Track Design Handbook for Light Rail Transit, Second Edition (2012) / Chapter Skim
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From page 72... ...
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
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From page 73... ...
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
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From page 74... ...
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
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From page 75... ...
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.
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From page 76... ...
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 speeddistance profiles as well as with the train control system design.
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From page 77... ...
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.
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From page 78... ...
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.
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From page 79... ...
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.
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From page 80... ...
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]
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From page 81... ...
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.
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From page 82... ...
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.
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From page 83... ...
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.
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From page 84... ...
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.
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From page 85... ...
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.
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From page 86... ...
Trac k Design Handbook f Figure 3.2 or Light Ra .1 Horizont il Transit, 3-12 al curve and Second Ed spiral nome ition nclature
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From page 87... ...
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]
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From page 88... ...
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]
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From page 89... ...
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'.
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From page 90... ...
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.
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From page 91... ...
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]
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From page 92... ...
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.
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From page 93... ...
Light Rail Transit Track Geometry 3-19 heights: usually 2 inches, 4 inches, and 6 inches [50 mm, 100 mm, and 150 mm]
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From page 94... ...
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)
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From page 95... ...
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.
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From page 96... ...
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)
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From page 97... ...
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)
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From page 98... ...
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)
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From page 99... ...
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.
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From page 100... ...
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.
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From page 101... ...
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]
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From page 102... ...
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.
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From page 103... ...
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.
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From page 104... ...
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%)
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From page 105... ...
Light Rail Transit Track Geometry 3-31 where Ls = spiral length in feet [meters] V = speed in mph [km/h]
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From page 106... ...
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.
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From page 107... ...
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)
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From page 108... ...
Track Design Handbook for Light Rail Transit, Second Edition 3-34 then Overturning Speed mm] [831 inches 32.7= 50 27.625)
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From page 109... ...
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.
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From page 110... ...
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.
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From page 111... ...
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.
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From page 112... ...
Trac In slo profile waive consid chang vehicl k Design H w-speed em s makes com d. Where a eration shou es in vertica e suspension andbook f bedded track pliance with tangent be ld be given t l acceleratio system wea Figu or Light Ra in urban a the above cr tween vertic o using reve n that could r.
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From page 113... ...
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.
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From page 114... ...
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.
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From page 115... ...
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.
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From page 116... ...
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]
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From page 117... ...
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.
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From page 118... ...
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.
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From page 119... ...
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.
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From page 120... ...
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%.
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From page 121... ...
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.
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From page 122... ...
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.
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From page 123... ...
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]
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From page 124... ...
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.
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From page 125... ...
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)
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From page 126... ...
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.
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From page 127... ...
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.
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From page 128... ...
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.)
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From page 129... ...
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)
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From page 130... ...
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.
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From page 131... ...
Light Rail Transit Track Geometry 3-57 Minimum running clearance to signals, signs, platform doors, and other non-structural members: 2 inches [50 mm]
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From page 132... ...
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
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From page 133... ...
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.
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From page 134... ...
Track Design Handbook for Light Rail Transit, Second Edition 3-60 Figure 3.8.4 Additional clearance for chorded construction
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From page 135... ...
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.
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From page 136... ...
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.
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From page 137... ...
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.
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From page 138... ...
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.
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From page 139... ...
Light Rail Transit Track Geometry 56-3 [8] Raymond P
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