# Degree of curvature

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

It is the repesentation and measurement of circular cuve in the form of angle in degrees subtended by an arc (cord) of lenght equal to standard chain measurement or industrial ruler measurement.

## Usage

Curvature is usually measured in radius of curvature. A small circle can be easily layed out by just using radius of curvature, But if the radius of curvature is large as 1km or 1mile it is very tedious to use the radius of curvature for laying out the curve. Hence Degree of curvature is used for laying out in large scale works like construction of roads, construction of rail roads, astronomical surveying etc. By this method curve setting can be easily done with the help of a chain, tape or rope of a prescribed length(Chain length).

A n-degree curve turns the forward direction by n degrees over Arc(Chain) length. The usual distance in US road work is 100 ft (30.48 m) of arc.[1] US railroad work traditionally used 100 ft of chord and this may be used in other places for road work. Other lengths may be used—such as 100 metres where SI is favoured, or a shorter length for sharper curves. Where degree is based on 100 units of arc length, the conversion between degree and radius is DR = 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 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.

## Formula

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

### Formula for Arc length

$R = \frac{A*180}{Da*\pi}$

here

$A$ is arc length
$R$ is radius of curvature
$Da$ is degree of curvature, arc definition

### Formula for Chord length

$R = \frac{\frac{C}{2}}{\sin (\frac{Dc}{2})}$

here

$C$ is chord length
$R$ is radius of curvature
$Dc$ is degree of curvature, chord definition