Module 9: Railway Track Alignment Design

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Module 9: Railway Track Alignment Design
May 2008 Module 9: Railway Track Alignment Design This is the heart of Railroad Design – Track Alignment. We will not get into the details of track alignment designing software, but we will look into the background and some basics of track alignment. The subject of this module is Track Alignment. First, off we have to settle an age old problem. That is how do you spell the word “Alignment”. COPYRIGHT © AREMA 2008

Objectives Railway vs. Highway Horizontal Curves Vertical Curves
May 2008 Railway vs. Highway Horizontal Curves Vertical Curves Superelevation Maximum Grade Practical Tips Cardinal Rules In this module we will provide a brief overview of railway track alignment both horizontal and vertical We will discuss the difference between highway and railroad curves. We will explore the mysterious world of superelevations and at the conclusion you will be given some practical tips and list of cardinal rules. For those of you familiar with track alignment design this module will serve as review and maybe give you some information you did not know, for others you will become familiar with the curve and alignment terminology. COPYRIGHT © AREMA 2008

Railway Alignment Safe to operate under all weather conditions
May 2008 Safe to operate under all weather conditions Minimum costs for: Construction Maintenance Operation Several critical design considerations Speed, type and volume of traffic Space considerations (Right-of-Way) Environmental concerns Politics and land use issues Other economic criteria A surface transportation corridor is comprised of a series of tangent routes connected with curves. It could be: between populated centers, along an existing railway, or out in the boondocks. Whether it is for a railway, highway, or pipeline, the challenge for locating the alignment is to avoid geotechnically undesirable and environmentally sensitive areas while keeping the construction, maintenance and operating costs to a minimum, but SAFE to operate under all weather conditions. Design criteria should be determined based on the following topics: Most existing rail lines are utilized by several types of trains with different speeds. (new lines are generally single purpose – coal, light rail, etc,) Alignment design should consider characteristics of main traffic types. Available space, especially in urban settings, environmentally sensitive area, or steep hilly areas may cause major restrictions to design Traffic volumes (number of trains per day, week, year, life cycle) Environmental concerns, politics and land use issues all place specific restrictions on most projects. COPYRIGHT © AREMA 2008

Railway vs. Highway Railway alignment differs from Highway:

Mainlines Critical issues Maximum curvature determines speed
May 2008 Critical issues Maximum curvature determines speed Speed (required) determines curvature Terrain governs size of curves Train tonnage and maximum lengths Traffic volumes and train makeup for capacity (number of tracks, density of crossovers, etc.) The required speed of rail traffic determines the curvatures used and vise versa the sharpest curve determines speed. The terrain and existing land use govern the size of the curves - Train characteristics necessary to ensure that design doesn’t restrict any of the movements (too sharp or too long grade) Mainline can have 1, 2, 3 or even 4 tracks, or a combination of them. This is based on traffic density and volumes. This also determines, how often and how long sidings are required for meetings of trains traveling to opposite directions and how often crossovers are installed to allow shifts from one track to another. COPYRIGHT © AREMA 2008

Horizontal Curve May 2008 The slide above shows a horizontal curve and all it’s components. From here we’ll break it down into parts and discuss their use and design. The major components are the spiral and the curve. The important parts between these key elements are noted here. TS = point of transition of Tangent to Spiral SC = Spiral to Curve CS = Curve to Spiral ST = Spiral to Tangent You will find these called different – PS PC PT ST or others COPYRIGHT © AREMA 2008

Horizontal Curves Horizontal curve definition:

Reverse Curve May 2008 When one curve follows another, the two curves having a common tangent at the point of junction and lying upon opposite sides of the common tangent form a Reverse Curve. The point of junction on the common tangent is called the Point of Reversed Curvature “PRC”. Plain and simple never, never have a PRC on a rail design – you need a tangent between reverse curves. The higher the speed of the track the longer this tangent needs to be. COPYRIGHT © AREMA 2008

Reverse Curves May 2008 Upper left- the reverse curve is left from a track rationalization which restricts the speed of the train to 10 MPH. Upper right- this reverse curve is left when the center siding has been removed between the main on the right and the siding on the left. Lower left- new construction of a concrete track on the right with sufficient tangent between the curves to allow 30 MPH. Lower right- new construction of triple track and realignment of the existing tracks allows for sufficient tangent between the curves for a speed of 40 MPH. Photo by Dave Clark Photo by Bob Ice COPYRIGHT © AREMA 2008

Avoid Reverse Curves Objectionable in track-train dynamics
May 2008 Objectionable in track-train dynamics Reversed track twist of spiral requires high maintenance Railways need tangent track between curves of opposite directions: Recommended 100 ft (Practical Tip No. 2) Recommended 2 second transit time for passenger operations Not less than the length of longest railcar expected to traverse the curves Avoid Reversed Curves Good idea – avoid reverse curves – easier said than done. Sometimes you just have to use a reverse curve –nothing else will fit. If there is no tangent or a very short tangent exists, the marked change in direction is objectionable in track-train dynamics for the rigid 2-axle truck assembly used in railcars, resulting in possible derailment. For main lines and high-speed tracks with spirals and super-elevation, the minimum tangent length between reversed spiral curves should be a very minimum of 100 feet and not less than the length of the longest car expected to traverse the curves. Ok what about an industry track – try to use the same rule – you can’t have a car going two different directions without problems. The AREMA manual includes a chart for reverse curves in yard tracks. AAR Train-Track Dynamics studies resulted in the recommendation that there should be at least 200 feet of tangent between reversing curves of 2 deg 30min or sharper otherwise the train speed should not exceed 40 MPH. COPYRIGHT © AREMA 2008

Railway Spirals Location for spirals in railroads:
May 2008 Location for spirals in railroads: In main track between tangents and curves Between curves of different curvatures in compound curves Form of railway spiral should have a linear rate of curvature increase Clothoid Spiral is almost exclusively used in Canada and the U.S.A. Spirals are use at two locations on railway curves On main tracks between the tangent and the curve – mainline because they are not generally used on side tracks and yards On mainline compound curves – between the curves The form of spirals used in railways should have a linear rate of curvature increase that varies directly with the length. The Clothoid Spiral is almost used exclusively in the U.S.A. and Canada for railways and highways. Such a spiral is sometimes referred to as a “Cubic Parabola”. COPYRIGHT © AREMA 2008

Spiral Transition Curves
May 2008 Spirals provide Gradual change from tangent to curve A desirable length for super-elevation run-off Highway spiral length: Ls = A2 / R A = spiral parameter Railways use the higher of two formula: To limit unbalanced lateral acceleration acting on passengers to 0.03 g per second: Ls = 1.63 Eu V Eu = unbalanced elevation (in.) To limit track twist to 1 inch in 62 feet: Ls = 62 Ea Ea = actual elevation (in.) Spiral Transition Curves  Spiral easements provide a gradual change in curvature from tangents to circular curves and a desirable length for super-elevation runoff. In highway design, spirals also provide flexibility to accommodate lane widening and improved aesthetics.  Highway spiral lengths are expressed mathematically as follows:  L = A2 / R  Where L = length of spiral in feet R = radius of circular curve in feet A = spiral parameter A2 = rate of change of length with respect to curvature  The spiral parameter “A” is a measure of the spiral flatness – a larger parameter signifies a flatter spiral. Highway designers often use longer spirals with larger parameters to enhance the aesthetics of the alignment. The minimum length of a railway spiral is calculated by 2 formula. The first one is for gradual change in curvature for passenger comfort, high center of gravity freight cars and better curve negotiation. As railway tracks are normally elevated with a cant deficiency for the passenger train speed, this formula ensure that the unbalanced lateral acceleration acting on a passenger does not exceed 0.03g per second. L = 1.63 Eu V Eu = unbalanced elevation in inches V = maximum train speed in miles per hour  The second formula limits the track twist as related to freight car suspension due to super-elevation runoff. The rate of elevating the outer rail through the spiral should not exceed 1 inch in 62 feet.  L = 62 Ea Ea = actual elevation in inches  The desirable spiral length is the higher length produced by the 2 formula. There are two ways of determining the spiral length – the first and easiest way is look up on the operating railroad’s spiral chart the length of spirals. The second way is to use the formula and calculate the distance – then most importantly round off to the closest 10 feet.   COPYRIGHT © AREMA 2008

Superelevation / Cross Level
May 2008 Highways Equilibrium elevation “e”: e = B V2 / (32.16 R ) V in ft./sec; e, B, R in ft. Highways use cross level “ e’ = e / B ” and side friction factor “ f ” to overcome centrifugal force: e’ + f = V2 / (14.65 R ) V in mph; R in ft. Super-elevation / Cross Level This is a slide showing the highway formulas for super in a highway – do not used on these on railroads curves.  COPYRIGHT © AREMA 2008

Super-elevation / Cross Level
May 2008 Railways Elevation of Curves (MRE 5.3.3) e= Bv2/32.2R e = Equilibrium elevation in feet B = Bearing Distance in feet center to center of rails ≈4’ 11-½” for standard gauge track v = Velocity in feet per second R = Radius in feet This converts to E = V2 D V in mph; D = Degree E = Equilibrium elevation in inches Super-elevation / Cross Level (SEE in AREMA MRE)  The bearing distance “B” of a standard gauge track is 4’ 11-½” from center to center of rails. The actual distance varies with the weight of rail and amount of head wear. The standard gauge in North America and most European Countries is 4’ 8-1/2”. Gauge is the distance between the inside of the heads of both rails. Railways traditionally express the super-elevation “E” of the outer rail in inches above the low rail. The centrifugal force equals the first equation To convert to common usage – change velocity to MPH – Radius to Degrees – and it becomes  E = V2 D.  Where E = super-elevation in inches V = velocity in miles per hour D = degree COPYRIGHT © AREMA 2008

Unbalanced Elevation May 2008 Different maximum allowed speeds for different trains on the same track: Passenger Express freight General freight Balance flange wear of both rails Actual elevation on track to balance head and flange wear of both rails: Bulk commodity – below equilibrium General freight – at or 1” above equilibrium Express freight – 1” to 2” above equilibrium Conventional passenger – 3” above equilibrium High speed passenger (100 mph+) – 4” above Unbalanced Elevation or Cant Deficiency  Railways specify different maximum allowed speeds for different types of trains - passenger, time sensitive express freight (container trains), and general freight – on the same section of track and power these trains with different mass/power ratios to save on energy cost. A full tonnage bulk train on the ruling grade may be running at less than 10 mph while a light passenger train may be at 60 mph. Even the same train running in opposite directions may be operating at different speeds depending whether it is running up or down the hill. Because of the large variation in train speeds on the same track, railways generally set the super-elevation to balance the head and flange wear on both rails. This elevation is normally within one inch of equilibrium for the general freights. The maximum allowed speed for conventional passenger trains is set at 3 inches of unbalance (cant deficiency) higher than the actual elevation. That is, if the actual elevation is 4 inches, the maximum allowed speed for conventional trains will be set at the equilibrium speed as if there is 7 inches of elevation. Certain specialized high speed passenger trains such as the AmTrak Acela Express between Washington, DC and Boston, MA may operate at 4 inches of cant deficiency. In railway practice, it is the inner rail that is maintained at designed grade while the outer rail is raised to the required super-elevation. The profile of a track is to show the elevation of the lower rail. This practice does not apply to rail transit on elevated guideway. COPYRIGHT © AREMA 2008

Maximum Curvature Good designers limit curvature to:
May 2008 Good designers limit curvature to: High Speed Passenger 1 Curve Main Lines - prairie 2 Curve Main Lines - mountain 4 Curve (if possible) Branch Lines – 25 mph 8 Curve Yard Tracks 12 Curve (varies) Over 13º curves may cause operational difficulties. Maximum Curvature / Minimum Radius All AAR approved railcars can negotiate a 13 curve during switching (say 5 mph) even with extreme long-short car combination. As railway tracks, particularly curves, do deteriorate due to use over time, it is good practice to limit the alignment of yard tracks to 12 curves. You need to check with the operating railroad – for example BNSF curves are limited to 9 30’. Due to limited drawbar swing, train crew may have difficulty in coupling cars on curves exceeding a 9. Sharp curves will result in more maintenance and more operating expense. COPYRIGHT © AREMA 2008

Maximum Superelevation

Vertical Curves Highway vertical curves:

New Shorter Vertical Curves
May 2008 Old railway formula developed in 1880’s for “link and pin” couplers in those days Present day couplers can accommodate shorter vertical curves New formula developed in recent years: L = 2.15 V2 D / A V = train speed in mph D = algebraic difference of grade in decimal A = vertical acceleration in ft./sec2 0.1 ft./ sec2 for freight, 0.6 ft./ sec2 for psgr or transit Practical Tip No. 3 – Verify RR uses new equation The old formula was developed in the 1880’s for the “link and pin” coupler system in those days. This formula provides excessive vertical curve length for the present day coupler system and a new formula has been developed by American Railway Engineering and Maintenance-of-way Association “AREMA” (working with Association of American Railroads “AAR”). The new formula takes account of train speed, vertical acceleration and percent gradient change. L = 2.15 V2 D / A Where L = length of vertical curve in feet but 100 ft. minimum V = speed of train in miles per hour D = algebraic difference of grade in decimal A = vertical acceleration in ft/sec2 2.15 = factor converting V2 from (mph)2 to (feet per second)2 The recommended vertical acceleration “A” for use in this formula is 0.1 ft/sec2 for freight and 0.6 ft/sec2 for passenger and transits. This formula makes the freight vertical curve 6 times as long as a passenger train. COPYRIGHT © AREMA 2008

Clearance Specific clearances necessary for safe operations
May 2008 Specific clearances necessary for safe operations Size of car clearance envelope is based on dimensions of: Locomotives Cars Potential large loads Requirements set by several agencies Clearance is the space required between track and other fixed objections. Size of envelope may vary, based on the level of service, type of track or type of object to be cleared. They are mandated by States and railway policies. AAR and AREMA publish “plates” to provide guidance. Clearance requirements should always be clarified with railroad and state prior to design. With new, larger equipment, minimum clearances have increased. This should be considered, when upgrading existing routes. COPYRIGHT © AREMA 2008

Horizontal Clearance Constant on tangent track Additional clearance:
May 2008 Constant on tangent track Additional clearance: In curves for car end swing and car overhang In superelevated tracks to provide room for cant - Car end swing and overhang are dependent of the dimensions of the railcar (the longer, the bigger) Maximum swingout occurs at the mid-point between two trucks of a railcar. (critical point) Total additional clearance requirement is the sum of swingout (due to curvature) and the tilt (due to superelevation) Special considerations, when determining side clearances: Fixed objects close to the envelope may represent significant obstacle in maintenance of track. Clearance point should be known. This is the minimum dimension between tracks, so two trains can safely meet pass each other. Railroad policy for clearance between centerlines of parallel tracks (typically 13 to 15 feet), but increased in the curves. If tilting-body passenger rail equipment used, additional clearance required to compensate for tilting. COPYRIGHT © AREMA 2008

Vertical Clearance Constant on tangent track Additional clearance:
May 2008 Constant on tangent track Additional clearance: In sag vertical curves In superelevated tracks For specialized equipment To provide threshold for future track maintenance and equipment changes In sag vertical curves, additional clearance required due to distance between railcar trucks. In superelevated tracks to provide room, because of cant Intermodal double-deck trains and auto rack cars much higher than conventional equipment Track maintenance often involves surfacing track, which is done by raising track slightly. If no threshold provided, expensive undercutting is required. Vertical clearances are extremely critical, when upgrading existing facilities, since most of them were not designed for current equipment. Traffic type should be identified, before determining vertical clearance criteria. Be aware that for both Horizontal and Vertical clearances that minimum clearances vary state by state and that the railroad generally have their own minimum clearances. COPYRIGHT © AREMA 2008

What’s wrong with this picture?
Turnouts May 2008 Answer: Avoid placing turnouts in curves if possible, and try to never have a turnout diverging on the inside of a curved track. Doing so creates much sharper curvature than the original track had. What’s wrong with this picture? COPYRIGHT © AREMA 2008

21 Cardinal Rules May 2008 SEE YOUR HANDOUT…DISPLAY IT SOMEWHERE CLOSE AND SHARE IT WITH YOUR FRIENDS! Location determines the length of spur track, but also what kind of geometry can be used for design Topography may cause major issues, especially at locations, where facility is close to main tracks. The elevation of tracks is quite fixed both at the loading decks of facility and where it connects to main line. Large differences in these values may be difficult to accommodate. Number of cars used by facility important to know, since they have to be stored on tracks. If large number must be stored, additional storage tracks may need to be constructed. Type of equipment (locomotives and cars) and traffic density should be known to determine limits for design. Industry spurs may use sharp curves that can be hard to accommodate with some equipment. Density of use determines, what type of switch should be used (# of switch, Hand or power operated). COPYRIGHT © AREMA 2008

Some Design Software May 2008 There are two major computer aided drafting (CAD) programs used in the industry AutoCAD (railroads, private industries) Microstation (state D.O.T.s, government) Each program has add-on Design software programs that are used for designing the horizontal alignments, vertical profiles, cross-sections Bentley Rail Track: (specifically rail design) Civil 3D Geopak: (highway or rail design) Inroads: (highway or rail design) Autodesk Civil 3D (highway or rail design) AREMA does not endorse or support any particular track design software program. COPYRIGHT © AREMA 2008

Design Software Views Rail Track Interface 3-D model May 2008
Here are some design software screen captures. On the left the track design software simultaneously shows the Plan view (in the upper left), the vertical track profile (in the bottom left) , and the cross-section (on right) with proposed earthwork cuts for ditches shown in green. The picture on the right shows a 3-dimensional wireframe image of the proposed track. COPYRIGHT © AREMA 2008

QUESTIONS? Author: Charley Chambers, P.E. John G. Green, Ph.D., P.E.
May 2008 Author: Charley Chambers, P.E. Hanson Professional Services, inc. (425) Revisions: John G. Green, Ph.D., P.E. CH2M Hill, inc. (312) Acknowledgements We will briefly entertain questions. For additional information please feel free to use the contact information shown above. COPYRIGHT © AREMA 2008