Metric degree of curve using a 30 m chord: For a simple circular curve with radius R = 300 m and the specified standard chord length c = 30 m, what is the degree of the curve (D)?

Introduction / Context:In metric practice, the degree of curve D is often defined as the central angle subtended by a standard chord length (commonly 30 m). This provides a convenient field measure linked directly to chords used during curve setting out by Rankine’s method.

Given Data / Assumptions:

• Radius R = 300 m.
• Standard chord c = 30 m.
• D is the central angle subtended by chord c (in degrees).

Concept / Approach:Geometry gives the chord–angle relation: c = 2R * sin(D/2). Solving for D yields D = 2 * arcsin(c / (2R)). Substituting the given values produces the numeric degree of curve appropriate for field deflection-angle calculations.

Step-by-Step Solution:

Verification / Alternative check:Approximate small-angle check: arcsin x ≈ x (radians). Using radians: 0.05 rad ≈ 2.8648°, doubled gives ≈ 5.7296°, matching the exact computation.

Why Other Options Are Wrong:

• 5.37°, 3.75°, 3.57° are inconsistent with the chord–radius relation for c = 30 m and R = 300 m.

Common Pitfalls:Using degrees in a calculator set to radians; confusing “degree of curve by arc length” with “degree by chord.”

Final Answer:5.73°