Horizontal Curve Layout
Tangent, length, external, middle ordinate, chord, and PC/PT stations for a circular curve.
Example
You enter
- Definition mode radius
- Radius R (ft) 1000
- Deflection angle delta (deg) 30
- PI station (ft, optional) 5000
You get
- Tangent T 267.95
- Curve length L 523.6 ft
- Long chord (ft) 517.64
Details, formula, and sources
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.
FM 5-233 is public-domain US Government work, free at US Army publication archives. The design of record and the engineer of record govern the alignment.
Estimate. Engineer of record governs the design and acceptance. Verify against the project structural drawings and the manufacturer's published capacity / chart.
Field names used by the API: mode, radius_ft, delta_deg, pi_station_ft, tangent_ft, curve_length_ft, long_chord_ft
- Degree definition arc definition D = 5729.58 / R unless the chord toggle is setAASHTO / FM 5-233