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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.

## Behaviour

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. [1] Formula 1 car tires may reach a peak side force at 3 degrees [2]

## Example

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 (lbf) max degrees 900 1.10 5.6 1350 1.08 6.0 1800 0.97 6.7

The same sensitivity is typically seen in the longitudinal forces, and combined lateral and longitudinal slip.

## Related Research Articles

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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.

## References

1. Milliken, W.F., Milliken, D.L., 1995, "Race Car Vehicle Dynamics", Society of Automotive Engineers (SAE) Warrendale, PA. page 27.
2. Wright P., 2001, "Formula 1 Technology", Society of Automotive Engineers (SAE) Warrendale, PA.