Recently I began to develop my own car physics in unity and tried to implement Pacejka’s Magic Formula, but I can’t know if I am in the right direction or not cause there are very few data and articles about the Magic Formula.

I read Marco Monster's article and a lot of gamedev discussions.
For now, I only implemented the longitudinal magic formula and it is very unstable even at high speeds

Here is the code:

      void HandleLongitudinal(RaycastHit hit)
    {

        float carLon = Vector3.Dot(rb.velocity, car.transform.forward); //The longitudinal veloctiy of the car
        slipRatio = ((angularVelocity * wheelRadius) - carLon) / Mathf.Max(Mathf.Abs(carLon), 0.00001f);

        weight = 1500 / 4; //In KG, For now it is a constant 

        longForce = PacejkaLon(slipRatio * 100, weight * 9.81f / 1000); //The longitudinal Force

        rb.AddForceAtPosition(longForce * -transform.right, hit.point); //Adding force in the contact patch area

        tractionTorque = longForce * wheelRadius;

        totalTorque = wheelTorque - tractionTorque; //For now there is no brake torque or any opposite torques only the traction torque 
        float wheelInertia = wheelMass * wheelRadius * wheelRadius / 2; //Wheel mass is 70kg and wheel radius is 0.34m
        angularAcceleration = totalTorque / wheelInertia;

        angularVelocity += angularAcceleration * Time.fixedDeltaTime;

    }

Wheel torque is calculated like this:

 float gearRatio = 2.66f;
 float diffRatio = 3.42f;
 float engineTorque = 50;
 float wheelTorque = engineTorque * gearRatio * diffRatio * .7f;//.7f is the transmission efficiency

Pacejka Formula:

public float PacejkaLon(float slip, float Fz)
    {
        C = lonSettings.b0;
        D = Fz * (lonSettings.b1 * Fz + lonSettings.b2);
        BCD = (lonSettings.b3 * Fz * Fz + lonSettings.b4 * Fz) * Mathf.Exp(-lonSettings.b5 * Fz);
        B = BCD / (C * D);
        H = lonSettings.b9 * Fz + lonSettings.b10;
        E = (lonSettings.b7 * Fz * Fz + lonSettings.b7 * Fz + lonSettings.b8) * (1 - lonSettings.b13 * Mathf.Sign(slip + H));
        V = lonSettings.b11 * Fz + lonSettings.b12;
        Bx1 = B * (slip + H);


        return D * Mathf.Sin(C * Mathf.Atan(Bx1 - E * (Bx1 - Mathf.Atan(Bx1)))) + V;
    }

I've printed Pacejka Formula on a graph and it does look like the references I took the formula from this link.

The video

As you can see the slip ratio graph is oscillating too much, and worth mentioning that the engine torque is constant in the video, I tried to increase it over time but still the same results.

Is this the kind of behavior that the Pacejka Fourmla do or not? If not, could you please guide me in the right direction because now I am a bit lost and don't know what is wrong :(

Sorry for taking your time <3

Whoops, I solved the problem by increasing the engine refresh rate from 50Hz to 500Hz and now it is working smoothly without oscillations at high speed.

But at low speeds (below 5m/s) I found another formula for slip ratio by Marco Monster here is the link.