This presentation was held at the 2020 NAFEMS UK Conference "Inspiring Innovation through Engineering Simulation". The conference covered topics ranging from traditional FEA and CFD, to new and emerging areas including artificial intelligence, machine learning and EDA.

Resource Abstract

In external ballistics, trajectography is the combination of calculation methods and techniques for predicting the trajectory of projectiles launched from firearms. When the projectile is not guided, it is thus a question of being able to predict the point of impact as soon as it has left the weapon, or inversely, to know the position to be given to the weapon in order to hit a target in a very precise manner. Depending on the application (artillery, small arms fire, anti-tank fire, etc...), more or less complex computational models must be considered, but generally speaking, if we go beyond the scope of short-range firing, it is necessary to know the aerodynamic coefficients of the projectiles in order to be able to evaluate all the forces and moments that apply to them in flight and then calculate a trajectory numerically. Nowadays, it is possible to find these aerodynamic coefficients by shooting in all velocity regimes, but the cost of the facilities and the time needed to carry out the tests are still considerable, especially for large calibres. This is why it is interesting to be able to simulate the flows numerically in order to quickly and reliably express these coefficients. Many CFD-based techniques have already been developed, but a major effort remains on the validation side of these techniques.

One of the applications generating a lot of interest for the moment is long-range shooting (sniping). Indeed, the trend for precision ammunition is to always hit a smaller target with a higher probability at an ever-increasing distance . The last two decades revealed many new calibres, new weapon features and a large number of trajectory software's to reach this goal. However, there is no unanimous criterion yet to define properly and scientifically why a projectile is better than another one. Until recently, the calculation of trajectories for projectiles launched from rifles did not pose any real problems because as long as the projectile remained in the supersonic domain, its behaviour remained predictable and was characterized by mainly semi-empirical models. The existing software's are often drag based (point-mass model), with a fitting established to match real firing, but they do not account specifically for the sharp changes in aerodynamic forces when the projectiles reach the transonic zone. Nonetheless, the transonic domain has to be crossed by precision ammunition when reaching high operational ranges with the classical propulsion and its inherent velocities.

Between the different aerodynamic coefficients, we can distinguish the so-called static coefficients (generated fairly easily by CFD), and the dynamic coefficients, linked to the different damping phenomena generated over time, which are more difficult to determine because of their connection to very unstable forces. While the first category is indispensable in all applications, the second category is above all necessary in the design phase of weapon-ammunition system, in order to ensure optimum projectile stability. If the damping is too small or too high, there is a risk that the projectile will not finish its trajectory with the right impact angle on its target, missing the desired effect (shaped charge, armour-piercing projectile, non-lethal impact, etc...). However, when a system is well dimensioned, knowledge of the static coefficients alone is in most cases sufficient for a fairly accurate trajectory calculation. The search for an efficient methodology for determining a complete set of aerodynamic coefficients numerically is nonetheless a priority for our department, in order to have all the data required to calculate the trajectories of any new weapon-ammunition system and assess its performance.