Degree of curvature

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Degree of curve or degree of curvature is a measure of curvature of a circular arc used in civil engineering for its easy use in layout surveying.

Definition

The

over the standard length of arc or chord.

Usage

Curvature is usually measured in

and a chain, tape, or rope of a prescribed length.

Length selection

The usual distance used to compute degree of curvature in North American

SI

is favoured or a shorter length for sharper curves. Where degree of curvature is based on 100 units of arc length, the conversion between degree of curvature and radius is Dr = 18000/π ≈ 5729.57795, where D is degree and r is radius.

Since rail routes have very large radii, they are laid out in chords, as the difference to the arc is inconsequential; this made work easier before electronic calculators became available.

The 100 feet (30.48 m) is called a station, used to define length along a road or other alignment, annotated as stations plus feet 1+00, 2+00, etc. Metric work may use similar notation, such as kilometers plus meters 1+000.

Formulas for radius of curvature

Degree of curvature can be converted to radius of curvature by the following formulae:

Formula from arc length

${\displaystyle r={\frac {180^{\circ }A}{\pi D_{\text{C}}}}}$

where ${\displaystyle A}$ is arc length, ${\displaystyle r}$ is radius of curvature, and ${\displaystyle D_{\text{C}}}$ is degree of curvature, arc definition

Substitute deflection angle for degree of curvature or make arc length equal to 100 feet.

Formula from chord length

${\displaystyle r={\frac {C}{2\sin \left({\frac {D_{\text{C}}}{2}}\right)}}}$

where ${\displaystyle C}$ is chord length, ${\displaystyle r}$ is radius of curvature and ${\displaystyle D_{\text{C}}}$ is degree of curvature, chord definition

Formula from radius

${\displaystyle D_{\text{C}}=5729.58/r}$

Example

As an example, a curve with an

changes by 1 degree. The radius of such a curve is 5729.57795. If the chord definition is used, each 100-unit chord length will sweep 1 degree with a radius of 5729.651 units, and the chord of the whole curve will be slightly shorter than 600 units.

See also

References

External links

This article includes a list of general references, but it lacks sufficient corresponding inline citations. Please help to improve this article by introducing more precise citations. (June 2021) (Learn how and when to remove this message)

• "Degree of Curvature". 2005-02-12. Archived from the original on 2005-02-12. Retrieved 2021-06-24.
• http://www.tpub.com/content/engineering/14071/css/14071_242.htm Archived 2005-01-27 at the Wayback Machine
• "Just how sharp is that curve?". 2005-02-23. Archived from the original on 2005-02-23. Retrieved 2021-06-24.
• "Interactive Highway Design".
• "Degrees of Curve". www.trainweb.org. Retrieved 2021-06-24.
• "CIRCULAR CURVE". 2004-12-13. Archived from the original on 2004-12-13. Retrieved 2021-06-24.
• "Horizontal circular curves are used to transition the change in alignment at angle points in the tangent (straight) portions of alignments". 2005-03-04. Archived from the original on 2005-03-04. Retrieved 2021-06-24.
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• "Sec. 5. Final subdivision plat". 2004-09-17. Archived from the original on 2004-09-17. Retrieved 2021-06-24.