Road Superelevation Calculator

Superelevation is the cross-slope banking applied on a horizontal curve so that a component of vehicle weight helps supply the centripetal force. Point mass equilibrium gives e + f = V squared divided by (127 x R), with V in km/h, R in metres and e as a decimal. The constant 127 is simply 3.6 squared times 9.81, folding in the conversion from km/h to m/s along with gravitational acceleration. Side friction f is not the available skid resistance but a comfort-based demand limit; AASHTO design values fall from about 0.17 at 30 km/h to roughly 0.08 at 120 km/h, reflecting the lower lateral acceleration drivers tolerate as speed rises. Maximum superelevation is a policy choice rather than a physical constant. Four percent is common in urban areas where vehicles may stop on the curve, 6 to 8 percent suits rural highways, and 10 to 12 percent is used only where snow and ice are not a concern. Rearranging the equilibrium with e at its maximum yields the minimum radius for a given design speed. The cross-slope cannot appear instantly, so it is developed over a superelevation runoff length governed by a maximum relative gradient between pavement edge and axis of rotation, on the order of 0.5 percent for a two-lane road, preceded by a tangent runout that removes the normal 2 percent crown. A near-zero cross-slope occurs partway through that transition and is a persistent drainage and hydroplaning concern.

Banking of curved alignments predates highway engineering. British and American railways applied cant to curves through the middle of the nineteenth century, raising the outer rail so the resultant force stayed close to perpendicular to the track and the wheel flanges were relieved of lateral thrust. The underlying mechanics are purely Newtonian, and the equilibrium expression used for roads is the same one railway engineers used with cant deficiency standing in place of side friction. The road problem required something the railway problem did not: a quantitative limit on how much lateral force drivers would accept, since a car chooses its own speed and path within the lane. Field studies during the 1930s, notably work reported through the Highway Research Board and associated with Joseph Barnett of the U.S. Bureau of Public Roads, measured the side friction actually demanded by drivers on existing curves and produced the descending schedule of design friction factors still recognisable in modern tables. AASHTO subsequently formalised five methods of distributing the required e and f between superelevation and friction, adopting the parabolic Method 5 for open highways because it avoids demanding maximum friction on flat curves. Those distribution curves and the resulting superelevation tables have been carried forward through successive editions of the Green Book.