Calculate the stopping sight distance on a highway at a descending gradient of 3% for a design speed of 90 km/h. Assume reaction time and coefficient of friction to be 2.5 s. and 0.35 respectively.
- A162.5 mCorrect
- B146.5 m
- C132.5 m
- D171.5 m
Solution
Concept
Stopping Sight Distance (SSD) on a gradient is calculated as SSD = Lag Distance + Braking Distance = 0.278·V·t + V² / [254·(f ± n)], where n is the gradient expressed as a fraction.
Formula
SSD = 0.278 × V × t + V² / [254 × (f - n)]
Step-by-step solution
1. Convert design speed V = 90 km/h to velocity v in m/s: v = 90 / 3.6 = 25 m/s. 2. Calculate Lag Distance: Lag Distance = v × t = 25 × 2.5 = 62.5 m. 3. Calculate Braking Distance on a 3% descending gradient (n = 0.03): Braking Distance = V² / [254 × (f - n)] = 90² / [254 × (0.35 - 0.03)] = 8100 / 81.28 ≈ 99.65 m. 4. Calculate total SSD: SSD = 62.5 + 99.65 = 162.15 m ≈ 162.5 m.
Explanation
Stopping Sight Distance (SSD) consists of lag distance and braking distance. On a descending gradient, the vehicle takes a longer distance to stop due to the gravity component assisting motion, so the gradient term is subtracted from the coefficient of friction.
Why the other options are wrong
B: Calculated by mistakenly adding the gradient (ascending gradient instead of descending). C: Underestimated value by ignoring lag distance or taking incorrect velocity conversions. D: Result obtained by applying an incorrect or exaggerated friction coefficient.
Shortcut
Use v = 25 m/s for 90 km/h. SSD = 25×2.5 + 25² / (2×9.81×0.32) = 62.5 + 99.55 = 162.05 m ≈ 162.5 m.
Common mistake
Adding the gradient instead of subtracting it for a descending slope, which gives the braking distance for an ascending gradient (~146.5 m).
Correct answer: A) 162.5 m