If b is the wheel track of a vehicle and h is the height of centre of gravity above road surface, then to avoid overturning and lateral skidding on a horizontal curve, the centrifugal ratio should always be

 

Explanation:

On a horizontal curve, a vehicle is subjected to centrifugal force acting outward. To ensure safe travel, two critical stability conditions must be satisfied:

1. Condition to Avoid Overturning:

• Overturning happens when the moment due to centrifugal force exceeds the restoring moment due to the vehicle’s weight.

• The condition to avoid overturning is centrifugal ratio should always be less than \(\text{b/2h}\) 

2. Condition to Avoid Lateral Skidding:

• Skidding occurs if the centrifugal force exceeds the maximum lateral frictional force that can be developed between the tyres and the road.

• So, the condition is the centrifugal ratio should always be less than coefficient of lateral friction.

Additional Information

• Centrifugal Force and Horizontal Curves
  When a vehicle negotiates a horizontal curve, it experiences an outward centrifugal force, which increases with the square of its speed and decreases with a larger radius. This force acts horizontally through the center of gravity and can lead to either skidding or overturning if not balanced by friction or geometry.

• Overturning Criteria
  Overturning occurs when the moment generated by the centrifugal force about the outer wheel exceeds the restoring moment due to vehicle weight. The critical ratio $\frac{b}{2h}$ is derived from equating these moments. A wider wheel track and lower center of gravity enhance stability against overturning.

• Skidding Resistance and Friction
  Skidding happens when the lateral frictional force between the tires and the pavement is exceeded by the centrifugal force. The coefficient of lateral friction, denoted as $f$, provides a threshold for safe travel, and it depends on pavement conditions, tire quality, and vehicle speed.