# Badminton racket deflection, comparison between rigid versus flexible according to different strokes

Michael Phomsoupha, Stéphane Ibrahime, Guillaume Laffaye

► To cite this version:

Michael Phomsoupha, Stéphane Ibrahime, Guillaume Laffaye. Badminton racket deflection, comparison between rigid versus flexible according to different strokes. International Journal of Racket Sports Science, inPress, 6 (1), pp.32-38. 10.30827/-. hal-04803487

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Distributed under a Creative Commons Attribution 4.0 International License
1 Badminton racket deflection, comparison between rigid versus flexible

2 according to different strokes

3 Michael Phomsoupha<sup>(1,2,3)</sup>, Stéphane Ibrahime<sup>(3)</sup> & Guillaume Laffaye<sup>(4)</sup>

4

5 ¹ APCoSS – Institute of Physical Education and Sports Sciences (IFEPSA), Université

6 Catholique de l'Ouest, Angers, France.

7 ² Fédération Française de Badminton, Saint-Ouen, France.

8 ³ Université Catholique de l'Ouest – Bretagne Sud, Arradon, France.

9 ⁴ Research Center for Sports Science, South Ural State University Chelyabinsk, Russia

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14 Funding: None

15 Conflict of Interest Disclosure: None

16 *Corresponding author

17 Michael PHOMSOUPHA, PhD

18 https://orcid.org/0000-0003-3061-4401

19 Assistant Professor / Consultant of Sports Physiotherapy

20 Université Catholique de l'Ouest Bretagne-Sud – Campus du Vincin, 56610 Arradon

21 Tel: +33 (0)2 97 46 33 60

22 E-mail: mphomsou@uco.fr

23 Running Title: Rigid versus flexible badminton racket

24
Badminton shuttlecock generate the highest projectile velocity among all sports. To deliver a powerful stroke, the design of a badminton racket is primordial, especially the deflection on the shaft. The purpose of the study was to analyse the gain of racket deflection compares with a rigid racket during four different strokes. Eight national and international standard badminton players participated in this study and performed a drop, a clear, a smash and a full smash. Six reflective markers were affixed to the racket and were recorded with Vicon cameras capture system set. Results showed racket deflection increased racket head velocity by shaft deflection by +13.2% during a full smash and a typical time around 60 ms during which the player accelerates the racket head. The gain obtained between head velocity related to the handle by +74% during a full smash. The deflection is caused by the relation between player ability, racket mass repartition and stiffness properties of the shaft. Finding suggest players should choose a racket with their badminton stroke pattern, especially the timing of the preparation phase before the impact with the shuttlecock to obtain the higher deflection and the best energy restitution during the impact.

**Keywords:** performance; equipment; biomechanic; sport science; technology
Shuttlecock generate highest projectile velocity among all sports (Phomsoupha & Laffaye, 2015) and has recorded at 157 m/s by the Indian Satwiksairaj Rankireddy (Guinness World Record, 2023). The speed is depended of the player expertise level whereas the shuttlecock velocity ranged from 24.4 to 81.6 m/s (Phomsoupha & Laffaye, 2014). Several studies have investigated power strokes as clear and smash to explain the general stroke pattern (Rambely et al., 2005; Tsai, Chang, et al., 2000; Tsai, Huang, et al., 2000). To produce the maximum velocity at the shuttlecock, players add velocity through a sequential proximo-distal joint action (Tsai, Chang, et al., 2000). Specifically, for an overhead stroke, players quickly stretch their forearm during the eccentric phase (lateral rotation of the shoulder and radio-ulnar supination), followed by a rapid concentric action (medial rotation the shoulder and radio-ulnar pronation) (Waddell & Gowitzke, 2000).

To deliver a powerful stroke, the design of a badminton racket is primordial. To simplify, a racket is composed of a rigid handle and a flexible shaft (Kwan, Skipper Andersen, et al., 2010). Although tennis racket technology has received much research interest focusing mainly on the mass properties and geometry of racket rather than their deflection (Cross & Bower, 2006). However, few studies have been conducted on the design of badminton rackets (Hsieh et al., 2004). Nowadays, the innovation has a great influence on badminton rackets by making them light (Singh & Yogesh, 2010). Golf club shaft has a similar pattern with badminton racket shaft. Unfortunately, the golf shaft is loaded with a heavy club head mass at the tip, permitted to increase the shaft deflection (Phomsoupha et al., 2015a).

It is therefore important to examine the deflection behaviour of the badminton racket to increase the racket head velocity during a stroke as a clear or a smash. Consequently, racket deflection plays an important role in increasing racket head velocity (Phomsoupha & Laffaye,
2015). Indeed, the badminton racket is subjected to significant dynamic effect (Kwan, Cheng, et al., 2010). Furthermore, the mechanism of the racket deflection influences the terminal velocity of the racket head (Rasmussen et al., 2010). Small differences in racket design have an influence on dynamics properties (Hsieh et al., 2004; Kwan, de Zee, et al., 2008), by modifying stiffness and mass properties (Kwan, de Zee, et al., 2008; Kwan & Rasmussen, 2011; Montagny, 2003). To the best of our knowledge, no study has investigated the benefits offered by the deflection between a rigid racket and a racket head velocity during different strokes.

Thus, the purpose of the present study was to analyse the gain of racket deflection compares with a rigid racket during four different strokes (drop, clear, smash and full smash) performed by elite badminton players.

## Methods

### Participants

Eight participants realised in this study (age 23.3 ± 3.1 years; body mass 76.3 ± 8.3 kg; height 179.2 ± 8.3 mm; amount of training undergone 16.1 ± 4.5 years) with national and international experience participated in this study. All participants were healthy and in good physical condition and reported no injuries at the time of the study. They were fully informed about the protocol before participating in this study and they signed an informed consent form. Ethical approval was granted by the university Human Ethics Committee and followed principles of the Declaration of Helsinki.

### Design & Procedures

After a general warm-up of 10 minutes, participants were allowed to perform as many practice movements as needed to familiarize themselves with the testing requirement under
coached supervision. The racket used during the test was identical for all participants (Yonex Astrox 88D Pro; 88g; 680 mm). Four conditions were included during each session slow compared as a drop, medium compared as a clear, fast compared as a smash and very fast compared as a full smash. Each condition was repeated 10 times within a counter-balance order. The timing of stroke is obtained by the beginning of the movement (acceleration phase) and the impact between the racket with the shuttlecock (figure 1). A shuttlecock is attached to the duct ceiling by using a wire and adjusted from the participant.

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<figure><img src="image_2.png" /><figcaption>Figure 1: Different phases during a badminton stroke</figcaption></figure>

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## Analysis

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The experimental setup consisted of a nine-camera Vicon V8i motion capture system set at a frequency of 500 Hz (Vicon Peak, Oxford, UK). For kinematic analysis, six reflective markers of 14 mm in diameter were affixed to specific anatomical landmarks (Plug-In Gait Marker Set, Vicon Peak) for each participant. The markers were fixed to the dominant side, as follows: (a) angulus acromialis; (b) medial and lateral humeral epicondyles; (c) radial and ulnar styloid processes; and (d) 2^nd^ metacarpal heads, as recommended by the International Society of Biomechanics (Wu et al., 2005).
The global x-axis was defined in the anteroposterior, the z-axis vertically and the y-axis laterally, whereas the xy-plane was identical to the court. The orientation of the humerus, radius, ulna and hand segments was determined by the longitudinal z-axis, the mediolateral y-axis, and the perpendicular anteroposterior x-axis, as described in detail by (Wu et al., 2005). All calculations were performed using Matlab R2023a software (The Math Works Inc, Natick, MA, USA). Only the arm holding the racket was analysed.

Six reflective markers were affixed to the racket, as proposed by Kwan et al. (2008b) in their model: (e) racket handle, bottom and top of the handle; (f) racket shaft, top of the shaft; and (g) racket head, left, right and top of the head (figure 2). To calculate the joint positions, a 3D model (Plug-In Gait Marker Set, Vicon Peak) was used by David et al. (1991). The reflective markers placed on the racket weighed 1.2 - 2.4 g each, increasing total mass by 12.4 g (14%). Static and dynamic calibrations were conducted to set up the global reference system and calibration volume. The accuracy of 3D calibration was 0.2 mm.

<figure><img src="image_3.png" /><figcaption>Figure 2: Reflective markers affixed to the racket</figcaption></figure>

To compare the racket head velocity to a virtual stiff racket velocity, a virtual marker was built using the two markers on the racket handle. This new marker is at the same position as the marker on the top of the head when the racket is not deflected but stay aligned with the handle when it is accelerated, allowing to create a virtual stiff racket. Deflection is obtained by calculating the distance between the real marker and the virtual marker.
The kinematics data was calculated by Vicon Nexus 1.8 software (Vicon Motion System Limited, Oxford, UK). Racket deflection was calculated between the head racket real marker and the head racket virtual marker on the global system.

## Statistical analysis

All statistical analyses were performed using Statistica 10 software (StatSoft Inc., Tulsa, OK). Mean and standard deviations of the variables were calculated for descriptive statistics. Assumptions of normality were verified using the Shapiro-Wilk W Test. Groups of variables were used for statistical analysis: (a) velocity between handle, shaft and head racket (m/s); (b) maximal velocity (m/s) (head and virtual marker); (c) maximal racket deflection (mm); and (d) wrist acceleration (m/s²). Where the ANOVA was significant, a Bonferroni post hoc test and power test (1-β) were performed. For all statistical analyses, significance was set at p < 0.05 and effect size (I²) was defined as small for I² > 0.01; medium I² > 0.09; and large for I² > 0.25 (Cohen, 1988). Lastly, Spearman correlation coefficients were calculated to determine the relationship between selected variables.

## Results

Racket deflection increased each part of the racket point from the racket handle to the head of the racket (p < 0.001); except for the drop shot (p > 0.05) (Table 1). The gain obtained between the head velocity related to the handle by +39% during a drop, by +62% during a clear, by +67% during a smash and by +74% during a full smash.

<table><caption>Table 1: Velocity on handle, shaft and head racket during four different strokes.</caption><thead><tr><th>Conditions</th><th>Racket handle (m/s)</th><th>Racket shaft (m/s)</th><th>Racket head (m/s)</th><th>p-value*</th><th>η²*</th><th>1-β*</th></tr></thead><tbody><tr><td>Drop (slow)</td><td>5.6 ± 2.7</td><td>5.8 ± 2.3</td><td>6.3 ± 1.9</td><td>&gt; 0.05</td><td>0.199</td><td>0.527</td></tr></tbody></table>
<table><tr><td>Clear (medium)</td><td>7.9 ± 2.9</td><td>13.2 ± 3.4</td><td>20.9 ± 4.1</td><td><strong>&lt; 0.001</strong></td><td><strong>0.714</strong></td><td><strong>0.989</strong></td></tr><tr><td>Smash (fast)</td><td>11.2 ± 2.3</td><td>24.2 ± 6.5</td><td>34.6 ± 3.4</td><td><strong>&lt; 0.001</strong></td><td><strong>0.836</strong></td><td><strong>0.992</strong></td></tr><tr><td>Full Smash (very fast)</td><td>12.8 ± 1.7</td><td>34.6 ± 3.6</td><td>49.2 ± 5.1</td><td><strong>&lt; 0.001</strong></td><td><strong>0.946</strong></td><td><strong>0.993</strong></td></tr></table>

* p-value: significant differences for values lower than 0.05; * η²: Effect size; *1-β: Power-test.

Racket deflection increased racket head compared to the virtual racket (p < 0.001); except for the drop and the clear (p > 0.05) (Table 2).

<table><caption>Table 2: Velocity on head racket and virtual during four different strokes.</caption><thead><tr><th>Conditions</th><th>Racket head (m/s)</th><th>Virtual racket (m/s)</th><th>p-value*</th><th>η²*</th><th>1-β*</th></tr></thead><tbody><tr><td>Drop (slow)</td><td>6.3 ± 1.9</td><td>6.2 ± 1.9</td><td>&gt; 0.05</td><td>&lt; 0.001</td><td>0.050</td></tr><tr><td>Clear (medium)</td><td>20.9 ± 4.1</td><td>18.5 ± 3.5</td><td>&gt; 0.05</td><td>0.022</td><td>0.262</td></tr><tr><td>Smash (fast)</td><td>34.6 ± 3.4</td><td>31.7 ± 4.6</td><td><strong>&lt; 0.001</strong></td><td><strong>0.198</strong></td><td><strong>0.984</strong></td></tr><tr><td>Full Smash (very fast)</td><td>49.2 ± 5.1</td><td>41.4 ± 4.1</td><td><strong>&lt; 0.001</strong></td><td><strong>0.438</strong></td><td><strong>0.998</strong></td></tr></tbody></table>

* p-value: significant differences for values lower than 0.05; * η²: Effect size; *1-β: Power-test.

All results of maximal velocity of the racket and the virtual racket, gain, maximal racket deflection and wrist acceleration were showed in Table 3.

<table><caption>Table 3: Virtual and real racket velocity, deflection racket, wrist velocity and acceleration during four different strokes.</caption><thead><tr><th>Condition</th><th>Drop (slow)</th><th>Clear (medium)</th><th>Smash (fast)</th><th>Full smash (very fast)</th><th>p-value*</th><th>η²*</th><th>1-β*</th></tr></thead><tbody><tr><td>Maximal velocity</td><td>6.3 ± 1.9</td><td>20.9 ± 4.1</td><td>34.6 ± 3.4</td><td>49.2 ± 5.1</td><td><strong>&lt; 0.001</strong></td><td><strong>0.921</strong></td><td><strong>0.975</strong></td></tr></tbody></table>
<table><tbody><tr><td>racket head (m/s)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Maximal velocity</td><td>6.2 ± 1.9</td><td>18.5 ± 3.5</td><td>31.7 ± 4.6</td><td>41.4 ± 4.1</td><td><strong>&lt; 0.001</strong></td><td><strong>0.931</strong></td><td><strong>0.984</strong></td></tr><tr><td>virtual head racket (m/s)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Gain (%)</td><td>0.2</td><td>3.8</td><td>6.3</td><td>13.2</td><td><strong>&lt; 0.001</strong></td><td><strong>0.828</strong></td><td><strong>0.993</strong></td></tr><tr><td>Maximal racket deflection (cm)</td><td>0.8 ± 0.3</td><td>2.6 ± 0.6</td><td>4.6 ± 0.8</td><td>8.4 ± 1.2</td><td><strong>&lt; 0.001</strong></td><td><strong>0.832</strong></td><td><strong>0.952</strong></td></tr><tr><td>Wrist acceleration (m/s²)</td><td>3.4 ± 0.7</td><td>10.2 ± 4.8</td><td>15.6 ± 0.8</td><td>23.1 ± 1.5</td><td><strong>&lt; 0.001</strong></td><td><strong>0.607</strong></td><td><strong>0.931</strong></td></tr><tr><td>Timing (ms)</td><td>73.7 ± 5.4</td><td>64.8 ± 2.8</td><td>60.1 ± 2.7</td><td>58.5 ± 3.1</td><td><strong>&lt; 0.001</strong></td><td><strong>0.665</strong></td><td><strong>0.954</strong></td></tr></tbody></table>

* p-value: significant differences for values lower than 0.05; * η²: Effect size; *1-β: Power-test.

A strong correlation was found between maximal racket deflection and gain obtained by the deflection (r = 0.933; p > 0.001) (figure 3), and maximal deflection and maximal racket velocity (r = 0.954; p < 0.001) (figure 4).

<figure><img src="image_4.png" /><figcaption>Figure 3: Correlation between rigid and flexible racket and deflection (p > 0.001)</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Figure 4: Correlation between racket head velocity and deflection (p > 0.001)</figcaption></figure>

Discussion

The aim of the study was to analyse to compare the velocity gain of the racket deflection
compared with a rigid one during four different strokes (drop, clear, smash and full smash)
performed by elite badminton players. In this experimentation, we compared the gain
obtained from a flexible racket with a rigid racket (a virtual stiff racket) to analyse the gain on
racket velocity. Simulate a new marker allows to be a new useful tool for analysing stroke
dynamics with a flexible racket. Starting from this virtual stiff racket, information about the
deflection during a stroke was extracted and could be compared between the type of stroke
and players.

The average values of the flexible racket head velocity (44.3 ± 17.6 m/s) are very
similar to the experimentally obtained values reported from 40 m/s to 50 m/s during a smash
in previous study (Kwan, Skipper Andersen, et al., 2010). The maximal head racket velocity
was obtained during a full smash stroke (49.2 ± 5.1 m/s). However, these values are higher
than those found in other study with 37.5 m/s (Rambely et al., 2005). This difference could be
due to a lower sampling rate (50 Hz) on their study.
197 Racket deflection showed a significant change in racket head velocity and was
198 influenced by shaft deflection by +13.2% during a full smash. Assuming consistent stroke
199 condition, it has been estimated that this could lead to an increase in racket head velocity of
200 approximately +24% during a full smash (Phomsoupha et al., 2015). A rigid racket showed
201 lower velocity than flexible one according to the kind of strokes, except for the drop and clear
202 where there is a low deflection (Table 2). A totally rigid racket produces a slightly highest
203 velocity at head than handle during a translation movement due to the lever effect (Kwan, de
204 Zee, et al., 2008), however, the head velocity could be increased during a rotational
205 movement. The racket properties have a great influence during a stroke and and particularly
206 the racket's deflection by providing about 4-6% through the elastic energy (Kwan &
207 Rasmussen, 2010).

208 Maximum deflection of the racket head in our study ranged between 4.1 and 102.2
209 mm during a drop to a full smash, which is higher than the values found in earlier studies,
210 where deflection ranged from 38.5 to 56.2 mm for a smash (Kwan, Skipper Andersen, et al.,
211 2010). This disparity can be explained, firstly, by differences in racket properties in our study;
212 the racket used was more flexible. In addition, our study was performed with human players
213 and they realised a complete stroke, whereas the earlier study used a rotational actuator with a
214 rotational movement. In addition, by storing and releasing more strain energy with a greater
215 flexibility, this results in a higher racket velocity (Phomsoupha et al., 2015). A similar pattern
216 has found with golf club, the effect of deflection amplified club head speed (Worobets &
217 Stefanyshyn, 2012). The correlation between racket head velocity and the gain showed the
218 influence of elastic deformation to increase the final velocity (figure 4). It seems to be
219 important to obtain a high deformation to produce a high velocity to transfer it to the
220 shuttlecock.
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To obtain the maximum benefit from deflection, impact between the racket and the shuttlecock should occur when racket deflection returns to its original position (± 0.05 s). In this way, the maximal advantage of racket elasticity can be obtained at the contact with the shuttlecock (Kwan & Rasmussen, 2010). For a given player, lighter strokes as drop shot were characterized by a lower deflection peak and a hard stroke as smash by a high deflection peak.

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The peak deflection and timing values are depending of each player (Table 3). A maximal head velocity is generated that is higher than the maximal velocity of the handle, due to the elastic deformation.

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Additionally, our study showed different acceleration phase according to the type of strokes. The optimal timing is obtained during a smash (60.1 ± 2.7) and a full smash (58.5 ± 3.1 ms). The timing seems to be constant whereas the peak deflection is depending of the players. The consistency of impact timing in all strokes indicates that players coordinate their stroke to allow the benefit from the deflection (Kwan & Rasmussen, 2010). Furthermore, Phomsoupha et al. (2015) showed expert have better used the deflection than novices by the fact the typical time during which the player accelerates the racket head is around 60 ms and could theoretically increase by +80% racket head velocity. Thus, players take advantage of the elastic effect of deflection to increase the racket velocity during the acceleration phase (Kwan, de Zee, et al., 2008; Smith et al., 1996).

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The drop showed the lowest racket head velocity as compared of the full smash. To produce the power needed, players take advantage of adding velocity with a sequential proximo-distal joint action. The rapid sequence constituted a stretch-shorten cycle to increase the efficiency of the force production. Higher force is generated by a high acceleration of the wrist (Phomsoupha & Laffaye, 2014). When the arm, especially at the end of the wrist movement, is accelerated, the head moves with a delay, resulting in a deflection of the shaft due to elastic deformation (Phomsoupha et al., 2015). Thus, elastic energy stored in racket

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246 deflection during the acceleration phase contribute to increase racket head velocity. A greater
247 flexibility increases the capacity of the racket to store and to release more strain energy
248 (Phomsoupha et al., 2015).

249 Additionally, our study showed different acceleration phase according to the type of
250 strokes. The optimal timing is obtained during a smash (60.1 ± 2.7) and a full smash (58.5 ±
251 3.1 ms). Phomsoupha et al. (2015) showed typical time to obtained the optimal value
252 predicted by their model is about 60 ms. Thus, players take advantage of the elastic effect of
253 deflection to increase the racket velocity during the acceleration phase (Kwan, de Zee, et al.,
254 2008; Smith et al., 1996). To produce a badminton stroke with a minimum energy cost,
255 players take advantage of adding velocity with a sequential proximo-distal joint action during
256 a rotational and a translation movement (Lees, 2003; Sakurai & Ohtsuki, 2000). Join
257 contribution attributed to 53% of the shuttlecock velocity during a smash output to the radio-
258 ulnar pronation (Gowitzke & Waddell, 1977) and showed that the combination of both
259 forearm acceleration impacts the deflection.

Conclusion

260
261 To conclude, the deflection is caused by the relation between player ability (stroke
262 technique), racket mass and stiffness properties (Kwan & Rasmussen, 2010). With the
263 increase of the shot frequency (Laffaye et al., 2015), the time to prepare the stroke (cocking
264 phase) is decreased and the racket should rapidly stroke the incoming shuttlecock. Thus, elite
265 players tend to select a stiff and light racket, permitted with their skill and ability to swing the
266 racket at high speed and short acceleration times. Players have better used the racket elasticity
267 and deflection is affected by stiffness and mass properties (Kwan, de Zee, et al., 2008).
268 Furthermore, players should choose a racket with the best fits and their badminton stroke
269 pattern.
270

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