# Problem 04 - Symmetrical Parabolic Curve

**Problem**

A highway engineer must stake a symmetrical vertical curve where an entering grade of +0.80% meets an existing grade of -0.40% at station 10 + 100 which has an elevation of 140.36 m. If the maximum allowable change in grade per 20 m station is -0.20%, what is the length of the vertical curve?

- 150 m
- 130 m
- 120 m
- 140 m

**Solution**

Total change in grade,

$A = g_1 - g_2$

*A*:$A = g_1 - g_2$

$A = 0.80 - (-0.40)$

$A = 1.20\%$

Number of meter-stations, *n*:

$n = \dfrac{\text{total change in grade, }A}{\text{change in grade per meter-station}}$

$n = \dfrac{1.20\%}{0.20\%}$

$n = 6 ~ \text{stations}$

Length of vertical curve, *L*:

$L = \text{number of meter-stations } ~ \times ~ \text{ length of a meter-station}$

$L = 6 \times 20$

$L = 120 ~ \text{m}$ [ C ] *answer*

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