The radius of a horizontal circular curve is 140 m. The design speed is 60 km/h and the coefficient of lateral friction is 0.15. What is the superelevation required if full lateral friction is assumed to develop?
- A0.041
- B0.053Correct
- C0.062
- D0.070
Solution
Concept
Superelevation counteracts the centrifugal force acting on a vehicle negotiating a horizontal curve, working together with lateral friction between the tires and the road surface.
Formula
e + f = V² / (127 × R)
Step-by-step solution
1. Identify the given parameters: V = 60 km/h, R = 140 m, and f = 0.15. 2. Write the standard equation: e + f = V² / (127 × R) 3. Substitute the values: e + 0.15 = 60² / (127 × 140) 4. Calculate the right side: e + 0.15 = 3600 / 17780 = 0.2025 5. Solve for e: e = 0.2025 - 0.15 = 0.0525 ≈ 0.053.
Explanation
The standard relationship between superelevation (e), lateral friction (f), speed in km/h (V), and curve radius in meters (R) is e + f = V² / (127R). Given full lateral friction (f = 0.15) develops, substituting the given values yields e = 0.0525, which rounds to 0.053.
Why the other options are wrong
A: Incorrect calculation or misapplication of friction factor. C: Result obtained by adding friction instead of subtracting it. D: This is the maximum allowable superelevation value (7%) in IRC for plain terrain, not the calculated value.
Shortcut
Calculate V²/(127R) = 3600/17780 ≈ 0.2025, then subtract 0.15 directly to get 0.0525 ≈ 0.053.
Common mistake
Neglecting the friction term f and calculating equilibrium superelevation e = V² / (127R) directly.
Correct answer: B) 0.053