How to calculate vertical curves

Written by stephanie ellen
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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. 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. 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. 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. 4

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

  5. 5

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

  6. 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."

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