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 (North American English) or tyre (Commonwealth 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 (engineeri ...

and the

road A road is a thoroughfare used primarily for movement of traffic. Roads differ from streets, whose primary use is local access. They also differ from stroads, which combine the features of streets and roads. Most modern roads are paved. Th ...

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

plane Plane most often refers to: * Aero- or airplane, a powered, fixed-wing aircraft * Plane (geometry), a flat, 2-dimensional surface * Plane (mathematics), generalizations of a geometrical plane Plane or planes may also refer to: Biology * Plane ...

. 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. The main use for planes of rotation is in describing more complex rotations in four-dimensional space and higher dimensions, where they can ...

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 In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...

where it meets the road surface by the mechanism of

slip Slip or The Slip may refer to: * Slip (clothing), an underdress or underskirt Music * The Slip (band), a rock band * ''Slip'' (album), a 1993 album by the band Quicksand * ''The Slip'' (album) (2008), a.k.a. Halo 27, the seventh studio al ...

. 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 * Disease vector, an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematics a ...

''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 analogue of linear force. It is also referred to as the moment of force (also abbreviated to moment). The symbol for torque is typically \boldsymbol\tau, the lowercase Greek letter ''tau''. Wh ...

applied to it by the vehicle's

brake A brake is a machine, mechanical device that inhibits motion by absorbing energy from a moving system. It is used for Acceleration, slowing or stopping a moving vehicle, wheel, axle, or to prevent its motion, most often accomplished by means of ...

s or

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

. 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 A chassis (, ; plural ''chassis'' from French châssis ) is the load-bearing framework of a manufactured object, which structurally supports the object in its construction and function. An example of a chassis is a vehicle frame, the underpart ...

via the

suspension Suspension or suspended may refer to: Science and engineering * Car suspension * Cell suspension or suspension culture, in biology * Guarded suspension, a software design pattern in concurrent programming suspending a method call and the calling ...

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