Inputs
m
decimal degrees
measured along tangent
Formulas
- Horizontal: T = R·tan(Δ/2), L = R·Δ (rad) = π·R·Δ°/180, LC = 2R·sin(Δ/2), M = R(1−cos(Δ/2)), E = R(sec(Δ/2)−1).
- PC = PI − T, PT = PC + L. Stations may carry through at PT.
- Vertical: A = G₂ − G₁; K = L/|A|. Curve is sag if A>0, crest if A<0.
- Crest SSD (AASHTO): L = A·S²/[100(√(2h₁)+√(2h₂))²]; h₁=1.08 m, h₂=0.6 m (metric). Imperial: L = A·S²/[200(√h₁+√h₂)²]; h₁=3.5 ft, h₂=2.0 ft (SSD).
- Sag SSD (headlight): L = A·S² / (200·(h+S·tan(α))) with α=1°, h=0.6 m.
Results
Tangent T—
Curve Length L—
Long Chord LC—
Middle Ordinate M—
External E—
PC station—
PT station—
Degree of Curve (arc, 100)—