I would like to calculate self aligning torque (SAT) to apply it for a simulating game with Logitech G29 steering wheel, the torque is gonna be inferred from steering wheel angle (plus car motion). I found a correlation between SAT and slip angle at the following article (Fig.4 shows how to infer SAT from slip angle)
However, slip angle is not steering wheel angle. Slip angle can be gotten by $$ -arctan(V_y/|V_x|), $$ I still dont know exactly but i guess i can estimate velocity of the car in my simulation.
How can i get slip angle from steering wheel angle?