401. Determination of Radius Р(1) The radius of a curve is determined by measuring the versine on a chord of known length, from the equation,


(2) Curves can be designated by the radius in metres or by its degree. The angle subtended at the center by a chord of 30.5 metres, is the degree of the curve.


Curves shall be described invariably by the radius in metres.

(3) For measuring versines of a curve, 20 metres overlapping chords should normally be used with stations at 10 metres intervals. For checking the radii of turn-out and turn-in curves overlapping curve of 6 metres should be used and the versine measuring stations should be located at every 1.5 metres. (The turn-out curve can also be checked by off-sets from the straight with the versine measuring stations 1.5 metres apart.)

(4) The versine is obtained by stretching a fishing/nylon chord or wire taut between the end of chord length decided upon, and the measuring distance between the cord/wire and gauge face of the rail at the middle point of the chord. Care should be taken that the cord or wire is applied to the side of the head of the rail at the gauge point.


402. The Reference Rail –

The level of inner rail of any curve is taken as reference level. Super elevation is provided by raising the outer rail. For reverse curves, however, stipulation as laid down in Para 408(3) shall apply.

403. Gauge On Curves – The gauge on curve shall be to the following standards : –

(1) On new lines and on lines where complete renewal or through sleeper renewal is carried out, the track should be laid to the following standards –


(2) Gauge on the wooden sleepered road however, need not be disturbed, if it is likely to cause spike killing of sleepers. Uniformity of the gauge should be stressed in all cases to get better track riding quality.

(3) These limits are not applicable to curves laid with different gauge widening by railways as trial measure in consultation with RDSO.

Note : For narrow Gauge sections for which special schedules have been prescribed by the Zonal Railways, provisions in those schedules should be observed.


404. Definitions – (1) Cant or superelevation is the amount by which one rail is raised above the other rail. It is positive when the outer rail on a curved track is raised above inner rail and is negative when the inner rail on a curved track is raised above the outer rail.

(2) Equilibrium speed is the speed at which the centrifugal force developed during the movement of the vehicle on a curved track is exactly balanced by the cant provided.

(3) Cant deficiency- Cant deficiency occurs when a train travels around a curve at a speed higher than the equilibrium speed. It is the difference between the theoretical cant required for such higher speed and actual cant provided.

(4) Cant excess – Cant excess occurs when a train travels around a curve at a speed lower than the equilibrium speed. It is the difference between the actual cant and the theoretical cant required for such a lower speed.

(5) Maximum permissible speed of the curve-It is the highest speed which may be permitted on a curve taking into consideration the radius of the curvature, actual cant, cant deficiency, cant excess and the length of transition. When the maximum permissible speed on a curve is less than the maximum sectional speed of the section of a line, permanent speed restriction becomes necessary.

(6) Cant gradient and cant deficiency gradient indicate the amount by which cant or deficiency of cant is increased or reduced in a given length of transition e.g., 1 in 1000 means that cant or deficiency of cant of 1 mm. is gained or lost in every 1000mm. of transition length.

(7) Rate of change of cant or rate of change of cant deficiency is the rate at which cant or cant deficiency is increased or reduced per second, at the maximum permissible speed of the vehicle passing over the transition curve, e.g., 35 mm. per second means that a vehicle when traveling at a maximum speed permitted will experience a change in cant or deficiency of cant of 35mm. in each second of travel over the transition.

(8) Transition curve is an easement curve, in which the change of radius is progressive throughout its length and is usually provided in a shape of a cubic parabola at each end of the circular curve. It affords a gradual increase of curvature from zero at the tangent point to the specified radius of circular are and permits a gradual increase of super elevation, so that the full superelevation is attained simultaneously with the curvature of the circular arc.

405. Safe Speed On Curves – (1) Fully transitioned curves – The maximum permissible speed for transitioned curves should be determined from the following formulae –


Graphs showing (i) maximum permissible speed for transitioned curves of different radii and equilibrium cant are appended in Annexures 4/1 and 4/2 for B G and M G respectively.

(2) (a) Non transitioned curves with cant on virtual transition –

The determination of the maximum permissible speed on curves without transition involves the concept of the virtual transition. The change in the motion of a vehicle from straight to curve conditions takes place over the distance between the bogie centres, commencing on the straight at half the distance before the tangent point and terminating on the curve at the same half distance beyond the tangent point. Normally, the length of virtual transition is taken as 14.6 meter on B G, 13.7 meter on M G and 10.3 meter on N G The cant or superelevation is gained over the virtual transition.

The cant gradient in any case should not be steeper than 1 in 360 ( 2.8 mm. per metre) on B.G. and 1 in 720 (1.4 mm. per metre ) on M. G. and N. G.

Graph showing the safe speeds over the non-transitioned curves in case of virtual transition, both for B. G. and M. G. is appended as Annexure 4/3.

(b) Non-transitioned curves with no cant provided –

In case of non-transitioned curves where no cant is provided, the safe speed over the curve can be worked out from the graph appended as Annexure 4/4.

(3) For curves laid with inadequate length of transition, the safe permissible speed should be worked out on the basis of actual cant/cant deficiency, which can be provided taking into consideration the limiting values of cant/cant deficiency gradient and the rate of change of cant and cant deficiency.

(4) The speed as determined above shall not exceed the maximum permissible speed of the section.

406. Superelevation, Cant deficiency and Cant excess – (1) Superelevation/cant

(a) The equilibrium superelevation/cant necessary for any speed is calculated from the formula 


Where C is cant/superelevation in mm. G is the gauge of track + width of rail head in mm. R is the radius of the curve in metres.

(b) The equilibrium speed for determination of cant to be provided shall be decided by the Chief Engineer, after taking into consideration the maximum speeds which can be actually attained by fast and slow trains, the proximity of permanent speed restriction in the route, junctions, stopping places, gradients which may reduce the speeds of goods trains, without appreciably affecting the speed of fast trains and their relative importance. For this purpose the entire section may be divided into a certain number of sub sections with a nominated equilibrium speed for each sub section, fixed on the basis of speeds which can be actually attained by fast or slow trains over the sub section, so that the need for imposing any speed restrictions for limiting the cant excess for slow trains and cant deficiency for fast trains is avoided. On sections where all trains run at about the same maximum permissible speeds like suburban section, it will be preferable to provide cant for that speed.

(c) The amount of superelevation to be actually provided will be calculated by the formula given in sub-para (a) for the equilibrium speed determined on the basis of sub- Para (b) above.

(d) Maximum cant on curved track shall be as under –

(1)(i) Broad Gauge – Group ‘A’, ‘B’ and ‘C routes-165 mm.

Note :- Maximum cant of 185 mm. may be assumed for the purpose of locating all permanent structures etc., by the side of the curves on new constructions and doubling on group ‘A’ routes having potential for increasing the speed in future. The transition length should also be provided on the basis of 185 mm. cant for the purpose of planning and layout of the curve.

(ii) Broad gauge -Group ‘D’ and ‘E’ routes-140 mm.

(iii) Metre Gauge -90 mm. (can be increased to 100 mm. with special permission of Chief Engineer)

(iv) Narrow Gauge (762 mm.) – 65 mm. (can be increased to 75 mm. with special permission of Chief Engineer)

For Narrow gauge sections for which special schedules are prescribed by the Zonal Railways provisions in these schedules should be observed.

(e) Cant for each curve should be specified and indicated on web of the inside face of the inner rail to the nearest 5 mm.

In every case, the superelevation to be provided should be specified when the line is originally laid and thereafter altered only with the prior approval of the Chief Engineer.

(2) Cant Deficiency – Maximum value of cant deficiency –

(a) For speeds in excess of 100……………..100 mm. km. p.h. on Groups ‘A’ and ‘B’ routes for nominated rolling stocks and routes with permission of the Chief Engineer.


(b) For Broad Gauge routes not covered by above………………………….75 mm.

(c) Metre Gauge………………………………..50 mm.

(d) Narrow Gauge (762 mm.) ………………40 mm.

For Narrow Gauge sections for which special schedules are prescribed by the Zonal Railways, provisions in those schedules should be observed.

(3) Cant Excess-Maximum values of cant excess –

On Broad Gauge cant excess should not be allowed to exceed 75 mm. and on Metre Gauge 65 mm. for all types of rolling stock. The cant excess should be worked out taking into consideration the booked speed of goods trains on a particular section. In the case of a section carrying predominantly goods traffic, the cant excess should be preferably kept low to minimize wear on inner rail.

407. Length Of Transition Curve And Setting Out Transitions –

(1) The desirable length of transition ‘L’ shall be maximum of the following three values –


The formula (a) and (b) are based on rate of change of cant and of cant deficiency of 35 mm. per second. The formula (c) is based on the maximum cant gradient of 1 in 720 or 1.4 mm. per metre.

(2) For the purpose of designing future layouts of curve, future higher speeds (such as 160 km./h. for Group ‘A’ routes and 130 km./h. for Group ‘B’ routes) may be taken into account for calculating the length of transitions.

(3) In exceptional cases where room is not available for providing sufficiently long transitions in accordance with the above, the length may be reduced to a minimum of 2/3 of the desirable length as worked out on the basis of formula (a ) and (b) above or 0.36 Ca (in metres ) whichever is greater. This is based on the assumption that a rate of change of cant/cant deficiency will not exceed 55 mm. per second and the maximum cant gradient will be limited to 2.8 mm. per metre or 1 in 360. This relaxation shall apply to Broad Gauge only. For Narrow Gauge and Metre Gauge sections, cant gradient should not be steeper than 1 in 720. For Metre Gauge the rate of change of cant/cant deficiency should not exceed 35 mm./ second.

(4) At locations where length of transition curve is restricted, and therefore, may be inadequate to permit the same maximum speed as calculated for the circular curve, it will be necessary to select a lower cant and/or a lower cant deficiency which will reduce the maximum speed on the circular curve but will increase the maximum speed on the transition curve. In such cases, the cant should be so selected as to permit the highest speed on the curve as a whole.

An example is illustrated with calculations below –

A curve of 600 metres radius has a limited transition of 40 metres length. Calculation of maximum permissible speed and superelevation is as follows :- 


which is within the permissible limits.

The rate of change of cant at 85 km.p.h. works out to 53.12 mm. / second which is also within the permissible limits.

(5) Laying transition – (a) A transition curve is laid out as a cubic parabola and to accommodate this, the main circular arc is moved inwards by an amount called the “Shift”.

“Shift” is calculated from the formula : 


Where S = shift in centimetres.

L & R being in metres.

(b) The off-set in centimetres from the straight to any point on the transition curve is calculated from the formula –


Where Y = off-set from the straight in centimetres.
X = distance from the commencement of the curve in metres, and L & R length of transition and radius of curve respectively in metres.
( c) The arrangement of a transition curve is shown in the figure below –


The original circular curve TC is tangential to the straight at T. The curve is shifted to ZY and TZ is the amount of shift. The transition curve MNP bisects the shift TZ at N. A typical example of working out maximum permissible speed on a curve, calculating the length of transition and detailed calculation of laying the transition are given in sub-para(6).

(6) Example – A 600 metres radius curve is introduced between straight portions of a Broad Gauge Railway line intersecting- to form a total deviation of 70 degrees. The speed for determining the equilibrium cant is fixed at 80 km.p.h. and the maximum sectional speed is 110 km.p.h. Calculate the equilibrium cant, the maximum permissible speed, length of transition and the off-set for setting out the transition curve. The maximum permissible cant and cant deficiency are 165 mm. and 100 mm. respectively.

Solution –


(7) When realigning old curves, transition curves on approaches should invariably be provided. It should should be ensured that there is no change of grade over the transition.

(8) Compound curves -In case of a compound curve which is formed by two circular curves of different radii but curving in the same direction, common transition curve may be provided between the circular curves. Assuming that such compound curve is to be traversed at uniform speed, the length of the transition connecting the two circular curves can be obtained from –

(i) L = 0.008 (Ca1-Ca2) x Vm

(ii) L = 0.008 (Cd1– Cd2) x Vm Whichever is greater where Ca1 and Cd1 are cant and cant deficiency for curve No. 1 in mm. Ca2 and Cd2 are cant and cant deficiency for curve No. 2 is mm., L is length of transition in metres., Vm is the Maximum permissible speed in Km. p. h. 

Cant gradient should be within the permissible limits as stated in Para 407(1).

Common transition may be provided when the length of common transition as worked out above is more than the length of virtual transition as specified in Para 406 (1) (b).

(9) Reverse Curves – (a) In case of a reverse curve which is formed by two circular curves which curve in opposite directions, common transition curve may be provided between circular curves. The total length of common transition, i.e., from circular curve to circular curve, may be obtained from –

(i) L=0.008 (Ca1 + Ca2 X Vor

(ii) L = 0.008 (Cd1 + Cd2 ) X Vm whichever is greater, where Ca1 and Cd1 are cant and cant -deficiency of curve No. 1 in mm.,Ca1 and Cd1  cant and cant deficiency of curve No. 2 in mm.

L = is the transition in metres.

Vm = maximum permissible speed in km.p.h.

Cant gradient should be within the permissible limits as stated in Parsa 407 (1).

(b) For high speeds, in group ‘A’ and ‘B’ routes, a straight with a minimum length of 50 M, shall be kept between two transitions of reverse curves. In the case of M. G. high speed routes the distance to be kept will be 30 metres. On groups ‘A’ and ‘B’ routes on B. G., straights less than 50 metres between reverse curves and on M. G. high speed routes, straights less than 30 metres should be eliminated by suitably extending the transition lengths. In doing so, it should be ensured that the rate of change of cant and versine along the two transitions so extended is kept the same. Whenever such straights between reverse curves can neither be eliminated nor the straight length increased to over 50 metres in B. G. and 30 metres in M. G. speed in excess of 130 km.p.h. in B. G. and 100 km.p.h. in M.G. should not be permitted.

408. Running out Superelevation – (1) On transitioned curves, cant should be run up or run out on the transition, not on the straight or on the circular curve, increasing or decreasing uniformly throughout its length.

(2) On non-transitioned curves, cant should be run up or run out on the ‘virtual transition’.

(3) Longitudinal profile of transition on the reverse curve may be in one of the following two alternatives :


In case No. 1 the level of one of the rails is maintained and the super elevation is run out in the other rail by lowering it over half the transition length and raising it to the required amount of cant over the remaining half portion of the transition 

In case no. 2, the level of the centre line of the track is maintained the same throughout, and the cant is provided by raising one rail by half the amount of cant and lowering the other rail by the equal amount. Cant is run out or gained over the length of the transition by raising and lowering both the rails by equal amount symmetrically, with respect to the level of the centre line track.

In case of no.1, the level of the centre of the track gets disturbed whereas in case of No. 2, it is maintained the same throughout.

(4) Special cases of superelevation run out may be approved by the Chief Engineer.

409. Indicators/Boards provided in curves- (1) Curve Board – Each approach of a curve should be provided with a curve board at the tangent point fixed on the outside of the curve. This Board should indicate the radius of the curve, the length of the curve, length of transition in metres and the maximum cant provided on the circular portion of curve in millimetres.

(2) Rail Posts Indicating Tangent Points – On the inside of the curve, rail posts should be erected on each approach of the curve, to indicate the positions of the beginning and end of transition curves. These rail posts may be painted in red and white colours respectively. In the case of non transitioned

curve, similar rail post should be erected on the tangent track and on the circular curve over which the cant is run out, indicating the begining and end of the virtual transition.

(3) Indication of cant on track- Superelevation or cant should be indicated by painting its value on the inside face of the web of the inner rail of the curve and at every versine station, begining with zero at the commencement of the transition curve. The value of cant should be indicated on the circular curve at its begining and at the end. In the case of long circular curve the cant value should be indicated at intermediate stations at a distant not exceeding 250 metres.

(4) Cant boards – Cant boards supplied to the gangs should be graduated in steps of 5 mm. The maximum height of these should be 165 mm. for B. G., 100 mm. for M. G. and 75 mm. for N. G.(762 mm.)

(5) When curves are realigned, the repositioning of the curve boards and posts and repainting of values of superelevation at intermediate points should be done, as required.

410. Speed over Turn-out Curves – (1) Provision in general rules-Relevant Para 4.10 of General Rules,1976 Edition is reproduced below-

(1) The speed of trains over non-interlocked facing points shall not exceeed 15 kilometres per hour in any circumstances and the speed over turnout and cross avers shall not exceed 15 kilometres per hour, unless otherwise prescribed by approved special instruction, which may permit a higher speed.

(ii) Subject to provision of sub-rules (i) a train may run over interlocked facing points at such speed as may be permitted by the standard of interlocking.

(2) Turn-outs on running lines with passenger traffic – Turn-outs in running lines over which passenger trains are received or dispatched should be laid with crossing, not sharper than 1 in 12 for straight switch. However, 1 in 8-1/2 turn-out with curved switches may be laid in exceptional circumstances, where due to limitation of room, it is not possible to provide 1 in 12 turn-outs. Sharper crossings may also be used when the turn-out is taken off from outside of a curve, keeping the radius of lead curve within the following limits :-

Gauge                                   Minimum radius of lead curve

Broad Gauge                         350 M.

Metre Gauge                         220 M.

Narrow Gauge(762 mm.)          165 M.

Where it is not practicable to achieve the radius of curvature of turn in curves as specified above on account of existing track centres for the turn-out taking off from curves, the turn in curves may be allowed upto a minimum radius of 220m for B.G. and 120m for M.G. subject to the following :-

(a) Such turn in curves should be provided either on PSC or steel trough sleepers only, with sleeper spacing same as for the main line.

(b) Full ballast profile should be provided as for track for main line

Emergency cross avers between double or multiple lines which are laid only in the trailing direction may be laid with 1 in 8-1/2 crossings.

In the case of 1 in 8-1/2 turn-outs with straight switches laid on passenger running lines, the speed shall be restricted to 10 km.p.h. However, on 1 in 8-1/2 turn-outs on non passenger running lines, speed of 15 km.p.h. may be permitted.

(3) Speed over interlocked turn-outs – (a) Speed in excess of 15 Kmph may be permitted for straights of interlocked turnouts only under approved special instructions in terms of GR 4.10/1976. (Advance Correction Slip No. 94 dated 01.06.2004)

(b) In the case of 1 in 8-1/2, 1 in 12 and flatter turnouts provided with curved switches, higher speeds as permitted under approved special instructions may be allowed on the turnout side, provided the turn-in curve is of a standard suitable for such higher speeds. Extra shoulder width of ballast of 150 mm should be provided on the outside of such turn-in curves. When these conditions are satisfied, the speeds indicated below may be permitted on turnouts provided with curved switches. While permitting speed beyond 15 kmph, provisions of para 410(4) may also be kept in view.


(c) the permissible speed on turn-outs taking off on the inside of the curve should be determined by taking into consideration the resultant radius of lead curve which will be sharper than the lead curve for turnouts taking off from the straight. 1 in 8-1/2 turn-outs should not be laid on inside of curves.

(4) Upgradation of speeds on turn-outs should cover a number of contiguous stations at a time. Before upgrading the speeds on Turn-out beyond 15 km/hr, the track structure of loop lines should b strengthened as prescribed.(Advance Correction Slip No. 94 dated 01.06.2004)

411. Permissible Speed over curved Main line at Turn-outs – Subject to the permissible run through speed governed by the interlocking standard, speed over the main line will be determined taking into consideration the maximum cant which can be provided on the main line and the permissible amount of cant deficiency. In the case of turn-out of similar flexure, the maximum cant that can be provided, on the main line will be the sum of equilibrium cant for the turn-out and permissible cant excess. In the case of turn-outs of contrary flexure, the maximum cant on the main line (negative superelevation on turn-out) will be the difference between the maximum permissible cant deficiency and cant determined for turn-out from the formula given in Schedule of Dimensions as indicated in Para 413. The permissible speed on the main line will be worked out by the formula as given in Para 405(1)

412. No change of superelevation over turn-outs– There should be no change of cant between points 20 metres on B. G.,15 metres on M. G., and 12 metres on N. G. outside the toe of the switch and the nose of the crossing respectively, except in cases where points and crossings have to be taken off from the transitioned portion of a curve. Normally, turn-outs should not be taken off the transitioned portion of a main line curve. However, in exceptional cases, when such a course is unavoidable a specific relaxation may be given by the Chief Engineer of the Railway. In such cases change of cant and/or curvature may be permitted at the rates specified in Para 407 or such lesser rates as may be prescribed.

413. Curves of contrary flexure – On the main line curve from which a curve of contrary flexure takes off, the cant of the main line (which is the negative superelevation on the turn-out) should be calculated from the formula given in the Schedule of Dimension and the permissible speed on the main line determined from the allowable cant deficiency and cant on the main line. The speed so determined shall be subject to limitations governed by the standard of interlocking and the sectional speed.

414. Curves of similar flexure – (1) Not followed by reverse curves-On a main line curve from which a curve of similar flexure takes off, not followed immediately by a reverse curve, the turnout curve shall have the same cant as the main line curve.

(2) Followed by reverse curves – A change of cant on the turn-out may be permitted starting behind the crossing and being run out at a rate not steeper than 2.8 mm. per metre and subject to the maximum cant on the main line turn-out being limited to 65 mm. on Broad Gauge, 35 mm. on Metre Gauge and 25 mm. on Narrow Gauge (762 mm.)

The permissible speed on the main line is then determined from the allowable cant-deficiency and subject to limitations governed by the standard of interlocking and the safe speed limit.

415. Curves with cross avers – On curves on double line connected by cross over road, the speed and the cant for both roads are governed by the inner road to which the cross over road is a curve of contrary flexure. On the outer road, it is a curve of similar flexure. The permissible speed and the necessary cant on the inner road shall be calculated in accordance with Para 413. The same speed and the same cant shall be allowed on the outer road.

The outer track shall be raised so that both roads lie in the same inclined plane in order to avoid change in cross-level on the cross over road. Where this is not possible, both main line and the turn-out should be laid without cant and suitable speed restriction imposed.

416. Curves with diamond crossing – Normally straight diamond crossings should not be provided in curves as these produce kinks in the curve and uniform curvature cannot be obtained. However, where provision of such diamonds cannot be avoided or in case where such diamonds already exists in the track, the approach curves of these diamonds should be laid without cant for a distance of at least 20 metres on either side of the diamond crossings. Cant should be uniformly run out at the rate specified in Para 407 beyond 20 metres. The speed restrictions on the approach curve shall be decided in each case by the Chief Engineer taking into consideration the curvature, cant deficiency and lack of transition but shall in no case be more than 65 km.p.h. in the case of Broad Gauge, 50 km.p.h. in the case of Metre Gauge and 40 km.p.h. in the case of Narrow Gauge (762 mm.) No speed restriction shall, however be imposed on the straight track on which the diamond is located. In the case of diamond crossings on a straight track located in the approach of a curve, a straight length of minimum 50 M. between the curve and the heel of acute crossing of diamond is necessary for permitting unrestricted speed over the diamond, subject to maximum permissible speed over the curve from considerations of cant deficiency, transition length etc.

417. Extra clearance on curves – On curves, additional lateral clearances, in excess of the fixed dimensions should be provided as laid down in the Schedule of Dimensions –

(a) between adjacent tracks and

(b) between curved track and fixed structure.

418. Compensation for curvature on gradient- Compensation for curvature should be given in all cases where the existing gradient when added to the curve compensation exceeds the ruling gradient. The compensation to be allowed should ordinarily be 70/R percent.(0.04 percent per degree of curvature) for Broad Gauge, 52.5/R per cent (0.03 percent per degree of curvature) for Metre Gauge and 35/R per cent (0.02 per cent per degree of curvature) for Narrow Gauge(762 mm.) where R is the radius of curvature in metres.

Thus for a ruling gradient of 0.5 per cent or 1 in 200, the gradient for 583 metre radius of curvature on Broad Gauge should be flattened to -0.5-70/583 – or 0.5 X 0.04 = 0.38 per cent or 1 in 264.

419. Vertical curve :– A vertical curve shall be provided only at the junction of the grade when the algebraic difference between the grades is equal to or more than 4 mm. per metre or 0.4 per cent.

The minimum radius of the vertical curve shall be kept as under –

Broad GaugeMetre Gauge
GroupMinimum RadiusGroupMinimum Radius
A                                   B                                  C, D & E4000 metres                                3000 metres                                 2500 metresAll Routes2500 metres


Realignment of Curve 

420. 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 Permanent Way Inspector in the curve register as per the pro forma given as Annexure 4/5. 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.(Advance Correction Slip No. 140)

421. – Criteria for realignment of a curve: (1) When as a result of inspection by trolley or from the foot plate 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 speed 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:

Speed RangeLimits of station to station Variation (mm)
120 Kmph and above10 mm or 25% of the average versine on circular curve whichever is more
Below 120 Kmph and upto 80 Kmph15 mm or 25% of the average versine on circular curve whichever is more
Below 80 Kmph and upto 50 Kmph40 mm or 25% of the average versine on circular curve whichever is more

In case exceedence 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.

422. Stringlining operations :– (1) 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.

(2) Chord Length – Chord length of 20 metres should be used for recording versine. The stations should be at 10 metres intervals and versines should be recorded at these stations with overlapping chord of 20 metres.

(3) Versine survey of curve – Operation No. 1 :- Versine readings shall be taken along the gauge face of the outer rail.

To ensure inclusion of the point of commencement of the curve, a mark is made on the gauge face of the outer rail at a distance of about three half-chord lengths behind the apparent tangent point and numbered zero. From this point, half-chord distances are measured with steel tape along the gauge face of the outer rail over the whole length of the curve and numbered serially 1,2, 3, 4 and so on and carried upto about three half-chord lengths beyond the apparent tangent point at the other end. These “stations” should be marked and numbered in white paint on the rail. With a fishing cord or wire stretched out over the full length of the chord, versines are measured to 1 mm. accuracy serially at each station from one end of the curve to the other with the rule held normal to the line and recorded.

Features which restrict slewing of the track either inwards or outwards should be recorded, mentioning the maximum extent inwards and outwards to which slewing is possible (i) in existing circumstances and (ii) if a moderate expenditure be incurred in removing the “restriction”. The existing superelevation should also be measured and recorded against each “Station”.

For purposes of check, this process should be repeated in the reverse direction with the persons recording and measuring versines interchanging their duties.

The record obtained would be in the following form

Curve from km…………………………………………………………………………… km……………………………………

Between station…………………………………………………………………..and station……………………………………..

Date of survey…………………………………………………………………………………………………………………………

Jurisdiction of Assistant Engineer/Permanent Way Inspector ……………………………………………………………………


Where there are two or more lines, track centres at intervals should be recorded. After the versine-survey, the curve alignment shall not be disturbed until the realignment is commenced. This interval should be the least possible.

In the case of reverse curves, the versine survey should be continuous, but transferred to the outer rail at points where the curvature changes sign. It is probable that the exact point will not be definite; it is therefore, desirable to keep the original rail face as the base until the change is certain to enable plus or minus versines to be read from the same rail, it is only necessary to hold the fishing cord or wire 20 mm. clear of the rail edge at each end by using special gadget and substracting 20 mm. from the reading at the centre.

(4) 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.

(b) Success in obtaining the most suitable alignment depends on the proper selection of versines.

(c) In actual practice the calculations are carried out in the following manner :-

(i) After recording the versines in mm., proposed versines are selected in such a way as to obtain uniform rate of change of versines over the transition curve and uniform versines over the circular portion of the curves.

(ii) The difference between the proposed and the existing versines are worked out for each station, the positive sign being used, if the proposed versine is greater than the existing versine and negative sign if it is less (Ref. Col. 4 -Table 1, at the end of this sub- Para (4), wherein a solution to a realignment of curve is worked out).

(iii) First and second summations of the differences of proposed and existing versines are then worked out (Ref. Cols. 5 & 6).

(iv) The first summation at any station, gives the cumulative versine difference at each station. To begin with this value for station ‘ 0 ‘ is the same as the versine difference (Col. 4). To obtain the corresponding value for station No. 1 the cumulative versine difference of station ‘0’ (Col. 5) is added to the versine difference of station No. 1 (Col. 4) diagonally downward as shown by the arrow indication and the resultant value is written against Station No. 1 (Col. 5) Similarly the cumulative versine difference is calculated at each station till the last station is reached. Since the sum total of the existing and the proposed versines is the same, the figure against the last station will be ‘0’ (Col. 5).

(v) The second summation at any station gives the cumulative effect of the figures of first summations upto the previous station. It can be proved theoretically that this represents half the slew required at each station to obtain the proposed versine. To start with, this value for station ‘O’ is taken as zero. To obtain the corresponding value of Station No.1, the second summation value of the station’0′(/’.e-, the previous station ) is added to the first summation value of the same station ‘O’. as shown by horizontal arrow. This value is shown against Station No. 1(Col. 6). Similarly the second summation for Station No. 2 is the sum of the figures of the first summation and second summation of Station No.1(Col.5 and 6). The second summation is obtained against each station till the last station is reached. The slew at the last station should be zero. Otherwise the track beyond the last station will be affected by the slew at the last station. Normally this figure at the last station will not be zero. To bring this to zero correcting couples are applied.

(vi) Method of applying correcting couples -For correcting the half-throws to zero the procedure shall be as follows :-

When the final half-throw is negative, add to the versines having the lower station numbers and substract an equal amount from the versines having the higher station numbers, selecting “station” in pairs such that the sum of the products of the difference of the “station” numbers taken in pairs and the amount added to the versines, equals the numerical amount of the negative half-throw to be cleared.

When the final half -throw is positive, substract from the versines having the lower station numbers and add an equal amount to the versiness having the higher station numbers, selecting the stations in pairs such that the sum of the product of differences of the station numbers in pairs and the amount substracted from the versines, equals the numerical amount of the positive half throw to be cleared.

(vii) For computing slews when realigning and/or transitioning a complete curve the following procedure should be adopted :-

Calculate the length of transition from Para 407(1). This determines the versine gradient on the transition.

Work out versine difference, first and second summations as discussed above at the initial stations with a view to foreseeing and exercising due control over the slews (col. 4, 5 and 6). Review the figures of proposed versines (col. 8) if necessary and continue the process until the transition at the other end on which the specific versine gradient should be observed. In the process it must be ensured that difference of versines (col. 4) should sum up to zero.

Apply correcting couples to control the slew at obligatory points and to close the slew at the end to zero. The slews must be limited to the minimum possible.

Determine correct cant to be provided, points of zero and maximum cant and the cant run-off.

Curve realignment can be worked out by graphical method. Mechanical and electronic devices where available may be used to determine the final values of slew, thus avoiding the lengthy process of first and second summation and application of correcting couples.

(viii) Maximum Slew – Maximum slew at any station is usually limited by practical considerations. The distance between tracks and adequate clearance to existing structures must be maintained and track must not be slewed too near the edge of the formation. At certain locations like bridges, it may not be possible to slew the curve at all.

(ix) In carrying out the calculations for the realignment of a long curve of more than 50 stations it is best to write down values of about 10 proposed versines at a time and see that the sum is approximately the same as that of the corresponding old versines and then workout the second summation to ensure that slews are minimum. A final adjustment to ensure that the sum of the existing and proposed versines is equal and that the slew at last station is zero can then be made.

A numerical example is given in table 1 on the next page which will illustrate the method of working out the solution for realignment of a curve.

(See Table No. 1)

(5) Slewing the curve to revised alignment :-

Operation No. 3 :- 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. In narrow cuttings with sharp curves or in tunnels it may not not be possible to measure versines on the pegs driven on the inner cess of the curve due to the face of the cutting fouling the fishing cord. In such cases, the pegs may be driven on the outer cess. Their correctness should be checked by measuring the versines on these pegs and verifying that they correspond with the final versines of the alignment. The curve should then be correctly slewed to the realignment of pegs.

Whether or not permanent pegs should be fixed is left entirely to the discretion of Divisional Engineer. In no case should these be fixed on formation that is not firm or at locations where they are liable to the disturbed or tampered with.

Where it is considered more expedient, the staking of the realigned curve may be done by driving tie-bar pegs of about 750 mm. in length against each station down to rail level along the centre line of the revised alignment and slewing the track to these pegs.

It is important that the slewing is done to 2mm. accuracy and actual versines again taken to ensure that they accord with the calculated versines of the realigned curve.

Along with slewing of the curve to the revised alignment correct superelevation should be provided at each station to accord with the curvature, particular attention being paid to the run-off on the transition. Repositioning of posts on the cess to indicate zero and maximum superelevation and remarking of cant values on the inside web of the inner rail should be done.

423. Realigning curves on double or multiple lines :- On double or multiple tracks each curve should be stringlined independently. No attempt should be made to realign any curve by slewing it to a uniform centre to centre distance from the realigned curve as –

(a) The existing track centres may not be uniform and relatively small throw on one may entail a much larger (even prohibitively large) throw on the adjacent track

(b) It is nearly impossible to measure the centre to centre distance of curved tracks along the true radial lines and a small error in angular direction of measurement would mean an appreciable error in true radial distance.

(c) The transitions at the entry and exit may be of different lengths which make it impracticable to maintain uniform centres on them even though the degree of the circular curves may be nearly the same.

424. Cuttings of rails on curves :- Rails are usually laid with square joints on curve. On curved track the inner rail joints gradually lead over the outer rail joints. When the inner rail of the curve is ahead of the outer rail by an amount equal to half the pitch of bolt holes, cut rails should be provided to obtain square joints. Cut rail is a rail which is shorter than the standard length of rail by an amount equal to the pitch of the bolt holes. The excess length ‘d’ by which the inner rail gains over the outer rail is calculated by the formula –

d = LG/R

where ‘d’ is the length in mm. by which the inner rail joint is ahead of the outer rail joint over the entire length of the curve, if cut rails are not provided. L = length of the curve in meters R= radius of the curve in meters G= the gauge + width of the rail head in mm.

The number of cut rails for a particular curve is worked out by the formula –

N = ————————————————–
              pitch of the bolt holes in mm.

It must be ensured that rail joints are square at beginning and at the end of the curve.

425. Joints on curves :- Rails joints on curves normally be laid square. On the sharp curves less than 400 meters on the Broad Gauge and 300 meters on the Metre Gauge the rail joints may be staggered, where elbows and kinks are likely to develop if rail joints are laid square.

426. Check rails on curves :- Check rails should be provided on the inside of the inner rail of the curve as stipulated in the schedule of dimensions.

Appropriate clearances should be provided between the check rail and the running rail as stipulated in the schedule of dimensions. Check rails reduce the risk of derailment on the sharp curves.

Location where check rails should be provided shall be decided by the Chief Engineer taking into considration the negotiability of the rolling stock and the curve geometry.

427. Wear on outer rail of curves :- (1) This can be reduced effectively

(a) by lubricating the gauge face of outer rails on the curves.

(b) by maintaining correct curve geometry and superelevation.

(c) Provision of the suitable check rail.

(2) Rail flange lubricators should be provided on curves of radius 600 meters and less on Broad Gauge and of radius 300 meters and less at Meter Gauge to avoid rail face wear, the first lubricator being provided a little ahead of the curve.

428. Measurement of rail wear on sharp curves:– The wear of rails of curves having radius of 600 M. or less on B. G. and 300 M. or less on M. G. shall be periodically recorded. Railways should prescribe the periodicity of measurement of wear on those sharp curves. The lateral, vertical and total loss of section should be recorded. Proper record of the measurements should also be maintained.


ANNEXURE – 4/3 PARA 405 (2)


ANNEXURE – 4/3 PARA 405 (2)


ANNEXURE – 4/4 PARA 405 (2)


ANNEXURE – 4/4 PARA 405 (2)


ANNEXURE – 4/5 PARA 405 (2)


ANNEXURE-4/4 PARA 420 (2) ……..Contd.


Note – No. of Pages to be allotted for each curve.

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