Vertical curves at a crest or at the top of a hill are called also called summit curves. Crest vertical curves are used to connect two separate inclined sections. In calculating crest curves, you only need to find a correct length for the curve that will match the correct sight distance. The sight distance as well as the distance of the curve can be compared to each other in two different ways. The first is that the sight distance is less than the length of the curve and the second is that the length of the curve could be less than the sight distance.
Vertical curves at the bottom of a hill are called sag curves. Sag vertical curves are used to connect two descending grades which form an upside down parabola, or a sag. Similar to crest vertical curves, the sight distance is the primary parameter needed to find the length of the curve. When designing sag curves however, you must take into account the positive change in grade which accounts for increased acceleration, or inertia. Using a dip in the road for example, sag vertical curves offer drivers a view of the roadway during daylight hours, but shorten the headlight views at night. For this reason, when calculating sag curves, an upward deviation of one degree is automatically assumed.
Unsymmetrical curves are sometimes have unequal tangents and are called dog-legs. The process for solving an unsymmetrical curve problem is almost the same as that used in solving a symmetrical curve. However, you use a different formula for the calculation of the middle vertical offset at the PVI. Be aware that an unsymmetrical curve is made up of two different parabolas, one on each side of the PVI, having a common POVC opposite the PVI.
A symmetrical vertical curve occurs when the horizontal distance from the VPC to VPI is equal to the tangent length from VPI to VPT. A symmetrical vertical curve is useful when developing a freeway entrance when the ramp alignment is on a curve. The symmetrical vertical curve allows you to compensate for the changing skew between horizontal alignments.