Curves provide extra resistance to the movement of trains. As a result, gradients are compensated to the following extent on curves

(a) On BG tracks, 0.04% per degree of the curve or 70/R, whichever is minimum

(b) On MG tracks, 0.03% per degree of curve or 52.5/R, whichever is minimum

(c) On NG tracks, 0.02% per degree of curve or 35/R, whichever is minimum where R is the radius of the curve in metres. The gradient of a curved portion of the section should be flatter than the ruling gradient because of the extra resistance offered by the curve.

Example 12.1 Find the steepest gradient on a 2° curve for a BG line with a ruling gradient of 1 in 200.

#### Solution

(i) Ruling gradient = 1 in 200 = 0.5%

(ii) Compensation for a 2° curve = 0.04 x 2 = 0.08%

(iii) Compensated gradient = 0.5 - 0.08 = 0.42% = 1 in 238 The steepest gradient on the curved track is 1 in 238.

#### Summary

The geometric design of a railway track is the scientific method of laying the various components of the track. It ensures the safety of the trains when they run at the maximum permissible speed and carry heavy axle loads. The gradient is a feature of the geometric design that is controlled by the hauling capacity of the engine. Other design features are horizontal curves, superelevation, and vertical curves. These features are discussed in Chapter.

#### Review Questions

2. What is meant by grade compensation for curvature? To what extent should a

ruling gradient of 1 in 150 on a broad gauge line be downgraded to accommodate a 3° curve? (Ans. 1 in 183)