Circle of forces
Encyclopedia
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
and the road
surface. In the diagram below we are looking at the tire from above, so that the road surface lies in the x-y plane
. The vehicle that the tire is attached to 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
of the tire is at an angle to the actual direction that the tire is moving (the positive y direction). That angle is the slip angle
.
A tire can generate horizontal force
where it meets the road surface by the mechanism of slip
. That force is represented in the diagram by the vector 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
applied to it by the vehicle's brakes or drive train. 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 Fx and Fy that does not exceed 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 (Fx) which, when transferred to the vehicle's chassis
via the suspension
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 (Fy). 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, is affected by many things, 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.
Tire
A tire or tyre is a ring-shaped covering that fits around a wheel rim to protect it and enable better vehicle performance by providing a flexible cushion that absorbs shock while keeping the wheel in close contact with the ground...
and the road
Road
A road is a thoroughfare, route, or way on land between two places, which typically has been paved or otherwise improved to allow travel by some conveyance, including a horse, cart, or motor vehicle. Roads consist of one, or sometimes two, roadways each with one or more lanes and also any...
surface. In the diagram below we are looking at the tire from above, so that the road surface lies in the x-y plane
Plane (mathematics)
In mathematics, a plane is a flat, two-dimensional surface. A plane is the two dimensional analogue of a point , a line and a space...
. The vehicle that the tire is attached to is moving in the positive y direction.
Plane of rotation
In geometry, a plane of rotation is an abstract object used to describe or visualise 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 two, four or more dimensions.Mathematically such...
of the tire is at an angle to the actual direction that the tire is moving (the positive y direction). That angle is the slip angle
Slip angle
In vehicle dynamics, slip angle or sideslip angle is the angle between a rolling wheel's actual direction of travel and the direction towards which it is pointing...
.
A tire can generate horizontal force
Force
In physics, a force is any influence that causes an object to undergo a change in speed, a change in direction, or a change in shape. In other words, a force is that which can cause an object with mass to change its velocity , i.e., to accelerate, or which can cause a flexible object to deform...
where it meets the road surface by the mechanism of slip
Slip (vehicle dynamics)
In 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...
. That force is represented in the diagram by the vector 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
Torque
Torque, moment or moment of force , is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist....
applied to it by the vehicle's brakes or drive train. 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 Fx and Fy that does not exceed 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 (Fx) which, when transferred to the vehicle's chassis
Chassis
A chassis consists of an internal framework that supports a man-made object. It is analogous to an animal's skeleton. An example of a chassis is the underpart of a motor vehicle, consisting of the frame with the wheels and machinery.- Vehicles :In the case of vehicles, the term chassis means the...
via the suspension
Suspension (vehicle)
Suspension is the term given to the system of springs, shock absorbers and linkages that connects a vehicle to its wheels. Suspension systems serve a dual purpose — contributing to the car's roadholding/handling and braking for good active safety and driving pleasure, and keeping vehicle occupants...
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 (Fy). This represents drag
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...
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
Cornering force
Cornering force or side force is the lateral 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 which cornering force builds up is described by relaxation length...
.
The diameter of the circle of forces, and therefore the maximum horizontal force that the tire can generate, is affected by many things, 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.
See also
- Racetrack (game)Racetrack (game)Racetrack is a paper and pencil game of unknown origins, played by two or more players. It is also known under names such as Vector formula, Vector rally, Vector race, Graph racers, PolyRace, Paper and pencil racing, or the Graph paper race game. Racetrack is played on a squared sheet of paper...
- Vehicle dynamicsVehicle dynamicsVehicle dynamics refers to the dynamics of vehicles, here assumed to be ground vehicles. Vehicle dynamics is a part of engineering primarily based on classical mechanics but it may also involve chemistry, solid state physics, electrical engineering, communications, psychology, control theory,...
- Cornering forceCornering forceCornering force or side force is the lateral 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 which cornering force builds up is described by relaxation length...
- Slip angleSlip angleIn vehicle dynamics, slip angle or sideslip angle is the angle between a rolling wheel's actual direction of travel and the direction towards which it is pointing...
- Slip (vehicle dynamics)Slip (vehicle dynamics)In 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...