1. Module 9: Railway Track Alignment Design

2. Objectives • Railway vs. Highway • Horizontal Curves • Vertical Curves • Superelevation • Maximum Grade • Practical Tips • Cardinal Rules

3. 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

4. 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

5. 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.)

6. Horizontal Curve

7. 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) = 5729.578 / R Practical Tip No. 1 – Railroads use “Degree” not “Radius”

8. Reverse Curve

9. Reverse Curves Photo by Dave Clark Photo by Bob Ice

10. 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

11. 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.

12. Spiral Transition Curves • 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.)

13. Superelevation / Cross Level 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.

14. Super-elevation / Cross Level 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 = 0.0007 V2 D V in mph; D = Degree E = Equilibrium elevation in inches

15. Unbalanced Elevation • Different maximum allowed speeds for different trains on the same track: • Passenger • Express freight • General freight • Balance flange wear of both rails

16. Maximum Curvature • 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.

17. 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

18. 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

19. 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 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

20. 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

21. 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

22. 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

23. 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

24. 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

25. Turnouts What’s wrong with this picture?

26. 21 Cardinal Rules SEE YOUR HANDOUT…DISPLAY IT SOMEWHERE CLOSE AND SHARE IT WITH YOUR FRIENDS!

27. 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 http://www.bentley.com/en-US • Rail Track: (specifically rail design) Civil 3D • Geopak: (highway or rail design) • Inroads: (highway or rail design) • Autodesk http://usa.autodesk.com/ • Civil 3D (highway or rail design)

28. Design Software Views • Rail Track Interface • 3-D model

29. QUESTIONS?