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Cant deficiency explained

The allowed speed in a given curve depends on two figures:

  1. The superelevation of the track, describing the height difference between left and right rail.
  2. The cant deficiency allowed by the railroad administration. This allowance is either given in general, or for a certain type of train.

"Cant deficiency" describes an acceleration. Instead of the usual ways to do that, the lateral acceleration to the outside of a curve is expressed by the amount of superelevation (or cant, since the term originated in Britain), that would be necessary to reach a balanced condition.

To give an example: An acceleration of 0.1 g, meaning 1/10 of the value towards mother earth, is expressed as "6 inches of cant deficiency":

Drawing of carriage on 6 inches of superelevation.

Drawing of carriage without superelevation, but
       acceleration to the side.

Drawing of carriage on 6 inches of superelevation,
       plus acceleration to the side.

Curve radius: 1000 feet Curve radius: 1000 feet Curve radius: 1000 feet
Speed: 39 mph Speed: 39 mph Speed: 55 mph
Superelevation: 6 inches Superelevation: none Superelevation: 6 inches
Cant deficiency: none Cant deficiency: 6 inches Cant deficiency: 6 inches
The first example shows perfectly superelevated track. The acceleration towards the outside of the curve is completely balanced by the superelevation, so the train can glide through the curve, without any forces felt by the passenger. The second example shows the same curve radius and the same speed, but the track isn't superelevated. Passengers are accelerated by 0.1 g towards the outside of the curve. As can be seen in the first example, 6 inches of superelevation would bring the train into a balanced condition. If the train goes faster than 39 mph in the 1000 feet radius curve, superelevation is missing again. 55 mph would need 12 inches of superelevation, but that's not allowed. These 12 inches can be replaced by 6 inches of actual superelevation plus 6 inches of cant deficiency.

For the calculation of allowed train speed, allowed cant deficiency is as good as actual superelevation. The two values add up. For the speed of a train on curvy track, cant deficiency is the decisive figure.

If the value of cant deficiency gets very high, a tilting system is needed to assure passenger comfort, but the existence of a tilting system does not make the train any faster. To operate faster, the allowed value for cant deficiency needs to be raised. The value depends on center of gravity, on axleload, on the quality of wheel/axle construction, on tracking ability, on track quality, and on the policy of the administration.

If all math is done by computers, the usefulness of calculation shortcuts like "cant deficiency" declines, and some railroads have begun to use standard metric acceleration figures instead. Within this article, conversion to acceleration in international units will be added in the page footer.

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Last modified: 2005-02-14