Question

A highway being designed to AASHTO guidelines with a 70 mph design speed, and at one section, an equal tangent vertical curve must be designed to connect grades of +1% and -2%. If the grades intersect at station 100+00, determine the stationing of the PVC, PVT and curve high point for the minimum curve length based pn SSD requirements.

Answer 1

Ans) Determine curve length (L) considering L > SSD using relation ,

L = A / (400 + 3.5S)

where, S = SSD at 70 mph suggested by AASTHO

A = Difference in grade as percent = G1 - G2 = 1 - (-2) = 3%

According to AASTHO, SSD for 70 mph speed is 730 ft

=> L = 3 / [400 + 3.5(730)]

=> L= 541 ft < 730 ft

Hence, our assumption L > SSD is not satisfied so we have to detemine cuve length by considering L < SSD

In this case, L = 2 S - [(400 + 3.5S) / A]

=> L = 2(730) - [(400 + 3.5(730)) / 3]

=> L = 475 ft < 730 ft

Hence, our assumption is now satisfied so,

Station at PVC = 100 + 00 - L/2 = 10000 - 475/2 = 9762.5 = 97 + 62.5  

Station at PVT = 100 + 00 + L/2 = 10000 + 475/2 = 10237.5 = 102 + 37.5

Station of high point = station at PVC + K G1

where, K = L / A = 475 / 3 = 158.33

G1 = Upgrade percent = 1%

=> Station of high point = 97 + 62.5 + 158.33(1)

=> Station at high point =   9762.5 + 158.33 = 9920.83 or 99 + 20.83