Question

A freeway exit ramp has a single lane and consists entirely of a horizontal curve with a central angle of 90 degrees and a length of 628 ft. If the distance cleared from centerline for sight distance is 19.4 ft., what design speed was used?

Answer 1

The calculation of design speed for a freeway exit ramp involves various factors beyond the central angle and length, such as the radius of curvature and sight distance, which require additional context from engineering standards to determine accurately.

Step-by-step explanation:

To determine the design speed used for the freeway exit ramp, we need to know the radius of curvature of the ramp and the sight distance provided. According to the given question, the ramp has a 90-degree central angle and a length of 628 feet; however, this complex calculation involves several steps and variables not provided in the question, such as the coefficient of friction, the grade of the roadway, and other factors considered in calculating stopping sight distance or design speed. Without these variables or further context from engineering standards, such as the AASHTO Green Book, it's not possible to provide an exact answer here.

However, we can discuss that according to transportation engineering principles, the design speed of a roadway is selected based on various factors including stop or manoeuvre around the object.

Answer 2

The design speed used for the freeway exit ramp can be determined using the formula for sight distance on a horizontal curve.

Step-by-step explanation:

To determine the design speed used for the freeway exit ramp, we can use the formula for sight distance. Sight distance is the maximum distance that a driver can see ahead on a curve to safely navigate it. The formula for sight distance on a horizontal curve is:

Sight Distance = (Radius + Clearance)^2 / (2 * Clearance)

Given that the central angle of the curve is 90 degrees and the length is 628 ft, we can calculate the radius using the formula:

Radius = Length / (2 * pi * (Central Angle / 360))

Using the given values, we find that the radius is approximately 100.53 ft.

Substituting the values into the formula for sight distance, we get:

Sight Distance = (100.53 + 19.4)^2 / (2 * 19.4) = 447.66 ft

Therefore, the design speed used for the freeway exit ramp is the speed at which a driver can safely navigate the curve and have a sight distance of 447.66 ft.