Transition lengths for rotating the pavement from normal crown to full superelevation on a horizontal curve, the chainages of the key cross-sections, and the superelevation diagram, per the AASHTO Green Book. Use it with the minimum radius calculator, which gives the design superelevation.
Effective width We = w · n1 · bw → Lr = We · ed / Δ (ed and Δ in %),
i.e. Lr = (w · n1 · ed · bw) / Δ.
Lt = (eNC / ed) · Lr.
For a ramp on a left-hand curve (crossfall already towards the inside): Lr = We · (ed − eNC) / Δ and Lt = 0.
Δ is the maximum relative gradient between the edge of the travelled way and the axis of rotation for the design
speed; bw reduces the length when more than one lane is rotated. Many agencies also avoid runoff shorter
than the distance travelled in about 2 s, for appearance.
highlighted = current design speed and superelevation.
Single carriageway (two-way). On the tangent the road has a normal crown (NC): both lanes fall at eNC away from the centreline. Over the tangent runout Lt the outside lane is raised until it is level (level crown, LC). The superelevation runoff Lr follows: at the reverse crown (RC) the whole section forms one plane at +eNC, and it keeps rotating about the centreline until the full superelevation (FS) ed is reached.
Interchange ramp (one-way). The whole ramp rotates as one unit about its right-hand edge, so the runoff is based on the full ramp width. Its normal crossfall is the same whichever way it turns: looking ahead, the left edge is low and the right edge high. On a left-hand curve this already falls to the inside (−eNC), so there is no tangent runout: the right-hand edge is the axis, the left-hand edge is lowered and Lr = We(ed − eNC) / Δ. On a right-hand curve it falls to the outside (−eNC), so it goes through the tangent runout to level and then the full runoff to ed: the right-hand edge is the axis and the left-hand edge is raised, Lr = We · ed / Δ.
Dual carriageway (divided). Each carriageway rotates about its median edge, so the width of the lanes in one direction is used. Both start with crossfall falling away from the median, like a crowned single carriageway. The outer carriageway goes through the tangent runout to level and on to ed; the inner carriageway keeps its crossfall until RC and is then steepened to ed.
Placing the runoff. The runoff is split between the tangent and the curve (60–80 % on the tangent without spirals) so drivers are not on a curve with too little superelevation, nor on a tangent with too much. Where spiral transitions are used, the runoff is usually placed over the length of the spiral. For a single or dual carriageway, a right-hand curve is the mirror image of the left-hand case.
It is the length over which the outside lane is rotated from a level cross slope to the full design superelevation. AASHTO gives Lr = (w·n1·ed·bw) / Δ, limiting how fast the pavement edge rises relative to the centreline.
It is the length over which the outside lane changes from the normal crown to level, just before the runoff: Lt = (eNC / ed)·Lr, which keeps the same edge rise rate as the runoff.
For curves without spirals, AASHTO recommends 60–80 % of the runoff on the tangent and the rest on the curve; two-thirds on the tangent is widely used.
Use the full width of the ramp, not a single lane. A ramp is normally rotated as one unit about one edge (here the right-hand edge), so the pavement edge moves over the whole ramp width. Select Interchange ramp, enter the number of ramp lanes and the lane width; the tool works out the full width automatically. On a left-hand curve the ramp crossfall already falls to the inside, so there is no tangent runout and Lr = We·(ed − eNC) / Δ; on a right-hand curve the normal runout and runoff apply.
From the curve radius, design speed and maximum superelevation rate. Use the minimum radius calculator to check the radius, then enter the superelevation of your curve here.