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What would be the length of the curve, if the degree of curvature is 5┬░ for 20 m arc and the deflection angle is given as 100╦Ъ?
320 m
480 m
600 m
400 m
400 m
The length of a simple circular curve is directly proportional to its deflection angle (central angle) for a given arc length definition. Using the relation between degree of curvature, arc length, and deflection angle, the total curve length is calculated as 400 m.
The length of a simple circular curve is directly proportional to its deflection angle (central angle) for a given arc length definition. Using the relation between degree of curvature, arc length, and deflection angle, the total curve length is calculated as 400 m.
╬ФLтАЛ=DsтАЛ тАФ Basic arc length-deflection relation
L=Ds├Ч╬ФтАЛ тАФ Formula for length of curve (L)
R=D1146тАЛ тАФ Radius of curve for a 20┬аm arc
The degree of curvature (D) represents the angle subtended at the center by an arc of standard length (s=20┬аm). By proportion, the ratio of total curve length (L) to total deflection angle (╬Ф) is equal to the ratio of standard arc length (s) to the degree of curve (D).
Degree of curve (D) can be defined either by arc definition (20┬аm or 30┬аm) or chord definition.
For a 20┬аm arc definition, R=D1145.92тАЛтЙИD1146тАЛ┬аm.
Deflection angle (╬Ф) is equal to the total central angle subtended by the circular curve.
Simple linear proportion method allows quick field calculations without finding radius.
Applicable directly to both 20┬аm and 30┬аm arc definition conventions.
Assumes uniform curvature, which applies only to simple circular curves and not transition curves.
Alignment design of roads and railways for setting out simple circular curves.
Surveying calculations for curve layout using chainage and deflection angles.
Option A (320 m): Incorrect calculation resulting from using D=6.25┬░ or wrong ratio.
Option B (480 m): Incorrect calculation resulting from using 30┬аm arc formula (30├Ч100/5=600┬аm) with an arithmetic error or wrong inputs.
Option C (600 m): Corresponds to a 30┬аm arc definition (L=530├Ч100тАЛ=600┬аm), but the question specifies a 20┬аm arc.
D is correct тАФ Using L=Ds├Ч╬ФтАЛ, L = \frac{20 \times 100┬░{5┬░ = 400\text{ m}.
Always verify whether the degree of curvature is specified for a 20┬аm arc or a 30┬аm arc before calculating curve length or radius in GATE/ESE exams.