What is the length of transition curve from the viewpoint of rate of introduction of superelevation which is 1 in 150? Total pavement width at the curve is 7.5 m, the superelevation rate is 0.07 and the pavement is rotated about its center line.
- A35 m
- B43 m
- C39 mCorrect
- D46 m
Solution
Concept
The length of a transition curve based on the rate of introduction of superelevation accounts for the gradual raising of the outer edge. When rotated about the centerline, only half the total width undergoes elevation change above the centerline.
Formula
Ls = N × (e × B / 2) where: Ls = Length of transition curve N = Rate of introduction of superelevation (1 in N) e = Rate of superelevation B = Total width of pavement (W + We)
Step-by-step solution
1. Identify the given parameters: Total width (B) = 7.5 m, Superelevation rate (e) = 0.07, Rate of introduction (1 in N) = 1 in 150, so N = 150. 2. Since the pavement is rotated about its centerline, raise of outer edge = (e × B) / 2 = (0.07 × 7.5) / 2 = 0.2625 m. 3. Calculate transition curve length: Ls = N × 0.2625 = 150 × 0.2625 = 39.375 m ≈ 39 m.
Explanation
When the pavement is rotated about its centerline, the maximum rise of the outer edge with respect to the centerline is (e × B) / 2. Multiplying this elevation by the rate of introduction of superelevation N (1 in N) gives the required length of the transition curve, which comes out to approximately 39 m.
Why the other options are wrong
A: Represents an incorrect calculation or wrong rounding. B: Obtained if rotation about the inner edge is partially applied with incorrect parameters. D: Value obtained if rotation is taken about the inner edge fully (Ls = 150 × 0.07 × 7.5 = 78.75 m, half of which is ~39.375 m, but miscalculated).
Shortcut
Ls = 150 × 0.07 × 7.5 / 2 = 39.375 m ≈ 39 m.
Common mistake
Correct answer: C) 39 m