After designing a horizontal curve with a radius of 1910 feet for a highway with a design speed of 70 mph, your final task is to design the transition segments. Your local design code requires that any superelevation within the curve be run-off over a distance equal to or greater than the distance a vehicle would travel in two seconds at your design speed. In addition, the spiral curves must have the minimum length given by the equation below.

L = (3.15*v3)/(RC)

Where:
L = Minimum length of the spiral curve (ft.)
v = Speed (mph)
R = Circular curve radius (ft.)
C = Centripetal acceleration development rate (usually between 1 and 3 ft/sec3)

If you use a centripetal acceleration development rate of 2 ft/sec3, what is the minimum length of your transition segments?

[Solution Shown Below]

Solution

We'll calculate the required length of your transition segments based on the superelevation restrictions first. At 70 mph (102.6 ft/s) you would travel a distance of 205.2 feet in two seconds. Your transition segments should, therefore, slowly change the cross-section of the road over the course of 205.2 feet. The minimum length of the spiral curve is investigated by substituting the correct values into the equation below.

L = (3.15*v3)/(RC)

Where:
L = Minimum length of the spiral curve (ft)
v = Design speed, 70 mph
R = Circular curve radius, 1910 ft
C = Centripetal acceleration development rate, 2 ft/sec3

Solving for the curve length yields a minimum spiral curve length of 282.8 ft.