# Dynamic Analysis of Underwater Torpedo during Straight-Line Navigation
## 6 Conclusions  
1. Based on the above derivation of the Munk moment formulas in classical torpedo navigation mechanics and the comparison of Munk moment expression in the software, OrcaFlex, it can be seen that the Munk moment coefficient mentioned in this paper is the product of the additional mass matrix and the mass of the displacement of the torpedo. Thus, the Munk moment coefficient is related to the additional mass matrix of the torpedo.
2. Under the same Munk moment coefficient, the navigation depth shows an increasing trend in the time domain. At the same time, the navigation depth of the torpedo will increase with the increase of the Munk moment coefficient, and the deviation from the initial navigation depth will gradually increase. Under the same Munk moment coefficient, the pitch angle also increases in the time domain. This is because the pitch moment is affected by the Munk moment coefficient and increases with the increase of the Munk moment coefficient.
3. Under the same Munk moment coefficient, the lateral displacement increases in the time domain. At the same time point, with the increase of the Munk moment coefficient, the lateral displacement of the torpedo will increase numerically, and the distance from the initial motion direction will increase gradually. Under the same Munk moment coefficient, the yaw angle increases in the time domain. This is because the yaw moment is affected by the Munk moment coefficient and increases with the increase of the Munk moment coefficient.
4. Under the same Munk moment coefficient, the roll angle increases in the time domain. At the same time, the amplitude of the roll angle of the torpedo will increase with the increase of the Munk moment coefficient, and the amplitude of the rotation angle of the mine body around the x-axis gradually increases. This is because the rolling moment is affected by the Munk moment coefficient and increases with the increase of the Munk moment coefficient.
5. According to classical torpedo navigation mechanics, the Munk moment is composed of pitch, roll, and yaw moments. With the expression of the Munk moment in OrcaFlex, it can only be concluded that the combined moment increases with the increase of the Munk moment coefficient, yet, the increase or decrease of each partial moment cannot be determined. However, according to conclusions (2), (3), and (4), the three moments can all increase with the increase of the Munk moment coefficient.
6. In conclusion, the increase of the Munk moment coefficient will lead to an increase in deflection of the torpedo's direct sailing motion at each degree of freedom, which has an adverse effect on the torpedo's accurate strike. According to conclusion (1), the Munk moment coefficient is related to the additional mass matrix. Therefore, in the design of the torpedo, we should reduce the additional mass of the torpedo by changing the shape of the torpedo so as to reduce the Munk moment coefficient of the torpedo and reduce the pitch, yaw, and roll moments of the torpedo.  
Conceptualization, D.Z. and B.Z.; methodology, D.Z. and H.J.; software, K.Z.; validation, D.Z. and K.Z.; formal analysis, D.Z. and B.Z.; investigation, K.Z. and B.Z.; resources, D.Z.; data curation, K.Z.; writing--original draft preparation, D.Z.; writing--review and editing, D.Z.; visualization, K.Z. and J.S.; supervision, D.Z. and J.S.; funding acquisition, D.Z. and H.J. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Program for Scientific Research Start-up Funds of Guangdong Ocean University, grant number 060302072101, the Zhanjiang Marine Youth Talent Project--Comparative Study and Optimization of Horizontal Lifting of Subsea Pipeline, grant number 2021E5011, and the National Natural Science Foundation of China, grant number 62272109.  
Not applicable.