# Research on the Hydrodynamic Performance of a Pentamaran in Calm Water and Regular Waves
## 5 Results and Discussions
### Hydrodynamic Performance in Regular Waves
#### 5.2.1 Resistance Performance  
For calculations in waves, the model remained positive floating at the initial time. The degree of freedom of the hull was released after 0.5 s. The total physical time was 20 s.  
Figure 18: The wave patterns of monohull (left) and pentamaran (right) in calm water: (**a**) case 1; (**b**) case 2; (**c**) case 3; (**d**) case 4; (**e**) case 5.  
Figure 20 shows the time history curve of total resistance under case 6. The horizontal axis represents the physical time, the vertical axis represents the total resistance, and the dotted line represents the total resistance in calm water. It can be known from Figure 20 that  
(1) When sailing in the regular head waves, the total resistance of the monohull and pentamaran showed obvious periodic changes.  
(2) When the wave period was \(\pi\), the change trend of the total resistance of the monohull ship was relatively intense, and the time history curve of the total resistance was not a regular positive (cosine) chord curve, indicating that the total resistance of the monohull was strongly nonlinear under such wave conditions. The change trend of the total resistance of the pentamaran was slower than that of the monohull, and the time-history curve of the total resistance was a relatively regular sine (cosine) wave, indicating that the total resistance of the pentamaran was linear under such wave conditions.  
(3) Compared with the resistance in calm water, the total resistance of the monohull was smaller most of the time in an encounter cycle, while the pentamaran showed the opposite trend. It was preliminarily speculated that due to the additional four side hulls, the total weight of the pentamaran was heavier than that of the monohull, the hulls sunk in the wave, the trim range in the wave was smaller, and the wetted area increased.  
Figure 21 shows the time history curve of total resistance under case 7. The horizontal axis represents the physical time, the vertical axis represents the total resistance, and the dotted line represents the total resistance in calm water. It can be known from Figure 21 that when the wave period changed from \(\pi\) to \(\pi/2\), the amplitude and frequency of the total resistance curve of the monohull did not change significantly. The amplitude of the total resistance of the pentamaran decreased from about 18,500 N to about 10,000 N. This showed that as the wave period became shorter, the resistance increment of the pentamaran became smaller in the wave.  
Figure 19: The streamline distribution of the monohull (left) and pentamaran (right) in calm water: (a) case 1; (b) case 2; (c) case 3; (d) case 4; (e) case 5.  
In conclusion, the calculation results show that the total resistance of the monohull oscillated near the calm water resistance, while the total resistance of the pentamaran was in an increasing state most of the time in an encounter cycle. The total resistance of the pentamaran was more affected by the wave period (wavelength). As the wave period became shorter, it developed in the direction that was conducive to drag reduction.