## 4 Discussion
### Full-Body Tension-Arc Formation  
The formation of a tension arc is an integral aspect of executing a powerful badminton smash and is closely associated with the act of jumping. The absence of a complete full-body tension-arc formation in novice groups underscores the necessity for players to master the coordination of their entire body during the execution of the smash. The 3D kinematics analysis of skilled players has unveiled the formation of a full-body tension-arc, achieved through a combination of hip over-extension, trunk external rotation, and shoulder over-extension, abduction, and external rotation (Figures 1 and 4). This full-body tension-arc likely accounts for the highly significant 60.2% increase in maximum shuttlecock speed observed in the skilled group compared to the novice group (Table 2). Additionally, the significantly greater ROMs observed in skilled players (Table 3), encompassing trunk rotation, shoulder flexion/extension, abduction/adduction, and rotation, elbow flexion/extension, as well as wrist flexion, signify the fundamental impact of these ROMs on smash quality. Therefore, increasing the amplitude of these determinants should be a focus for novice training. From a biomechanical perspective, the formation of the tension arc offers several advantages for enhancing smash power. It notably increases the X-factor (trunk rotation), resulting in an ideal body posture conducive to executing a powerful whip-like smash. Regarding the X-factor, our study aligns with previous research, such as [PERSON] et al. [5], underscoring the pivotal role of increasing the X-factor in achieving higher maximal shut-tlecock release speeds. Consequently, it is imperative to consider and analyze the trunk segment when comprehensively defining the factors governing the forehand smash. This perspective finds support in research across various sports disciplines, including golf, baseball, tennis, and volleyball, where trunk movement has consistently been recognized as a significant contributor to increased ball release speed [56; 57; 58; 59]. For example, golf research highlights the importance of a substantial X-factor during a golf backswing for generating higher club head velocity upon impact [14; 60]. Similarly, in baseball, variations in ball velocity among pitchers have been linked to different degrees of trunk rotation [61; 62; 63]. Tennis strokes involving trunk and shoulder rotation also highlight the X-factor's significance [57; 64]. Research conducted by [PERSON] and [PERSON] [56] in volleyball has drawn connections between the movement sequence of a spike and that of the badminton forehand smash and tennis serve, emphasizing that trunk rotation plays a pivotal role in initiating these actions. In short, trunk rotation (X-factor) emerges as a pivotal element in power generation across various sports-specific skills. However, even more crucial than the X-factor, the formation of the tension-arc should be considered the primary contributor enabling a whip-like movement that generates explosive power in the smash. This concept of utilizing the tension-arc formation for explosive power generation is not limited to badminton but also applies to other sports skills, such as the javelin throw [47; 48] and the maximal instep soccer kick [49; 50]. Researchers studying the javelin throw have found that the tension-arc formation is imperative for enabling a powerful whip-like throw. In the case of the maximal instep soccer kick, two relevant advantages have been identified: firstly, the tension arc provides an ideal initial condition that increases the lengths of trunk flexors, hip flexors, and quadriceps before their contraction. This dynamic muscle pre-lengthening generates greater muscle forces thanks to a muscle control pattern known as the SSC (stretch-shortening cycle) [65; 66]. This, in turn, increases the effectiveness of the kicking motion. Studies have revealed that when compared to a pure concentric action, the SSC demonstrates a considerable performance enhancement with increased muscle force [65; 66; 67].