# Cornering force

The cornering force is that component of the force on the wheel in the contact zone between the wheel and the "road" that is perpendicular to the intersection of the road and the wheel center plane. In the case of road vehicles, the lane is to be understood as the road, in the case of rail vehicles the rail .

## tire

Bracing of the profile particles in the laces under an oblique run

In the case of tires , the cornering force depends on the slip angle , wheel load , slip , wheel camber and the coefficient of friction between the tire and the road surface.

The lateral forces that can be transmitted between the tires and the road limit the lateral acceleration of vehicles when cornering. If circumferential forces act at the same time, this influences the lateral force. The relationships can be illustrated with the Kamm circle or the Krempel friction ellipse.

In order for a tire to build up lateral forces, the part of the elastic tread that has direct contact with the road must be deformed. The mechanism of the force generation of the rolling tire can be explained with the brush model. The tread particles run unstrained into the patch and, as they pass through the contact zone due to the rotation of the wheel, are increasingly deformed by the transverse speed between the carcass and the road. With small slip angles, the profile particles adhere to the road; an approximately triangular tension builds up. Only at the end of the contact zone do the profile particles begin to slide and return to their original position. In the case of large slip angles, the sliding zone covers almost the entire contact zone, so that there is no longer a triangular shape. ${\ displaystyle u}$

Since the sidewall of the tire is also elastic, the side forces cannot build up immediately. This can e.g. B. be observed on the stationary tire, which deforms transversely when lowering the vehicle from the lift. The tire behaves like a spring here. In general, the rolling tire therefore also needs a certain distance before the cornering force becomes effective. This distance (relaxation length) can be up to half of the rolling circumference.

If the tire runs under a camber angle to the road like a two-wheeler, a parabolic tension builds up. The side force with one degree of camber is a maximum of 10% of the side force with one degree of slip angle. In the case of a motorcycle that is moved at the frictional connection limit, there is always an additional slip angle.

The lateral force can be measured on tire test stands and is represented as a function of the slip angle with the parameter wheel load. Since not all operating points can be measured, mathematical tire models must be used in simulations with combined stress on the tire .

## Rail vehicles

In the case of rail vehicles , the design of the rail (especially the inclination of the curve) and the wheel determine the maximum cornering force. Dynamic instabilities and the tilt angle defined by the position of the center of gravity limit the maximum possible cornering speed for the vehicle in question.

## literature

• Karl-Heinz Dietsche, Thomas Jäger, Robert Bosch GmbH: Kraftfahrtechnisches Taschenbuch 25th edition, Friedr. Vieweg & Sohn Verlag, Wiesbaden, 2003, ISBN 3-528-23876-3

## Individual evidence

1. Günter Leister: Vehicle tires and chassis development: strategy, methods, tools . Vieweg + Teubner, 2009, ISBN 978-3-8348-0671-0 , p. 109 ( limited preview in Google Book search).
2. Michael Trzesniowski: Racing car technology: basics, construction, components, systems . Vieweg + Teubner, 2010, ISBN 978-3-8348-0857-8 , pp. 215 ( limited preview in Google Book search).