Realignment of Curve

Running on curves –

(1) For smooth and satisfactory running on curves –

(a) There should be no abrupt alteration of curvature and/or superelevation (cant), and

(b) The superelevation should be appropriate to the curvature, at each point.

(2) On Group ‘A’ and ‘B’ routes, gauge, versines and superelevation on each curve must be checked once in every four months and on other routes every six months. Such checks should also be carried out whenever the running over curves is found to be unsatisfactory. The versines, superelevation and gauge should be recorded by the PWI in the curve register as per the pro forma

Curve registers of groups ‘A’ and ‘B’ routes should also be provided with cumulative frequency diagrams for each curve to get a graphic idea about the condition of geometry of curve. The A.E.N shall check at least one curve of each Permanent way Inspector every quarter by taking its versine and superelevation as well as gauge from end to end. The decision to realign should be taken by the Permanent Way Inspector-in charge or Assistant Engineer. The realignment of curve should be carried out in dry season and not during rainy season except when this is unavoidable.

Criteria for realignment of a curve:

(1) When as a result of inspection by trolley or from the footplate of locomotive or by carriage or as a result of Track Recording carried out, the running on a curve is found to be unsatisfactory the curve should be realigned.

(2) The running over a curve depends not only on the difference between the actual versine and the designed versine but also on the station-to-station variation of the actual versine values. This is because it is the station to station variation of

versine which determines the rate of change of lateral acceleration, on which depends the riding comfort.

Service limit for station to station versine variation for 3 speeds group viz. 120 Km/h and above, below 120 Km/h and upto 80 Km/h and below 80 Km/h and upto 50 Km/h, should be considered as tabulated below

In case exceedance of the above limit is observed during an inspection, local adjustments may be resorted to in cases where the variation of versines between adjacent stations is only at few isolated locations, at the earliest possible. If more than 20% of the stations are having versine variation above the limits prescribed, complete realignment of the curve should be planned within a month.

Speed Range Limits of station to station Variation (mm)

120 Kmph and above 10 mm or 25% of the average versine on circular curve whichever is more Below 120 Kmph and upto 80 Kmph 15 mm or 25% of the average versine on circular curve whichever is more Below 80 Kmph and upto 50 Kmph 40 mm or 25% of the average versine on circular curve whichever is more In case exceedance of the above limit is observed during an inspection, local adjustments may be resorted to in cases where the variation of versines between adjacent stations is only at few isolated locations, at the earliest possible. If more than 20% of the stations are having versine variation above the limits prescribed, complete realignment of the curve should be planned within a month

String lining operations: – The work of realigning and transitioning curves consist of the following three main operations :–

(a) Survey of the existing curve by measurement of versines.

(b) Determination of the revised alignment and computation of slews, including provision of correct superelevation.

(c) Slewing of the curve to the revised alignment.

Chord Length: - Overlapping Chord length 20meters and intervals of 10meters. Versine survey of curve:- Versine readings shall be taken along the gauge face of

the outer rail.

Determination of revised alignment and computation of slews :–

Operation No. 2 :–

(a) The basic principles of string lining are as follows:–

(i) The chord length being identical, the sum total of the existing versines should be equal to the sum total of the proposed versines.

(ii) The slew in any direction at a station affects the versines at the adjacent stations by half the amount in the opposite direction, when the track is not disturbed at the adjacent stations.

(iii) The second summation of versine difference represents half the slew at any station.

(iv) At the first and at the last station, the slews should be zero.

Slewing the curve to revised alignment:–

The revised alignment of the curve should be staked out with a steel tape by using the pegs cut from the bars (or wooden stakes with tack marks) which should be fixed on the cess on the inner side of the curve square to the track and at such a distance according to the value of the slews, so that the final alignment of the track is at one gauge distance from the face of the pegs or the tacks on wooden pegs to the outer edges of the inner rail. Their correctness should be checked by measuring the versines on these pegs and verifying that they correspond with the final versions of the alignment. The curve should then be correctly slewed to the realignment of pegs.

Limitation of String lining method -

1. If proposed versines are correct but beginning of curve is not correct it result in Heavy residual slew at the end of curve.

2. If proposed versines are not correct but beginning of curve is correct it result in Heavy inward or outward slew over the entire curve.

Above problem can be solved by using OPTIMISATION METHOD of curve realignment

a. By finding out correct beginning & end of the curve.

b. By keeping slew at centre of curve as zero.

Basic principle of - OPTIMISATION METHOD

1. First summation of versines represent the Area of versine diagram(in station distance Unit).

2. Second summation of versines represents the moment of versine diagram about the last station(in station distance units).

Procedure –

• Workout FS and SS of existing versines(Ve).

• Find out chainage of CC from beginning,              x = N – SS upto N/FS upto N

• Find out offset at x from table of SS by interpolation.

• Find out Vp by solving equations                         – aVp 2 +bVp +c = 0

• Therefore:                                                              Vp=(-b ±√ b2-4ac)/2a.

• Length of equivalent curve                                   = FS of Ve / Vp. (N′ = N + l)

• Total length L = Length of equivalent curve +Transition length.

• Beginning of curve = Chanage of centre of curve –L/2

• End of curve = Change of centre of curve + L/2

• Decide value of Vp.

• Proceed as per string lining method