# Design and Study of a New Wave Actuator for a Boat
## 3 Computer Simulation of the Ship Thrusting Performance of the Wave Actuator
### Simulation Results and Discussions
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**bt = 20.0; ct = 20.0; V = 4.0; Frequency = 0.3 Hz**} \\ \hline  & Cycle: 1 & Cycle: 2 & Cycle: 3 & Cycle: 4 & Cycle: 5 \\ \(P_{c}\) (W) & 22,925.9 & 33,895.2 & 44,202.3 & 53,611.8 & 62,404 \\ \(P\) (W) & 79,094.3 & 81,552.3 & 81,651.2 & 80,870.6 & 80,703 \\ _Mean_\(V_{drag}\) (m/s) & 6.127 & 6.042 & 6.06 & 6.1 & 6.12 \\ \hline  & Cycle: 6 & Cycle: 7 & Cycle: 8 & Cycle: 9 & Cycle: 10–11 \\ \(P_{c}\) (W) & 71,576.6 & 78,523.3 & 80,348.3 & 80,355.8 & 80,335.9 \\ \(P\) (W) & 82,948.6 & 86,387.9 & 94,915.6 & 105,155 & 115,362 \\ _Mean_\(V_{drag}\) (m/s) & 6.115 & 6.107 & 6.102 & 6.102 & 6.103 \\ \hline  & \multicolumn{2}{c}{_Cruise speed_: 6.098 m/s} & \multicolumn{2}{c}{\(\eta\): 67.9\%} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results of simulation for Case 2. Figure 13: Amplitude graph for Case 3. The wave energy conversion potential is highest in Case 2. Referring to Figure 5, the larger intersected area between the boat and wave motion implies more energy. In Case 1, the crests are too closely spaced due to high wave frequency, while Cases 3 and 4, the wavelengths are extended due to low wave frequency. Case 2 emerges as the optimal choice. In Case 2, the difference between the crest of the boat motion and the crest of the wave is the greatest, resulting in the highest pressure on the wave actuator out of the four cases. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **bt = 25.0; ct = 40.0; V = 8.0; Frequency = 0.2 Hz** & \\ \hline  & Cycle: 1 & Cycle: 2 & Cycle: 3 & Cycle: 4 \\ \(P_{c}\) (W) & 4542.35 & 7497.1 & 10,408.998 & 13,265.786 \\ \(P\) (W) & 27,125.891 & 27,643.309 & 28,221.379 & 28,631.233 \\ \(Mean\)\(V_{drag}\) (m/s) & 5.428 & 5.33 & 5.259 & 5.212 \\ \hline  & Cycle: 5 & Cycle: 6 & Cycle: 7 & Cycle: 8 \\ \(P_{c}\) (W) & 16,118.897 & 18,764.279 & 21,223.052 & 23,432.669 \\ \(P\) (W) & 29,268.216 & 29,821.467 & 30,550.743 & 31,532.541 \\ \(Mean\)\(V_{drag}\) (m/s) & 5.183 & 5.163 & 5.144 & 5.141 \\ \hline  & \multicolumn{3}{c}{\(\eta\): 49.5\%} \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results of simulation for Case 4. Figure 14: Amplitude graph for Case 4. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **bt = 20.0; ct = 20.0; V = 4.0; Frequency = 0.2 Hz** & \\ \hline  & Cycle: 1 & Cycle: 2 & Cycle: 3 \\ \(P_{c}\) (W) & 2923.52 & 4407.67 & 5248.25 \\ \(P\) (W) & 16,700.1 & 16,544.7 & 14,413.7 \\ \(Mean\)\(V_{drag}\) (m/s) & 4.787 & 4.7 & 4.822 \\ \hline  & Cycle: 4 & Cycle: 5 & Cycle: 6 \\ \(P_{c}\) (W) & 7055.82 & 8132.06 & 9455.58 \\ \(P\) (W) & 15,930.3 & 15,679.1 & 16,583 \\ \(Mean\)\(V_{drag}\) (m/s) & 4.76 & 4.771 & 4.768 \\ \hline  & \multicolumn{3}{c}{\(\eta\): 38.8\%} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of simulation for Case 3. Figures 15 and 16 present the intersected area during the first 6 s of simulation for all four cases. Wave frequency is reduced from 0.4 to 0.2 Hz in all simulations. Tank coefficients and initial velocity are changed only in Case 4 to demonstrate the feasibility of increasing the input. As shown in Figure 15, the wave period has increased, allowing the system more time to convert wave energy. In Case 1, absorbed wave energy during one-cycle transition phase is smaller than in Case 2 (\(P_{c}\) in Case 1 = 9621.806 W and \(P_{c}\) in Case 2 = 22925.896 W). During the bullish wave phase, the area between the orange and blue lines is larger in Case 2 than Case 1. To evaluate the prediction and simulation, we compare Cases 2 and 3, aiming to exploit the waves better with longer periods. Case 3 has a much larger wave period than Case 2, resulting in a smaller area between the orange and blue lines during the rising phase, as the boat moves with waves close to each other. The absorbed wave energy in Case 3 is converted in a shorter period (\(P_{c}\) in Case 2 = 22925.896 W and \(P_{c}\) in Case 3 = 2923.522 W).