Effect of the mathematical model and integration step on the accuracy of the results of computation of artillery projectile flight parameters

Abstract

In the paper the three different mathematical models of motion of a spin-stabilized, conventional artillery projectile, possessing at least trigonal symmetry, have been introduced. The vector six-degrees-of-freedom (6-DOF) differential equations of motion are an updated edition of those published by Lieske and McCoy and are consistent with STANAG 4355 (Ed. 3). The mathematical models have been used to developing software for simulating the flight of the Denel 155mm Assegai M2000 series artillery projectile and to conduct comprehensive research of the influence of the applied model and integration step on the accuracy and time of computation of projectile trajectory.

Control of the non-stationary gyroscopic system in the target tracking process

“…In the following simulation tests, the following parameter values were adopted: 1) Gyroscopic system parameters: a) longitudinal and transverse moment of inertia of the rotor: The studies were conducted with an integration step amounting to 00001 . 0 = dt (Baranowski, 2013). Some results of the GS control simulation in the target tracking process are presented and compared using the optimal PD regulator and the modified LQR regulator.…”

A comparative analysis of contemporary 155 mm artillery projectiles

“…Model 1 is a model of motion for conventional artillery projectiles. In a recent study, researchers explored the effectiveness of a mathematical model based upon a vector-based six degrees-of-freedom (6 DOF) system of differential equations (Baranowski, 2013). The subsequent system, which assumed a projectile could be represented as a rigid body, was formed using three 6 DOF modelsa ground-fixed system, body axis system and velocity axis system.…”

“…155 mm artillery projectiles accuracy can be obtained by varying the number of integration steps. To obtain a defined computational accuracy for a parameter, the model based on the body axis system should use the smallest integration step, the model based on the velocity axis system should use an integration step five times larger, and the model based on the ground-fixed system should use an integration step that is 100 times larger (Baranowski, 2013). The researchers subsequently calculated trajectory parameters to less than 0.1 per cent accuracy.…”

Analysis of two-channel control according to the proportional navigation method

“…Paper #194, pp. 49-52, doi: 10.21495/91-8-49 and using the known vector equation of the movement of the missile's mass centre (Liebiediew and Cziernobrowkin, 1973) in a movable reference system connected with the flight trajectory Ox k y k z k (Baranowski, 2013) m dt…”