from racket to trajectory

Badminton shuttlecock flight provides a useful test of how a simple projectile model changes when aerodynamic effects, equipment interactions, and environmental conditions are considered. This investigation develops a layered physical framework beginning with ideal projectile motion and progressively incorporating racket–shuttle collision, aerodynamic drag, shuttlecock geometry, wind, and human trajectory prediction. A controlled practical investigation was conducted on an indoor BWF badminton court. A Yonex A2 shuttlecock of mass 4.72 g was released from rest at 3.00 m and allowed to fall onto a stationary Yonex isometric-frame racket held at 45° with 26 lb string tension. The racket was positioned 1.00 m above the court, and a new shuttle was used for each trial. A coefficient of restitution of 0.41 was used as a collision-model parameter. Under the ideal no-drag model, the calculated impact speed is 6.26 m/s, rebound speed is 2.57 m/s, maximum rebound height is approximately 1.17 m, flight time is approximately 0.673 s, and predicted horizontal range is approximately 122.2 cm. The release height was corrected from an earlier, incorrect 5.00 m draft assumption to the measured 3.00 m (see Appendix E). Ten drop trials, repeated at the corrected setup, produced ranges from 79.30 to 86.40 cm, with a mean of approximately 83.30 cm — far below the ideal no-drag prediction of 122.2 cm, but closely matching a numerically integrated drag-inclusive (M4) prediction of approximately 78.5–91.6 cm (mean absolute percentage error approximately 2.38% against the M4 central estimate of 85.0 cm, versus approximately 31.83% against the ideal model). Flight time was consistent across trials at approximately 0.60 s, close to the M4-predicted 0.646 s (about 7.1% error) and closer than the ideal M1 prediction of 0.673 s (about 10.8% error). Because the dataset is limited to ten trials from a single measurement session, these statistical conclusions are provisional. The collision coefficient is assumed rather than independently measured, and the drag model uses working parameter ranges for C_D and effective area rather than shuttle-specific measured values. The investigation therefore treats the ideal projectile model as a useful baseline that the shuttlecock clearly departs from, with aerodynamic drag providing a substantially closer description of the observed flight.