Railway/highway geometric design – grade compensation due to curvature If D is the degree of curve, what is the percentage reduction to be applied to the ruling gradient (grade compensation) to account for curvature?

Introduction / Context:
When an alignment transitions into a horizontal curve, vehicles experience extra resistance. In railroad and classic highway geometrics, designers apply a small reduction in the ruling gradient so the combined grade-plus-curvature resistance does not exceed permissible limits. This reduction is called grade compensation and is often expressed as a percentage per degree of curve.

Given Data / Assumptions:

• D = degree of curve (standard chord definition).
• Ruling gradient is the limiting maximum grade used for design.
• Objective is to select the conventional compensation rate used in practice.

Concept / Approach:
Classic practice adopts a linear rule: compensation (%) = k * D, where k is a small coefficient. For broad-gauge railway work and many textbook treatments, k ≈ 0.04. This value keeps train traction demands or vehicle effort within limits when negotiating curvature.

Step-by-Step Solution:
Identify typical compensation coefficient k ≈ 0.04.Compute compensation = 0.04 * D percent.Match with options → 0.04 D.

Verification / Alternative check:
Empirical practice tables consistently lie near 0.04% per degree. Even where slight variations exist, 0.04 D is the standard textbook choice.

Why Other Options Are Wrong:

• 0.01 D, 0.02 D, 0.03 D: underestimate compensation and may overstrain traction on curves.
• 0.005 D: far too small; does not reflect customary design rules.

Common Pitfalls:
Confusing grade compensation (percent) with superelevation (cross slope). They address different phenomena.

Final Answer:
0.04 D