Grade compensation on horizontal curves (hill roads) For a hill road having a horizontal curve of radius 50 m, what percentage grade compensation should be applied to the ruling/upgradient?

Introduction / Context:On horizontal curves, vehicles experience additional tractive resistance. To maintain similar effort as on tangent sections, gradients are often reduced (grade compensation) by a specified amount depending on curve sharpness.

Given Data / Assumptions:

• Radius R = 50 m.
• Use the standard hill-road compensation rule with an upper cap used in practice.

Concept / Approach:A widely used rule for roads states the compensation in percent is 75/R (with R in metres) subject to a maximum cap (often about 0.75%). For sharp curves (small R), the computed value may exceed the cap, in which case the cap governs.

Step-by-Step Solution:Compensation = 75 / R = 75 / 50 = 1.5% (before capping).If the governing cap is 0.75%, the designer would apply 0.75% in detailing. The formula asked, however, is the rule: 75/R.

Verification / Alternative check:Design aids and manuals list identical expressions, emphasizing the cap when the curve is very sharp.

Why Other Options Are Wrong:60/R, 70/R, 80/R, 100/R are not the standard values used in road design practice for this purpose.

Common Pitfalls:Applying compensation to downgrade sections unnecessarily; forgetting to respect the maximum compensation cap; mixing up railway and highway rules.

Final Answer:75/R