Because the stopping sight distance should always be adequate, the length of the curve is normally dependent upon the stopping sight distance. Occasionally, as with any other section of a highway, the decision sight distance is a more appropriate sight distance. In these instances, the decision sight distance governs the length of the vertical curve.The stopping sight distance (depending on the perception reaction time + braking time) is usually the controlling sight distance.
Stopping Sight Distance (SSD) : is calculated using the formula stated in reference [ 2], pp. 57
SSD is the stopping sight distance in ft (m)
is the initial vehicle speed in ft/s (m/s)
g is the gravitational constant, 32.3 ft/s/s (9.807 m/s/s)
a is the deceleration rate in ft/s/s (m/s/s)
G is the roadway grade (+ for uphill, - for downhill) in percentage/100, and
is the perception/reaction time in second.
Note: 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.