" I would argue with that. In your post #6, the blue arrow IS the real velocity of the tyre, which is perpendicular to the vector from CG to wheel pos, but not to the wheel's heading. So it WILL generate both long/lat forces. If you do the same calculations for the remaining 3 wheels the sum of all Fx's will be zero if the CG is at the center of the car, so that's why there is no movement of the car body. "
Thanks for the explanation Bmarci.
I see there were flaws in my understanding.
I was assuming that a stationary car spinning on the spot has zero linear velocities and as a result no slip angles could be generated.
But in fact, you show that although the car chassis has no linear velocites, the wheels actually do and therefore the slip angles can be calculated whilst ignoring the angular velocity of the chassis.
The Pacejka formula's work in wheel local coordinates.
Longtitude pointing in the direction the wheel rolls in and Lateral at 90 degrees to Longtitude direction.
So,as i understand it, Case 1 Example is correct.
Although i'm no expert, i always understood that a stationary car spinning on the spot with the steering centred produces no longtitude forces from the tires to move the car forwards or backwards. But only lateral forces to slow down the rate of spin.
But, maybe someone with more detailed knowledge than me can give a more accurate explanation.
I havn't read all of your post but a quick glance brought me to question 4.
To clarify Part 4.
If the car is stationary and spining on it's axis, and the front wheels arn't turned to any steering angle (yaw) but pointing in the direction the chassis points, then each wheel generates +- 90 degrees slip angle. The wheels only have lateral movement. ie they are only sliding sideways as the car spins.
The sign of the slip angle depends on whether the car is spinning clockwise or anti clockwise.
My statement about not generating slip angles was because the car is stationary and no slip angles are generated from the code that uses linear velocities of the car chassis to determine the slip angles. My basic method was using 1 wheel (chassis) to determine the slip angles and Bmarci was using 4 wheels.
Slip angles are generated by the difference between the longitude and lateral velocities of the tire.
The confusion comes from the fact that i was using the car chassis to determine the slip angle and not for each tire.
So when writing your sim, you need to take into consideration the angular velocity of the car and the slip angle that generates for each wheel and the linear velocities of the wheel (chassis , since the wheel is attached to the chassis).
The car can be moving with no angular velocity (moving forwards or sliding sideways), stationary but spinning on it's axis or any combination of the two.
And both situations need to be considered to determine your actual slip angle for each wheel.
The steering angle of the front wheels also needs to be taken into consideration for the front wheels slip angle.