Most highways will change directions several times over the course of their lengths. These changes may be in a horizontal plane, in a vertical plane, or in both. The engineer is often charged with designing curves that accommodate these transitions, and consequently must have a good understanding of the physics involved.
The superelevation of the highway cross-section and the side-friction factor are two of the most crucial components in the design of horizontal curves. The superelevation is normally discussed in terms of the superelevation rate, which is the rise in the roadway surface elevation as you move from the inside to the outside edge of the road. For example, a superelevation rate of 10% implies that the roadway surface elevation increases by 1 ft for every 10 ft of roadway width. The side-friction factor is simply the coefficient of friction between the design vehicle's tires and the roadway.
Whenever a body changes directions, it does so because of the application of an unbalanced force. In the special case of a body moving in a circular path, the force required to keep that body traveling in a circular path is called the centripetal force. When vehicles travel over a horizontal curve, it is this centripetal force that keeps the vehicles from sliding to the outside edge of the curve. In the simplest case, where the road is not banked, the entire centripetal force is provided by the friction between the vehicle's tires and the roadway. If we add some side-slope or superelevation to the cross-section of the roadway, some of the centripetal force can be provided by the weight of the car itself.
High rates of superelevation that make cornering more comfortable during the summer by requiring less frictional force, can make winter driving ponderous by causing slow-moving vehicles to slip downhill toward the inside of the curve. Because of this, there are practical maximum limits for the rate of superelevation. In areas where ice and snow are expected, a superelevation rate of 8% seems to be a conservative maximum value. In areas that are not plagued by ice and snow, a maximum superelevation rate of 10-12% seems to be a practical limit. Both modern construction techniques and driver comfort limit the maximum superelevation rate to 12%.
The side-friction factor has practical upper limits as well. As was discussed in the braking distance module, the coefficient of friction is a function of several variables, including the pavement type and the vehicle speed. In every case, the side-friction factor that is used in design should be well below the side-friction factor of impending release. In addition to the safety concerns, drivers don't feel comfortable if the roadway seems to rely heavily on the frictional force. Several studies aimed at determining the maximum side-friction factors that are comfortable for drivers have been conducted. Some of the results from these studies are tabulated below. (AASHTO, 1994)
The side-friction factors that are employed in the design of horizontal curves should accommodate the safety and comfort of the intended users.
The module on horizontal curve minimum radii will bring the effects of the superelevation rate and the side-friction factor together. Both of these concepts contribute to the final alignment of horizontal curves.