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