A 800 unequal tangent vertical curve is to be laid out from

A 800’ unequal tangent vertical curve is to be laid out from a PI at station 40+00.00 which has an elevation of 5888.27’. The PVC station is 37+40.00. The grade from the PVC to the PI is -3.3% while the grade from the PI to the PVT is +2.6%. Compute the centerline elevations at the PVC, PVCC, PVT, and all 50’ stations. Find the highest/lowest centerline point on the curve and give its station and elevation.

Compute all work to nearest 0.01 feet.

Solution

VPI Station = 40+00.00
VPI Elevation = 5,888.27
g1 = -3.30%
g2 = +2.60%
First tangent = 260.00
Second tangent = 540.00
BVC Station = 37+40.00
BVC Elevation = 5896.85
Station x (Sta) g1*x r/2*x² Elevation
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45+40.00 4.00 3.69 5.18 5,902.31
45+00.00 5.00 3.41 4.44 5,901.30
44+50.00 4.50 3.07 3.60 5,900.11
44+00.00 4.00 2.73 2.84 5,899.02
43+50.00 3.50 2.39 2.17 5,898.01
43+00.00 3.00 2.05 1.60 5,897.09
42+50.00 2.50 1.71 1.11 5,896.26
42+00.00 2.00 1.37 0.71 5,895.52
41+50.00 1.50 1.02 0.40 5,894.87
41+00.00 1.00 0.68 0.18 5,894.31
40+50.00 0.50 0.34 0.04 5,893.83
40+00.00 0.00 0.00 0.00 5,893.45
CVC
40+00.00 2.60 -8.58 5.18 5,893.45
39+50.00 2.10 -6.93 3.38 5,893.30
39+00.00 1.60 -5.28 1.96 5,893.53
38+50.00 1.10 -3.63 0.93 5,894.15
37+40.00 0 0 0 5,896.85
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