Grade compensation on curves: To compensate the loss of tractive effort on a highway curve of radius R (in metres), the percentage reduction of gradient to be provided is

Introduction / Context:
On curves, vehicles experience additional resistance due to curvature (tire scrub and alignment of axles), effectively making the grade feel steeper. Designers therefore reduce the ruling grade by a small amount on curves, known as grade compensation.

Given Data / Assumptions:

• Curve radius R in metres.
• Ruling gradients applicable to hilly/rolling terrain.
• Standard highway design practice for compensation.

Concept / Approach:
A commonly adopted relation is: grade compensation (%) = 75/R, with an upper cap of 0.75%. This keeps tractive effort within acceptable limits for heavy vehicles without over-flattening the alignment.

Step-by-Step Solution:
Identify curve radius R.Compute compensation = 75/R percent.If computed value > 0.75%, adopt 0.75% (cap).

Verification / Alternative check:
For R = 100 m, compensation = 75/100 = 0.75% which equals the cap; for R = 300 m, compensation = 0.25% < 0.75%. These results align with accepted practice, providing modest reductions on gentler curves and stronger relief on sharper curves within the cap.

Why Other Options Are Wrong:

• 30/R or 50/R: underestimate compensation on sharper curves.
• 100/R: too high; risks unnecessary earthwork and cost.
• No compensation: ignores real added resistance on curves.

Common Pitfalls:

• Applying compensation to grades already very flat; unnecessary reductions complicate drainage.
• Forgetting to check maximum cap, leading to excessive flattening on very small R.

Final Answer:
75/R, limited to a maximum of 0.75%