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 (ß), the headlight intersects the road at D,
restricting the available sight distance to S. The values for H and ß 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.