One of the most important areas of research in modern aviation is supporting the launch procedure of unmanned aerial vehicles (UAVs) for formation flights in a swarm. The main research problem associated with this type of launcher is the accumulation of high-density energy necessary for launching/ejection of the UAV, the repeatability of launch parameters, and the control of energy control during UAV launch. Mismatches in the convergence of UAV parameters with launcher parameters, as well as mismatches in UAV launch speed and energy, significantly impact the safety of its launch. The aim of this paper is to describe the operating cycle model of the pneumatic trigger-trigger system of a barrel launcher using airflow models and to determine the effect of flow parameters on the velocity of the UAV sabot in the launcher barrel. A computational model of the pneumatic trigger-trigger system and the results of its simulation calculations in the MATLAB/Simulink environment and a proprietary computational program using the EXCEL spreadsheet, are presented, with various design and initial parameters. The influence of design parameters such as ball valve diameter and barrel volume, as well as initial parameters such as tank pressure and ball valve opening time, on changes in internal ballistics was demonstrated and determined. The computational model provides a reliable and useful approximation of simulating the actual conditions of UAV launching from a launcher barrel, as well as guidance for designing the structure and adjusting the parameters of pneumatic barrel launchers.