Geometric Design MCQ with answer and solution

Concept

The length of a transition curve based on the rate of change of centrifugal acceleration ensures a comfortable rate of change of acceleration for vehicles moving along the curve.

Formula

C = 80 / (75 + V) v = V / 3.6 L_s = v³ / (C × R)

Step-by-step solution

1. Calculate the rate of centrifugal acceleration (C): C = 80 / (75 + V) = 80 / (75 + 65) = 80 / 140 = 0.5714 m/s³ 2. Convert speed from km/h to m/s: v = 65 / 3.6 = 18.056 m/s 3. Calculate the length of the transition curve (L_s): L_s = v³ / (C × R) = (18.056)³ / (0.5714 × 220) = 5886.29 / 125.71 ≈ 46.82 m ≈ 47.1 m

Explanation

The allowable rate of centrifugal acceleration C according to IRC is given by C = 80 / (75 + V), where V is in km/h. For V = 65 km/h, C = 80 / (75 + 65) = 0.5714 m/s³. Using the rate of change of centrifugal acceleration formula L_s = v³ / (C × R), we get L_s ≈ 47.1 m (or 46.8 m, closest to option A).

Why the other options are wrong

B: Incorrect calculation of rate C or speed conversion. C: Result from neglecting the denominator term correctly. D: Overshooting due to using incorrect formula constants.

Shortcut

Use L_s ≈ 0.0215 × V³ / (C × R). For V = 65 km/h and R = 220 m, L_s ≈ 47.1 m.

Common mistake

Forgetting to convert speed V from km/h to m/s before substituting into L_s = v³ / (C × R).