Fm = π

^{2}* ρ * ω * v * r

^{3}

My main issue with this formula is that the lift coefficient is not included in this formula, meaning it doesn't matter if the ball is smooth or (as in the case with golf balls) dimpled.

Fm = S*(ω x v)

I found this formula here http://farside.ph.utexas.edu/teaching/329/lectures/node43.html but it was not noted what S was, only a way to calculate it for the example of baseballs.

Fm = ½ * C

_{L}* ρ * A * v

^{2}(ω x v)

I found this formula a lot, but the thing that bugs me with this one is that the cross product of ω and v is not a cross product of the vectors, but of the unit vectors, meaning that the last part is just to calculate the direction of the force. This would not be a problem if that was not the only place ω is used in that formula. Meaning that according to that formula ω is only used to calculate the direction, not the actual size of the force. I find it highly unlikely that the speed of which the ball is rotating does not affect the force, only the fact it is or is not rotating.

I could be wrong of course about these formulas. Or I could be interpreting them wrong. If any of you actually know something about the magnus force that could help me, I'd love for you to reply to this topic and maybe help me out, since I'm stuck at the moment.