摘要
随着一些高新技术的应用,常规弹箭的射程越来越大,对应的弹道高度也越来越高。在已开展的超远程弹箭研制过程中,发现了按通常外弹道、弹箭空气动力学等理论设计的火箭弹,其试验射程与计算射程相差较多的现象。这种现象产生的原因是由于火箭飞行的射程和高度很大,按以往方法计算重力、空气动力和弹道所带来的误差将不可忽略；另一方面弹箭在全弹道飞行过程中所处的大气参数以及所受的空气动力变化很大,因此,与在一般射程和弹道高范围内飞行的常规弹箭相比,经历高空环境飞行的弹箭将表现出不同的弹道特性,进而可能对质心运动产生较大的影响。而对于上述问题,目前尚缺乏深入的理论研究,因此对于这种经历高空飞行的无控弹箭,有必要对其弹道特性进行进一步的研究,为此类弹箭的研制提供理论基础。
根据在超远程火箭在研制中发现的现象和问题,该文主要研究以下内容：
(1)根据标准气象条件的定义、特点及目的,基于炮兵标准气象条件和现有的气象资料,将炮兵标准气象条件扩展至高空,供经历高空环境飞行弹箭的气动力及弹道计算参考使用。
(2)根据重力学理论,将正常重力的斯托克斯算法扩展至总地球椭球地表外空间,从而得到了弹道计算中正常重力的一个新的计算方法。基于该方法,分析了常规弹箭弹道学中各种重力计算模型的精度并讨论了其使用范围。计算结果表明：当射程较小时,采用常值重力模型(g=9.8m/s2)可满足弹道计算精度的要求；随着射程的进一步增加,若地表处采用正常重力,而重力值随高度的变化采用平方反比公式的重力模型并不能提高重力的计算精度,此时应采用圆球地表重力模型,即除了考虑纬度和高度变化的影响外,还应考虑重力方向随飞行过程的变化；弹箭射程超过一百公里时,采用正常重力模型计算重力将有助于提高弹道计算的精度。
(3)基于空气动力学及稀薄气体动力学理论,分析了弹箭经历高空环境飞行过程中空气动力系数的变化情况及特点,并讨论了这种变化对弹道计算精度及弹道特性的影响。结果表明,低密度气体效应对空气动力系数的计算有一定的影响,对于经历高空环境飞行的弹箭,这种效应所导致的高空空气动力系数与地面值的差异对弹道计算的影响应当予以考虑；另一方面,在分析变系数对弹箭角运动特性的影响时,可忽略低密度气体效应对弹道空气动力系数的影响,这是由于低密度效应对弹道空气动力系数的影响与空气密度随高度变化对弹道空气动力系数的直接影响相比要小得多,可忽略不计。
(4)建立了适用于超远程弹箭的弹道计算模型,研究了椭球地表模型假设下的弹道飞行高度及曲面地表射程的计算方法,讨论了不同地表模型、不同重力模型以及气动力系数随高度变化对弹道计算的影响。结果表明,上述因素对超远程弹道的计算均有不同程度的影响,有必要采用更为完善的弹道模型以提高其计算精度。(5)建立了同时适用于高低空的弹箭角运动模型,比较和分析了弹道学中各种弹箭角运动模型的差异及其产生原因。研究了变系数对弹箭角运动稳定性的影响,讨论了弹箭在高空飞行时的工程稳定性。在气动力与攻角幅值平方δ2成线性的假设下,推导了弹箭的非线性角运动模型,推导结果表明,弹箭的非线性角运动模型中还含有与(δ2)′有关的项。基于新建立的弹箭非线性角运动模型改进了弹箭角运动的动稳定判据。改进的非线性动稳定判据不但考虑了更完善的模型,而且还给出了攻角初始值的允许范围,可更好地判断经历高空飞行弹箭非线性角运动的动稳定性。
以上研究结果对经历高空飞行弹箭的弹道计算和总体设计具有一定的参考价值。
The firing range of conventional projectile is becoming further and further with the application of new and advanced technology. It was found that the experimental firing range differ fairly from the calculated firing range in the research process of ultra range projectile designed basing on the classical ballistic and aerodynamic theory. The cause of these phenomena is that the span and altitude range the rocket experienced is so large that on the one hand the traditional method used to calculate the gravity, aerodynamic forces and trojectory cause non-negligible error, on the other hand the aerodynamic forces and moments vary greatly during the flight and leading the projectile to behave different characteristics compared with the projectiles flying at low altitude. It is necessary to make a further study on the aerodynamic and ballistic characteristics for the projectile experiencing high altitude environment so that we can provide the theoretical basis for developing it.
This paper is devoted to the research of the following content according to the phenomena observed in the development of ultra range rocket.
(1) Referencing to the Artillery Standard Atmosphere and other available atmosphere data, the Artillery Standard Atmosphere is extended to the high altitude basing on its definition, characteristic and purpose.
(2) Basing on the gravimetric theory, a new method for calculating normal gravity is proposed. Basing on this method, the various gravity calculation model introduced in ballistics is compared and their application range is analyzed. The calculation result show that the constant value gravity model with g= 9.8m/s2 is appropriate for trajectory calculation when the range is short. With the increase of the trajectory range, the sphere earth gravity model should be adopted. For ultra range trajectory, adopting normal gravity model makes for trajectory calculation precision.
(3) Basing on the theory of aerodynamic and rarified aerodynamic, the variation of aerodynamic coefficient versus height and its effect on ballistics is analyzed for conventional projectile experiencing high altitude environment. The result shows that the effect of aerodynamic variation versus height on trajectory calculation should be considered while its effect on angular motion analyzation is negligible.
(4) The calculation model fit for ultra range projectile is built. The calculation method for flying height and curve earth surface range is researched. The effect of different earth surface model, different gravity model and the variation of aerodynamics vesurs height on trajectory calculation are discussed. The result shows that the above mentioned factor may affect trajectory calculatin quite a little. They should be considered to improve the precision of trajectory calculation.
(5) The angular motion model suitable for both low and high altitude environment is built. The nuance of angular motion model introduced in different ballistics is compared and the cause of this difference is analyzed. The effect of coefficient variation on the stability of angular motion is analyzed; the engineering stablility of projectile flying at high altitude environment is researched. With the hypothesis that the aerodynamics coefficient is linear inδ2, the square of attach angle amplitude, the nonlinear angular motion model is derived. The result shows that the nonlinear angular motion model also contain item relative to (δ2). Basing on the new derived nonlinear angular motion model, the criterion of dynamical stability is researched considering algebra and aerodynamic nonlinearity. The research results achieved are of important reference to the calculation and designation of projectile experiencing high altitude environment.
引文
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