Curves for roads and railways

Roads and railways cannot change direction abruptly, so straights are joined by curves. A simple circular curve has one radius. A compound curve has two or more arcs of different radii turning the same way; a reverse curve turns one way then the other. Between a straight and a circular curve, a transition curve, usually a clothoid or cubic spiral, gradually changes the curvature from zero to the circular value, so that superelevation and centrifugal force build up smoothly. Vertical curves, parabolic in shape, join changes of gradient.

A simple curve is defined by its radius R and the deflection angle Δ between the two straights, measured at the intersection point (PI). From these come the tangent length, curve length, external distance and mid-ordinate. Chainages of the tangent points fix where the curve starts and ends. Degree of curve is an older way of describing sharpness, defined by the angle subtended by a standard chord.

Setting out uses either linear methods, such as offsets from the tangent or from long chords, for short curves with good access, or angular methods. Rankine's method of tangential (deflection) angles sets out successive chord points with a theodolite at the tangent point and a tape. With a total station, coordinates of every curve point are computed and set out directly from any convenient station, which is now standard practice.