The radius of a horizontal circular curve is 120 m and the design speed is 50 km/h. What is the coefficient of friction needed if no superelevation is provided?
- A0.146
- B0.154
- C0.164Correct
- D0.174
Solution
Concept
For a horizontal curve without superelevation, the centrifugal force ratio is counteracted solely by lateral friction.
Formula
e + f = V² / (127 × R)
Step-by-step solution
1. Identify the given values: Design speed V = 50 km/h, Radius R = 120 m, Superelevation e = 0. 2. Apply the IRC equilibrium equation: e + f = V² / (127 × R). 3. Substitute the values: 0 + f = (50)² / (127 × 120) = 2500 / 15240 = 0.16404. 4. Therefore, the required coefficient of friction is approximately 0.164.
Explanation
When no superelevation is provided (e = 0), the centrifugal force developed by the vehicle traveling along the horizontal curve must be entirely resisted by lateral friction between the tires and the pavement. Using the equilibrium equation for horizontal curves, the required coefficient of friction is calculated as f = V² / (127 × R).
Why the other options are wrong
A: Incorrect calculation using wrong constants or rounding errors. B: Standard maximum allowable lateral friction coefficient is 0.15, which is not the value calculated here. D: Result of calculation errors or using g = 9.81 incorrectly with unrounded speed values.
Shortcut
Directly use f = V² / (127 × R) when e = 0.
Common mistake
Using the maximum allowable coefficient of friction (0.15) instead of calculating the actual required coefficient for the given speed and radius.
Correct answer: C) 0.164