Tire load sensitivity describes the behaviour of tires under load. Conventional pneumatic tires do not behave as classical friction theory would suggest. The load sensitivity of most real tires in their typical operating range is such that the coefficient of friction decreases as the vertical load, Fz, increases. The maximum lateral force that can be developed does increase as the vertical load increases, but at a diminishing rate.
Coulomb friction theory says that the maximum horizontal force developed should be proportional to the vertical load on the tire. In practice, the maximum horizontal force Fy that can be generated is proportional, roughly, to the vertical load Fz raised to the power of somewhere between 0.7 and 0.9, typically.
Production car tires typically develop this maximum lateral force, or cornering force, at a slip angle of 6-10 degrees, although this angle increases as the vertical load on the tire increases.Formula 1 car tires may reach a peak side force at 3 degrees
As an example, here is data extracted from Milliken and Milliken's "Race Car Vehicle Dynamics", figure 2.9:
|Vertical load||Fy/Fz||Slip Angle|
The same sensitivity is typically seen in the longitudinal forces, and combined lateral and longitudinal slip.
A tire or tyre is a ring-shaped component that surrounds a wheel's rim to transfer a vehicle's load from the axle through the wheel to the ground and to provide traction on the surface over which the wheel travels. Most tires, such as those for automobiles and bicycles, are pneumatically inflated structures, which also provide a flexible cushion that absorbs shock as the tire rolls over rough features on the surface. Tires provide a footprint, called a contact patch, that is designed to match the weight of the vehicle with the bearing strength of the surface that it rolls over by providing a bearing pressure that will not deform the surface excessively.
For motorized vehicles, such as automobiles, aircraft, and watercraft, vehicle dynamics is the study of vehicle motion, e.g., how a vehicle's forward movement changes in response to driver inputs, propulsion system outputs, ambient conditions, air/surface/water conditions, etc.
The circle of forces, traction circle, friction circle, or friction ellipse is a useful way to think about the dynamic interaction between a vehicle's tire and the road surface. The diagram below shows the tire from above, so that the road surface lies in the x-y plane. The vehicle to which the tire is attached is moving in the positive y direction.
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In vehicle dynamics, slip angle or sideslip angle is the angle between the direction in which a wheel is pointing and the direction in which it is actually traveling. This slip angle results in a force, the cornering force, which is in the plane of the contact patch and perpendicular to the intersection of the contact patch and the midplane of the wheel. This cornering force increases approximately linearly for the first few degrees of slip angle, then increases non-linearly to a maximum before beginning to decrease.
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Rolling resistance, sometimes called rolling friction or rolling drag, is the force resisting the motion when a body rolls on a surface. It is mainly caused by non-elastic effects; that is, not all the energy needed for deformation of the wheel, roadbed, etc., is recovered when the pressure is removed. Two forms of this are hysteresis losses, and permanent (plastic) deformation of the object or the surface. Note that the slippage between the wheel and the surface also results in energy dissipation. Although some researchers have included this term in rolling resistance, some suggest that this dissipation term should be treated separately from rolling resistance because it is due to the applied torque to the wheel and the resultant slip between the wheel and ground, which is called slip loss or slip resistance. In addition, only the so-called slip resistance involves friction, therefore the name "rolling friction" is to an extent a misnomer.
Cornering force or side force is the lateral force produced by a vehicle tire during cornering.
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Slip ratio is a means of calculating and expressing the slipping behavior of the wheel of an automobile. It is of fundamental importance in the field of vehicle dynamics, as it allows to understand the relationship between the deformation of the tire and the longitudinal forces acting upon it. Furthermore, it is essential to the effectiveness of any anti-lock braking system.
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Hans Bastiaan Pacejka was an expert in vehicle system dynamics and particularly in tire dynamics, fields in which his works are now standard references. He was Professor emeritus at Delft University of Technology in Delft, Netherlands.
In (automotive) vehicle dynamics, slip is the relative motion between a tire and the road surface it is moving on. This slip can be generated either by the tire's rotational speed being greater or less than the free-rolling speed, or by the tire's plane of rotation being at an angle to its direction of motion.
Self aligning torque, also known as aligning torque, aligning moment, SAT, or Mz, is the torque that a tire creates as it rolls along, which tends to steer it, i.e. rotate it around its vertical axis. In the presence of a non-zero slip angle, this torque tends to steer the tire toward the direction in which it is traveling, hence its name.
Pneumatic trail or trail of the tire is a trail-like effect generated by compliant tires rolling on a hard surface and subject to side loads, as in a turn. More technically, it is the distance that the resultant force of side-slip occurs behind the geometric center of the contact patch.
Camber thrust and camber force are terms used to describe the force generated perpendicular to the direction of travel of a rolling tire due to its camber angle and finite contact patch. Camber thrust is generated when a point on the outer surface of a leaned and rotating tire, that would normally follow a path that is elliptical when projected onto the ground, is forced to follow a straight path while coming in contact with the ground, due to friction. This deviation towards the direction of the lean causes a deformation in the tire tread and carcass that is transmitted to the vehicle as a force in the direction of the lean.
Relaxation length is a property of pneumatic tires that describes the delay between when a slip angle is introduced and when the cornering force reaches its steady-state value. It is also described as the distance that a tire rolls before the lateral force builds up to 63% of its steady-state value. It can be calculated as the ratio of cornering stiffness over the lateral stiffness, where cornering stiffness is the ratio of cornering force over slip angle, and lateral stiffness is the ratio of lateral force over lateral displacement.