Question

On a section of B.G track, the ruling gradient is 1 in 200. If the track is laid in that place at a curve of 5°, then the allowable ruling gradient on the curve will be
1. 1 in 333
2. 1 in 555
3. 1 in 666
4. 1 in 444

Answer 1

Correct Answer - Option 1 : 1 in 333

Concept:

Grade compensation:

The ruling gradient is the maximum gradient on a particular section, but if a curve lies on a ruling gradient, the resistance due to gradient is increased by that due to curvature, and this further increases the resistance beyond the ruling gradient. In order to avoid resistances beyond the allowable limits, the gradients are reduced on curves, and this reduction is known as the grade compensation for the curve.

Allowable ruling gradient = Ruling gradient - Grade compensation 

Grade compensation (GC) for BG = 0.04% per degree of curve
Grade compensation (GC) for MG = 0.03% per degree of curve
Grade compensation (GC) for NG = 0.02% per degree of curve

Calculation

Given,

Degree of curve D = 5° 

Ruling Gradient = 1 in 200 

So for 5° curve, compensation,

= 0.04 × 5 = 0.20%

∴ Ruling gradient \(= \frac{1}{{200}} \times 100 = 0.5{\rm{\% }}\)

∴ Allowable gradient = (0.5 - 0.2)% =\( {\rm{\;}}\frac{{0.3}}{{100}} = \frac{1}{{333}}\)

∴ Allowable Gradient = 1/333