Gradients are provided to negotiate the rise or fall in the level of the railway track. A rising gradient is one in which the track rises in the direction of the movement of traffic and a down or falling gradient is one in which the track loses elevation in the direction of the movement of traffic.

A gradient is normally represented by the distance travelled for a rise or fall of one unit. Sometimes the gradient is indicated as per cent rise or fall. For example, if there is a rise of 1 m in 400 m, the gradient is 1 in 400 or 0.25%, as shown in Fig. 12.1.

Gradients are provided to meet the following objectives.

(a) To reach various stations at different elevations

(b) To follow the natural contours of the ground to the extent possible

(c) To reduce the cost of earthwork.

The following types of gradients are used on the railways.

(b) Pusher or helper gradient

(d) Gradients in station yards

The ruling gradient is the steepest gradient that exists in a section. It determines the maximum load that can be hauled by a locomotive on that section. While deciding the ruling gradient of a section, it is not only the severity of the gradient but also its length as well as its position with respect to the gradients on both sides that have to be taken into consideration. The power of the locomotive to be put into service on the track also plays an important role in taking this decision, as the locomotive should have adequate power to haul the entire load over the ruling gradient at the maximum permissible speed.

The extra force P required by a locomotive to pull a train of weight W on a gradient with an angle of inclination d is

P = W Sin0

= W tan d (approximately, as d is very small)

= W x gradient

Indian Railways does not specify any fixed ruling gradient owing to enormous variations in the topography of the country, the traffic plying on various routes, and the speed and type of locomotive in use on various sections. Generally, the following ruling gradients are adopted on Indian Railways when there is only one locomotive pulling the train.

In plain terrain: 1 in 150 to 1 in 250 In hilly terrain: 1 in 100 to 1 in 150

Once a ruling gradient has been specified for a section, all other gradients provided in that section should be flatter than the ruling gradient after making due compensation for curvature.

## Pusher or Helper Gradient

In hilly areas, the rate of rise of the terrain becomes very important when trying to reduce the length of the railway line and, therefore, sometimes gradients steeper than the ruling gradient are provided to reduce the overall cost. In such situations, one locomotive is not adequate to pull the entire load, and an extra locomotive is required.

When the gradient of the ensuing section is so steep as to necessitate the use of an extra engine for pushing the train, it is known as a pusher or helper gradient. Examples of pusher gradients are the Budni-Barkhera section of Central Railways and the Darjeeling Himalayan Railway section.