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Relaxation length is a property of pneumatic tires that describes the delay between when a
Relaxation length is a property of pneumatic tires that describes the delay between when a slip angle
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 (i.e., the angle between the forward velocity vector v_x and the vector su ...
is introduced and when the cornering force
Cornering force or side force is the lateral (i.e., parallel to wheel axis) force produced by a vehicle tire during cornering.
Cornering force is generated by tire slip and is proportional to slip angle at low slip angles. The rate at wh ...
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.
Values
Pacejka gives a rule of thumb that "at nominal vertical load the relaxation length is of the order of magnitude of the wheel radius". Relaxations lengths have been found to be between 0.12 and 0.45 meters, with higher values corresponding to higher velocities and heavier loads. Tests on motorcycle tires have found that the ratio of cornering stiffness over lateral stiffness produces values 20-25% higher than those calculated as 63% of the steady state-value. The relaxation length associated withcamber thrust
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 ...
has been found to be nearly zero.
Importance
A tire's relaxation length controls how much the tire will contribute tospeed wobble
Wobble, shimmy, tank-slapper, speed wobble, and even death wobble are all words and phrases used to describe a quick (4–10 Hz) oscillation of primarily just the steerable wheel(s) of a vehicle. Initially, the rest of the vehicle remain ...
.
See also
*Bicycle and motorcycle dynamics
Bicycle and motorcycle dynamics is the science of the motion of bicycles and motorcycles and their components, due to the forces acting on them. Dynamics falls under a branch of physics known as classical mechanics. Bike motions of interest ...
*Pneumatic trail
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 th ...
*Vehicle dynamics
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 ...
References
{{Tires, state=collapsed Tires Automotive steering technologies Motorcycle dynamics