一种测试弹丸落炸点的数学模型

A Mathematical Model of Gun Ball Fall-Explosion Point Measurement

为了解决弹丸落炸点坐标的实时、动态和精确测试,分析和推导了光学交汇法的数学模型。首先根据弹丸着地前某时刻通过两台面阵CCD时分别在各自像片坐标系上所成像的像点坐标,经过坐标系转换得到其大地坐标系下空间坐标,再推导出各自像点和物镜焦点所在的直线方程,由预先给定的两条直线公垂线长度门限值对像点进行取舍判断,计算出这两条直线的近似交点即为该时刻弹丸空间点坐标。从而为模拟弹丸着地前弹道运动轨迹、求解弹丸落炸点坐标建立了基础。经过靶场试验验证,该测试方法更适用于远程和大口径火炮弹丸终端参数的测试。

In order to deal with real-time, dynamic, accurate measuring problems of gun ball fall-explosion point coordinate, the mathematical model based on optical intersecting method was deduced. First of all, according to the positions and coordinates of image points formed in two camcorders before the gun ball landed on the ground, the two space coordinates of image points under the geodetic coordinate system were acquired by means of coordinate system conversion, then the two beeline-equations established in the image points and field-lens focuses were deduced. Judged from the length gate limiting values of two com- mon vertical lines given in advance to accept or reject, approximate intersecting point of two beelines was the space coordinate of gun ball at that moment. Therefore the model laid the foundation for simulating the trajectory moving track of gun ball before it landed on the ground and for solving the gun ball fall-ex- plosion point coordinate. By use of experimentation and validation on the firing range, the method is more suitable for terminal parameters measurement of long range and large caliber gun ball.