Математична модель розрахунку аеродинамічних сил, утворюваних роторним рушієм для пропульсивних крил

The subject of the study is the modeling and obtaining of aerodynamic characteristics and determining the aerodynamic forces acting on an aircraft with a propulsive wing using a mathematical model. The research is based on mathematical methods and proposes a comprehensive model that accurately describes the interaction of airflow with wing and rotor propulsion. The aim of this study is to find solutions for faster calculations and approximate analysis of wings and aircraft that use them, compared to CFD methods. The task is to find methods that can perform calculations based only on geometric shapes and a minimal set of data that can be obtained by the researcher. The article begins with a review of previous research in the field of aerodynamics, demonstrating the need for the development of new models to better understand the aerodynamic forces generated by wing and rotor propulsion. A new mathematical model is considered, using methods based on Bernoulli's equation and taking into account parameters such as wing shape, angle of attack, airflow velocity, and rotor propulsion characteristics. This article describes the mathematical equations and approaches used to model aerodynamic forces. They include physical laws such as Newton's laws, the conservation of mass and momentum, and basic aerodynamic equations. Validation of the model was conducted by comparing the obtained results with experimental data. To verify the correctness of the presented claims, a series of computational experiments using numerical methods are performed to calculate the dynamic characteristics for different wing and rotor propulsion configurations, and the obtained data are compared. Through careful experiments and data analysis, the research results are expected to provide valuable insights into the practical implementation of an integrated tangential fan system in a wing by evaluating its efficiency, limitations, and potential advantages. This work can help engineers determine optimal wing and rotor propulsion configurations to achieve better aerodynamic efficiency and ensure the desired flight characteristics. This research can make an important contribution to the development of aviation technology and to the improvement of aircraft with rotor propulsion. Conclusions: the article proposes a new mathematical model for calculating the aerodynamic forces generated by wing and rotor propulsion and demonstrates its speed and efficiency by comparing it with experimental data. This research is just the first step in creating a mathematical framework. To improve calculation results and enable automation for greater variability in shape, the panel-vortex method with the consideration of flow acceleration over panel surfaces is more suitable. However, even at this stage, the research results can contribute to the development and optimization of aircraft structures with propulsive devices embedded in the wing design.