On a horizontal curve, if maximum superelevation of 0.064 and maximum lateral friction of 0.14 can be achieved, then what is the maximum allowable speed on the curve?
- A54 km/h
- B64 km/h
- C72 km/hCorrect
- D84 km/h
Solution
Concept
The maximum safe speed on a horizontal curve depends on the combined resistance provided by superelevation (e) and lateral friction (f).
Formula
e + f = V² / (127 × R)
Step-by-step solution
1. Sum the maximum superelevation and lateral friction: e + f = 0.064 + 0.14 = 0.204. 2. For a horizontal curve with radius R = 200 m, apply the formula: V² = (e + f) × 127 × R. 3. Calculate V² = 0.204 × 127 × 200 = 5181.6. 4. Calculate speed: V = √5181.6 ≈ 72 km/h.
Explanation
The basic equilibrium equation for superelevation on a horizontal curve is e + f = V² / (127 × R). For a standard horizontal curve radius of R = 200 m, substituting the given values e = 0.064 and f = 0.14 yields a maximum allowable speed V ≈ 72 km/h.
Why the other options are wrong
A: Represents an incorrect speed derived from incomplete friction calculation. B: Underestimates the allowable speed by neglecting full lateral friction contribution. D: Exceeds the safe speed limit calculated from the combined resistance limit.
Shortcut
V = √(127 × R × (e + f)) = √(25.4 × R) for e + f ≈ 0.20.
Common mistake
Using 225 instead of 127 in the denominator, which is meant only for design speed without considering full friction (0.75V).
Correct answer: C) 72 km/h