What specific type of road curve smoothly connects a straight road to a circular curve?

The specific type of road curve that smoothly connects a straight road to a circular curve is called a transition curve, most commonly a spiral curve, such as a clothoid. Its fundamental purpose is to provide a gradual change in curvature, and therefore in lateral acceleration, ensuring driver comfort and safety. A straight road has an infinite radius of curvature (zero curvature), while a circular curve has a constant, finite radius of curvature. A transition curve's radius of curvature decreases uniformly from infinity at its beginning, where it connects to the straight road, to the specific radius of the circular curve at its end, where it meets the circular curve. This means the curvature itself increases uniformly along the transition curve. This uniform change in curvature, and the corresponding uniform increase in the centrifugal force or lateral acceleration experienced by vehicle occupants, prevents the abrupt sensation of being pulled sideways that would occur if a vehicle directly entered a circular curve from a straight path. Additionally, the transition curve provides the necessary distance to gradually introduce superelevation, which is the banking of the roadway where the outer edge is progressively raised relative to the inner edge. This gradual banking helps vehicles safely counteract the centrifugal force on the circular curve. The simultaneous and progressive change in both the radius of curvature and the superelevation ensures a smooth and safe transition for traffic.