Track Design Handbook for Light Rail Transit, Second Edition (2012)

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3-i Chapter 3—Light Rail Transit Track Geometry Table of Contents 3.1 INTRODUCTION 3-1 3.1.1 Design Criteria—General Discussion 3-1 3.1.2 Design Criteria Development 3-1 3.1.3 Minimum and Maximum Criteria Limits 3-2 3.2 LRT TRACK HORIZONTAL ALIGNMENT 3-3 3.2.1 Minimum Tangent Length between Curves 3-4 3.2.2 Speed Criteria—Vehicle and Passenger 3-8 3.2.2.1 Design Speed—General 3-8 3.2.2.2 Design Speed in Curves 3-9 3.2.3 Circular Curves 3-10 3.2.3.1 Curve Radius and Degree of Curve 3-10 3.2.3.2 Minimum Curve Radii 3-11 3.2.3.3 Minimum Curve Length 3-13 3.2.4 Curvature, Speed, and Superelevation—Theory and Basis of Criteria 3-14 3.2.4.1 Superelevation Theory 3-14 3.2.4.2 Actual Superelevation 3-17 3.2.4.3 Superelevation Unbalance 3-17 3.2.4.4 Vehicle Roll 3-18 3.2.4.5 Ratio of Ea to Eu 3-20 3.2.5 Spiral Transition Curves 3-23 3.2.5.1 Spiral Application Criteria 3-23 3.2.5.2 Spirals and Superelevation 3-23 3.2.5.3 Types of Spirals 3-24 3.2.5.4 Spiral Transition Curve Lengths 3-24 3.2.5.4.1 Length Based upon Superelevation Unbalance 3-25 3.2.5.4.2 Length Based upon Actual Superelevation 3-27 3.2.5.4.3 Length Based upon Both Actual Superelevation and Speed 3-30 3.2.6 Determination of Curve Design Speed 3-32 3.2.6.1 Categories of Speeds in Curves 3-32 3.2.6.2 Determination of Eu for Safe and Overturning Speeds 3-32 3.2.6.2.1 Overturning Speed 3-33 3.2.6.2.2 Safe Speed 3-34 3.2.7 Reverse Circular Curves 3-35 3.2.8 Compound Circular Curves 3-36 3.2.9 Track Twist in Embedded Track 3-36 3.3 LRT TRACK VERTICAL ALIGNMENT 3-37 3.3.1 Vertical Tangents 3-37 3.3.2 Vertical Grades 3-39 3.3.2.1 Main Tracks 3-39 3.3.2.2 Pocket Tracks 3-40 3.3.2.3 Main Tracks at Stations and Stops 3-40

Track Design Handbook for Light Rail Transit, Second Edition 3-ii 3.3.2.4 Yard and Secondary Tracks 3-40  3.3.3 Vertical Curves 3-41  3.3.3.1 Vertical Curve Lengths 3-41  3.3.3.2 Vertical Curve Radius 3-42  3.3.3.3 Vertical Curves in the Overhead Contact System 3-43  3.3.4 Vertical Curves—Special Conditions 3-43  3.3.4.1 Reverse Vertical Curves 3-43  3.3.4.2 Combined Vertical and Horizontal Curvature 3-43  3.4 TRACK ALIGNMENT AT SPECIAL TRACKWORK 3-43  3.5 STATION PLATFORM ALIGNMENT CONSIDERATIONS 3-43  3.5.1 Horizontal Alignment of Station Platforms 3-44  3.5.2 Vertical Alignment of Station Platforms 3-45  3.6 YARD LAYOUT CONSIDERATIONS 3-46  3.7 JOINT LRT-RAILROAD/FREIGHT TRACKS 3-48  3.7.1 Joint Freight/LRT Horizontal Alignment 3-48  3.7.2 Joint Freight/LRT Tangent Alignment 3-49  3.7.3 Joint Freight/LRT Curved Alignment 3-49  3.7.4 Selection of Special Trackwork for Joint Freight/LRT Tracks 3-49  3.7.5 Superelevation for Joint Freight/LRT Tracks 3-50  3.7.6 Spiral Transitions for Joint Freight/LRT Tracks 3-50  3.7.7 Vertical Alignment of Joint Freight/LRT Tracks 3-51  3.7.7.1 General 3-51  3.7.7.2 Vertical Tangents 3-51  3.7.7.3 Vertical Grades 3-51  3.7.7.4 Vertical Curves 3-52  3.8 VEHICLE CLEARANCES AND TRACK CENTERS 3-52  3.8.1 Track Clearance Envelope 3-52  3.8.1.1 Vehicle Dynamic Envelope 3-53  3.8.1.2 Track Construction and Maintenance Tolerances 3-53  3.8.1.3 Curvature and Superelevation Effects 3-54  3.8.1.3.1 Curvature Effects 3-54  3.8.1.3.2 Superelevation Effects 3-56  3.8.1.4 Vehicle Running Clearance 3-56  3.8.2 Structure Gauge 3-59  3.8.3 Station Platforms 3-59  3.8.4 Vertical Clearances 3-59  3.8.5 Track Spacings 3-61  3.8.5.1 Track Centers and Fouling Points 3-61  3.8.5.2 Track Centers at Pocket Tracks 3-62  3.8.5.3 Track Centers at Special Trackwork 3-62  3.9 SHARED CORRIDORS 3-63  3.10 REFERENCES 3-64 

Light Rail Transit Track Geometry iii-3 List of Figures Figure 3.2.1 Horizontal curve and spiral nomenclature 21-3 Figure 3.2.2 LRT vehicle on superelevated track 51-3 Figure 3.2.3 Example of ratio of Eu to Ea 12-3 Figure 3.2.4 Force diagram of LRT vehicle on superelevated track 3-33 Figure 3.2.5 Superelevation transitions for reverse curves 53-3 Figure 3.3.1 Vertical curve nomenclature 83-3 Figure 3.8.1 Horizontal curve effects on vehicle lateral clearance 55-3 Figure 3.8.2 Dynamic vehicle outline superelevation effect on vertical clearances 3-57 Figure 3.8.3 Typical tabulation of dynamic vehicle outswing for given values of curve radius and superelevation 85-3 Figure 3.8.4 Additional clearance for chorded construction 06-3 List of Tables 5-3 srotcaf gnitimil ngised tnemngilA 1.2.3 elbaT 93-3 stneidarg kcart niam muminim dna mumixaM 1.3.3 elbaT 14-3 stneidarg kcart dray muminim dna mumixaM 2.3.3 elbaT

3-1 CHAPTER 3—LIGHT RAIL TRANSIT TRACK GEOMETRY 3.1 INTRODUCTION The most efficient track for operating any railway is straight and flat. Unfortunately, most railway routes are neither straight nor flat. Tangent sections of track need to be connected in a way that steers the train safely and ensures that the passengers are comfortable and the cars and track perform well together. This dual goal is the subject of this chapter. 3.1.1 Design Criteria—General Discussion The primary goals of geometric criteria for light rail transit are to provide cost-effective, efficient, and comfortable transportation while maintaining adequate factors of safety with respect to overall operations, maintenance, and vehicle stability. In general, design criteria guidelines are developed using accepted engineering practices and the experience of comparable operating rail transit systems. Light rail transit (LRT) geometry standards and criteria differ from freight or commuter railway standards, such as those described in applicable sections of the American Railway Engineering and Maintenance-of-Way Association’s (AREMA’s) Manual for Railway Engineering (MRE), Chapter 5, in several important aspects. Although the major principles of LRT geometry design are similar or identical to that of freight/commuter railways, the LRT must be able to safely travel through restrictive alignments typical of urban central business districts, including rights-of-way shared with automotive traffic. Light rail vehicles are also typically designed to travel at relatively high operating speeds in suburban and rural settings. AREMA Committee 12 is in the process of adding such information to MRE Chapter 12. However, as of 2011, that process is incomplete. The LRT alignment corridor is often predetermined by various physical or economic considerations inherent to design within urban areas. One of the most common right-of-way corridors for new LRT construction is an existing or abandoned freight railway line.[1] However, while the desirable operating speed of the LRT line is usually 40 to 55 mph [65 to 90 km/h] or higher, many old rail corridors in densely developed urban areas were originally configured for much slower speeds, often 30 mph [45 km/h] or less. 3.1.2 Design Criteria Development General guidelines for the development of horizontal alignment criteria should be determined before formulating any specific criteria. This includes knowledge of the vehicle configuration and a general idea of the maximum operating speeds. Design speed is usually defined in terms of what is desirable whenever possible—typically 55 mph [90 km/h]—tempered by a realistic evaluation of what is actually achievable within a given corridor. Physical constraints along various portions of the system, together with other design limitations, may preclude achievement of the desirable speed objective over a significant percentage of the length of the route. Sharp curves in areas of constrained right-of-way are an obvious example. Also, where the LRT operates within a municipal right-of-way, either in or adjacent to surface streets, the maximum operating speed for the track alignment might be limited to the legal speed of the parallel street

Track Design Handbook for Light Rail Transit, Second Edition 3-2 traffic even if the track itself is capable of higher speeds. The civil design speed should also be coordinated with the operating speeds used in any train performance simulation program speed- distance profiles as well as with the train control system design. Where the LRT system includes at-grade segments where light rail vehicles will operate in surface streets in mixed traffic with rubber-tired vehicles, the applicable geometric design criteria for such streets will need to be met in the design of the track alignment. Where the LRT system includes areas where light rail vehicles will operate in joint usage with railroad freight traffic, the applicable minimum geometric design criteria for each type of rail system needs to be considered. The more restrictive criteria will then govern the design of the track alignment and clearances. In addition to the recommendations presented in the following articles, it should be noted that combinations of minimum horizontal radius, maximum grade, and maximum unbalanced superelevation are to be avoided in the geometric design. The geometric guidelines discussed in this chapter consider both the limitations of horizontal, vertical, and transitional track geometry for cost-effective designs and the ride comfort requirements for the LRT passenger. 3.1.3 Minimum and Maximum Criteria Limits In determining track alignment, several levels of criteria may be considered.[4] Note that an individual criteria limit could be either a minimum or a maximum. In the case of a curve radius, a minimum value would be the controlling limit. In the case of track gradient, there may both a maximum and a minimum—the maximum being controlled by the vehicle’s capabilities and the minimum defining the minimum slope necessary to achieve storm water drainage. However, three conditions should be considered: the desirable condition, the acceptable condition, and the absolute condition, each as defined below. • Desired Minimum or Maximum—This criterion is based on an evaluation of maximum passenger comfort, initial construction cost, and maintenance considerations on ballasted, embedded, and direct fixation track. It is used where no physical restrictions or significant construction cost differences are encountered. An optional “preferred” limit may also be indicated to define the most conservative possible future case; i.e., maximum future operating speed for given conditions within the alignment corridor. • Acceptable Minimum or Maximum—This threshold defines a level that, while less than ideal, is considered to be “good enough” to meet the operating objectives without either compromising ride quality or taxing the mechanical limits of the vehicle. The use of acceptable criteria limits typically does not require the designer to produce detailed explanations of why it wasn’t possible to do better. Determination of the limits for acceptable criteria is usually project-specific and driven by an interest in maintaining a specific level of service to the maximum degree possible at reasonable cost. As such, the limits of acceptable criteria may be established by qualitative methods rather than a rigorous quantitative analysis.

Light Rail Transit Track Geometry 3-3 • Absolute Minimum or Maximum—Where physical restrictions prevent the use of both the desired and acceptable criteria, an absolute criterion is often specified. This criterion is determined primarily by the vehicle design, with passenger comfort a secondary consideration. The use of an absolute minimum or maximum criterion should be a last resort. The need for doing so should be thoroughly documented in the project’s basis-of- design report and accepted by the project owner. In addition to the above, lower thresholds of criteria are often stipulated for conditions where ordinary operating speeds are much lower than the desired figures noted above and/or site constraints are extraordinary. These include • Main Line Embedded Track—Where the LRT is operated on embedded track in city streets, with or without shared automotive traffic, there generally are multiple physical site restrictions. Overcoming these requires a special set of geometric criteria that accommodates existing roadway profiles, street intersections, and narrow horizontal alignment corridors that are typical of urban construction and also recognizes the municipal or state design criteria for the roadway surface. • Yard and Non-Revenue Track—These criteria are generally less stringent than main line track, due to the low speeds and low traffic volumes of most non-revenue tracks. The minimum criteria are determined primarily by the vehicle design, with little or no consideration of passenger comfort. Some yard and non-revenue track criteria may not be valid for frequently used tracks such as when the yard’s main entrance leads to and from the revenue service line. For all types of track, the criteria should consider that work train equipment will occasionally use the tracks. The use of absolute minimum and absolute maximum geometric criteria, particularly for horizontal alignment, has several potential impacts in terms of increased annual maintenance, noise, and vehicle wheel wear, and shorter track component life. The use of any “absolute” criterion should therefore be done only with extreme caution. One or two isolated locations of high track maintenance may be tolerated and included in a programmed maintenance schedule, but extensive use of absolute minimum design criteria can result in revenue service degradation and unacceptable maintenance costs, in both the near term and far term. Designers should therefore attempt to either meet or do better than the “desired” criteria limits whenever it is feasible to do so. 3.2 LRT TRACK HORIZONTAL ALIGNMENT The horizontal alignment of track consists of a series of tangents joined to circular curves, preferably with spiral transition curves. Track superelevation in curves is used to maximize vehicle operating speeds wherever practicable. An LRT alignment is often constrained by both physical restrictions and minimum operating performance requirements. This generally results in the effects on the LRT horizontal alignment and track superelevation designs discussed below. All other things being equal, larger radii are always preferable to tighter turns. In addition to wear and noise, small radius curves limit choices on the vehicle fleet both now and in the future. The

Track Design Handbook for Light Rail Transit, Second Edition 3-4 minimum main line horizontal curve radius on most new LRT systems is usually 82 feet [25 meters], a value that is negotiable by virtually every available vehicle. Some modern LRVs and streetcars can negotiate curves as tight as 59 feet [18 meters], and a few can negotiate much smaller radii. Vintage streetcars, including both heritage equipment and modern replicas, can usually negotiate curves as tight as 35 feet [10.7 meters]. Superelevation unbalance (also variously known as “underbalance,” “cant deficiency,” or simply “unbalance”) can range from 3 to 9 inches [75 to 225 mm] depending on vehicle design and passenger comfort tolerance.[3] Vehicle designs that can handle higher superelevation unbalance can operate at higher speeds through a given curve radius and actual superelevation combination. LRT design criteria for maximum superelevation unbalance vary appreciably from as low as 3 inches [75 mm] on some projects to as high as 4 ½ inches [115 mm] on others. The latter value is consistent with a lateral acceleration of 0.1 g, a common, albeit conservative, metric also cited in most design criteria manuals. See Article 3.2.4 for additional discussion on this topic. LRT spiral transition lengths and superelevation runoff rates are generally shorter than corresponding freight/commuter railway criteria. The recommended horizontal alignment criteria herein are based on the LRT vehicle design and performance characteristics described in Chapter 2. The limiting factors associated with alignment design can be classified as shown in Table 3.2.1. 3.2.1 Minimum Tangent Length between Curves The discussion of minimum tangent track length is related to circular curves (see Article 3.2.3). The complete criteria for minimum tangent length will be developed here and referenced from other applicable sections. The development of this criterion usually considers the requirements of the AREMA Manual for Railway Engineering, Chapter 5, which specifies that the minimum length of tangent between curves is equal to the longest car that will traverse the system.[5] This usually translates into a desired minimum criterion of 100 feet [30 meters]. However, that limitation generally addresses operation of freight equipment at low speeds, such as in a classification yard. For passenger operation, ride comfort criteria must be considered. Considering the ability of passengers to adjust for changes of direction, the minimum length of tangent between curves is usually given as LT = 3V [LT = 0.57V] where LT = minimum tangent length in feet [meters] V = operating speed in mph [km/h] This formula is based on vehicle travel of at least 2 seconds on tangent track between two curves. This same criterion also applies to the lengths of circular curves, as indicated below. This criterion has been used for various transit designs in the United States since BART in the

Light Rail Transit Track Geometry 3-5 early 1960s.[6] The desired minimum length between curves is thus usually expressed as an approximate car length or in accordance with the formula above, whichever is larger. Table 3.2.1 Alignment design limiting factors Alignment Component Major Limiting Factors Minimum Length between Curves • Passenger comfort • Vehicle truck/wheel forces • Vehicle twist Circular Curves (Minimum Radius) • Trackwork maintenance • Vehicle truck/wheel forces • Noise and vibration issues Compound and Reverse Circular Curves • Passenger comfort • Vehicle frame forces Spiral Transition Curve Length • Passenger comfort • Vehicle twist limitations • Track alignment maintenance Superelevation • Passenger comfort • Vehicle stability Vertical Tangent between Vertical Curves • Passenger comfort Vertical Curve/Grade (Maximum Rate of Change) • Passenger comfort • Vehicle frame forces Special Trackwork • Passenger comfort • Trackwork maintenance • Noise and vibration issues • Vehicle twist (especially at “jump frogs”) Station Platforms • Vehicle clearances • ADAAG platform gap requirements Joint LRT/Freight RR Usage • Trackwork maintenance • Railroad alignment criteria • Compatibility of LRT and freight vehicle truck/wheels • Special trackwork components and geometry Main line absolute minimum tangent length depends on the vehicle and degree of passenger ride quality degradation that can be tolerated. One criterion is the maximum truck center distance plus axle spacing, i.e., the distance from the vehicle’s front axle to the rear axle of its second truck. In other criteria, the truck center distance alone is sometimes used. When spiral curves are used, the difference between these two criteria is not significant. An additional consideration for ballasted trackwork is the minimum tangent length for mechanized lining equipment, which is commonly based on multiples of 31-foot [10-meter] chords. Very short

Track Design Handbook for Light Rail Transit, Second Edition 3-6 curve lengths have been noted to cause significant alignment throw errors by automatic track lining machines during surfacing operations. The 31-foot [10-meter] length can thus be considered an absolute floor on the minimum tangent distance for ballasted main line track in lieu of other criteria. The preceding discussion is based on reverse curves. For curves in the same direction, it is preferable to have a compound curve, with or without a spiral transition curve, than to have a short length of tangent between the curves. The latter condition, known as a “broken back” curve, does not affect safety or operating speeds, but it does create substandard ride quality. As a guideline, curves in the same direction should preferably have no tangent between curves or, if that is not possible, the same minimum tangent distance as is applicable to reverse curves. In embedded trackwork on city streets and in other congested areas, it may not be feasible to provide minimum tangent distances between reverse curves. Unless the maximum vehicle coupler angle is exceeded, one practical solution to this problem is to waive the tangent track requirements between curves if operating speeds are below about 20 mph [30 km/h] and no track superelevation is used on either curve.[4] However, the designer must carefully consider unavoidable cross slope that is placed in the street pavement to facilitate drainage and whether light rail vehicle twist limitations might be exceeded. Pavement cross slope can have a direct effect on actual superelevation (Ea) and unbalanced superelevation (Eu) and must be considered when computing minimum spiral lengths. See Article 3.2.9 for additional discussion on this topic. For yards and in special trackwork, it is very often not practicable to achieve the desired minimum tangent lengths. AREMA Manual for Railway Engineering, Chapter 5, provides a series of minimum tangent distances based on long freight car configurations and worst-case coupler angles. It is also noted in the AREMA Manual for Railway Engineering that turnouts to parallel sidings can also create unavoidable short tangents between reverse curves. The use of the AREMA table would be conservative for an LRT vehicle, which has much shorter truck centers and axle spacings than a typical freight railroad car. As speeds in yards are restricted by operating rules and superelevation is generally not used, very minimal tangent lengths can be employed between curves. However, because yards typically lack a train control system that would monitor and limit speed, train velocities appreciably higher than those authorized can occur. For this reason alone, compromising on criteria is discouraged. Existing LRT criteria do not normally address minimum tangent lengths at yard tracks, but leave this issue to the discretion of the trackwork designer and/or the individual transit agency. To permit the use of work trains and similar rail-mounted equipment that are designed around standards for railroad rolling stock, it is prudent to utilize the AREMA minimum tangent distances between reverse curves in yard tracks. Extremely small radius reverse curves, such as those common for streetcar operations, have an additional consideration. Whenever one light rail vehicle is pushing or towing another, such as commonly occurs around a yard and shop, the angle that the couplers assume to the long axis of both cars must not exceed the vehicles’ design limits. A maximum angle of 30 degrees is acceptable, but less would be desired. An angle of 45 degrees to the vehicle should be considered an absolute maximum since, beyond that threshold, the force component tending to push or pull the dead car along the track will be less than the force component that acts to push or pull the vehicle

Light Rail Transit Track Geometry 3-7 laterally and hence off the track. One project included an alignment where, during pre-revenue service testing, it was discovered that the tow bar between the streetcar being pushed and the streetcar doing the pushing was at an angle of nearly 90 degrees, at which point all forward motion obviously ceased. The alignment needed to be reconstructed to achieve a smaller angle. Curves with no intervening tangent are discouraged but can be employed under strict circumstances as described in Article 3.2.7 of this chapter. Considering the various criteria discussed above for tangents between reverse curves, the following is a summary guideline criteria for light rail transit. Main Line Desired Minimum The greater of either LT = 200 feet [60 meters] or LT = 3V [LT = 0.57V] where LT = minimum tangent length in feet [meters] V = maximum operating speed in mph [km/h] Main Line Acceptable Minimum The greater of either LT = length of LRT vehicle over couplers in feet [meters] or LT = 3V [LT = 0.57V] where LT = minimum tangent length in feet [meters] V = maximum operating speed in mph [km/h] Note: So as to not limit future vehicle purchases, the vehicle length is often rounded up for purposes of the equation above. If the actual vehicle is about 90 feet [27 meters] long, the value used in the equation might be 100 feet [30 meters]. Main Line Absolute Minimum The greater of either LT = 31 feet [9.5 meters] or LT = (Vehicle Truck Center Distance) + (Axle Spacing) where the maximum speed is restricted as follows: VMAX = LT / 3 [VMAX = LT / 0.57] or LT = zero

Track Design Handbook for Light Rail Transit, Second Edition 3-8 where the curves meet at a point of reverse spirals, and the spiral lengths and actual superelevation Ea meet the following equation: LS1 x Ea2 = LS2 x Ea1 where LS1 = length of spiral on the first curve LS2 = length of spiral on the second curve and maximum vehicle twist criterion is not exceeded. Speed will be limited by the acceptable limits for Eu in the adjoining curves. See Article 3.2.7 for additional discussion of reverse spiraled curves. Yard and Non-Revenue Secondary Track The use of main line criteria is preferred in secondary track. When that’s not possible, the acceptable minimum tangent lengths would be the smaller of either LT = 31 feet [9.5 meters] or LT = zero feet [meters] for R > 950 feet [290 meters] LT = 10 feet [3.0 meters] for R > 820 feet [250 meters] LT = 20 feet [6.1 meters] for R > 720 feet [220 meters] LT = 25 feet [7.6 meters] for R > 640 feet [195 meters] LT = 30 feet [9.1 meters] for R > 573 feet [175 meters] where the specified radius is the smaller of the two curves. Note that the radii thresholds stipulated above are approximations; hence the conversions between U.S. customary and S.I. units are somewhat coarse. Common sense should be exercised in the application of these rules. Where nothing else will work, the absolute minimum will be LT = zero provided coupler angles are not exceeded, superelevation is zero, and unbalanced superelevation in both curves is 2 inches [50 mm] or less. 3.2.2 Speed Criteria—Vehicle and Passenger 3.2.2.1 Design Speed—General Desirable LRT operating speeds are in the range of 40 to 55 mph [65 to 90 km/h]. Some LRT projects have used speeds as high as 66 mph [106 km/h]. However, few LRT projects have sufficient tangent track, flat curves, and unrestricted right-of-way for higher speeds to result in meaningful travel time savings. Restricted operating speeds are always possible at discrete points along the alignment corridor, but, for a stadtbahn-type operation, proposed design speeds

Light Rail Transit Track Geometry 3-9 below 40 mph [60 km/h] generally create unacceptable constraints on the train control design and proposed operations. Streetcar/strassenbahn-type LRT operations are generally much slower. It is often presumed that maximum speed in embedded track needs to be restricted, and 35 mph [55km/h] is often cited as a maximum. This is not quite correct. It is not the embedded trackform that limits speed rather than the operating environment surrounding it. Speeds up to the vehicle’s maximum can be achieved on embedded track if the guideway is configured appropriately. The reason shared- lane, embedded track is likely to be operated more slowly than track in an exclusive lane is because of traffic conditions, adjacent parking lanes, pedestrian crosswalks, and other community-related issues. Some legacy streetcar lines that operated in shared lanes along wide- open streets and boulevards routinely operated at the vehicles’ balancing speed—sometimes as fast as 40 to 50 mph [65 to 80 km/h]. There is a requirement in the Manual of Uniform Traffic Control Devices (MUTCD) that requires LRT crossings to be equipped with flashing lights if trains are running faster than 35 mph [55 km/h]. Technically, that rule has no effect on what happens between intersections, although transit agencies may elect to limit speed in such areas merely to avoid cycles of acceleration and deceleration when passing through a multiple crossing zone. Furthermore, if the LRT is in a mixed traffic lane, flashing light signals and gates would be completely impractical at each intersecting street regardless of speed. As of 2010, TCRP Project A-32 is investigating the MUTCD requirement for railroad-style warning systems at LRT crossings. Users of this Handbook should consult the TCRP program and the current edition of the MUTCD for the latest information. See Chapter 10 for additional discussion on this topic. 3.2.2.2 Design Speed in Curves The speed criteria for curved track is determined by carefully estimating passenger comfort and preventing undue forces on the trackwork, vehicle trucks/wheels, and vehicle frames. Vehicle stability on curved track is also an important consideration in the determination of LRT speed criteria. Curved track that cannot be used at the same speed as the adjoining tangent track slows down the operation by increasing the overall running time between terminals. This wastes kinetic energy in the form of the momentum the vehicle had prior to slowing down and requires the consumption of additional energy to speed back up. It takes more than 0.62 mile [1 kilometer] for a rail vehicle to decelerate from 70 mph [110 km/h] to 55 mph [90 km/h], run through a 1000 foot [300-meter] long circular curve, and accelerate back up to 70 mph [110 km/h]. The same curve designed for a reduction down to 45 mph [70 km/h] reduces the speed over a length of about 0.75 mile [1.2 kilometers]. The actual increase in running time is relatively small, but cumulative run time losses at successive curves can significantly increase the overall travel time from terminal to terminal. Repetitive slowing down and speeding back up often annoys passengers (particularly standees) by subjecting them to a jerky ride. This unpleasant experience could have an effect on individuals’ subsequent personal decisions as to whether or not to ride transit. Such a ride also causes additional wear and tear on both the vehicle and the track.

Track Design Handbook for Light Rail Transit, Second Edition 3-10 Therefore, it is generally desirable to eliminate as many speed restrictions as possible and to maximize the design speed of all curves that must unavoidably be designed with speed restrictions. This can be achieved in three ways: • Using curve radii that are as broad as possible. This is the preferred method, but not always practical within the constraints of available right-of-way. • Maximizing the speed on the curves by introducing actual superelevation (Ea) in the track and maximizing the value of unbalanced superelevation (Eu) used. • Combinations of the above. See Article 3.2.6 for additional discussion on determination of appropriate speeds in curved track. 3.2.3 Circular Curves Intersections of horizontal alignment tangents are connected by circular curves. The curves may be simple curves or spiraled curves, depending on the curve location, curve radius, and required superelevation. In very nearly all cases, spiraled curves are preferable so as to improve ride quality and minimize impacts to rolling stock. 3.2.3.1 Curve Radius and Degree of Curve LRT alignment geometry differs from freight railroad design standards such as AREMA in that the arc definition is used to define circular curves. Also, curves for LRT designs are generally defined and specified by their radius rather than degree of curvature. This becomes an important distinction when designing in metric units, as degree of curve is defined entirely in traditional U.S. units and has no direct equivalent in metric units. Railroads have traditionally employed the chord definition of degree of curvature for calculating curves. The reasons for this practice date back to the surveying equipment and centerline stakeout methods that were employed during the mid-19th century. Railroads have persisted in requiring the chord definition for new railroad design despite radical advances in surveying methods. However, rail transit in general and light rail in particular use curve radii that are so sharp as to make degree of curvature impractical for ordinary use. For this reason, arc definition with lengths computed along the centerline of the curve is recommended for LRT design. Modern computer-aided design and drafting (CADD) alignment computation software can easily compute curvature in either arc or chord definition. Any curves that have been computed using the chord definition should be clearly labeled as such on the plan and profile drawings. In the case of any project to be designed using S.I. units of measurement but utilizing an existing right-of-way that is based on traditional U.S. units, particularly the degree of curvature, it is most efficient to determine the radius in traditional U.S. units, and then to convert to metric.

Light Rail Transit Track Geometry 3-11 As a guideline for LRT design, curves should be specified by their radius. Degree of curvature, when needed for calculation purposes, should be defined by the arc definition of curvature as determined by the following formula: Da = 5729.58 / R where Da is the degree of curve using the arc definition and R is the radius in feet. There is no equivalent formula using S.I. units since degree of curvature is not used in metric design. 3.2.3.2 Minimum Curve Radii Circular curves for LRT design are, as noted above, defined by curve radius and arc of curve length. The geometric properties of the circular curve are summarized in Figure 3.2.1. The straighter the route, other factors being equal, the less maintenance it will require. For this reason, the designer should seek alignments that minimize curves, especially very sharp curves. The minimum curve radius is determined by the physical characteristics of the vehicle. For most modern LRV designs, whether high- or low-floor, the most common absolute minimum radius is 82 feet [25 meters]. Some vehicles can negotiate curves with radii of 59 feet [18 meters]. A very few vehicles can negotiate even smaller curves. Light rail vehicles in Boston and San Francisco go around radii of 42 feet [12.8 meters], and legacy streetcars in hundreds of cities and towns throughout the United States routinely traversed curves with radii of 35 feet [10.7 meters]. However, while extremely tight curves are possible, they limit carbuilders’ options and hence the universe of candidate LRVs that could be used on a system. The use of curves tighter than 82 feet [25 meters] is therefore strongly discouraged. Refer to Chapter 2 for additional information on vehicle limitations. Refer to Chapter 12 for additional discussion on use of small radius curves in urban areas. On-track maintenance-of-way (M/W) equipment must also be considered in the selection of minimum horizontal curve criteria. Depending on the maintenance plan for the system, this could include a wide variety of hy-rail trucks, tampers, ballast regulators, ballast cars, catenary maintenance vehicles, and even small locomotives. It is highly desirable for the alignment to allow such equipment to operate from the maintenance depot to any point on the LRT system where they might be used. This affects track geometry, clearance, and trackwork issues. For example, a segment of sharply curved, embedded track located at a midpoint of the system may make it impossible for M/W equipment to access one end of the route from a yard and shop on the opposite end of the line. This could have a distinct impact on the equipment requirements for supporting the LRT maintenance-of-way plan. Curves that cannot be negotiated by the M/W fleet are therefore optimally confined to tracks where on-track access is not essential, such as terminal loops and yard turnaround tracks that can be serviced using off-track roadways.[12]

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Light Rail Transit Track Geometry 3-13 One frequently employed criterion for the desired minimum curve radius is the threshold limit for employing restraining rail, as determined from Chapter 4. In many cases, this is around 500 feet [150 meters]. Other possible thresholds for desirable minimum radius are either the limit selected for employing premium rail versus standard strength rail or the limit between the use of plain continuously welded rail (CWR) versus shop-curved rail. Sometimes a slight increase in radius will eliminate the need to utilize a more expensive trackform. Carrying that thought beyond trackwork costs, it should also be noted that sharply curved tunnels and aerial structures can have significantly higher construction costs than similar structures on tangent track or flat curves. In view of the design considerations indicated above, guideline criteria for modern LRV equipment are as follows for minimum curve radii. Main Line Track At-Grade Acceptable Minimum. Greater of • 500 feet [150 meters] or • Threshold radius for employment of more expensive trackforms. Tunnels and Aerial Structures Acceptable Minimum. Greater of • 500 feet [150 meters] or • Other value as suggested by the project’s structural designers. Ballasted At-Grade Track, Absolute Minimum. • 300 feet [90 meters] Embedded Track or Direct Fixation Track, Absolute Minimum. Lesser of • 82 feet [25 meters] or • Other value as permitted by the vehicle design. Yard and Non-Revenue Secondary Track Acceptable Minimum. Lesser of • 100 feet [30 meters] or • Other value as required by the vehicle design. Absolute Minimum. Lesser of • 82 feet [25 meters] or • Other value as required by the vehicle design. 3.2.3.3 Minimum Curve Length The minimum circular curve length is dictated by ride comfort and is, hence, unlike minimum tangent length, not related to vehicle physical characteristics. The acceptable minimum circular curve length is generally determined by the following formula: L = 3V [L = 0.57V] where L = minimum length of curve in feet [meters] V = design speed through the curve in mph [km/h]

Track Design Handbook for Light Rail Transit, Second Edition 3-14 For spiraled circular curves in areas of restricted geometry, the length of the circular curve added to the sum of one-half the length of both spirals is an acceptable method of determining compliance with the above criteria. The absolute minimum length of a superelevated circular curve should be approximately 10 to 15 feet [3 to 5 meters] longer than the truck center distance on the light rail vehicle so that the vehicle is not simultaneously twisting through two superelevation transitions. In such cases, a speed restriction should be imposed based on the formula above. Curves that include no actual circular curve segment (e.g., double-spiraled curves) should be permitted only in areas of extremely restricted geometry (such as embedded track in an urban area), provided no actual superelevation (Ea) is used. This type of alignment is potentially difficult to maintain for ballasted track. The design speed for a given horizontal curve should be based on its radius, length of spiral transition, and the actual and unbalanced superelevation through the curve as described in the following sections. 3.2.4 Curvature, Speed, and Superelevation—Theory and Basis of Criteria This article summarizes the basis of design for determination of speed and superelevation in curved track. This material is based on information provided by Nelson,[7] but has been condensed and modified as necessary for specific application to current LRT designs and to include the use of metric units. 3.2.4.1 Superelevation Theory The design speed at which a light rail vehicle can negotiate a curve is increased proportionally by increasing the elevation of the outside rail of the track, thus creating a banking effect called superelevation. When rounding a curve, a vehicle and the passengers within it are subjected to lateral acceleration acting radially outward. The forces acting on the vehicle are illustrated in Figure 3.2.2. Ride comfort criteria, including making certain that any standing passengers on the rail vehicle do not fall, requires limiting train speed so that lateral acceleration does not exceed certain thresholds. This is traditionally expressed in terms of a fraction of the acceleration of gravity. The traditional value used was one-tenth the acceleration of gravity, or 0.1 g. That value, which was empirically derived from studies dating back to the beginning of the 20th century, is a conservative value and good for ordinary applications. More recent research has indicated that higher values can be tolerated. Lateral acceleration as high as 0.15 g has been successfully used on some high-speed railways and can be used for rail transit under the following circumstances: • Spirals of appropriate length are provided to limit jerk. • The trackform is rigid, such as either direct fixation track or embedded track, so that deterioration of track geometry is nearly impossible. Use of high values of lateral acceleration in ballasted track will require extraordinary maintenance attention to track surfacing and crosslevel so as to avoid misalignments that result in values of lateral acceleration higher than 0.15 g.

Light Rail Transit Track Geometry 3-15 Figure 3.2.2 LRT vehicle on superelevated track To counteract the effect of the lateral acceleration and the resulting centrifugal force (Fc), the outside rail of a curve is raised by a distance above the inside rail ‘e’. A state of equilibrium is reached in which both wheels exert equal force on the rails, i.e., where ‘e’ is sufficient to bring the resultant force (Fr) to right angles with the plane of the top of the rails. The AREMA Manual for Railway Engineering, Chapter 5, gives the following equation to determine the distance that the outside rail must be raised to reach a state of equilibrium, where both wheels bear equally on the rails: r g 2V B = e where e = equilibrium superelevation in feet or meters. (Note: not inches or mm in this formula) B = bearing distance of track in feet or meters. This value is equal to the track gauge plus the distance to the center of the railheads. The absolute value will therefore be different for standard gauge, broad gauge, and narrow gauge tracks. V = velocity in feet [meters] per second. (Note: not mph or km/h in this formula). g = acceleration due to gravity in feet per second per second, or feet/sec2 [meters per second per second, or meters/sec2]. r = radius in feet [meters].

Track Design Handbook for Light Rail Transit, Second Edition 3-16 To convert these units to common usage: • ‘e’ in feet or meters is usually expressed as either ‘E’ or ‘Eq’ (preferred) in either inches or millimeters. • ‘B’ is usually considered to be 60 inches [1524 millimeters] on standard gauge track; however, the 60-inch value is actually a fairly crude approximation. The actual value, assuming 115RE rail, would be 59 ¼ inches [1505 mm]. Hence, a valid conversion to S.I. units (i.e., one consistent with the tolerances implied by the rounding of 59 ¼ inches up to 60 inches) would be 152 cm (expressed as 1520 mm in the calculations below). • Vehicle velocity ‘V,’ expressed in feet per second [meters per second] is changed to ‘V’ in mph [km/h]. • The acceleration of gravity ‘g’ is equal to 32.2 feet/sec2 [9.81 meters/sec2]. When working in traditional U.S. units, the curve radius ‘r’ can be replaced with 5729.58/D, where ‘D’ is equal to the arc definition degree of curvature expressed as a decimal of whole degrees. However, there is no S.I. equivalent for degree of curve. Moreover, since it is extremely rare that an LRT track curve will have a radius exactly equal to some convenient even number degree of curve, it is recommended that these calculations be based on the radius in feet and decimals of a foot. The AREMA formula hence can be expressed as follows: ( ) ( ) R 2V 11.96 2 1,000 3,600 R 9.81 2V 1,520 = E 2V 3.96 2 5,280 3,600 R 32.2 2V 59.25 = E R ⎥⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢⎢ ⎢ ⎢ ⎢ ⎣ ⎡ ⎟⎠ ⎞⎜⎝ ⎛ = ⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛ = The traditional U.S. units version of the equation above is sometimes seen as E = 4.01 V2/ R. That occurs when the designer used the rough 60-inch value for the bearing distance as opposed to the somewhat more accurate 59 ¼ inches. In truth, given the rounding of the actual value of g used in the development of the equations, the fact that the bearing distance will vary depending on both the rail section used and the wear on both rails and wheels, plus the rational construction and maintenance tolerances for track gauge, both 3.96 and 4.01 are unnecessarily precise. The same pragmatism can be applied to the S.I. version of the equation. Therefore, the simplified equations: Eq = 4.0 V2/ R (U.S. traditional units) and Eq = 12.0 V2/ R (S.I. units) are actually sufficiently accurate for ordinary purposes at the speeds to be encountered in LRT design. The formulae above compute the amount of superelevation necessary for equilibrium. So as to clearly distinguish that figure from other values of superelevation discussed below, the shorthand designation “Eq” is recommended when discussing superelevation needed for equilibrium.

Light Rail Transit Track Geometry 3-17 Experience has shown that safety and comfort can be optimized if vehicle speed and curvature are coordinated such that Eq falls in the range of 3 to 4 ½ inches [75 to 115 mm]. This is an extremely conservative goal and can provide a very gentle ride. However, it is rarely practical to achieve without substantial civil works that are typically well outside the budget for most light rail transit projects. Accordingly, higher values of Eq are typically necessary so as to avoid negative impacts on the LRT system running times from terminal to terminal. 3.2.4.2 Actual Superelevation The actual value of superelevation installed in the track is typically somewhat less than required for equilibrium. This “actual superelevation” is commonly abbreviated as “Ea.” Most railway route design texts recommend an absolute limit of 8 inches [200 mm] of actual superelevation for passenger operations unless slow-moving or freight traffic is mixed with passenger traffic. Values of Ea that large are very seldom used, in part because the passengers on any train that might stop on such a curve would be extremely uncomfortable. Therefore, LRT superelevation is generally limited to 6 inches [150 mm] or less. All railroads administered by the Federal Railroad Administration (FRA) are limited to no more than 6 inches [150 mm] of Ea, primarily because the FRA mandates that all tracks that are a part of the nation’s general railroad system must be capable of handling mixed traffic. Track that is not part of the general railroad system or that is used exclusively for rapid transit service in a metropolitan or suburban area, generally does not fall within the jurisdiction of the FRA. This includes the vast majority of LRT systems. Even in the case of LRT lines that share some track with a freight railroad operation, the FRA might not choose to exercise any authority over LRT tracks that are not used by the freight operator. In view of the foregoing, railways that are not subject to oversight by the FRA may, when appropriate, use up to 8 inches [200 mm] of actual superelevation on curved track. This has been applied to at least two North American metro rail transit systems. However, it is far more common on LRT systems to limit maximum actual superelevation to 6 inches [150 millimeters], as it becomes more difficult to consistently maintain ride comfort levels at higher actual superelevation, particularly in cases where running speeds may vary. 3.2.4.3 Superelevation Unbalance The equations in Article 3.2.4.1 above are expressed in terms of a single speed at which the rail vehicle is at equilibrium with the resultant vector, Fr, aimed directly at the centerline of track. However, for a variety of reasons, rail vehicles often run at different speeds on the same segment of track and hence would require some different value of track superelevation for each of those speeds. This is obviously impossible; however, it is perfectly acceptable, within limits, to operate at speeds either greater than or less than the equilibrium speed. When the operating speed is greater than the equilibrium speed, the variance is termed superelevation underbalance. This is sometimes contracted to simply “unbalance.” The term “cant deficiency” is also sometimes seen, “cant” being a British vernacular for superelevation. Underbalance is commonly abbreviated as Eu. Operation at speeds less than the equilibrium condition results in “overbalance,” which can be considered as “negative” Eu.

Track Design Handbook for Light Rail Transit, Second Edition 3-18 Limited superelevation unbalance is intentionally incorporated into most curve design speed calculations to avoid the negative effects of occasional operation at speeds less than equilibrium speed. For rail transit, the principal issue is passenger discomfort; negative Eu is not tolerated well by passengers, who sometimes have the perception that they are falling out of their seats. In freight operations, negative Eu can result in excessive loading of the low (inside) rail of the curve leading to a variety of metallurgical defects. This is generally not an issue with LRT since transit axle loadings are far smaller than those of freight cars. The development of high-speed intercity passenger rail operations using rolling stock with sophisticated suspension systems has led to extensive research in the field of superelevation and allowable amounts of unbalance. As noted above, high-speed rail operations typically allow higher values of lateral acceleration and hence higher values of Eu. Ignoring vehicle roll (see Article 3.2.4.4), 0.1 g of lateral acceleration equates to almost exactly 6 inches [150 mm] of unbalance on standard gauge track. Per AREMA, vehicles with stabilized suspensions have vehicle roll (to the outside of the curve) equivalent to about 1 ½ inches [38 mm] of unbalance. Subtracting 1 ½ inches from 6 inches leaves 4 ½ inches [114 mm] for Eu. Hence, any criterion that restricts Eu to be less than 4 ½ inches is actually restricting lateral acceleration to something less than 0.1 g. Nevertheless, maximum allowable superelevation unbalance varies among transit agencies. For instance, a now-obsolete criterion for one large legacy heavy rail transit operator allowed only 1 inch [25 mm] of Eu, while newer systems, beginning with PATCO (the Lindenwold High-Speed Line, which opened in 1968), usually allowed 4 ½ inches [115 mm]. That larger value is consistent with a lateral acceleration of 0.1 g while the obsolete value is equivalent to less than 0.02 g. Generally, it is recognized that 3 to 4 ½ inches [75 to 115 mm] of Eu is acceptable for LRT operations, depending upon the vehicle design. 3.2.4.4 Vehicle Roll In a curve with no actual superelevation, Ea, all of the lateral acceleration effectively becomes unbalance. Speed then becomes limited by the value selected for lateral acceleration. If the value of lateral acceleration is the customary 0.1 g, the unbalance on standard gauge track works out to 6 inches [150 mm]. At 0.15 g, the unbalance would be 9 inches [230 mm]. However, those values are not actually Eu. To determine Eu, one must first subtract a factor for vehicle roll. All types of rail vehicles have suspension systems that allow the car or locomotive to react to variations in the track surface and to dampen impacts. A consequence of these suspension systems is that when the vehicle is passing through a curve, it will roll about a rotation point or points within its suspension system. The vehicle will roll toward the outside of the curve until it reaches a point where either the springs in the suspension system counteract the rotating force or the rotation reaches a mechanical stop in the vehicle’s trucks. The AREMA Manual for Railway Engineering (2008) Chapter 5, Article 3.3.1, explains: Equipment designed with large center bearings, roll stabilizers and outboard swing hangers can negotiate curves comfortably at greater than 3 inches [75 mm] of unbalanced superelevation because there is less body roll....Lean tests may be made on tangent track by running one side of the car onto oak shims, using winches to move the car on and off the shims. Cars should be elevated to three

Light Rail Transit Track Geometry 3-19 heights: usually 2 inches, 4 inches, and 6 inches [50 mm, 100 mm, and 150 mm]. If the roll angle is less than 1°-30’, experiments indicate that cars can negotiate curves comfortably at 4.5 inches [115 millimeters] of unbalanced elevation. Because the carbody roll in a moving vehicle is toward the outside of the curve, it has the effect of being “negative superelevation” and thus cancels out some portion of either the actual superelevation or unbalanced superelevation of the curve. The 1o30’ roll value noted by AREMA, applied over the width of standard gauge track, is effectively equal to 1 ½ inches [about 38 mm] of additional unbalance. So, if the maximum acceptable unbalance for the system based on a lateral acceleration of 0.1 g is 6 inches [152 mm], the value of Eu actually available to the track designer is only 4 ½ inches [about 114 mm]. The difference—call it “superelevation roll,” or “Er”—has effectively been appropriated by the vehicle’s suspension system. Naturally, the actual value of Er on any given curve will vary. Depending on the design of the rail vehicle, its maintenance condition, and its instantaneous speed, the actual value of Er could be less than or perhaps even greater than AREMA’s figure of 1 ½ inches [38 mm]. Those factors are outside of the track designer’s control. There is also a lack of firm data on the roll factor (Er) of various types of light rail vehicles/streetcars. Notably, the possible carbody roll, as indicated by the dynamic envelope for a typical light rail vehicle (see Chapter 2, Figure 2.3.2), is generally much larger than the AREMA figure. This is an area that requires further investigation. In the absence of specific information for the proposed light rail vehicle, the AREMA guidance can be used. However, the track designer should verify with the project’s vehicle designers and carbuilders what the maximum carbody roll is for the design vehicle(s). Notably, the AREMA static lean test procedure quoted above is not commonly included in vehicle procurement specifications. If the vehicle fleet includes any heritage, antique, or replica streetcar equipment, the suspension systems and hence the body roll angle may be appreciably different from that of newer rolling stock. If so, it may be necessary to impose speed restrictions on heritage equipment so as to keep the lateral acceleration at or below the selected value. Therefore, equilibrium superelevation can be expressed as Eq = Ea + Er + Eu = 4 V2 / R [Ea = Ea +Er + Eu = 12 V2 / R] and the actual superelevation for maximum comfortable speed (Ec) may be expressed as Ec = Eq – Er = Ea + Eu The value of Er, once it has been deducted from the maximum allowable value of superelevation unbalance, is not used in any subsequent calculations. Thus, if an LRT vehicle is of modern design, it is appropriate to use up to 4 ½ inches [114 mm] of Eu as a parameter in the design of track curves. The formulae from Article 3.2.4.1 may therefore be restated as Eq = Ea + Eu = 4.0 V2/ R (U.S. traditional units) and Eq = Ea + Eu = 12.0 V2/ R (S.I. units)

Track Design Handbook for Light Rail Transit, Second Edition 3-20 3.2.4.5 Ratio of Ea to Eu How to balance Ea and Eu is largely a qualitative decision, and several strategies are employed by different transit agencies: • No (or minimal) superelevation unbalance is applied until actual superelevation (Ea) reaches the maximum allowable level. Actual superelevation is thus equal to the equilibrium superelevation for most curves. Under ideal conditions, where all vehicles operate at the same speed and do not stop (or slow down) on curves, this strategy creates the least amount of passenger and vehicle lateral acceleration for a given transition curve length. Under less-than-ideal operating conditions, however, the minimum superelevation unbalance strategy produces unfavorable ride comfort conditions. • No unbalanced superelevation (Eu) until Ea has reached some figure. This recognizes that carbody roll (Er) in response to lateral acceleration is one of the first results of vehicle entry into a curve. By introducing Ea immediately, some of the jerk experienced by the passengers is mitigated, providing for a smoother ride. • Maximum superelevation unbalance is applied before any actual superelevation is considered. This option is often used by freight and suburban commuter railroads. Where a wide variety of operating speeds is anticipated on the curved track, particularly on joint LRT-freight trackage, this strategy is usually the least disruptive to passenger comfort. • No actual superelevation Ea until Eu has reached some figure. This simplifies track construction (but not necessarily track maintenance) by eliminating superelevation on large radius curves. This approach is generally not recommended; however, it may become necessary in specific circumstances. For example, when constructing embedded track in a public street, it may not be possible to have any actual superelevation without causing problems with pavement contours and drainage. In such cases, most or all of the value of Eq would be taken up by Er and Eu. • Actual superelevation (Ea) and superelevation unbalance (Eu) are applied equally or in some proportion. Because a certain amount of superelevation unbalance, applied gradually, is generally considered to be easily tolerated by both vehicle and passenger and tolerable superelevation unbalance increases with speed, this strategy is preferred for general usage. Other combinations might be considered. For example, it might be considered desirable to ordinarily limit Eu to some fairly low threshold value and blend Ea and Eu up until Ea reaches the maximum. Thereafter, Eu only would be increased until it reached its maximum. As a practical matter for construction, curves with a large radius in comparison to the desired operating speed should not be superelevated. This can be accomplished by not applying actual superelevation (Ea) until the calculated total equilibrium superelevation (Eq) is over a minimum value, usually ½ to 1 inch [12 to 25 millimeters]. However, despite the lack of Ea, such curves usually still need a spiral so as to counteract the lateral acceleration effects of Eu and Er.

Light Rail Transit Track Geometry 3-21 LRT systems are typically operated under the manual control of the vehicle operator, subject to both the commands of the signal systems and printed operating rules. This is distinctly different from modern metro rail systems, where automatic train operation results in the exact same train speeds at any given location a very high percentage of the time. By contrast, LRT train speeds on any given curve can vary over a relatively wide margin from virtually stopped up to the maximum speed permitted by the train control system. Operation at an optimal design speed actually occurs only a fraction of the time. It therefore becomes important to select an appropriate balance between Ea and Eu. If Ea is too high, the passengers on board slow or stopped trains could be uncomfortable. If Eu is too high, passengers will be subjected to a rougher ride than necessary. So as to optimize ride comfort, the normal practice is to introduce Eu and Ea nearly simultaneously. The following example (using traditional U.S. units) illustrates the process given the following design criteria policy decisions: Maximum Ea = 6 inches. Maximum Eu = 4 ½ inches. No Eu until Ea has reached ½ inch. Eu and Ea increased linearly once Eu is initiated. Plotting those parameters, as shown in Figure 3.2.3, sets the slope and y-axis intercept of a line defining Eu in terms of Ea. Figure 3.2.3 Example of ratio of Eu to Ea

Track Design Handbook for Light Rail Transit, Second Edition 22-3 Mathematizing this line in the classic y = mx + b equation format results in Eu = 0.82 Ea – 0.4 Substituting into the modified AREMA equation developed in Article 3.2.4.1 above: Ea + (0.82 Ea – 0.4) = 3.96 V2 / R and solving for Ea results in Ea = 2.18 (V2 / R) – 0.22 Subtracting that calculated Ea from Eq then gives the value of Eu. Naturally, different assumptions concerning maximum values of both Ea and Eu and when Eu should be introduced would result in an appreciably different formula. As an example, one U.S. metro rail transit project very conservatively limited Eu to an maximum of 2 ½ inches [64 mm], held Ea to no more than 6 inches [152 mm], and introduced Eu only after Ea equaled 1 inch [25 mm]. Their version of the previous equation (in traditional U.S. units) therefore became Ea = 2.64 (V2 / R) – 0.66 Use of equations such as the examples above will result in the gradual introduction of both actual and unbalanced superelevation and avoid unnecessarily high values of lateral acceleration and jerk to both the light rail vehicles and their passengers. As a practical matter for construction, calculated values for actual superelevation should be rounded up to the next ¼ inch when working in traditional U.S. units. Use 5 mm as the working increment for Ea when using S.I. units. The difference between Eq and that rounded value of Ea becomes the actual Eu at the design speed. For a total superelevation (Ea + Eu) of 1 inch [25 millimeters] or less, actual superelevation (Ea) is not usually applied. In specific cases where physical constraints limit the amount of actual superelevation (Ea) that can be introduced, a maximum of 1 ½ inch [40 mm] of superelevation unbalance (Eu) is often permitted before applying any actual superelevation (Ea). On curves where speed is likely to vary, such as on the approaches to passenger stations, the actual superelevation (Ea) is usually set so that trains will have a positive value of superelevation unbalance (Eu). This is because large values of negative Eu (i.e., Ea is greater than Eq) are not tolerated well by passengers. For this reason, consideration should be given to the difference in speed between the front and rear of the train as they pass the cardinal points along the curve. As noted above, differing circumstances at different locations on the same rail transit project may require different ratios and formulae for balancing Ea and Eu. However, along any given route segment it is desirable to keep them as consistent as is reasonably possible. Individual curves that have a much higher proportion of Eu than other nearby curves could catch passengers unaware and cause incidents. High values of superelevation unbalance increase track/vehicle forces and hence maintenance of both. Conversely, operations closer to balance speed result in a more comfortable ride and less impact on the vehicle and track. Therefore, given consistent speeds and circumstances it is preferable to maximize actual superelevation and minimize

Light Rail Transit Track Geometry 3-23 superelevation unbalance to reduce the effects of centrifugal force upon the passengers, vehicles, track structures, and roadbed. 3.2.5 Spiral Transition Curves When an LRT vehicle operating on straight (tangent) track reaches a circular path, the vehicle axles must be set at a new angle, depending upon the radius of the curve. This movement is not done instantly but over a measurable time interval, thus creating the need for a transitional or easement curve, the length of which equals speed multiplied by time. Superelevated circular curves virtually always require such easement curves so as to control the acceleration and resulting forces exerted upon the track, the passengers, and the vehicle. These easement curves are usually spirals with the radius decreasing from infinity, where they meet the adjoining tangent track, down to the radius of the circular curve being entered. A similar (and usually symmetrical) transition is provided at the exit end of the curve. Spiral curves also provide the ramp for introducing superelevation into the outside rail of the curve. Spirals are also used as transitions between compound circular curves, as discussed in Article 3.2.8. 3.2.5.1 Spiral Application Criteria Spirals should be used on all main line track horizontal curves with radii less than 10,000 feet [3,000 meters], wherever practicable. For operation at speeds likely to be encountered in LRT design, spirals can be omitted if the calculated length of spiral (Ls) is less than 0.01R, where R is the radius of the curve. (The formula is the same using either feet or meters for both Ls and R.) A spiral is preferred, but not required, for yard and secondary tracks where design speeds are less than 10 mph [16 km/h]. Curves on yard lead and secondary tracks that have greater design speeds should have spiral transition curves and superelevation. 3.2.5.2 Spirals and Superelevation Actual superelevation (Ea) should normally be attained and removed linearly throughout the full length of the spiral transition curve by raising the outside rail while maintaining the inside rail at the profile grade. One exception to this customary method of achieving superelevation is sometimes employed for direct fixation tracks in circular tunnels, such as might be created by a tunnel-boring machine, where superelevation is achieved by rotating the track section about the tracks profile grade line. This usually minimizes the overall size of the bored tunnel required through the curve. Since the tunnel diameter, as created by the boring machine, will be the same in both curved and tangent track, a substantial amount of tunnel excavation can be avoided if the curved track section is as small as possible. Note that there will be a substantial difference between the profile grade line of the track and the bored tunnel through curves. Some projects have employed this rotation method to achieve superelevation on aerial structures. Achieving superelevation in this manner can create very complex relationships between the plan and the profile of the track versus that of the structure, particularly on a two-track structure. The twisting of the deck affects the actual profile grade line (PGL) of one or both tracks depending on the point of deck rotation. One project rotated the deck about the low rail of the inside track, resulting in a very large jump in the profile grade line of the outer track through the length of the spiral and an even higher jump in the profile of the outermost rail. Another project rotated the

Track Design Handbook for Light Rail Transit, Second Edition 3-24 deck about a structure PGL centered between the tracks and in the plane of the four rails. Note that deck rotation may require the tracks to have identical values of Ea and that the cardinal points of the curves (TS, SC, CS, and ST) on both tracks will need to be directly opposite each other. The vertical component caused by the deck twisting also requires spirals appreciably longer than those normally used since the raising or lowering of each track’s PGL effectively induces an additional amount of actual superelevation. In extraordinary cases, the superelevation may be developed along the tangent preceding the point of curvature (PC), or run off in the tangent immediately beyond the point of tangency (PT). The transition length is then determined from the minimum spiral length formulae presented herein. The maximum amount of superelevation that is run off in tangent track should be no more than 1 inch [25 mm]. Note that this process induces a rotational acceleration that is in the opposite direction from the lateral jerk that occurs when the vehicle enters the horizontal curve, exacerbating the effect of the latter. For this reason alone, introducing superelevation along tangent track is discouraged. In areas of mixed traffic operation with roadway vehicles, the desired location for a pavement crown is at the centerline of track. Where this is not feasible, a maximum pavement crown of 2.0% (1/4 inch per foot) across the rails may be maintained in the street pavement to promote drainage. This practice will normally introduce a constant actual superelevation (Ea) of approximately 1.2 inches [30 millimeters]. If, at curves, the street pavement is neither superelevated nor the crown removed, this crown-related superelevation may also dictate the maximum allowable operating speed. See Chapter 12 for additional discussion on this issue. 3.2.5.3 Types of Spirals There are many formulae that either mathematically define or approximate a spiral curve with a progressively varying radius. Types of spirals found in railway alignment design include the AREMA Ten Chord; the cubic spiral; several forms of clothoid spirals as defined by Bartlett, Hickerson, and others; plus various forms of Searles spirals, including some still used by some legacy light rail operations. (Searles spirals are a series of compounded circular curves that approximate the alignment of a clothoid curve.) For the spiral lengths and curvatures found in LRT, all of the above spiral formulae will generally describe the same physical alignment laterally to within ordinary construction tolerances. The choice of spiral easement curve type is thus not critical. It is important, however, to utilize only one of the spiral types and to define it as succinctly as possible. Vague terms such as “clothoid spiral” should be clarified as more than one formula describes this type of spiral curve. For LRT design, a spiral transition curve that is commonly used in transit work is the Hickerson spiral. Its main advantage is that it is well-defined in terms of data required for both alignment design and field survey work. Figure 3.2.1 depicts a spiraled curve with the associated mathematical formulae as defined by Hickerson.[13] 3.2.5.4 Spiral Transition Curve Lengths Spiral curve length and superelevation runoff are directly related to passenger comfort. Both the radius and superelevation change at a linear rate through the spiral. The centrifugal force for a given speed is inversely proportional to the instantaneous radius of the superelevation at each

Light Rail Transit Track Geometry 3-25 point along the spiral. Thus, lateral acceleration increases at a constant rate until the full curvature of the circular portion of the curve is reached, where the acceleration remains constant until the curve’s exit spiral is reached. As a general rule, any speed and transition that provides a comfortable ride through a curve is well within the limits of safety. Determining easement curve length allows for establishment of superelevation runoff within the allowable rate of increase in lateral acceleration due to superelevation unbalance. Also, the transition must be long enough to limit possible racking of the vehicle frame and torsional forces from being introduced to the track structure by the moving vehicle. Three parameters must be considered when determining the appropriate spiral length: • Rate of introduction of unbalance. • Actual superelevation. • Rate of change of superelevation. Depending on the circumstances, one of the three will require a longer spiral and hence govern over the other two criteria. Each of these will be discussed below. 3.2.5.4.1 Length Based upon Superelevation Unbalance This criterion is fundamentally an issue of passenger ride comfort and controlling the rate at which unbalance (and hence lateral acceleration) is introduced. The steadily increasing lateral acceleration that the passenger feels as the rail vehicle passes through the spiral is aptly known as “jerk,” and the pace at which it is introduced is known as the “jerk rate.” As noted previously, the generally recognized maximum acceptable rate of lateral acceleration due to cant deficiency, or superelevation unbalance, for passenger comfort is 0.1 g, where ‘g’ is the acceleration of gravity, i.e., 32.2 feet per second per second [9.8 meters per second per second]. This pace has been a standard for over a century and was derived empirically based on test observations of trains running at various speeds. It is a conservative value based on average conditions of both rolling stock and track. In the case of track, a design standard of 0.1 g recognizes that the as-built geometry of ordinary ballasted track deteriorates over time and that those incremental deficiencies will collectively result in circumstances where the actual lateral acceleration will be greater than 0.1 g. Hence, a factor of safety is built into the parameter. However, track geometry is extremely unlikely to deteriorate in direct fixation and embedded trackforms. Short of a significant structural failure, superelevation and horizontal alignment will not change in such rigid track. Therefore, it is possible to allow higher values of lateral acceleration in rigid trackforms. Values up to 0.15 g have been demonstrated to be both safe and comfortable if they are introduced smoothly over the length of spirals of appropriate length. The same value could be used in ballasted track only if the track owner commits to a comprehensive program of track surfacing to maintain track geometry within extremely tight maintenance tolerances. Few, if any, transit authorities have the budget necessary to make that commitment over the long term. In a curve with no spirals and no superelevation, the lateral acceleration, or jerk, is introduced instantaneously at the point of curvature. Essentially the jerk rate is infinite. Since this is obviously undesirable, the spiral length is usually governed by controlling the jerk rate to a tolerable level.

Track Design Handbook for Light Rail Transit, Second Edition 3-26 The preferred formulas presented in Chapter 5 of the AREMA Manual for Railway Engineering are based on a maximum rate of change of acceleration of 0.03 g per second. So, if the maximum lateral acceleration is 0.10 g, the spiral should be long enough that a train traveling at the design speed will take 3.33 seconds to traverse it, i.e.: seconds 3.33 g/sec 0.03 g 0.10 = Chapter 5 of the AREMA Manual for Railway Engineering allows the jerk rate to rise to an absolute maximum of 0.04 g per second when realigning existing tracks if spiral length is constrained by geographic conditions. However, research associated with the introduction of high-speed passenger rail service in Europe and elsewhere has determined that the jerk rate can be much higher—as high as 0.1 g per second—under controlled circumstances, such as the rigid trackforms noted above. Hence, if both jerk and jerk rate are maximized, the length of the spiral, measured in time, could as little as seconds 1.50 g/sec 0.10 g 0.15 = However, spirals that short should only be employed under extraordinary circumstances after exhaustive investigation has documented that nothing else will work. Using the more conservative 3.33 seconds for the spiral length, the actual length of the spiral required is 3.33 seconds multiplied by the speed of the vehicle. Converting to miles per hour [kilometers per hour] the formula may be expressed as V(km/h)] 0.925 [ 3.33 3600 1000 V(km/h)(meters) L (mph) 4.89V 3.330/3600)V(mph)(528(feet) sL S = ×= = ×= ⎥⎦ ⎤ ⎢⎣ ⎡ Assuming that 4 ½ inches [115 millimeters] is the maximum allowable superelevation unbalance, a formula to determine the length of the spiral necessary to ensure passenger comfort can therefore be stated as: uVE1.09sL oruVE4.5 4.89 sL == ⎟⎠ ⎞⎜⎝ ⎛ uVE0.008sL oruVE115 0.925 sL ⎥⎦ ⎤ ⎢⎣ ⎡ =⎟ ⎠ ⎞⎜ ⎝ ⎛= As a review, the formulae immediately above are based on the parameters stated earlier: Max Eu = 4.5 inches [115 mm] Max Jerk = 0.10 g Max Jerk Rate = 0.03 g/s

Light Rail Transit Track Geometry 3-27 By contrast, the preferred formula given in the AREMA Manual for Railway Engineering, Ls = 1.63EuV, is based on Max Eu = 3.0 inches [76 mm] Max Jerk = 0.10 g Max Jerk Rate = 0.03 g/s and the alternate acceptable AREMA formula, Ls = 1.22 EuV, is based on Max Eu = 3.0 inches [76 mm] Max Jerk = 0.10 g Max Jerk Rate = 0.04 g/s By carefully considering the ramifications of higher values of Eu, jerk, and jerk rate, it is possible to derive even shorter spirals. For example, if lateral acceleration is allowed to rise to 0.15 g (equivalent to 9 inches [230 mm] of unbalance less vehicle roll) and a jerk rate of 0.1 g/s is accepted, the formulae above would become: uVE0.29sL or uVE1.5 - 9.0 1.71 sL == ⎟⎠ ⎞⎜⎝ ⎛ ⎥⎦ ⎤ ⎢⎣ ⎡ ⎟⎠ ⎞⎜⎝ ⎛ == uVE0.002sL or uVE190 0.417 sL As noted above, such extraordinarily short spirals should be used only after extensive investigation and documentation and only in embedded or direct fixation trackforms, where geometric deterioration is virtually impossible. Ordinary alignment work should use either the Ls = 1.09 VEu formula or its S.I. units equivalent. 3.2.5.4.2 Length Based upon Actual Superelevation This criterion evaluates twist of the vehicle measured over the distance between the trucks. AREMA Manual for Railway Engineering, Chapter 5, gives the following formula for determining the length of an easement spiral curve: Ls = 62 Ea [Ls = 0.75 Ea] where Ls is in feet [meters] and Ea is in inches [millimeters]. The only variable in this AREMA formula is the actual superelevation; there’s no consideration of speed. The factor of “62” in the U.S. traditional units version of the equation was empirically derived by one of the AREMA’s predecessor organizations based on two considerations: • 62 feet [19 meters] is roughly the distance between the trucks on a conventional passenger railroad car that is 85 feet [26 meters] long. Observations of such equipment revealed that satisfactory vehicle behavior could be ensured if the difference in track crosslevel from one truck to the other was limited to 1 inch [25 mm] or less. • “String Lining,” the time-honored method for realigning railroad curves, is based on middle ordinate offset distances measured from the outer rail to the midpoint of 62-foot long chords. Hence, by defining superelevation in terms of 62-foot increments, the AREMA formula used dimensions that were already very familiar to American trackmen. At the time when these

Track Design Handbook for Light Rail Transit, Second Edition 3-28 guidelines we developed, much of the field supervision of track construction and maintenance was done by persons who might have had a high school education at most. Hence, unambiguous simplicity was best. For 6 inches [150 millimeters] of Ea, this AREMA formula produces a spiral 372 feet [113 meters] long. This results in a minimum ratio of superelevation change across truck centers of 1:744. This is an empirical value that accounts for track crosslevel tolerances, car suspension type, and fatigue stresses on the vehicle sills. Also note that the AREMA Manual for Railway Engineering formula is applicable to both passenger and freight cars. Light rail vehicles have a far greater range of suspension travel than freight or intercity passenger cars. The magnitude of the LRV frame twist is relatively small compared to the nominal LRV suspension movement. The maximum actual superelevation runoff rate and minimum ratio of superelevation change across truck centers are thus not fixed values, but are functions of the LRV truck center distance. The twist-based formula is effectively based on the ability of the vehicle trucks to rotate in a vertical plane relative to the carbody they support. However, truck centers in light rail vehicles are much shorter than in railroad passenger cars. Hence, it is possible to replace the 62 feet in the traditional U.S. units version of the formula with the truck centers of the light rail vehicle. Most light rail vehicles have truck center distances in the range of 25 to 30 feet [8 to 9 meters]. Hence the value of 62 can be replaced by 30. More commonly, a value of 31 is used, half of 62, effectively hearkening back to the time-honored practice of curve string lining. Hence, a traditional formula that appears in many LRT design criteria manuals is Ls = 31 Ea [Ls = 0.38 Ea] However, the development of low-floor light rail vehicles with independently rotating wheels has changed the issues. Trucks with solid axles and conventional suspensions are generally sufficiently loose vertically to “equalize” the load on all four wheels when the track is twisting. The new trucks under low-floor cars are not necessarily as limber. It is therefore necessary to consider the short twist between one axle and the next on the same truck. The requirements vary by truck design, but, in general, the builders of low-floor cars require that track twist be limited to an appreciably greater degree than suggested by the traditional formulae above. A guideline that appears in some European criteria is that twist should not exceed a ratio of 1:400, as in 1 mm of crosslevel difference in 400 mm of track length. That works out to the following version of the equations: Ls = 33.3 Ea [Ls = 0.40 Ea] One U.S. transit property, having had appreciable problems with derailments of the center trucks of their partial low-floor LRVs, determined that part of the resolution was to establish a maintenance standard stipulating that superelevation transitions and other track twist situations should be no greater than 7/8 inch in 31 feet [about 22 mm in 9.45 meters]. That would be equivalent to Ls = 35.4 Ea [Ls = 0.425 Ea]

Light Rail Transit Track Geometry 3-29 However, that threshold is a maintenance standard, not a design and construction criterion. It therefore implies the threshold at which corrective maintenance actions are required and is not a desired design criterion to which the track should initially be constructed. One very large international carbuilder, so as to accommodate their 100% low-floor LRVs, stipulates that track twist should not result in a difference in gradient between one rail and the other greater than 0.2%. Using that as a guideline, the formulae above become Ls = 41.7 Ea [Ls = 0.50 Ea] resulting in minimum spirals about 33% longer than those required by the traditional formula. At the opposite end of the spectrum are various designs of vintage streetcars, such as operate on many legacy and heritage trolley operations. Data from San Francisco Muni suggest that their heritage PCC cars can reliably negotiate track twist about twice as severe as the traditional formula. However, while it may be tempting to use such values for a proposed heritage streetcar line, doing so is not recommended. The guideway on any rail transit line is far more permanent than any rolling stock that might run over it. Accordingly, the track alignment designer must anticipate that even if the rail transit service is initiated with rolling stock that is quite limber with respect to twist, it is very likely that some more restrictive vehicle might be used at some future date. A real danger is the possibility that the persons involved in that future vehicle procurement might not realize there is a twist limitation in the track. Sharp horizontal curves are visually apparent; high values of twist are more subtle and hence more likely to be overlooked as an existing condition to which a new LRV must comply. As a guideline, the following are recommended for defining minimum spiral length as a function of track twist: Desired minimum (Also, the absolute minimum for LRT tracks shared with freight trains): Ls = 62 Ea [Ls = 0.75 Ea] Absolute minimum for systems using 100% low-floor LRVs or which might use such cars in the future: Ls = 41.7 Ea [Ls = 0.50 Ea] The formula above can also be considered as an acceptable minimum for systems using only high-floor LRVs with solid axles. The absolute minimum for systems using high-floor LRVs and which cannot reasonably ever use low-floor cars because of infrastructure constraints (such as train-length high level platforms in subways) would be Ls = 31 Ea [Ls = 0.38 Ea]

Track Design Handbook for Light Rail Transit, Second Edition 3-30 As with all criteria, use of absolute minimums is discouraged, and the track designer should use greater values whenever possible. Deliberate twist in the track can occur not only in superelevation transitions but also in embedded track whenever the track crosslevel transitions from a normal pavement crown (typically 2%) to a zero cross slope condition, such as might occur in advance of special trackwork. The requisite length of such twist transitions should be calculated in the same fashion as for spiraled superelevation transitions. In cases where the deck of an aerial structure is twisted so as to create a superelevated condition, the deck twisting will alter the profile grade line of the track and create additional actual superelevation in the track. So as to avoid rapid vertical accelerations, this induced superelevation, plus the normal Ea, needs to be factored into the determination of the minimum spiral lengths. 3.2.5.4.3 Length Based upon Both Actual Superelevation and Speed Prior to 1962, the AREMA (then AREA) Manual for Railway Engineering included only one formula for minimum spiral length. It considered how actual superelevation and train speed affected rotational acceleration as the rail vehicle was entering the curve. However, testing during the 1950s revealed that this formula, which ignored superelevation unbalance, could result in spirals with jerk rates in excess of the desired maximum. Because of this, the old formula based on Ea and V was dropped and replaced with those currently in the manual.[8], [9], [10] A decade later, the Federal Railroad Administration implemented the Track Safety Standards, formally known as 49 CFR 213. Among many other things, the FRA standards establish safety criteria for the maximum allowable track twist at various track classes, each class being based on maximum allowable train speed. Track twist can be the result of superelevation transitions, track that is out of crosslevel, or both. Based on the FRA’s minimum standards and other factors, each railroad establishes their own criteria for track safety, maintenance, and construction. The construction standards are based on what is achievable when building track so as to provide better than the minimum desired ride quality results at a given speed. The maintenance standards establish a threshold at which corrective action is recommended so as to keep ride quality above a desirable level. Safety standards establish a threshold at which either corrective action or a reduction in train speed is mandatory. Amtrak has a very comprehensive set of such standards in their field handbook, Limits and Specifications for the Safety, Maintenance and Construction of Track (MW-1000).[16] The values that Amtrak uses for twist in new track construction are based on the FRA track speed classifications. The track class of most interest for purposes of rail transit design is Class 3, which accommodates passenger rolling stock at up to 60 mph [97 km/h]. For Class 3, MW-1000, Subpart C, Paragraph 59.1, requires the design value of twist to be no greater than a ½ inch in 31 feet [13 mm in 9.45 meters]. Plugging those values into a equation in the format of Ls = f V Ea and solving for “f” results in Ls = 1.03 V Ea [Ls = 0.0076 V Ea]

Light Rail Transit Track Geometry 3-31 where Ls = spiral length in feet [meters] V = speed in mph [km/h] Ea = actual superelevation in inches [mm] In contrast to that, the MW-1000 criteria for Class 9 track (200 mph) allows twist to be up to only a ¼ inch per 31 feet [6mm in 9.34 meters]. However, because of the much higher train speed, that actually allows twist to occur over a much shorter period of time and resolves into the following formulae: Ls = 0.62 V Ea [Ls = 0.0046 V Ea] The smaller value of “f” in that equation results in shorter spirals than those required by the MW- 1000 at slower speeds. This apparent conundrum is because the specified rates of change of crosslevel per length of track are already extremely conservative compared to the FRA safety limits. Use of the more conservative rates could, at extremely high speeds, result in impossibly long spirals. One European standard[17] (as promulgated by “LibeRTiN,” the “Light Rail Thematic Network”) stipulates that acceptable track twist (including superelevation transitions) can be related to track speed in terms of a ratio in the following format: 1:10 V This essentially dictates that the longitudinal distance (in millimeters) necessary to achieve 1 mm of crosslevel is equal to 10 times the velocity (in km/h). This formula is proposed for speeds greater than 30 km/h; at lower speeds a straight 1:300 ratio is proposed. If the LibeRTiN formula is expressed in the format of Ls = f V Ea, substituting 300 mm for Ls, 1 mm for Ea, and 30 km/h for V and converting each of those into feet, inches, and mph respectively, results in a value of f = 1.34. Hence, the LibeRTiN formula can be expressed in the following form: Ls = 1.34 V Ea [Ls = 0.0100 V Ea] where Ls = the spiral length in feet [meters] Ea = the actual superelevation in inches [millimeters] V = train speed in mph [km/h] As a guideline, the following formulae are suggested for minimum spiral lengths when considering both actual superelevation and speed: Desired minimum: Ls = 1.34 V Ea [Ls = 0.0100 V Ea] Acceptable minimum: Ls = 1.03 V Ea [Ls = 0.0076 V Ea] Absolute minimum: Ls = 0.62 V Ea [Ls = 0.0046 V Ea]

Track Design Handbook for Light Rail Transit, Second Edition 3-32 The result should be compared against the minimum spiral lengths defined by the formulae that considered unbalanced superelevation and track twist and the longest spiral selected. Unless Eu has been artificially constrained so as to keep lateral acceleration well under 0.1 g, the formula considering unbalance will usually govern. As noted in the last paragraph of Article 3.2.5.4.2, the minimum lengths for deliberate track twist situations should be based on the formulae given in this chapter for minimum spiral lengths. Such situations include both changes in crosslevel in embedded track and twisted decks on aerial structures. In addition to the discussion above, there are a number of documents with good explanations of the derivation of runoff theory; the references at the end of this chapter contain extensive background on the subject.[8], [9], [10], [11] 3.2.6 Determination of Curve Design Speed The calculation of design speed in curves is dependent on vehicle design and passenger comfort. In addition to the preceding guidelines, curve design speed can be determined from the following principles if specific vehicle performance characteristics are known. This analysis is also necessary if the vehicle dimensions are significantly different than the LRT vehicles described in Chapter 2. 3.2.6.1 Categories of Speeds in Curves Speed in curves may be categorized as follows: • Overturning Speed: The speed at which the vehicle will derail or overturn because centrifugal force overcomes gravity. • Safe Speed: The speed limit above which the vehicle becomes unstable and in great danger of derailment upon the introduction of any anomaly in the roadway. • Maximum Authorized Speed (MAS): The speed at which the track shall be designed utilizing maximum allowable actual superelevation and superelevation unbalance. • Signal Speed: The speed for which the signal speed control system is designed. Ideally, signal speed should be just a little faster than the speed at which an experienced operator would normally operate the vehicle so that the automatic overspeed braking system is not deployed unnecessarily. 3.2.6.2 Determination of Eu for Safe and Overturning Speeds Figure 3.2.4 illustrates a typical transit car riding on superelevated track and the forces associated with the vehicle’s center of gravity. Due to the characteristics of the vehicle’s suspension system, as it negotiates the curve the center of gravity will shift outboard of a point over the centerline of the track. The resultant vector of the mass of the vehicle and centrifugal force will shift toward the outer rail. A typical high-floor transit car has a center of gravity shift (x) and height (h) of 2.50 inches [63.5 mm] and 50.00 inches [1270 mm], respectively. By contrast, a freight railroad diesel locomotive has typical ‘x’ and ‘h’ values of 3 inches [76 mm] and 62 inches [1575 mm], respectively.

Light Rail Transit Track Geometry 3-33 Figure 3.2.4 Force diagram of LRT vehicle on superelevated track 3.2.6.2.1 Overturning Speed Overturning speed is dependent upon the height of the center of gravity above the top of the rail (h) and the amount that the center of gravity moves laterally toward the high rail (x). When the horizontal centrifugal forces of velocity and the effects of curvature overcome the vertical forces of weight and gravity, causing the resultant vector to rotate about the center of gravity of the vehicle and pass beyond the outer rail, derailment or overturning of the vehicle will occur. The formula for computing superelevation unbalance for ‘Overturning Speed Eu’ is derived from the theory of superelevation: Overturning Speed Eu = Be/h where B = rail bearing distance = 59.25 inches [1520 mm] as discussed earlier e = B/2 – x h = height of center of gravity = 50 inches [1270 mm], which is an average for a typical high-floor LRV If ‘x’ = 2 inches [50 mm], then e = [(59.25/2) – 2] = 27.625 inches [702 mm]

Track Design Handbook for Light Rail Transit, Second Edition 3-34 then Overturning Speed mm] [831 inches 32.7= 50 27.625)*(59.25 =Eu and Overturning Speed 3.96 R*Ea)+(Eu =V For example, if ‘Ea‘ is given as 6 inches [150 mm] and curve radius is 1145.92 feet [349.3 meters] ( a 5o00’00” curve in arc definition), then Overturning Speed km/h] [170 mph 106= 3.96 1145.92*6)+(32.7 =V Obviously, the overturning speed will always be far in excess of the curve’s maximum authorized speed. 3.2.6.2.2 Safe Speed It is generally agreed that a rail vehicle is in a stable condition while rounding a curve if the resultant horizontal and vertical forces fall within the middle third of the distance between the wheel contact points on the rails. This equates to roughly the middle 20 inches [500 mm] of the bearing zone ‘B’ indicated in Figure 3.2.4. Safe speed is therefore an arbitrarily defined condition where the vehicle force resultant projection stays within the one-third point of the bearing distance. That speed is entirely dependent upon the location of the center of gravity, which is the height above the top of rail ‘h’ and the offset ‘x’ of the center of gravity toward the outside rail. From the theory of superelevation, we derive the formula for computing superelevation unbalance for maximum safe speed ‘Eu.’ Safe Speed Eu = Be/h where B = rail bearing distance = 59.25inches [1520 mm]) e = B/6 – x If ‘x’ = 2 inches [50 mm], then e = (59.25/6) – 2 = 7.875 inches [200 mm] h = height of center of gravity = 50 inches [1270 mm] then Safe Speed mm] [237 inches 9.3= 50 7.875)*(59.25 =Eu and Overturning Speed V = square root (((Eu + Ea) x R) /3.96)

For e meter 3.2.7 Wher tange revers where A sep lieu of The s rails o throug This m increa requir It is e This incorp accele comfo xample, if ‘E s] ( a 5o00’0 Ove Reverse Cir e an extrem nt length be e spiral (PRS Ea1 = Ea2 = LS1 = LS2 = aration of up meeting at a uperelevation f the track t h the transit ethod of su sed ballast s ements. Suc ntirely possib is indeed th orated into ration chang rt should be a‘ is given a 0” curve in ar rturning Spee cular Curves ely restrictive tween revers ). As a guid actual super actual super the length of the length of to about 3 fe point of reve transition b hroughout th ion, both rail perelevation ection width h issues mus Figure 3.2.5 le to have re e practice fo North Ame es at the PR made appre s 6 inches [1 c definition), d +(9.3 =V horizontal ed superele eline, the PR LS1 x elevation app elevation of t the spiral lea the spiral en et [1.0 meter rsal. etween reve e entire tran s will be at a transition cr at the point o t be investiga Superelev verse spiral r European rican practic S, the spiral ciably longer Lig 3-35 50 mm] and then 3.96 1145.92*6) geometry ma vated curves S should be s Ea2 = LS2 x lied to the fir he second ci ving the first tering the se ] of tangent tr rsed spirals i sition spiral, n elevation eates additio f the reverse ted in detail ation transit s and remain interurban r e.[6] Howe lengths requ than the abs ht Rail Tr curve radiu mph 66.6= kes it impo , the curves et so that Ea1 st curve in in rcular curve i curve in feet cond curve in ack between s usually acc as shown i above the th nal design c spiral and po before incorp ions for reve within acce ailway alignm ver, because ired for reve olute minimu ansit Trac s is 1145.92 km/h] [107.1 ssible to pro may meet ches or millim n inches or m or meters feet or mete the spirals is omplished b n Figure 3.2 eoretical pro onsiderations ssible increa oration into t rse curves ptable ride c ents and is the direct rse spirals to m by limiting k Geometr feet [349 vide sufficie at a point o eters illimeters rs acceptable y sloping bot .5. Note tha file grade line , including a sed clearanc he design. omfort criteria occasional ion of later maintain rid the jerk rate y .3 nt f in h t . n e . ly al e ,

Track Design Handbook for Light Rail Transit, Second Edition 3-36 with 0.03 g/s as a suggested absolute maximum. See Article 3.2.4 for additional discussion on jerk rate and lateral acceleration. Refer to Article 3.2.1 for additional discussion on desirable minimum tangent distances between curves. 3.2.8 Compound Circular Curves A transition spiral should be used at each end of a superelevated circular curve and between compound circular curves. Between compound curves, the spiral segment, instead of having an infinite radius at one end, will match the radius of the larger curve. The remainder of the spiral between that radius and the theoretical spiral-to-tangent point, where the radius would be infinity, is effectively not used. The minimum compound curve spiral length is the greater of the lengths as determined by the following: V )a1Ea2(E f3 = SL V )u1Eu2(E f2= SL )a1Ea2(E f1 =SL − − − where LS = minimum length of spiral, in feet [meters] f1 = the factor used in the corresponding equations for ordinary spiral length based on track twist (i.e., “desirable,” “acceptable,” and “absolute,” minima as appropriate to the design circumstances) Ea1 = actual superelevation of the first circular curve in inches [millimeters] Ea2 = actual superelevation of the second circular curve, in inches [millimeters] f2 = the factor used in the corresponding equations for ordinary spiral length based on unbalanced superelevation and speed Eu1 = superelevation unbalance of the first circular curve, in inches [millimeters] Eu2 = unbalanced superelevation of the second circular curve, in inches [millimeters] f3 = the factor used in the corresponding equations for ordinary spiral length based on actual superelevation and speed V = design speed through the circular curves, in mph [km/h] Ride comfort in spiraled compound curves is optimized if Eu is the same value in both circular curve segments. 3.2.9 Track Twist in Embedded Track When LRT tracks are embedded in pavement and particularly where they are in a shared mixed traffic lane, in many cases the track geometry will be dictated by the roadway agency’s criteria for pavement surface. These are typically dictated by the need to drain storm water off of the pavement surface. As a consequence, there will often be some cross slope in tangent lanes to which the track will need to conform. If this cross slope changes when the street (and track)

Light Rail Transit Track Geometry 3-37 enters a curve, twist will occur over some distance. The track designer must verify that this rate of twist does not exceed the criteria specified in this chapter. It is also important to note that it is unlikely that the street alignment will be spiraled. The spiral lengths in the track must be carefully coordinated with the roadway design so as to both match the pavement surface and keep the horizontal track alignment in an optimal position relative to the traffic lanes. See Chapter 12 for additional discussion on this topic. 3.3 LRT TRACK VERTICAL ALIGNMENT The vertical alignment of an LRT alignment is composed of constant grade tangent segments connected at their intersection by parabolic curves having a constant rate of change in grade. The nomenclature used to describe vertical alignments is illustrated in Figure 3.3.1. The percentage grade is defined as the rise or fall in elevation, divided by the length. Thus a change in elevation of 1 foot over a distance of 100 feet is defined as a 1% grade. When using European reference sources, it is fairly common to see gradients defined in terms of the rise or fall in meters per kilometer. This ratio is known as “per mille” (literally, “per thousand” in Latin) and is usually abbreviated as 0/00. The similarity between that symbol and the more familiar “percent” symbol (%) can result in much confusion. The profile grade line in tangent track is usually measured along the centerline of track between the two running rails and in the plane defined by the top of the two rails. In superelevated track, the inside rail of the curve normally remains at the profile grade line, and superelevation is achieved by raising the outer rail above the inner rail. One exception to this recommendation is in circular tunnels, such as might be created by a tunnel-boring machine, In such cases, the superelevation may be rotated about the centerline of track in the interest of minimizing the size of the tunnel without compromising clearances. Note that circular rail transit tunnels follow a different mathematized alignment than the track. The tunnel’s profile grade line (PGL) effectively is coincident with the geometric center of the boring machine. In curved segments, the relationship between the tunnel PGL, the track PGL, and the rails will be complex as the tunnel PGL shifts inboard of the track centerline through curves so that clearances can be maintained. The vehicle’s performance, dimensions, and tolerance to vertical bending stress dictate criteria for vertical alignments. The following criteria are used for proposed systems using a modern low- floor vehicle. It can be used as a basis of consideration for general use. 3.3.1 Vertical Tangents The minimum length of constant profile grade between vertical curves should be as follows: Condition Length Main Line Desired Minimum 100 feet [30 meters] or 3 V [0.57 V] where V is the design speed in mph [km/h], whichever is greater Main Line Absolute Minimum 40 feet [12 meters]

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Light Rail Transit Track Geometry 3-39 3.3.2 Vertical Grades Maximum grades in track are controlled by vehicle braking and tractive capabilities. As explained in Chapter 2, the vehicle capabilities can vary depending on many factors. In addition, because the coefficient of friction between the rail and the wheel can vary depending on environmental conditions, the maximum grade can be affected by the presence of not only water, snow, and ice but also by vegetation, particularly wet and oily fallen leaves. Such rail surface contamination can be a significant issue in embedded track and “grass track.” On main line track, civil drainage provisions often dictate a minimum recommended profile grade. In yards, shops, and at station platforms, there is usually secondary or cross drainage available. Provided adequate drainage can be ensured, tracks that are level or nearly so can be acceptable in ballasted and direct fixation trackforms. See Chapter 4 for additional discussion of trackway drainage. Embedded tracks need to have some minimum gradient so that not only the pavement surface but also the flangeways will drain. Flangeways accumulate dirt and street debris that needs to be flushed away by storm water runoff. In colder climates, if the flangeways do not drain, there is a possibility of water and debris freezing in the flangeway and causing a derailment. A 2% track grade would be desirable, but may be impractical on many flat urban streets where existing adjoining development prevents any meaningful adjustments in pavement grades. 3.3.2.1 Main Tracks As a guideline, Table 3.3.1 provides recommended profile grade limitations for general use in LRT main track design. The desired maximums stated should be acceptable for all light rail vehicles. Some vehicles may be suitable for operation on somewhat steeper “acceptable maximum” gradients. Table 3.3.1 Maximum and minimum main track gradients Desired Maximum Unlimited Sustained Grade (any length) 4.0% Desired Maximum Limited Sustained Grade (up to 2500 feet [750 meters] between points of vertical intersection (PVIs) of vertical curves) 6.0% Desired Maximum Short Sustained Grade (no more than 500 feet [150 meters] between PVIs of vertical curves) 7.0% Absolute Maximum Grade Unless Restricted by the Vehicle Design (acceptable length to be confirmed with vehicle designers) 9.0% Acceptable Minimum Grade for Drainage on Embedded Track 0.5% Acceptable Minimum Grade for Direct Fixation and Ballasted Trackforms (provided other measures are taken to ensure drainage of the trackway) 0.0%

Track Design Handbook for Light Rail Transit, Second Edition 3-40 There are ample examples of grades in existing LRT lines that are both steeper and longer than the desired figures given in Table 3.3.1. For that reason alone, the gradients and lengths above are general guidelines and, within reason, should not be considered as inviolate. For example, there is no compelling reason why a 6.05% grade that is 2,567 feet in length should be automatically rejected. On the other hand, a 6.79% grade that is 3,215 feet in length should be scrutinized more closely, including coordination with the LRV engineers, before being accepted. Very long hills that incorporate multiple segments with gradients at or near the maximums should also be carefully coordinated with the vehicle engineers. For example, inserting a short segment of 2.0% grade between two segments of 6% grade, each of which individually meets the maximum length criteria, does not necessarily mean that the vehicle won’t have issues—for example, the thermal capacity of the friction braking system. Engineering judgment, guided by an interdisciplinary systems approach and considering project and site-specific information, should govern, not arbitrary guidelines such as the figures cited in Table 3.3.1. On any gradient, tractive forces at the wheel/rail interface (including braking) will always tend to push the rail downhill. Maintaining ballasted track horizontal alignment at the foot of a steep grade is sometimes very difficult, particularly if there is a coincident sharp horizontal curve at that location. Because of this maintenance issue, a rigid trackform (direct fixation or embedded) is preferred for steeply graded tracks. Track designers should consider rigid trackforms for grades steeper than 6%, particularly if combined with sharp curvature and/or frequent hard braking. 3.3.2.2 Pocket Tracks Where pocket tracks are provided for the reversal of revenue service trains, track grades should preferably not exceed the values stipulated below for yard running tracks. Flatter grades are preferred for pocket tracks since they are often used as temporary storage points for unattended maintenance-of-way equipment and disabled light rail vehicles. 3.3.2.3 Main Tracks at Stations and Stops See Article 3.5.2 for discussion concerning track gradients at station platforms. 3.3.2.4 Yard and Secondary Tracks Yard sites are generally preferred to be level so that unattended vehicles cannot roll away. Topography often makes this impractical. In addition, modern transit cars, unlike railroad freight equipment, typically have brakes that are applied by spring action and can only be released by pneumatic or hydraulic pressure. So, as a practical matter, there is little chance that an LRV, parked in ready-for-service condition, might ever roll away. The same cannot be said about vehicles that are either in the shop or stored outside awaiting repair, since their braking systems may be ineffective. Similarly, maintenance-of-way equipment could potentially roll away if parked without hand brakes set. Yards and shop facilities sometimes employ a small locomotive or “car mover” to shift out-of-service vehicles from one track to another. Maximum track grades in the yard should be such that the locomotive’s available tractive effort is more than sufficient to move an AW0 light rail vehicle. Table 3.3.2 provides guidelines that can be used for yard track gradients:

Light Rail Transit Track Geometry 3-41 Table 3.3.2 Maximum and minimum yard track gradients Yard Running Tracks Desired 0.5% Acceptable Maximum 1.0% Absolute Maximum Maximum grade for towing or pushing disabled LRVs with the yard’s shifting equipment Yard Storage Tracks Desired 0.0% Acceptable Maximum 0.2% All tracks entering a yard should either be level, sloped downward away from the main line, or dished to prevent rail vehicles from rolling out of the yard onto the main line. For yard running tracks, a slight grade, usually about 0.5%, is recommended to achieve good track drainage at the subballast level. Through storage tracks generally have a sag in the middle of their profile to prevent rail vehicles from rolling to either end. Similarly, it is recommended that the profile grade of a stub end storage track descend toward the stub end and, if it is adjacent to a main line or secondary track, it should be horizontally curved away from that track at its stub end. If it is necessary for the profile grade of a storage track to slope up toward the stub end, the grade should not exceed 0.20%. Tracks located within maintenance shops and other buildings are generally level. However, so that storm water flows away from the building and not into the maintenance pits, it is customary for shop tracks to have a very slight upward slope (typically 0.5% or less) into the building up to the second column line of the building. This distance is typically about 20 to 25 feet [6 to 8 meters]. This gradient would continue across the apron driveway that typically runs around the shop building perimeter. 3.3.3 Vertical Curves All changes in grade are connected by vertical curves. Vertical curves are defined by parabolas having a constant rate of change in grade. Parabolic curves are, for all practical purposes, equivalent to circular curves for LRT design, but parabolic curves are easier to calculate and are thus preferable for this purpose. 3.3.3.1 Vertical Curve Lengths The minimum length of vertical curves can be determined as follows: • Desired Minimum Length: LVC = 200A [LVC = 60A] • Acceptable Minimum Length: LVC = 100A [LVC = 30A]

Track Design Handbook for Light Rail Transit, Second Edition 3-42 • Absolute Minimum Length: Crest Curves: ⎥⎥⎦ ⎤ ⎢⎢⎣ ⎡ == 215 2AV LVC 25 2AV LVC Sag Curves: ⎥⎥⎦ ⎤ ⎢⎢⎣ ⎡ == 387 2AV LVC 45 2AV LVC where LVC = length of vertical curve in feet [meters] A = (G2 – G1) algebraic difference in gradients connected by the vertical curve, in percent G1 = percent grade of approaching tangent G2 = percent grade of departing tangent V = design speed in mph [km/h] The numerical results from the formulas above are minimums. The designer should use longer vertical curves whenever possible. Both sag and crest vertical curves should have the maximum possible length, especially if approach and departure tangents are long. Vertical broken back curves and short horizontal curves at sags and crests should be avoided. 3.3.3.2 Vertical Curve Radius As noted in Chapter 2, vehicle manufacturers typically specify a product’s vertical capability in terms of either a radius or as a maximum angle that can be tolerated by the articulation joint. Since light rail vehicles are universally designed and built using S.I. dimensional units, these vertical radii are commonly specified in meters. Common figures stipulated by carbuilders (who universally use S.I. units of measurement) for high-floor LRVs for the minimum equivalent radius of curvature for vertical curves located in tangent track are 250 meters [820 feet] for crests and 350 meters [1150 feet] for sags. The track alignment designer must therefore evaluate whether a particular parabolic vertical curve meets the carbuilder’s criteria. This equivalent radius of curvature can be calculated from the following formula, which works in either U.S. traditional units or S.I. units: ( ) GG 0.01 LVCR 12 v −= where Rv = minimum radius of curvature of a vertical curve in either feet or meters and LVC in the same units Conversely, the following formula can be used to calculate the requisite vertical curve length given the vehicle manufacturer’s criteria for either crest or sag vertical curves. LVC = 0.01 (G2 – G1) Rv

Light Rail Transit Track Geometry 3-43 3.3.3.3 Vertical Curves in the Overhead Contact System The profile of the contact wire cannot precisely mimic a vertical curve in the track. Instead it is a series of chords with a slight vertical angle at each suspension point with a smoothing of severe trolley grade changes through hanger modifications. Minimum vertical curve length and/or design speed may be governed by the overhead contact system (OCS) due to the maximum permissible rate of separation or convergence between the track grade and the contact wire gradient. Coordination with the OCS designer is strongly recommended to ensure compliance with these limitations. 3.3.4 Vertical Curves—Special Conditions 3.3.4.1 Reverse Vertical Curves Reverse vertical curves are feasible, provided each curve conforms to the requirements stated in Article 3.3.3 and the restrictions imposed by the LRT vehicle design. 3.3.4.2 Combined Vertical and Horizontal Curvature Where possible, areas of combined vertical and horizontal curvature should be avoided. Where this is not possible, the track geometry should be as gentle as possible, preferably with neither parameter at or close to a minimum. When extremely constrained site conditions dictate, combined curves should generally not be more severe than an 82-foot [25-meter] radius horizontal combined with a 820-foot [250-meter] equivalent radius vertical crest curve. These parameters must be conformed to the vehicle design specifications. 3.4 TRACK ALIGNMENT AT SPECIAL TRACKWORK The track alignment must consider the requirements of the special trackwork layouts that will permit tracks to diverge, merge, and cross one another. Users of this Handbook should refer Chapter 6 for guidance on this issue. The track layout should be supportive of the operating plan, including the location of special trackwork units. In addition to the obvious special trackwork locations, such as junctions and terminal stations, the operating plan should identify locations where emergency crossover tracks are desired so as to facilitate non-scheduled “short turns” movements and temporary single track operations. When there is a reasonable expectation that an additional branch of the light rail system might be constructed in the future, and the location of the proposed junction can be predicted, it is good design practice to consider the geometric constraints of the future special trackwork in the initial project’s track design. Some projects have even included the construction of the junction needed for the future route in the starter project’s construction. By doing so, it is possible to avoid most of the service disruption that would ensue if the special trackwork installation was deferred. 3.5 STATION PLATFORM ALIGNMENT CONSIDERATIONS Many of the light rail projects constructed from the 1970s through the 1990s utilized high-floor rolling stock with steps at the doors. Various methods were devised so that riders with disabilities could bypass the steps when boarding and alighting from the trains. In general, those mitigation

Track Design Handbook for Light Rail Transit, Second Edition 3-44 measures restricted such passengers to using only one door per train. Use of these specially equipped doors also often required the intervention of the vehicle operator and usually increased station dwell time. However, as the incorporation of ADAAG requirements into projects has advanced, the trend has been toward a strategy of providing level or near-level boarding for all passengers at all doorways of the train. While this course has not been adopted as policy by federal regulatory agencies, it seems likely that level boarding at all doors could be the de facto standard for new start transit projects in the future. With that paradigm as foundation, this article will discuss several issues relative to track alignment at transit station platforms. 3.5.1 Horizontal Alignment of Station Platforms Tracks through light rail transit stations are preferably horizontally tangent so as to facilitate compliance with the ADAAG requirement for a horizontal gap not greater than 3 inches [75 mm] between the platform edge and the LRV doorway threshold. So as to minimize the chances that the dynamic envelope might intercept the platform, it is typically necessary to continue this tangent track beyond the end of the platform a minimum distance of one truck center distance plus the vehicle end overhang dimension. This dimension will naturally vary by the vehicle, but 45 feet [13.7 meters] is commonly seen as an absolute minimum in LRT design criteria. Longer dimensions are preferred so that the vehicle suspension system has more time to dampen any carbody roll or translation before the vehicle enters the constrained lateral clearances at the platform. Shorter dimensions are sometimes possible if the vehicle has a significant end taper. The following can be used as general design guidelines for two- and three-section LRVs up to about 90 feet [27.5 meters] long. Condition Minimum Tangent Length Desired Minimum 75 feet [25 meters] Acceptable Minimum 60 feet [20 meters] Absolute Minimum 45 feet [15 meters] For various institutional reasons, it may be necessary to place a station platform in a zone where it is impossible to generate a stretch of tangent track of the preferred length. In such cases, the following options are available: • The usable platform edge (as opposed to the overall length of platform that is available for passenger queuing) can be limited to the distance from the front edge of the leading door on the first LRV in the train to the back edge of the last door on the last car, plus a stopping tolerance distance. This method can typically shorten the overall length of tangent track required by 30 feet [10 meters] or more. This requires the LRV operator to be more precise about stopping the train so that all doors are on the platform. The platform itself could extend beyond this minimum length but barriers would be required to block access to trackside where the gap is greater than the ADAAG requirement. • The track through the platform can be placed on a very flat curve—typically no sharper than about 2000 feet [about 600 meters]. This method is often used in conjunction with “sacrificial” thresholds projecting beyond the nominal sides of the light rail vehicle so that any collision causes minimal damage to both the vehicle and the platform edge.

Light Rail Transit Track Geometry 3-45 Use of either of these methods requires close coordination with the project architects and vehicle engineers and should be considered for implementation only if extensive study has proven that a full length tangent platform is not possible. Note also that it could become a restriction on the doorway arrangement of any future vehicle procurements. Stations on sharper radius curves are possible only with gaps that exceed the ADAAG maximum dimension. Some sort of bridge plate would therefore be required to span the gap. This could either be a manually operated device or a device that is automatically deployed when the door opens. However, such arrangements are not recommended for general use. A manually operated device slows down transit operations while it is being deployed, used, and stowed. Further, when the device is not used, the gap will be greater than expected by all passengers and could lead to incidents. Automatically deployed bridge plates have been provided on some LRVs, but are not common. They increase vehicle cost, are still likely to add station dwell time, and complicate the door mechanisms. Doors are frequently one of the least reliable subsystems on any light rail vehicle, and vehicle engineers are understandably reluctant to make them any more complicated than they already are. Those perspectives may change as more experience is gained from current installations. 3.5.2 Vertical Alignment of Station Platforms Stations should be located on straight tangent grades with a low gradient whenever possible as this simplifies the design and installation of architectural finishes. The following guidance is suggested for track gradients at stations: • Desirable Minimum: 0.5% • Acceptable Minimum 0.0% • Acceptable Maximum 1.0% • Absolute Maximum: 2.0% If the track gradient through the station platforms is less than 0.5%, special design measures may be necessary to be certain that the trackway drains. Even if the station is nominally under cover, as it would be in a subway, water will end up on the trackway due to wash water from station janitorial work, precipitation that drips off of the LRVs, and uncontrolled tunnel leakage. In rigid trackforms, vertical curves can begin immediately beyond the ends of the platform. In ballasted track, the point of vertical curvature should usually be some distance beyond the end of the platform so that any track-surfacing maintenance operations beyond the station can more easily be feathered into the station track profile without affecting the vertical relationship between the platform and the vehicle floor. When the LRT station is located in a street right-of-way in urban areas, the existing roadway profile will usually govern the profile grade within the station. Sometimes a key station location will fall in a location where the track grade is more severe than the criteria above. While LRT stations have been constructed on gradients as steep as 5%, those installations predate the Americans with Disabilities Act. This creates a potential issue concerning compliance with the ADAAG. While ADAAG permits ramps with gradients up to 8%, they must be periodically interrupted by a landing where persons with disabilities can rest. Such landings are obviously

Track Design Handbook for Light Rail Transit, Second Edition 3-46 inconsistent with a platform that follows the track grade. In addition, ADAAG stipulates that paths used by persons using mobility assistance devices such as walkers and wheelchairs should not have a cross slope greater than 2%. A wheelchair sitting facing a track that is on a grade in excess of 2% would hence be a violation of ADAAG. As a result, as of 2010, there is no clear method of having station track grades in excess of 2%. Projects that potentially require stations in constrained urban locations where existing street grades are steeper than 2% will need to work closely with ADA advocacy groups and agencies having jurisdiction to determine if a station is even going to be possible. Such coordination efforts, including documentation of any concessions achieved, should occur as early as possible in the project development process. While stations are preferably located on straight track gradients, they can and have been constructed on vertical curves as sharp as 2.5% per 100 feet [2.5% per 30 meters]. The platform profile at trackside must be carefully defined so that the vertical step from the platform to the vehicle threshold is within ADAAG criteria. As noted in Chapter 2, it is preferred that passengers have a very slight step downward when exiting the vehicle. Stations on aerial structures have an additional consideration. If the platform and the track are supported on independent superstructures, their live load deflections could differ substantially. For example, an LRV loaded to AW3 pulling up to an unoccupied platform could, because of the deflection of the superstructure supporting the track, be at a substantially different elevation than the platform, potentially leading to an ADAAG compliance issue. This has occurred on projects where the structure supporting the track was prepared by a different design team than the structure supporting the station. There is nothing the track designer can do about this directly; however, in his/her role as an ad hoc coordinator between disciplines (in this case, the structural engineers and the architects), the track designer can highlight the issue and possibly eliminate a potentially embarrassing issue for the entire design team. 3.6 YARD LAYOUT CONSIDERATIONS Rail transit yards are very often constructed on oddly-shaped and constrained sites with the result that the track geometrics are unusually complex. The operating plan will typically dictate a routine flow of traffic through the yard, and the track alignment should accommodate this, preferably without requiring reversing movements. For example, there is usually a preferred sequence for what happens when a train comes in off the revenue service route until it is parked in the yard. This sequence could be relatively simple or fairly complex depending on the size and needs of the transit system and when particular daily maintenance activities are performed. The following are the steps for one LRT yard in the northeastern United States: • The train comes off the revenue service line and proceeds to a cash-handling facility where the fareboxes are emptied. • The train is advanced to a holding yard where the revenue service operator parks the train. • A yard hostler picks up the train and runs it through a daily inspection bay in the shop. In addition to inspection of basic issues such as the condition of the wear strip on the pantograph and refilling traction sand boxes, the interior of the car is vacuumed. If necessary or scheduled, the exterior of the car is then washed.

Light Rail Transit Track Geometry 3-47 • The hostler moves the car to the main storage yard and proceeds back to the holding yard to pick up another train. In this case, the yard layout was configured so that all of the activities above could occur while the trains followed a continuous path through the yard, without requiring the hostler to change ends in the vehicle. Other yards will have different sequences depending on the specifics of their operations and maintenance plan. For example, LRT systems located in temperate climates often do car interior cleaning in the main storage yard, after the train has been parked, with the car cleaners carrying their equipment on the equivalent of a golf cart. That methodology requires a different track layout than the example described above, including making the aisles between tracks sufficiently wide to accommodate the golf carts. If the yard will also be a base for the system’s maintenance-of-way (M/W) department, additional tracks will be required for the storage of on-track equipment such as tampers, ballast regulators, overhead line maintenance vehicles, etc. Off-track space should also be provided for the parking of rubber-tired maintenance vehicles, including hy-rail trucks. A location should be provided where hy-rail equipment can get on and off the track. Ideally, the M/W base should have access to the revenue service route without interrupting other yard operations. Yard layouts can be challenging for the OCS engineer as well as the track engineer because they require consideration of not only the layout of the tracks but also the yard roadway system. The various design disciplines must closely coordinate so as to make certain there are sufficient locations between tracks and also between tracks and roadways so that OCS poles can be installed without requiring special structures. Because yards are on constrained sites, it is usually necessary to use small turnout sizes. Number 6 turnouts are common in transit yards, and Number 5 and even Number 4 turnouts are not uncommon. Frogs with curved frogs (which technically have no “number”) can often be used to good advantage to configure tracks in a tight area; however, it is recommended to avoid special designs unless the overall layout of the yard requires many of them. Since turnouts are involved in a high percentage of derailments, flatter turnouts are always preferred, and it is generally good practice to avoid turnouts with radii that match the minimum curving capability of the vehicle. The track layout and the layout of the yard’s roadway circulation system need to be closely coordinated, and the track alignment engineer is therefore often charged with designing both. The number of track/roadway crossings obviously should be limited, but site constraints make them inevitable. Closely spaced crossings should generally be avoided. The minimum distance between two crossings of the same track should ideally be larger than the longest train so that roadways are not routinely blocked. It is also highly desirable that any roadways within the yard that are routinely used by persons other than transit agency employees (such as outside vendor’s delivery trucks) should cross as few tracks as possible and preferably none. One feature that is very useful in a transit yard is a long stretch of embedded track without OCS. This would become the location where new light rail vehicles can be offloaded from a lowboy tractor trailer. The roadway system should be configured so that these oversized load trucks can

Track Design Handbook for Light Rail Transit, Second Edition 3-48 access the embedded track, offload the LRV, and then exit the site, preferably without requiring long backup movements. With delivery of LRVs, the truck leaves the yard complex usually after the teamster has compressed the stretched trailer down to an ordinary legal length. However, the reverse situation also occurs—LRV’s being loaded onto a trailer and heading off site, perhaps for a mid-life rebuild at a manufacturer’s facility. Accordingly, the roadway system to and from the unloading track should be as flexible as possible. Additional discussion relative to yard and shop trackwork can be found in Chapters 4, 5, and 6. 3.7 JOINT LRT-RAILROAD/FREIGHT TRACKS Railroad tracks to be relocated or in joint usage areas are designed in conformance with the requirements of the operating railroad and the AREMA Manual for Railway Engineering, except as recommended herein. As a guideline, recommended criteria are given below. 3.7.1 Joint Freight/LRT Horizontal Alignment The horizontal alignment for joint LRT-railroad/freight tracks consists of tangents, circular curves, and spiral transitions based on the preferred maximum LRV design speed and the required FRA freight class of railroad operation. The track designer will frequently need to consult several criteria documents so as to determine the most restrictive requirements for any given parameter. These would include • The AREMA Manual for Railway Engineering and Portfolio of Trackwork Plans. • The standard plans and design standards of the freight railroad operator. • The design criteria, standard drawings, and directive drawings for the LRT project. As noted previously, railroads usually insist on the use of chord definition for curves and will likely require that for any tracks they will maintain. In addition, it can be expected that freight railroads in the United States will insist that tracks intended for their exclusive use be designed using U.S. traditional units of measurement. References to S.I. units in the text that follows are therefore merely for convenience of reference and metric equivalents have been omitted from the formulae. The alignment of tracks used by freight trains should preferably be designed for use at not less than 25 mph [40 km/h], which is the FRA maximum freight speed for Class 2 track. When this is not possible, yard track alignment should be designed for an acceptable minimum of 15 mph [25 km/h]. Lead track and industrial sidetracks should be designed for an absolute minimum of 10 mph [15 km/h]. Curves adjacent to turnouts on tracks that diverge from the main track should ordinarily be designed to be no less than the maximum allowable speeds of the adjoining turnouts. If the existing freight trains in the corridor operate at speeds higher than the above, or could be operated at higher speeds if the physical condition of the tracks was better, it can be reasonably expected that the freight operator will require that existing (or potentially possible) velocities be maintained.

Light Rail Transit Track Geometry 3-49 3.7.2 Joint Freight/LRT Tangent Alignment For joint LRT-railroad/freight main tracks, the desired tangent length between curves should comply with the freight railroad’s standards. A desired minimum of 300 feet [90 meters], with an absolute minimum of 100 feet [30 meters], can be used in the absence of more specific guidance. For lead tracks and industrial spurs, a minimum tangent distance of either 60 feet [18 meters] or the longest car using the track should be provided between curve points. All turnouts should be located on tangents. In general, nothing smaller than a No. 8 turnout should be used unless it is a replacement-in-kind for an existing turnout. No. 10 or larger turnouts are preferred. See Article 3.7.4 for additional discussion concerning turnouts used by freight traffic. 3.7.3 Joint Freight/LRT Curved Alignment The desired maximum degree of curvature (chord definition) for railroad main line tracks should be either 3 degrees [R = 1910.08 feet/582.193 meters] or the maximum presently in use along the route. As general guidance, main line curves should not exceed 9° 30’ [R = 603.80 feet/184.038 meters]. See Article 3.2.3.1 for additional discussion concerning degree of curve as it relates to railroad work. Chord definition should only be used for tracks that will be owned and maintained by the railroad company and then only if they insist upon it. The maximum curvature for lead tracks and industrial sidetracks should be 12°00’ [R = 478.34 feet /145.798 meters]. Larger radii may be appropriate in cases where long freight cars (such as intermodal container cars) use the track. In extreme cases, revisions to existing industrial sidetracks may be designed with curve radii that match the existing values. Exceptions to the above criteria may be permitted as authorized by both the transit authority and the operating freight railroad. The minimum length of circular curves for main line freight tracks should be 100 feet [30 meters]. Spiral lengths should be as discussed in Article 3.7.6. 3.7.4 Selection of Special Trackwork for Joint Freight/LRT Tracks Special trackwork in tracks used by freight trains should comply with the standards of the entity that will be responsible for the maintenance of each particular specialwork unit. The reason for this is to simplify maintenance inventory. In joint use tracks, it is typically the transit agency, not the railroad, that will be maintaining the turnouts and hence stocking the spare parts. Conversely, turnouts in freight-only track will typically be maintained by the railroad. On one shared track LRT project, the freight operator had long before adopted odd-numbered turnouts (e.g., No. 7, No. 9, and No. 11) as their standards. Meanwhile, the LRT system’s turnout standards were even numbered (e.g., No. 6, No. 8, and No. 10). The shared main track included several turnouts that led to industries. The track alignment designer used odd-numbered turnouts at these locations even though the transit agency would be maintaining them. The transit agency not only had no spare parts for turnouts of those sizes, they didn’t even use the same rail section as the freight operator. Hence, the transit authority maintenance department needed to begin

Track Design Handbook for Light Rail Transit, Second Edition 3-50 stocking spare parts for non-standard turnouts even though their LRVs operated over only the straight side of the turnout. Since the freight trains could have easily operated through No. 10 turnouts built using the LRT standard rail section, those maintenance issues could have been avoided by simply using the LRT design at the freight sidetracks. 3.7.5 Superelevation for Joint Freight/LRT Tracks Superelevation in shared tracks and freight-only tracks should be provided on main line and secondary line tracks only, based on a maximum of 1 ½ inches [38 mm] of unbalance at the freight design operating speed. It will typically be necessary to limit maximum Ea to a range of 3 to 4 inches [75 to 100 mm] depending on the standards of the freight railroad involved. The following assumptions: • Maximum Ea = 3 inches • Maximum Eu = 1 ½ inches • No Ea until Eu has reached ½ inch result in this equation for determining the preferred value of Ea for the freight speed: 0.38 R Vf 1.98E 2 a −⎟⎟⎠ ⎞ ⎜⎜⎝ ⎛= where Ea = actual superelevation in inches Vf = curve design speed for freight traffic in mph R = radius of curve in feet As discussed earlier, the calculated values of Ea should be rounded up to the next ¼ inch increment. [Use 5 mm increments when working in S.I. units.] There sometimes will be a wide divergence between the operating speeds for freight trains versus LRVs. The freight operating speed may also not be consistent, as in cases where freight trains may occasionally be operating slowly in a curve while shifting a nearby industrial sidetrack. A freight speed of 10 mph [16 km/h] would not be unusual under such circumstances. Meanwhile, the LRT operating speed at the same location might be 55 mph [89 km/h]. This may require some compromises, restricting Ea to what the railroad can tolerate and increasing Eu for the LRT to values greater than the customary maximum. Determination of the appropriate spiral length based on all factors is very important. 3.7.6 Spiral Transitions for Joint Freight/LRT Tracks Spiral transition curves are generally used for railroad/freight main line and secondary line tracks only. Low-speed yard and secondary tracks without superelevation generally do not require spirals. Spirals should be provided on all curves where the superelevation required for the design speed is ½ inch [12 mm].

Light Rail Transit Track Geometry 3-51 As a guideline, the minimum length of a spiral in freight-only railroad track and joint use freight railroad and LRT track can be determined from the following formulae, rounded off to the next meter (or 5 feet), but preferably not less than 18 meters (60 feet). Ls = 62 Ea [Ls = 0.75 Ea] (same as AREMA and the desired formula for LRT use) Ls = 3.26 Eu V [Ls = 0.018 Eu V] (This is based on Eu maximum = 1 ½ inches versus 3 inches in the equivalent AREMA formula.) Ls = 1.03 Ea V [Ls = 0.0076 Ea V] (same as the desired formula for LRT use) where Ls = minimum length of spiral in feet [meters] Ea = actual superelevation in inches [mm] Eu = unbalanced superelevation in inches [mm] V = curve design speed in mph [km/h] In the case of tracks shared by LRT and freight traffic, the spiral length values calculated from the formulae above must then be compared against the values calculated for the same curves at the proposed LRT speed. The longest dimension will govern. 3.7.7 Vertical Alignment of Joint Freight/LRT Tracks 3.7.7.1 General The profile grade is defined as the elevation of the top of the low rail. Vertical curves should be defined by parabolic curves having a constant rate of grade change. 3.7.7.2 Vertical Tangents The absolute minimum length of vertical tangents in joint use track is 100 feet [30 meters]. Turnouts should be located only on tangent grades. 3.7.7.3 Vertical Grades On main line tracks, the desired maximum grade should be 1.0%. This value may only be exceeded in cases where the existing longitudinal grade is steeper than 1.0%. Grades within horizontal curves are generally compensated (reduced) at a rate of 0.04% per horizontal degree of curvature. Locations where freight trains may frequently stop and start are compensated at a rate of 0.05% per degree of curvature. This compensation reduces the maximum grade in areas of curvature to reflect the additional tractive effort required to pull the train. For yard tracks and portions of industrial sidetracks where cars are stored, the grades should preferably be 0.20% or less, but should not exceed 0.40%. Running portions of industrial sidetracks should have a maximum grade of 2.5%, except that steeper grades may be required to match existing tracks. Grade compensation is usually not required in railroad yard and industrial tracks.

Track Design Handbook for Light Rail Transit, Second Edition 3-52 3.7.7.4 Vertical Curves Vertical curves shall be provided at all intersections of vertical tangent grades. Length of vertical curves for freight operation should comply with the AREMA Manual for Railway Engineering, Chapter 5, Section 3.6. Because of issues associated with the safe operation of freight trains, the AREMA requirements will always result in longer vertical curves than those indicated in article 3.3.4 of this Chapter. If an existing railroad vertical curve is below the length calculated in accordance with AREMA criteria, a replacement vertical curve with a rate of change of grade not exceeding that of the existing curve may be acceptable at the discretion of the freight railroad. 3.8 VEHICLE CLEARANCES AND TRACK CENTERS This article discusses the minimum dimensions that must be established to provide minimum clearances between light rail vehicles and adjoining structures or other obstructions and to establish a procedure for determining minimum track center distances. The provision of adequate clearances for the safe passage of vehicles is a fundamental concern in the design of transit facilities. Careful determination of clearance envelopes and enforcement of the resulting minimum clearance requirements during design and construction are essential to proper operations and safety. The following discussion concentrates on the establishment of new vehicle clearance envelopes and minimum track centers. On existing LRT systems, this is normally established in the initial design criteria or by conditions in the initial sections of the transit system. 3.8.1 Track Clearance Envelope The track clearance envelope (TCE) is defined as the space occupied by the maximum vehicle dynamic envelope (VDE) as defined in Chapter 2, Article 2.3, plus effects due to curvature and superelevation, construction and maintenance tolerances of the track structure, construction tolerances of adjacent wayside structures, and running clearances. The relationship between the vehicle and clearance envelopes can thus be expressed as follows:[14] TCE = VDE + TT + C&S + RC where TCE = track clearance envelope VDE = vehicle dynamic envelope TT = trackwork construction and maintenance tolerances C&S = vehicle curve and superelevation effects RC = vehicle running clearance The clearance envelope represents the space into which no physical part of the transit system, other than the vehicle itself, should be placed, constructed, or allowed to protrude. A second part of the clearance equation is what is termed structure gauge, which is basically the minimum distance between the centerline of track and a specific point on the structure.

Light Rail Transit Track Geometry 3-53 Although structure gauge and track clearance envelope elements are often combined, it is not advisable to construct a track clearance envelope that includes wayside structure clearances and tolerances, as the required horizontal or vertical clearances for different structures may vary significantly. The factors used to develop the clearance envelope are discussed in further detail in the following sections. It should be noted that in some LRT designs, some of the factors listed above are combined; for example, trackwork construction and maintenance tolerances are frequently included in the calculation of the vehicle dynamic envelope.[2] Regardless of how the individual factors are defined, it is important that all of these items are included in the determination of the overall clearance envelope. 3.8.1.1 Vehicle Dynamic Envelope Determination of the VDE is discussed in Chapter 2, Article 2.3 as it is typically the responsibility of a project’s vehicle design team. 3.8.1.2 Track Construction and Maintenance Tolerances Track construction and maintenance tolerances should be included in the determination of the track clearance envelope, preferably as a separate item outside of the VDE. This separate consideration is because these track factors will vary depending on the trackform. The track maintenance tolerances are generally far greater than the initial construction tolerances and thus take precedence for the purpose of determining clearances. It should also be noted that embedded, direct fixation, and ballasted trackwork have different track maintenance tolerances. It is possible to determine separate clearance envelopes for ballasted and direct fixation track or to use the more conservative clearance envelope based on the ballasted trackwork case. Both options have been used in actual practice; however, using a ballasted track clearance envelope for track in a subway could appreciably increase the interior size and hence the cost of the tunnel structure. Trackwork-based factors to be considered in the development of the clearance envelope, with typical values, include the following: • Lateral rail wear: ½ inch [13 mm] • Lateral track alignment maintenance tolerance: − Direct fixation and embedded track: ½ inch [13 mm] − Ballasted track: 1 inch [25 mm] (Consider larger values for very sharp curves where thermal forces may tend to cause the rail to “breathe” in and out with temperature.) • Vertical maintenance tolerance: − Rail wear: ½ inch [13 mm] − Ballasted track settlement/raise: –1 inch / +2 inch [-25 mm / +50 mm] − Embedded or direct fixation track slab settlement/heave: As per geotechnical design recommendations.

Track Design Handbook for Light Rail Transit, Second Edition 3-54 • Crosslevel variance, direct fixation and embedded track: ½ inch [13 mm] (Largely due to possible temporary differences in rail elevation during future rail changeouts, where one rail might be worn and the other rail new, but also to account for possible differential settlement or heave across the track section.) • Crosslevel variance, ballasted track: 1 inch [25 mm] Crosslevel variance creates a condition of vehicle rotation rather than lateral shift. Effects on the clearance envelope are similar to the superelevation effects noted below. It must be understood that the extreme values suggested above are only for the purposes of determining a track clearance envelope. They are hypothetical worst-case conditions and do not represent thresholds for acceptable maintenance. Similarly, they have nothing to do with the tolerances to be used for construction of new track. 3.8.1.3 Curvature and Superelevation Effects In addition to the VDE and track maintenance factors, track curvature and superelevation have a significant effect on the determination of the clearance envelope. These effects will be covered separately. Some authorities consider the effects of curvature and superelevation as part of the VDE and calculate separate VDE diagrams for each combination of curvature and superelevation. As a guideline, this Handbook considers only one VDE and determines curvature and superelevation effects separately to establish multiple clearance envelopes. 3.8.1.3.1 Curvature Effects In addition to the dynamic carbody movements described above, carbody overhang on horizontal curves also increases the lateral displacement of the VDE relative to the track centerline. For design purposes, both mid-car inswing (mid-ordinate) and end-of-car outswing (end overhang) of the vehicle must be considered. While AREMA Chapter 28 includes formulae and tabulated data on clearances, these are generally inapplicable to rail transit vehicles and guideways. The amount of mid-car inswing and end-of-car outswing depends primarily on the vehicle truck spacing, vehicle end overhang, and track curve radius. The truck axle spacing also has an effect on clearances, although it is relatively small and frequently ignored.[6] Low-floor LRVs with articulation joints that are not centered on the trucks can also measurably shift the position of the end overhang. Collectively, the inswing and outswing and the vehicle’s lateral dynamic movements define the edges of what is commonly called the “swept path” of the vehicle. Refer to Chapter 2, Article 2.3.3 for discussion of the vehicle dynamic outline. To determine the amount of vehicle inswing and outswing for a given curve radius, one of two formulas is generally used, depending on whether the vehicle axle spacing is known. Both methods are sufficiently accurate for general clearance envelope determinations for LRT vehicles. Figure 3.8.1 illustrates the basic concepts on a hypothetical double-truck rigid car. If truck axle spacing effects are ignored, the effects of vehicle inswing and outswing are determined from the

Light Rail Transit Track Geometry 3-55 assumption that the vehicle truck centers are located at the center of track. In this case, the vehicle inswing and outswing can be found from the following equation: 2R 2L1-sin=a wherea) cosR(1oMInswing where Mo = mid-ordinate of vehicle chord R = track curve radius L2 = vehicle truck spacing oMR L1tanb and b cos L oR whereRoROutswing where R = track curve radius L = half of overall vehicle length Figure 3.8.1 Horizontal curve effects on vehicle lateral clearance In determining the outswing of the vehicle, it must be noted that some vehicles have tapered ends and that the outer edge of their swept path will be based on whichever is the worst-case: the vehicle width at the anticlimber or bumper or the full vehicle width at the beginning of the taper. Exterior mirrors on the LRV will often govern outswing, but only at the elevation of the mirror. Hence, the mirror may govern clearances to a wall, but not necessarily to features lower than the mirror. Vehicles that use small cameras as opposed to mirrors will have less impact on outswing

Track Design Handbook for Light Rail Transit, Second Edition 3-56 clearance. However, some such vehicles have multiple cameras at strategic points along the side of the vehicle, and one of those might govern inswing at the camera elevation. When calculating the swept path for horizontal curves with spirals, the tangent clearance envelope will end at some distance ahead of the track tangent-to-spiral (TS) point. The full curvature clearances will similarly begin some distance ahead of the spiral-to-curve point. For an ordinary articulated LRV with two main body sections, these locations can be spotted at one-half the length of the vehicle ahead of the point in question. Typically, this will be about 45 feet [13.7 meters] ahead of the TS and the SC. Between those points, the offsets to the edges of the swept path can be interpolated with sufficient accuracy for most clearance purposes. Similar approximations can be made on simple curves. Where more precise information is required, CADD software makes it relatively easy to graphically determine the edges of the swept path at any location. The clearance envelope (CE) through turnouts is calculated based on the centerline radius of the turnout. It is of interest to note that the vehicle designer does not always provide the calculations for the effects of horizontal curvature clearance. This task is frequently left to the trackwork or civil alignment engineer. 3.8.1.3.2 Superelevation Effects Superelevation effects on the swept path are limited to the vehicle lean induced by a specific difference in elevation between the two rails of the track and should be considered independently of other effects. In determining the effects of superelevation, the shape of the VDE is not altered, but is rotated about the centerline of the top of the low rail of the track for an amount equal to the actual track superelevation. This rotation is illustrated in Figure 3.8.2. For any given coordinate on the VDE, the equations indicated in Figure 3.8.1 are sufficiently accurate to convert the original VDE coordinate (xT,yT) into a revised clearance coordinate (x2, y2) to account for superelevation effects. Collectively, the effects of all of the factors considered above define the swept path. For convenience, this clearance information is then typically tabulated giving the values of vehicle outswing and inswing for various curve radii and increments of superelevation. Figure 3.8.3 is a typical example. 3.8.1.4 Vehicle Running Clearance The clearance envelope must include a minimum allowance for running clearance between the vehicle and adjacent obstructions or vehicles. Running clearance is generally measured horizontally (laterally) to the obstruction, although some clearance envelopes are developed with the running clearance added around the entire perimeter of the vehicle. The most common minimum value assigned to running clearances is 2 inches [50 mm]. Station platforms are an exception since, per ADAAG, their offset is defined to the static vehicle. Some items are occasionally assigned a higher minimum running clearance. These include structural members and adjacent vehicles. A typical assignment of running clearance criteria includes the following data:

Light Rail Transit Track Geometry 3-57 Minimum running clearance to signals, signs, platform doors, and other non-structural members: 2 inches [50 mm]. Minimum running clearance to an emergency walkway envelope: 2 inches [50 mm]. (See note below.) Minimum running clearance along an aerial deck parapet, walls, fences, and all structural members, including OCS poles: 6 inches [150 mm]. Note that if a close clearance to a parapet, wall, or fence exists on one side of the track, it is essential that space for personnel to take refuge must be provided on the opposite side. Minimum running clearance to adjacent LRT vehicles: 6 inches [150 mm]. Emergency egress safety walkways are located outside of the vehicle clearance envelope. The actual dimensions of the safety walkways are effectively set by NFPA 130, Standard for Fixed Guideway Transit and Passenger Rail Systems.[15] As of 2010, NFPA has increased the recommended sizes of egress paths compared to earlier standards. While dimensions of existing installations may be “grandfathered,” transit line extensions and new construction will typically be required to meet the latest standard. Before setting track locations relative to existing structures or setting structure locations relative to new or existing tracks, track designers are advised to work closely with project safety specialists who are thoroughly familiar with the current NFPA 130 requirements. Figure 3.8.2 Dynamic vehicle outline superelevation effect on vertical clearances

Track Design Handbook for Light Rail Transit, Second Edition 85-3 Figure 3.8.3 Typical tabulation of dynamic vehicle outswing for given values of curve radius and superelevation

Light Rail Transit Track Geometry 3-59 3.8.2 Structure Gauge The second part of the clearance equation is what is termed structure gauge, which is basically the minimum distance between the centerline of track and a specific point on the structure. This is determined from the TCE above, plus structure tolerances and minimum clearances to structures. Thus: SG = CE + SC + ST + AA where SG = structure gauge CE = clearance envelope SC = required clearance to wayside structure ST = wayside structure construction tolerance AA = acoustic allowance The required clearance to wayside structures may be specified separately from the running clearance described above. In other words, the running clearance envelope is stated as a constant value, such as 6 inches, and a separate, additional, required clearance criterion is specified for each type of wayside structure. Construction tolerances for wayside structures include the construction tolerances associated with wayside structural elements such as walls, catenary poles, and signal equipment. A minimum construction tolerance for large structural elements is normally 2 inches [50 mm]. A larger construction tolerance may be necessary for some types of retaining walls, such as secant pipe walls and soldier pile and lagging walls. It is generally not necessary to include a maintenance tolerance for wayside structures since, unlike track, such items generally are not subject to either wear or post-construction misalignment. Another item that must be considered is an allowance for chorded construction of tunnel walls, large precast aerial structure sections, and walkways. In lieu of exact construction information, general guidelines that can be used as a basis for design are 50-foot [15-meter] chords for curve radii greater than 2500 feet [750 meters] and 25-foot [7.5-meter] chords for smaller radius curves. See Figure 3.8.4 for a typical chart of supplemental clearance requirements for chorded construction. Finally, provisions for present or future acoustical treatments are often required on walls and other structures. Typical values for this range from 2 to 3 inches [50 to 75 mm]. 3.8.3 Station Platforms Station platforms require special clearance considerations because of ADAAG regulations. See Chapter 2 for discussion on this topic. 3.8.4 Vertical Clearances Vertical clearances are typically set by the collective requirements of the minimum operating height of the vehicle pantograph and the depth of the catenary system. Catenary depth, as discussed in Chapter 11, is the distance from the bottom of the contact wire up to the top of the

Track Design Handbook for Light Rail Transit, Second Edition 3-60 Figure 3.8.4 Additional clearance for chorded construction

Light Rail Transit Track Geometry 3-61 support system, plus any required electrical clearances between those supports and adjoining structures. In ballasted track areas, it is desirable to set vertical clearances to accommodate future track surfacing. Allowances of 4 to 6 inches [100 to 150 mm] are customary. However, the OCS designer will usually want to maximize the depth of the catenary system and he/she and the vehicle engineer will want to maximize the operating height of the pantograph. Therefore, the track engineer may need to defend the track-surfacing allowance from being appropriated by the other disciplines. Extremely close clearance situations may require using a rigid trackform (e.g., either direct fixation or embedded) or having the authority’s maintenance organization commit to track undercutting whenever track surfacing becomes necessary. The design report for the project should specifically address these issues so the project owner understands the options considered and the commitments made. Because of electrical codes and railroad standards, vertical clearances in shared track areas are far more restrictive than for LRT-only track. Close coordination is required with the OCS designer when setting track profiles in shared track that passes beneath other structures. 3.8.5 Track Spacings 3.8.5.1 Track Centers and Fouling Points The minimum allowable spacing between tracks and the location of fouling points is determined using the same principles as those used for determining clearances to structures. Referring to the previous discussion on clearances, minimum track centers can be determined from the following equation if catenary poles are not located between tracks: TC = Tt + Ta + 2(OWF) + RC where TC = minimum track centers Tt = half of vehicle CE toward curve center Ta = half of vehicle CE away from curve center RC = running clearance OWF = other wayside factors (see structure gauge) Where catenary poles are located between tracks, the minimum track centers are determined from the following: TC = Tt + Ta + 2(OWF + RC) + P where TC = minimum track centers Tt = half of vehicle CE toward curve center Ta = half of vehicle CE away from curve center

Track Design Handbook for Light Rail Transit, Second Edition 3-62 RC = running clearance OWF = other wayside factors (see structure gauge) P = maximum allowable catenary pole diameter Where the LRT track is designed for joint usage with freight railroads, the clearances mandated by the operating freight railroad and/or state regulatory agencies will prevail. Because railroad employees will occasionally be riding on the side of moving equipment, lateral clearances from the track are usually much greater than for LRT-only tracks. A typical minimum clearance from tangent freight track to any obstruction (such as a catenary pole or signal) is 8’6” [2590 mm]. Some state regulations require even more. The AREMA Manual for Railway Engineering, Chapter 28, contains useful information on general freight railway clearances, but the individual railroads often have specific clearance requirements that will supersede the AREMA recommendations. 3.8.5.2 Track Centers at Pocket Tracks Where a pocket track is placed between two main tracks, it is often necessary to provide space for a walkway between the pocket track and one or both of the main tracks. This is because the train operator needs to be able to walk from one end of the train to the other before he/she can run the train in the opposite direction, but LRVs are not typically equipped with end doors that allow direct movement between cars. The walkway typically should not be less than 3 feet (1 meter) wide and should be clear of the swept path on the main track and the static vehicle on the pocket track. 3.8.5.3 Track Centers at Special Trackwork The track alignment designer must carefully consider the track center distances at any special trackwork layout to make certain the special trackwork can be constructed in accordance with accepted design principles. One such principle is guarding of open frog points. Double crossover tracks are particularly problematic in this regard since the end frogs of the crossing diamond are generally close to being opposite two of the turnout frogs. For standard gauge track, if the track centers are at or close to 14’-0” [4.267 meters], the open throats of the frogs will be virtually opposite each other, making it impossible to guard either point. Unfortunately, 14’-0” is a popular standard track center distance, and this issue has come up on several projects. To mitigate this problem, track centers at double crossovers should be either less than 13’-6” [4.1 meters] or greater than 14’-6” [4.4 meters]. As a general recommendation, whenever a track alignment designer is preparing an area including complex special trackwork, it is strongly recommended that the alignment work and the preliminary trackwork design be done concurrently so that potential problems and issues can be identified before the alignment design is finalized. Doing so will minimize the chance that the alignment might need to be rescinded and revised after it had already been issued to other project design disciplines.

Light Rail Transit Track Geometry 3-63 3.9 SHARED CORRIDORS Where LRT shares a right-of-way (but not tracks) with a freight railroad, the track alignment designer must carefully consider a number of factors when setting horizontal and vertical alignment. These include the following: • Regulatory Environment: The Federal Railroad Administration generally does not exercise any jurisdiction over rail transit tracks and operations. Exceptions include the obvious case of shared tracks and any tracks that are within 30 feet [9.15 meters] of a track that is part of the national railroad system of transportation. The recordkeeping work of the LRT maintenance-of-way organization could therefore be simplified if the LRT tracks are at least 30 feet [9.15 meters] from the freight tracks. • Crash Walls: Many freight railroads will insist on a crashwall between their tracks and the transit line if the track-to-track distance is 25 feet [8.7 meters] or less, that requirement being loosely based on AREMA’s recommendations concerning crashwalls to protect overhead bridge piers. Notably, the crashwall itself could take a substantial amount of right-of-way width. The issue can sometimes be completely avoided by spacing the tracks no closer than about 26 feet [7.9 meters]. However, some freight railroads have demanded crashwalls even when the separation distance is much greater than 25 feet. • Ownership of the Right-of-Way: The quality of the title of the real estate occupied by the LRT tracks may be a factor in whether the railroad company can dictate issues concerning the location of the LRT track. If the transit authority purchased property from the railroad, there may be terms in the sales agreement that dictate how the property can be used, including factors related to track location. In some cases, more than one railroad company may use a set of tracks. Depending on the language in legal agreements between the various parties, it may be necessary to meet the minimum standards of both railroads. • Differences in Track Profile: If the LRT track is at a substantially higher profile than the freight track, but relatively close horizontally, it may be necessary to have retaining walls to support the LRT trackbed, adding substantially to the cost of the LRT construction. On the other hand, some projects prefer to have the transit facility several feet higher than the freight railroad so that, in the event of a freight derailment, railroad equipment is less likely to end up on the transit guideway. The freight railroad may dictate the clearances between the face of the wall and their track. • Drainage: Both the transit guideway and the freight railroad trackbed will require drainage. Railroads generally dislike closed drainage systems (e.g., underdrains) because they know that such concealed systems have a higher probability of becoming dysfunctional because of neglected maintenance. Hence, the railroad will usually want to have their trackbed drained via open ditches. At the same time, they will not want their ditches used to drain property outside of their right-of-way, including the transitway. Hence, it may be necessary to have two parallel drainage systems—one for the transit line and another for the railroad, particularly if the track profiles are substantially different. • Right-of-Way Fencing: For various reasons, it may be desirable or necessary to install a fence between the freight railroad and the transit line. There needs to be sufficient space

Track Design Handbook for Light Rail Transit, Second Edition 3-64 to install the fence without interfering with either the position or maintenance of other structures, such as drainage systems, train control system signals and bungalows, etc. The fencing will need to be far enough away from each track so as to not interfere with track maintenance activities. Emergency evacuation of the LRVs could be an issue. The freight rail operator may also need safe walking space alongside of the track for train crew members, particularly in switching yards. • Maintenance Issues: Maintenance-of-way personnel for both the transit agency and the freight railroad need to have access to locations along the guideway and sufficient room to perform their work once they get there. The preferred means of access is an “off-track driveway” usable by maintenance-of-way trucks. In addition, in order to more easily comply with FRA requirements for the safety of their maintenance employees with minimal impact on maintenance productivity, the railroads prefer to have no more than two tracks closely spaced at their standard track center dimension. Looking at the complete cross section of the railroad and transit rights-of-way, this might force the placement of an off-track drive between the two. It may require far more right-of-way to collectively address the issues noted above than might be apparent at first glance. Notably, decisions about the potential use of shared right-of-way are often finalized during the project planning process, long before many of the topics above are even thought about, much less addressed in any comprehensive manner. At that stage of project development, the track alignment engineer may be one of the few persons on the planning team with any understanding of the physical space requirements that could develop as the project design matures. The track designer should therefore bring these issues to the attention of the project planning staff, carefully evaluate the space requirements, and notify project management should it appear that insufficient right-of-way is being identified to actually construct the infrastructure and systems that will be required. 3.10 REFERENCES [1] American Railway Engineering and Maintenance-of-Way Association (AREMA), Manual for Railway Engineering (Washington, DC: AREMA, 2008), Chapters 5 and 12. [2] New Jersey Transit, Hudson-Bergen Light Rail Project, Manual of Design Criteria, Feb. 1996, Chapter 4. [3] American Railway Engineering Association, “Review of Transit Systems,” AREA Bulletin 732, Vol. 92, Oct. 1991, pp. 283–302. [4] Maryland Mass Transit Administration, Baltimore Central Light Rail Line, Manual of Design Criteria, Jan. 1990. [5] AREMA Manual for Railway Engineering, Chapter 5. [6] Parsons Brinckerhoff-Tudor-Bechtel, “Basis of Geometrics Criteria,” submitted to the Metropolitan Atlanta Rapid Transit Authority (Atlanta: MARTA, Aug. 1974), p. 3. [7] Harvey S. Nelson, “Speed and Superelevation on an Interurban Electric Railway,” presentation at APTA Conference, Philadelphia, PA, June 1991.

Light Rail Transit Track Geometry 56-3 [8] Raymond P. Owens and Patrick L. Boyd, “Railroad Passenger Ride Safety,” report for U.S. Department of Transportation, FRA, Feb. 1988. [9] American Railway Engineering Association, “Passenger Ride Comfort on Curved Track,” AREA Bulletin 516, Vol. 55 (Washington, DC: AREA, 1954), pp. 125–214. [10] American Association of Railroads, “Length of Railway Transition Spiral Analysis— Analysis and Running Tests,” Engineering Research Division (Washington, DC: AAR, September 1963), pp. 91–129. [11] F.E. Dean and D.R. Ahlbeck, “Criteria for High-Speed Curving of Rail Vehicles” (New York; ASME, Aug. 1974), 7 pp. [12] Los Angeles County Mass Transportation Administration, “Rail Transit Design Criteria & Standards, Vol. II,” Rail Planning Guidebook (Los Angeles: LACMTA, 6/94). [13] Thomas F. Hickerson, Route Location and Design, 5th ed. (New York: McGraw-Hill, 1964), pp. 168–171, 374–375. [14] Jamaica-JFK/Howard Beach LRS, “Basic Design Criteria Technical Revisions,” (New York: NYCTA, 2/97). [15] National Fire Protection Association, NFPA 130, Standard for Fixed Guideway Transit and Passenger Rail Systems, 2010 edition. [16] National Railroad Passenger Corporation (Amtrak) Limits and Specifications for the Safety, Maintenance and Construction of Track, MW-1000, September, 1998. [17] Topic Report: “Derailment Prevention and Ride Quality,” Light Rail Thematic Network (LibeRTiN).