The goal is to determine possible soccer ball launch configurations that result in the ball returning to the launch site. A returning soccer ball is possible with the proper launch angle and velocity. A headwind is required except for the purely vertical case.

Trajectories with long free fall times are extremely sensitive to their initial conditions. These critical trajectories have outgoing and incoming paths that are vastly different.

Flow regimes and the resulting drag coefficients dominate the launch configuration. The transition to fully turbulent flow increases the required launch angle. Higher headwinds quicken the appearance of the turbulent region.

The document is available here