Spiral (Transition) Curve Layout

Whose radius eases from infinity at the tangent to R at the SC - and the length superelevation is run in over. Spiral angle theta_s = Ls/(2R), throw p = Ls^2/(24R), total tangent Ts = (R+p) tan(delta/2) + k with k = Ls/2 - Ls^3/(240 R^2), external Es = (R+p)/cos(delta/2) - R, SC deflection = theta_s/3. A 1,000 ft curve with a 250 ft spiral on a 20-deg deflection: theta_s 7.16 deg, throw 2.60 ft, Ts 301.7 ft, Es 18.1 ft, a 5.68-deg circular arc, 599 ft total. Symmetric spirals, series approximation. AASHTO / Ghilani & Wolf; the engineer of record governs.

theta_s = Ls/(2R); p = Ls^2/(24R); k = Ls/2 - Ls^3/(240 R^2); Ts = (R+p) tan(delta/2) + k; Es = (R+p)/cos(delta/2) - R; SC deflection = theta_s/3; circular central = delta - 2 theta_s; total length = 2 Ls + R (delta - 2 theta_s).

Spiral (transition/clothoid) curve geometry per the AASHTO A Policy on Geometric Design of Highways and Streets (the Green Book) and Ghilani & Wolf, Elementary Surveying, by name; standard route-surveying series approximation.

The spiral geometry (theta_s, throw, tangent, external, deflection) 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: radius_ft, spiral_length_ft, delta_deg, theta_s_deg, throw_p_ft, total_tangent_ft, external_ft, circular_central_deg

• Spiral angle and throw theta_s = Ls/(2R); p = Ls^2/(24R)AASHTO / Ghilani & Wolf
• Tangent and external Ts = (R+p) tan(delta/2) + k, k = Ls/2 - Ls^3/(240 R^2); Es = (R+p)/cos(delta/2) - Rroute-surveying geometry
• Scope symmetric equal spirals, series approximation; Ls is a separate superelevation/comfort design stepscope of this tile