Horizontal Curve Tangent Length

Two straight alignments meet at the point of intersection, and the curve that softens the corner has to start back down each tangent by the distance T. Because the two tangent lines are symmetric about the bisector of the deflection angle, T falls straight out of the right triangle formed by the centre, the PC and the PI: the half-angle Δ/2 sits at the centre, R is the adjacent side, and T is opposite. That symmetry is also the field check: the tangent distance is identical on both sides, so a crew that stakes PC and PT and finds unequal distances back to the PI has an error somewhere.

A worked example: a 500 ft radius curve turning through Δ = 60° needs T = 500 tan 30° = 288.68 ft, so the PC lies 288.68 ft before the PI and the PT the same distance beyond it. The trap is the half: Δ/2, not Δ. Using the full angle on that 60° curve returns 866 ft, three times too long, and the mistake announces itself only when the curve refuses to close. Note also that T grows without bound as Δ approaches 180°: a near-reversal of direction needs an enormous tangent run, which is why tight radii are used instead.