Vertical Curve Elevation

y = \frac{r x ^{2}}{2} r = \frac{g _{2} - g _{1}}{L} Y = Y_{VPC} + g_{1} x + \frac{r x ^{2}}{2}

Equal-tangent parabolic vertical curve. g1, g2 in decimal (or % / 100). x from VPC. r is the rate of grade change per station. High/low point where slope = 0: x = −g1 / r (if on the curve).

$g_{1}, g_{2}$: Initial and final grades (decimal)
$L$: Curve length
$x$: Distance from VPC

Step-by-step solved example

g1=+2%, g2=−2%, L=400 ft. Offset y at midspan x=200 ft?

Offset from the grade line: y = (r x²)/2 on the survey profile.

1. r
r=(−0.02−0.02)/400= −0.00010 /ft.
2. y
y= r x²/2 = −0.00010×40000/2= −2.00 ft (below the g1 tangent).

Answer: y = −2.00 ft from the initial tangent

10 practice questions

0/10 correct

1.r equals

2.Offsets from the g1 tangent are

3.Crest vs sag is from the sign of

4.VPC is

5.Station of VPT = station of VPC +

6.High point for a crest: slope 0 at x=

7.If g1=−g2 and equal-tangent, the turning point is at

8.Grades 4% as decimal are

9.The offset at x=L (VPT) is

10.Sight distance on a crest uses