Mathematics of Skidding When Cornering I want to do a top down computer model with rectangles representing cars and then the wheels drawn separately. I want this for a road safety class.
I want to represent the movement of that car when it skids in a corner . If possible, I would like to show drifting when you repeatedly alternate turning in to the corner then putting on the opposite lock.
Does anyone know how I can do a mathematical model with
D: representing the direction the car (rectangle) is pointing
d: representing the direction the car (rectangle) is actually moving (which is likely going to be different than D) A: representing the angle of the wheels
V: the velocity vector
If possible, I would like to show how turning more into the corner will make your car spin. Turning opposite lock will correct the skid. And if possible show how to drift - like rally drivers do on the TV.
I would also like different road types, eg tarmac and those gravel corners seen on rally driving.
Does anyone know where I can find these types of equations?
A: A first step is to look up the equations for how the force generated by a wheel varies depending on its orientation to the direction of travel.  At very low angles the wheel generates a side force proportional to the steering angle.  As you increase the steering angle the side force decreases.  This is usually presented as the steering angle necessary to maintain a circular trajectory.  The steering angle increases more and more rapidly when the radius of the turn decreases.  When the car is truly skidding there is (almost) no side force generated.
A critical thing is how this differs between the front and rear wheels.  If the required angle on the front wheels increases faster than the rear wheels the car will understeer.  You must turn the front wheels more than geometry would dictate to have the car turn a circle.  If the required angle on the rear wheels increases faster, the car will oversteer, and once the turn is initiated the driver must steer less or even back to the other side.  This can be driven by the weight distribution between the axles, the different tires mounted front and rear, and the way the suspension is designed.
Once you have this data you just have a mechanical simulation.  At each time step, calculate the force the road exerts on the tire based on the angle of attack, the current speed, and the force supplied by the engine.  Calculate the net forces and torques on the car and apply that to the center of mass.  You will get new velocity and heading vectors for the next time step.
