Length of Parabolic Sag Curve with Given Change in Grade Per Station | CE Board Problem in Mathematics, Surveying and Transportation Engineering

Date of Exam

November 2016

Subject

Mathematics, Surveying and Transportation Engineering

Problem
A grade of -5% is followed by a grade of 1%, the grades intersecting at the vertex (Sta. 10 + 060). The change of grade is restricted to 0.4% in 20 m. Compute the length of the vertical parabolic sag curve in meters.

A. 360 m	C. 300 m
B. 320 m	D. 340 m

Answer Key

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[ C ]

Solution

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Total change in grade:
$A = g_2 - g_1 = 1 + 5$

$A = 6\%$

Rate of change in grade
$\Delta g = \dfrac{0.4}{20} = 0.02\% ~ \text{per meter}$

Length of Parabolic Sag Curve
$L = \dfrac{A}{\Delta g} = \dfrac{6}{0.02}$

$L = 300 ~ \text{m}$ ← Answer: [ C ]

On CASIO Calculator: f(x)-991ES PLUS
MODE → 3:STAT → 2:A+BX

X	Y
0	-5
20	-5 + 0.4

AC

$L = 1\hat{x} = 300 ~ \text{ft}$ ← Answer: [ C ]

Note:
$\hat{x}$ = SHIFT → 1:[STAT] → 5:Reg → 4:x-carret