低速火箭弹弹道主动段的近似解法

An Approximate Solution to Trajectory of Low-Speed Rocket in Working Time

本文根据单兵火箭弹、扫雷弹及烟幕弹等火箭弹飞行速度低(马赫数M<0.7)的特点,建立了一组求解低速火箭弹主动段任意点弹道诸元的近似公式.此组公式不同于以往的任何解法,它直接假设V_x、V_y对时间t的函数关系,并由此得到V和θ的表迭式,而射程x和弹道高y则通过对V_X和V_y的积分获得;式中的待定系数,则是以原火箭弹主动段的运动方程组(常微分方程组)及其一、二阶导函数的对应方程组作为初始条件来确定. 由于近似公式中V_x、V_y均为独立表达式,不需联立求解,故从事该类弹丸设计的工程技术人员.用此组公式进行迅速、简便的计算,即可获得主动段任意点弹道诸元.

This paper's author,on the basis of a long-period practice of scientific re-search,in the light of the special feature of the low flight speed (Mach numberM<0.7) of the rockets including the individual soldier rocket,mine clearing rocket andsmoke rocket,created a set of approximate formulae which could be used to work outthe elements of an arbitary point in the trajectory of the rocket projectile in workingtime.This set of differential equation differs from any former classical solution,itdirectly assume the functional relations of V_x and V_y toward t (time) and from this ob-tain the experssions of V and θ.As for x and y,they can be achieved by integratingV_x and V_y The undetermined coefficients in the formulaes can be determined with origi-nal ballistic equations set (system of ordinary differential equations) of the rocket inworking time and their firt and second derivatives as the preliminary condition. In the approximate formulaes the V_x and V_y have their own expressions respec-tively.Then it is unnecessary to work the equations simultaneously.So the engineeringtechnicians which design such kind of projectile can use this set of formulae to achievethe quick and convenient calculation,and obtain the ballistic elements of an arbitarypoint in the trajectory of the rocket in working time.