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.

• Much more limiting in railroads than on highways– Limited friction available– Smaller power to weight ratio

Grade

• Amount of elevation change in 100 ft of length, expressed in percent.

Grade

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.

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.

Source: http://www.hnd.usace.army.mil/techinfo/ti/850-02.pdf

Grade Categories

Source: http://www.trains.com/trn/default.aspx?c=a&id=193

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

• Curves that transition between different grades.• Necessary for smooth train operation• More difficult to construct than uniform grades.

Vertical Curves

Source: J. Rose power point 26

Vertical Curves

• Parabolic in nature• Sag - concave upwards, valley• Summit - concave downward, hills

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

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

2* *D V KL

A

Alignment Design

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

• 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

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

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 problems1.) Restricted amount of swivel of the trucks

under the cars2.) Increasing horizontal forces from other

cars as curve tightens

3.) Problems with a longer car coupled to a short car

• Long car basically pulls shorter car off the track

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

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/