Degree of curvature

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

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 degree of curvature is defined as the central angle to the ends of an arc or chord of agreed length.^[1] Various lengths are commonly used in different areas of practice. This angle is also the change in forward direction as that portion of the curve is traveled.

Usage

Curvature is usually measured in radius of curvature. A small circle can be easily laid out by just using radius of curvature, But if the radius is large as a km or a mile, degree of curvature is more convenient for calculating and laying out the curve of large scale works like roads and railroads. By this method curve setting can be easily done with the help of a transit or theodolite and a chain, tape or rope of a prescribed length.

A n-degree curve turns the forward direction by n degrees over arc (or chord) length. The usual distance in North American road work is 100 feet (30.48 m) of arc.^[2] North American railroad work traditionally used 100 feet of chord and this may be used in other places for road work. Other lengths may be used—such as 30 metres or 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 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:

Diagram showing different parts of the curve used in the formula

Formula from arc length

$r={\frac {180A}{\pi D_{A}}}$

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

Formula from chord length

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

where $C$ is chord length, $r$ is radius of curvature and $D_C$ is degree of curvature, chord definition

References

↑ Wolf and Ghilani. Elementary Surveying, 11th ed., 2006
↑ Davis, Foote, and Kelly. Surveying Theory and Practice, 1966

External links

Note the variation in usage among these samples.

Railway infrastructure

Permanent way	Permanent way (history) Permanent way (current) Railroad tie/Sleeper Rail fastening system Track ballast Rail profile Fishplate Breather switch Datenail Axe ties Ladder track Baulk road Cant Minimum radius Track transition curve Clip and scotch

Trackwork and track structures	Junction Wye Railroad switch Gauntlet track Railway electrification system Third rail Overhead lines Guide bar Track gauge Track geometry Railway turntable Water crane Track pan Rail track Tramway track Classification yard Rail yard Siding Passing loop Balloon loop Headshunt Refuge siding Dual gauge Roll way

Signalling and safety	Derail Railway signalling Signalling control Wayside horn Railway signal Interlocking Level crossing Buffer stop Catch points Loading gauge Structure gauge Block post Train stop Signal bridge

Buildings	Railway station Station building Railway station layout Station clock Train shed Goods shed Motive power depot Roundhouse Railway platform

Railway track layouts

Running lines	Single track Passing loop Double track Quadruple track Crossover

Rail sidings	Balloon loop Headshunt Refuge siding Rail yard Classification yard

Junctions	Flying junction Level junction Double junction Facing and trailing Grand union Wye Switch / turnout / points Swingnose crossing Level crossing

Stations	Railway platform Side platform Island platform Bay platform Split platform Terminal station Balloon loop Spanish solution Cross-platform interchange Interchange station

Hillclimbing	Horseshoe curve Zig Zag / Switchback Spiral

Track geometry	Track gauge Ruling gradient Minimum curve radius Cant Cant deficiency

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