Considering that a badminton player can reach a maximum height hmax, that is, his/her own height (1.78 m for Lin Dan and 1.74 m for Lee Chong Wei), plus his/her jumping height (0.7 m for Lin Dan), plus the racket length (0.65 m), we estimate the total cross-sectional area Σ reachable by a player. Table B1. Figure 7. In the first section, we study the 'versatile' behavior of a shuttlecock. According to experienced players, the trajectories of feathered shuttlecocks are more 'triangular', as indeed seen in figure 11. We have {\bf GB}\wedge {{{\bf U}}_{B}}={{l}_{GB}}(U{\rm sin} \varphi +{{l}_{GB}}\dot{\varphi }){{{\bf e}}_{z}} and {\bf GC}\wedge {{{\bf U}}_{C}}={{l}_{GC}}(-U{\rm sin} \varphi +{{l}_{GC}}\dot{\varphi }){{{\bf e}}_{z}}, so that we can express equation (11) as: Assuming that {{U}_{B}}\simeq {{U}_{C}}\simeq U, we get: As the point G is the center of mass of the two spheres placed in B and C of respective mass MB and MC, the distances lGB and lGC are linked by the relation {{M}_{B}}{{l}_{GB}}={{M}_{C}}{{l}_{GC}}. A rally ends once the shuttlecock has hit the floor or a player commits a fault.
(b) The shuttlecock initial velocity is {{U}_{0}}\approx 10.4\;{\rm m}\;{{{\rm s}}^{-1}} and its initial angular velocity is \dot{{{\varphi }_{0}}}=28\;{\rm rad}\;{{{\rm s}}^{-1}}. In order to answer this question, shuttlecock prototypes have been constructed. The damping term, 1/{{\tau }_{s}}=\rho S{{C}_{D}}U/2{{M}_{B}}(1+{{M}_{B}}/{{M}_{C}}), results from the drag associated with the orthoradial movement of the shuttlecock as varies. Alternatively, they do not hesitate to fold the extremities of feathers toward the interior or the exterior in order to modify the shuttlecock cross-section and adapt the aerodynamic length to the present atmospheric conditions. The evolution of {{\tau }_{f\,{\rm exp} }} and {{\tau }_{s\,{\rm exp} }} with Λ is reported in figure 9(c). (b) Chronophotography of a prototype launched upside down without initial velocity in a water tank. In figure 3(a), the flip lasts four time intervals, which corresponds to 15 ms. RIS. They measured the air drag {{F}_{D}}=\rho S{{C}_{D}}{{U}^{2}}/2 exerted by air on a shuttlecock (where ρ is the air density, S=\pi {{(D/2)}^{2}} the shuttlecock cross-section and U its velocity) and showed that the drag coefficient CD is approximatively constant for Reynolds numbers (\operatorname{Re}=DU/\nu, with ν the air kinematic viscosity) between 1.0\times {{10}^{4}} and 2.0\times {{10}^{5}}.
Each player (or team) stands on opposite halves of a rectangular court which is 13.4 meters long, 5.2 meters wide and divided by a 1.55 meter-high net (figure 2(a)). Shuttlecocks are usually classified in two categories, namely plastic and feathered. Figure 7(b) shows the stabilizing time as a function of the one predicted by equation (5). In badminton, the initial launching velocity U0 is often much larger than {{U}_{\infty }} and players can feel the saturation of the range with initial velocity. Drag coefficient ({{C}_{D}}=2{{F}_{D}}/\rho \pi {{(D/2)}^{2}}{{U}^{2}}) as a function of the Reynolds number (\operatorname{Re}=DU/\nu). Export citation and abstract On the one hand, the angular momentum of this object is J{{\Omega }^{2}} where J is the moment of inertia of the shuttlecock relative to its axis of rotation and Ω the angular velocity. For similar initial conditions, the skirt deformability indeed induces a modified trajectory which is more triangular than the normal one.
The geometry of commercial shuttlecocks is empirically chosen to minimize flipping and stabilizing times. Structures at the micro-scale are good precursors for small water droplets resulting from vapor condensation. Beyond this study, many questions concerning the physics of badminton remain to be solved. The exposed section S=\pi {{(D/2)}^{2}} is equal to 28\;{\rm c}{{{\rm m}}^{2}} for both shuttlecocks. . The conical shape of a shuttlecock allows it to flip on impact. Figure 4. Numerical solutions of the equation of motion for various initial conditions are plotted in figure 10 with solid lines. The difference in rotating speed between the two kinds of shuttlecock (plastic and feathered) also plays a role in this choice since a faster rotation of feather projectile limits its precession. The effect of rotation on the flight can also be discussed. The shuttle I hit with great power and speed in a downwards trajectory into the opponent's court. Table B2. (b) Feathered shuttlecock.
We can look at the evolution of the stabilizing time with the shuttlecock velocity for different impacts. Finally, we discuss in the third section how the shuttlecock flight influences the badminton game in terms of techniques, strategies and rules.
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