Practice Question: Length of Crest Curve Based on Stopping Distance

NCEES Civil PE Specification Geometrics: Basic vertical curve elements

Problem

You are driving in your brand-new Porsche that you purchased after switching from design to construction. You take a turn onto the pictured canyon crest curve that was designed for drivers to see deer up to 350 feet away. Based on the maximum sight distance given and grades shown in the figure, calculate the length of the curve.

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CORRECT 😃

INCORRECT 😟

% Students Correctly Answered:

41.7%

Solution

Answer: B) 455 ft

The required curved length for stopping sight along a crest curve can be calculated based on requirements found in the AASHTO document A Policy on Geometric Design of Highways and Streets.
Define design parameters:
$$ A=absolute\ value\ of\ grade\ difference $$
$$ S=stopping\ sight\ distance $$
$$ L=length\ of\ curve $$

If the stopping distance is less than the curve length (S < L), curve length can be calculated as:
$$ L=\frac{A\ast S^2}{2158} $$
If the stopping distance is greater than the curve length (S > L), curve length can be calculated as:
$$ L=2\ast\ S-\frac{2158}{A} $$
where:
$$ A=\left|G_2-G_1\right| $$

$$ G_1 = 3.0% $$

$$ G_2 = -5.0% $$

$$ A=8.0% $$
Assume S < L:
$$ L=\frac{8.0\ast\left(350\ ft\right)^2}{2158}\approx455\ ft>S=350\ ft\rightarrow\ confirmed $$
$$ L=455\ ft $$