An engineer is assigned to design a vertical curve for a highwas with the design speed is $70mph.$ Knowing that the gradients are $3$ ; uphill and $-2\%$ downhill. What is the minimum design length of the vertical curve?

Solution:

Find the value of $K$ from exhibit $3-72.($page $272$ of AASHTO $2004)$

For $70mphK=247$

Find the value of algebraic difference in grade

$A=G1-G2$

$A=3-(-2)$

$A=5$

Find minimum length of the vertical curve by using equation

$L=K**A$

$L=247**5=1235ft$

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