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Luo Musheng, Yu Fengquan, Wang Junmin, Li Mansi. Analytical calculation method of the maximum attack angle of an infrared guided air-to-ship missile[J]. Infrared and Laser Engineering, 2022, 51(7): 20210558. doi: 10.3788/IRLA20210558
Citation: Luo Musheng, Yu Fengquan, Wang Junmin, Li Mansi. Analytical calculation method of the maximum attack angle of an infrared guided air-to-ship missile[J]. Infrared and Laser Engineering, 2022, 51(7): 20210558. doi: 10.3788/IRLA20210558

Analytical calculation method of the maximum attack angle of an infrared guided air-to-ship missile

doi: 10.3788/IRLA20210558
  • Received Date: 2021-08-12
  • Rev Recd Date: 2021-10-11
  • Publish Date: 2022-08-05
  • Aiming at the angle of attack, which is an important influencing factor of infrared guided air-to-ship missile path planning, constraint models of the attack angle were built, including the number of waypoints, distance between two adjacent waypoints, turning angle and pathway distance. An analytical calculation method of the maximum attack angle was proposed. Applying the principle of geometry, the maximum angle of attack calculation model was built, which could be used to solve the pathway with one waypoint, two waypoints and multiple points. Finally, the maximum attack angle under different conditions was simulated when the waypoint number, turning angle and missile range were changed separately. The results show that the maximum angle of attack would increase rapidly as the missile path waypoint increased; it would also increase as the turning angle decreased if the waypoint number was constant. However, the attack angle increased at the expense of the infrared guided air-to-ship missile range.
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    [2] Ma Xinxing, Ding Guangwei. “Man-in-the-Loop” target capture probability model of infrared imaging guided anti-ship missile [J]. Tactical Missile Technology, 2017(2): 47-51. (in Chinese)
    [3] Xiang Zhe, Zhu Ying, Guo Xiaowei, et al. Analysis of impact on acquiring probability to certain type of air-to-ship missile with data link support [J]. Modern Defence Technology, 2019, 47(2): 166-172. (in Chinese)
    [4] Zhang Xiaoyang, Xu Yanke, Fu Kuisheng. Field of view selection and search strategy design for infrared imaging seeker [J]. Infrared and Laser Engineering, 2014, 43(12): 3866-3871. (in Chinese)
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    [7] Qiu Rongchao, Lv Junwei, Gong Jian, et al. Research on general detection method of coastline and sea-sky line in flir image [J]. Acta Armamentarii, 2019, 40(6): 1171-1178. (in Chinese)
    [8] Dai Jun, Tang Xiangcheng, Gao Zhifeng. Design and implementation of an infrared image processing system under sea and sky background [J]. Infrared Technology, 2016, 38(2): 121-125. (in Chinese)
    [9] Du Cuilan. Interference of strong light on infrared guided anti-ship missile [J]. Laser & Infrared, 2016, 46(6): 752-754. (in Chinese)
    [10] Wang Peiyuan, Wang Rui, Wang Yanna, et al. Influence and countermeasures for air-to-ship missile operation in island coastal environment [J]. Ship Electronic Engineering, 2020, 40(5): 13-16. (in Chinese)
    [11] Zhang Leilei, Wang Duo. Research on guidance technology for composite seeker [J]. Infrared, 2019, 40(5): 18-22. (in Chinese)
    [12] Sun Weidong, Wang Bo. Optimization method of attacking angle based on operational effectiveness analysis of missile [J]. Journal of Dalian Naval Academy, 2016, 39(5): 26-28. (in Chinese)
    [13] Ci Xuan, Shi Ying, Wang Zhixin. Research on method of programming air-to-ship missile penetration track based on tactics [J]. Fire Control & Command Control, 2015, 40(6): 115-118. (in Chinese)
    [14] Wang Zongjie, Luo Musheng, Hou Xuelong. The model design for clover leaf search and attack of anti-ship missile [J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2018, 38(2): 155-160. (in Chinese)
    [15] Che Menghu. Research on time base of multi-platform coordinated missile attacking route planning [J]. Computer Measurement & Control, 2018, 26(8): 123-126. (in Chinese)
    [16] Zhang Chengguo, Ding Yong, Shen Xingpan. Cooperative path planning for anti- ship missiles on multi- platform based on quantum bidirectional RRT algorithm [J]. Fire Control & Command Control, 2017, 42(4): 36-41. (in Chinese)
    [17] Zeng Jiayou, Wang Guowei, Zhong Jianlin, et al. Research on cooperative saturation attack problems and models of ship-to-ship missiles from multi-ship platforms [J]. Acta Armamentarii, 2014, 3(5): 256-261. (in Chinese)
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    [20] Li Hongliang, Song Guibao, Li Gaochun. Route planning and re-planning of anti-ship missiles in coordinated operation [J]. Electronics Optics & Control, 2012, 19(12): 18-22. (in Chinese)
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Analytical calculation method of the maximum attack angle of an infrared guided air-to-ship missile

doi: 10.3788/IRLA20210558
  • 1. Naval Aviation University, Yantai 264001, China
  • 2. Unit 91001 of PLA, Beijing 100841, China

Abstract: Aiming at the angle of attack, which is an important influencing factor of infrared guided air-to-ship missile path planning, constraint models of the attack angle were built, including the number of waypoints, distance between two adjacent waypoints, turning angle and pathway distance. An analytical calculation method of the maximum attack angle was proposed. Applying the principle of geometry, the maximum angle of attack calculation model was built, which could be used to solve the pathway with one waypoint, two waypoints and multiple points. Finally, the maximum attack angle under different conditions was simulated when the waypoint number, turning angle and missile range were changed separately. The results show that the maximum angle of attack would increase rapidly as the missile path waypoint increased; it would also increase as the turning angle decreased if the waypoint number was constant. However, the attack angle increased at the expense of the infrared guided air-to-ship missile range.

    • 红外制导空舰导弹具有被动探测、隐蔽性好,且抗岛岸背景干扰小等特点,是复杂环境下实施对舰攻击的重要武器。航路规划功能进一步增强了其多方向协同攻击能力。而最大攻击角是确定空舰导弹飞行航路、实施多弹多方向协同攻击的关键参数之一。研究最大攻击角的计算方法,对于红外制导空舰导弹作战运用与决策具有重要意义。

      攻击角,是指红外制导空舰导弹开启弹载导引头实施搜索时的飞行方向相对水面舰艇目标的舷角。攻击角的取值空间越大,可实现从更多方向、协同使用更多红外制导空舰导弹同时攻击。但攻击角的取值区间不仅受导弹机动能力制约,且与导弹的射程、航路点数量、射击距离等因素有关,需根据红外制导空舰导弹发射时的敌我态势进行实时解算。

      目前,关于红外制导空舰导弹搜捕概率[1-3]、搜索策略与识别算法[4-6]、导引头设计[7-8],以及环境对红外制导空舰导弹的影响[9-11]等方面均开展了较多研究。针对攻击角影响下的反舰导弹作战效能[12]、发射距离[13]、末端搜索方法[14]等方面的研究也较多。特别是在航路规划[15]方面,建立了数学模型以解决多平台协同攻击[16]、饱和攻击[17]等背景下的航路设置问题;提出了航路规划方法[18]和求解算法[19],并对反舰导弹航路重规划[20]等问题进行了研究。但这些研究仅将攻击角作为影响因素、约束条件或输入变量,并未就攻击角的取值区间、最大攻击角的计算方法和求解模型展开深入研究。因此,文中将在建立红外制导空舰导弹攻击角约束模型的基础上,提出最大攻击角的解析计算方法。

    • 设红外制导空舰导弹发射点为L,经P1P2、···、Pn$ n $个航路点,最终到达目标点T,如图1所示。其中,$ \vartheta $为导弹攻击角,$ {\theta _0} $为发射角,$ {D_0} $为发射点L与目标点T之间的距离。

      Figure 1.  Schematic diagram of infrared guided air-to-ship missile flyway

      (1)航路点数量 $ n $

      为了规避特定区域,实现多弹协同攻击等需要,通常在导弹的飞行路线上设定若干航路点。但航路点数量$ n $不得超过红外制导空舰导弹性能指标中规定的最大值$ {N_0} $,即

      航路点数量的增加不可避免地增加了导弹航路长度,同时也会影响红外导引头对目标的发现概率。因此,航路点应按需设置,越少越好。

      (2)相邻航路点之间的距离$ {s_i} $

      图1中,令发射点LP0、目标点TPn+1$ {s_i} $$ i = 1,2, \cdots ,n + 1 $)表示Pi-1Pi之间的距离。为确保红外制导空舰导弹起飞后稳定飞行并进入预设航路,顺利完成各航路点的转弯、转向以及末端的稳定搜索,$ {s_i} $需满足

      式中:$ {s_{{\text{start}}}} $表示发射点L与第一个航路点P1之间的最短距离;$ {s_{{\text{cent}}}} $表示相邻航路点之间的最短距离;$ {s_{{\text{end}}}} $表示最后一个航路点Pn与目标T的最短距离。

      (3)航路点转弯角$ {\theta _i} $

      $ {\theta _i} $表示红外制导空舰导弹第$ i $个航路点与前后相邻航路点连线的夹角,定义为转弯角,如图1所示。受机动能力的制约,导弹通过航路点时的航向变化不得超过性能指标要求的$ {\theta _{\max }} $,即有

      (4)航路路程$ {R_{{\text{Mis}}}} $

      受最大航程$ {R_{\max }} $的制约,红外制导空舰导弹飞行航路的路程$ {R_{{\text{Mis}}}} $需满足

      式中:$ \kappa $表示航程系数,满足$ \kappa \in (0,1] $。考虑到红外制导空舰导弹飞行过程中的爬升、降高、转弯等机动,并留有一定的裕度,可取0.95~0.99。

    • 为了清晰阐述红外制导空舰导弹最大攻击角的解析计算方法,分别从一个、两个和多个航路点三种情况进行描述。

    • 若红外制导空舰导弹飞行航路只设置一个航路点P1,即$ n = 1 $时,如图2所示。

      Figure 2.  The maximum attack angle with one waypoint

      在三角形$ \Delta LT{P_1} $中,为使得攻击角$ \vartheta $越大,$ {\theta _0} $$ {\theta _1} $应取最小值。根据转弯角约束条件(公式(3)),取

      发射点L、航路点P1、目标点T三点确定的圆中,由相同弦对应的圆周角相等可知,当P1在圆弧$ L{P_1}T $上不同位置时,弦$ LT $对应的圆周角$ {\theta _1} $均相等。因此,当航路点P1的转弯角$ {\theta _1} $为定值时,$ {s_2} $越小,才能使得$ {\theta _0} $越小。根据距离约束条件(公式(2)),取

      由余弦定理有

      将公式(5)~(6)代入公式(7),可解算得出$ {s_1} $,代入公式(8)即可得出一个航路点时的最大攻击角$ {\vartheta _{\max }} $,即

    • 若红外制导空舰导弹飞行航路设置两个航路点P1P2,即$ n = 2 $时,如图3所示。其中,两个航路点之间的距离为$ {s_2} $,第二个航路点到目标的距离为$ {s_3} $

      Figure 3.  The maximum attack angle with two waypoints

      四边形$ L{P_1}{P_2}T $的内角和为$ 2\pi $,因而有

      那么,只有当$ {\theta _i} $均取最小值时才能获得最大的攻击角$ \vartheta $。根据转弯角约束条件(公式(3)),取

      为了使得$ {\theta _0} $值尽可能小,需使得图3$ \Delta L{P_1}{P_2} $的边$ {s_2} $$ \Delta L{P_2}T $的边$ {s_3} $尽可能小。根据距离约束条件(公式(2)),取

      $ \Delta {P_1}{P_2}T $中,由余弦定理有

      同理,在$ \Delta L{P_1}T $中,由余弦定理有

      将公式(12)得出的结果$ d_{{P_1},T}^{} $$ {\theta _{1,(2)}} $代入公式(13)中,可解算得出$ {s_1} $,代入公式(14)可得

      因此,两个航路点时的最大攻击角

    • 若红外制导空舰导弹飞行航路设置$ n $$ n = 3,4, \cdots $)个航路点,如图4所示。其中,$ {s_{n + 1}} $表示第$ n $个航路点与目标T的距离。

      Figure 4.  The maximum attack angle with any number waypoints

      在发射点L$ n $个航路点(n$\geqslant1 $)、目标点T为顶点构成的$ n + 2 $边形中,内角和为[(n+2−2)]×π。因而,攻击角

      $ {\theta _i} $均取最小值才能使得攻击角$ \vartheta $最大。根据转弯角约束条件(公式(3)),取

      图4中,$ \Delta L{P_i}{P_{i + 1}} $$ i = 1,2, \cdots ,n - 1 $)的边$ {s_{i + 1}} $$ \Delta L{P_n}T $的边$ {s_{n + 1}} $均取最小值,可使$ {\theta _0} $尽可能小。根据距离约束条件(公式(2)),取

      令发射点LP0,在$ \Delta {P_i}{P_{i + 1}}T $$ i = n - 1,n - 2, \cdots ,1,0 $)中,由余弦定理有

      式中:$ {\theta _{n,(1)}} = {\theta _n} $$ d_{{P_0},T}^{} = {D_0} $

      将公式(19)得出的结果$ d_{{P_1},T}^{} $$ {s_1} $代入公式(20)可得

      因此,最大攻击角

      由对称性可知,只需使得$ {\vartheta _{\max }} = \pi $便可实现从任意方位对目标实施攻击。因此,当公式(21)计算结果为$ {\vartheta _{\max }} > \pi $时,可考虑从目标的另一舷角实施攻击,从而减少航路点数量,缩短航路路程。

    • 设红外制导空舰导弹发射点位于坐标原点,水面舰艇目标位于X轴正方向上距原点300 km;红外制导空舰导弹航路从发射点起、经若干航路点到达目标点,$ {s_{{\text{start}}}} $$ {s_{{\text{cent}}}} $$ {s_{{\text{end}}}} $均为50 km;$ {\theta _{\max }} $取40°。

      (1)航路点数量对最大攻击角的影响

      当航路点数量从一个逐渐增加到六个时,最大攻击角的仿真结果如表1所示。

      Waypoints number123456
      The maximum angle of attack/(°)33.8564.2695.44131.8175.44224.26
      Range/km309.97341.77400.88489.38594.85685.74

      Table 1.  Simulation results of the maximum attack angle when waypoints changed (turning angle is 140°)

      表1可知,随着航路点数量的增加,最大攻击角也快速增加。当前条件下,设置五个航路点,最大攻击角可达175.44°。考虑到红外制导空舰导弹可从目标左舷、右舷同时攻击,那么攻击方向可有效覆盖目标350.88°的范围,极大地提高了红外制导空舰导弹的多方向协同攻击能力。

      但同时也应注意到,红外制导空舰导弹的航程也在迅速增加。虽然与目标的距离为300 km,但在五个航路点最大攻击角时,红外制导空舰导弹的飞行航程已经达到594.85 km,几乎是前者的两倍。因此,红外制导空舰导弹是以牺牲航程来换取攻击角的增加。若红外制导空舰导弹航程为500 km,则其最大攻击角只稍大于131.80°。

      如果红外制导空舰导弹最多可设置三个航路点,则其最大攻击角为95.44°,对应的飞行航路如图5所示。

      Figure 5.  The flyway of infrared guided air-to-ship missile when three waypoints

      (2)航路点转弯角对最大攻击角的影响

      如果航路点转弯角能够更小,设为130°,可得仿真结果如表2所示。

      表2可知,在相同航路点数量的条件下,相比于表1,最大攻击角均更大,即若能减少航路点转弯角,则能增加最大攻击角。由表2可知,四个航路点就可以实现对目标的全方位攻击,但要求红外制导空舰导弹的航程不得小于551.24 km。

      若只设置三个航路点,可仿真得不同航路点转弯角对应的最大攻击角及所需航程,如图6所示。

      Waypoints number123456
      The maximum angle of attack/(°)42.6683.03127.97181.45240.7299.02
      Range/km315.41363.49447.93551.246230658.89

      Table 2.  Simulation results of the maximum attack angle when waypoints changed (turning angle is 130°)

      Figure 6.  The maximum attack angle with different turning angle (three waypoints)

      图6(a)可知,随着航路点转弯角的减小,最大攻击角迅速增大,甚至超过180°;但为达成最大攻击角所需航程急剧增加,如图6(b)所示。因此,可通过提高红外制导空舰导弹的转弯机动能力,减小航路点最小转弯角,从而增大最大攻击角,但同时对导弹的航程有更高要求。当前条件下,航路点最小转弯角若可减少至115°,则最大攻击角可达181.37°,所需航程为500.86 km;若从目标左右两舷实施攻击,即可实现对目标全方位的攻击。

    • 攻击角是红外制导空舰导弹作战使用中的一个重要决策参数,而最大攻击角的计算是确定攻击角的基础。在确立航路约束的基础上,给出了红外制导空舰导弹最大攻击角的解析计算方法。仿真计算及其结果分析既验证了方法的可行性,又得出了多个有益的结论,可为红外制导空舰导弹的作战使用决策与航路规划提供依据和参考。

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