CE 515 Railroad Engineering Vertical Alignments & Alignment Design Source: AREMA Ch. 6 “Transportation exists to conquer space and time -”

Straight line tangents in the vertical plane. Grade Straight line tangents in the vertical plane. Much more limiting in railroads than on highways Limited friction available Smaller power to weight ratio

Amount of elevation change in 100 ft of length, expressed in percent. Grade Amount of elevation change in 100 ft of length, expressed in percent. Source: J. Rose power point 26

Grade Resistance Equals 20 lb for each ton of train weight and percent of grade. Thus, it takes twice the force to pull a train up a 2-percent grade as it does a 1-percent grade. For this reason, the choice of maximum gradient (the rate of elevation change on a particular grade) can have a great effect on operations over a route. Source: http://www.hnd.usace.army.mil/techinfo/ti/850-02.pdf

Ruling Grade When a particular grade limits train size and speed over a route. If too severe, a railway may have a helper district The ruling grade is not always the steepest grade. Because a train’s momentum may help carry it over a grade steeper, but shorter, than the ruling grade. Source: http://www.hnd.usace.army.mil/techinfo/ti/850-02.pdf

Grade Categories Grade description 0.1% to 0.4% mild; the grade obtained on a highly engineered super-railroad 0.4% to 1.0% average; used on super-railroads in difficult terrain 1.0% to 1.5% steep; used by a super-railroad in very difficult terrain 1.5% to 2.2% heavy; common for a railroad engineered to moderate standards 2.2% to 3.3% very heavy; unusual and used only in very difficult terrain 3.3% plus exceptionally steep; almost never encountered on main lines Corps of Engineers --1.5 % Suggested Limit for Ruling Grades Source: http://www.trains.com/trn/default.aspx?c=a&id=193

Vertical Curves Curves that transition between different grades. Necessary for smooth train operation More difficult to construct than uniform grades. Also increase the amount of surveying and staking required Source: J. Rose power point 26

Vertical Curves Parabolic in nature Sag - concave upwards, valley Summit - concave downward, hills - Unlike horizontal curves Source: CE 453 power point 18 vertical alignment

Vertical Curves R = D/L R= rate of change per station (standard measurement of vertical curves) D= change in grades L= length of vertical curve (in stations) R should equal 0.05 for sags and 0.10 for summits (AREMA)

Example of calculations for a vertical curve R= D/L = (.50 + .22) / 6 = 0.12 Source: http://www.bnsf.com/tools/fieldengineering/pdf/IndyTrkStds_1007a.pdf

This method sometimes results in longer vertical curves than really necessary Doesn’t take into account train speed or vertical acceleration

New AREMA method L= Length of vertical curve A= vertical acceleration AREMA recommends a value of 0.10 and 0.60 for freight and passenger operations respectively for both sag and summit curves. D= difference in rates of grades K=2.15 V=train velocity -Produces shorter vertical curves - Similar to what is used by light rail and some passenger rail -Constraints AREMA recommends against using this equation within horizontal spirals or within 100 feet of adjacent vertical curves

Alignment Design Many considerations go into choosing railway routes Economics Environmental concerns Politics Land use Long term traffic levels

Designer uses experience to make an educated decision. Alignment needs to be: Cost effective Easy to maintain Efficient Safe to operate Designer uses experience to make an educated decision.

Reversing Curves Should be avoided at all costs Can lead to train buckling derailment excessive wear on tracks Source: http://www.dot.state.co.us/S_Standards/Sign_Layout_2004/SHS/GIF/W1-4R%20ReverseCurve.gif

Reversing curves causes a couple about the center of the car Increases likelihood of derailment explain Source: AREMA textbook

Reversing Curves Should be separated by a tangent Allows cars to stabilize before adding new forces Length varies Freight: 150 – 300 ft Passenger: two seconds Light-use tracks: one car length -Different railways have own criteria -These are general numbers Source: http://www.railbrit.org.uk/images/13000/13860.jpg

Maximum Allowable Horizontal Curvature Sharper curves result in more wear on track, more maintenance and more $$$. Source: http://www.thebluecomet.com/pc2873rockville.jpg

Also increase chance of derailment and car damage Extreme curvature has 3 problems 1.) Restricted amount of swivel of the trucks under the cars 2.) Increasing horizontal forces from other cars as curve tightens 1.If they swivel too much, will hit physical features of the car, or damage components such as brake rigging 2. The forward and backward forces between cars through the coupler will result in a horizontal component

3.) Problems with a longer car coupled to a short car Long car basically pulls shorter car off the track -the ends of the longer are farther off of the track centerline than the shorter one. Source: AREMA textbook

Curvature Limits Cant of rail will guide rail on curves up to 3 degrees More than 3, flange/rail contact occurs much more Sometimes avoiding obstacles are more inexpensive than increased maintenance Freight: 6 – 7.5 degree limit Yards/terminals: 9.5 – 12.5 degree limit Light rail: much higher, depends -more flange/rail contact results in much more wear of rail - Light rail is much higher because every vehicle is very similar

References http://www.bnsf.com/tools/fieldengineering/pdf/IndyTrkStds_1007a.pdf http://www.hnd.usace.army.mil/techinfo/ti/850-02.pdf http://www.engr.uky.edu/~jrose/ce533_html/PowerPoint/