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

摘要/Abstract

摘要：

为快速、精确地求解高原环境下的航空炸弹弹道, 在经典弹道模型的基础上, 面向高原环境提出一种基于改进Runge-Kutta的航空无控炸弹弹道解算(improved Runge-Kutta based uncontrolled bombs trajectory calculation, IRK-UBTC)方法。首先, 针对炸弹下落过程中时刻变化的环境参数, 提出了基于起飞点的空气比重函数估算方法。然后, 引入战斗机所处环境的温度、湿度、纬度、科尔奥利力等信息对经典炸弹质心运动微分方程组进行重构。最后, 在三阶Runge-Kutta算法的基础上, 提出了带误差控制机制的微分方程组实时解算方法。实验结果表明, 该方法在1.4 GHz主频的嵌入式计算机中的解算周期小于5 ms, 且最大射程误差小于0.2%, 能够被有效应用于高原地区航弹弹道的实时解算。

关键词: 航空无控炸弹, 弹道解算, 外弹道方程, 数值计算

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

中图分类号:

V271.4+4

张百川, 毕文豪, 张安, 李铭浩. 拓展高原环境的航空炸弹弹道快速解算方法[J]. 系统工程与电子技术, 2024, 46(6): 2073-2081.

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.

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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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