What is the extra widening required for pavement of width 7.0 m on a horizontal curve of radius 196 m if the longest wheel base of vehicle expected on the road is 6.5 m? Assume the design speed to be 60 km/h.
- A0.45 m
- B0.22 m
- C0.76 m
- D0.67 mCorrect
Solution
Concept
Extra widening is provided on horizontal curves to account for off-tracking of long vehicles (mechanical widening) and to allow safe clearance for drivers operating at higher speeds (psychological widening).
Formula
We = Wm + Wps = (n × l²) / (2 × R) + V / (9.5 × √R)
Step-by-step solution
1. Identify the number of lanes (n): A pavement width of 7.0 m corresponds to a 2-lane road, so n = 2. 2. Calculate mechanical widening (Wm): Wm = (n × l²) / (2 × R) = (2 × 6.5²) / (2 × 196) = 42.25 / 196 ≈ 0.216 m 3. Calculate psychological widening (Wps): Wps = V / (9.5 × √R) = 60 / (9.5 × √196) = 60 / (9.5 × 14) = 60 / 133 ≈ 0.451 m 4. Calculate total extra widening (We): We = Wm + Wps = 0.216 + 0.451 = 0.667 m ≈ 0.67 m
Explanation
Extra widening on horizontal curves consists of mechanical widening and psychological widening. For a standard 2-lane road with a width of 7.0 m (n = 2), calculating both mechanical and psychological components gives a total extra widening of approximately 0.67 m.
Why the other options are wrong
A: Represents psychological widening only (0.45 m). B: Represents mechanical widening only (0.22 m). C: Incorrect calculation using wrong number of lanes or incorrect formula.
Shortcut
Calculate Wm (≈ 0.22 m) and Wps (≈ 0.45 m) and sum them directly to get 0.67 m.
Common mistake
Confusing standard single-lane width with 2-lane pavement width, or calculating only one type of widening (mechanical or psychological).
Correct answer: D) 0.67 m