Question

Determine the minimum length of a vertical curve necessary for it to be adequate, under the visibility criteria for braking, for a design speed of 80 mph. The slopes corresponding to the PVC and PVT of the curve in question are 4% and -3% respectively. the PVI station is 120 + 70 and its elevation is 810 meters. The coefficient of lateral friction is 0.08. All circular curves in the segment under study have been designed using an 8% superelevation rate of change and 12-foot rails (two per direction). The road is located in a rural area.

Answer 1

Ans) We know,

Braking distance(BD) = / 30(f + G)

where, f = coefficient of friction = 0.08

G = grade = 4% or 0.04

=> BD = (80 x 80)/[30(0.08 + 0.04)]

=> BD = 1777.8 ft or 542 m

For BD < L

Length of curve (L) = A x / 658

where, A = change in grade % = G1 - G2 = 4 -(-3) = 7%

BD = braking distance required

Putting values,

=> L = 7 x 542 x 542 / 658

=> L = 3125 m BD

We have to recalculate 'L' by considering L > BD

For L > BD,

L = 2 BD - 658/A

=> L = 2(542) - (658 / 7)

=> L = 990 m > 542 m

Hence, provide minimum length of curve = 990 m