If the degree of a road curve is defined using a standard arc length of 30 m, what is the radius of a 1° curve?

Introduction / Context:The degree of curve provides a convenient measure of curvature used in highway and railway alignment. Two common definitions are the arc definition and the chord definition. Here, the arc definition with a 30 m standard arc length is specified.

Given Data / Assumptions:

• Arc definition of degree of curve.
• Standard arc length = 30 m.
• Degree D = 1° (central angle subtended by the 30 m arc).

Concept / Approach:For the arc definition, the relation between radius R and degree D (in degrees) for an arc length s is s = (π/180) * R * D. Solving for R with s = 30 m and D = 1° gives the desired radius.

Step-by-Step Solution:s = (π/180) * R * D30 = (π/180) * R * 1R = 30 * 180 / πR ≈ 5400 / 3.1416 ≈ 1718.9 m ≈ 1719 m

Verification / Alternative check:Rule of thumb for arc definition with 30 m arc: R ≈ 1720 / D (with R in metres, D in degrees). For D = 1°, R ≈ 1720 m, consistent with 1719 m when calculated precisely.

Why Other Options Are Wrong:

• 1146, 1046, 1619, 1573 m: do not satisfy the arc-length relation for D = 1° with s = 30 m; they correspond to other D values or alternate definitions.

Common Pitfalls:

• Using the chord definition formula instead of arc definition.
• Mixing units (degrees vs radians) when computing.

Final Answer:1719 m