Question

1)Determine the minimum length of a crest vertical curve on a freight and passenger intercity main line track, connecting two tangents of +0.75% and -1.5% traveling at 112.5 km/h. 2)Repeat the problem for a crest vertical curve on a light rail transit main line with a design speed of 90 km/h.

3)Repeat the problem for a sag vertical curve on a light rail transit main line track with a design speed of 75 km/h.

Answer 1

1) Given,

V = 112.5 kmph = 31.25 m/s

G1 = 0.75%

G2 = -1.5%

S = Vt + V​​​​​​2/2a = 31.25 * 2.5 + 31.252/(2 * 3.4) = 78.125 + 143.612 = 221.737 ~ 225 m

A = |G1 - G2| = 2.25%

Assume, S > L,

Minimum Length of Crest Vertical curve:

L = 139.15 m ~ 140 m

Minimum Length of Crest Vertical curve = 140 m

2) Given,

V = 90 kmph = 25 m/s

G1 = 0.75%

G2 = -1.5%

S = Vt + V​​​​​​2/2a = 25 * 2.5 + 252/(2 * 3.4) = 62.5 + 91.912 = 154.412 ~ 155 m

A = |G1 - G2| = 2.25%

Minimum Length of Crest Vertical curve:

L = KA = 39 * 2.25 = 87.75 m

3) Given,

V = 75 kmph = 20.83 m/s

G1 = 0.75%

G2 = -1.5%

S = Vt + V​​​​​​2/2a = 20.83 * 2.5 + 20.832/(2 * 3.4) = 52.075 + 63.807 = 115.882 m ~ 120 m

A = |G1 - G2| = 2.25%

Minimum Length of Sag Vertical curve:

L = K A = 27 * 2.25 = 60.75 m