Question

A +7.5% grade meets a horizontal grade on a section of a rural mountainous highway. If the length of the crest vertical curve formed in that section is 300 ft long, determine the safe operating speed on the highway.

Answer 1

Using the formula of comfort condition it is possible to determine the safe operating speed on the highway.

What is a deflection angle?

In physics, we define angular deviation as the angle resulting from the deflection of light when reflected from a prism. A prism has the ability to separate white light into several other colors, which are reflected by the object.

The comfort condition formula is given by: $L=2(\frac{NV^{3} }{C} )^{\frac{1}{2} }$

Where, L is the length of the vertical curve, N is the grade, V is the safe speed operation and assuming the standart value for C (0,6 m/s3) it is possible to calculate:

$C = 0,6 m/s^{3} = 1,968 ft/s^{3}\\ N= N1 - N2 = 7,5-0 = 7,5% = 0,075$

Changing the values in the formula:

$L=2(\frac{NV^{3} }{C}){\frac{1}{2} } \\300 = 2(\frac{0,075.V^{3} }{1,968})^{\frac{1}{2} } \\V = 83,89 ft/s$

So, the safe operating speed on the highway is 83,89 ft/s.

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