Analytical Method for Hitting Probability of Supercavity Torpedoes
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摘要: 建立超空泡鱼雷命中概率的解析模型, 是明确鱼雷射击过程中各项误差源影响规律的有效途径。文中针对超空泡鱼雷直航攻击过程, 考虑平台探测误差和鱼雷航行误差的影响, 建立了鱼雷脱靶量散布模型。同时考虑目标水线面对命中概率的影响, 建立了目标命中范围模型, 并且通过理论分析提出将目标运动误差统一到平台探测误差上, 既能保证计算准确度, 还可有效避免目标二维散布带来的建模困难问题。在此基础上, 建立了超空泡鱼雷命中概率解析模型, 通过与统计方法的对比, 验证了解析模型的计算准确性。此外, 文中还通过灵敏度分析, 明确了初始视线角的探测误差和鱼雷航向误差是对命中概率影响最大的误差源, 可为超空泡鱼雷作战效能的提升提供参考。Abstract: Formulating an analytical model for the hitting probability of supercavity torpedoes is an effective approach to clarify the influence of errors in the attack process. This study establishes a distribution model of the torpedo miss distance during the straight attack of supercavity torpedoes by considering the influence of platform detection and torpedo navigation errors. Simultaneously, considering the influence of the target waterline on the hitting probability, the hitting range model of a target is established, and based on theoretical analysis, this paper proposes unifying the target navigation and platform detection errors, which can ensure the calculation accuracy and effectively avoid modeling difficulties caused by the two-dimensional distribution of the target location. Based on this, an analytical model for the hitting probability of a supercavity torpedo is established, and the computational accuracy of the analytical model is verified by comparing it with a statistical method. A sensitivity analysis is conducted, and the results clarify that the errors with the greatest impact on the hitting probability are the detection errors of the initial line of a sight angle and the torpedo course errors, providing a reference for improving the operational effectiveness of supercavity torpedoes.
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Key words:
- supercavity torpedo /
- hitting probability /
- analytical method /
- error sensitivity
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图 4 命中概率随初始距离和目标舷角变化曲线
Figure 4. Curves of hitting probability changing with initial distance and target board angle
图 5 不同速度比下灵敏度随舷角变化图
Figure 5. Curves of sensitivity changing with board angle at different velocity ratios
表 1 鱼雷及目标仿真参数列表
Table 1. List of simulation parameters of the torpedo and the target
名称 参数 单次仿真次数 10 000 鱼雷速度/kn 200 目标速度/kn 30 鱼雷速度误差标准差/kn 5 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 目标初始视线角误差标准差/(°) 0.3 初始雷目距离/km 2~7, 间隔为1 初始目标舷角/(°) 0~180, 间隔为1 
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表 2 目标船水线半宽值
Table 2. Halfbreadth waterline of target vessel
站号 实际长度/mm 水线半宽/mm −0.6 −5 175.0 9 212.5 0 0 12 640.0 0.5 4 312.5 15 730.0 1.0 8 625.0 18 380.0 1.5 12 937.5 20 502.5 2.0 17 250.0 22 090.0 2.5 21 562.5 23 195.0 3.0 25 875.0 23 847.5 4.0 34 500.0 24 120.0 5.0 43 125.0 24 125.0 6.0 51 750.0 24 125.0 7.0 60 375.0 24 125.0 8.0 69 000.0 24 125.0 9.0 77 625.0 24 125.0 10.0 86 250.0 24 125.0 11.0 94 875.0 24 125.0 12.0 103 500.0 24 125.0 13.0 112 125.0 24 125.0 14.0 120 750.0 24 125.0 15.0 129 375.0 24 125.0 16.0 138 000.0 24 085.0 17.0 146 625.0 22 692.5 18.0 155 250.0 18 240.0 18.5 159 562.5 14 580.0 19.0 163 875.0 10 457.5 19.5 168 187.5 5 795.0
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表 3 解析法与统计法偏差范围比较
Table 3. Contrast of deviation range between analytical method and statistical method
偏差范围 态势数 态势占比/% <1% 853 78.55 1%~2% 194 17.86 2%~3.76% 39 3.59 合计 1086 100
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