Insufficiency of cant

In the profile across a Railway in curve, the insufficiency of cant is the variation, negative, between the cant theoretically necessary to compensate for the Centrifugal force and the real cant.

Centrifugal force, danger and discomfort of the passengers

In the curves, the railway vehicles are subjected, like any mobile in displacement, with a centrifugal force proportional to the square rate of travel and inversely proportional to the ray of the curve, which tends to push them towards the outside of the curve.

Of this fact the vehicles exert on the way of the lateral forces which can present a danger beyond certain speed.

Moreover, the travellers present in the Véhicule S feel also this push, source of discomfort.

Three possibilities

To raise the external rail

To compensate for the centrifugal force, the manufacturers of railways incline the way by raising the external file of Rail. The difference in level between the two files of rail is called the “cant”.

Need for a compromise

This variation results in practice from a compromise, always lower than the maximum value theoretically necessary.

Indeed, the speed of the Train S is variable, that is to say because it is about a mixed line where circulate of the trains from which the authorized speed limit is different (rapids, slow train, freight…), that is to say on a specialized line where circulate of the homogeneous trains (for example a line LGV) in consequence of the risks of circulation, a which can train if required to even, be stopped in the curve.

It results from it:

for the faster trains a insufficiency of cant
for the slower trains contrary a excess to cant .

Theoretical and practical cant

In France, the cant is in general taken equal to the 7/10 of the theoretical cant calculated for the maximum speed practiced on the line, while remaining framed within certain limits established by the experiment.

This theoretical cant is worth D = 11,8 v2/r, D in mm, v being maximum speed in km/h and R the ray of the curve in meters.

To increase the ray of the curves

The other means of reducing the centrifugal force is to increase the ray of the curves. Thus on the lines traversed to 160 km/h, one does not go down in lower part from 1000 m for the rays from the curves, and 4000 m for the lines at high speed LGV.

To use train pendular

For the comfort of the travellers, one can also use pendular trains.

In this case the slope of the case compensates for the insufficiency of cant at least partially.

But that does not change anything with the efforts imposed on the way, which on the contrary are amplified if one agrees to negotiate a curve given at higher speed.

Parabolic connection and comfort of the travellers

The comfort of the travellers also depends on the variations of this insufficiency of cant at the entry and the exit on the curves.

To counter, one adopts in these zones of the forms of progressive curve known as “parabolic connection”.

They are delicate zones for the stability of the vehicles, because it is formed because of progressive slope of the way a “left”, which means that the four points corresponding to the contact points of the wheels of a vehicle are not in the same plan.

Discussion on the advantage of the pendular oars

The networks which strongly use the insufficiency of cant have little interest to use pendular oars because the device owes " to return confort" with the passengers and prohibited, consequently, to preserve the same insufficiency of cant as out of not pendulée oar.

To some extent, the pendulation is nibbled from 1/3 to 2/3 by this restitution of comfort (absence of lateral force inflicted to the passengers).

When one adds the investments on the bench of ballast to contain the increase in the lateral forces, the modifications of indication and the level crossings, of the electric traction, the creation of avoidances to pass the slower trains (with constant traffic), the reserve of materials at each point to make the hour, one realizes that the local government agencies balk to finance such an assembly.

Random links: