Article Index

2. Geometry

a. Nomenclature; Geometric elements 

Δ: Central angle; also the deflection angle between the tangents.

R: Radius

L: Arc length

C: Chord length

T: Tangebt distance

  Figure F-1
Parts and Nomenclature



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Equation F-1 Equation F-2 Equation F-3


When dealing with highway or railroad alignments, another geometric element is often specified: degree of curvature, D. There are two different degree of curvature definitions:

DA, arc definition; the angle subtended by a 100.00' arc, Figure F-2(a).

DC, chord definition; the angle subtended by a 100.00' chord, Figure F-2(b).

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(a) Arc Definition (b) Chord Definition
Figure F-2
Degree of Curvature


Arc definition is used in highway and street design while the Chord definition is used in railroad design. Because each definition differs, there is a slightly different radius relationship for each:

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Equation F-4 Equation F-5

R: Radius (ft)
D: Degree of curvature (DMS)
     DA: Arc Definition
     DC: Chord Definition


Degree of curvature is an exclusively English units system attribute as there is no 100.00' equivalent in the metric system. Because of this, we won't use it here in the COGO section.

b. Sectors; Segments

Sectors and segments are parts of a circle and used to compute areas enclosed by curvilinear boundaries.

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Figure F-3 Figure F-4
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Equation F-6 Equation F-7

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