基于级数解法进行射角迭代的弹道数值积分方法研究

Research on Ballistic Numerical Integration Method Based on Series Method for Iterative Firing Angle

采用基于弹道解算模型积分方式求解弹道诸元时,需要依据射表数据推导出大量的模型和参数,计算出实际射击条件影响的射角初值,使得计算量大且步骤繁杂。弹道级数解法可通过对任意初始射角进行不断迭代,使得积分的弹道快速满足收敛条件,计算出满足精度的射击诸元。该方法基于泰勒公式推导出射角和高角变化1 mrad的距离改变量的计算公式,在弹道积分过程中对射角进行修订,使射程的误差达到精度要求。通过对不同初始射角所对应的弹道、精度等统计分析,以及与目前常用方法计算射击诸元的比较分析,得出该方法不仅可以省略精确初始射角值的推导和计算,在程序体大小、解算速度和解算精度上均有提升,具有较强的实用意义和工程推广价值。

When using the integration method[JP2]based on trajectory calculation model to solve firing data,[JP]it is necessary to derive a large number of models and parameters based on the firing table,and calculate the initial firing angle on the actual firing conditions,which brings large amount of calculation and complicated steps.The series method can continuously iterate on any initial firing angle,so that the integrated trajectory can quickly meet the convergence conditions and the firing data that meet the accuracy requirements can be calculated.This method is based on the Taylor formula to derive the calculation formula for the distance change when the firing angle and the elevation angle change by 1 mrad,and the firing angle is revised during the trajectory integration process to make the range error meet the accuracy requirements.Through statistical analysis of the trajectory and accuracy corresponding to different initial firing angles,as well as comparison with commonly used methods for calculating firing data,it is concluded that this method can not only omit the derivation and calculation of accurate initial firing angle,but also improve the program size,calculation speed and accuracy.It has strong practical significance and engineering promotion value.