# Vehicle dynamics

**Vehicle dynamics** refers to the dynamics of vehicles, here assumed to be ground vehicles. Vehicle dynamics is a part of engineering primarily based on classical mechanics.

This article applies primarily to automobiles. For single-track vehicles, specifically the two-wheeled variety, see bicycle and motorcycle dynamics. For aircraft, see aerodynamics. For watercraft see Hydrodynamics.

## Components

Components, attributes or aspects of vehicle dynamics include:

- Automobile layout
- Electronic stability control (ESC)
- Steering
- Suspension
- Traction control system (TCS)

### Aerodynamic specific

Some attributes or aspects of vehicle dynamics are purely aerodynamic. These include:

- Automobile drag coefficient
- Automotive aerodynamics
- Center of pressure
- Downforce
- Ground effect in cars

### Geometry specific

Some attributes or aspects of vehicle dynamics are purely geometric. These include:

- Ackermann steering geometry
- Axle track
- Camber angle
- Caster angle
- Ride height
- Roll center
- Scrub radius
- Steering ratio
- Toe
- Wheelbase

### Mass specific

Some attributes or aspects of vehicle dynamics are purely due to mass and its distribution. These include:

### Motion specific

Some attributes or aspects of vehicle dynamics are purely dynamic. These include:

- Body flex
- Body roll
- Bump Steer
- Bundorf analysis
- Directional stability
- Critical speed
- Noise, vibration, and harshness
- Pitch
- Ride quality
- Roll
- Speed wobble
- Understeer, oversteer, lift-off oversteer, and fishtailing
- Weight transfer and load transfer
- Yaw

### Tire specific

Some attributes or aspects of vehicle dynamics can be attributed directly to the tires. These include:

- Camber thrust
- Circle of forces
- Contact patch
- Cornering force
- Ground pressure
- Pacejka's Magic Formula
- Pneumatic trail
- Radial Force Variation
- Relaxation length
- Rolling resistance
- Self aligning torque
- Slip angle
- Slip (vehicle dynamics)
- Steering ratio
- Tire load sensitivity

### Roadway specific

Some attributes or aspects of vehicle dynamics can be attributed directly to the roads on which they travel. These include:

- Banked turn, cross slope, drainage gradient, and cant or superelevation
- Road slipperiness and Split friction
- Surface roughness, International Roughness Index, Profilograph, Texture

## Driving techniques

Driving techniques which relate to, or improve the stability of vehicle dynamics include:

- Cadence braking
- Threshold braking
- Double declutching
- Drifting (motorsport)
- Handbrake turn
- Bootleg turn
- Heel-and-Toe
- Left-foot braking
- Opposite lock
- Scandinavian flick
- Ski (driving stunt)
- Wheelie

## Analysis and simulation

The dynamic behavior of vehicles can be analysed in several different ways.^{[1]} This can be as straightforward as a simple spring mass system, through a three-degree of freedom (DoF) bicycle model, to a large degree of complexity using a multibody system simulation package such as MSC ADAMS or Modelica. As computers have gotten faster, and software user interfaces have improved, commercial packages such as CarSim have become widely used in industry for rapidly evaluating hundreds of test conditions much faster than real time. Vehicle models are often simulated with advanced controller designs provided as software in the loop (SIL) with controller design software such as Simulink, or with physical hardware in the loop (HIL).

Vehicle motions are largely due to the shear forces generated between the tires and road, and therefore the tire model is an essential part of the math model. The tire model must produce realistic shear forces during braking, acceleration, cornering, and combinations, on a range of surface conditions. Many models are in use. Most are semi-empirical, such as the Pacejka Magic Formula model.

Racing car games or simulators are also a form of vehicle dynamics simulation. In early versions many simplifications were necessary in order to get real-time performance with reasonable graphics. However, improvements in computer speed have combined with interest in realistic physics, leading to driving simulators that are used for vehicle engineering using detailed models such as CarSim.

It is important that the models should agree with real world test results, hence many of the following tests are correlated against results from instrumented test vehicles.

Techniques include:

- Linear range constant radius understeer
- Fishhook
- Frequency response
- Lane change
- Moose test
- Sinusoidal steering
- Skidpad
- Swept path analysis

## See also

- Automotive suspension design
- Hunting oscillation
- Important publications in vehicle dynamics
- Multi-axis shaker table
- Vehicular metrics
- 4-poster
- 7 post shaker

## References

- ↑ Elkady, Mustafa; Elmarakbi, Ahmed (26 September 2012). "Modelling and analysis of vehicle crash system integrated with different VDCS under high speed impacts".
*Central European Journal of Engineering*.**2**(4): 585–602. doi:10.2478/s13531-012-0035-z.

## Further reading

- Egbert, Bakker; Nyborg, Lars; Pacejka, Hans B. (1987). "Tyre modelling for use in vehicle dynamics studies" (pdf).
*Society of Automotive Engineers*. A new way of representing tyre data obtained from measurements in pure cornering and pure braking conditions. - Gillespie, Thomas D. (1992).
*Fundamentals of vehicle dynamics*(2nd printing. ed.). Warrendale, PA: Society of Automotive Engineers. ISBN 978-1-56091-199-9. Mathematically oriented derivation of standard vehicle dynamics equations, and definitions of standard terms. - Milliken, William F. (2002). "Chassis Design – Principles and Analysis".
*Society of Automotive Engineers*. Vehicle dynamics as developed by Maurice Olley from the 1930s onwards. First comprehensive analytical synthesis of vehicle dynamics. - Milliken, William F.; Douglas L. (1995).
*Race car vehicle dynamics*(4. printing. ed.). Warrendale, Pa.: Society of Automotive Engineers. ISBN 978-1-56091-526-3. Latest and greatest, also the standard reference for automotive suspension engineers. - Limited, Jörnsen Reimpell; Helmut Stoll; Jürgen W. Betzler (2001).
*The automotive chassis : engineering principles*. Translated from the German by AGET (2nd ed.). Warrendale, Pa.: Society of Automotive Engineers. ISBN 978-0-7680-0657-5. Vehicle dynamics and chassis design from a race car perspective. - Guiggiani, Massimo (2014).
*The Science of Vehicle Dynamics*(1st. ed.). Dordrecht: Springer. ISBN 978-94-017-8532-7. Handling, Braking, and Ride of Road and Race Cars. - Meywerk, Martin (2015).
*Vehicle Dynamics*(1st. ed.). West Sussex: John Wiley & Sons. ISBN 978-1-118-97135-2. Lecture Notes to the MOOC Vehicle Dynamics of iversity