For a Simple circular curve which one of the following gives the correct relation between the radius R and degree of curve D, for 30m arc length?
- AR = 5729.6 / D
- BR = 1718.9 / DCorrect
- CR = 1145.9 / D
- DR = 572.9 / D
Solution
Concept
Radius and degree of curve relation
Formula
R = 1718.9 / D
Step-by-step solution
1. Degree of curve D is defined as the angle subtended at the center by an arc of specified length. 2. For an arc length of 30 m, the relation in radians is arc length / radius = D × (π / 180 degrees). 3. Rearranging for radius R gives R = (30 × 180) / (π × D) = 1718.87 / D m, which simplifies to R = 1718.9 / D. Answer: B
Explanation
For a 30-meter arc length, the degree of curve D is defined by the angle subtended by a 30m arc at the center. Using the relation R = (30 × 180) / (π × D), the value evaluates to approximately 1718.9 divided by D. Therefore, the radius R and degree of curve D are related by R = 1718.9 / D.
Why the other options are wrong
A) R = 5729.6 / D corresponds to an arc length of 100 ft or chord definition. C) R = 1145.9 / D corresponds to a 20 m arc length. D) R = 572.9 / D corresponds to a 10 m arc length.
Shortcut
For 30 m arc: R = 1718.9 / D (30 x 57.3 = 1719); for 20 m arc: R = 1145.9 / D.
Common mistake
Confusing the formula for a 30m arc length with the 20m arc length formula (1145.9/D) or 100 ft arc length formula.
Correct answer: B) R = 1718.9 / D