拓展高原环境的航空炸弹弹道快速解算方法

doi:10.12305/j.issn.1001-506X.2024.06.25

Abstract

Abstract:

In order to solve the trajectory of aviation bombs in the plateau environment fast and accurately, based on the traditional trajectory model, an method based on improved Runge-Kutta based uncontrolled bombs trajectory calculation (IRK-UBTC) is proposed. Firstly, an estimation method of the air specific gravity function based on the take-off point is proposed considering the changing environmental parameters during the bomb's falling process. Then, the temperature, humidity, latitude, Colorili force and other information of the fighter's environment are introduced to the system of the traditional differential equations of the bomb's center motion. Finally, based on the third-order Runge-Kutta algorithm, a real-time solution method for differential equations with error control mechanism is proposed. Experiment results show that the calculation period of the proposed method is less than 5 ms in an embedded computer with a main frequency of 1.4 GHz, and the maximum result error is less than 0.2%, which can be applied to real-time calculation of bomb trajectory in plateau areas effectively.

Key words: aerial uncontrolled bomb, bomb trajectory solution, exterior ballistic equation, numerical calculation

CLC Number:

V271.4+4

Baichuan ZHANG, Wenhao BI, An ZHANG, Minghao LI. Fast calculation method of aviation bomb trajectory adapted to plateau environment[J]. Systems Engineering and Electronics, 2024, 46(6): 2073-2081.

Figures/Tables 9

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References 31

1	SENAY N. The strategic level optimization of air to ground missiles for turkish air force decision support system[R]. Ohio: Wright-Patterson Air Force Base, 2012.
2	ABOUSEADA H A H A. Modeling, simulating and control of free falling bomb using PID[C]//Proc. of the International Undergraduate Research Conference, 2022.
3	KOZLOVSKA M , SYBKOVA H , OTAHAL P P . Radiation monitoring after experimental dirty bomb explosion[J]. Radiation Protection Dosimetry, 2023, 199 (8/9): 1012- 1020.
4	CARPENTER C , MONTGOMERY A H . The stopping power of norms: saturation bombing, civilian immunity, and US attitudes toward the laws of war[J]. International Security, 2020, 45 (2): 140- 169. doi: 10.1162/isec_a_00392
5	ZHANG A , XU H , BI W H , et al. Adaptive mutant particle swarm optimization based precise cargo airdrop of unmanned ae-rial vehicles[J]. Applied Soft Computing, 2022, 130, 109657. doi: 10.1016/j.asoc.2022.109657
6	LEONARD A , ROGERS J , GERLACH A . Probabilistic release point optimization for airdrop with variable transition altitude[J]. Journal of Guidance, Control, and Dynamics, 2020, 43 (8): 1487- 1497. doi: 10.2514/1.G004959
7	ATANASOV M . Mathematical model for operation of aviation systems for delivery of special means to air and earth objects[J]. Aerospace Research Bulgaria, 2022, 1 (34): 138- 148.
8	王勇亮, 赵成仁, 卢颖. 炸弹空气阻力加速度的仿真与实现[J]. 弹箭与制导学报, 2006, (S1): 251-252, 256.
	WANG Y L , ZHAO C R , LU Y . Simulation and realization of bomb air drag force acceleration[J]. Journal of Projectiles, Rockets, Missiles and Guidance, 2006, 26 (S1): 251-252, 256.
9	SAHU J . Time-accurate numerical prediction of free-flight aerodynamics of a finned projectile[J]. Journal of Spacecraft and Rockets, 2008, 45 (5): 946- 954. doi: 10.2514/1.34723
10	SAHU J. Unsteady aerodynamic simulations of a finned projectile at a supersonic speed with jet interaction[C]//Proc. of the 52nd AIA Aerospace Sciences Meeting, 2014: 3024
11	郝永平, 陈闯, 张嘉易, 等. 固定舵二维修正弹外弹道仿真与动态模拟[J]. 兵工学报, 2018, 39 (4): 67- 76.
	HAO Y P , CHEN C , ZHANG J Y , et al. Trajectory and dynamic simulations of two-dimensional trajectory correction projectile with fixed canards[J]. Acta Armamentarii, 2018, 39 (4): 67- 76.
12	王莎莎, 张东东, 李新娥, 等. 基于FLUENT和ADAMS的外弹道加速度仿真[J]. 探测与控制学报, 2019, 41 (5): 47- 52.
	WANG S S , ZHANG D D , LI X E , et al. Exterior trajectory acceleration simulation based on FLUENT and ADAMS[J]. Journal of Detection & Control, 2019, 41 (5): 47- 52.
13	AHMADIANFAR I , HEIDARI A A , GANDOMI A H , et al. RUN beyond the metaphor: an efficient optimization algorithm based on Runge Kutta method[J]. Expert Systems with Applications, 2021, 181, 115079. doi: 10.1016/j.eswa.2021.115079
14	LI J W , LI X , JU L L , et al. Stabilized integrating factor Runge-Kutta method and unconditional preservation of maximum bound principle[J]. SIAM Journal on Scientific Computing, 2021, 43 (3): 1780- 1802. doi: 10.1137/20M1340678
15	CHEN H , AHMADIANFAR I , LIANG G , et al. A successful candidate strategy with Runge-Kutta optimization for multi-hydropower reservoir optimization[J]. Expert Systems with Applications, 2022, 209, 118383. doi: 10.1016/j.eswa.2022.118383
16	QIAO Z L , LI L , ZHAO X C , et al. An enhanced Runge-Kutta boosted machine learning framework for medical diagnosis[J]. Computers in Biology and Medicine, 2023, 160, 106949. doi: 10.1016/j.compbiomed.2023.106949
17	DIETHELM K , FORD N J , FREED A D . A predictor-corrector approach for the numerical solution of fractional differential equations[J]. Nonlinear Dynamics, 2002, 29 (1/4): 3- 22. doi: 10.1023/A:1016592219341
18	WU G C , WEI J L , LUO C , et al. Parameter estimation of fractional uncertain differential equations via Adams method[J]. Nonlinear Analysis: Modelling and Control, 2022, 27 (3): 413- 427.
19	ZABIDI N A , MAJID Z A , KILICMAN A , et al. Numerical solution of fractional differential equations with Caputo derivative by using numerical fractional predict-correct technique[J]. Advances in Continuous and Discrete Models, 2022, 2022 (1): 1- 23. doi: 10.1186/s13662-021-03638-9
20	ODIBAT Z , ERTURK V S , KUMAR P , et al. Dynamics of generalized Caputo type delay fractional differential equations using a modified predictor-corrector scheme[J]. Physica Scripta, 2021, 96 (12): 125213. doi: 10.1088/1402-4896/ac2085
21	QI Z , LYSTER D . Multi-spline technique for the extraction of drag coeffidents from radar data[J]. Journal of Beijing Institute of Technology, 1994, 3 (1): 33- 42.
22	李杰, 马宝华. 迫击炮弹一维射程修正引信技术研究[J]. 兵工学报, 2001, 22 (4): 553- 555. doi: 10.3321/j.issn:1000-1093.2001.04.031
	LI J , MA B H . Research on one-dimensional range correction fuze technology of mortar shells[J]. Acta Armamentarii, 2001, 22 (4): 553- 555. doi: 10.3321/j.issn:1000-1093.2001.04.031
23	雷晓云, 张志安, 杜忠华. 基于改进无迹卡尔曼滤波的弹道射程修正算法研究[J]. 兵工学报, 2018, 39 (9): 1701- 1710. doi: 10.3969/j.issn.1000-1093.2018.09.005
	LEI X Y , ZHANG Z A , DU Z H . Ballistic range correction algorithm based on an improved unscented Kalman filter[J]. Acta Armamentarii, 2018, 39 (9): 1701- 1710. doi: 10.3969/j.issn.1000-1093.2018.09.005
24	左军涛, 朱恩成, 黄四牛, 等. 基于GPU的弹道快速计算方法[J]. 火力与指挥控制, 2012, 37 (9): 193- 197. doi: 10.3969/j.issn.1002-0640.2012.09.052
	ZUO J T , ZHU E C , HUANG S N , et al. Fast calculation method base on GPU for trajectory[J]. Fire Control & Command Control, 2012, 37 (9): 193- 197. doi: 10.3969/j.issn.1002-0640.2012.09.052
25	项帆, 王雨时, 闻泉, 等. 无控弹丸刚体外弹道学应用综述[J]. 探测与控制学报, 2021, 43 (4): 14- 26.
	XIANG F , WANG Y S , WEN Q , et al. Summary of uncontrolled projectile rigid exterior ballistics application[J]. Journal of Detection & Control, 2021, 43 (4): 14- 26.
26	杨青, 李若, 蔡振宁. 六自由度外弹道方程组的快速数值方法[J]. 高等学校计算数学学报, 2014, 36 (3): 253- 270.
	YANG Q , LI R , CAI Z N . A fast numercial method for the six degrees of freedom model in the exrernal ballistics[J]. Journal of Computational Mathematics of Colleges and Universities, 2014, 36 (3): 253- 270.
27	丁天宝, 何朝, 王良明, 等. 高速旋转炮弹宽海拔弹道解算方法[J]. 兵工学报, 2021, 42 (1): 209- 213. doi: 10.3969/j.issn.1000-1093.2021.01.024
	DING T B , HE Z , WANG L M , et al. Calculation method of firing trajectory of high spinning projectile adapted to wide altitude[J]. Acta Armamentarii, 2021, 42 (1): 209- 213. doi: 10.3969/j.issn.1000-1093.2021.01.024
28	赵静, 杜忠华, 赵永平, 等. 基于三次B样条曲线的一维弹道修正弹空气阻力系数拟合[J]. 火力与指挥控制, 2015, 40 (4): 123- 126. doi: 10.3969/j.issn.1002-0640.2015.04.030
	ZHAO J , DU Z H , ZHAO Y P , et al. Simulation for air resistance coefficient of one-dimension trajectory projectile based on cubic B-spline curve[J]. Fire Control & Command Control, 2015, 40 (4): 123- 126. doi: 10.3969/j.issn.1002-0640.2015.04.030
29	FENRICK W J . Targeting and proportionality during the NATO bombing campaign against Yugoslavia[J]. European Journal of International Law, 2001, 12 (3): 489- 502. doi: 10.1093/ejil/12.3.489
30	MAHMOUDIAN M , FILHO J , MELICIO R , et al. Three-dimensional performance evaluation of hemispherical coriolis vibratory gyroscopes[J]. Micromachines, 2023, 14 (2): 254. doi: 10.3390/mi14020254
31	浦发. 航空炸弹的标准落下时间和阻力定律及弹道系数关系问题的探讨[J]. 兵工学报, 1985, (3): 1- 7.
	PU F . Discussion on the relationship between the standard falling time and the drag law and the ballistic coefficient of air bombs[J]. Acta Armamentarii, 1958, (3): 1- 7.

参数	取值
炸弹弹道系数C	0.462 859
战斗机起飞时海拔高度H_ON/m	0
战斗机起飞时大气压强h_ON/(mmHg)	750
战斗机起飞时大气温度T_ON/K	288.15
战斗机起飞时大气湿度RH_ON	50%
战斗机投弹时海拔高度H₀/m	2 000~10 000
战斗机投弹时大气压强h₀/(mmHg)	288.15-6.328×10^-3×H₀
战斗机投弹时大气温度T₀/K	760×(1-2.190 5×10^-5×H₀)^5.4
战斗机投弹时大气湿度RH₀	50%
战斗机投弹时所处纬度φ	30
目标海拔高度H_t/m	1 000
战斗机投弹时炸弹速度v₀/(km/h)	800
战斗机投弹时航向角θ	0
步长基准控制参数及步长增量控制参数(a, b, c)	(0.02, 270, 15 000)

参数	标准三阶Runge-Kutta			变步长三阶Runge-Kutta			IRK-UBTC^*
参数	最小值	平均值	最大值	最小值	平均值	最大值	最小值	平均值	最大值
射程相对误差/%	0.390 0	3.491 7	9.911 0	0.476 0	3.842 9	10.388 0	0.167 0	0.585 2	1.162 0
射程误差/m	0.011 0	14.308 7	25.037 0	4.572 0	6.098 5	10.258 0	0.752 0	2.735 4	8.645 0
下落时间误差/s	0.017 0	0.104 4	0.124 0	0.105 0	0.116 7	0.146 0	0.010 0	0.022 5	0.051 0
算法运行时长/ms	3.913 0	4.317 7	5.373 0	1.316 0	2.115 2	3.115 0	2.781 0	4.293 9	4.919 0

目标海拔高度/m	目标相对高度/m	机场大气参数				投弹参数					传统算法误差/%	本文算法误差/%
目标海拔高度/m	目标相对高度/m	温度/K	湿度/%	气压/mmHg	高度/m	温度/K	湿度/%	气压/mmHg	高度/m	真空速度/(km/h)	传统算法误差/%	本文算法误差/%
4 400	1 032	283.15	50	437	4 110	273.63	50	382.3	5 432	601.63	1.041 941	0.444 573
4 336	2 034	281.15	50	435.7	4 110	280.74	50	336.3	6 370	605.13	2.032 601	1.029 315
4 394	1 036	288.15	50	760	0	273.63	50	382.4	5 430	590.88	0.462 543	0.286 683
4 120	5 011	288.15	50	760	0	246.64	50	226.1	9 131	734.88	1.749 418	1.584 682
4 398	3 056	280.15	60	435	4 110	253.15	50	288.79	7 454	647.13	2.301 516	0.547 754
4 331	5 046	280.15	60	435	4 110	241.12	50	217.96	9 377	742.88	3.443 107	0.593 857
4 303	5 082	280.15	60	435	4 110	240.92	50	217.69	9 385	751.125	3.167 299	0.862 63
4 400	1 032	283.15	50	437	4 110	273.63	50	382.3	5 432	601.63	1.041 941	0.444 573
4 336	2 034	281.15	50	435.7	4 110	280.74	50	336.3	6 370	605.13	2.032 601	1.029 315

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Fast calculation method of aviation bomb trajectory adapted to plateau environment

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