Compound Circular Curve

Two circular arcs of different radii turning the same way, meeting at a point of compound curvature (PCC).

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Details, formula, and sources

The interchange-ramp / curb-return geometry between the simple and spiral curves. Each arc T = R tan(delta/2), L = R delta_rad; the tangents back to the PI follow from the law of sines: back tangent t1 = T1 + (T1+T2) sin(delta2)/sin(delta), forward t2 = T2 + (T1+T2) sin(delta1)/sin(delta), delta = delta1 + delta2. A 500 ft/30-deg arc into an 800 ft/25-deg arc gives 134.0 and 177.4 ft semi-tangents, a 294.6 ft back tangent, a 367.4 ft forward tangent, 610.9 ft total. Reduces to a simple curve at equal radii/angles. Same-direction arcs (a reverse curve is separate); AASHTO limits successive radii to ~1.5:1. The engineer of record governs.

T1 = R1 tan(delta1/2); T2 = R2 tan(delta2/2); L = R delta_rad; back tangent t1 = T1 + (T1+T2) sin(delta2)/sin(delta); forward tangent t2 = T2 + (T1+T2) sin(delta1)/sin(delta); delta = delta1 + delta2.

Compound circular-curve geometry per the AASHTO A Policy on Geometric Design of Highways and Streets (the Green Book) and Ghilani & Wolf, Elementary Surveying, by name; first-principles trig with the law of sines.

The compound-curve tangent geometry (semi-tangents and the law-of-sines vertex triangle) is standard published route-surveying math; 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: r1_ft, r2_ft, delta1_deg, delta2_deg, arc1_tangent_ft, arc2_tangent_ft, back_tangent_ft, forward_tangent_ft, total_length_ft

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