The total length L of valley transition curve for comfort condition is (where N is deviation angle, v is design speed and C is allowable rate of change of centrifugal acceleration.)
- A2 [N v³ / C]1/2Correct
- B½ [N v² / C]1/2
- C2 [N v² / C]1/2
- D½ [N v³ / C]1/2
Solution
Concept
Valley transition curve (comfort criterion)
Formula
L = 2 √(N V³ / C)
Step-by-step solution
1. For a cubic parabola valley curve, the centrifugal acceleration changes at the rate C. 2. Solving for the half length and doubling gives L = 2 (N V³ / C)1/2.
Explanation
The comfort criterion limits the rate of change of centrifugal acceleration. This leads to a length proportional to the square root of N V³/C.
Why the other options are wrong
Options with v² have wrong dimensions, and the factor ½ halves the length.
Shortcut
L = 2√(N v³ / C).
Common mistake
Using v² instead of v³.
Correct answer: A) 2 [N v³ / C]^(1/2)