A 1200-ft equal-tangent crest vertical curve is currently designed for 50 mi/h. A civil engineering student contends that 60 mi/

Question

2 months ago

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A 1200-ft equal-tangent crest vertical curve is currently designed for 50 mi/h. A civil engineering student contends that 60 mi/

h is safe in a van because of the higher driver’s-eye height. If all other design inputs are standard, what must the driver’s-eye height (in the van) be for the student’s claim to be valid?

Physics

1 answer:

serg [3.5K] · Answer 1 · 2026-03-08T06:41:52+03:00

Response:

8.95ft

Explanation:

For tackling this issue, two key concepts should be evaluated:

First, the design of vertical curves should be considered using the general equation defining the length of a vertical crest curve, based on the differences in gradients. Also, the Design Controls for Crest vertical curves table is useful (a table is attached at the bottom).

The equation for this is written as:

$L = \frac{AS^2}{200(\sqrt{h_1}+\sqrt{h_2})^2}$

Where,

L = length of vertical curve

S = Sight distance

A = Algebraic difference in gradients

$h_1 =$ Height of eye above road level

$h_2 =$ height of object above road surface

From the provided table, it's determined that at a design speed of 60 mi/h, S measures 570 ft. The vertical curve rate K at a design speed of 50 mi/h is 84.

Next, we can calculate the algebraic difference in gradients as follows:

$A= \frac{L}{K}$