Circle of forces

The Kamm's circle or Kamm's friction circle (named after Wunibald Crest) is a graphical representation of the allocation of the total possible force on the wheel in the cornering force in the transverse direction and the braking force and driving force in the longitudinal direction of the wheel until it reaches the maximum friction force.


The Kamm's circle represents the idealized relationship between longitudinal and lateral force on the wheel of a vehicle dar. The radius corresponds to the maximum available total force that can transmit the wheel on the road. The maximum friction force is dependent on the maximum adhesion coefficient - influenced by the condition of the road and the rolling speed - and the normal force on the wheel If, for example, by wet coefficient of friction between wheel and road surface, the total available power is reduced.

Approaches in the comb circle between the exploited ( = actual ) Radgesamtkraft the limit shown at first grows the slip until finally slide all profiled particles in the tire contact patch. The slip or sliding occurs basically in the direction of the total force, ie pro rata may also transverse to the rolling direction; this effect results in the absence of guidance to a skidding by under-or oversteer.

The main message of the comb between the circle is, therefore, that longitudinal force and lateral force are interdependent and that the resultant of these forces, the total force, the maximum available friction force can not exceed. In general, the increase in the longitudinal force less cornering force is available, thus the need for cornering force may not be able to be covered. Conversely, that maximum acceleration or deceleration in non -guideway vehicles thus is possible only when driving straight ahead.

Although the Kamm's circle represents an idealized simplification, however, is well suited to explain the basis of dynamic relationships. An extended model, in which, inter alia, depending on the direction of the force flows, provides krempelsche friction ellipse. Here is, inter alia, attempts to address the circumstances in which the maximum tangential force is greater than the maximum lateral force, such as in passenger cars

Vehicle Technical measures

By mechatronic systems it is possible to avoid exceeding the power limit circuit largely. With traction control (ASR ) and anti -lock braking systems (ABS ) of the slippage of the tires is so limited that a block or wheel spin is prevented. Ideally, this gets the steerability of the vehicle because of the attention to a sufficiently high cornering potential.

This condition is not always achieved, inter alia, during braking or acceleration in curves. To optimize the longitudinal and lateral forces on the wheel Electronic Stability programs are developed ( ESP / ESC) since the 1990s. As an extension of ABS, mostly with ASR by ESP / ESC is trying to prevent by targeted (automatic ) braking of individual wheels or more, both the over-and understeer a vehicle. ESP / ESC influenced here except the power distribution between longitudinal and lateral force at individual wheels also targeted the total resulting from these wheel forces yaw moment to the vehicle.

For vehicles with all-wheel drive, the acceleration force on four or more wheels is distributed, what the total force distribution improves. During braking, but the distributed drag torque of the motor can interfere with the ABS.