What is the formula for the 3D trajectory of a curving ball?

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The trajectory of a curving ball in 3D is a complex problem rooted in fluid dynamics, lacking a straightforward formula. There are no pre-existing equations that apply universally to every scenario, making it necessary to approach the problem by breaking it down into its x, y, and z components. Numeric solutions may be generated for simplified cases, but a closed-form solution is unlikely. Additional information about the ball's initial conditions, such as whether it starts from rest or is in motion, is essential for further analysis. Overall, the intricacies of the problem require a detailed understanding of projectile motion and related physics.
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Hello.
Does anybody knows the formula for trajectory of curving ball (in 3D).
 
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Sorry Physics doesn't work that way. There is no store of "equations" on the shelf waiting for each and every situation.

We can say that it is a difficult problem of fluid dynamics. You could possibly generate numeric solutions to simplified versions of the problem. But there will be no closed form solution. It is not clear to me that there can even be a "simple" functional description of the general case.
 
You'd definitely have to begin by splitting the problem into its x, y and z components and working from there. Think about projectile motion, etc. Anyway, you haven't given us enough info. Does it start from rest, is it moving, accelerating?
 

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