![Tire coordinate system](https://upload.wikimedia.org/wikipedia/commons/f/fa/Tire_coordinate_system.png)
In
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 ...
, 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
and the vector sum of wheel forward velocity
and lateral velocity
, as defined in the image to the right).
This slip angle results in a force, 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 ...
, 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.
The slip angle,
is defined as
Causes
A non-zero slip angle arises because of deformation in the
tire
A tire (American English) or tyre (British English) is a ring-shaped component that surrounds a Rim (wheel), wheel's rim to transfer a vehicle's load from the axle through the wheel to the ground and to provide Traction (engineering), t ...
carcass and tread. As the tire rotates, the friction between the contact patch and the road results in individual tread 'elements' (finite sections of tread) remaining stationary with respect to the road. If a side-slip velocity ''u'' is introduced, the
contact patch will be deformed. When a tread element enters the contact patch, the friction between the road and the tire causes the tread element to remain stationary, yet the tire continues to move laterally. Thus the tread element will be ‘deflected’ sideways. While it is equally valid to frame this as the tire/wheel being deflected away from the stationary tread element, convention is for the co-ordinate system to be fixed around the wheel mid-plane.
While the tread element moves through the contact patch it is deflected further from the wheel mid-plane. This deflection gives rise to the slip angle, and to 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 ...
. The rate at which the cornering force builds up is described by the
relaxation length
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 late ...
.
Effects
The ratios between the slip angles of the front and rear axles (a function of the slip angles of the front and rear tires respectively) will determine the vehicle's behavior in a given turn. If the ratio of front to rear slip angles is greater than 1:1, the vehicle will tend to
understeer
Understeer and oversteer are vehicle dynamics terms used to describe the sensitivity of a vehicle to steering. Oversteer is what occurs when a car turns (steers) by more than the amount commanded by the driver. Conversely, understeer is what occ ...
, while a ratio of less than 1:1 will produce
oversteer
Understeer and oversteer are vehicle dynamics terms used to describe the sensitivity of a vehicle to steering. Oversteer is what occurs when a car turns (steers) by more than the amount commanded by the driver. Conversely, understeer is what occ ...
.
Actual instantaneous slip angles depend on many factors, including the condition of the road surface, but a vehicle's
suspension
Suspension or suspended may refer to:
Science and engineering
* Suspension (topology), in mathematics
* Suspension (dynamical systems), in mathematics
* Suspension of a ring, in mathematics
* Suspension (chemistry), small solid particles suspende ...
can be designed to promote specific dynamic characteristics. A principal means of adjusting developed slip angles is to alter the relative roll couple (the rate at which weight transfers from the inside to the outside wheel in a turn) front to rear by varying the relative amount of front and rear lateral
load transfer
Weight transfer and load transfer are two expressions used somewhat confusingly to describe two distinct effects:
*the change in load borne by different wheels of even perfectly rigid vehicles during acceleration
*the change in center of mas ...
. This can be achieved by modifying the height of the
roll centers, or by adjusting
roll stiffness, either through suspension changes or the addition of an
anti-roll bar
An anti-roll bar (roll bar, anti-sway bar, sway bar, stabilizer bar) is a part of many automobile suspensions that helps reduce the body roll of a vehicle during fast cornering or over road irregularities. It connects opposite (left/right) whee ...
.
Because of asymmetries in the side-slip along the length of the contact patch, the resultant force of this side-slip occurs away from the geometric center of the contact patch, a distance described as the
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 ...
, and so creates a torque on the tire, the so-called
self aligning torque
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, thi ...
.
Measurement of slip angle
There are two main ways to measure slip angle of a tire: on a vehicle as it moves, or on a dedicated testing device.
There are a number of devices which can be used to measure slip angle on a vehicle as it moves; some use optical methods, some use inertial methods, some
GPS
The Global Positioning System (GPS), originally Navstar GPS, is a Radionavigation-satellite service, satellite-based radionavigation system owned by the United States government and operated by the United States Space Force. It is one of t ...
and some both GPS and inertial.
Various test machines have been developed to measure slip angle in a controlled environment. A
motorcycle tire test machine is located at the
University of Padua
The University of Padua ( it, Università degli Studi di Padova, UNIPD) is an Italian university located in the city of Padua, region of Veneto, northern Italy. The University of Padua was founded in 1222 by a group of students and teachers from B ...
. That uses a 3-meter diameter disk that rotates under a tire held at a fixed steer and camber angle, up to 54 degrees. Sensors measure the force and moment generated, and a correction is made to account for the curvature of the track.
Other devices use the inner or outer surface of rotating drums, sliding planks, conveyor belts, or a trailer that presses the test tire to an actual road surface.
See also
*
Camber 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 ...
*
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 ...
*
Slip (vehicle dynamics)
*
Traction circle
References
{{Sim racing
Automotive safety
Automotive steering technologies
Automotive suspension technologies
Tires
Motorcycle dynamics