# Sag curve length when S<L (Vertical curves for highway design)

## Description

When a driver is driving on a sag curve at night, the sight distance is limited by the higher grade in front of the vehicle. This distance must be long enough that the driver can see any obstruction on the road and stop the vehicle within the headlight sight distance. The headlight sight distance (S) is determined by the angle of the headlight and angle of the tangent slope at the end of the curve. By first finding the headlight sight distance (S) and then solving for the curve length (L) in each of the equations below, the correct curve length can be determined. If the S<L curve length is greater than the headlight sight distance, then this number can be used. If it is smaller, this value cannot be used. Similarly, if the S>L curve length is smaller than the headlight sight distance, then this number can be used. If it is larger, this value cannot be used.

These equations assume that the headlights are 600 millimetres (2.0 ft) above the ground, and the headlight beam diverges 1 degree above the longitudinal axis of the vehicle.

The geometric design of roads is the branch of highway engineering concerned with the positioning of the physical elements of the roadway according to standards and constraints. The basic objectives in geometric design are to optimize efficiency and safety while minimizing cost and environmental damage. Geometric design also affects an emerging fifth objective called “livability,” which is defined as designing roads to foster broader community goals, including providing access to employment, schools, businesses and residences, accommodate a range of travel modes such as walking, bicycling, transit, and automobiles, and minimizing fuel use, emissions and environmental damage.

Geometric roadway design can be broken into three main parts: alignment, profile, and cross-section. Combined, they provide a three-dimensional layout for a roadway.

1) The alignment is the route of the road, defined as a series of horizontal tangents and curves. (Curve sight Distance)

2) The profile is the vertical aspect of the road, including crest and sag curves, and the straight grade lines connecting them. (Sag curves, Crest curves)

3) The cross section shows the position and number of vehicle and bicycle lanes and sidewalks, along with their cross slope or banking. Cross sections also show drainage features, pavement structure and other items outside the category of geometric design.

Related formulas## Variables

L | curve length (along the x-axis) (dimensionless) |

A | absolute value of the difference in grades (dimensionless) |

S | headlight sight distance (dimensionless) |