What is side force

Single track model

The Single track model is a simplified model for describing the Lateral dynamics of a vehicle. In this post, we'll take a look at what this is all about.

Lateral forces

When we put the vehicle in Transverse direction move - for example with a Cornering - then we give one via the steering wheel Steering impulse. Through this the Front wheels inclined to Longitudinal axis aligned. If we drive slowly, then work no lateral forces. At fast cornering generate the Front wheels by the steering angle Lateral forces. These accelerate the vehicle in Transverse direction.

Calculating the transverse forces for the entire vehicle is quite time-consuming. Hence the vehicle model simplified: We assume that the main emphasis of the vehicle at road level lies. This prevents rolling and lifting movements. Furthermore, we bring the two wheels to an axle a wheel in the Vehicle center together.

If we look at the model, we see that the vehicle only consists of a rear and a front wheel. However, the wheels each have the properties of both wheels on the respective axle.

If we fast by a Curve drive, then shows the Longitudinal axis of the vehicle Not in the direction of the Speed ​​vector. The deviation is with the Slip angle specified. The deviation the Longitudinal axis to the fixed X axis will be with the Yaw angle described. At the Give in of the wheel Steering angle between the wheel and the longitudinal axis. For one cornering without lateral force this is also called Ackermann steering angle designated. The movement of the vehicle can be controlled by the translational center of gravity speed and the rotational yaw rate describe around the z-axis.

Cornering force

How do the Lateral forces? If we drive through a curve, that creates Centripetal acceleration a side force. You can get it by using the Vehicle speed to the square by the Curve radius share and with the Vehicle mass multiply:

The side force is after the Principle of d'Alembert as Inertial force considered. If you don't yet know what this principle is all about, please have a look at ours Video to do this.

Inertia is that acceleration of the vehicle opposite. When we're in a car, that fast by a Curve drives, then we feel it because we are following pressed outside become. To the Counteract force, act on the front and rear wheels Cornering forcesthat the vehicle is on the Circular path hold. We can calculate this using the following formulas:

The side forces on the tires can just generated when they are with a Roll off the slip angle. That means that the Longitudinal axis of the wheel offset to his Speed ​​vector must stand. There is one slip angle for the front wheel and one for the rear wheel. The Slip angle as follows:

Equations of motion

Next we want those Equations of motion for the vehicle taking into account the Circumferential forces examine. You can watch our video for repetition Vehicle coordinate system look at. For the Equilibrium of forces The following formulas apply in the longitudinal and transverse directions:

On the left side we find the Acceleration forces in x or Longitudinal direction and y- respectively Transverse direction. The terms on the right side look very similar out. We have to do this here Steering angle, the Circumferential force at the front and the Cornering force at the front consider . While for the equation in x direction nor the Rear circumferential force is taken into account, this is the case second equation the Cornering force at the rear.

There is also one more Yaw motion of the vehicle around the z-axis. We can do this with the Moment equilibrium to describe the focus:

Accelerations in the single-track model

When we're in a vehicle, we're interested in them acting accelerations of the vehicle, however, more than the forces. That's why we're looking at the context once closer to between the accelerations. They can be described with the radial and tangential acceleration. The Radial acceleration works for Center of the curve and the Tangential acceleration works tangential to the circular path. This results in the following formulas for the longitudinal and lateral acceleration:

We need both for that Longitudinal acceleration as well as for the Lateral acceleration note the same sizes: The Tangential acceleration, the Radial acceleration and the Slip angle.

If we now insert the centripetal acceleration for the radial and the vehicle acceleration for the tangential, then we get:

With these Formulas you can now easily do the Calculate accelerations.

Very good! Let's summarizewhat we learned in this post! The Single track model is a simplified vehicle model to describe the Lateral forces. At Cornering act on the Tire cornering forces, the the Counteract centripetal force.