Versine ( θ ) = ( 1 – Cos θ ).
In colloquial use the ‘versine’ on a curved portion of track is the extent to
which the track turns sideways through the curve – the transverse
displacement (offset).
v = r Versine ( θ ),
where ‘r’ is the radius of curvature and ‘θ’ the change in direction. ‘v’ is
used in the calculation of the additional structural clearance on curves.