Ndtyjky

Aight so I've been at this for several days and with how much it's slowing the project down I've made the hard decision to come beg the internet.
I'm working on a physics-based golf game in Unity and am working on implementing the magnus effect. This is my calculation for tangential force based on torque:

    void FixedUpdate()

        {

            float _BallRadius = .0427f;

            float _halfmass = Mathf.Sqrt(_BallRadius*.5f );

            float _vv = new Vector3(GetComponent<Rigidbody>().velocity.x, 0, 

            GetComponent<Rigidbody>().velocity.z).magnitude;

            //MAGNUS FORMULA (SIDESPIN ONLY)//

            float _mag = -((1.429f * Mathf.Abs(_vv)* (2 * Mathf.PI * _halfmass * 

            GetComponent<Rigidbody>().angularVelocity.y))) * (_BallRadius * .5f);

            Vector3 _xmagdir = new Vector3(GetComponent<Rigidbody>().velocity.x, 0, GetComponent<Rigidbody>().velocity.z);     

GetComponent<Rigidbody().AddForce(Vector3.Cross(_xmagdir.normalized,Vector3.up)*_mag, ForceMode.Acceleration);

        }

This works well enough, but now I need to figure out the correct amount to give the ball to get this result:
Diagram of Desired Curve

I've tried several different approaches, and I've come to the conclusion that this is mostly comes down to trigonometry. Here is where I'm at currently (this is before the tangential direction is applied to the final velocity vector):

Vector3 GetMagnusTorque(float Distance, Vector3 V_BallForce, float xdir)

{

    float _BallRadius = .0427f;

    float _halfmass = Mathf.Sqrt(_BallRadius*.5f);

    Vector3 v = GO_Camera.transform.InverseTransformDirection(V_BallForce);

    float HorizontalRange = Distance;

    //THIS IS THE LATERAL DISTANCE WE NEED TO TRAVEL//

    float opposite = (Mathf.Abs(Mathf.Tan(Mathf.Deg2Rad * xdir))) * (HorizontalRange*.5f);

    //THIS IS THE TIME IT WILL NEED TO TAKE//

    float time = ((2 * v.magnitude * Mathf.Sin((2 * (v.normalized.y )))) / -Physics.gravity.y);

    //THIS IS THE SPEED THE MAGNUS EFFECT WILL NEED TO PRODUCE//

    float linearSpeed =Mathf.Abs((opposite/time))*Mathf.Sign(xdir)Mathf.Abs((opposite/time))*Mathf.Sign(xdir)*(Time.timeScale+Time.fixedDeltaTime);

    return GO_Camera.transform.TransformDirection((((linearSpeed /( 2 * Mathf.PI * _halfmass * (_BallRadius * .5f))) / 1.429f))*Mathf.Deg2Rad*GO_PGolfBall.transform.up);

}

Logic behind this

The result is very inconsistent based on xdir and V_BallForce, sometimes travels further, sometimes barely at all. This has been a pretty sobering adventure in discovering that I'm pretty bad at math.
If anyone has any advice for this issue I would forever be in your debt.

Update: Here is some visualization of the issue:
visualization

Update: I figured I should include a code sample of the function GetMagnusTorque is called from, to better put things in context:

 void BallApplyForce()

    {

        //_rmult is a [0,1] value that is dependent on the accuracy of the player's swing//

        float _rmult = GetRMult();

        //GETS BALL READY BY ENABLING PHYSICS AND SETTING ITS ROTATION TO THE CAMERA//

        GO_PGolfBall.transform.rotation = new Quaternion(0, GO_Camera.transform.rotation.y, GO_Camera.transform.rotation.z, GO_Camera.transform.rotation.w);

        GO_PGolfBall.GetComponent<SCR_GOLFBALLCONTROL>().B_PhysicsActive = true;

        //YDIR = PITCH, XDIR = YAW. V_ContactPoint is a [-1,1] Vector2 used similar to Mario Golf//

        Vector3 _vdir = Vector3.zero;

        float ydir = ((Mathf.Rad2Deg * DIC_Clubs[I_CurrentClub].LandAngle) + (-2.5f * (.1f) * (DIC_Clubs[I_CurrentClub].LoftAngle * Mathf.Rad2Deg)));

        float _xdir = Mathf.Rad2Deg * (-(V_ContactPoint.x) * (DIC_Clubs[I_CurrentClub].LoftAngle)*3f);



        _vdir.y = ydir;

        _vdir = _vdir.normalized;

        _vdir.y *= Mathf.Rad2Deg;



        //MAX DISTANCE OF THE CLUB BEING USED TO METERS//

        float _dist = ((DIC_Clubs[I_CurrentClub].MaxDistance * F_UPower) * _rmult) * .9144f;



        //GET FORWARD AND UPWARDS VELOCITIES BASED ON THE DISTANCE GIVEN, XDIR ISN'T FACTORED FOR NOW//

        float Vi = Mathf.Sqrt(_dist * -Physics.gravity.y / (Mathf.Sin(Mathf.Deg2Rad * _vdir.y * 2)));

        float Vy, Vz;

        Vy = Vi * Mathf.Sin(Mathf.Deg2Rad*_vdir.y);

        Vz = Vi * Mathf.Cos(Mathf.Deg2Rad*_vdir.y);

        GO_Camera.transform.eulerAngles = new Vector3(0, GO_Camera.transform.eulerAngles.y, 0);

        Vector3 _velo = GO_Camera.transform.TransformVector(new Vector3(0f, Vy, Vz));



        //CALCULATE VERTICAL ANGULAR VELOCITY, THIS DOESNT NEED TO FOLLOW ANY SORT OF PATTERN FOR NOW//

        float _verRoll = Mathf.Sign(V_ContactPoint.y - .1f) * ((.7135f) * _dist) * Mathf.Sin(DIC_Clubs[I_CurrentClub].LoftAngle +

            ((Mathf.Abs(V_ContactPoint.y + .1f)) * (DIC_Clubs[I_CurrentClub].LaunchAngle))) * 60 * Mathf.Deg2Rad;

        GO_PGolfBall.GetComponent<Rigidbody>().AddTorque(Vector3.Scale(GO_PGolfBall.transform.right, new Vector3(1, 0, 0)) * _verRoll, ForceMode.VelocityChange);

        //CALCULATE HORIZONTAL ANGULAR VELOCITY//

        Debug.Log("MAGNUS CALC:" + GetMagnusTorque(_dist, _velo, _xdir));

        GO_PGolfBall.GetComponent<Rigidbody>().AddTorque(GetMagnusTorque(_dist, _velo, _xdir), ForceMode.VelocityChange);



        //APPLY XDIR TO THE CAMERA ANGLE AND RECALCULATE VELOCITY//

        GO_Camera.transform.eulerAngles = new Vector3(0, GO_Camera.transform.eulerAngles.y+_xdir, 0);

        _velo = GO_Camera.transform.TransformVector(new Vector3(0f, Vy, Vz));



        //APPLY VELOCITY//

        GO_PGolfBall.transform.GetComponent<Rigidbody>().AddForce(_velo, ForceMode.VelocityChange);

    }

Update 11/21: I'm currently in the process of faking it through trial and error. But for those still interested in solving this anomaly, I may have found in issue in how I'm calculating the direction to apply the side-spin derived force to the ball. Hitting the ball with a lob wedge, which has a maximum distance of 70 yards and a loft angle of 60 deg, the desired curve looks something like this: Lob Wedge This obviously makes no sense, because the ball flies behind the golfer for a short period of time. I'll report back with the final numbers and calculations, though it will not answer the question it could help point it in the correct direction.