Curve Deflection-Angle Stakeout
How to set a circular curve in the field by deflection angles.
Example
You enter
- Definition mode radius
- Radius R (ft) 500
- Arc length from PC (ft) 100
You get
- Deflection angle from PC 5.72958
- Sub-chord from PC 99.833 ft
- Degree of curve 11.4592 deg
Checked against published worked examples from: AASHTO Green Book / FM 5-233 (by name).
Details, formula, and sources
Scopean arc length l from the PC turns a deflection from the back tangent of delta = (l/2R)(180/pi) deg and pulls a sub-chord c = 2R sin(l/2R). On a 500 ft radius, 100 ft of arc is a 5.7296 deg deflection and a 99.83 ft chord (degree of curve 11.459). Enter radius or degree of curve. Simple circular curve, no spiral; the design of record governs.
Formula or tabledeflection from the back tangent at the PC: delta = (l / (2R)) x (180/pi) deg for an arc length l; sub-chord from the PC c = 2R sin(l / (2R)); arc-definition D = 5729.58 / R. The deflection at the PT equals half the curve's total central angle.
Source and editionDeflection-angle curve-stakeout method per FM 5-233 Construction Surveying and the AASHTO A Policy on Geometric Design of Highways and Streets (the Green Book), 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, arc_length_ft, deflection_deg, chord_ft, degree_of_curve
- Degree definition arc definition D = 5729.58 / RAASHTO / FM 5-233
- Reference deflection measured from the back tangent at the PC; chord is the straight sub-chord from the PCFM 5-233 deflection-angle method