Question

A vertical curve joins a –1.2% grade to a +0.8% grade. The P.I. of the vertical curve

is at station 75 + 00 and elevation 50.90 m above sea level. The centerline of the
roadway must clear a pipe located at station 75 + 40 by 0.80 m. The elevation of the
top of the pipe is 51.10 m above sea level. What is the minimum length of the vertical
curve that can be used

Answer 1

To determine the minimum length of the vertical curve, we need to consider the difference in grades and the clearance required for the pipe. The minimum length of the curve is determined by the formula:

L = (G1 - G2) x K

where:
L = Length of the curve
G1 = Initial grade (in decimal form)
G2 = Final grade (in decimal form)
K = Rate of change of grade (0.01 for each percent change in grade)

In this case, the initial grade is -1.2% (-0.012 in decimal form) and the final grade is +0.8% (0.008 in decimal form).

So, the rate of change of grade (K) = G2 - G1 = 0.008 - (-0.012) = 0.02

Now we can calculate the minimum length of the curve:

L = (0.008 - (-0.012)) / 0.02
L = 0.02 / 0.02
L = 1

Therefore, the minimum length of the vertical curve that can be used is 100 meters (1 x 100).