Understanding Cornering Force and Slip Angle

Cornering Force

A cornering force is a lateral force that is exerted on a vehicle's tires when it is turning. This force is essential for maintaining the vehicle's path during a turn and is influenced by several factors, including tire characteristics, vehicle speed, and the radius of the turn. Mathematically, it can be represented as:

Cornering Force (F) m (v^2 / r)

Where:

(m) is the mass of the car (v) is the velocity of the car (r) is the radius of the turn

Essentially, the cornering force is the lateral force needed to turn the car around a curve. If the car can provide sufficient traction force between the tires and the road, it can navigate the turn without sliding.

The Relationship Between Cornering Force and Slip Angle

The slip angle is the angle between the direction in which a tire is pointing and the actual path that the tire is traveling. When a vehicle turns, the tires may not roll in the exact direction they are pointed due to the lateral forces acting on them, leading to a slip angle.

The relationship between cornering force and slip angle is critical for understanding vehicle dynamics. Let's delve into the details:

Linear Relationship

At small slip angles, the cornering force increases linearly with the slip angle. This means that as the slip angle increases, the cornering force also increases up to a certain point.

Non-linear Behavior

Beyond a certain slip angle, known as the peak slip angle, the relationship becomes non-linear, and the cornering force begins to decrease. This is often due to tire saturation, where the tire can no longer generate additional lateral grip.

Tire Characteristics

Different tires have different characteristics in terms of how they generate cornering force relative to slip angle. Performance tires, for example, may have a higher peak cornering force and a larger slip angle before losing grip compared to standard road tires.

The Role of Coefficient of Friction

The relationship between the coefficient of friction and the slip angle is a crucial factor in understanding cornering force and its impact on vehicle dynamics. Unlike Newton's law of friction, race car tires often exhibit a coefficient of friction greater than 1. This can be attributed to the design and materials used in high-performance tires.

Take a look at the curve plotted between slip angle and coefficient of friction:

Note: The curve consists of three main regions:

Region OB: Upto a certain limit, when the slip angle increases, the coefficient of friction also increases. This region is steep to allow for maximum cornering force with small slip angles. Region BC: The coefficient of friction remains constant, creating a flat region. This is the threshold range. It's essential for drivers to know the limit of the slip angle to maintain optimal cornering force. Region Beyond C: The coefficient of friction decreases as the slip angle increases. Contact patch of the tyre starts to slide, so it should not be too steep to prevent the coefficient of friction from dropping too quickly.

Understanding these regions helps in optimizing vehicle performance and ensuring safe and efficient cornering in various driving conditions.