AREMA Annual Conference and Exposition 2007

PROPOSED TECHNICAL PAPER ABSTRACT

Submitted: December 20, 2006 via fax

Principal Contact: Greg Toth, (312) 803-6511, toth@pbworld.com

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

Greg Toth i

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…………………………………………………

Greg Toth

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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...

Greg Toth

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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.