# Research on the Hydrodynamic Performance of a Pentamaran in Calm Water and Regular Waves
## 5 Results and Discussions
### Hydrodynamic Performance in Calm Water
#### 5.1.1 Resistance Performance  
According to the direction of force, the total resistance can be divided into pressure resistance \(R_{p}\) and friction resistance \(R_{f}\). Pressure resistance \(R_{p}\) is the force acting on the hull surface vertically caused by wave making and vortex. The calculation results of \(R_{p}\) and \(C_{p}\) under five cases are shown in Table 9 and Figure 14.  
It can be known from Table 9 and Figure 14 that  
(1) The change trends of the \(R_{p}\) curve of the monohull and the pentamaran were basically the same. The difference of \(R_{p}\) increased with the increase in the speed. Under case 1 and case 2, the pressure resistance of the pentamaran was about twice that of the monohull. With the increase in the speed, the increment of the pressure resistance of the pentamaran relative to the monohull was about 1/3 of that of the monohull. The \(C_{p}\) of the monohull decreased significantly, while the \(C_{p}\) of the pentamaran was always in a downward state. Both had the same value at the speed of 15 kn. Figure 13: The wave pattern at typical time in regular waves. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Case**} & \multicolumn{3}{c}{\(R_{p}\)/N} & \multicolumn{3}{c}{\(C_{p}\times\mathbf{10^{3}}\)} \\ \cline{2-5}  & **Monohull** & **Pentamaran** & **Monohull** & **Pentamaran** \\ \hline
1 & 773.8 & 1511.4 & 3.238 & 4.183 \\
2 & 2519.0 & 4633.0 & 2.635 & 3.206 \\
3 & 5920.2 & 8892.8 & 2.752 & 2.735 \\
4 & 10,859.6 & 14,553.4 & 2.840 & 2.517 \\
5 & 16,319.4 & 21,816.0 & 2.731 & 2.415 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Calculation results of pressure resistance. (2) The \(C_{p}\) is a dimensionless dimension of \(R_{p}\), which mainly depends on the pressure difference between the bow and stern, and it can reflect the wave-making ability of the hull to a certain extent. In the medium-speed range, the \(C_{p}\) of the pentamaran was larger than that of the monohull, indicating that the wave-making ability of the pentamaran was weaker than that of the monohull. It was preliminarily inferred that the waves arising from the side hulls and the main hull were superimposed on each other, resulting in unfavorable interference. In the high-speed range, the \(C_{p}\) of the pentamaran was slightly lower than that of the monohull, indicating that the waves arising from the side hulls and the main hull at this time had favorable interference. In conclusion, the calculation results show that whether it was a monohull or a pentamaran, the speed change had a significant impact on the \(C_{p}\). The pentamaran may have better wave-making performance than the monohull in high-speed range. The friction resistance \(R_{f}\) is the tangential force of the water point along the hull surface, which is mainly affected by the wetted surface area. The calculated values of \(R_{f}\) and \(C_{f}\) under five cases are shown in Table 10 and Figure 15.  
(1) The \(R_{f}\) of the pentamaran was always about twice that of the monohull. There was little difference between the two in the low-speed range. The difference was obvious in the high-speed range. (2) The \(C_{f}\) of the pentamaran was always greater than that of the monohull. It is worth noting that the \(C_{f}\) curve of the monohull showed a significant downward curve in the entire speed range, while the downward trend of the pentamaran was relatively slow. Considering that the hull model used in this paper was a high-speed shuttle hull, the reason for this phenomenon was preliminarily inferred as follows: due to the addition of two front hulls, the pentamaran had a smaller tilting motion than the monohull at medium and high speeds, and the immersion area of the pentamaran at high speed was larger than that of the monohull. In conclusion, the calculation results show that the side hulls had an adverse effect on the friction resistance of the pentamaran. Total resistance \(R_{t}\) is the sum of \(R_{p}\) and \(R_{f}\).