REALIGNMENT OF CURVES

1. REALIGNMENT OF CURVES

2. WHY SLEW REQUIRED ? • Because curve geometry gets disturbed under passage of traffic as • Trains are not moving at equilibrium speed • Large horizontal forces on the rails due to slight variations in curvature and due to vehicle imperfections

3. WHAT IS MEANT BY ROC ? • Bringing the curve back to proper alignment • Doesn’t necessarily mean restoring to original alignment • Infinite number of curves are possible between same set of tangents

4. OBJECTIVES OF ROC • No abrupt variation of curvature or superelevation • Superelevation should be in proportion to the curvature • Solution shall be practical • Least slews and subject to obligatory points NOTE: In electrified territory, there is severe restriction of the maximum amount of slews which can be permitted

5. REQUIREMENTS OF REALIGNMENT • Local adjustments • Realignments of transitions • Complete realignment • During laying • During up-gradation • During remodelling • During service

6. CRITERIA FOR ROC • Unsatisfactory running • Based on results of curve inspection • Station to station variation is the primary consideration • Service limits laid down in IRPWM • If values go beyond service limits at more than 20% stations—realign within a month • If the variation is only at few stations, local adjustments shall be done

7. SERVICE LIMITS FOR STATION TO STATION VARIATION OF VERSINE

8. CURVE INSPECTIONS • By AEN : At least one curve in section of each sse/pway every quarter • By sse/pway incharge and assistant: • : Once in 6 months by rotation • Results to be recorded in Proforma given in Annexure 4/5 of IRPWM

9. STRING LINING METHOD BASIC PRINCIPLES

10. 1stPRINCIPLE • Also known as 1st property of versine of any curve. • “The slewing a station on curve affects the versines at the adjoining two stations by half the amount in opposite direction .”

11. C D B b’ b A C’ Ab=bC=AC/2  bb’= (-)CC’/2

12. 2ndPRINCIPLE • “The sum total of versines on equal chords of any number of curves between the same tangents are equal.”

13. Proof M ∆ J α γ V1 2γ 2α K β β I V2 V0 γ α H L

14. Proof • V0=α*(c/2) • V1=β*(c/2) • V2=γ*(c/2) • ΣV=V0+V1+V2= (α+ β+ γ)*(c/2) • In ∆IMK, <MIK+<MKI=Deflection Angle • i.e. ∆= (2α+ β) + (2γ+ β)=2(α+ β+ γ) • i.e. ∆=2(ΣV)*(2/c), ΣV=∆*c/4 • i.e. If station units are constant and ∆ does not change, the sum of all versines will be constant

15. COROLLARY TO 2nd PRINCIPLE • “The chord length being equal, the sum total of the existing versines should be equal to the sum total of the proposed versines.”

16. First and Second summations

17. 3rd PRINCIPLE • “First summation of versines represents the area of versine diagram (in station distance units) • Summation means the sum of all the items above a certain station in the table

18. V0 Vn Vn-3 Vn-2 Vn-1 V1 V2 V3 V4 If station to station distance is taken as unit, Area of each histogram segment= Ordinate at center i.e., V0, V1, V2, …., Vn-1 etc Total Area of the versine diagram= Sum of areas of each histogram segment = V0 + V1 + V2 + …. + Vn-1 Lever Arm for each histogram segment= n-station number • Moment of versine diagram about station n= n* V0+(n-1)* V1+ (n-2)V2+ ….. + 2* Vn-2+ Vn-1

19. 4th PRINCIPLE • “Second summation of versines represents the moment of versine diagram about the last station ( in station distance units).”

20. 5th PRINCIPLE • Twice the second summation of the difference of proposed and existing versines up to a point gives the slew at a station. OR • “The second summation of versine difference represents half the slew at any station”

21. 3’ 3x2V0 K 2x2V1 L 2xV2 M 2’ 3 N 2x2V0 G 2V1 H I V2 J 2 1’ D E 1 2xV0 V1 F 0 B The offset from straight for the station no n: 2*n*V0+2*(n-1)V1+2*(n-2)V2+ … + 2*Vn-1 V0 C -1 A

22. COROLLARY TO 5TH PRINCIPLE • The second summation of the difference of proposed and existing versines at first and last stations shall be zero. • Means there should not be any residual slew value if any than should be distributed through correcting couple .

23. PRINCIPLES APPLIED IN ROC • Existing versines are available from measurements and the solution has to be ‘proposed’ • Take the difference between the existing and proposed versines and then work out first and second summation • The second summation of versine difference at the first and the last station should be zero. [Slew at the first and last stations shall be zero] • The first summation of versine difference shall be zero at last station • ROC AS DONE IN FIELD IS ALSO CALLED “STRING LINING OPERATIONS”

24. STEPS IN STRING LINING OPERATION • Survey existing versines • Find sum of existing versines and get an idea of the average versines • Propose new versines for the curve according to the principles : • Sum of existing versines = Sum of proposed versines • Uniform rate of change of versine in transition portion • Uniform versine over circular portion

25. STRING LINING METHOD--OPERATIONS • Workout Versine Difference (vp-ve) • Workout First Summation of Versine Difference • FS at last station shall be zero • Workout Second Summation of Versine Difference • Value at first and last station shall be zero

30. STEPS IN STRING LINING OPERATIONS • If SS at last station is non-zero, apply correcting couple so that SS at last station becomes zero • Workout FS,SS for CC • Add the SS for original versine difference and the SS for the correcting couple. • Workout Resultant Slew (These slews are to be actually applied in field) (when we calculate as per procedure in IRPWM table1 +slew inside, - Slew outside ) • Workout Resultant Versines, for checking the slews (=vp+CC)

31. Correcting Correcting

32. Use of correcting couple • There is a residual second summation of versine difference is +104 at the last station, it means that the second summation of existing and proposed versines are not equal. • This also means that centre of gravity of existing versine diagram does not coinside with the proposed versines. • The correcting couple which is small correction in the proposed versine diagram.

33. Principles of choosing correcting couple. • These are equal and opposite. • If the residual second summation of versine difference at the last station is positive, a negative correction is applied at the initial stations of the curve and positive correction is applied at the later station of the curve. So SS will be negative. Similarly vice versa for negative residual value.

34. Principle contd.. • The correcting couple disturbed trapezoidal distribution of the proposed versines , and consequently correction shall be as small as possible in value. • If the correction are applied farther apart , the second summation of the correcting couple will be higher.

35. Correcting Correcting

36. Correcting Correcting

37. SHORTCOMINGS IN METHOD • Difficult to decide proposed versines, especially when the stations are more. • There is no way to know if the length of existing curve was ok • Curve may increase or decrease in length during service • affects assumed proposed versines • Correct beginning of curve is not known

40. REALIGNMENT PROGRAMS AVAILABLE Program by Sh M S Ekbote • Available in IRICEN website Member’s Download Area • Has modules for ROC of simple curves by • Pure trapezoidal solution • Realignment in segments • Averaging method • Limited maximum slews • Incorporates obligatory points • Check need for complete realignment required • Attention to transitions only if required Contd…

41. REALIGNMENT PROGRAMS AVAILABLE Program by Sh M S Ekbote • Has modules for ROC of • Reverse curves • Only transitions • Vertical curves • Algorithm based on equating the maximum inward and outward slews (Shifts the curve inwards or outwards to equalize the maximum values of slews)

42. SUGGESTED FURTHER READINGS • IRPWM CHAPTER 4 • IRICEN BOOK ON “RAILWAY CURVES” • WRITE UP WITH THE PROGRAM “REALIGNMENT OF CURVES” IN MEMBERS’ AREA OF IRICEN WEBSITE

43. THANK YOU