Horizontal Curve: Problem Solving

The station of the point of intersection (P.I.) is calculated by adding the tangent distance to the station of the point of curvature (P.C.). The tangent distance depends on the radius and the tangent of half the intersection angle. In the example with a 400-meter radius and 30-degree intersection angle at P.C. 0 + 150 meters, this calculation determines the P.I. station location along the roadway centerline.

The station of the point of tangency (P.T.) is determined by adding the curve length to the station of the point of curvature. Curve length depends on the radius and the intersection angle converted to radians. This calculation ensures precise stationing for the endpoint of the horizontal curve, which is essential for accurate field layout and design integrity.

The station of the midpoint of the curve is calculated by adding half the curve's length to the station of the point of curvature. This midpoint represents the location equidistant along the arc between the P.C. and P.T., and is useful for verification and intermediate staking during field procedures for staking out curves.

The long chord is the straight-line distance that spans directly between the point of curvature and the point of tangency across the curve. Its length is derived using trigonometric relationships involving the radius and intersection angle. The long chord provides a direct measurement useful for verification and design calculations in horizontal curve layout.

The tangent distance is critical because it connects the point of curvature to the point of intersection along the tangent line. It depends on the radius and the tangent of half the intersection angle, making it foundational for calculating the P.I. station. Accurate tangent distance ensures proper alignment and stationing of all curve elements.

The radius and intersection angle are the primary parameters controlling all horizontal curve calculations. The radius determines the sharpness of the curve, while the intersection angle defines how much the tangent lines deviate. Together, they govern the tangent distance, curve length, and long chord length, making them essential inputs for determining all station values.

The solution sequence begins by calculating tangent distance and curve length using the radius and intersection angle. Next, determine the P.I. station by adding tangent distance to the P.C. station, then find the P.T. station by adding curve length to the P.C. station. Finally, calculate the midpoint station and long chord length to complete the design example setting a curve using design data.