Curve Setting-Out Calculator
Circular curves, transition (clothoid) curves and parabolic vertical curves — all the elements, the chainages of every tangent point, and a setting-out table you can take to the field: Rankine deflection angles with chords, tangent offsets, and coordinates when you give a bearing.
The curve
Setting out
Give the back-tangent bearing and the PC coordinates and the table adds the bearing and coordinates of every peg; leave them empty and you still get the deflection angles, chords and tangent offsets.
The transition
The spiral length is a design decision — it comes from your project's design speed, superelevation run-off and the standard being followed. This tool takes the Ls you give and works out the geometry; it does not choose one for you.
The grades
Grades are signed the way a road drawing writes them: uphill in the direction of increasing chainage is positive.
The intersection point
Circular curves use the standard relations — T = R·tan(Δ/2), L = R·Δ, E = R(sec(Δ/2) − 1), M = R(1 − cos(Δ/2)), long chord = 2R·sin(Δ/2) — and the setting-out table is Rankine's: the deflection from the back tangent to a point one arc l along is l/2R, and the chord to it is 2R·sin of that. The table gives the chord from the previous peg as well as from the PC, because that is what a tape measures. Degree of curve is shown on both the arc and the chord definition over the base length you choose. Transition curves are true clothoids: the offsets are obtained by integrating the spiral rather than from the two-term series, so they stay right for long or sharp spirals where the series drifts, and the shift is taken from the integrated geometry instead of the Ls²/24R approximation. Vertical curves are equal-tangent parabolas; the turning point is reported only when it actually falls inside the curve. Every element is checked against its closed form on each release.
Setting out on site, with control you can trust
BTPL establishes the control, sets out alignments and structures, and records the as-built — for highways, railways, canals and urban infrastructure.