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How to identified curve by a degree of curvature
Radius
By chord
By arc
Both B and C
Both B and C
The degree of curvature (D) defines the sharpness of a circular curve in surveying. It is identified either by the Arc Definition or the Chord Definition, based on the angle subtended at the center by a standard arc length or a standard chord length (typically 20 m or 30 m).
The degree of curvature (D) defines the sharpness of a circular curve in surveying. It is identified either by the Arc Definition or the Chord Definition, based on the angle subtended at the center by a standard arc length or a standard chord length (typically 20 m or 30 m).
D=R1718.9โ โ Degree of curvature for 30 m arc definition (where R is radius in meters)
D=R1145.9โ โ Degree of curvature for 20 m arc definition
R=2sin(D/2)Sโ โ Exact relationship for chord definition where S is standard chord length
In the Arc Definition, the degree of curvature is the angle subtended at the center by an arc of standard length (e.g., 20 m or 30 m), which is widely used in highway engineering. In the Chord Definition, it is the angle subtended at the center by a chord of standard length, commonly used in railway engineering.
Arc definition is predominantly used in highway engineering surveys.
Chord definition is predominantly used in railway engineering surveys.
For flat curves (large radius), arc length and chord length are nearly equal, giving practically identical values of D.
Allows field surveyors to set out curves using standard chain or tape lengths without calculating exact radius.
Provides an intuitive measure of curve sharpness (higher degree means sharper curve).
Slight discrepancy exists between arc and chord definitions for very sharp curves.
Formula conversions (D=1718.9/R) are approximations relying on small-angle assumptions.
Setting out horizontal circular curves on highways and railways.
Determining safe design speed and superelevation required for a curve.
| Feature | Arc Definition | Chord Definition |
|---|---|---|
Definition Standard | Angle subtended by a standard arc | Angle subtended by a standard chord |
Primary Application | Highways and Roads | Railways |
30m Relation Formula | R=D1718.9โ | R=sin(D/2)15โ |
Radius alone defines the physical size of a curve, but degree of curvature (D) is designated specifically via standard chord or arc length definitions.
Option A is incorrect because Radius is the distance metric, whereas degree of curvature is explicitly identified by chord or arc definitions.
D is correct โ Degree of curvature is defined by either the angle subtended by a standard arc (Arc Definition) or a standard chord (Chord Definition).
For Indian competitive exams (GATE/ESE/SSCJE), always check whether a 20 m or 30 m chain is specified in the problem; use D=1146/R for 20 m chain and D=1719/R for 30 m chain.
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