# 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 forces**that 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 summarize**what 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**.

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