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COPYRIGHT © AREMA : 1 of 29 Module 9: Railway Track Alignment Design
COPYRIGHT © AREMA : 2 of 29 Objectives Railway vs. Highway Horizontal Curves Vertical Curves Superelevation Maximum Grade Practical Tips Cardinal Rules
COPYRIGHT © AREMA : 3 of 29 Railway Alignment 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
COPYRIGHT © AREMA : 4 of 29 Railway vs. Highway Railway alignment differs from Highway: Operator has no horizontal control Higher mass/power ratio – flatter grade required Rail 286,000 lbs vs. 80,000 lbs gross truck Rail up to 70 ft. truck centers – higher curve resistance Extremely long stopping distance Faster trains require tighter tolerances in track alignment Opposing trains may operate on same track
COPYRIGHT © AREMA : 5 of 29 Mainlines 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.)
COPYRIGHT © AREMA : 6 of 29 Horizontal Curve
COPYRIGHT © AREMA : 7 of 29 Horizontal Curves Horizontal curve definition: –Railways: Based on D and defined as angle subtended by 100-ft. chord. R (ft.) = 50 ft. / sin ( D / 2 ) - Highways: Based on angle subtended by 100-ft. arc. D (hwy) = / R Practical Tip No. 1 – Railroads use “Degree” not “Radius”
COPYRIGHT © AREMA : 8 of 29 Reverse Curve
COPYRIGHT © AREMA : 9 of 29 Reverse Curves Photo by Bob IcePhoto by Dave Clark
COPYRIGHT © AREMA : 10 of 29 Avoid Reverse Curves 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
COPYRIGHT © AREMA : 11 of 29 Railway Spirals 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.
COPYRIGHT © AREMA : 12 of 29 Spiral Transition Curves Spirals provide Gradual change from tangent to curve A desirable length for super-elevation run-off Highway spiral length: Ls = A 2 / RA = 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 E u V E u = unbalanced elevation (in.) To limit track twist to 1 inch in 62 feet: Ls = 62 E a E a = actual elevation (in.)
COPYRIGHT © AREMA : 13 of 29 Superelevation / Cross Level Highways Equilibrium elevation “e”: e = B V 2 / (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 = V 2 / (14.65 R ) V in mph; R in ft.
COPYRIGHT © AREMA : 14 of 29 Super-elevation / Cross Level Railways Elevation of Curves (MRE 5.3.3) e= Bv 2 /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 = V 2 D V in mph; D = Degree E = Equilibrium elevation in inches
COPYRIGHT © AREMA : 15 of 29 Unbalanced Elevation Different maximum allowed speeds for different trains on the same track: Passenger Express freight General freight Balance flange wear of both rails
COPYRIGHT © AREMA : 16 of 29 Maximum Curvature Good designers limit curvature to: High Speed Passenger1 Curve Main Lines - prairie2 Curve Main Lines - mountain4 Curve (if possible) Branch Lines – 25 mph8 Curve Yard Tracks12 Curve (varies) Over 13º curves may cause operational difficulties.
COPYRIGHT © AREMA : 17 of 29 Maximum Superelevation Highway Authorities: Range 0.06 to 0.08 ft./ft. as maximum FRA: 8” cross-level for Class 1 & 2 – 30 mph psgr., 25 mph frt. 7” for Class 3 through 5 tracks Transport Canada: 6” for tracks of all Classes Railways usually adopt 1” less than regulatory limit to ensure compliance if the tracks move due to use or over winter Railways often superelevate curves ½” even when not required to prevent reverse elevation due to settlement
COPYRIGHT © AREMA : 18 of 29 Vertical Curves Highway vertical curves: L = K A K = coefficient defining length per gradient change A = algebraic difference of grade (%) Railway vertical curves – old formula: L = D / R D = algebraic difference of grade (ft. per 100-ft. station) R = rate of change per 100-ft. station 0.05 ft. per station for crest on main track 0.10 ft. per station for sag on main track Secondary line may be twice those for main line Railways moving to shorter vertical curves
COPYRIGHT © AREMA : 19 of 29 New Shorter Vertical Curves 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 V 2 D / A V = train speed in mph D = algebraic difference of grade in decimal A = vertical acceleration in ft./sec ft./ sec 2 for freight, 0.6 ft./ sec 2 for psgr or transit Practical Tip No. 3 – Verify RR uses new equation
COPYRIGHT © AREMA : 20 of 29 Design Grade for Railways Maximum design grade: Primary Line = 0.4% railway – 3.0% highway Secondary Line = 1.0% railway – 6.0% hwy Ideal maximum for railway grade: Trains can roll safely down 0.3% grade without wasting energy on brakes Tracks dedicated for passenger or transit use only may have steeper grade
COPYRIGHT © AREMA : 21 of 29 Stationing Milepost and Stationing might not increase in the same direction Milepost not accurate Establish stationing from a set object Equations Practical Tip No. 4 – Know when to station to the 100th
COPYRIGHT © AREMA : 22 of 29 Clearance 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
COPYRIGHT © AREMA : 23 of 29 Horizontal Clearance Constant on tangent track Additional clearance: –In curves for car end swing and car overhang –In superelevated tracks to provide room for cant
COPYRIGHT © AREMA : 24 of 29 Vertical Clearance 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
COPYRIGHT © AREMA : 25 of 29 Turnouts What’s wrong with this picture?
COPYRIGHT © AREMA : 26 of Cardinal Rules SEE YOUR HANDOUT…DISPLAY IT SOMEWHERE CLOSE AND SHARE IT WITH YOUR FRIENDS!
COPYRIGHT © AREMA : 27 of 29 Some Design Software 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)
COPYRIGHT © AREMA : 28 of 29 Design Software Views 3-D modelRail Track Interface
COPYRIGHT © AREMA : 29 of 29 QUESTIONS? Author: Charley Chambers, P.E. Hanson Professional Services, inc. (425) Revisions: John G. Green, Ph.D., P.E. CH2M Hill, inc. (312)
COPYRIGHT © AREMA : 30 of 29 REVISION HISTORY
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