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 Geometric Design: Theory and Concepts

 
Crest Vertical Curves

Crest vertical curves are curves that connect inclined sections of roadway, forming a crest, and they are relatively easy to design. As you know from the module entitled ‘Vertical Curves,’ we only need to find an appropriate length for the curve that will accommodate the correct sight distance. The stopping sight distance is usually the controlling sight distance, but the decision sight distance or even the passing sight distance could be used if desired. The passing sight distance is rarely ever used as the design sight distance, because it demands long, gentle curvatures that are expensive and difficult to construct.

The sight distance and the length of the curve can be related to each other in one of two ways. The first possibility is that the sight distance is less than the length of the curve. Alternatively, the length of the curve could be less than the sight distance. See figure 1.0.

Picture illustrating sight distance and curve length.

Figure 1.0:  Sight Distance Possibilities

In any case, there are equations that relate these two parameters to the change in grade for both possible conditions. The designer must double-check that the equation that is used agrees with its own assumptions. For example, if the equation that is based on sight distances that are less than the curve length produces a curve length that is less than the sight distance, you know that the result is invalid. The equations that are normally used to calculate the lengths of crest vertical curves are given below.

If S > L then

L=2*S - (200*(h1^0.5 + h2^0.5)^2)/A

If S < L then

L=(A*S^2)/(100*((2*h1)^0.5 + (2*h2)^0.5)^2)

Where:
L = Length of the crest vertical curve (ft)
S = Sight distance (ft)
A = The change in grades ( |G2-G1| as a percent)
h1 = Height of the driver's eyes above the ground (ft)
h2 = Height of the object above the roadway (ft)

The heights in the calculations above should be those that correspond to the sight distance of interest. For the stopping sight distance, h1 = 3.5 ft and h2 = 0.5 ft.   For the passing sight distance, h1 = 3.5 ft and h2 = 4.25 ft.

While the sight distance has been portrayed as the only parameter that affects the design of vertical curves, this isn't entirely true. Vertical curves should also be comfortable for the driver, aesthetically pleasing, safe, and capable of facilitating proper drainage. In the special case of crest vertical curves, it just so happens that a curve designed with adequate sight distances in mind is usually aesthetically pleasing and comfortable for the driver. In addition, drainage is rarely a special concern for crest vertical curves.