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
Checked against published worked examples from: AASHTO Green Book / FM 5-233 (by name).
Details, formula, and sources
Formula or tableT = 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.
Source and editionSimple 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.
Free accessFM 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.
What governsEstimate. Engineer of record governs the design and acceptance. Verify against the project structural drawings and the manufacturer's published capacity / chart.
API field namesmode, radius_ft, delta_deg, pi_station_ft, tangent_ft, curve_length_ft, long_chord_ft
- Degree definition arc definition D = 5729.58 / R (no chord option)AASHTO / FM 5-233