## 3 Results and Discussion
### Part II: Case Study
#### 3.2.2 In-Run  
The analysis started with dGNSS measurements of the ski jumper leaving the start gate to the take-off (i.e., the in-run phase). The trajectories of the jumps in the in-run are not presented, since no spatial difference was observed between the two jumps in this phase. The last \(15\,\mathrm{m}\) is greyed out in the plots to symbolise the take-off phase, i.e., the region  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Phase [m]** & \(-5\)**–\(0\)** & \(0\)**–\(5\)** & \(5\)**–\(10\)** & \(10\)**–\(15\)** & \(15\)**–\(20\)** \\ \hline \(\mathrm{Tr}\) [m] & \(0.10\) & \(0.04\) & \(0.02\) & \(0.03\) & \(0.03\) \\ \(v_{x}\) [\(\mathrm{m}\,\mathrm{s}^{-1}\)] & \(0.49\) &where the dGNSS outcome cannot be assumed a valid measure for the CoM trajectory. The resultant, horizontal and vertical velocities from the dGNSS are shown in Figure 6.  
An instant velocity difference of 1 m s\({}^{-1}\) was observed, with the difference in the velocity components being 0.86 m s\({}^{-1}\) and 0.60 m s\({}^{-1}\) in \(v_{x}\) and \(v_{y}\), respectively. During the in-run, the difference in \(v_{y}\) diminished to zero and \(v_{x}\) to approximately half, and thus the difference in \(v\) was 0.43 m s\({}^{-1}\) approaching the edge of the in-run. About 0.3 m s\({}^{-1}\) of the speed difference was expected due to the lower start gate in Jump 2 [6], but 0.1 m s\({}^{-1}\) (0.36 km h\({}^{-1}\), equivalent to the effect of 1 gate) cannot be explained by the gate difference. In other words, Jump 1 showed a 0.1 m s\({}^{-1}\) better performance regarding in-run speed. This is a substantial difference, since a difference in in-run speed at take-off of \(\sim\)0.3 m s\({}^{-1}\) can increase the jump distance by 3.8-10.1 m approximately, depending on hill size and wind conditions [51; 52]. The measured \(F_{p}\) from the dGNSS is shown in Figure 7.  
The measured force curves were within the range of recent wind tunnel data [45]. In both jumps, the \(F_{p}\) showed a steady increase through the curved section of the in-run and was observed to increasing more rapidly from \(-\)15 m. This force enhancement was due to the athlete's head no longer following the in-run trajectory, i.e., the take-off action had commenced, around 15 m (around 0.6 s) before the in-run edge. This is almost twice the length and time that the current literature has stated for the take-off [1; 2; 7]. This may be because of the discrepancy between dynamics and resulting kinematics; the noticeable onset of motion is delayed compared to the onset of forces driving this motion. Thus, a ski jumper may start the take-off action earlier than has been recently assumed. The total force parallel to the direction of motion, i.e., the braking force is shown in Figure 8.  
Figure 6: Velocity components of the in-run phase for the two jumps in the case analysis. (**a**) shows the resultant velocity \(v\), (**b**) the horizontal velocity \(v_{x}\) and (**c**) the vertical velocity \(v_{y}\). The horizontal length from the in-run edge is shown on the x-axis and velocity is shown on the y-axis. Figure 7: Perpendicular force action on the ski jumper during the in-run. The horizontal length from the in-run edge is shown on the x-axis and velocity is shown on the y-axis. By neglecting ski friction, one can use Equation (2) to estimate the drag area (\(C_{D}A\) value) of the in-run position. By assuming an air density of \(\rho=1.225\,\mathrm{kg\,m^{-3}}\) (\(101.325\,\mathrm{kPa}\) at \(15\)\({}^{\circ}\)C), the \(C_{D}A\) values of both jumps decreased from around \(0.25\) to \(0.15\,\mathrm{m^{2}}\) throughout the in-run. Here, friction is neglected, thus the actual \(C_{D}A\) is expected to be somewhat lower. Nevertheless, this is within the range that [PERSON] and [PERSON] [6] measured for ski jumpers' in-run positions in a wind tunnel. Hence, the measurements of both the normal force and the braking force were within the range of what has been measured in separate investigations performed in wind tunnels.