What is the maximum limit of grade compensation for the gradient on the horizontal curve along highways, if 'R' is the radius of the circular curve in metres?
- A50 / R
- B75 / RCorrect
- C150 / R
- D300 / R
Solution
Concept
On a horizontal curve, the gradient is reduced (grade compensation) because of the extra tractive resistance on the curve. IRC limits this reduction to a maximum of 75/R percent.
Formula
Grade compensation (%) = (30 + R) / R, subject to a maximum of 75 / R
Step-by-step solution
1. A curve adds extra resistance, so the road gradient on the curve is eased. 2. As per IRC, grade compensation = (30 + R) / R percent. 3. The maximum value of this compensation is limited to 75 / R percent. 4. Grade compensation is not needed if the compensated gradient would be 4% or flatter. 5. So the answer is (B) 75 / R.
Explanation
When a vehicle moves on a curve, it faces more resistance than on a straight road. So the gradient on the curve is reduced by an amount called grade compensation. IRC fixes the maximum value of this reduction as 75/R percent.
Why the other options are wrong
(A) 50/R, (C) 150/R and (D) 300/R are not the IRC limit; only 75/R is the maximum grade compensation.
Shortcut
Remember (30 + R)/R, but the maximum is 75/R.
Common mistake
Writing (30 + R)/R as the answer and forgetting that the question asks for the maximum limit, which is 75/R.
Correct answer: B) 75 / R