Degree of curvature

Encyclopedia

**Degree of curve**or

**degree of curvature**is a measure of curvature

Curvature

In mathematics, curvature refers to any of a number of loosely related concepts in different areas of geometry. Intuitively, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line, but this is defined in different ways depending on the context...

of a circular arc used in civil engineering

Civil engineering

Civil engineering is a professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including works like roads, bridges, canals, dams, and buildings...

for its easy use in layout surveying

Surveying

See Also: Public Land Survey SystemSurveying or land surveying is the technique, profession, and science of accurately determining the terrestrial or three-dimensional position of points and the distances and angles between them...

.

A

*n*-degree curve turns the forward direction by

*n*degrees

Degree (angle)

A degree , usually denoted by ° , is a measurement of plane angle, representing 1⁄360 of a full rotation; one degree is equivalent to π/180 radians...

over some agreed-upon distance. The usual distance in US road work is 100 ft (30.48 m) of arc

Arc (geometry)

In geometry, an arc is a closed segment of a differentiable curve in the two-dimensional plane; for example, a circular arc is a segment of the circumference of a circle...

. US railroad work traditionally used 100 ft of chord

Chord (geometry)

A chord of a circle is a geometric line segment whose endpoints both lie on the circumference of the circle.A secant or a secant line is the line extension of a chord. More generally, a chord is a line segment joining two points on any curve, such as but not limited to an ellipse...

and this may be used in other places for road work. Other lengths may be used—such as 100 metres where SI

Si

Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

is favoured, or a shorter length for sharper curves.

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

The 100 ft (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.

## See also

- CurveCurveIn mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...
- Highway engineeringHighway engineeringHighway engineering is an engineering discipline branching from civil engineering which involves the design, construction and maintenance of Highway Systems. Highway Engineering become prominent towards the latter half of the 20th Century after World War 2. Standards of highway engineering are...
- Lateral motion deviceLateral motion deviceLateral motion devices permit the axles in some railroad locomotives to move sideways relative to the frame.-Purpose:The coupled driving wheels on steam locomotives were held in a straight line by the locomotive's frame...
- Minimum railway curve radiusMinimum railway curve radiusThe minimum railway curve radius, the shortest design radius, has an important bearing on constructions costs and operating costs and, in combination with superelevation in the case of train tracks, determines the maximum safe speed of a curve. Superelevation is not a factor on tramway tracks...

- Railway systems engineeringRailway systems engineeringRailway systems engineering is a multi-faceted engineering discipline dealing with the design, construction and operation of all types of railway systems....
- Track transition curveTrack transition curveA track transition curve, or spiral easement, is a mathematically calculated curve on a section of highway, or railroad track, where a straight section changes into a curve. It is designed to prevent sudden changes in centripetal force...
- Transition curve

## External links

*Note the variation in usage among these samples.*

- http://www.du.edu/~jcalvert/railway/degcurv.htm
- http://www.tpub.com/content/engineering/14071/css/14071_242.htm
- http://www.steamlocomotive.com/model/curve.html
- http://www.cee.mtu.edu/~balkire/ce3401tc/ce3401Lec20.doc
- http://www.trainweb.org/freemoslo/Modules/Tips-and-Techniques/degrees_of_curve.htm
- http://www.fairview-industries.com/standardmodule/circurve.htm *http://ceprofs.tamu.edu/rbruner/curves/circularcrvs.htm
- http://www.memun.org/SchoolsProject/html/Resources/Roads/Fundamentals.htm
- http://www.cityoffrederick.com/departments/Planning/APPENDIX_C_SUBDIVISION_REGULATIONS/Sec__5__Final_subdivision_plat.html