﻿ 空投鱼雷水中弹道以及弹道散布模拟研究
 舰船科学技术  2020, Vol. 42 Issue (6): 180-184    DOI: 10.3404/j.issn.1672-7649.2020.06.037 PDF

1. 中国船舶及海洋工程设计研究院 上海 200001;
2. 哈尔滨工程大学 船舶工程学院 黑龙江 哈尔滨 150001

The simulation research of underwater trajectory and trajectory distribution about airdropped torpedo
ZHU Xin1, SHI Zhang2, HUANG Li-min2
1. Marine Design and Research Institute of China, Shanghai 200001, China;
2. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
Abstract: The accurate prediction of underwater trajectory of airdropped torpedo is vital to attack specific targets. Lots of factors can influence the underwater trajectory of airdropped torpedo due to the complex marine environment. In order to analyze the influence of current velocity and torpedo attitude to the torpedo trajectory, based on six-degree motion equation, this thesis adds the influence of random current to the motion equation to stimulate the underwater trajectory of torpedo as well as the torpedo's trajectory distribution under different current velocity and attitude. And finally the corresponding simulation results are posed and the distribution regularity of torpedo trajectory is discussed as well.
Key words: airdropped torpedo     underwater trajectory     random current     distribute regular
0 引　言

1 鱼雷水中运动模型

1.1 运动坐标系

 图 1 运动坐标系 Fig. 1 Motion coordinate system
1.2 动力学方程

 ${{ A}_m}\left( \begin{array}{l} {{\dot v}_x} \\ {{\dot v}_y} \\ {{\dot v}_z} \\ {{\dot \omega }_x} \\ {{\dot \omega }_y} \\ {{\dot \omega }_z} \\ \end{array} \right)+{A_{vw}}\left( {{A_m}\left( \begin{array}{l} {v_x} \\ {v_y} \\ {v_z} \\ {\omega _x} \\ {\omega _y} \\ {\omega _z} \\ \end{array} \right)} \right) = {A_F}\text{。}$ (1)

 ${{ A}_{ m}} = \left[\!\!\! {\begin{array}{*{20}{c}} m&0&0&0&{m{z_c}}&{ - m{y_c}} \\ 0&m&0&{ - m{z_c}}&0&{m{x_c}} \\ 0&0&m&{m{y_c}}&{ - m{x_c}}&0 \\ 0&{ - m{z_c}}&{m{y_c}}&{{J_{xx}}}&{ - {J_{xy}}}&{ - {J_{xz}}} \\ {m{z_c}}&0&{ - m{x_c}}&{ - {J_{yx}}}&{{J_{yy}}}&{ - {J_{yz}}} \\ { - m{y_c}}&{m{x_c}}&0&{ - {J_{zx}}}&{ - {J_{zy}}}&{{J_{zz}}} \end{array}} \!\!\!\right]\text{，}$ (2)

${{ A}_{{vw}}}$ 是速度矩阵，且有

 ${{ A}_{{vw}}} = \left[ {\begin{array}{*{20}{c}} 0&{ - {\omega _z}}&{{\omega _y}}&0&0&0 \\ {{\omega _z}}&0&{ - {\omega _x}}&0&0&0 \\ { - {\omega _y}}&{{\omega _x}}&0&0&0&0 \\ 0&{ - {v_z}}&{{v_y}}&0&{ - {\omega _z}}&{{\omega _y}} \\ {{v_z}}&0&{ - {v_x}}&{{\omega _z}}&0&{ - {\omega _x}} \\ { - {v_y}}&{{v_x}}&0&{ - {\omega _y}}&{{\omega _x}}&0 \end{array}} \right]\text{，}$ (3)

${{ A}_{ F}}$ 是力矩阵，且有

 ${{ A}_{{F}}} = \left[ {\begin{array}{*{20}{c}} {{F_x}} \\ {{F_y}} \\ {{F_z}} \\ {{M_x}} \\ {{M_y}} \\ {{M_z}} \end{array}} \right] = \left[ \begin{array}{l} {F_{x1}} - {F_{x2}} - {F_{x3}} \\ {F_{y1}} - {F_{y2}} - {F_{y3}} \\ {F_g} - {F_f} - {F_{z2}} - {F_{z3}} \\ {M_{x1}} - {M_{x2}} \\ {M_{y1}} - {M_{y2}} \\ {M_{z1}} - {M_{z2}} \\ \end{array} \right]\text{。}$ (4)

 \begin{aligned} {F_1} = & 0.5\rho {A_w}{C_d}{u^2},\;{F_2} = 0.5\rho {A_w}{C_d}{V^2},\; \hfill \\ {F_3} =& 0.5\rho {A_w}V{C_d}wL \text{，} \end{aligned} (5)
 ${M_1} = 0.5\rho {A_w}{V^2}{C_d}L, \;{M_2} = 0.5\rho {A_w}V{C_d}w{L^2}\text{。}$ (6)

2 数值模拟

2.1 均匀海流下鱼雷的水中弹道模拟分析

 图 2 鱼雷水下弹道 Fig. 2 The underwater trajectory of torpedo

 图 3 鱼雷速度变化曲线 Fig. 3 The curve of torpedo speed
2.2 随机海流下鱼雷的弹道散布模拟分析

 图 4 海流速度幅值 Fig. 4 The velocity amplitude of current

 图 5 随机海流作用下的鱼雷弹道落点散布图 Fig. 5 Torpedo trajectory sinking position distribution under random current

3 结　语

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