# 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  
The first paragraph of this section describes the main parameters that will change in each simulation case. Table 2 presents each case's wave parameters used for simulation. The main focus of this study is the calculation of the wave force acting on the boat (Equation (27)), which is derived from the formation of the intersected area--overlap between the wave and the boat's motion profile. The wave frequency (expressed in Hz) is the number of waves passing a fixed point in a given time. We conducted simulations for different wave frequencies from 0.4 Hz to 0.2 Hz. For Case 1 and Case 2, 0.4 Hz and 0.3 Hz, respectively, and for Cases 3 and 4 being the same, 0.2 Hz. The wave height is set to be the same in all four cases at 1.25 m, meeting the conditions outlined in Section 2.2 with the wave slope being less than 0.1412, and compatible with the frequencies mentioned above. The wave angle is set to 180 degrees in all four cases, representing the boat moving against the wave flow. The conditions are arbitrarily selected to evaluate the wave actuator's performance. The tank coefficients are reiterated here for a more detailed description. Both the damping and spring coefficients are set to 20 in Cases 1, 2, and 3, while in Case 4, the damping coefficient is 25, and the spring coefficient is 40. They are tuned through trial and error. The boat's initial velocity (Equation (11)) is 4.12 m/s for Case 4 and 2.06 m/s for the remaining three cases. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Boat Parameters** & **Unit** & & **Tank Parameters** & **Unit** & \\ \hline Length of waterline, \(L\) & m & 7.13 & Length of tank, \(Lt\) & m & 5.00 \\ Beam of waterline, \(B\) & m & 2.26 & Beam of tank, \(Bt\) & m & 2.00 \\ Boat draft, \(d\) & m & 0.50 & Height, \(Ht\) & m & 0.50 \\ Deck height, \(H\) & m & 1.06 & Nozzle radius, \(r\) & m & 0.10 \\ Weight of boat displacement, \(We\) & kg & 4397.932 & Damping coefficient, \(bt\) & Ns/m & 20–25 \\ Added mass coefficient, \(a\) & Ns\({}^{2}\)/m & 607.377 & Spring coefficient, \(ct\) & N/m & 20–40 \\ Damping coefficient, \(b\) & Ns/m & 2002.124 & & & \\ Restoring spring coefficient, \(c\) & N/m & 162194.42 & & & \\ Initial velocity of boat, \(V\) & m/s & 2.06–4.12 & & & \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters of boat used in the simulation. Figure 10: Down-wave phase. Figure 9: Up-wave phase. This paragraph introduces the types of simulation parameters and explains the reasons for their selection. In this study, the boat's weight is fixed. Therefore, in Cases 1 and 4, the most influencing parameter affecting the force on the boat is the wave frequency (from 0.4 to 0.2 Hz), assuming that more wave crests will generate greater force on the wave actuator. The next influencing parameter is the boat's initial velocity (2.06-4.12 m/s); the faster the boat, the more wave crests it encounters. Also, other important ones are the tank's damping coefficient (from 20 to 25) and spring coefficient (from 20 to 40). These are the four parameters affecting the performance of the wave actuator. Considering the above, the following four simulation cases were conducted. Before presenting the simulation results, here is a list of the information that will appear. In the graphs for all four cases, the orange line represents wave amplitude, and the blue line represents boat motion in the upper frame. Also, in all the vertical wave force figures, the lower frame shows the force amplitude, and the blue line represents the force over time acting on the wave actuator. These graphs assess the performance and behavior of the wave actuator under various wave conditions affecting the boat. The simulation results in all the tables in the four cases present the key information. The simulation parameters are reiterated, with the differences between the cases highlighted. The number of cycles refers to the upper half of the cycle shown in the amplitude graph.