1. Module 1-E Railway Alignment Design and Geometry – AREMA/FRA Basis
Alignment Examples

2. Reference Sources
The tables used in the following examples come from mixed sources to obtain clearest presentation of data.
Similar tables can be obtained from the FRA in the track safety standards.
title49-vol4/CFR-2011-title49-vol4-part213

3. Reference Sources
Additionally CSX, NS, UP, BNSF publish tables in their Grade Separation Design guidelines or Industrial sidetrack documents available from their websites.
tools/Public_Projects_Manual.pdf

4. References – Curve Ea Table 1.5” Eu

5. References – Curve Ea Table 3” Eu

6. References – Minimum Spiral Lengths

7. References – Minimum Element Lengths
Minimum length of any track element feet
Preferred length of any track element - 3 times the velocity in mph. Example Track speed 60 mph, preferred length = 3 X 60 = 180’
Note: These guidelines are for educational purposes only, actual requirements vary drastically between railroads and transit agencies

8. Example 1 – Allowable Speeds
Dc = 2d 15’
Ea = 2 ½”
How fast can a freight train operate through this Eu = 1 ½”? ______
How fast can a passenger train operate through this Eu = 3” ? ______
Note: Round speed to nearest lower multiple of 5 mph.
TS 10+00
SC 11+55
CS 15+00
ST 16+55
SP-1
SP-2
C-1

9. Example 1 – Answers Dc = 2d 15’ Ea = 2 ½” TS 10+00 SC 11+55 CS 15+00
How fast can a freight train operate through this Eu = 1 ½”? __50 mph__
How fast can a passenger train operate through this Eu = 3” ? __50 mph__
Note: Round speed to nearest lower multiple of 5 mph.
TS 10+00
SC 11+55
CS 15+00
ST 16+55
SP-1
SP-2
C-1

10. Example 1a – Solution 1 of 3
How fast can a freight train operate through this Eu = 1 ½”? __50 mph__
Steps
Check the Curve’s Ea.
Using the Curve Ea Table 1 ½” Eu as shown the following pages
Enter the Table with the Dc of 2d 15’
Drop down to the Ea of 2 ½”
Read across to the speed 50 mph
Round to the nearest lower 5 mph multiple – 50 mph
Check Spiral #1 Length
Using the Minimum Spiral Length table as shown the following pages
Enter the table with the 50 mph and read the ½” runoff in 31 feet
2 ½” ½” per 31 feet = (2.5” / 0.5”) X 31 feet = 5 X 31 = 155’ Minimum
SC – TS = Spiral Length = Ls = – = 1+55 = 155’ >= 155’ Min. 50 mph
Check Spiral #2 Length
Ls = ST – CS = – = 1+55 = 155’ >= 155’ Min. 50 mph

11. Example 1a – Solution 2 of 3

12. Example 1a – Solution 3 of 3

13. Example 1b – Solution 1 of 3
How fast can a passenger train operate through this Eu = 3” ? __50 mph__
Steps
Check the Curve’s Ea.
Using the Curve Ea Table 3” Eu as shown the following pages
Enter the Table with the Dc of 2d 15’
Intersect with the Ea of 2 ½”
Read across to the speed 59 mph
Round to the nearest lower 5 mph multiple – 55 mph
Check Spiral #1 Length
Using the Minimum Spiral Length table as shown the following pages
Enter the table with the 55 mph and read the ½” runoff in 39 feet
2 ½” ½” per 39 feet = (2.5” / 0.5”) X 39 feet = 5 X 39 = 195’ Minimum
SC – TS = Spiral Length = Ls = – = 1+55 = 155’ << 195’ Min. FAIL
Lower Speed to 55 mph and recheck spiral
2 ½” ½” per 31 feet = (2.5” / 0.5”) X 31 feet = 5 X 31 = 155’ Minimum
SC – TS = Spiral Length = Ls = – = 1+55 = 155’ >= 155’ Min. 50 mph
Check Spiral #2 Length
Same as Spiral #1

14. Example 1b – Solution 2 of 3

15. Example 1b – Solution 3 of 3

16. Example 2 – Spiral Manipulations
Dc = 2d 15’ Ea = 3 ¼ ” If the spirals on Curve #1 were increased in length to allow a passenger of at least 60 mph, what would the approximate stations of the TS and SC of Spiral #1 be? TS ≅ _____________ SC ≅ _______________
TS 10+00
SC 11+55
CS 15+00
ST 16+55
SP-1
SP-2
C-1

17. Example 2 – Answers
Dc = 2d 15’ Ea = 3 ¼ ” If the spirals on Curve #1 were increased in length to allow a passenger of at least 60 mph, what would the approximate stations of the TS and SC of Spiral #1 be? TS ≅ __9+50.5__ SC ≅ ____ ____
TS 10+00
SC 11+55
CS 15+00
ST 16+55
SP-1
SP-2
C-1

18. Example 2 – Solution 1 of 3
What would the approximate stations of the TS and SC of Spiral #1 be?
Steps
Check the Curve’s Ea.
Using the Curve Ea Table 3” Eu as shown the following pages
Enter the Table with the Dc of 2d 15’
Drop down to the Ea of 3 ¼ ”
Read across to the speed 63 mph
Round to the nearest lower 5 mph multiple – 60 mph
Determine Spiral #1 Length
Using the Minimum Spiral Length table as shown the following pages
Enter the table with the 60 mph and read the ½” runoff in 39 feet
3 ¼ ” ½” per 39 feet = (3.25” / 0.5”) X 39 feet = 6.5 X 39 = 253.5’ Minimum, SAY Ls = 254’
The length of the spiral is split approximately 50/50 around the perpendicular to the center of the circular curve C #1
Use existing spiral TS and SC to set approximate location of the perpendicular
11+55 – = 155’
(155/2) = ≅
TS ≅ – (254/2) = – 127 =
SC ≅ TS + Ls = =

19. Example 2 – Solution 2 of 3

20. Example 1b – Solution 3 of 3

21. Example 3 – Element Length Control
Dc = 2d 15’
Ea = 3 ¼ ” Dc = 2d 15’
Ea = 3 ¼ ”
Existing Freight Speed 55 mph
If the spirals on Curves #1 & #2 were increased in length to allow a passenger of at least 60 mph, would the connecting tangent length be adequate for Desirable / Minimum Criteria?
For Freight ___________ / ___________
For Passenger ___________ / __________
CS 25+00
C-1
SP-1
ST 26+55
C-2
TS 29+30
SP-2
SC 30+85

22. Example 3 – Answer CS 25+00 C-1 SP-1 ST 26+55 C-2 TS 29+30 SP-2
Dc = 2d 15’
Ea = 3 ¼ ” Dc = 2d 15’
Ea = 3 ¼ ”
Existing Freight Speed 55 mph
If the spirals on Curves #1 & #2 were increased in length to allow a passenger of at least 60 mph, would the connecting tangent length be adequate for Desirable / Minimum Criteria?
For Freight ____YES____ / _____ YES ___
For Passenger ____NO____ / ____ YES ____
CS 25+00
C-1
SP-1
ST 26+55
C-2
TS 29+30
SP-2
SC 30+85

23. Example 2 – Solution 1 of 4
Would the connecting tangent length be adequate for Desirable / Minimum Criteria?
A. For Freight __YES_ /__ YES _ B. For Passenger __ NO___ / ___ YES __
Steps
Check the Curve’s Ea.
Using the Curve Ea Table 3” Eu as shown the following pages
Enter the Table with the Dc of 2d 15’
Drop down to the Ea of 3 ¼ ”
Read across to the speed 63 mph
Round to the nearest lower 5 mph multiple – 60 mph
Determine Spiral #1 Length
Using the Minimum Spiral Length table as shown the following pages
Enter the table with the 60 mph and read the ½” runoff in 39 feet
3 ¼ ” ½” per 39 feet = (3.25” / 0.5”) X 39 feet = 6.5 X 39 = 253.5’ Minimum, SAY Ls = 254’
The length of the spiral is split approximately 50/50 around the perpendicular to the center of the circular curve C #1
Use existing spiral TS and SC to set approximate location of the perpendicular
26+55 – = 155’ – = 155’
(155/2) = ≅ (155/2) = ≅
ST1 ≅ (254/2) = =
TS2 ≅ (254/2) = =

24. Example 2 – Solution 2 of 4 Steps - continued
Check the Tangent Length - Freight
Using the Element Length Criteria
Desirable Length = 3V = 3(55) = 165’
Actual Length = – = 176’ > 165’ OK
Check the Tangent Length – Passenger
Desirable Length = 3V = 3(60) = 180’
Actual Length = – = 176’ < 180’ FAIL
Minimum Length 176’ >> 100’ OK

25. Example 2 – Solution 3 of 4

26. Example 1b – Solution 4 of 4

27. Michael Loehr Practice Leader Rail & Transit – Americas - Civil
Transportation Business Group
CH2M HILL
8720 Stony Point Parkway, Suite 110
Richmond, VA
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