Last reviewed 30 Sept 2026 · 6 min read
Why gradients matter
A locomotive has a limited tractive effort. On level track it needs enough to overcome the rolling and air resistance; on a gradient it must in addition lift the weight of the train against gravity. The steeper the gradient, the smaller the load a single locomotive can haul — or the more locomotives (or helpers) are needed. The steepest gradient on a section therefore controls the haulage capacity of the whole line, which is why the gradient is chosen carefully during alignment.
Gradient is expressed as 1 in n (a rise of 1 unit in a horizontal distance of units) or as a percentage %. Example: 1 in 200 = 0.5 %.
Types of gradients
| Gradient | Meaning |
|---|---|
| Ruling gradient | The steepest gradient on a section which decides the maximum load that a single locomotive can haul at a speed on that section. It determines the design train load. The ruling gradient is not necessarily the steepest gradient in the section — the steeper gradients may be pusher or momentum gradients |
| Pusher (helper) gradient | A gradient steeper than the ruling gradient, where the trains are assisted by a second locomotive (a "pusher" or "banker") attached at the rear or in front, to negotiate the steep length — typical of ghat sections (with gradients as steep as about 1 in 37) |
| Momentum gradient | A gradient steeper than the ruling gradient that a train can climb by using the momentum (speed) gained on a preceding downgrade; suitable only where the train approaches at speed and the gradient is short |
| Minimum gradient | The flattest gradient required for drainage in cuttings and yards |
| Gradient in station yards | As flat as possible — a level or nearly level track, with a maximum of the order of 1 in 400, to prevent standing vehicles from rolling away and to make shunting easy |
Typical ruling gradients on Indian Railways lie between 1 in 150 and 1 in 200 in plains, and around 1 in 100 or steeper in hills — see the current standards for each class of line.
Effect of gradient on hauling capacity
The tractive effort available at the drawbar is used to overcome the resistances. Let be the tractive effort of the locomotive, the weight of the train, the resistance per tonne on a level track and the gradient:
so that the hauling capacity
falls as the gradient becomes steeper.
A locomotive has a tractive effort of 20 000 kgf at the wheel-rail interface. The train resistance on level track is 5 kgf per tonne.
- On level track: t.
- On a gradient of 1 in 200: gradient resistance = 1000/200 = 5 kgf/t → .
- On a gradient of 1 in 100: gradient resistance = 10 kgf/t → .
The 1 in 100 gradient reduces the load to a third of the level-track load.