An ascending gradient of 1 in 100 meets a descending gradient of 1 in 120. What should be the length of the vertical curve given the design speed of 80 km/h and have an overtaking sight distance of 470 m?
- A417 mCorrect
- B411 m
- C422 m
- D407 mM
Solution
Concept
A summit curve is designed to provide adequate sight distance for safe driving and overtaking maneuvers. The deviation angle N is the algebraic difference between the two gradients.
Formula
N = n₁ - n₂ For L < S: L = 2S - (9.6 / N)
Step-by-step solution
1. Calculate deviation angle N: N = (+1/100) - (-1/120) = 1/100 + 1/120 = 11/600 ≈ 0.01833 2. Assume L < S (where S = OSD = 470 m): L = 2S - (9.6 / N) L = 2 × 470 - (9.6 / 0.01833) L = 940 - 523.64 = 416.36 m 3. Check assumption: Since L (416.36 m) < S (470 m), the assumption is valid. 4. Rounding to the nearest integer gives 417 m.
Explanation
To find the length of the summit curve for OSD when the curve length is less than the sight distance (L < S), IRC specifies the formula L = 2S - (9.6 / N). Substituting N = 11/600 and S = 470 m gives L = 416.36 m, which rounds off to 417 m.
Why the other options are wrong
B: Incorrect rounding or arithmetic error during calculation. C: Result obtained from using the L > S formula (L = N S² / 9.6 ≈ 422 m), which violates the condition L > S as 422 m < 470 m. D: Incorrect formula or calculation typo.
Shortcut
L = 2S - (9.6/N) = 940 - (9.6 × 600 / 11) = 940 - 523.6 = 416.4 m ≈ 417 m.
Common mistake
Using the formula for L > S, which yields L = N S² / 9.6 = 421.7 m (Option C) without checking if L > S holds true.
Correct answer: A) 417 m