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 A tire (American English) or tyre (British English) 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 t ...

and the

road A road is a linear way for the conveyance of traffic that mostly has an improved surface for use by vehicles (motorized and non-motorized) and pedestrians. Unlike streets, the main function of roads is transportation. There are many types of ...

surface. The diagram below shows the tire from above, so that the road surface lies in the ''xy''-

plane Plane(s) most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface Plane or planes may also refer to: Biology * Plane (tree) or ''Platanus'', wetland native plant * ''Planes' ...

. The vehicle to which the tire is attached is moving in the positive ''y'' direction. In this example, the vehicle would be cornering to the right (i.e. the positive ''x'' direction points to the center of the corner). Note that the

plane of rotation In geometry, a plane of rotation is an abstract object used to describe or visualize rotations in space. In three dimensions it is an alternative to the axis of rotation, but unlike the axis of rotation it can be used in other dimensions, such as ...

of the tire is at an angle to the actual direction that the tire is moving (the positive ''y'' direction). Put differently, rather than being allowed to simply "roll" in the direction that it is "pointing" (in this case, rightwards from the positive ''y'' direction), the tire instead must "slip" in a different direction from that which it is pointing in order to maintain its "forward" motion in the positive ''y'' direction. This difference between the direction the tire "points" (its plane of rotation) and the tire's actual direction of travel is the

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 ...

. A tire can generate horizontal force where it meets the road surface by the mechanism of

slip Slip or SLIP may refer to: Science and technology Biology * Slip (fish), also known as Black Sole * Slip (horticulture), a small cutting of a plant as a specimen or for grafting * Muscle slip, a branching of a muscle, in anatomy Computing and ...

. That force is represented in the diagram by the

vector Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...

''F''. Note that in this example ''F'' is perpendicular to the plane of the tire. That is because the tire is rolling freely, with no

torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...

applied to it by the vehicle's brakes or

drive train A drivetrain (also frequently spelled as drive train or sometimes drive-train) is the group of components that deliver mechanical power from the prime mover to the driven components. In automotive engineering, the drivetrain is the components o ...

. However, that is not always the case. The magnitude of ''F'' is limited by the dashed circle, but it can be any combination of the components ''F''_''x'' and ''F''_''y'' that does not extend beyond the dashed circle. (For a real-world tire, the circle is likely to be closer to an ellipse, with the ''y'' axis slightly longer than the ''x'' axis.) In the example, the tire is generating a component of force in the ''x'' direction (''F''_''x'') which, when transferred to the vehicle's chassis via the

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 ...

system in combination with similar forces from the other tires, will cause the vehicle to turn to the right. Note that there is also a small component of force in the negative ''y'' direction (''F''_''y''). This represents drag that will, if not countered by some other force, cause the vehicle to decelerate. Drag of this kind is an unavoidable consequence of the mechanism of slip, by which the tire generates lateral force. The diameter of the circle of forces, and therefore the maximum horizontal force that the tire can generate, depends upon many factors, including the design of the tire and its condition (age and temperature, for example), the qualities of the road surface, and the vertical load on the tire.

References

{{DEFAULTSORT:Circle Of Forces Force Automotive suspension technologies Automotive safety Tires Motorcycle dynamics

See also

References