# Vertical Curve - Parabolic formula

## Description

Vertical Curves are the second of the two important transition elements in geometric design for highways, the first being Horizontal Curves. A vertical curve provides a transition between two sloped roadways, allowing a vehicle to negotiate the elevation rate change at a gradual rate rather than a sharp cut. The design of the curve is dependent on the intended design speed for the roadway, as well as other factors including drainage, slope, acceptable rate of change, and friction. These curves are parabolic and are assigned stationing based on a horizontal axis.

Two types of vertical curves exist: (1) Sag Curves and (2) Crest Curves. Sag curves are used where the change in grade is positive, such as valleys, while crest curves are used when the change in grade is negative, such as hills. Both types of curves have three defined points: PVC (Point of Vertical Curve), PVI (Point of Vertical Intersection), and PVT (Point of Vertical Tangency). PVC is the start point of the curve while the PVT is the end point.

The parabolic formula for a vertical curve is shown.

Related formulas## Variables

y | elevation of the parabola (dimensionless) |

e_{PVC} | elevation of the Point of Vertical Curve (PVC) (dimensionless) |

g_{1} | Initial Roadway Grade (m/m) (dimensionless) |

x | x parabolic component (dimensionless) |

g_{2} | Final Roadway Grade (m/m) (dimensionless) |

L | Length of Curve (m) (dimensionless) |