Extra (mechanical) widening on horizontal curves – off-tracking of a vehicle For a vehicle of wheel-base length L negotiating a horizontal circular curve of radius R, the additional mechanical width b to be provided on the curve to accommodate off-tracking is given by:

Introduction / Context:
When a vehicle turns, the rear axle follows a path of smaller radius than the front axle, causing “off-tracking.” On horizontal curves, this demands extra pavement width so that vehicles stay within the carriageway without encroaching on shoulders or opposing lanes.

Given Data / Assumptions:

• L = wheel-base length (distance between front and rear axle).
• R = radius of the curve traced by the front axle.
• Low-speed off-tracking dominates (mechanical widening), psychological widening not considered here.
• Small-angle geometry and typical highway speeds are assumed for the formula’s applicability.

Concept / Approach:
For low-speed turning, the path of the rear axle is geometrically inside that of the front axle by a distance approximated from simple circular-arc geometry. The standard approximation for mechanical widening on a curve is b = L^2 / (2R) per lane, which captures the dependence on longer wheel-base and sharper curves (smaller R).

Step-by-Step Solution:

Verification / Alternative check:
For gentle curves (large R), b tends toward zero, matching intuition. For articulated vehicles, effective L is larger and extra widening increases accordingly (practical design may further add psychological widening).

Why Other Options Are Wrong:
Forms like L^2/R or L/R exaggerate widening and are dimensionally inconsistent with observed practice; L/(2R) is too small; 2L^2/R doubles the standard value without basis.

Common Pitfalls:
Ignoring additional widening for speed (psychological widening); applying per-lane widening incorrectly to total carriageway.

Final Answer:
b = L^2 / (2R)