# The Influence of Effective Mass on the Striking Force of Lead Jab and Rear Cross Punches of Boxers
## 1 Introduction  
As with all modern combat sports, boxing divides participants into body-mass-dependent categories to ensure fairness and safety of athletes. Differences between divisions range from 3 to 6 kg, depending on the weight category, from 46 to 48 kg for flyweight to 92 kg+ for heavyweight. It ensures fair competition--fighters in the ring face each other under identical or very similar physical conditions. They have similar body mass and height, comparable arm length, and reach. Crucially, they are capable of generating similar striking force and accept the risk of receiving similarly powerful blows with respect to the technique used. Variations in the power of punches also depend on the specific punch type--cross, hook, or uppercut--and can develop varying values of impact force and limb acceleration [1]. The effectiveness of a strike is linked not only to the athlete's body mass [2] but also to their technical skill level [3]. Within each category, participants have similar body mass, so they gain advantages in endurance, technical-tactical preparation, and the power of their strikes by utilizing their mass and giving their body segments proper acceleration. This leads us to the concept of effective mass, which refers to the phenomenon of increasing the effective mass of the body or limb during movement, which can influence the ability to generate force and torque [3, 4]. Effective mass, often referred to as \"inertial mass\", is the portion of an athlete's body mass that actively contributes to the power of a strike. In the context of boxing, the concept of effective mass is crucial for understanding how a boxer can maximize punch force through optimal utilization of body mass, especiallyduring a fist strike. A higher effective mass means that more of the boxer's body or limb mass is biomechanically engaged at the moment of impact, thereby enhancing the force delivered to the target. This integration is essential for maximizing punch power, as it ensures that the entire body contributes to the force of the strike, rather than just the arm or fist. Understanding and optimizing effective mass is, therefore, a key component in boxing biomechanics, directly influencing the effectiveness of a punch. Essentially, increasing effective mass means that the boxer's body or limb becomes biomechanically integrated at the moment of contact with the target, potentially enhancing the striking force [2]. There are a few studies, proposing different ways of its computation, but overall understanding of this concept lies in the percentage value of the whole body mass that contributes to the generated force. There can be different ways to achieve it. Initial stance and shift of the body weight, with center of gravity swaying towards a target, can contribute more mass into a strike at cost of stability [1]; stiffening of body segments at the moment of contact with a target to act as a solid block instead of a whip-like movement (which is more demanding and could be obtained only with specific martial art techniques) [2], or integrating more segments into the kinematic chain, forcing more joints to contribute to summary degrees of freedom of movement [5]. Also, biomechanical differences between seemingly identical straight punch techniques like lead jab and rear cross result in the striker achieving varied values of striking force and fist acceleration, which will be reflected in the effective mass coefficient. In combat sports, effective mass is determined in various ways [3; 6]. Some researchers opt for the use of simple momentum conservation models--it is assumed that during a strike on the target, the limb transfers all of its momentum to the target, resulting in its displacement with a measurable velocity [2]. However, the obtained value of effective mass may vary depending on the mass of the target. Therefore, the use of this model is not fully justified. There is also a method that involves the application of a modified form of [PERSON]'s second law with the equation \"Me = Fmax/a\" [4].