glossary

The longitudinal slip ratio $\kappa$ quantifies the difference between the rotational speed of the wheel and the actual speed of the vehicle. It’s a measure of how much the wheel is slipping relative to the road surface, and it can indicate whether the wheel is spinning (in acceleration) or skidding (in braking).

Definition

For a driven wheel (during acceleration), the longitudinal slip ratio is defined as:

$$\kappa =\frac{R_e\omega -V_x}{V_x}$$

where:

• $R_e$ is the effective rolling radius of the tire.
• $\omega$ is the angular velocity of the wheel.
• $V_x$ is the longitudinal velocity of the vehicle at its center of mass.

Relation to High-Performance Driving

In high-performance driving, managing the slip ratio is crucial for maximizing traction and performance:

• Acceleration: During aggressive acceleration, a high slip ratio indicates wheel spin. Some level of slip can be beneficial as it allows the tire to generate maximum traction, but excessive slip leads to a loss of traction and control.
• Braking: During hard braking, the slip ratio becomes negative. Anti-lock braking systems (ABS) are designed to manage the slip ratio to prevent the wheels from locking up, thus maintaining steering control and maximizing braking efficiency.
• Cornering: During cornering, both longitudinal and lateral slip are involved. High-performance driving requires balancing these to maintain optimal grip and vehicle stability.

In Practice

1. Traction Control Systems (TCS): These systems monitor the slip ratio and adjust engine power or brake force to maintain optimal traction, preventing excessive wheel spin during acceleration.
2. Anti-lock Braking Systems (ABS): ABS prevents the wheels from locking by modulating brake pressure, ensuring the slip ratio stays within a range that maximizes braking performance and vehicle control.