Horizontal Curve Layout

Tangent, length, external, middle ordinate, chord, and PC/PT stations for a circular curve.

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Formula and source

T = R*tan(delta/2); L = R*delta_rad (arc definition); E = R*(sec(delta/2)-1); M = R*(1-cos(delta/2)); LC = 2*R*sin(delta/2); arc-definition D = 5729.58/R; PC = PI - T, PT = PC + L.

Simple circular-curve geometry per the AASHTO A Policy on Geometric Design of Highways and Streets (the Green Book) and FM 5-233 Construction Surveying, by name; first-principles trig.

Audience

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Posture

Rough Logic answers the math question the working professional asks on the job. The site is a calm, fast, ad-free, account-free, ever-free reference. It does not interpret code. It does not replace the licensed professional. It does not store your inputs. The Authority Having Jurisdiction governs all installations and inspections.