momentum in badminton

(Phys.org)—When it comes to flying projectiles, the badminton shuttlecock or "birdie" is unusual in that it flips on impact with a racket so that it always flies cork-first. This section quantitatively describes this effect shown in figure 15(a). This object weighs M=5\;{\rm g}, its length is L=10\;{\rm cm} and its diameter is D=6\;{\rm cm}. Beyond this study, many questions concerning the physics of badminton remain to be solved. As the shuttlecock geometry is critical for the badminton game, we have imagined a way to approach the pure triangular trajectory. Figure 3. (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}}. During vertical fall, wind blowing horizontally at a velocity Uw deviates the impacting point of the shuttlecock by a quantity U_{w}^{2}{{{\rm sin} }^{2}}{{\theta }_{0}}/g.

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(c) Flipping (blue dots) and stabilizing (red squares) times are plotted as a function of the shuttlecock opening angle Λ. Shuttlecocks have a mass M=2.2\;{\rm g} and a section S=\pi {{(D/2)}^{2}}\;=\;12.4\;{\rm c}{{{\rm m}}^{2}}. Volume 17, Figure 10. The cork being denser than the skirt, a shuttlecock has distinct centers of mass and pressure, and thus undergoes a stabilizing aerodynamic torque setting its nose ahead. The time interval between two positions is 100 ms. The first games important to the creation of badminton were practised in Asia 2500 yr BC [].Soldiers played ti-jian-zi, which consisted of exchanging with their feet a shuttle generally made of a heavy leather ball planted with feathers (figure 1(a)). In this regime, x0 highly depends on shuttlecock and air properties through the aerodynamic length \mathcal{L}. Aerodynamics is the study of forces and the resulting motion of objects through the air. We find {{\tau }_{f\,th-a}}=15\;{\rm ms} and {{\tau }_{f\,th-b}}=42\;{\rm ms} for experiments (a) and (b). Figure 8. (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. The dark line indicates 1 cm. Its publishing company, IOP Publishing, is a world leader in professional scientific communications. The geometry of commercial shuttlecocks is empirically chosen to minimize flipping and stabilizing times. and Terms of Use. For a typical flip sequence, the footage revealed a 1-millisecond (ms) contact time with the racket, 20 ms for the initial flip, and an 80-ms oscillation time during which the shuttlecock stabilized. The DPG sees itself as the forum and mouthpiece for physics and is a non-profit organisation that does not pursue financial interests. A torque balance around G provides the following equation in the realistic limit S{{M}_{C}}\gg s{{M}_{B}}: where CD is the drag coefficient of a sphere and lGC the distance between the points G and C ({{l}_{GC}}={{M}_{B}}/{{M}_{C}}\;{{l}_{BC}}). Equation (1) describes the shuttlecock dynamics.

Because this light particle experiences a large drag, its trajectory is nearly triangular [8] and it highly depends on the projectile properties. The flipping dynamics of a shuttlecock is sensitive to the players only if the stabilizing time {{\tau }_{s}} compares to the total flying time {{\tau }_{0}}. The content is provided for information purposes only. White lines indicate 50 cm. Thin blue arrows indicate the drag force on each feather. Figure 4. During this period, shuttles were composed of the fruits of the Savonnier tree, which look like beans and were again furnished with feathers. New Journal of Physics, The effect of air humidity is less obvious to understand. This leads to a high sensitivity of the badminton game to wind. (b) Shuttle used in chien-tsu. In a closed system, such as when two objects collide, the total momentum remains the same, though some may transfer from one object to the other. After contact with the racket (typical time of 1 ms), it takes typically 20 ms for the projectile to flip. Badminton and Biomechanics Generating Momentum Biomechanics Sweet Spot The sweet spot of the racquet is the spot on the racquet where there is no jarring effect and the ball seems to fly off easily and is also known at the centre of percussion. Caroline Cohen1, Baptiste Darbois Texier1, David Quéré2 and Christophe Clanet1, Published 1 June 2015 • Your opinions are important to us. Forces exerted on each feather (as represented in figure 15(a) with blue arrows) create a torque which puts a projectile into rotation so that feathers rip through air. June 2015, 1 LadHyX, UMR 7646 du CNRS, Ecole Polytechnique, 91128 Palaiseau Cedex, France, 2 PMMH, UMR 7636 du CNRS, ESPCI, 75005 Paris, France, Received 15 December 2014 (b) Chronophotography of a prototype launched upside down without initial velocity in a water tank. Figure 6(a) compares the experimental flipping time {{\tau }_{f\,{\rm exp} }} with the theoretical one {{\tau }_{f\,th}} predicted by solving equation (2). (a) The time interval between each position is 5 ms, the shuttlecock initial velocity is {{U}_{0}}\approx 18.6\;{\rm m}\;{{{\rm s}}^{-1}} and its initial angular velocity is \dot{{{\varphi }_{0}}}=206\;{\rm rad}\;{{{\rm s}}^{-1}}. (a) Plastic shuttlecock MAVIS 370. Goose feathers possess structures at different scales (figure B1 Structures at the micro-scale are good precursors for small water droplets resulting from vapor condensation. (b) Feathered shuttlecock. We do not guarantee individual replies due to extremely high volume of correspondence. We first study the flip phenomenon and the dynamics of the flight and then discuss the implications on the game. For each impact, the initial rotational velocity \dot{{{\varphi }_{0}}} and shuttlecock speed U are measured. For small opening angles, the shuttlecock is elongated and the skirt has a high momentum of inertia. The equation of motion for such a projectile is M\frac{d{\bf U}}{dt}=M{\bf g}-\frac{1}{2}\rho S{{C}_{D}}U{\bf U}. Table B2. If {{\dot{\varphi }}_{0}}\gg {{\omega }_{0}}, equation (2) reduces to \dot{\varphi }(t)={{\dot{\varphi }}_{0}} and the flipping time, defined as \varphi ({{\tau }_{f\,th}})=0, becomes: This limit corresponds to the experiments reported in figures 3(a) and 4(a) where \dot{{{\varphi }_{0}}}=206\;{\rm rad}\;{{{\rm s}}^{-1}} and {{\omega }_{0}}=23\;{\rm rad}\;{{{\rm s}}^{-1}}. Snapshots are separated by 160 ms and the bar indicates 2 cm. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. For typical shuttlecocks, this relation becomes L{{\dot{\varphi }}_{0}}/U\gtrsim 2.2. Since 2008, all the finals of the Olympic Games and the World Championships have been contested by Lin Dan (China) and Lee Chong Wei (Malaysia). Shuttlecocks have a top speed of up to 137 m s−1 [2]. Soldiers played ti-jian-zi, which consisted of exchanging with their feet a shuttle generally made of a heavy leather ball planted with feathers (figure 1(a)). The larger deformation gives the feather shuttlecocks a more triangular trajectory that contributes to their appeal. The oscillating time of a shuttlecock can also be predicted by equation (1). (a) Engraving of a ti-jian-zi game extracted from Le Tour du Monde: Nouveau Journal des Voyages written by Edouard Charton in 1860.

Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Table 1. Thus the ratio between the down-going stroke area {{\Sigma }_{down}} and the total Σ is equal to 1-\frac{3}{2}\frac{{{h}_{net}}}{{{h}_{{\rm max} }}}=0.26, hnet being the height of the net. Finally, we discuss in the third section how the shuttlecock flight influences the badminton game in terms of techniques, strategies and rules. The effect of rotation on the flight can also be discussed. What does physics reveal about the sizes of sports fields? Figure 6(b) highlights the dependency between the initial angular velocity {{\dot{\varphi }}_{0}} and its initial velocity U. If {{U}_{w}}=1\;{\rm m}\;{{{\rm s}}^{-1}} (modest wind) and {{\theta }_{0}}=60{}^\circ, the deviation is about 8 cm which is larger than the shuttlecock size. If the condition {{\dot{\varphi }}_{0}}\gg {{\omega }_{0}} is not satisfied, equation (2) must be integrated numerically using: {{\tau }_{f\,th}}=\int _{\pi }^{0}d\varphi /{{\sqrt{{{{\dot{\varphi }}}_{0}}}}^{2}}+2\omega _{0}^{2}(1+{\rm cos} \varphi ), as for the data reported in figures 3(b) and 4(b). By performing tests in wind tunnels, the scientists found that feathered shuttlecocks become more deformed than their plastic counterparts. Data are extracted from [16]. The calculation leading to equation (1) is detailed in appendix A. it is measured specifically with speed and direction of movement. Using a pendular system, Cooke measured different shuttlecocks' moments of inertia and concluded that J is 1.2\times {{10}^{-6}}\;{\rm kg}\;{{{\rm m}}^{-2}} [3]. Blue dots stand for plastic shuttlecocks whereas red squares are used for feathered projectiles. Figure 13. This document is subject to copyright.

The first one is the flipping time {{\tau }_{f}} needed for to vary from 180° to 0°.

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