Optimising soccer passing mechanics: a two-dimensional simulation of flight time and playable arrival height

This study used a two-dimensional, mechanics-based simulation to examine how impact offset and foot-trajectory angle influence sagittal-plane passing performance in soccer over 30 and 45 m. Two objectives were evaluated independently: minimising flight time and optimising playable arrival height at the target distance. Flight-time optimisation consistently favoured near-centre impact (offset = -0.016 to -0.017 m) and shallow foot-trajectory angles, yielding launch speeds of 27.2-30.9 m·s⁻¹ and minimum flight times of 1.27/1.18/1.11 s (U15/U17/U19) at 30 m and 2.13/1.94/1.81 s at 45 m. Optimisation for playable arrival height required larger impact offsets and steeper foot-trajectory angles, producing greater backspin (290-370 rpm versus 83-110 rpm) and flatter trajectories. At 30 m, all reference launch-speed conditions remained within the predefined reception-height window. At 45 m, performance within this window increased from 19% in the lowest launch-speed condition to 66% in the highest, exceeding the corresponding flight-time-optimised cases (22%-36%). These findings demonstrate a task-dependent trade-off between launch speed and spin and show that passing outcomes are sensitive to small variations in ball-foot interaction. Practically, coaching cues may be adjusted according to task priority: rapid ball circulation is supported by near-centre impact and shallow approach mechanics, whereas maintaining a playable arrival height at the receiver benefits from larger impact offsets and greater backspin. These implications should, however, be interpreted within the limits of the present two-dimensional model.