სიმეტრიული ფრთის პროფილის კონტურის განსაზღვრის თეორიული მოდელი წინაღობის მინიმიზაციის მიზნით

Abstract

This paper presents a new methodology for determining the contour of a symmetrical wing profile based on the principle of least action and the application of variational calculus. The proposed mathematical model aims to minimize aerodynamic drag while satisfying geometric and physical boundary conditions. The theoretical analysis represents a significant step toward the design and optimization of aerodynamic surfaces in aircraft structures, as various issues arise when operating at low Reynolds numbers. The developed model enables the evaluation of the relationship between the wing profile geometry, flow characteristics, and the resulting aerodynamic resistance. Furthermore, it is demonstrated that for a symmetrical profile at zero angle of attack, achieving minimum drag purely by theoretical means is impossible, indicating the necessity of further investigation into more complex, asymmetrical airfoils. The obtained results provide a foundation for the development of improved optimization and modification methods for wing contour design.