## 3 Results  
The algorithm successfully analyzed the velocity profiles across three series, providing comprehensive visualizations for each trial. For each series, four distinct analytical representations were generated: a velocity-time profile, a velocity distribution histogram, a polynomial fit analysis, and a space-time relationship plot. These visualizations enabled detailed examination of performance characteristics across different phases of each trial (Figure 3). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Phase** & **Description** & **Identification Criteria** \\ \hline \multirow{3}{*}{Initial Acceleration} & The athlete generates powerful & Starts at movement onset (velocity \textgreater{} 0.5 km/h) and \\  & strokes to overcome inertia and & continues until the velocity reaches 95\% of the \\  & quickly gain speed & cruising speed and stays within \(\pm\)5\% for at least 2 s \\ \hline \multirow{3}{*}{Steady-State Cruising} & The paddler maintains a consistent & Begins at the stabilization point (as defined above) \\  & and efficient velocity with a rhythm & and lasts until velocity increases by more than 10\% \\  & that balances effort and endurance & over cruising speed with positive acceleration \\  & & sustained for at least 1.5 s. \\ \hline \multirow{3}{*}{Final Sprint} & The athlete increases stroke rate and & Starts when the velocity increases \textgreater{}10\% over \\  & intensity to maximize speed and & cruising speed with sustained positive acceleration \\  & performance in the final segment & (\(\geq\)1.5 s) and continues until the end of the trial \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Algorithm criteria for identifying phase transitions. Figure 3: _Cont._  
The velocity-time profiles (Figure 3A) revealed distinct performance patterns, with Series 1 demonstrating an aggressive acceleration profile and reaching peak velocities more rapidly than subsequent trials. Series 2 and 3 showed more gradual acceleration patterns, with smoother transitions between phases. The velocity distribution histograms (Figure 3B) highlighted variations in speed maintenance, with Series 1 exhibiting the widest distribution of velocities post-stabilization, while Series 2 and 3 showed progressively narrower distributions, suggesting more consistent but generally lower velocity maintenance patterns. Polynomial fitting analysis of the acceleration phase (Figure 3C) revealed marked differences in performance efficiency between series, with Series 1 demonstrating the steepest acceleration curve, while Series 2 and 3 displayed more gradual polynomial curves. The space-time relationship plots (Figure 3D) further confirmed these patterns, clearly demonstrating the superior acceleration characteristics of Series 1, particularly in the initial phase, whereas Series 2 and 3 showed similar patterns to each other but with notably different profiles from Series 1, especially in the distance required to achieve stabilization. Analysis of the performance parameters compiled in Table 2 revealed several significant trends across the three series. The stabilized speed showed minimal variation between series (14.98, 14.93, and 14.62 km/h, respectively), but the space required to achieve these speeds increased substantially from Series 1 (13.49 m) to Series 2 and 3 (31.39 and 31.70 m). The time until stabilized speed followed a similar pattern, with Series 1 requiring only 5 s compared to 9 and 10 s for Series 2 and 3. The slope values recorded in Table 2 further quantified these differences, with Series 1 showing a markedly higher slope (2.58%) compared to Series 2 (0.74%) and Series 3 (0.84%). Maximum speeds after stabilization demonstrated a consistent decline across series (18.58,  
Figure 3: Visual representation of performance analysis for each canoe trial showing four complementary analyses: velocity–time profile (**A**), velocity distribution histogram (**B**), polynomial fitting of the acceleration phase (**C**), and space–time relationship (**D**).