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CarSim Math Models

Here are some features of the CarSim mathematical models. More details about the math models are provided in this PDF file.

Control Inputs

The three main control inputs involve steering, braking, and speed. CarSim has options for open-loop and closed-loop inputs for steering, braking, throttle, and gear shifting. There are also options for building complex control sequences as a series of "events," where a new control can be triggered by any output variable reaching a specified value.

Environmental Inputs

CarSim includes an advanced description of 3D road surfaces. You can quickly build descriptions of roads with arbitrary horizontal, vertical, and cross-elevation geometry. Friction between the tire and the ground is specified as a function of distance along the road and lateral position relative to the centerline.

The CarSim graphical user interface (GUI) also provides a road building tool for rapidly assembling a 3D road surface from sections.

Besides providing the 3D road information to the math models, the GUI also generates shapes for the CarSim animator automatically. In this regard, the 3D surface can always be visualized.

CarSim also includes aerodynamic effects and wind inputs.

3D Vehicle Dynamics

The equations of motion in the CarSim math models are valid for full nonlinear 3D motions of rigid bodies. The major kinematics and compliance effects of the suspensions and steering systems are specified with properties that can be measured directly. Details of the linkages and gears in the suspensions and steering systems are not needed, reducing the amount of information needed to obtain accurate predictions.

Many of the components that have the greatest effect on handling, braking, and acceleration are represented with nonlinear tables of measurable data. For example, CarSim uses detailed nonlinear kinematical relationships, nonlinear spring models, and other nonlinear component models. These properties can be calculated with suspension kinematics tools such as SuspensionSim or by measurement in Kinematics and Compliance test facilities.


The CarSim tire models reproduce the shear forces and moments applied to the tires from the 3D road surface. They provide the full nonlinear behavior of rolling tires subject to combined braking/acceleration and cornering on roads with variable friction. The models have dynamic responses due to relaxation length, and handle the transision to zero speed to properly simulate parking lot maneuvers and driving simulator conditions.

CarSim includes several tire models with alternate ways to provide the tire data. It supports nonlinear tables that would be obtained directly from laboratory measurements, and also includes the TNO Delft-Tyre model with standardized Magic Formula coefficients.


Complicated sequences of inputs can be specified as events. For example, accelerate until a speed is reached, then shift to neutral and coast down, then apply the brakes until a low speed is reached, then accelerate, etc. Conditions can also be in place for changing vehicle properties. For example, change the tire data for one wheel if the friction under that wheel drops below some limit.


You can view simulation results with a virtual camera (animation) and with plots of output variables with a single button click. The number and order of the output variables can be specified at run-time from a list of hundreds of available variables.

Extending a CarSim Model

The CarSim math models include almost 300 variables that you can use to extend the models. This method has been used for years by CarSim users to include controllers or alternate component models in Simulink. The same methods can also be used with LabView, ETAS LabCar and ASCET, custom Visual Basic, MATLAB, and ANSI C. Extensions can even be made at runtime with no external software, using built-in VS commands.

These available variables that can be defined at runtime include all control and environmental inputs, as well as all forces and moments generated by the powertrain, brakes, steering system, tires, and some suspension components.

CarSim Information

Data Sources
Customers: OEMs, Suppliers, Others

PDF Documents

CarSim Brochure
CarSim Math Models
CarSim Model and License Options
New CarSim Features
QuadDS and HexDS Driving Simulators
3D Animator Shapes
System and Software Compatibility
Unreal Plugin
VS Connect Example

VS Vehicle Model Features

Paths and Roads
Moving Objects and ADAS Sensors

Core VehicleSim Technology

GUI, Database, and Documentation
Fast and Parametric Math Model Solvers
Viewing Results: Animation and Plotting

Advanced Applications

Simulink, LabVIEW, and ASCET
VS Commands
Automation and COM
Custom Work

Real-Time Options

Real-Time HIL Testing
Driving Simulators

Specification of 3D road surface with variable friction. Animation shapes are generated automatically. Click for full size.
CarSim and TruckSim include several advanced tire models. Click for full size.
Suspension kinematics are specified potentially nonlinear functions that are configured at runtime. They can be constant, linear or use tables of measurable values. Click for full size.
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and VehicleSim are registered trademarks of Mechanical Simulation Corporation in the USA and other countries.