Considering typical values (l\simeq 3\;{\rm cm}, R\simeq 3\;{\rm cm} and \rho =1.2\;{\rm kg}\;{{{\rm m}}^{-3}}), we deduce the following criterion for gyroscopic stabilization: R\Omega /U\gg 0.1. Experiments show that the flipping time is smaller than the stabilizing time. Shuttlecock drag coefficients ({{C}_{D}}=2{{F}_{D}}/\rho \pi {{(D/2)}^{2}}{{U}^{2}}) as function of the Reynolds number (\operatorname{Re}=DU/\nu) for projectiles free to rotate or not (full and empty symbols, respectively). The exposed section S=\pi {{(D/2)}^{2}} is equal to 28\;{\rm c}{{{\rm m}}^{2}} for both shuttlecocks. (a) Sketch indicating the rotation of a shuttlecock moving with the cork ahead. We conduct an experimental study of shuttlecock mass as a function of humidity conditions at T = 20{{\;}^{\circ}}C. Corresponding results are gathered in table B2 The aerodynamic length of the projectile is determined for S=28\;{\rm c}{{{\rm m}}^{2}}, CD = 0.6 and \rho =1.2\;{\rm kg}\;{{{\rm m}}^{-3}}. They are made with a dense iron ball and a light plastic skirt (figure 9(a)). The conical shape of a shuttlecock allows it to flip on impact. push and pull,muscular force gravitational force. Figure 9. The dynamics of a shuttlecock and its influence on the badminton game have been questioned. The graph reveals that there is only a small domain of the court ({{x}_{0}}\lesssim 0.25\;{{L}_{field}}=3\;{\rm m}) where players can receive a shuttlecock not yet aligned with its velocity direction. As a light and extended particle, it flies with a pure drag trajectory.

Figure 11 reports two shuttlecock trajectories with the same initial conditions but with a different kind of projectile. (b) Experimental initial angular velocity {{\dot{\varphi }}_{0}} times the skirt length L, as a function of the shuttlecock initial velocity U after its impact with a racket. Figure 1. Such movies allow us to measure the angle between the shuttlecock axis and the velocity direction, as defined in figure 3. For each one, the flipping dynamics was captured and analyzed in a free fall experiment where the shuttlecock was released upside down without initial velocity. One observes the superimposition of numerical and experimental trajectories. (b) Rotation velocity R\;\Omega as a function of the translation speed U for a plastic (blue dots) and a feathered shuttlecock (red squares). On the other hand, the aerodynamic torque scales as \rho {{R}^{2}}{{U}^{2}}l. Gyroscopic stabilization only occurs if we have R\Omega /U\gg {{R}^{2}}\sqrt{\rho l/J}.

Plot of the experimental angle between the shuttlecock axis and its velocity as a function of the coordinate s of the shuttlecock along its trajectory divided by the curvilinear coordinate when the projectile reaches the floor (s={{s}_{{\rm max} }}). The second one, denoted as {{\tau }_{o}}, is the pseudo-period of oscillations. These predictions are close to the experimental values of {{\tau }_{f\,{\rm exp} -a}}=16\;{\rm ms} and {{\tau }_{f\,{\rm exp} -b}}=39\;{\rm ms}. (b) Shuttle used in chien-tsu. The oscillating time of the shuttlecock direction is estimated as 80 ms. After 130 ms, the shuttlecock axis of symmetry is aligned along the velocity direction. For similar initial conditions, the skirt deformability indeed induces a modified trajectory which is more triangular than the normal one. These latter reduce to drag, the application point of which being the pressure center, where the aerodynamic torque vanishes [10]. It depends on what specific component of badminton.

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