# calculate self aligning torque from steering wheel angle

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)

https://www.jstor.org/stable/pdf/44470677.pdf?refreqid=excelsior%3A809f6eb40ec4d08aaed017d1a0371a81

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?