Driving physics (car)

This article addresses the physical effects of driving a vehicle. For the science of vehicle motion, see Driving Dynamics .

The driving physics of motor vehicles deals with the effects of physical laws on driving behavior and the perceptions of vehicle occupants. Knowledge of the physical limits is particularly important in motorsport and when driving commercial vehicles .

Forces between the tire and the road

In motor vehicles, the contact between the vehicle and the road is only mediated by the tire contact areas, each about the size of a palm. The generation of forces in these contact surfaces is therefore of particular interest for the driving dynamics .

The simplest model concept is the Kamm circle . This means that the total force from the side force and the circumferential force cannot exceed a maximum value .

The maximum force depends on the maximum coefficient of adhesion between the tire and the road and the wheel load . The road condition (dry, damp, wet, snow, ice, gravel, ...) has the greatest influence on the coefficient of adhesion.

During normal driving, the effort of all wheels is well within the Kamm's circle. However, if a wheel is additionally decelerated by heavy braking while cornering in the border area , it can generate less cornering force. This leads to understeer on the front axle and oversteer on the rear axle . If a wheel were to lock, it would continue to slide in the current direction of movement of the wheel contact point regardless of the steering angle; the resulting (“braking”) force is then exactly in the opposite direction. The direction of the total force would then not change due to a steering angle. A vehicle can no longer be steered with its wheels locked, which is why an anti-lock braking system is mandatory for today's cars .

Spinning wheels as a result of drive torque when cornering lead to similar effects (understeer in front-wheel drive vehicles, oversteer in rear-axle drive vehicles). Modern vehicles therefore have control systems ( vehicle dynamics control , ESP) that prevent large slippage when braking (ABS) and driving ( traction control , ASR) and in the transverse direction. Situations that are critical in terms of driving dynamics are avoided as far as possible.

In motorsport, on the other hand, slip on the rear axle is deliberately used to make the vehicle drift .

Since the tire tread is elastically deformable, lateral forces can only arise if there is a slip angle . This law has far-reaching consequences for driving behavior, especially at high driving speeds (see single-track model ). Correspondingly, only one force can act in the circumferential direction if there is slip.

Principle of inertia

The physical principle that one experiences most clearly as a driver or passenger of vehicles is the principle of inertia formulated by Isaac Newton . It says that a body remains in a state of rest or uniform movement if it is not forced to change this by acting forces.

External forces act on the vehicle during normal driving. The tire forces are of particular importance, since without them a controlled movement of the vehicle is not possible. Both the vehicle and the occupants can experience acceleration due to these external forces . The force of inertia is opposite to the acceleration. When cornering, it is perceived by the occupants as centrifugal force , when braking as force forward.

Large forces can also occur in a collision. In the event of a head-on collision, the occupants would continue their movement in the direction of the windshield if restraint systems such as seat belts did not prevent this.

Cornering

Driving on a curve with the radius of curvature r and the driving speed v requires lateral acceleration . Since the side force potential of the tires is limited, the maximum possible speed is: ${\displaystyle a_{y}=v^{2}/r}$

${\displaystyle v_{\mathrm {max} }={\sqrt {a_{y,\mathrm {max} }\cdot r}}}$.

If this cornering speed limit is exceeded, the vehicle can no longer follow the radius and leaves the lane . A curve must therefore be approached more slowly on a slippery road than on a road with good grip.

Typical maximum lateral accelerations of cars on dry roads are between 8 m / s ² and 10 m / s ² . In racing, significantly higher values ​​are achieved here because the body and wings at the front and rear generate downforce, which increases the wheel load. On snow the values ​​decrease to about 3 m / s ² or less . The values ​​can be reduced to 1 m / s ² on wet ice . Snow and ice are not to be expected on the moon. Nevertheless, due to the very low gravity, one would have to be prepared for constantly "slippery" conditions. In the construction of rovers , other technologies for locomotion must be used instead of frictional engagement .

For reasons of driving safety, modern vehicles are designed in such a way that the front axle first reaches the adhesion limit (slip limit) when cornering stationary. The vehicle is understeering. In the past, the reverse situation occurred in vehicles with a rear engine. These vehicles were notorious as “rear skids”. The coordination takes advantage of the fact that the maximum adhesion coefficient of tires decreases with increasing wheel load. By stabilizing the wheel load of the front axle is greater than that of the selected rear axle. In vehicles with rear-wheel drive, this is often not enough, so that the front and rear axles are fitted with tires of different widths (mixed tires).

Ideal line

Lines located at the apex ( Apex cross). Green - highest cornering speed, light blue - highest speed at the corner exit, blue - at the entrance.

The driver has the option of choosing different lines within the given lane . In racing, the ideal line is the one that enables the shortest lap time on the given route. This can either be the maximum speed in the curve or the maximum speed at the exit of the curve , which results in shorter lap times on the following straight stretch.

Curve entrances and exits are used to brake or accelerate. If the longitudinal acceleration is plotted against the transverse acceleration of the vehicle, this provides information on how far the driver and vehicle utilize the physical limits of friction.

Tipping limit

Vehicles with a high center of gravity, for example commercial vehicles or off-road vehicles with an unfavorable load, can reach the tipping limit before the adhesion limit. The maximum lateral acceleration from which stationary tilting is possible (cube model) is calculated from the track width S and the height of the center of gravity h :

${\displaystyle a_{y,K}=g\cdot \underbrace {\frac {S}{2\cdot h}} _{SSF}}$

( g = acceleration due to gravity)

The SSF factor is called the static stability factor and is a measure of the rollover probability. It is determined by the American traffic safety authority NHTSA for all new cars. The vehicles are divided into five classes: 1 star for a very high rollover risk, 5 stars for a low rollover risk.

The actual tipping limit is lower than calculated with the above formula, since the shift in the center of gravity due to the roll angle and the elasticity of the tires have a reducing effect.

Brakes

Braking in the curve

During stationary cornering, a moment equilibrium is established around the vertical axis of the vehicle through the center of gravity. When braking, the axle load increases on the front axle, while it decreases by the same amount on the rear axle. With braking forces well below the locking limit, the lateral force initially decreases on the rear axle and increases on the front axle. When the steering wheel is held, the vehicle shows a pure turning reaction (orbit radius becomes smaller) in which a new state of equilibrium is sought. This is done by increasing the yaw rate and the slip angle . In extreme cases there is no new equilibrium and the vehicle skids. In vehicles with vehicle dynamics control , unequal braking forces are generated on the outside / inside of the curve in such cases, and thus a stabilizing yaw moment .

Braking on one-sided slipperiness

Forces and moments when braking on one-sided slippery roads

Since only small braking forces can be applied on the smooth side, a yaw moment arises which pulls the vehicle in the direction of the non-slip side. A counter-torque from the side forces is required for stabilization. The smooth side only makes a very small contribution. The vehicle becomes a "two-wheeler".

The driver ultimately has to apply the counter-torque by counter-steering. In order to keep driving straight ahead, the sum of the lateral forces on the front and rear axles must be zero. There is therefore a slip angle.

In order to give the driver time to react, control systems weaken the yaw moment, i.e. they delay the build-up of the destabilizing yaw moment. On the rear axle, a “ select-low control ” ensures that there is no additional difference in braking force.

Vehicle components

Vehicle components essential for driving physics are:

• tires
• Control systems
• Mass distribution (axle load distribution, height of the center of gravity)
• Suspension & damping
• Suspension
• Drive concept
  • Front wheel drive
  • Standard drive
  • Rear wheel drive
  • all wheel drive
• aerodynamics

literature

• Hans-Hermann Braess, Ulrich Seiffert: Vieweg manual automotive technology. 2nd edition, Friedrich Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig / Wiesbaden, 2001, ISBN 3-528-13114-4
• Karl-Heinz Dietsche, Thomas Jäger, Robert Bosch GmbH: Automotive pocket book. 25th edition, Friedr. Vieweg & Sohn Verlag, Wiesbaden, 2003, ISBN 3-528-23876-3

Web links

• Clear explanations with graphics on stopping distances and thought experiments with heights of fall ( memento from March 11, 2007 in the Internet Archive )
• Example of the rollover rating

Individual evidence

1. ↑ Hermann Winner, Stephan Hakuli, Gabriele Wolf (eds.): Handbook driver assistance systems . 2nd Edition. Vieweg + Teubner, 2012, ISBN 978-3-8348-1457-9 , pp. 522 ( limited preview in Google Book search).
2. ↑ Konrad Reif (ed.): Driving stabilization systems and driver assistance systems . 1st edition. Vieweg + Teubner, 2010, ISBN 978-3-8348-1314-5 , pp. 20 ( limited preview in Google Book search).
3. ↑ Bernt Spiegel: The upper half of the motorcycle . 5th edition. Motorbuch Verlag, 2006, ISBN 3-613-02268-0 , p. 131 .
4. ↑ Hermann Winner, Stephan Hakuli, Gabriele Wolf (eds.): Handbook of driver assistance systems: Basics, components and systems for active safety and comfort . 2nd Edition. Vieweg + Teubner, 2012, ISBN 978-3-8348-1457-9 , pp. 433 ( limited preview in Google Book search).
5. ^ C. Rill: Vehicle Dynamics . Pp. 42–44 , accessed January 1, 2019 .