Tire slip angle

• Also called: slip angle, lateral slip angle
• Category: Control › Locomotion control
• Tags: vehicle-dynamics, tire-models, autonomous-driving, friction, wheeled-robots

The angle between the direction a wheel is pointing and the direction its contact patch is actually moving; it is the main variable that sets the lateral force a tire produces.

Definition

The tire slip angle is the angle between the heading of a wheel, the line of its wheel plane on the ground, and the direction in which the tire's contact patch is actually traveling. When a vehicle corners, its tires do not move exactly where they point: the rubber and carcass deform, the contact patch moves partly sideways relative to the wheel, and that deformation produces the lateral force that turns the vehicle. At small slip angles the lateral force grows roughly in proportion to the slip angle, with a slope called the cornering stiffness. As the slip angle increases the force levels off at a peak set by friction and normal load, and beyond the peak more of the contact patch slides and the force stays flat or falls.

In a bicycle model, slip angles are computed per axle from the vehicle's motion. For the front axle, the slip angle is the steering angle minus the angle of the front axle's velocity, which depends on longitudinal speed, lateral speed and yaw rate times the distance from the center of mass to the axle; the rear axle has the same form without the steering term. Sign conventions differ between texts and standards, and the formulas divide by longitudinal speed, so they become ill-defined near standstill; simulators and estimators add low-speed handling for that reason. Nonlinear tire models, such as Pacejka's Magic Formula or the brush model, map slip angle, normal load and friction to lateral force, and combined-slip models reduce the available lateral force when the tire is also braking or accelerating.

Slip angle is one of two slip quantities. Longitudinal slip, or slip ratio, compares the wheel's rolling speed with its forward speed and governs traction and braking force; slip angle governs cornering force. Both differ from the vehicle's sideslip angle, which is the angle between the whole vehicle's heading and its velocity at the center of mass. A slip angle also does not mean the tire is skidding: at small angles most of the contact patch is gripping the road, and the angle comes mostly from deformation.

Why it matters

Tire forces decide what a wheeled vehicle can actually do, and slip angle is the variable that governs lateral grip. Controllers for autonomous cars, limit-handling systems and drifting all need to estimate slip angles and keep them within, or deliberately beyond, the range where tire force is predictable.

Key applications

• Dynamic bicycle and four-wheel vehicle models
• Tire model identification from driving data
• Electronic stability control and limit-handling control
• Autonomous drifting and racing controllers
• Vehicle sideslip and tire force estimation

In practice

A team building an autonomous drifting controller logs speed, yaw rate, steering angle and vehicle sideslip on a test track, the sideslip from a dual-antenna GNSS and inertial system. From these signals they compute front and rear slip angles at every time step, plot lateral force against slip angle for each axle, and fit a tire model, either a Magic Formula curve or a learned model. In a sustained drift the rear tires operate well past their force peak while the front tires stay near it, and the controller uses the fitted curves to choose steering and throttle that hold this balance. Data from very low speeds is discarded, since the slip-angle formulas are unreliable there.

Common misconceptions

• A nonzero slip angle means the tire is skidding — at small slip angles most of the contact patch grips the road and the angle comes from tire deformation
• Tire slip angle and vehicle sideslip angle are the same — sideslip describes the whole vehicle's velocity relative to its heading, while slip angle is defined for each tire or axle
• Lateral force keeps rising with slip angle — it peaks and then levels off or falls as the tire saturates
• Slip angle covers all tire slip — longitudinal slip, or slip ratio, is a separate quantity that governs traction and braking force, and the two interact under combined slip

Who should know this

• Vehicle dynamics and autonomous driving engineers
• Controls researchers working on limit handling and drifting
• Engineers building simulators for wheeled robots
• Field robotics developers working on fast wheeled platforms

Related technologies

• Pacejka Magic Formula
• Brush Tire Model
• Electronic Stability Control
• GNSS-Inertial Navigation
• Friction Circle

Related terms

• Bicycle model
• Coulomb Friction
• Friction Cone
• System Identification
• Model Predictive Control

Related projects

• Vision Pilot: Autoware Foundation's open-source L2 ADAS stack from a single camera
• python_simple_mppi: MPPI control derived and implemented in numpy, with four worked examples

Videos

• Explained: Tire Slip Angle: JoshTheEngineer