Definition check (degree of curve): In highway engineering, the degree of a road curve is defined as the central angle (in degrees) subtended by an arc length of how many metres?

Introduction / Context:
The “degree of curve” is a convenient way to express curvature without directly quoting the radius. Indian highway practice defines degree of curve with a fixed arc length so that designers and surveyors can translate between degree and radius easily.

Given Data / Assumptions:

• Highway (not railway) convention.
• Degree is the central angle for a specified arc length.
• We must choose the correct reference arc length.

Concept / Approach:

For roads, the degree of curve is based on an arc length of 30 metres. Therefore, if D is the degree of curve, the radius can be computed by R = 30 * 180 / (π * D) ≈ 1718.9 / D (metres). This linkage supports quick conversion between geometry set-out (by degrees) and design radius.

Step-by-Step Reasoning:

Verification / Alternative check:

Survey and geometric design texts for roads consistently adopt the 30 m arc definition; railways commonly use a chord-based 30 m definition in some contexts, but for highway curves, the 30 m arc is the standard reference.

Why Other Options Are Wrong:

• 10, 20, 25, 50 m: not the standard arc length used to define road curve degree in highway design.

Common Pitfalls:

• Confusing arc-based road definition with chord-based railway definitions.

Final Answer:

30 metres.