Curve Deflection-Angle Stakeout
The field method horizontal-curve leaves out: to set a circular curve by deflection angles, an 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 and source
deflection 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.
Deflection-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.
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