Question

The steepest gradient computed for a 2 degree curve with a ruling gradient of 1 in 200 is done for broad gauge (BG) and metre gauge (MG) railway lines. Select the correct inference from the given options.
1. Steepest gradient = 0.44% for the BG and MG lines
2. Steepest gradient for the BG line = 0.42% and for the MG line = 0.44%
3. Steepest gradient for the BG line = 0.44% and for the MG line = 0.42%
4. Steepest gradient = 0.42 % for the BG and MG lines

Answer 1

Correct Answer - Option 2 : Steepest gradient for the BG line = 0.42% and for the MG line = 0.44%

Concept:

The ruling gradient:

• It 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.

Grade compensation for different types of gauge is given in the below table:

Type of gauge	Grade Compensation
B.G	0.04% per degree of curve
M.G	0.03% per degree of curve
N.G	0.02% per degree of curve

 

Calculation:

Given

Ruling gradient = 1 in 200 = \({1 \over 200} \times 100\) = 0.5 %

Degree of curve = 2°

Case - I: For Broad Gauge(BG)

Grande compensation = 0.04% per degree of curve = 0.04 \(\times\) 2 = 0.08%

Now,

Grade provided = Ruling gradient – grande compensation

Grade provided = 0.5 – 0.08 = 0.42%

Case - II: For Meter Gauge(MG)

Grande compensation = 0.03% per degree of curve = 0.03 \(\times\) 2 = 0.06%

Now,

Grade provided = Ruling gradient – grande compensation

Grade provided = 0.5 – 0.06 = 0.44%

Hence, Steepest gradient for the BG line = 0.42% and for the MG line = 0.44%.