In the following, the influence of the shuttlecock and fluid characteristics on trajectories is studied. Finally, the laws established for shuttlecock flights could be discussed with other projectiles having a non-homogeneous mass along their axis, such as air missiles [17] or dandelion achenes [18]. To report a Copyright Violation, please follow Section 17 in the Terms of Use. Figure 9.
Considering that the behavior of a feather is similar to the one of a thin plate in an air flow, the fluid force is perpendicular to the object and in a direction opposite to its velocity. Then, the shuttlecock axis undergoes damped oscillations until it aligns along the velocity direction {\bf U}.
Players usually counterbalance this effect by using lighter shuttlecocks when air is hotter. The maximal range xmax is calculated for the maximal velocity recorded in a badminton court, {{U}_{0}}=117\;{\rm m}\;{{{\rm s}}^{-1}}, and for the corresponding optimal initial angle {{\theta }^{\star }} which verifies (\partial {{x}_{0}}/\partial {{\theta }_{0}})({{U}_{{\rm max} }},{{\theta }^{\star }})=0. (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}}. The sketch in figure 5(a) highlights the effect of the drag {{{\bf F}}_{D}} on an inclined shuttlecock. (b) Model system composed of a sphere of large section S and mass MB, which stands for the skirt, and a sphere of small section s and large mass MC, which represents the cork. Sketch of a feather showing its microstructure. The first one stands for the skirt of mass MB and large cross-section S positioned in B, and the second one represents the cork of mass MC and smaller cross-section s placed in C (figure 5(b)). Such a phenomenon happens if the angular momentum of the shuttlecock is high compared to the aerodynamic torque applied to it. Pagkakaiba ng pagsulat ng ulat at sulating pananaliksik?
Its publishing company, IOP Publishing, is a world leader in professional scientific communications. This explains that shuttlecocks generally perform less than a complete turn after an impact with a racket. BibTeX
Whatever the rotation, the drag coefficient is found to remain between 0.65 and 0.75.
We propose classifying badminton strokes in the diagram drawn in figure 19(b). It is practically not very easy to reduce the mass of a plastic projectile while keeping its robustness and price unchanged, which explains why the two masses are different. Figure 7(b) shows the stabilizing time as a function of the one predicted by equation (5). 17 063001, https://doi.org/10.1088/1367-2630/17/6/063001. It has a worldwide membership of around 50 000 comprising physicists from all sectors, as well as those with an interest in physics. SPEED AND VELOCITY Speed and velocity are two of the main elements to any activity including sports. Wind tunnel measurements also reveal that there is no lift force on a shuttlecock when its axis of symmetry is aligned along the velocity direction. Find out more. (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}}. Finally, we discuss in the third section how the shuttlecock flight influences the badminton game in terms of techniques, strategies and rules.
In the case of standard impacts, we saw in figure 6(b) that L{{\dot{\varphi }}_{0}}/U\sim 1.
The fact that the shuttlecock with a cut skirt has a lower range means that the increase of its cross-section at low speed predominates over its reduction at high velocity.
Thus the shuttlecock is always aligned with the velocity direction, corresponding to the trajectories studied in section 2. One guesses that a change in the net height would modify this frequency and impact the characteristics of the game, such as the mean number of exchanges per rally and the mean number of points per unit time. The equation of motion for shuttlecocks has an analytical solution [8]. The evolution of {{\tau }_{f\,{\rm exp} }} and {{\tau }_{s\,{\rm exp} }} with Λ is reported in figure 9(c). Figure B1.
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. The fact that axial rotation does not lead to gyroscopic stabilization can be understood. (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}}. The exposed section S=\pi {{(D/2)}^{2}} is equal to 28\;{\rm c}{{{\rm m}}^{2}} for both shuttlecocks.
THE MAIN EQUIPMENT FOR BADMINTON.
For other strokes, the stabilizing time is much shorter than the total flying time. Figure 15. For the maximal initial speed ever recorded ({{U}_{{\rm max} }}=137\;{\rm m}\;{{{\rm s}}^{-1}}), the shuttlecock maximum range xmax is 13.8 m [14].
All rights reserved. (b) Feathered shuttlecock. For each impact, the shuttlecock speed U and its oscillating time are measured. The skirt rigidity of a plastic shuttlecock is reduced by cutting it longitudinally (first image in figure 13).
Figure 1. Comparison between the trajectory of a standard plastic shuttlecock (full blue dots) and the one of a cut shuttlecock (empty blue dots).
Contemporary badminton is a racket sport originating from the Indian game tomfool, modified by British colonials, and played with a feathered shuttlecock and a racket made with strings, as attested by the painting of Jean-Siméon Chardin, reproduced in figure 1(d). Moreover, we can inspect experimentally the oscillating time {{\tau }_{o\,{\rm exp} }} of a given shuttlecock submitted to impacts of various intensities.
Figure 20. The shuttlecock characteristics are condensed in a heavy small cork and a large light skirt.
Using the previous values for shuttlecock characteristics and the initial velocities in experiments shown in figures 3(a) and (b), we estimate the oscillating times using relation (4). 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. We plot in figure 18 the ratio {{\tau }_{s}}/{{\tau }_{0}}, where {{\tau }_{s}} is deduced from relation (5), as a function of the horizontal traveled distance x0 normalized by the court length Lfield. Figure 9(b) shows a chronophotograph of a prototype flipping during its fall in water. Figure 10. It is made of 16 goose feathers planted into a cork (figure 2(c)). . RIS. Plastic and feathered shuttlecock trajectories obtained with the same initial conditions, {{\theta }_{0}} and U0.
Only projectiles reaching the corridor on the opposite side are selected for the game. For each impact, the initial rotational velocity \dot{{{\varphi }_{0}}} and shuttlecock speed U are measured. In order to understand the difference between both types, we observed their trajectories. 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 Does Jerry Seinfeld have Parkinson's disease?
(a) Sketch indicating the rotation of a shuttlecock moving with the cork ahead. Figure 5.
For example, the impact dynamics of a shuttlecock with a racket is not considered in this paper.
New Journal of Physics,
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)). (a) Engraving of a ti-jian-zi game extracted from Le Tour du Monde: Nouveau Journal des Voyages written by Edouard Charton in 1860. This situation also corresponds to large values of flipping and stabilizing times.
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(c) Drawing of Three Beauties Playing Battledore and Shuttlecock by Utagawa Toyokuni in 1800. Rackets were introduced for the first time in Japan with hagoita (figure 1(c)). The questions we address in this work are: what makes the shuttlecock flight unique, and how does it influence the badminton game?
It eventually leads to a non-zero value of the angle between the axis of the shuttlecock and its velocity direction along the trajectory. Players score points by striking a shuttlecock with their rackets (a typical racket is shown in figure 2(b)) so that it passes over the net and lands in the opponent's half-court. Figure 13 shows that increasing air flow reduces the cross-section S of the projectile by a factor 2 as the flow velocity increases from 0 m s−1 to 50 m s−1. If you feel that this video content violates the Adobe Terms of Use, you may report this content by filling out this quick form. The characteristics of these prototypes (length L, diameter D, mass M and opening angle Λ) can be easily varied. Acceleration takes place in a badminton smash. Numerical solutions of the equation of motion for various initial conditions are plotted in figure 10 with solid lines.
We find {{\tau }_{f\,th-a}}=15\;{\rm ms} and {{\tau }_{f\,th-b}}=42\;{\rm ms} for experiments (a) and (b). For clear strokes, the trajectory ends with a nearly vertical fall.
Such movies allow us to measure the angle between the shuttlecock axis and the velocity direction, as defined in figure 3. On the x-axis, one finds the flying time {{\tau }_{0}} divided by the time of reaction {{\tau }_{r}} of a player ({{\tau }_{r}} is about 1 s for trained players). The smash (6) is a fast ball with a sharp straight trajectory aimed either at the opponent's body or at the limits of the court. The characteristic times associated with the motion are measured, and we develop an aerodynamical model to predict them. The initial launching conditions correspond to a high clear: {{U}_{0}}=26\;{\rm m}\;{{{\rm s}}^{-1}} and {{\theta }_{0}}=56{}^\circ.
Figure 11. The effect of rotation on the flight can also be discussed.
One may wonder whether rotation induces gyroscopic stabilization. The probability of each family can be approached with geometrical considerations. Different sequences of the flip of a shuttlecock are recorded using a high speed video camera (figure 3). You do not need to reset your password if you login via Athens or an Institutional login.
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]. For comparison, this number falls to 3.5 in top level tennis competitions consistently with the fact that the maximum range of a tennis ball ({{x}_{{\rm max} }}=66.9\;{\rm m}) is much larger than the court length ({{L}_{field}}=24\;{\rm m}). This difference leads to a smoother early path for the second case. Only the 'spin in' or 'spin out' techniques allow one to outweigh this criterion and make the projectile turn several times before stabilizing with the nose ahead.
(b) Experimental stabilizing time {{\tau }_{s\,{\rm exp} }} as a function of the predicted one {{\tau }_{s\,{\rm th}}} estimated by the way of relation (5).
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