The Use Of Computer Algebra And Nonlinear Optimization For Real Time Computation Of Fire Orders For Direct Fire
Free (open access)
A. Kuhrt & H. Rothe
For real time calculation of flat fire trajectories, a simple and efficient mathematical model is developed by using computer algebra systems. These systems not only allow one to find analytical solutions to difficult mathematical problems, but are also able to generate runtime-optimized C code. Therefore, it was possible to develop a real time code for the solution of flat fire problems. This code includes influences given by the thermodynamic state of the atmosphere, wind of any strength and direction and shooting at higher or lower targets. For finding the appropriate ballistical coefficients of our model, a two dimensional non-linear global optimization was necessary. The results of our flat fire code are compared with a number of NATO standard ballistic tables. Keywords: direct firing, analytical solution, nonlinear optimization, varying terrain angle, Ma dependent drag coefficients, changing air pressure and temperature, wind, real time. 1 Introduction Especially for modern stabilized weapon platforms, built for firing in motion at moving targets, probably using a target tracking system, real time fire command generation is necessary. This problem can be solved by using a new approach, which is based on ballistical models for flat fire trajectories, given e.g. by McCoy . In the following, the necessary terms of the mathematical model will be explained in detail. All equations are related to a reference inertial coordinate system (x, y, z) as displayed in fig. 1. Following the model of a flat fire trajectory, all external forces
direct firing, analytical solution, nonlinear optimization, varying terrain angle, Ma dependent drag coefficients, changing air pressure and temperature, wind, real time.