A clothoid is a plane curve whose curvature changes linearly with distance along the curve. It is used as a transition curve in roads and railways because it smoothly connects straight and circular sections.
Highway and railroad curves are not circular arcs — they use a special shape called a "clothoid" (Euler spiral). Its curvature changes gradually, so centrifugal force increases smoothly when transitioning from a straight section to a curve, rather than hitting suddenly.