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What is Vertical Curve?

A vertical curve is a curve provided in vertical plane. This is required to be provided at the meeting of grades. The vertical curves can be of two types:

  • Summit type; and
  • sag type

When a vehicle moves from a steeper up gradient to a less steep up gradient (or less steep down gradient to steeper down gradient), the junction is called summit. When a vehicle moves from a less steep up gradient to a steeper up gradient (or steeper down gradient to a less steep down gradient), the junction is called sag.

Just as in the case of horizontal curves, when a vehicle is moving on vertical curve, centrifugal force is acting on the vehicle in the vertical plane. The force acts away from the center of the vertical curve. These forces act in addition to the weight of the vehicle and have to be managed to avoid undesirable effects on the vehicle. This effect is similar to the experience of people moving in a lift. When the lift moves down (similar to sag type vertical curve) there is on-loading and when the lift moves up (similar to summit type vertical curve) there is off-loading.

The following considerations are there in providing the vertical curves:


a)Summit type vertical curves: The centrifugal force acts upwards in case of vehicle moving on summit type vertical curves. This is opposite to the weight of the vehicle and causes off-loading (reduction in wheel load) of the vehicles. The offloading of wheels coupled with lateral forces may lead to derailment of vehicle on track. Therefore, while designing the vertical curves, the radius is to be chosen such that this offloading is within safe limits.

b)Sag type vertical curves: The centrifugal force acts downwards in case of vehicles moving on sag type vertical curves. This acts in the same direction as the weight and normally does not have any harmful effect on the vehicle except slightly higher load on springs and axles. However, if the train is on sag type vertical curve and brake is applied from locomotive, the front portion near locomotive will start decelerating, whereas the rear portion, which is on a down gradient, will continue to move forward due to the effect of gravity. In such a case, the vehicles may bunch together and if the vehicles on the sag are empty, these may get lifted up, causing off-loading. In this case, the vehicles may be prone to derailment. Properly designed vertical curves will reduce the chances of this off loading.

Passenger Discomfort:

As discussed above, in case of vertical curves of summit type, off-loading is there and in case of sag type vertical curves, on-loading is there. In either of the two cases, passengers will be discomforted if the acceleration is high. The limits of vertical acceleration are generally accepted as 0.3 to 0.45m/sec2.


The radius of these curves shall be as flat as possible as these:

  • Badly affects the visibility, which in turn affects
    • Safety in the approach of Level crossings,
    • Safety of trolley movement
    • Safety of gang working
    • Safety of keyman.


To keep the vertical acceleration to minimum, properly designed vertical curve is necessary to be provided.

However, these curves are required to be provided only where the difference in the gradients meeting is large and the forces generated may lead to unsafe conditions/ discomfort. The vertical curves provided on IR are circular. In vertical curves, there is no requirement of transitions, since there is no superelevation and also since the forces generated are small due to the very large radii of the vertical curves. The vertical curves are to be provided when the algebraic difference in gradients meeting at a point is equal to or more than 4 mm per metre or 0.4 percent.

Classifications of RoutesMinimum Radius (metre)
Group A – BG4000
Group B – BG3000
Group C, D, E – BG2500

Providing Vertical Curves

The vertical curves of the summit type can only be provided in the formation during earthwork. It is very difficult to provide the same in service. Extra care shall be taken during construction/ gauge conversion of a line to provide proper summit type vertical curves. As regards the sag type vertical curves, some improvement can be made in service by increasing the ballast cushion. But it will be good from maintenance perspective if properly designed vertical curves are provided in the formation during the construction of new lines/ gauge conversion.

Maintenance Issues with Vertical Curves

  • Drainage at junction of gradients: On sag type of vertical curves, the drainage is a very important consideration and therefore, such curves shall not be located in cuttings or tunnels as far as possible.
  • Vertical curves in Long Tunnels: In the long tunnels, the summit type vertical curves shall be avoided. The exhaust fumes, being hot and lighter than the surrounding air, will tend to collect near the crown of the tunnel and will create the problems of ventilation in long tunnels.
  • Vertical Curve in Horizontal Curve: In horizontal curves, the vertical curves of summit type shall be avoided, especially where LWR is also there. The track will tend to lift up on such summit curves and may lead to buckling of track. Also, since there is a tendency for off-loading of the vehicles, coupled with the lateral forces due to the horizontal curves, the stability of the track under load will be adversely affected. Maintaining of the vertical curve in a horizontal curve will be much more difficult as compared to two separate curves.
  • Maintenance of Vertical curves had been neglected,so far since there was no checking of longitudinal levels of track was done except in case of

accidents,major regradation during box pushing or RUB works. Nowadays we take very often the longitudinal levels of track,for Design mode tamping and BCM work etc. We can mark permanently the location where a vertical curve starts,ends radius and the vertical correction factor.And during tamping the necessary vertical correction factor shall be fed to the lift potentiometer. Most of the vertical curves are provided with minimum recommended radius.Except sag or valley curves,the radius do not improve in service on summit or crest curves,contrarily the radius decreases during manual packing or machine tamping in smoothening mode.

Prohibited Locations for change in gradient

There shall be no change in gradient in the points and crossing zone, on unballasted deck girder bridges, transition portion of horizontal curves etc and therefore, the vertical curves shall not be laid in such locations.

Issues with Vertical Curve in Level Crossing Approach

The minimum visibility required in the approach of Level crossings and in the vicinity of work sites as per IPWM is 600m. What should be the minimum vertical radius considering clear visibility of 600m on track?

600×600=(2R-V)V; Considering V=2.1M as Eye level of Driver

360000=2RV; V2 being small neglected

R = 360000/2×2.1 = 85714M.

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