## 4 Discussion  
The purpose of the present study was to quantify the effect of postural changes between takeoff and landing on jump height overestimation. The jump height from flight time was 0.025 m (6.4%) higher than the jump height calculated from velocity. We confirmed that the current result was reasonable compared to the previous studies, which showed 2-11% overestimation of CMJ height [7; 8; 9]. The difference in the vertical components of the foot and shank segment lengths were the main contributions to the difference in the COM\({}_{\text{wb}}\) height. Also, the inter-participant differences were large (range \(-0.092\) to \(0.018\) m for foot and \(-0.040\) to \(0.003\) m for the shank, see Figure 4). Therefore, the observed lower COM\({}_{\text{wb}}\) height at landing was mostly due to lower ankle dorsiflexion. In some previous studies, experimenters instructed each participant not to flex their knees [22] and hips [23] at landing. In other studies, experimenters instructed participants to land in a similarly extended position at takeoff [24; 25]. From these previous studies, it is suggested that ankle dorsiflexion at landing was considered a less serious effect on the jump height, whereas our results indicate that it is the most critical motion. In these studies, each trial was also watched and judged by the experimenter subjectively to ensure that the instructions had been followed. To reduce the difference in the COM\({}_{\text{wb}}\) height, it is recommended that an experimenter instruct participants about the landing technique for the jump tests, primarily focusing on foot and shank segments, such as \"landing with toes pointing downwards\" [26]. However, such instruction seems to be inappropriate. One reason for this is that the posture at landing is essential because high impacts cause lower joint injuries [27]. Preparatory flexing at the hip, knee, and ankle is an effective strategy to reduce the impact of landing [28]. Moreover, a previous study revealed that extra attention increased the impact of landing [29]. It may be difficult to control the posture at landing in detail without increasing the risk of injury and excess stress. It is unlikely--but not impossible--that the control of the upper body affects the lower limb bending. Because the total momentum and total angular momentum of a system both remain constant unless acted upon by an external influence, when a segment moves relative to the COM\({}_{\text{wb}}\), the other segments have to move to compensate. Therefore, there is a possibility that the upper trunk movement affected the shank and foot postures. It is notable that the causal relationships between these postural effects are unknown. Figure 5: An illustration of the influence of the difference in the COM\({}_{\text{wb}}\) height (\(\Delta\)COM\({}_{\text{wb}}\)) and jump height (\(H_{\text{v}}\)) on jump height overestimation (\(\Delta H\)) (Equation (8)). The top-left triangular area in white shows there are no real roots because \(\Delta\)COM\({}_{\text{wb}}\) cannot be greater than \(H_{\text{v}}\). The red circles represent each experimental data point. In this study, the difference in the arm COM height relative to the suprasternal notch also affected the difference in the COM\({}_{\text{wb}}\) height between takeoff and landing, though there was a large inter-participant variability (from \(-0.046\) m to \(0.008\) m). Although no previous study has reported the effect of arm posture on flight time overestimation, some studies reported that an arm swing contributes to increased the COM\({}_{\text{wb}}\) height [11]. The height of the arm COM in 23 out of 27 participants was above the proximal joint at takeoff, and in 14 of the 23 participants, it was below the proximal joint at landing. When VJ is performed, experimenters do not instruct the participants regarding the height of arm movement before takeoff, because they want to evaluate jump performance using arm swing as much as possible, comparing it to jumps without arm swing.