Degree of curvature

This article is about the measure of curvature. For other uses, seedegree (angle).

Degree of curveordegree of curvatureis a measure ofcurvatureof a circular arc used incivil engineeringfor its easy use in layoutsurveying.

Definition

Thedegreeofcurvatureis defined as thecentral angleto the ends of an agreed length of either anarcor achord;various lengths are commonly used in different areas of practice. This angle is also thechange in forward directionas that portion of the curve is traveled. In ann-degree curve, the forwardbearingchanges byndegreesover the standard length of arc or chord.

Usage

Curvature is usually measured inradius of curvature.A small circle can be easily laid out by just using radius of curvature, but degree of curvature is more convenient for calculating and laying out the curve if the radius is as large as a kilometer or mile, as is needed for large scale works like roads and railroads. By using degrees of curvature, curve setting can be easily done with the help of atransitortheodoliteand a chain, tape, or rope of a prescribed length.

Length selection

The usual distance used to compute degree of curvature in North Americanroad workis 100 feet (30.5 m) ofarc.Conversely, North Americanrailroadwork traditionally used 100 feet ofchord,which is used in other placesfor road work. Other lengths may be used—such as 100 metres (330 ft) whereSIis 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 isDr= 18000/π ≈ 5729.57795,whereDis degree andris 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

Diagram showing different parts of the curve used in the formula

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

Formula from arc length

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

where$A$isarc length,$r$is radius of curvature, and$D_{\text{C}}$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

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

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

Formula from radius

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

Example

As an example, a curve with anarc lengthof 600 units that has an overall sweep of 6 degrees is a 1-degree curve: For every 100 feet of arc, thebearingchanges 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

• Geometric design of roads
• Highway engineering
• Lateral motion device
• Minimum railway curve radius
• Radius of curvature (applications)
• Railway systems engineering
• Track geometry
• Track transition curve
• Transition curve
• Turning radius

External links

• "Degree of Curvature".2005-02-12. Archived fromthe originalon 2005-02-12.Retrieved2021-06-24.
• http://www.tpub.com/content/engineering/14071/css/14071_242.htmArchived2005-01-27 at theWayback Machine
• "Just how sharp is that curve?".2005-02-23. Archived fromthe originalon 2005-02-23.Retrieved2021-06-24.
• "Interactive Highway Design".
• "Degrees of Curve".www.trainweb.org.Retrieved2021-06-24.
• "CIRCULAR CURVE".2004-12-13. Archived fromthe originalon 2004-12-13.Retrieved2021-06-24.
• "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 fromthe originalon 2005-03-04.Retrieved2021-06-24.
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• "Sec. 5. Final subdivision plat".2004-09-17. Archived fromthe originalon 2004-09-17.Retrieved2021-06-24.