## 1 Introduction  
To design effective training interventions, coaches must carefully manipulate key training variables such as the intensity [1], volume [2], exercise type [3], and sequence [4]. Among these, training intensity is widely regarded as the most critical determinant of adaptation [1]. In recent years, velocity-based training (VBT) has gained increasing attention as a method of prescribing and monitoring intensity, using movement speed as a proxy instead of traditional percentage-based approaches [5, 6]. VBT offers several advantages, including the ability to estimate the one-repetition maximum (1 RM) more accurately and to individualize resistance levels for athletes of varying training backgrounds [7].  
Flywheel resistance training, which utilizes rotational inertia to generate resistance, allows for both concentric and eccentric loading, including eccentric overload beyond what is achievable through traditional weight training [8,9]. This modality has been shown to promote muscle hypertrophy, improve explosive performance, and reduce injury risk [10, 11, 12]. Its portability and applicability across various environments further enhance its utility in sport settings. These characteristics also make flywheel training a viable method for inducing post-activation potentiation (PAP), a phenomenon that acutely enhances muscle force output following a high-intensity stimulus [11,13].  
PAP is typically elicited through resistance exercises performed before explosive activities such as sprinting or jumping. It is believed to result from both neural and muscular mechanisms, including increased motor unit recruitment, phosphorylation of myosin regulatory light chains, and changes in muscle stiffness [14, 15, 16, 17]. Traditional PAP-inducing exercises--such as barbell squats or isometric contractions--can be effective but often require extensive equipment and controlled environments [18, 19, 20, 21]. Flywheel training offers an alternative that can potentially produce similar or greater PAP effects with added practical advantages.  
However, a major challenge in flywheel-based PAP research is standardizing load intensity. Unlike traditional resistance training, flywheel devices lack a clear 1 RM reference point, and the eccentric load depends on factors such as the moment of inertia and the speed of concentric movement. Consequently, using fixed inertial loads across individuals may produce inconsistent physiological responses. Notably, [PERSON] et al. introduced the concept of using concentric velocity as a surrogate for intensity in flywheel exercises, proposing a load-velocity relationship whereby higher inertial resistance results in slower movement speeds [13]. Building on this framework, [PERSON] and [PERSON] reported that flywheel training using lower inertial loads improved jump height and power output, indicating enhanced post-activation performance benefits [22]. Similarly, [PERSON] et al. observed that high-velocity flywheel squats yielded comparable gains in sprint and jump performance to traditional heavy-load training, further supporting the use of velocity-based strategies for enhancing explosive athletic output [23]. Together, these findings highlight the potential role of movement speed in optimizing PAP outcomes in flywheel training.  
Despite these insights, there remains a lack of systematic investigation into how concentric movement velocity in flywheel squats influences PAP effects and lower-limb performance. Therefore, the present study aimed to evaluate the acute effects of flywheel half squats performed at three different concentric speeds--fast (0.95-1.05 m/s), medium (0.65-0.75 m/s), and slow (0.35-0.45 m/s)--on vertical jump performance and related biomechanical measures in high-level male athletes. We hypothesized the following: (1) Fast-speed flywheel squats would elicit stronger PAP effects than medium- or slow-speed protocols. (2) The performance enhancements would be most evident between 4 and 12 min post-stimulation.