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

2. 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

3. 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

4. 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:

5. 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:

6. 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 % Suggested Limit for Ruling Grades
Source:

7. 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

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

9. 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)

10. Example of calculations for a vertical curve
R= D/L = ( ) / 6 = 0.12
Source:

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

12. 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

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

14. 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.

15. Reversing Curves Should be avoided at all costs Can lead to
train buckling
derailment
excessive wear on tracks
Source:

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

17. 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:

18. Maximum Allowable Horizontal Curvature
Sharper curves result in more wear on track, more maintenance and more $$$.
Source:

19. 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

20. 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

21. 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

22. References