隨機外彈道六自由度模型與蒙地卡羅法

Stochastic Exterior Ballistic Modeling of 6-DOF with Monte Carlo Solution

10.29548/BGYY.201109.0009

王旭萍(Shiu-Ping Wang)；楊伯華(Pao-HwaYang)；洪浚瑋(Chun-Wei Hung)

六自由度模型 ； 砲口初速 ； 砲口跳躍 ； 蒙地卡羅法 ； 6-DOF Modeling ； Muzzle velocity ； Muzzle jump ； Monte Carlo

修平學報

23期（2011 / 09 / 01）

157 - 173

繁體中文

傳統六自由度理論計算彈體飛行軌跡，輸入起始條件後，解算六自由度微分方程組，計算在相同起始條件下之彈體飛行軌跡，其軌跡為唯一解，亦即其每一發彈的飛行軌跡與彈著點都是相同的。但在實際射擊上，在相同的射擊起始條件下，彈體在射擊過程中會受到砲口的初速變化、砲口跳躍、砲口的噴流及空氣動力改變等隨機因素影響，造成在相同的發射條件下每一發彈的飛行軌跡與彈著點都不盡相同。本文研究是以蒙地卡羅法將砲口的初速變化、砲口跳躍的角度產生符合隨機因素的量化值，加入起始條件中，建構成一隨機外彈道數學模型，以分析彈著精度散布與砲口影響參數，運用此模型模擬計算M107 155公厘榴彈砲的彈體飛行軌跡，並與其相關實測數據或射表進行驗證。

The six degrees of freedom (6-DOF) trajectory model was used to calculate the trajectory and altitude of the projectile. Under the same initial conditions, the solution of 6-DOF trajectory model is a unique solution. But from the really firing test, the projectile trajectory is hard to be same even though the firing conditions were kept. Muzzle velocity variance, muzzle jump, muzzle blast and aerodynamic jump are the random factors, which can affect the exterior ballistic of the projectile. Especially Muzzle velocity variance and muzzle jump are the main factors to cause the dispersion of the projectile.A stochastic exterior ballistic model of Muzzle velocity variance and muzzle jump are constructed to analysis the dispersion of the projectile. Monte Carlo method was used to generate the random variance and quantize the direction of the muzzle jump. A sample of M107 155 mm projectile trajectories was calculated by applying this model.The computational result gives satisfactory agreement with experimental data.

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