How do we model vehicle dynamics and which vehicle parameters do we use? Well, the very first step to analyzing the dynamics of a vehicle is to consider Newton's Second Law! What physics again? Yes, you should be comfortable with Newton's Second Law which states that "If a body is accelerating, there is a force on it"!

So how do we start analyzing the forces on the vehicle? Well firrst we need to set a few ground rules to properly model our car. One of the main assumptions utilized is to assume that the whole vehicle acts as a lumped mass, in that all of the components in the vehicle move together as a single body. This is later broken down into sprung mass(body) and the unsprung mass(wheels). The other assumptions include: fixed coordinate system where the motions are based on a right-hand orthogonal cordinate system and the forces are defined as they act __ON__ the vehicle.

Now we will look at the free body diagram above and define all of the variables and forces.

W: weight of the vehicle

Wf: dynamic weight on front axle

Wr: dynamic weight on rear axle

Fxr: tractive force on the rear tire contact patch

Fxf: tractive force on the front tire contact patch

Rxr: rolling resistance force on the rear tire contact patch

Rxf: rolling resistance force on the front tire contact patch

r: tire radius

h: center of gravity height

L: wheelbase

b: longitudinal distance from the front axle to the center of gravity

c: longitudinal distance from the rear axle to the center of gravity

t: track

Da: aerodynamic force

From here we will apply Newton's Second Law and sum the torques around a single point at the rear tire. Assuming zero pitch acceleration, the forces will yield an equation for us to develop the dynamics of the vehicle.

I will leave the rest to a future discussion and to the program simulation. For now, I wanted to include a simple free body diagram for everyone to reference on the simulation page. Check out the wiki link below for further discussion of vehicle dynamics!

Wikipedia Vehicle DynamicsComments!