Analytical Method for Hitting Probability of Supercavitating Torpedo Salvo
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摘要: 双雷平行航向齐射, 是直航鱼雷提高命中概率的有效手段之一。文中建立了超空泡鱼雷双雷齐射模型, 并根据命中方程将齐射两雷一次转角射击等效为直进射击, 明确了鱼雷命中目标的实质, 即鱼雷末弹道相对速度方向与等效初始目标方位角方向重合, 使得齐射问题得以简化。根据鱼雷直进射击规律, 以脱靶量作为命中指标、以目标水线面形状作为命中范围建立双雷齐射命中概率解析模型, 并考虑诸如平台探测误差、鱼雷航行误差和目标航行误差影响, 利用统计方法作为对比试验, 试验结果表明解析计算模型与统计计算模型结果相吻合, 验证了解析模型的正确性。最后分析了各误差源灵敏度, 明确了提高鱼雷航向控制精度和方位探测精度是提升命中概率的有效途径。Abstract: Parallel salvo method is effective in increasing the hitting probability of straight running torpedoes. This study establishes a salvo model of supercavitating torpedoes wherein the shoot with a one-time turning angle is transferred into that with a straight-forward shooting. This clarifies the fact that the torpedo hits the target whenever the direction of relative velocity with respect to the target in the terminal trajectory coincides with the equivalent initial azimuth of the target. The proposed method simplifies the salvo problem. Herein, an analytical model of the salvo is established according to the law of shoot with straight trajectory. The miss distance is used as the hit index, and the shape of the target’s water plane is used as the hit range. Moreover, the analytical model considers the effects of platform detection error, torpedo navigation error, and target navigation error. Using statistical methods for comparison, simulations show that the results of the analytical model are consistent with those of the statistical model; this verifies the accuracy of the analytical model. The study also analyzes the sensitivity of each error source and clarifies that improving the torpedo heading control accuracy and azimuth detection accuracy is effective in increasing the hitting probability.
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Key words:
- supercavitating torpedo /
- hitting probability /
- torpedo salvo /
- sensitivity of error
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图 3 鱼雷一次转角射击等效直进射击示意图
Figure 3. Diagram of transform from one-time turning shoot to straight-forward shooting
图 8 命中概率随初始距离和目标舷角变化曲线
Figure 8. Curves of hitting probability with initial distance and target board angle
图 10 双雷齐射与直进射击命中概率对比曲线
Figure 10. Comparison of hitting probability curves between torpedoes salvo and straight-forward shooting
图 11 初始雷目距离100 m时误差灵敏度
Figure 11. Sensitivity of errors of initial distance between torpedo and target at 100 m
图 12 初始雷目距离3 km时误差灵敏度
Figure 12. Sensitivity of errors of initial distance between torpedo and target at 3 km
表 1 仿真参数列表
Table 1. Simulation parameters
名称 参数 单次仿真次数 10 000 鱼雷1级速度/kn 200 鱼雷2级速度/kn 50 目标速度/kn 30 鱼雷1级速度误差标准差/kn 5 鱼雷2级速度误差标准差/kn 1 散开航程/m 20 鱼雷齐射散角/(°) 15 鱼雷航向误差标准差/(°) 0.3 探测目标速度误差标准差/kn 3 探测目标航向误差标准差/(°) 1 目标速度误差标准差/kn 3 目标航向误差标准差/(°) 1 目标初始方位探测误差标准差/(°) 0.3 初始雷目距离/m 2 000∶1 000∶7 000 初始目标舷角/(°) 10∶1∶170 
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表 2 水线半宽值
Table 2. Half-breadth of waterlines
站号 实际
长度/mm水线
半宽/mm站号 实际
长度/mm水线
半宽/mm−0.6 −5 175.0 9 212.5 9.0 77 625.0 24 125.0 0 0 12 640.0 10.0 86 250.0 24 125.0 0.5 4 312.5 15 730.0 11.0 94 875.0 24 125.0 1.0 8 625.0 18 380.0 12.0 103 500.0 24 125.0 1.5 12 937.5 20 502.5 13.0 112 125.0 24 125.0 2.0 17 250.0 22 090.0 14.0 120 750.0 24 125.0 2.5 21 562.5 23 195.0 15.0 129 375.0 24 125.0 3.0 25 875.0 23 847.5 16.0 138 000.0 24 085.0 4.0 34 500.0 24 120.0 17.0 146 625.0 22 692.5 5.0 43 125.0 24 125.0 18.0 155 250.0 18 240.0 6.0 51 750.0 24 125.0 18.5 159 562.5 14 580.0 7.0 60 375.0 24 125.0 19.0 163 875.0 10 457.5 8.0 69 000.0 24 125.0 19.5 168 187.5 5 795.0
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表 3 解析法与统计法偏差
Table 3. Deviation between analysis method and statisicaltical method
偏差范围 态势数 态势占比/% <1% 867 89.75 1%~2% 96 9.94 2.00%~2.85% 3 0.31 合计 966 100.00
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