12. Summary

Although more geometrically complex than circular arcs, spirals are relatively easy to compute using approximate relationships. The argument against their use due to computation complexity really isn't valid as shown by the example.

However, despite their transportation applications advantages, spiral use is limited primarily to railroads. Trains have a mechanical connection between wheel flanges and rails, in essence, infinite friction. Because the train's wheels cannot slip across the rails as can tires on pavement, lateral force is directly imparted to the rails as the train enters and travels around a curve. If a simple curve is used, then maximum centrifugal force is instantaneously introduced at BC the since the train must follow the tracks. A spiral's changing radius allows the centrifugal force to gradually increase (entrance) then decrease (exit), balancing the forces. Running a train over an simple horizontal curve over time will eventually shift the rail alignment into a spiraled configuration because of the forces.

In high speed highway designs, horizontal circular curves are typically long and flat, making for smooth tangent-curve-tangent transitions, minimal centrifugal force, and lower superelevation rates. Spirals aren't needed in these situations. Spirals can be used beneficially in case of large direction changes over limited areas, such as interchanges.

Spiral use is up to the designer but as shown in this Chapter, they are no more difficult to understand or compute than circular arcs.