## 4 Discussion  
The purpose of this study was to investigate the relationships between peak upper limb moments of the racket arm joints and racket head centre speed at contact during the performance of the jump smash. The racket head speed (61.2 \(\pm\) 3.9 m/s) and shutlecock speed (95.2 \(\pm\) 5.8 m/s) were similar to previous research within elite populations, as well as shutlecock speeds [5,13]. Three joint moments were correlated with racket head speed. Most significantly, greater racket head speed was associated with greater peak shoulder internal moments (high, \(r\) = 0.737, CI: 0.424, 0.892, \(p\) < 0.001). This has also recently been found to be a differentiating factor between skilled and unskilled badminton players, where skilled players produce greater shoulder internal rotation moments [23]. This result is unsurprising given that much of the racket head speed is derived from the shoulder internal rotation angular velocity contribution in overhead motions [22, 23, 24]. In addition to shoulder internal rotation, a smaller backwards plane of elevation moment (noting backwards plane of elevation is negative and resists the forwards movement of  
Figure 4: Normalised time histories for wrist resultant moments; (**a**). Wrist flexion [+]/extension [-], and (**b**). Wrist ulnar deviation [+]/radial deviation [-]. Vertical dashed line indicates the mean end of back swing instant (Figure 1). Figure 5: Correlations between racket head speed and (**a**) shoulder internal rotation; (**b**) shoulder backwards plane of elevation and (**c**) wrist extension. Regression line and 95% confidence intervals represented by solid and dashed lines, respectively. the arm relative to the trunk) had a moderate correlation with racket head speed (\(r=0.614\), CI: 0.221, 0.835, \(p=0.005\)). This peak moment typically occurred at racket-shuttlecock contact and suggests that those who produce greater racket head speed slow down the forwards movement of the arm less prior to racket-shuttlecock contact, and therefore must perform the large proportion of this resistive action after impact, which has been observed in baseball pitching, i.e., after ball release [25]. Finally, participants who produced greater wrist extension moments produced greater racket head speeds (moderate, \(r=-0.564\), CI: \(-0.810\), \(-0.147\), \(p=0.012\)). This may be a similar mechanism where the motion of the whole arm would drive the wrist into flexion too early within the movement, and therefore resisting this motion via an extension moment is necessary for a rapid wrist flexion to occur just before contact. This large wrist extension moment during racket motions has been previously observed in tennis [26], in which the wrist extensor muscles counteract the movements of wrist flexion. It could be recommended that players/coaches should incorporate training that strengthens the musculature that opposes both the forwards shoulder plane of elevation (e.g., posterior deltoid, lower and middle trapezius and infraspinatus, etc.) and wrist flexion (e.g., extension carpi radialis longus and brevis), i.e., acting eccentrically, such that a player can slow the shoulder forwards motion after impact and additionally keep the wrist 'held back' so that it does not come through too early during the swing. The primary limitation of the present study is the small sample size, where post hoc power analysis (G*Power version 3.1.9.6, Dusseldorf, Germany) revealed that a sample size of 29 subjects would provide an 80% chance of achieving \(\alpha=0.05\) in a two-tailed bi-variate correlation, assuming a moderate effect size of \(r=0.5\); therefore, the study was underpowered. Due to the strict inclusion criteria set for the elite population, further recruitment of similar athletes was not possible. Although this limits the power of any statistical test, there is a sufficient sample to identify those variables that best explain the observed variation in each dependent variable, particularly when considering the primary elite athletes studied here.