasons.
Railroads require minimum tangents based on individual railroad requirements and may
often differ from one railroad to another. The main reason that a tangent is required
between reversing movements is to avert derailments. Railroad cars are connected by
‘couplers’ that are designed to keep the cars connected, but can also be ‘uncoupled’ under
certain conditions. In short, if the cars are placed in a position where the couplers are
moving in opposite directions resulting in opposing forces, they can uncouple or possibly
cause a derailment.
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To avert this, tangent sections between curves are introduced to allow the cars to ‘steady
up’ on tangent before a change in direction occurs when entering a curve. Normally the
shortest allowable tangent between reversing curves is 100 ft, but some railroads will
allow less, depending on the location, degree of curvature of the curves and speed at
which the cars are trying to negotiate the reversing movement.
As an example, the Union Pacific Railroad (UPRR) allows a minimum tangent of 36 ft on
industry track or in yards for 7o-30’ or less curves but requires 60 ft for curves greater
than 7o-30’. On mainline and branch lines they require 500 ft for speeds of 60 mph and
above, 300 ft for speeds between 40 mph and 59 mph, and 150 ft for speeds of 39 mph
and below (UPRR Engineering STD DWG 0018).
However, in cases where these values can not be met, it is sometimes possible to obtain a
waiver if authorized by the railroad’s Chief Engineer. This is true of most railroads and it
must be mentioned that not all railroads have the same standards regarding minimum
tangents.
I was once told that as long as there are three trucks on tangent track that the couplers
will have a sufficient length of tangent to line up. By using this reasoning one must also
take into consideration the type of cars that will be hauled over that particular section of
track since cars come in various lengths. Where no standards may be found on some of
the smaller railroads, contact the railroad’s Engineering Department and inquire.
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In Highway design, the critical factor in placing a tangent between reversing curves
occurs on alignments where spirals are not used and superelevation is applied. As
discussed earlier, many State DOT’s do not use spirals and therefore have to apply the
superelevation required over a portion of the tangent. In cases where there is a reversing
movement, sufficient tangent must be determined to allow the transition from one
superelevation rate to the other. In some cases the distance required to ‘roll-over’ the
superelevation without a set length of tangent with normal crown is allowed, but this
situation may require approval or sometimes a waiver by the governing agency.
In states where spirals are used, it is sometimes required to have a short length of tangent
between reversing curves and their spirals.
A prime example was a project I worked on in the state of Michigan where spirals were
used. The project was back in the late 80’s and early 90’s. I recall that MDOT required
spirals on the mainline of a divided highway with a minimum of 300 ft tangent between
reverse curves. Reverse curves with spirals without tangent between the reversing moves
were allowed on ramps in interchanges. Spirals were not required on the crossroads but a
minimum of 200 ft of tangent was necessary for reversing movements.
In LRT design reverse curves are acceptable on most systems since they do not impact
ride comfort. It is a common practice to have a 3.3 ft minimum tangent between reverse
curves if reverse spirals without a tangent between them is not possible. In embedded
trackwork where the track is actually embedded in the pavement of a roadway and shares
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the travel-way with other vehicles (cars, tracks, and buses), it may not be feasible to
provide a minimum tangent provided the operating speeds are below 20 mph. It should be
noted however, that reverse face-to-face spirals may cause increased clearance problems
so their use must be investigated to determine if there would be any impacts to the
design. On some systems, the authority will set minimum tangent values between reverse
curves.
Another situation closely associated with reverse curves is broken back curves. Similar to
reverse curves in that there is a section of tangent between the curves, broken back curves
are a series of two consecutive curves that are in the same direction having a short section
of tangent between them. In both railroad and highway design this situation should be
avoided wherever possible. It is recommended that the alignment be revised if possible
by adjusting the radii to form a compound curve (consecutive curves in the same
direction) or to provide sufficient tangent between the curves that would be approved by
the railroad or governing agency.
In LRT design, this condition may result in substandard ride quality, but does not affect
safety or operating speeds. As a preference, there should be no tangent between
consecutive curves in the same direction, but if required, the same minimum tangent of
3.3 ft should be used as in reverse curves.
Compound curves on the other hand are acceptable in railroad, LRT and highway design
and can be found in locations where space is limited.
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In highway design most agencies require a ratio of no greater than 1.5:1 between the radii
of compound curves on mainline curves and 2:1 on ramps or at intersections of roadways.
However, AASHTO suggests discretion in over-using them in design of mainline
alignments.
In railroad design there are no requirements regarding ratios between the radii of
compound curves. However, a spiral between the curves is recommended with the length
determined by the design speed and the difference in elevation between the two curves
with half the spiral falling in each of the curves. The length can be determined by using
the difference in the degree of curvature between the two curves once the spiral constant
has been calculated for the curve with the higher degree of curvature. Normally the
calculated length should be at least the minimum spiral length accepted by the railroad
and is commonly set at 100 ft if the calculated value is shorter. In some cases a 50 ft
length spiral is acceptable but approval from the railroad is suggested.
Compound curves are acceptable in LRT design and are preferable to broken back curves
and can be designed with or without spirals. If a spiral is used, it follows the same
application as in railroad placement and if no spiral is introduced, the spiral is placed
such that half the spiral falls on each curve.
Another point that one must take into account when designing a railroad is to minimize
the number of curves along the alignment by trying to keep long tangents between them.
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Considering that trains can approach and sometimes exceed 1.5 miles in length,
alignments with short tangents and many curves can result in introducing forces at the
couplers that could increase the chances of a derailment. When designing the track
alignment it is wise to keep the maximum number of tangents the train would be on to
two if possible.
Many railroads will require any new design to have vertical curves on horizontal tangents
only, keeping the combination of vertical curves within horizontal curves to an absolute
minimum.
There is also an equation used for grade compensation through a horizontal curve.
(13) Gc = G – 0.04D Where, Gc = compensated grade in percent G = grade before compensation in percent D = degree of curve in decimals of degrees This equation must be checked to assure that the maximum ‘compensated’ grade does not
exceed the railroad’s maximum design grade criteria.
An example being, if the maximum allowable grade for a specific railroad line is 1%, any
profile through a horizontal curve must be decreased by 0.04% per degree of curvature. If
a 2-degree curve were introduced into the proposed grade, the maximum allowable
compensated grade would be 0.92% since the curve within the grade would require a
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0.08% adjustment. And since most alignments have two-way traffic, a ‘compensated’
grade can not exceed the railroad’s maximum allowable grade regardless if it is an
ascending or descending grade.
Vertical Alignment
Since alignment is a 3-dimensional design, the remaining part that still needs to be
addressed is the vertical alignment. As mentioned earlier, the vertical alignment is
normally shown along what is referred to as the profile and is measured as the rate of a
set amount of feet measured in the vertical plane over a set horizontal distance of 100
feet. Grades can either be shown as a percentage, where a 1% grade represents a 1-foot
change in vertical for every 100-foot length or in a feet per foot ratio, where 0.01 ft/ft
would be the same as a 1% grade. It is also common practice to indicate the grade as
descending or ascending in the direction of increasing stationing, by using a negative (-)
or positive (+) sign, hence a -1.5% grade would indicate a descending grade of 1.5 feet
per 100 foot of length and a +0.5% would indicate an ascending grade of 0.5 feet per 100
foot of length in the direction of stationing.
Vertical Curves
To allow for a smooth ride, vertical curves are introduced with their lengths calculated by
equations set forth in criteria by the railroads, LRT authorities, and AASHTO, State
DOT’s or governing agencies for highways. For most railroad, LRT and highway designs
the vertical curve is based on a parabola although on some LRT systems it may be based
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on the radius of a simple curve. Figure 2 below illustrates summit and sag vertical curves
with their associated variables labeled.
Figure 2 – Vertical Curves
Where,
L = Length of vertical curve (sometimes called LVC) g1 = Grade leading into the vertical curve g2 = Grade leading out of the vertical curve PVC = Point of Vertical Curvature PVI = Point of Vertical Intersection PVT = Point of Vertical Tangency
Summit vertical curves have grades where the approaching grade is greater than the
departing grade in the direction of stationing, whereas sag vertical curves have grades
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where the approaching grade is less than the departing grade in the direction of
stationing.
Originally, the criteria for railroads were set back in the 1800’s and was based on a
different set of criteria than today. I will go over both the new and the old equations since
some railroads still use the old criteria on their existing alignments.
The old criteria were based on grades only and whether the vertical curve was a summit
or sag, whereas the new criteria are a function of both the grades and design speed with
no differentiation to whether they are summits or sags.
The current criteria to determine the minimum length of vertical curve for railroads is as
follows:
(14) L = (DV2 K) / A
Where, L = length of vertical curve in feet D = the absolute value of the difference in rates of grades, expressed as a decimal V = design speed in mph K = 2.15 conversion factor to give L in feet A = vertical acceleration in ft/sec/sec (ft/sec2) The vertical acceleration (A) should be selected based on the type of operation and is as
follows:
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Freight operations:
A = 0.10 ft/sec/sec
Passenger and Transit operations:
A = 0.60 ft/sec/sec
As can be seen by the value of ‘A’, the vertical curve length for freight operations will
normally be six (6) times longer than for passenger operations. Also, the minimum length
of a vertical curve shall be no less than 100 ft.
The following example shows the difference in length for both freight and passenger
operations.
A ‘sag’ curve has grades of -0.6% and +0.6% with a maximum operating speed of 40
mph.
D = the absolute value of ((+0.006) – (-0.006)) = 0.012 V = 40 mph K = 2.15 A = 0.10 ft/sec/sec vertical acceleration (freight)
L = (DV2 K) / A = (0.012) (40)2 (2.15) / 0.10 = 412.8 ft, or rounded up to 415 ft
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Using the same values for passenger operations with the speed set at 60 mph,
L = (DV2 K) / A = (0.012) (60)2 (2.15) / 0.6 = 154.8 ft, or rounded to 155 ft. When designing for joint operations, e.g. freight and passenger, the larger value
calculated shall be used for the length of vertical curve. For the above example the freight
speed would dictate the length of vertical curve. It can be seen that the class of track for
this example would be Class 3 Track as per Table 1 found earlier in this document.
The old criteria I alluded to earlier was based solely on grades and was a function of
whether the vertical curve was a summit or sag curve
(15) L = D / R Where, L = length of vertical curve in 100 ft stations (L = 2 stations would be 200 ft) D = the algebraic difference in rates of grade in 100 ft stations R = rate of grade of grade per station (100 ft) For crest curves, ‘R’ should be 0.05 for sags and 0.10 for summits for main lines and
twice the values for secondary and branch lines. With these values of ‘R’ it can be seen
that sag curves were twice as long as summit curves.
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Using the same example as above where a ‘sag’ curve has grades of -0.6% and +0.6%,
the length would be calculated as follows:
L = ((0.6) – (-0.6)) / (0.05 / 100) = 2400 ft As can be seen, the length using the new criteria yields far shorter vertical curve lengths
than from the old criteria. If the grades in this example had been reversed resulting in a
summit condition, the vertical curve length would be 1200 ft, which is still longer than
the length when using the new criteria.
Two of the reasons for the change in criteria were due to curves calculated using the old
criteria caused problems where vertical clearance became an issue when railroads started
using container cars and ‘hicube’ boxcars that required a higher vertical clearance and
when higher speeds on passenger trains resulted in long vertical curves that required large
amounts of earthwork for new lines.
Amtrak first used a modified version of equation (14) along the Northeast Corridor when
they began high-speed rail operations back in the 1970’s. AREMA started looking into
revising the criteria in the mid to late 90’s and it was developed, approved and adopted
around 2003.
Many LRT systems have their own set of equations and criteria that are used in
determining vertical curve lengths although some may use the current AREMA criteria
also.
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The TRB has developed the following equations to determine vertical curve lengths for
use with LRT design:
(16) LVC = 200A (Desired Length)
(17) LVC = 100A (Preferred Minimum Length)
(18) LVC = AV2 / 25 (Absolute Minimum Length for Summit Curves)
(19) LVC = AV2 / 45 (Absolute Minimum Length for Sag Curves) Where, LVC = length of vertical curve in ft A = (G2 – G1) algebraic difference in grade in percent G1 = percent grade on approach G2 = percent grade on departure V = design speed in mph TRB states that sag and summit vertical curves should be designed at the maximum
possible length and that vertical broken back curves and short horizontal curves within
vertical curves should be avoided.
If the LRT authority requires simple radius curves and not parabolic curves, the minimum
equivalent radius for a vertical curve can be determined by the following equation:
(20) Rv = LVC / 0.01 (G2 – G1) Where, Rv = minimum equivalent radius of a vertical curve in ft
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Reverse vertical curves are acceptable in some LRT systems provided they meet the
equations listed above and conform to the system’s LRT vehicle specifications.
Determination of vertical curve lengths for highway design takes into consideration the
grades, speed and a third factor known as sight distance. AASHTO also states that the
design should be safe and comfortable in operation, in appearance, and adequate for
drainage. Asymmetrical vertical curves, which are acceptable, are vertical curves that
have different tangent lengths and are used in locations where critical clearances can not
be met when using the standard symmetrical parabolic curve.
There are numerous equations mentioned in AASHTO and State DOT manuals that are
used for different design conditions. However, AASHTO and State DOT’s have
simplified the design process by introducing tables for various design speeds that can be
used to determine the minimum length of vertical curve required. The following simple
equation can be used in almost all situations provided the design speed is known.
(21) L = K A Where, L = the length of vertical curve in ft K = the site distance determined by the design speed ft / percent A = (G2 – G1) algebraic difference in grade in percent G1 = percent grade on approach G2 = percent grade on departure
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The sight distance value ‘K’ can be based on either ‘stopping sight distance’, where a
stop condition exists, ‘decision sight distance’, where the driver has time to maneuver
around an object seen on the roadway, or ‘ passing sight distance’, where the driver has
sufficient time to see and pass a slower vehicle on the road.
The stopping sight distance is determined by the height of the driver’s eye, estimated at
3.5 ft, and the height of an object to be seen by the driver at 2 ft, or the equivalent of a
passenger car’s taillight.
Decision sight distance is determined using the same heights above but is based on the
driver’s ability to (simply put) see something unexpected and be able to safely maneuver
around it without stopping. Decision sight distances are substantially longer than stopping
site distances to allow the driver time to make the complete sight, decision, maneuver
process.
Passing sight distance is determined based on the driver’s ability to safely pass a slower
car on a two-lane road without hindering an approaching car coming from the opposite
direction and is determined based on the 3.5 ft height of the driver’s eye and 3.5 ft height
of an object being passed.
Generally in highway design, the stopping sight distance is used for both summit and sag
vertical curves since the passing sight distance K values are significantly higher whereas
on two-lane roadways the passing sight distance is used. Table 4 on the next page is a
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compilation of tables from the AASHTO 2004 manual listing the K values for summit
and sag vertical curves.
Design Speed (mph)
Passing Sight Distance Design K (Summit)
Stopping Sight Distance Design K (Summit)
Stopping Sight Distance Design K
(Sag) 15 - 3 10 20 180 7 17 25 289 12 26 30 424 19 37 35 585 29 49 40 772 44 64 45 943 61 79 50 1203 84 96 55 1407 114 115 60 1628 151 136 65 1865 193 157 70 2197 247 181 75 2377 312 206 80 2565 384 231
Table 4 – Design Controls for Vertical Curves
It can be seen that the vertical curve lengths for passing sight distance are extremely
longer than for stopping sight distance on summit curves based on the K value. Using the
stopping sight distance will result in longer summit curves above 55 mph and longer sag
curves for design speeds of 55 mph and less. The minimum length of both summit and
sag vertical curves is set at three times the design speed of the roadway
Typical Roadway Sections
The basic component for railroads and transit systems is the track, which is comprised of
two rails at a set distance apart placed on ties of either wood or concrete construction.
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There are various types of fastening systems that connect the rail to the tie, some of
which are tie plates and spikes or clips on wood ties and fastener assemblies with a
spring-type clip and pad for concrete ties. There are also other types of construction such
as embedded track and direct-fixation track.
The distance between the rails is referred to as the gage of the track and is normally set at
a distance of 4’-8 ½” measured between the inside of the rails taken 5/8” below the top of
rail. The rail sets atop a plate which is connected to the rail by clips or spikes on timber
ties or clips and embedded inserts in concrete ties. The ties set on a bed of ballast that
varies depending on the load and other design conditions. The ballast depth can vary
from six or nine inches to two feet, depending on the railroad’s or transit system’s
standards. Below the ballast section is the subballast which is similar to ballast but of a
different (smaller) gradation and whose depth is also usually set by the railroad’s or
transit system’s standards. This track structure sets on the top of a subgrade that is
normally crowned at the center of a single track section or at the centerline of a multi-
track section with the cross-slope set to provide positive drainage into ditches set to the
outside of the track section . The cross-slope is normally set using the railroad’s or transit
system’s typical section and is normally between 1% and 2.5%. On the following page,
Figures 3 and 4 are typical sections for single and double track systems illustrating timber
and concrete tie construction.
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Figure 3 – Single Track (Timber Tie Construction)
Figure 4 – Double Track (Concrete Tie Construction)
The distance between centerlines of multiple track, or track centers, can be as little as 13
feet on some of the older railroad lines found on many systems. Over the years it has
become standard practice to use 14 or 15 foot track centers as railroads have opted to go
with wider distances. In some cases the track centers can be wider and are usually based
on the railroad’s standard track section and type of track being designed. In yard
locations, track centers may be as much as 20 to 30 feet to allow for maintenance or
inspection vehicles to pass. Where LRT lines share a common right-of-way with a
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railroad, it is common to provide a 25-foot track center between the transit and railroad
alignments. This is often at the request of the railroad and is usually due to legal issues if
it becomes necessary to have passengers exit the vehicles due to an emergency. When 25-
foot track centers are prohibited by right-of-way or other restrictions, it is common to
construct a wall to separate the two alignments.
When designing multiple track systems it is always wise and prudent to obtain the
railroad’s standard sections and if not available, ask the engineering department what
track centers to use.
As mentioned above, when developing the typical section of the track, the designer will
normally use existing standards provided by the railroad. However, there are elements
that will need to be confirmed prior to the design, such as the rail section and type of
fastening system used, along with whether the ties will be timber or concrete construction
and what depths of ballast and subballast are required. These items are critical in that they
will set the distance between the top of rail and top of subgrade. Most railroads will build
the track from the top of subgrade with the remaining earthwork and grading work done
by a contractor.
It is also important to know what rail section is to be used (and how it is defined).
Normally rail is designated by a number such as 115 or 140, which signifies the
approximate weight in pounds per yard of length. On the next page, Figure 5 illustrates
two common rail sections found on railroads today.
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Figure 5 – 115RE and 140RE Rail Sections
As can be seen in Figure 5 above, the heavier rail section has increased height, web and
base dimensions. Heavier rail sections are normally found on freight railroads with higher
tonnage, whereas the lighter rail sections are found on transit systems and low tonnage
freight railroads that may also carry passenger service. Other typical rail sections are
119RE, 132RE, 133RE, 136RE, and 141AB. There are a number of older rail sections
that can be found on systems, such as 90 and 100 and possibly even lighter rail sections.
However, they are no longer rolled since they are now more or less non-standard and
would be extremely expensive to procure. There are also a number of European rail
sections that are available for LRT and can be found on some systems in North America.
For estimating purposes one must always remember that there are two rails that need to
be accounted for when measuring the length of track; i.e., there are two linear feet of rail
per foot of track (track-foot or TF). Also, when estimating the rail, in many cases the rail
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is purchased by the ton, so the amount of rail required must be calculated based on the
type and size of rail to be procured and used.
The last item to discuss regarding typical sections for railroads is the requirement for
ditches. They are normally designed as per the individual railroads standards and are
normally three feet deep, measured from the top of subgrade. They can be either ‘V’ or
trapezoidal with most railroads preferring trapezoidal with anywhere from 2-foot to 10-
foot bottoms. Again, the shape and depth of ditch should be set in accordance with the
individual railroad’s standard practice. If the typical section provided by the railroad does
not cover ditches, it is always wise to contact the railroad’s engineering department.
Typical sections for LRT are very similar to those used on railroads. However, transit
systems often have typical sections that cover additional conditions other than at-grade
ballasted situations.
Many existing systems have elevated structures that may be open-deck with the rails set
directly on the ties that are an integral part of the structure. There is no ballast and the
structure is very similar to trestles in appearance. Other systems may have either a
ballasted deck or what is known as direct-fixation track, which has special designed
plates called fasteners that are mounted directly to the surface of the deck, or in some
systems, on concrete plinths that are normally constructed as a second pour of concrete
placed on the track surface. On the next page, Figures 6 illustrates a typical section for
‘Direct Fixation’ track.
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Figure 6 – Direct Fixation Typical Section
Other types of track include subways that can be either ballasted construction in older
systems or direct-fixation in tunnels or in cut and cover construction in newer systems.
On some systems, both old and new, embedded track construction as in Figure 7 can be
found.
Figure 7 – Embedded Track Typical Section
In this type of construction, the track is embedded in concrete in streets that may be
shared by other types of traffic or has dedicated lanes specifically for the transit system’s
vehicles.
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In highway design, roads are normally designed as either non-divided or divided. The
standard lane width in most cases is 12-feet with exceptions for ramps and some county
road designs. In all cases shoulders are required with widths based on type and class of
roadway to be designed. On most two lane bi-directional roads, 8-foot shoulders are
common while on multi-lane divided highways, 10 to 12 foot shoulders are required on
the outside edges of pavement and between 6 to 12 foot shoulders on the inside edge of
pavement. The inside shoulder width is normally set based on the number of lanes and
the type of roadway being designed.
Roadway typical sections are always dictated by State and/or Local DOT standards and
all must meet AASHTO requirements. In cases where the standard typical sections can
not be used due to restrictions or local conditions, waivers are required and must be
approved by the governing agency.
Pavement thicknesses and type of pavement materials are normally determined by the
agency that is responsible for the roadway, but there are times when the engineer will be
required to determine these values. In those cases a traffic study is normally undertaken
with levels of service determined based upon traffic counts or projections of both car and
trucks. Once the study is completed, pavement thicknesses can be determined.
Ditches are designed based on drainage studies and must meet the governing agency’s
design standards and criteria. In urban areas, it is common to provide a curb and gutter
section to allow drainage to be diverted to underground systems. In many cases it has
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become common practice to provide underdrain systems to divert water from the
roadway subgrade which will periodically outlet into ditches or tie directly into an
existing underground drainage system.
Figures 8 and 9 are examples of typical 2-lane undivided and 4-lane divided roadways,
respectively.
Figure 8 – 2-Lane Roadway Typical Section
Figure 9 – 4-Lane Divided Roadway Typical Section
Note that underdrains have been shown in both figures and that in Figure 9, curb and
gutter is shown on the outside of the right lanes. Median widths as shown in the second
figure are normally set by requirements stated in State DOT criteria and standards and
can vary in width depending on locale and whether the median is paved or depressed (as
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shown in Figure 9). In cases where paved medians are designed, it is common to have a
barrier wall installed along the roadway centerline for high-speed designs or where
median widths warrant them.
On all types of roadway systems, alignments are usually designed for two-way traffic
with a few exceptions such as ramps in interchanges.
Normally, railroad mainline track consists of one or two tracks depending on operational
requirements, where frequency and length of trains is a major factor. On mainlines that
have low frequency operation; one track is the common choice due to construction and
maintenance costs. Where the frequency of trains is higher, railroads will use a two track
system where each track is usually dedicated to one direction of movement. However, in
emergency situations or when one track is taken out of service for maintenance, trains
can be transferred to the other track when necessary.
In transit systems, it is common to have a two track system where each track can be either
bi-directional or dedicated to only one direction. However, on most transit systems the
system is designed to accommodate trains in either direction on either track in emergency
situations or when one track is being maintained. Due to impacts to service, it is rare that
single track service is provided on a two track system except in an emergency with all
maintenance normally being performed during off-peak hours or at night.
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As mentioned earlier, roadways are normally designed in multi-lane configurations, as
either undivided or divided, based on traffic requirements as determined by the engineer
and dictated by the governing agency’s standards and criteria.
Clearances
Another design feature that must be accounted for in railroad, LRT, and highway design
is clearance and their impacts to the design.
In railroad design, both lateral and vertical clearances are critical and are normally set at
9 feet and 23 feet, respectively. Figure 10 illustrates a ‘Clearance Outline’ for tangent
track which shows the minimum values with measurements taken from the centerline of
track and top of rail.
Figure 10 – Clearance Outline
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It should be noted that each state has a specific set of requirements that apply which will
vary between states. AREMA provides diagrams that show the ‘General Outline’ for
clearances and also tables that define each state’s requirements that should be reviewed
prior to proceeding with any design. Often times the railroad’s and state’s requirements
differ, in which case the strictest set should be used.
As can be seen in the diagram in Figure 10, there are locations where the clearances vary
with respect to the track centerline and top of rail. For example, the 5’-1” dimension
offset from the centerline and with 8” and 4’-0” dimensions above the top of rail are used
to set low level and high level platform heights, respectively, for passenger train service.
These values will usually vary for transit design and are normally found in the governing
authority’s criteria with the dimensions determined based on the vehicle’s outline, also
known as the vehicle’s ‘clearance envelope’.
Additional diagrams can be found in AREMA that define the dimensions for railway
bridges, single-track and double-track railway tunnels, and railway side tracks and
industry tracks. There are also requirements for overhead electrification for trains where
overhead catenary systems are in use.
When determining lateral clearances within horizontal curves, it is required that the
dimensions above be increased on both sides of the centerline by 1 ½ inches per degree
of curvature as noted in the AREMA design manual. This requirement is due to the
overhangs of the cars which are present while negotiating curves. Since the trucks are set
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in from the ends of the cars, there will be both an end overhang and middle ordinate
overhang at the center of the car. Often times the offset distance will have to be
calculated based on the length of car. AREMA provides tables that list offset distances
per degree of curvature and chord distance that the engineer can use in determining the
lateral clearances required.
In transit design, there are usually diagrams, tables and charts provided by the authority
that illustrates the vehicle ‘Clearance Envelope’, which is another name for the railroad’s
“Clearance Outline’. In some authority criteria, clearance envelopes are developed for
both ‘static’ and ‘dynamic’ cases where the static envelope is for a vehicle at rest and the
dynamic envelope is for the vehicle in motion. The values will vary from authority to
authority and from vehicle to vehicle where more than one type of vehicle may be used.
In systems where there is more than one type of vehicle, the authority will normally have
a combined or composite clearance envelope for all types of vehicles found on the system
to assure that proper clearances will be met in the design of the alignment and allow for
all vehicle types to meet clearance requirements.
On the next page in Figure 11, a typical ‘dynamic’ clearance envelope is illustrated for an
LRT vehicle, showing critical clearance points that must be checked during design. As
noted, dimensions are in inches and measured left or right of the centerline and from the
top of rail.
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Figure 11 – Maximum Vehicle Dynamic Envelope
As can be seen, the critical points in this diagram are labeled P1 through P14 and are
symmetrical about the centerline of the vehicle – this is due to the vehicle’s ability to run
in either direction. For P5, the dimensions (71.1, 123.3) represent an offset distance from
the centerline of 71.1-inches to the right and a vertical distance of 123.3-inches above the
top of rail. P10 would be the same point on the left side of the vehicle where the
dimensions (-71.1, 123.3) represent an offset distance of 71.1-inches to the left of the
centerline with the same vertical distance of 123.3 inches above the top of rail (as in
nearly all types of civil design, negative is to the left and positive is to the right.)
To determine whether an off-track object clears the vehicle’s clearance envelope one only
needs to use the ‘X’ and ‘Y’ values of that point and determine whether the object falls
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outside the vehicle’s clearance envelop. This can be done either graphically or by
calculation if the point is critical and close to the centerline or top of rail.
Determining the ‘dynamic’ envelope requires the vehicle specifications, some of which
are the manufacturer’s criteria for pitch, roll and yaw, along with values for failed/broken
suspension and the authority’s acceptable amounts of vertical and lateral wheel wear.
Other factors will include the acceptable variances in the track structure, such as lateral
and vertical rail wear, cross level and the construction tolerances of the track system. In
some states, it may be required to factor in seismic allowances into the final values.
All these values are tabulated and placed in a table for designated critical points and
normally have an illustration (as in Figure 11) of the vehicle’s shape to determine the
clearance envelope which in turn is used to determine the clearance to wayside clear
points. Additional tables may be provided for superelevation through curves along with
any cross level variations (construction tolerance or superelevation).
In most cases, these tables will be provided by the authority, although there is always the
possibility that the tables will have to be developed by the engineer. I speak from
experience and can claim that my understanding is based on the later situation where I
was responsible for developing tables to compare with the manufacturer’s tables for a
project years ago…
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In Figure 12 below, a Chicago Transit Authority ‘Clearance Car’ is shown on the ‘Blue
Line’ near River Road in January of 1983. Vehicles of this type are used by various
authorities to check car clearances with wayside objects along the alignment.
Figure 12 – CTA ‘Clearance Car’ circa 1983
Highway design also has clearance requirements for both horizontal and vertical. The
vertical is based on the type of roadway classification and can range from a minimum of
14.5 ft to a desirable of 16.5 ft. These values allow for future resurfacing, snow or ice
accumulation in northern states and for an occasional slightly overheight load. AASHTO
states that for routes with traffic restricted to passenger vehicles that the desirable vertical
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clearance should be 15 ft with an absolute minimum of 12.5 ft. It should be noted that
state laws vary and should be checked prior to any highway design.
The term ‘clear zone’ is used in highway design to designate the area beyond the edge of
roadway for determining lateral clearance. This area is unobstructed and relatively flat
and allows errant vehicles to recover from maneuvers that take them beyond the edge of
pavement. Clear-zone widths are determined based on design speed, traffic volume and
embankment slope and are set by AASHTO criteria. Information concerning the
determination of clear zones can be found in AASHTO ‘Roadside Design Guide’ and
should be consulted prior to finalizing any alignment.
Lateral clearances for structures will vary depending on the design criteria and for the
particular classification and traffic volume. Normally the minimum clearance to walls on
the left side of divided highways is governed by the median width and number of lanes,
whereas on the right side the clearance is set by the normal shoulder width with the
measurement taken to the base of a barrier which is usually constructed integrally with
the wall. In all cases, suitable protective devices should be used at the ends of all piers,
abutments and columns.
Where obstacles are present along the alignment it is sometimes necessary to include
guardrail or some type of barrier system. A considerable amount of research has gone
into this subject and publications from AASHTO are available for use in the
determination whether such systems are required.
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Variances from the Norm
There are always designs, both old and new, that do not meet current criteria for
railroads. Two examples that come to mind are alignments from the late 1800’s and early
1900’s, the Southern Pacific’s (now Union Pacific) ‘Tehachapi Loop’ in south central
California and the Camas Prairie Railroad (now Great Northwest Railroad) in
southeastern Washington and the panhandle of Idaho.
The ‘Tehachapi Loop’ has been considered by some as the greatest engineering feat of its
day. The loop is 3,799-ft long, has a maximum grade of 2.2% and typical radius of 1,210-
ft (D = 4.73o). The alignment crosses itself which results in 100-car plus trains looping
over themselves.
Figure 13 is an aerial view which shows the complexity of the design that includes long
sweeping curves, minimum tangents and reversing movements over very short distances.
Figure 13 – ‘Tehachapi Loop’ Aerial Photograph
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As can be seen in the photo, there are a multitude of minimum and maximum values that
were exceeded in the design of this alignment. However, the solution was unique and
solved the problem by meeting the current day requirements.
The second example mentioned is the (then) Camas Prairie Railroad’s 2nd Subdivision
that had a 3% compensated grade with degrees of curvature ranging from 0o18’ to 15o
over a portion of its alignment.
On the next page, Figure 14 shows portions of what are known as track charts which
illustrate general information of the alignment. The uppermost section calls out the
structures along the alignment along with their location and description. The next portion
shows the track profile and road crossings, followed by a schematic of the horizontal
alignment with left and right hand curves designated by the direction of the curves
shown. The central angles of the curves and degrees of curvature are also called out. The
lower portion shows the rail section used along the alignment and the date(s) it was laid.
Note the (compensated) 3% grades between MP 11.8 and MP 24.99 along with the
double-digit degrees of curvature.
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Figure 14 – Camas Prairie Railroad (Great Northwest Railroad)
2nd Subdivision Track Chart
Figures 15 and 16 on the next page are photos taken of Bridges #22 and #22.1 at
approximately MP 22 and MP 22.1 that are on the 3% compensated grade and within 14o
and 15o curves, respectively. The structures are old timber trestles where the alignment
negotiates its way along rather mountainous terrain.
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Figure 15 – Bridge #22 at MP 22 Camas Prairie Railroad 2nd Subdivision
Figure 16 – Bridge #22.1 at MP 22.1 Camas Prairie Railroad 2nd Subdivision
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At the time the previous photographs were taken the railroad was still the Camas Prairie
Railroad and had joint trackage rights with both the BNSF and UP railroads. Only 4-axle
locomotives were allowed on this subdivision by the Supervisor of Maintenance due to
its severe curvature and steep grades. The railroad consisted of four subdivisions and had
123 bridges (totaling almost 27,000 feet) in approximately 262 miles of track and was
known as the ‘Railroad on Stilts’.
I’m sure there are other locations where railroads have constructed alignments or
currently use existing ones designed in years past where current criteria is waived when
necessary. These examples also prove that when required, railroads will allow the
designer to exceed certain criteria limitations if and when the situation warrants the
request.
In transit design, most variances will require the approval of the authority and will only
be approved if no other options are available and the variances still meet the absolute
minimums stated in the criteria. Since all criteria are generally based on the capabilities
of the vehicles, the variances must meet those requirements.
It is not uncommon in highway designs to request waivers from State and Federal
agencies, provided the request is reasonable and no other options are available. The types
of waivers normally occur on reconstruction projects where right-of-way constraints
prohibit meeting current criteria or on new construction where property acquisitions are a
sensitive issue.
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Conclusions
As can be seen throughout this paper, there are a number of similarities but also a number
of differences between rail, transit and roadway design. In all cases it is up to the
engineer to become acquainted with all criteria and standards with whichever design they
are to perform – and to remember that any questions that arise should be documented and
passed on to the railroad, authority or agency for discussion and direction. The
client/designer relationship should always be open and two-way to assure that the design
meets the requirements and expectations of the client and conforms to the railroad’s,
authority’s or governing State and Federal agencies’ policies.
The author would like to extend a special thank you to the following for their assistance during the writing of this document; Art Peterson for his time spent on reviews and comments along with the photos found in the document, Noreen Zuniga and Todd Channer for the creation of the cover. Many thanks to you all.