Vertical curves are used by engineers in road design. According to The University Transportation Center for Alabama (UTCA), second order equations are used to describe vertical curves: these equations can be solved for both station and elevation for either sag vertical curves (which look similar to a concave lens) or crest vertical curves (which look similar to a convex lens). The procedure for calculating both is the same, UCTA states, except that each has a different minimum length that needs to be taken into account when computing the curve.

- Skill level:
- Easy

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## Instructions

- 1
Calculate A, the percentage difference in grades, by subtracting the smaller grade from the largest. For example, if grade one is 5 per cent and grade two is 15 per cent, then 15 per cent - 5 per cent =10 per cent .

- 2
Compute the required vertical length. According to King Fahd University (KFU), this is obtained by multiplying the absolute value of A (from step 1) by K, the rate of vertical curvature. K is usually obtained from pre-defined tables, according to the type of curve and speed of the road. If K is 50, then vertical length = 50*10=500m.

- 3
Calculate the station of VPC (the vertical point of curvature) and VPT (the vertical point of tangency) using the following equations:

VPC=VPI-1/2L VPT=VPI+1/2L

The University of Idaho states that the VPI is the vertical point of intersection--the place where the two roads would have intersected if they had been allowed to meet instead of being diverted with the vertical curve.

- 4
Calculate the distance from VPC to the maximum and minimum elevations using the following equation: x=-(LG1)/A

- 5
Calculate how high VPC and VPT high. KFU states that G1, G2, and L should be used in this calculation.

- 6
Use the equation y=a(xsquared)+bx+c to calculate the curve elevation at each mandatory station. That's according to KFU, who states that:

y=curve elevation a=(G2-G1)/200L b=g1/100 c="elevation of VPC" x="horizontal distance from VPC to station of interest."