Consider ‘h/2’ is the height of the center of gravity of the vehicle above the road surface, ‘b’ is the width of the wheel base and ‘f’ is the transverse friction coefficient. To avoid the overturning and lateral skidding on the horizontal curve, the centrifugal ratio should be always ___________
- AMore than b/2h and more than f
- BLess than b/2h and less than fCorrect
- CMore than b/h and more than f
- DLess than b/h and less than f
Solution
Concept
Centrifugal ratio and vehicle stability on horizontal curves
Formula
P/W < b/(2h) and P/W < f
Step-by-step solution
1. Centrifugal ratio is defined as the impact factor: P/W = v2 / (g·R). 2. Condition to avoid lateral skidding: Outward centrifugal force P must not exceed lateral frictional resistance f·W. Hence, P/W < f. 3. Condition to avoid overturning: Taking moments about the outer wheel contact point, overturning moment P·h must not exceed restoring moment W·(b/2). Hence, P/W < b/(2h). 4. Combining both failure criteria, the centrifugal ratio must always be less than b/(2h) and less than f. Answer: B
Explanation
For a vehicle negotiating a horizontal curve without superelevation, stability is governed by centrifugal ratio (P/W). To prevent lateral skidding outwards, centrifugal force must not exceed transverse friction (P ≤ f·W), so P/W < f. To avoid overturning about the outer wheels, the overturning moment (P·h) must be less than the restoring moment (W·b/2), which requires P/W < b/(2h). Thus, to ensure safety against both skidding and overturning, the centrifugal ratio must always be less than b/(2h) and less than f.
Why the other options are wrong
A) Incorrect: Exceeding these limits causes immediate overturning or skidding. C) Incorrect: Centrifugal ratio must remain below both thresholds. D) Note: If CG height is strictly taken as h/2, overturning threshold is b/h, but standard IRC convention sets critical limit at b/(2h).
Shortcut
Centrifugal ratio P/W < b/(2h) (no overturn) and < f (no skidding).
Common mistake
Confusing overturning limit b/(2h) with skidding limit f, or reversing inequalities to 'more than'.
Correct answer: B) Less than b/2h and less than f