Spiral / Transition Curve Designer

Lay out a clothoid spiral into a circular curve. Enter the spiral length Lₛ (or derive it from design speed), the radius R, and the intersection angle I — the app finds the spiral angle θₛ, shift p, the SC coordinates Xc/Yc, the spiral tangent Tₛ, and the TS · SC · CS · ST stations.

⭐ Design 1 EP per layout · Balance … EP

① Circular curve

Radius R of circular curve (m)

Spiral table interval (m)

Intersection angle I (total, both spirals + arc)

degrees

minutes

seconds

② Spiral length Lₛ

Spiral length Lₛ (m)

Design speed V (km/h)

Uses the empirical (Royal Road / Shortt) formula Lₛ = 0.036 V³ / R with V in km/h and R in m.

③ Stationing (optional)

Known station is at

Its station

Give a station to get the TS, SC, CS and ST stations. Metric: 14+080 = 14 080 m.

📐 Spiral layout

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Spiral–circular–spiral curve

Spiral angle θₛ

—

Shift p

—

Xc (SC)

—

Yc (SC)

—

Total tangent Tₛ

—

External E

—

Long tangent

—

Short tangent

—

Central angle (arc)

—

Worked solution

Spiral deflection table (TS → SC)

Deflection angle from the tangent at the TS for a point at arc length ℓ along the spiral: i ≈ θₛ·(ℓ/Lₛ)² / 3 (= ℓ²/(6 R Lₛ)).

Point	ℓ from TS (m)	Spiral ∠ (ℓ²/2RLₛ)	Deflection ∠