## 2 Materials and Methods
### Data Reduction  
Two methods of calculating jump height were used: (1) the vertical velocity of the COM\({}_{\text{wb}}\) at takeoff, and (2) flight time. The vertical GRFs (\(F_{\text{ver}}\)) were integrated by trapezoid rule integration to estimate the vertical velocity [6]. The vertical velocity at takeoff (\(V_{\text{to}}\)) was calculated using the following equation:  
\[V_{\text{to}}\ =\ \frac{1}{m_{\text{wb}}}\int_{t_{\text{th}}}^{t_{\text{lo}}}(F_{ \text{ver}}-m_{\text{wb}}g)\text{dt} \tag{1}\]where \(m_{\rm{wb}}\), \(F_{\rm{ver}}\), \(g\), \(t_{\rm{st}}\), and \(t_{\rm{to}}\) represent the body mass, vertical GRF, gravitational acceleration (9.806 m/s\({}^{2}\)[16]), the time of the start of the initial jumping motion, and the time of its termination at takeoff, respectively. The body mass was calculated by averaging \(F_{\rm{ver}}\) over the 0.3 s quiet stance [7] and dividing by gravitational acceleration. We confirmed that the coefficient of variance (CV) of \(F_{\rm{ver}}\) during the quiet phase in each trial was low (less than 1%). The start of the motion was identified as the first \(F_{\rm{ver}}\) detected to deviate above or below body weight by 1%. To eliminate the influence of inter-participant variance in body weight, takeoff and landing times were defined as the first intersection of \(F_{\rm{ver}}\) with 1% of body weight (7.4 \(\pm\) 1.2 N, range 5.0 to 9.9 N). The jump height from \(V_{\rm{to}}\) (\(H_{\rm{v}}\)) was calculated using the following equation:  
\[H_{\rm{v}}\ =\ \frac{1}{2g}{V_{\rm{to}}}^{2}. \tag{2}\]  
\(H_{\rm{v}}\) was used in this study as the criterion for comparison. Jump height from flight time (\(H_{\rm{t}}\)) was calculated using the following equation:  
\[H_{\rm{t}}\ =\ \frac{1}{8}{g}{t_{\rm{flight}}}^{2} \tag{3}\]  
where \(t_{\rm{flight}}\) represents the flight time (see Appendix A). The COM\({}_{\rm{wb}}\) position was calculated as the weighted sum of a 15-segment model (i.e., head, upper trunk, lower trunk, upper arms, forearms, hands, thighs, shanks, and feet) based on body-segment parameters [17]. To compare the difference in the whole-body posture between takeoff and landing, we used a seven-segment model of the head, arm, upper trunk, lower trunk, thigh, shank, and foot (Figure 1). The positions of the arm, thigh, shank, and foot segments were the average of the right and left side. Once an object is projected into the air, the COM of the system must follow a parabolic trajectory, and the trajectory cannot be altered in the air until landing. When the position of a segment moves relative to the COM\({}_{\rm{wb}}\), it affects the other segments' positions relative to the COM\({}_{\rm{wb}}\) to keep the COM\({}_{\rm{wb}}\) trajectory constant. As a result, the difference in a segment posture influences the COM\({}_{\rm{wb}}\) height at landing. To understand the effects of the postural difference between takeoff and landing on the COM\({}_{\rm{wb}}\) height, we quantified the contributions of the changes in the vertical component of each segment on the COM\({}_{\rm{wb}}\) height. When one segment changes its posture, it affects (1) the segment COM  
Figure 1: The definition of (**a**) vertical component of the segment center of mass length (COM\({}_{\rm{k}}\)) and (**b**) vertical component of the segment length (SEG\({}_{\rm{k}}\)). height and (2) the COM height of all segments above it. We defined the vertical component of the segment COM length (COM\({}_{k}\)) by the following equations:  
\[\text{COM}_{k}\ =\ h_{\text{C}_{k}/l_{k}}\ (k\ =\ 1\ \text{to}\ 6) \tag{4a}\] \[\text{COM}_{k}\ =\ h_{\text{C}_{k}/l_{6}}\ (k\ =\ 7) \tag{4b}\]  
where \(k\) represents the segment number (see Figure 1) and \(h_{\text{C}_{k}/l_{k}}\) represents the height from the lower edge point (joint) of the segment to the segment COM (Figure 1a). COM\({}_{7}\) (i.e., the arm segment) was defined relative to the proximal joint (the suprasternal notch).