Sag Vertical Curve

Sag vertical curves are in the shape of a parabola. Typically, they are designed to allow the vehicular headlights to illuminate the roadway surface (i.e., the height of object= 0 feet for a given distance S. The light beam from the headlights is assummed to have a 1 degree upward divergence from the longitudinalaxis of the vehicle. There are four criteria used to set the minimum length of a sag vertical curve: headlight criterion, comfort criterion, drainage criterion, and appearance criterion (California).

Headlight Criterion:

The headlight is angled upward at an inclined angle (), the headlight intersects the road at D, restricting the available sight distance to S. The values for H and are 0.6m and 1 degree.A is the   absolute value of the differences in grades () expressed as a percentage.

For  S > L

              

For  S < L

                   


 

Sag Vertical Curve Design : calculated using the formula stated in reference [ 2], pp. 64

 

 

For SSD < L                           US Customary                                                      Metric

                                                                               

 

 

For SSD > L                           US Customary                                                      Metric

                                                          

 

                Where,

                                SSD = stopping sight distance in ft (m),

                                = minimum length of vertical curve in ft (m), and

                                           A = absolute value of the differences in grades () expressed as a percentage.

 


               The general form of the parabolic equation, as applied to sag vertical curves, is

                               

                               

                Where,

                                y = roadway elevation at distance x from the beginning of the vertical curve in ft (m)

                                x = distance from the beginning of the vertical curve in stations or ft (m)

                                c = elevation of the point of vertical curvature (PVC) in ft (m),

                                = initial roadway grade in percent, it is as referred as the initial tangent grade

                               = final roadway (tangent) grade in percent.