BikeSim Math Models

Here are some features of the BikeSim mathematical models.

Complete Bike Model

BikeSim is delivered with a complete bike model, which has 26 degrees-of-freedom (DOF). The suspension model (a telescopic front fork and a rear swing-arm) and non-linear tire model calculate accurate bike dynamics. The swing-arm involves a non-linear lever ratio, which can express various types of ‘monoshock’ linkage suspension. Steer system involves 2DOF, rotations about steer axis and twist axis. The geometry of the steering system is expressed by a caster angle, which is defined by the user.

The model includes a brake system and powertrain (selectable either chain drive or shaft drive) that can be easily modified. Aerodynamic data inputs are also available for drag, lift and pitch.

Rider upper body can lean and move laterally relative to the bike frame. Therefore, you can set the riding positions (e.g. hang-on) with time or road station.

(In BikeSim version 2, now being prepared for shipping in March 2008, more detailed suspension models can also be simulated.)

Control Inputs

The four main control inputs involve steering, braking, speed, and riding position. BikeSim has options for open-loop and closed-loop inputs for steering, braking, throttle, and gear shifting (riding position is open-loop input only). 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

BikeSim 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. Users can create 3D roads such as banked curves, hills and race tracks with a range of simulated friction coefficients.

Events

Complicated sequences of inputs can be specified as events. For example, open throttle until an engine speed is reached, then engage the clutch to lift the front wheel, etc. Conditions can also be in place for changing vehicle properties. For example, change the tire crown radius in the middle of the maneuver to simulate the stability with a blown tire.

Outputs

The solver programs generate over 300 output variables. Any subset of the list of variables can be specified at run time, to control the size and organization of output files. BikeSim provides a graphical interface for browsing the list of available variables, sorting by several categories. All variables are described in documentation text files.

Extending a BikeSim Model

The BikeSim math models include nearly 90 inputs that you can specify in Simulink or with your own C code. These inputs include all control and environmental inputs, and all forces and moments generated by the powertrain, brakes, steering system, tires, and some suspension components. These inputs are used to extend the Bike math models by defining them with MATLAB/Simulink, available from The MathWorks, Inc, or with custom C code.

BikeSim Information

Technical Background